if the cone has a diameter of 12, thus its radius is half that, namely 6.
[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ h=20 \end{cases}\implies V=\cfrac{\pi (6)^2(20)}{3}\implies V=240\pi \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill V\approx 753.98~\hfill[/tex]
The volume of cone is 240π m³.
What is volume?The mathematical term "volume" indicates the amount of three-dimensional space that an object or closed surface occupies. The volume is measured in cubic units like m³, cm³, in³, and so on.
Volume is also sometimes referred to as capacity.
Given diameter of cone = 12m
radius = diameter/2 = 12/2 = 6m
height of cone = 20m
volume of cone is given by 1/3πr²h
where r = radius and h = height
volume = 1/3 x π x (6)² x 20
volume = 240π m³
Hence the volume is 240π m³.
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What is ∑n=14[100(−4)n−1] equal to? Enter your answer in the box.
The value of ∑n=14[100(−4)n−1] is -5368709100
How to evaluate the series?The sequence is given as:
∑n=14[100(−4)n−1]
The above sequence is a geometric sequence, with the following properties
First term, a = 100Common ratio, r = -4Number of terms = 14The sum of n terms of a geometric series is:
[tex]S_n = \frac{a* (r^n - 1)}{r - 1}[/tex]
So, we have:
[tex]S_n = \frac{100* ((-4)^{14} - 1)}{-4 - 1}[/tex]
Evaluate
[tex]S_{14} = -5368709100[/tex]
Hence, the value of ∑n=14[100(−4)n−1] is -5368709100
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The sum [tex]\(\sum_{n=1}^4 [100(-4)^{n-1}]\)[/tex] is [tex]\[\boxed{-5100}\][/tex]
To find the sum [tex]\(\sum_{n=1}^4 [100(-4)^{n-1}]\),[/tex] we will calculate the individual terms of the sequence and then sum them up.
The general term of the sequence is [tex]\(100(-4)^{n-1}\)[/tex]. Let's compute the terms from [tex]\(n = 1\) to \(n = 4\):[/tex]
1. For [tex]\(n = 1\):[/tex]
[tex]\[ 100(-4)^{1-1} = 100(-4)^0 = 100 \cdot 1 = 100 \][/tex]
2. For [tex]\(n = 2\):[/tex]
[tex]\[ 100(-4)^{2-1} = 100(-4)^1 = 100 \cdot (-4) = -400 \][/tex]
3. For [tex]\(n = 3\):[/tex]
[tex]\[ 100(-4)^{3-1} = 100(-4)^2 = 100 \cdot 16 = 1600 \][/tex]
4. For [tex]\(n = 4\):[/tex]
[tex]\[ 100(-4)^{4-1} = 100(-4)^3 = 100 \cdot (-64) = -6400 \][/tex]
Now, let's sum these terms:
[tex]\[100 + (-400) + 1600 + (-6400)\][/tex]
Perform the calculations step-by-step:
1. [tex]\(100 - 400 = -300\)[/tex]
2. [tex]\(-300 + 1600 = 1300\)[/tex]
3. [tex]\(1300 - 6400 = -5100\)[/tex]
SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
Answer:
[tex]4w^4-7z^4+6w^2z^2[/tex]
Step-by-step explanation:
We can reformat this equation so we can vertically add.
Then, we can just add down.
Since all the degrees and the variables are the same, we only have to worry about the coefficients.
5 - 1 = 4 --> [tex]4w^4[/tex]
-7 + 13 = 6 --> [tex]6w^2z^2[/tex]
-3 - 4 = -7 --> [tex]-7z^4[/tex]
Now let's rewrite this.
[tex]4w^4-7z^4+6w^2z^2[/tex]
Which rule yields the dilation of the figure KLMN centered at the origin?
