By substitution of formula, the expression of principle P is P = I/(r*t) .
What is substitution of formula ?Substitution of formula is a method to find any parameter from the given expression by substituting the required value from the expression or equation mentioned.
Given expression is I = Prt .
Substituting the parameter of principle(P) from the above expression -
P = I/(r * t)
Thus, by substitution of formula, the expression of principle P is P = I/(r*t) .
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What is the perimeter of a polygon with the vertices at (-2,1),(-2,7),(1,11),(4,7) and (4,1) enter your answer in the box do not around any side lengths
Answer:
28
Step-by-step explanation:
It helps to plot the points on a graph. It is easy to see that three of the sides are of length 6, and the remaining two are the hypotenuse of a 3-4-5 triangle, hence length 5.
3×6 +2×5 = 28
The perimeter of this polygon is 28 units.
BRAINLIEST! find the LCM of the set of polynomials.
121x^2-9y^2,11x^2+3yx
Answer:
[tex]\large\boxed{LCM(121x^2-9y^2,\ 11x^2+3xy)=121x^3-9xy^2}[/tex]
Step-by-step explanation:
[tex]121x^2-9y^2=11^2x^2-3^2y^2=(11x)^2-(3y)^2\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(11x-3y)\underline{(11x+3y)}\\\\11x^2+3yx=x\underline{(11x+3y)}\\\\LCM(121x^2-8y^2,\ 11x^2+3yx)=\underline{(11x+3y)}(11x-3y)(x)\\\\=(121x^2-9y^2)(x)=121x^3-9xy^2[/tex]
You paint a border around the top of the walls in your room. What angle does X repeat the pattern? 154
What does 154 mean in your question?
I assume your room is a square. If so, each corner of the room has a 90 degree angle for a total of 360 degrees.
The angle that is repeated, I assumed based on your obscure question, is 90 degrees.
So, x = 90 degrees.
One hundred thirty people were asked to determine how many cups of fruit and water they consumed per day. The results are shown in the frequency table. Identify the conditional relative frequency by row. Round to the nearest percent. The conditional relative frequency that someone ate more than 2 cups of fruit, given the person drank less than or equal to 4 cups of water is approximately . The conditional relative frequency that someone ate less than or equal to 2 cups of fruit, given the person drank more than 4 cups of water is approximately .
Answer:
1. 24%
2.38%
Step-by-step explanation:
Answer:
The first one is 24% and the second one is 38%
Step-by-step explanation:
i did it on egdenuity
Given the lease terms below, what monthly lease payment can you expect on this vehicle?
Terms:
•Length of Lease: 60 months
•MSRP of the car: $28,500
•Purchase value of the car after lease: $12,900
•Down Payment:$1900
•Lease Factor:0.0005
•Security Deposit:$375
•Aquisition Fee: $300
A.$232.50
B.$279.99
C.$227.50
D.$248.08
Answer:
D. $248.08
Step-by-step explanation:
Your question does not involve any taxes, so we'll compute the lease payment based on car value. We presume the Down Payment, Security Deposit, and Acquisition Fee are paid at the time the lease is signed, so are not part of the financing.
Then we have ...
lease payment = depreciation fee + financing fee
where these fees are calculated from ...
depreciation fee = ((net capitalized cost) - (residual value))/(months in lease)
and ...
financing fee = ((net capitalized cost) + (residual value))×(lease factor)
___
Using the given numbers, we have ...
net capitalized cost = MSRP - Down Payment = $28,500 -1,900 = $26,600
depreciation fee = ($26,600 -12,900)/60 = $13,700/60 = $228.33
financing fee = ($26,600 +12,000)×0.0005 = $39,500×0.0005 = $19.75
lease payment = $228.33 + 19.75 = $248.08
_____
In the attached, the "new car lending rate" is 2400 times the lease factor, so is 1.2. This is an equivalent APR.
Effectively, the monthly lease fee is the average of the depreciating car value over the life of the lease multiplied by this APR. The depreciation for this purpose is assumed to be linear.
It’s D because you add all of them up
The weekly incomes of trainees at a local company are normally distributed with a mean of $1,100 and a standard deviation of $250. If a trainee is selected at random, what is the probability that he or she earns less than $1,000 a week?
Select one:
a. 0.8141
b. 0.1859
c. 0.6554
d. 0.3446
Answer:
d. 0.3446
Step-by-step explanation:
We need to calculate the z-score for the given weekly income.