A) (x, y) → (2x, 2y)
B) (x, y) → (1/2x, 1/2y)
C) (x, y) → (x + 2, y + 2)
D) (x, y) → (x + 1/2, y + 1/2)
Answer:
The rule of dilation centered at the origin is (x , y) → (2x , 2y) ⇒ answer A
Step-by-step explanation:
* Lets talk about dilation
- A dilation is a transformation that changes the size of a figure.
- It can become larger or smaller, but the shape of the
figure does not change.
- The scale factor, measures how much larger or smaller
the image will be
- If the scale factor greater than 1, then the image will be larger
- If the scale factor between 0 and 1, then the image will be smaller
- The dilation rule for any point (x , y) is (kx , ky), where k is the
factor of dilation centered at origin
* Now lets solve the problem
- The figure KLMN has for vertices:
K (3 , -3) , L (3 , 4) , M (5 , 4) , N (5 , -3) ⇒ (1)
- The image K'L'M'N' of figure KLMN after dilation about the origin
has four vertices:
K' (6 , -6) , L' (6 , 8) , M' (10 , 8) , N' (10 , -6) ⇒ (2)
- From (1) and (2)
# (3 , -3) ⇒ (6 , -6)
# (3 , 4) ⇒ (6 , 8)
# (5 , 4) ⇒ (10 , 8)
# (5 , -3) ⇒ (10 , -6)
- Each point in KLMN multiplied by 2
∴ The scale of dilation is 2
∴ The rule of dilation centered at the origin is (x , y) → (2x , 2y)
Answer: A) (x, y) → (2x, 2y)
The pre-image is enlarged. The coordinates of KLMN have been multiplied by 2.
Find the exact value.
tan240°
Answer:
1.732050808
Step-by-step explanation:
https : // www. desmos. com/ scientific
EDIT square root of 3
The exact value of tan240° is the same as tan60° because of the periodicity of the tangent function and the fact that 240° lies in the third quadrant of the unit circle. The value of tan60° is √3 or about 1.732.
To find the exact value of tan240°, we should recall that the tangent function is periodic with a period of 180°, meaning tan(θ) is the same as tan(θ + 180°). Also, in the unit circle, 240° lies in the third quadrant, where tangent values are positive because both sine and cosine are negative. Therefore, tan240° is the same as tan(240° - 180°), which is tan60°. The exact value of tan60° is √3) or approximately 1.732. This calculation leverages trigonometric principles and the geometric interpretation of angles on the unit circle, demonstrating how to derive accurate values for trigonometric functions in specific angular contexts.
Graph a system of equations to solve log (−5.6x + 1.3) = −1 − x. Round to the nearest tenth. From the least to the greatest, the solutions are: x ≈ and x ≈ .
Answer:
See the graph attachedx₁ ≈ - 2.1x₂ ≈ 0.2Explanation:
To solve log (−5.6x + 1.3) = −1 − x graphycally, you must graph this system of equations on the same coordinate plane:
Equation 1: y = log (5.6x + 1.3)Equatin2: y = - 1 - x1) To graph the equation 1 you can use these features of logarithmfunctions:
Domain: positive values ⇒ -5.6x + 1.3 > 0 ⇒ x < 13/56 (≈ 0.23)Range: all real numbers (- ∞ , ∞)x-intercept:log ( -5.6x + 1.3) = 0 ⇒ -5.6x + 1.3 = 1 ⇒x = 0.3/5.6 ≈ 0.054
y-intercept:x = 0 ⇒ log (0 + 1.3) = log (1.3) ≈ 0.11
Pick some other values and build a table:x log (-5.6x + 1.3)
-1 0.8
-2 1.1
-3 1.3
You can see such graph on the picture attached: it is the red curve.2) Graphing the equation 2 is easier because it is a line: y = - 1 - x
slope, m = - 1 (the coeficient of x)y - intercept, b = - 1 (the constant term)x - intercept: y = 0 = - 1 - x ⇒ x = - 1The graph is the blue line on the picture.3) The solution or solutions of the equations are the intersection points of the two graphs. So, now the graph method just requires that you read the x coordinates of the intersection points. From the least to the greatest, rounded to the nearest tenth, they are:
x₁ ≈ - 2.1x₂ ≈ 0.2Answer:
x = -2.1
& .2
Step-by-step explanation:
14. (08.07 MC) A polynomial function is shown below: f(x) = x3 − 4x2 − x + 4 Which graph best represents the function? (5 points) Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, 2, and 3. The graph intersects the y axis at a point between 10 and 15. Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, 2, and 3. The graph intersects the y axis at a point between 15 and 20. Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, 1, and 3. The graph intersects the y axis at a point between 5 and 10. Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 1, 1, and 4. The graph intersects the y axis at a point between 0 and 5.