We calculate the z-score of $1000 using the formula
[tex]z=\frac{x-\mu}{\sigma}[/tex]
From the question, the standard deviation is [tex]\sigma=250[/tex] dollars.
The average weekly income is [tex]\mu=1,100[/tex] dollars.
Let us substitute these values into the formula to obtain:
[tex]z=\frac{1,000-1,100}{250}[/tex]
[tex]z=\frac{-100}{250}[/tex]
[tex]z=-0.4[/tex]
We now read from the standard normal distribution table the area that corresponds to a z-score of -0.4.
From the standard normal distribution table, [tex]Z_{-0.4}=0.34458[/tex].
We round to 4 decimal places to obtain: [tex]Z_{-0.4}=0.3446[/tex].
Therefore the probability that a trainee earns less than $1,000 a week is [tex]P(x\:<\:1000)=0.3446[/tex].
The correct choice is D.
what is the perimeter of a triangle with vertices located at (1.4) (2,7) and (0,5)
Answer:
The perimeter of triangle is [tex]P=(\sqrt{10}+3\sqrt{2})\ units[/tex]
Step-by-step explanation:
Let
[tex]A(1.4),B(2,7),C(0,5)[/tex]
we know that
The perimeter of the triangle is equal to
[tex]P=AB+BC+AC[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance AB
[tex]A(1.4),B(2,7)[/tex]
substitute the values
[tex]AB=\sqrt{(7-4)^{2}+(2-1)^{2}}[/tex]
[tex]AB=\sqrt{(3)^{2}+(1)^{2}}[/tex]
[tex]AB=\sqrt{10}\ units[/tex]
step 2
Find the distance BC
[tex]B(2,7),C(0,5)[/tex]
substitute the values
[tex]BC=\sqrt{(5-7)^{2}+(0-2)^{2}}[/tex]
[tex]BC=\sqrt{(-2)^{2}+(-2)^{2}}[/tex]
[tex]BC=\sqrt{8}\ units[/tex]
[tex]BC=2\sqrt{2}\ units[/tex]
step 3
Find the distance AC
[tex]A(1.4),C(0,5)[/tex]
substitute the values
[tex]AC=\sqrt{(5-4)^{2}+(0-1)^{2}}[/tex]
[tex]AC=\sqrt{(1)^{2}+(-1)^{2}}[/tex]
[tex]AC=\sqrt{2}\ units[/tex]
step 4
Find the perimeter
[tex]P=AB+BC+AC[/tex]
[tex]P=\sqrt{10}+2\sqrt{2}+\sqrt{2}[/tex]
[tex]P=(\sqrt{10}+3\sqrt{2})\ units[/tex]
Data is often displayed using numbers and categories. Which types of graphs are most appropriate for displaying categorical data? Check all of the boxes that apply. bar graphs histograms pie charts or circle graphs stem-and-leaf plots
Answer:
A. bar graphs
C. pie charts or circle graphs
Step-by-step explanation:
The most suitable graphs for displaying categorical data are bar graphs and pie charts, as bar graphs are used to compare categories or show changes over time, while pie charts are ideal for displaying parts of a whole.
Explanation:The most appropriate types of graphs for displaying categorical data are bar graphs and pie charts or circle graphs. In a bar graph, the length of each bar represents the number or percent of individuals in each category. Bars in a bar graph can be vertical or horizontal and are used to compare categories or show changes over time. Pie charts show categories of data as wedges in a circle, with each wedge representing a percentage of the whole, making it ideal for showing parts of a whole.
A stem-and-leaf plot, on the other hand, is useful for showing all data values within a class and mainly represents quantitative data rather than categorical data. Histograms, while similar to bar graphs, are used for displaying the distribution of quantitative, not categorical, data. Therefore, for categorical data, bar graphs and pie charts are most suitable.
Calculate the discriminant to determine the number solutions. y = x ^2 + 3x - 10
Two irrational solutions
Not solutions
two rational solutions
one rational solution
1. The first step is to find the discriminant itself. Now, the discriminant of a quadratic equation in the form y = ax^2 + bx + c is given by:
Δ = b^2 - 4ac
Our equation is y = x^2 + 3x - 10. Thus, if we compare this with the general quadratic equation I outlined in the first line, we would find that a = 1, b = 3 and c = -10. It is easy to see this if we put the two equations right on top of one another:
y = ax^2 + bx + c
y = (1)x^2 + 3x - 10
Now that we know that a = 1, b = 3 and c = -10, we can substitute this into the formula for the discriminant we defined before:
Δ = b^2 - 4ac
Δ = (3)^2 - 4(1)(-10) (Substitute a = 1, b = 3 and c = -10)
Δ = 9 + 40 (-4*(-10) = 40)
Δ = 49 (Evaluate 9 + 40 = 49)
Thus, the discriminant is 49.
2. The question itself asks for the number and nature of the solutions so I will break down each of these in relation to the discriminant below, starting with how to figure out the number of solutions:
• There are no solutions if the discriminant is less than 0 (ie. it is negative).
If you are aware of the quadratic formula (x = (-b ± √(b^2 - 4ac) ) / 2a), then this will make sense since we are unable to evaluate √(b^2 - 4ac) if the discriminant is negative (since we cannot take the square root of a negative number) - this would mean that the quadratic equation has no solutions.
• There is one solution if the discriminant equals 0.
If you are again aware of the quadratic formula then this also makes sense since if √(b^2 - 4ac) = 0, then x = -b ± 0 / 2a = -b / 2a, which would result in only one solution for x.
• There are two solutions if the discriminant is more than 0 (ie. it is positive).
Again, you may apply this to the quadratic formula where if b^2 - 4ac is positive, there will be two distinct solutions for x:
-b + √(b^2 - 4ac) / 2a
-b - √(b^2 - 4ac) / 2a
Our discriminant is equal to 49; since this is more than 0, we know that we will have two solutions.
Now, given that a, b and c in y = ax^2 + bx + c are rational numbers, let us look at how to figure out the number and nature of the solutions:
• There are two rational solutions if the discriminant is more than 0 and is a perfect square (a perfect square is given by an integer squared, eg. 4, 9, 16, 25 are perfect squares given by 2^2, 3^2, 4^2, 5^2).
• There are two irrational solutions if the discriminant is more than 0 but is not a perfect square.
49 = 7^2, and is therefor a perfect square. Thus, the quadratic equation has two rational solutions (third answer).
~ To recap:
1. Finding the number of solutions.
If:
• Δ < 0: no solutions
• Δ = 0: one solution
• Δ > 0 = two solutions
2. Finding the number and nature of solutions.
Given that a, b and c are rational numbers for y = ax^2 + bx + c, then if:
• Δ < 0: no solutions
• Δ = 0: one rational solution
• Δ > 0 and is a perfect square: two rational solutions
• Δ > 0 and is not a perfect square: two irrational solutions
The Anza-Borrego Desert State Park is one of the best places in the United States for viewing stars. During one 50-day period, cloud cover obstructed nighttime views just 6% of the time. Based on that sample, how many days a year would you predict that clouds there will interfere with stargazing? Complete the explanation.
The clouds wlll interfere for 21 ⁹/₁₀ days in a year
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here one 50-day period, cloud cover obstructed nighttime views just 6% or for the 50 day period the cloud obstructed t = 6% of 50
= 3 days
the number of 50 days period in a year = 365/50
= 350/50 + 15/50
= 7 + 15/50
Therefore the number of days the cloud will obstruct is = (7 + 15/50)×3
= 21⁹/₁₀
Hence the clouds will obstruct 21⁹/₁₀ days in a year.
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Final answer:
Based on a 50-day sample with 6% cloud coverage, one would predict that at Anza-Borrego Desert State Park, clouds will interfere with stargazing for approximately 22 days out of the year.
Explanation:
The Anza-Borrego Desert State Park had cloud coverage that obstructed nighttime views 6% of the time during a 50-day period. To predict how many days a year clouds would interfere with stargazing, you would use this percentage. The calculation is as follows:
Find the total number of days in a year, which is 365.
Calculate 6% of 365 days to find the number of days with cloud coverage. This is done by multiplying 365 by 0.06.
The result gives you the predicted number of days with cloud coverage obstructing stargazing. In numbers: 365 days/year × 0.06 (6%) = 21.9 days/year.
Therefore, based on the given sample, you would predict that clouds will interfere with stargazing at Anza-Borrego Desert State Park for approximately 22 days each year (rounding 21.9 up to the nearest whole number).
** WILL MAKE BRAINLIST **What is the quadratic regression equation for the data set? What is the quadratic regression equation for the data set?
Answer:
Now I am not completely sure but...maybe is it that:
A quadratic regression is the process of finding the equation of the parabola that best fits a set of data. As a result, we get an equation of the form:
y = a x 2 + b x + c where a ≠ 0 .
Cause I think it might be the best way to find this equation manually is by using the least squares method. That is, we need to find the values of a , b , and c such that the squared vertical distance between each point ( x i , y i ) and the quadratic curve y = a x 2 + b x + c is minimal.