The correct graph for the function f(x) = x3 - 4x2 - x + 4 should intersect the y-axis at 4, should have three x-intercepts and should fall to the left and rise to the right. From given options, the best representation would be a cubic polynomial that has x intercepts negative 1, 1, and 4, and intersects the y axis at a point between 0 and 5.
Explanation:To choose the correct graph of the function f(x) = x3, we need to consider its properties: the y-intercept, x-intercepts, and overall shape. The y-intercept can be found by substituting x = 0 into the equation, which gives us f(0) = 4. Thus, we are looking for a graph that crosses the y-axis at 4.
The x-intercepts of the function are the values of x for which f(x) = 0. In this case, solving this equation might be complex, but we should look for a graph with 3 x-intercepts as it's a cubic equation.
As for the overall shape, since the function is cubic and the sign of the leading coefficient is positive, its graph falls to the left and rises to the right. Therefore, the graph that best represents the function is a graph of a cubic polynomial that falls to the left and rises to the right, has x intercepts negative 1, 1, and 4, and intersects the y axis at a point between 0 and 5.
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50 points!! will give brainliest <3
Describe how the line of best fit and the correlation coefficient can be used to determine the correlation between two variables on a graph.
Using line of best fit and correlation coefficient, the correlation coefficient of determination represent the percentage of data that is closest to the lines of best fit.
What is line of best fit?Line of best fit refers to the "a line through a scatter plot of data points that best expresses relationship between those points". Lines of best fit is used to describe data and predict data where the new data will appear. Examples for lines of best fit is 'Least square method'.
What is correlation coefficient?Two variables wherein "change in the value one variable produces a change in the variable other variable then it is called variables are correlated or there is a correlation coefficient".
According to the question,
In order to determine the correlation between two variables on a graph using line of best fit and correlation coefficient.
Correlation coefficient holds only if there is a linear correlation between the variables; that is the relationship between the variables is linear in graph. Variation in 'y' is caused by variation in 'x' on graph . Variation in 'x' is caused by variation 'y' on graph. Variable 'x' and variable 'y' are jointly dependent on graph. This is how we determine the correlation coefficient between two variables on the graph.
Line of best fit suppose (x₁, y₁) (x₂, y₂) ..... (xₙ, yₙ) be 'n' pairs of values on a graph to determine the line of best for this data. Assume 'y = a + b x' as a line of best fit (trend line). Using the principle of least squares we can determine the parameter 'a' and 'b'. It can be shown that 'a' and 'b' are determined by the equation.
n a + b∑ x = ∑y -->(1)
a ∑x +b ∑x² = ∑x y --->(2)
These equations are called Normal equation. Therefore, the line of best fit is y=a x+ b where 'a' and 'b x' are given by the equation. This is how we determine the correlation or relationship between two variables on a graph.
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Find the slope of the line.
A-4
B--1/4
C-1/4
D--4
Answer:
slope=-1/4
Step-by-step explanation:
point 1: -4,-1
point 2: 0,-2
y1-y2/x1-x2
1/-4
-1/4
20 points!
Which transformations are rigid motions?
Check all that apply!
Question options:
Dilations
Rotations
Translations
Reflections
Translations, rotations, and reflections are all rigid transformations.