The matrix equation for the quadratic curve is given by:
[ ∑ x i 4 ∑ x i 3 ∑ x i 2 ∑ x i 3 ∑ x i 2 ∑ x i ∑ x i 2 ∑ x i n ] [ a b c ] = [ ∑ x i 2 y i ∑ x i y i ∑ y i ]
The quadratic regression equation for the given data set is approximately:
[tex]y \approx -0.043x^2 + 1.333x + 5.895[/tex]
How to find the quadratic regression equationTo find the quadratic regression equation for the given data set
Denote the independent variable (x) as x and the dependent variable (y) as y. We want to find the quadratic equation of the form
[tex]y = ax^2 + bx + c[/tex]that best fits the data.
Start by creating a system of equations using the given data points.
Substitute the x and y values into the equation and obtain three equations:
[tex](2^2)a + 2b + c = 10.1\\(4^2)a + 4b + c = 7.3\\(6^2)a + 6b + c = 5.9\\(7^2)a + 7b + c = 5.1\\(11^2)a + 11b + c = 6.3\\(12^2)a + 12b + c = 8.2\\[/tex]
Now, we have a system of three linear equations with three unknowns (a, b, c). We can solve this system to find the values of a, b, and c.
Using a calculator or software, find the following approximate values:
a ≈ -0.043
b ≈ 1.333
c ≈ 5.895
Therefore, the quadratic regression equation for the given data set is approximately:
[tex]y \approx -0.043x^2 + 1.333x + 5.895[/tex]
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The vertex of a quadratic function is located at (1,4) and the y-intercept of the function is (0,1). What is the value of a if the function is written in the form y=a(x-h)^2+k
Answer:
a = -3
Step-by-step explanation:
Put the y-intercept values into the equation and solve for a.
1 = a(0 -1)^2 +4 . . . . with (h, k) filled in, this is y=a(x-1)^2+4
-3 = a . . . . . . . . . subtract 4, simplify
The value of a is -3.
You have a circular rug with a circumference of 40.82 feet that you are trying to fit in your perfectly square room. What is the minimum width that your room needs to be for the rug to fit
Answer:
13.0 feet
Step-by-step explanation:
The circumference of a circle is given by the formula ...
C = πd . . . . . . where d represents the diameter
Then the diameter is ...
d = C/π = 40.82 ft/π ≈ 12.9934 ft
Rounded to the nearest tenth foot, the width of the room must be 13.0 ft.
Express tan B as a fraction in simplest form.
Based on the given triangle, tan(B) as a fraction in its simplest form is 3/4. Option 1 (None of the listed answers are correct)
How to calculate angle in a triangle
In a right-angled triangle ABC, where the adjacent side (AC) is 4, the opposite side (BC) is 3, and the hypotenuse side (AB) is 5, use the tangent function to find the value of tan(B).
The tangent function is defined as the ratio of the opposite side to the adjacent side:
tan(B) = BC / AC
tan(B) = 3 / 4
To express tan(B) as a fraction in simplest form, simplify the ratio by dividing both the numerator and denominator by their greatest common divisor, which in this case is 1:
tan(B) = 3 / 4
Therefore, tan(B) is already in its simplest form as the fraction 3/4.
To express tan B as a fraction in its simplest form, you need to have information about the angle B or, if it pertains to a right triangle, you need to know the lengths of the sides of the triangle that form angle B.
The expression for tan B is based on the ratio of the length of the opposite side to the length of the adjacent side in a right-angled triangle. In mathematical terms, this is written as:
\[ \tan(B) = \frac{\text{opposite side}}{\text{adjacent side}} \]
To write this as a fraction in simplest form, you would follow these steps:
1. Identify the lengths of the opposite and adjacent sides relative to angle B.
2. Write the ratio of these lengths as a fraction.
3. Simplify the fraction by dividing both the numerator (opposite side) and the denominator (adjacent side) by their greatest common divisor (GCD).
As an example, suppose in a right triangle the length of the side opposite angle B is 6 units and the length of the side adjacent to angle B is 8 units:
\[ \tan(B) = \frac{6}{8} \]
Now, we simplify the fraction by finding the GCD of 6 and 8:
The GCD of 6 and 8 is 2.
So, we divide both numerator and denominator by 2:
\[ \tan(B) = \frac{6 \div 2}{8 \div 2} = \frac{3}{4} \]
Therefore, in this example, tan B is \( \frac{3}{4} \) in simplest form.
If you do not have the lengths of the opposite and adjacent sides or a specific value for angle B (for example, B is a special angle such as 30°, 45°, or 60° for which the tangent values are known), then you cannot express tan B as a fraction in simplest form without additional information.
How many blocks are in the 10th figure
Answer:
11 squared, or 121.
Step-by-step explanation:
Fig. 1 = 4 b(locks)
or 2 squared
Fig. 2 = 9 b
or 3 squared
Fig. 3 = 16 b
or 4 squared
Fig. 4 = 25 b
or 5 squared
Fig. 10 would be 11 squared, or 121.
Answer:
The answer is 121
Step-by-step explanation:
The question is in the picture.
Answer:
42 = (3 +x)(4 +x)
Step-by-step explanation:
The only equation that has the existing dimensions increased by x is the first one.
Help calculus module 7 DBQ
please show work
1. Filling in the table is just a matter of plugging in the given [tex]x,y[/tex] values into the ODE [tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{xy}3[/tex]:
[tex]\begin{array}{c|ccccccccc}x&-1&-1&-1&0&0&0&1&1&1\\ y&1&2&3&1&2&3&1&2&3\\\frac{\mathrm dy}{\mathrm dx}&-\frac13&-\frac23&-1&0&0&0&\frac13&\frac23&1\end{array}[/tex]
2. I've attached what the slope field should look like. Basically, sketch a line of slope equal to the value of [tex]\dfrac{\mathrm dy}{\mathrm dx}[/tex] at the labeled point (these values are listed in the table).
3. This ODE is separable. We have
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{xy}3\implies\dfrac{\mathrm dy}y=\dfrac x3\,\mathrm dx[/tex]
Integrating both sides gives
[tex]\ln|y|=\dfrac{x^2}6+C\implies y=e^{x^2/6+C}=Ce^{x^2/6}[/tex]
With the initial condition [tex]f(0)=4[/tex], we take [tex]x=0[/tex] and [tex]y=4[/tex] to solve for [tex]C[/tex]:
[tex]4=Ce^0\implies C=4[/tex]
Then the particular solution is
[tex]\boxed{y=4e^{x^2/6}}[/tex]
4. First, solve the ODE (also separable):
[tex]\dfrac{\mathrm dT}{\mathrm dt}=k(T-38)\implies\dfrac{\mathrm dT}{T-38}=k\,\mathrm dt[/tex]
Integrating both sides gives
[tex]\ln|T-38|=kt+C\implies T=38+Ce^{kt}[/tex]
Given that [tex]T(0)=75[/tex], we can solve for [tex]C[/tex]:
[tex]75=38+C\implies C=37[/tex]
Then use the other condition, [tex]T(30)=60[/tex], to solve for [tex]k[/tex]:
[tex]60=38+37e^{30k}\implies k=\dfrac1{30}\ln\dfrac{22}{37}[/tex]
Then the particular solution is
[tex]T(t)=38+37e^{\left(\frac1{30}\ln\frac{22}{37}\right)t}[/tex]
Now, you want to know the temperature after an additional 30 minutes, i.e. 60 minutes after having placed the lemonade in the fridge. According to the particular solution, We have
[tex]T(60)=38+37e^{2\ln\frac{22}{37}}\approx\boxed{51^\circ}[/tex]
5. You want to find [tex]t[/tex] such that [tex]T(t)=55[/tex]:
[tex]55=38+37e^{\left(\frac1{30}\ln\frac{22}{37}\right)t}\implies\dfrac{17}{37}=e^{\left(\frac1{30}\ln\frac{22}{37}\right)t}[/tex]
[tex]\implies t=\dfrac{30\ln\frac{17}{37}}{\ln\frac{22}{37}}\approx\boxed{45\,\mathrm{min}}[/tex]
Which expressions are equivalent to 8(-10x+3.5y-7)
For this case we must find an expression equivalent to:
[tex]8 (-10x + 3.5y-7) =[/tex]
We apply distributive property to each of the terms within the parentheses, then:
[tex]8 * (- 10x) + 8 * (3.5y) +8 * (- 7) =\\-80x + 28y-56[/tex]
Finally, an equivalent expression is:
[tex]-80x + 28y-56[/tex]
Answer:
[tex]-80x + 28y-56[/tex]
Answer:
-80x +28y-56
Step-by-step explanation:
Evaluate x + 3y, if x = 9 and y = -4.
To solve this you must plug in 9 for x and -4 for y in the equation
X + 3y like so...