What is the value of matrix B if A+B=C?
Answer:
option B
Step-by-step explanation:
Step 1
A + B = C
[tex]A=\left[\begin{array}{ccc}8&-3\\3&y+2\end{array}\right][/tex][tex]+B=\left[\begin{array}{ccc}3x&z+4\\w&1/2y\end{array}\right][/tex]
=
[tex]C=\left[\begin{array}{ccc}x&2z\\4&y\end{array}\right][/tex]
Step 2
[tex]\left[\begin{array}{ccc}8+3x&-3+z+4\\3+w&y+2+y/2\end{array}\right][/tex][tex]=\left[\begin{array}{ccc}x&2z\\4&y\end{array}\right][/tex]
Step 3
4 equations are form
Equation 1
8 + 3x = x
8 = -2x
x = -4
Equation 2
-3 + z + 4 = 2z
1 + z = 2z
1 = z
z = 1
Equation 3
3 + w = 4
w = 1
Equation 4
y + 2 + y/2 = y
2 + y/2 = 0
4 + y = 0
y = -4
Step 4
[tex]\left[\begin{array}{ccc}3(-4)&1+4\\1&1(-4)/2\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}-12&5\\1&-2\end{array}\right][/tex]
Answer:
B
Step-by-step explanation:
I got 100% on EDGE 2020 Unit test
The perimeter of a triangle can be found by adding the lengths of its three sides. If the three sides of a triangle measure 3.4 inches, 5 inches, and 7.32 inches, what is the perimeter of the triangle.
16.06 in.
16.47 in.
13.41 in.
16.38 in.
Answer:
16.47 in.
Step-by-step explanation:
Add the lengths of the sides:
3.4 in. + 5.75 in. + 7.32 in. = 16.47 in.
The perimeter of the triangle will be equal to 16.47 in. The correct option is B.
What is a triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.
The perimeter is defined as the sum of all the sides of the figure. The perimeter of the triangle is the sum of all three sides of the triangle.
Given that the three sides of a triangle measure 3.4 inches, 5 inches, and 7.32 inches.
The perimeter of the triangle is calculated as,
P = 3.4 in. + 5.75 in. + 7.32 in.
P = 16.47 in.
Therefore, the perimeter of the triangle will be equal to 16.47 in. The correct option is B.
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Simplify the algebraic expression: x(x + 3) + x(2x – 4) + 6
A. 3x2 + 5
B. 2x4 – x2 + 6
C. 3x2 + x + 6
D. 3x2 – x + 6
Thanks !! Will mark for Brainlest if answered correctly.
answer for this question is (d)3x2-x+6
This is the answer:)
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
A number generator was used to simulate the percentage of students in a town who enjoy playing video games. The process simulates randomly selecting 100 students from the town and was repeated 20 times. The percentage of students who play video games is shown in the dot plot. Which statement is true about the student population of the town?
Answer:
Most likely 60-75%
Step-by-step explanation:
60-75 is where most of the data points lie, so it is most likely that the actual percentage is within that interval.
8. The trapezoids are similar. The area of the smaller trapezoid is 131 m2. Find the area of the larger trapezoid to the nearest whole number.
Answer:
[tex]3,726\ m^{2}[/tex]
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
Let
z----> the scale factor
x----> corresponding side of the larger trapezoid
y----> corresponding side of the smaller trapezoid
[tex]z=\frac{x}{y}[/tex]
we have
[tex]x=64\ m[/tex]
[tex]y=12\ m[/tex]
substitute
[tex]z=\frac{64}{12}[/tex]
step 2
Find the area of the larger trapezoid
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z----> the scale factor
x----> area of the larger trapezoid
y----> area of the smaller trapezoid
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{64}{12}[/tex]
[tex]y=131\ m^{2}[/tex]
substitute
[tex](\frac{64}{12})^{2}=\frac{x}{131}[/tex]
[tex]x=(\frac{4,096}{144})(131)[/tex]
[tex]x=3,726\ m^{2}[/tex]
What is the amplitude and period of f(t)=-cos t
Answer:
c. amplitude: 1; period: [tex]2\pi[/tex]
Step-by-step explanation:
The given function is [tex]f(t)=- \cos t[/tex]
This function is of the form;
[tex]y=A \cos Bt[/tex]
where [tex]|A|[/tex] is the amplitude.