9 + 3(-4)
In accordance to the rules of PEMDAS you must multiply first, which will get you...
9 + (-12)
Add these two together and you get:
-3
Hope this helped
~Just a girl in love with Shawn Mendes
Answer:
-2
Step-by-step explanation:
A quadrilateral has one pair of parallel sides with lengths 1 3/4 inches and 1 1/4 inches, and two angles that measure 36 degrees. What is the mane of the quadrilateral you drew?
Answer:
The name of the quadrilateral is isosceles trapezoid.Explanation:
1) The two parallel sides of different legths [tex]1\frac{3}{4}[/tex] and [tex]1\frac{1}{4}[/tex] constitute the bases of a trapezoid.
2) The two equal anglesare the base angles of the trapezoid, and mean that it is an isosceles trapezoid.
An isosceles trapezoid is truncated isosceles triangle.
The definition of trapezoid is a quadrilateral with at least two parallel sides.
The drawing is attached: only the green lines represent the figure, the dotted lines just show how this is derived from an isosceles triangle.
Answer:
trapezoid
Step-by-step explanation:
Can someone help me with translation
Answer:
P' = (4, 4)
Step-by-step explanation:
T(x, y) is a function of x and y. Put the x- and y-values of point P into the translation formula and do the arithmetic.
P' = T(8, -3) = (8 -4, -3 +7) = (4, 4)
_____
Comment on notation
The notation can be a little confusing, as the same form is used to mean different things. Here, P(8, -3) means point P has coordinates x=8, y=-3. The same form is used to define the translation function:
T(x, y) = (x -4, y+7)
In this case, T(x, y) is not point T, but is a function named T (for "translation function") that takes arguments x and y and gives a coordinate pair as a result.
Translation is the process of transferring text from one language into another, aiming to maintain the original message's style, tone, and nuances. This practice requires a solid understanding of both the source and target languages.
Explanation:Translation refers to the process of converting text from one language into another. The goal of translation is to accurately convey the meaning of the source language into the target language, while preserving the style, tone, and nuances. For example, if you want to translate the English phrase 'Hello, how are you?' into French, the translation would be 'Bonjour, comment ça va?'.
Handling translations can be tricky due to cultural differences, idiomatic expressions, and grammatical rules of the different languages. Practice and immersion in both languages can help improve translation skills.
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Part A
What is the area of triangle i? Show your calculation.
Part B
Triangles i and ii are congruent (of the same size and shape). What is the total area of triangles i and ii? Show your calculation.
Part C
What is the area of rectangle i? Show your calculation.
Part D
What is the area of rectangle ii? Show your calculation.
Part E
Rectangles i and iii have the same size and shape. What is the total area of rectangles i and iii? Show your calculation.
Part F
What is the total area of all the rectangles? Show your calculation.
Part G
What areas do you need to know to find the surface area of the prism?
Part H
What is the surface area of the prism? Show your calculation.
Part I
Read this statement: “If you multiply the area of one rectangle in the figure by 3, you’ll get the total area of the rectangles.” Is this statement true or false? Why?
Part J
Read this statement: “If you multiply the area of one triangle in the figure by 2, you’ll get the total area of the triangles.” Is this statement true or false? Why?
Answer:
Part A) The area of triangle i is [tex]3\ cm^{2}[/tex]
Part B) The total area of triangles i and ii is [tex]6\ cm^{2}[/tex]
Part C) The area of rectangle i is [tex]20\ cm^{2}[/tex]
Part D) The area of rectangle ii is [tex]32\ cm^{2}[/tex]
Part E) The total area of rectangles i and iii is [tex]40\ cm^{2}[/tex]
Part F) The total area of all the rectangles is [tex]72\ cm^{2}[/tex]
Part G) To find the surface area of the prism, we need to know only the area of triangle i and the area of rectangle i and the area of rectangle ii, because the area of triangle ii is equal to the area of triangle i and the area of rectangle iii is equal to the area of rectangle i
Part H) The surface area of the prism is [tex]78\ cm^{2}[/tex]
Part I) The statement is false
Part J) The statement is true
Step-by-step explanation:
Part A) What is the area of triangle i?
we know that
The area of a triangle is equal to
[tex]A=\frac{1}{2} (b)(h)[/tex]
we have
[tex]b=4\ cm[/tex]
[tex]h=1.5\ cm[/tex]
substitute
[tex]A=\frac{1}{2} (4)(1.5)[/tex]
[tex]Ai=3\ cm^{2}[/tex]
Part B) Triangles i and ii are congruent (of the same size and shape). What is the total area of triangles i and ii?
we know that
If Triangles i and ii are congruent
then
Their areas are equal
so
[tex]Aii=Ai[/tex]
The area of triangle ii is equal to
[tex]Aii=3\ cm^{2}[/tex]
The total area of triangles i and ii is equal to
[tex]A=Ai+Aii[/tex]
substitute the values
[tex]A=3+3=6\ cm^{2}[/tex]
Part C) What is the area of rectangle i?
we know that
The area of a rectangle is equal to
[tex]A=(b)(h)[/tex]
we have
[tex]b=2.5\ cm[/tex]
[tex]h=8\ cm[/tex]
substitute
[tex]Ai=(2.5)(8)[/tex]
[tex]Ai=20\ cm^{2}[/tex]
Part D) What is the area of rectangle ii?
we know that
The area of a rectangle is equal to
[tex]A=(b)(h)[/tex]
we have
[tex]b=4\ cm[/tex]
[tex]h=8\ cm[/tex]
substitute
[tex]Aii=(4)(8)[/tex]
[tex]Aii=32\ cm^{2}[/tex]
Part E) Rectangles i and iii have the same size and shape. What is the total area of rectangles i and iii?
we know that
Rectangles i and iii are congruent (have the same size and shape)
If rectangles i and iii are congruent
then
Their areas are equal
so
[tex]Aiii=Ai[/tex]
The area of rectangle iii is equal to
[tex]Aiii=20\ cm^{2}[/tex]
The total area of rectangles i and iii is equal to
[tex]A=Ai+Aiii[/tex]
substitute the values
[tex]A=20+20=40\ cm^{2}[/tex]
Part F) What is the total area of all the rectangles?
we know that
The total area of all the rectangles is
[tex]At=Ai+Aii+Aiii[/tex]
substitute the values
[tex]At=20+32+20=72\ cm^{2}[/tex]
Part G) What areas do you need to know to find the surface area of the prism?
To find the surface area of the prism, we need to know only the area of triangle i and the area of rectangle i and the area of rectangle ii, because the area of triangle ii is equal to the area of triangle i and the area of rectangle iii is equal to the area of rectangle i
Part H) What is the surface area of the prism? Show your calculation
we know that
The surface area of the prism is equal to the area of all the faces of the prism
so
The surface area of the prism is two times the area of triangle i plus two times the area of rectangle i plus the area of rectangle ii
[tex]SA=2(3)+2(20)+32=78\ cm^{2}[/tex]
Part I) Read this statement: “If you multiply the area of one rectangle in the figure by 3, you’ll get the total area of the rectangles.” Is this statement true or false? Why?
The statement is false
Because, the three rectangles are not congruent
The total area of the rectangles is [tex]72\ cm^{2}[/tex] and if you multiply the area of one rectangle by 3 you will get [tex]20*3=60\ cm^{2}[/tex]
[tex]72\ cm^{2}\neq 60\ cm^{2}[/tex]
Part J) Read this statement: “If you multiply the area of one triangle in the figure by 2, you’ll get the total area of the triangles.” Is this statement true or false? Why?
The statement is true
Because, the triangles are congruent
PLEASE HELP! I'm on a time limit!!
Which of the following represents a rotation of △PQR, which has vertices P(−2,4), Q(−3,−9), and R(4,−2), about the origin by 180°?
P (2, −4)
Q (3, 9)
R (−4, −2)
P (2, −4)
Q (−9, −3)
R (−4, −2)
P (2, −4)
Q (3, 9)
R (−4, 2)
P (−4, −2)
Q (9, −3)
R (2, 4)
Answer:
P = (2,-4)
Q = (3,9)
R = (-4,2)
Step-by-step explanation:
rotation by 180 degrees means that the points are inverted. the answers would be the opposite of the given
To find the triangle's vertices after a 180° rotation about the origin, simply change the sign of each coordinate. P(-2,4) becomes P(2,-4), Q(-3,-9) becomes Q(3,9), and R(4,-2) becomes R(-4,2).
Explanation:When you rotate a point 180° about the origin, each coordinate (x, y) simply changes its sign to become (-x, -y). Therefore, we can apply this to the vertices of △PQR.
P(-2,4) becomes P(2,-4) after a 180° rotation.Q(-3,-9) becomes Q(3,9) after a 180° rotation.R(4,-2) becomes R(-4,2) after a 180° rotation.The correct choice for the rotation of △PQR by 180° about the origin will have these new coordinates. Therefore, the answer is:
P (2, −4)Q (3, 9)R (−4, 2)Use the recursive formula f(n) = 0.4 ⋅ f(n − 1) + 11 to determine the 2nd term if f(1) = 4.