When we compare [tex]f(t)=- \cos t[/tex] to [tex]y=A \cos Bt[/tex], we have
[tex]A=-1[/tex], therefore the amplitude of the given cosine function is [tex]|-1|=1[/tex]
The period is given by;
[tex]T=\frac{2\pi}{|B|}[/tex]
Since B=1, the period is [tex]T=\frac{2\pi}{|1|}=2\pi[/tex]
Answer:
c. amplitude: [tex]\displaystyle 1;[/tex]period: [tex]\displaystyle 2\pi[/tex]
Explanation:
[tex]\displaystyle f(t) = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 1[/tex]
With the above information, you now should have an idea of how to interpret graphs like this.
I am joyous to assist you at any time.
What is true about the dilation?
It has a scale factor between zero and one and is a reduction.
It has a scale factor greater than one and is a reduction.
It has a scale factor between zero and one and is an enlargement.
It has a scale factor greater than one and is an enlargement.
Answer:
im pretty sure its the first one
Answer with explanation:
When the size of Preimage is greater than size of Image than dilation factor will be less than 1 and greater than zero.
And, when Size of preimage is greater than Size of Image than dilation factor will be greater than 1.
In the given diagram
Size of Preimage > Size of Image
Dilation Factor=0 <Dilation factor <1
Option A: It has a scale factor between zero and one and is a reduction.
40 POINTS PLEASE HELP ASAP!!
Daniel is going to use 6/3 pounds of strawberries to make 4 pitchers of strawberry lemonade. If each pitcher has the same amount of strawberries, how many pounds of strawberries will be in each?
A.1/2 pounds
B.1 pound
C. 2 pounds
D. 8 pounds
Answer:
The correct answer is A) 1/2 pound
Step-by-step explanation:
im not good with geometry
Answer:
neither am i bro no worries
Step-by-step explanation:
no cap
Answer:
Step-by-step explanation:
It's parallel to the side BC, from a known theorem (the segment linking the midpoints of two sides of a triangle is parallel to the third, and its lenght is half of it.
Sonja's house is 4 blocks west and 1 block south of the center of town. Her school is 3 blocks east and 2 blocks north of the center of town.
What is the direct distance from Sonja's house to her school?
(Hint: The center of town should be the origin, and north is up.)
Answer:
The answer is √58 = 7.62
Step-by-step explanation:
So, if you draw this down, you will see that the direct distance is hypotenuse c of a right triangle which sides are 3 blocks (1 south and 2 north) and 7 blocks (4 west and 3 east).
Use the Pythagorean theorem:
c² = a² + b²
a = 3
b = 7
c² = 3² + 7²
c² = 9 + 49
c² = 58
c = √58
c = 7.62
Answer:
It's this graph
Step-by-step explanation:
I ran into this one on an assignment
HELP PLEASE ASAP!!!!! BRAINLIEST+20 POINTS!!!!!!!
Which statements are true about parabolas represented by the equation
y=ax²+bx+c?
Select four that apply.
If a>0, then the parabola opens up.
If a>0, then the parabola has a minimum.
If a<0, then the parabola opens down.
If a>0, then the parabola has a maximum.
C. If a<0, then the parabola opens down
Leon is going to toss two number cubes, each labeled 1-6. What is the probability that Leon will toss a sum of 6?