A.f(2) = 11.8
B.f(2) = 12.2
C.f(2) = 12.6
D.f(2) = 13
Answer:
C.f(2) = 12.6
Step-by-step explanation:
f(n) = 0.4 ⋅ f(n − 1) + 11
f(1) = 4
Let n=2
f(2) = .4 f(1) +11
= .4 (4) +11
= 1.6 +11
= 12.6
Answer:
c-12.6
Step-by-step explanation:
Use the formula and substitute the n for the value and u will find it.
Pls help brainliest will be given
Step-by-step explanation:
according to the equation, y= mx
which of the following sets are discrete? check all that apply.
A. {1,3,5,7,...}
B. (-10,20)
C. {5,8}
D. (1,99)
E. {-3,6,9,17,24}
Answer:
All are discrete sets
Step-by-step explanation:
Any set for which you can list the elements is a discrete set, even if that list has "..." (continues in like fashion). Sets that are not discrete are those that are continuous, such as "all real numbers" or "the numbers between 0 and 1".
The discrete sets from the options given are A. {1,3,5,7,...}, C. {5,8}, and E. {-3,6,9,17,24}.
A discrete set is one where the elements are separate and distinct, often meaning each member can be counted and there is no continuous spectrum of values between any two elements.
A. {1,3,5,7,...} - This set represents odd numbers which is discrete because we can identify each individual element.
B. (-10,20) - This is not a set but an interval representing a continuous range of real numbers; therefore, it is not discrete.
C. {5,8} - This set has only two elements, each distinct and countable, making it discrete.
D. (1,99) - Similar to B, this is an interval showing a continuous range of real numbers, and thus not discrete.
E. {-3,6,9,17,24} - This set includes separate, identifiable numbers and is therefore discrete.
What would be the answer
Answer:
90 minutes
Step-by-step explanation:
We know that distance = rate * time
We know the distance and the rate, and need to find the time
distance = 60 miles
rate = 40 mile per hour
60 = 40 * t
Divide each side by 40
60/40 = 40t/40
1.5 = t
1.5 hours
Now we need to change it to minutes
1.5 hours * 60 minutes/1 hours = 90 minutes
Which of the following best describes the graph below?
A. It is a function, but it is not one-to-one.
B. It is a one-to-one function.
C. It is not a function.
D. It is a many-to-one function.
Answer:
B. It is a one-to-one function.
Step-by-step explanation:
Each value of the domain maps to a unique value of the range. It is a one-to-one function.
Answer:
B. It is a one to one function.
Step-by-step explanation:
It is a function, if we trace the vertical line [tex]x=a[/tex] it intersects exactly one point of the graph (in the case that [tex]a\neq0[/tex].Moreover, the line [tex]x=0[/tex] doesn't intersects the graph, hence the given graph is the graph of a function with domain [tex]\mathbb{R}-\{0\}[/tex]. On the other hand, a function f(x) is one to one, if whenever f(x)=f(y) it holds that x=y, in terms of the graph of a function this mean that whenever we trace a vertical line [tex]y=b[/tex] it intersects exactly one point, which is exactly the case fo our given graph. Threfore, it is the graph of a one to one function
Kelsey painted one fourth of her bedroom in three seventh of an hour. At this rate, how long would it take her to paint the entire room?
three over twenty eight hour
twenty eight over three hours
twelve over seven hours
seven over twelve hour
The time it will take Kelsey to paint the entire room is:
Twelve over seven hours Step-by-step explanation:It is given that:
Kelsey painted one fourth of her bedroom in three seventh of an hour.
This means that:
1/4 of bedroom takes 3/7 of an hour
This means that the whole of the bedroom will take 4 times the time it took to cover 1/4 th of bedroom.
i.e. it will take:
[tex]\dfac{3}{7}\times 4\\\\\\=\dfrac{12}{7}\ hour[/tex]
Hence, the total time it will take to paint the whole room is:
twelve over seven hours
Your answer is C, as it says in the photo below. You can see the amount of points it is worth, and the amount of points it gave me. Hope this helps somebody!
8 people went to a football game together in one van they spent $4 to park in the rest on tickets the total spent was $88 what was the cost for each ticket
Answer:
$10.5
Step-by-step explanation:
88-4 = $84
84/8 = 10.5