Answer:
[tex]\dfrac{5}{36}[/tex]
Step-by-step explanation:
When tossing two number cubes, Leon can get such sample space
[tex]\begin{array}{cccccc}(1,1)&(1,2)&(1,3)&(1,4)&(1,5)&(1,6)\\(2,1)&(2,2)&(2,3)&(2,4)&(2,5)&(2,6)\\(3,1)&(3,2)&(3,3)&(3,4)&(3,5)&(3,6)\\(4,1)&(4,2)&(4,3)&(4,4)&(4,5)&(4,6)\\(5,1)&(5,2)&(5,3)&(5,4)&(5,5)&(5,6)\\(6,1)&(6,2)&(6,3)&(6,4)&(6,5)&(6,6)\\\end{array}[/tex]
There are 36 possible outcomes. Only (1,5), (2,4), (3,3), (4,2), (5,1) gives the sum of 6.
Hence, the probability that Leon will toss a sum of 6 is
[tex]\dfrac{5}{36}[/tex]
The probability that Leon will toss a sum of 6 is;
P(that Leon will toss a sum of 6) = 5/36
A cube here is same as a dice.
Now, a dice has 6 faces numbered from 1 to 6.
Now,we want to find the probability of tossing a sum of 6.
When we have 2 dices, the possible number of sums we can have are 36 total possible outcomes.
Now, the number of outcomes out of the 36 that can sum up to 6 are;
(1, 5), (2, 4), (3, 3), (5, 1) and (4, 2).
Thus, there are 5 possible sums that can be 6.
Therefore;
P(that Leon will toss a sum of 6) = 5/36
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which house is worth more after two years?
Answer:
Hello cheaters lol jk, Answer is B.
Step-by-step explanation:
more interest equals more money, if you divide the amount of the house by 6% and do the same for the other by 5, the amount for B is greater.
The House A is more worth than House B .
What is compound interest?Compound interest is an interest accumulated on the principal and interest together over a given time period. The interest accumulated on a principal over a period of time is also accounted under the principal.
Formula of Compound interest :
[tex]A = P (1+\frac{r}{100} )^{n}[/tex]
Where,
A = Final amount
P = initial principal
r = rate per annum
n = Time in years
According to the question
House A:
Principal = 125260
Rate = 5%
Time in years = 2
Applying Formula of Compound interest for final amount
[tex]A = P (1+\frac{r}{100} )^{n}[/tex]
[tex]A = 125260 (1+\frac{5}{100} )^{2}[/tex]
[tex]A = 125260 (1.05)^{2}[/tex]
A = 138,099.15
House B:
Principal = 120160
Rate = 6%
Time in years = 2
Applying Formula of Compound interest for final amount
[tex]A = P (1+\frac{r}{100} )^{n}[/tex]
[tex]A = 120160 (1+\frac{6}{100} )^{2}[/tex]
[tex]A = 120160(1.06)^{2}[/tex]
A = 135,011.776
Hence , House A is more worth than House B .
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Please help me out!!!!!
Answer:
Okay I might not be right on this one but, I believe you divide 27 and 3. As to the part about simplifying, you might want to give me so details.
Step-by-step explanation:
Please please help ...
A triangle's sides are suppose to add up to 360 degrees. So create a alegbraic equation with x as the variable. So the equation should add up to 720 degrees for two triangles.
720 = 15x - 3 + 56
720 = 15x + 53
667 = 15x
x = 44.5 (rounded to tenth)
Tell me if I'm incorrect.
Answer:
x = 3
Step-by-step explanation:
The line segment is an angle bisector thus the following ratios are equal
[tex]\frac{32}{24}[/tex] = [tex]\frac{6x+6}{9x-9}[/tex], that is
[tex]\frac{4}{3}[/tex] = [tex]\frac{6x+6}{9x-9}[/tex] ( cross- multiply )
4(9x - 9) = 3(6x + 6) ← distribute parenthesis on both sides
36x - 36 = 18x + 18 ( subtract 18x from both sides )
18x - 36 = 18 ( add 36 to both sides )
18x = 54 ( divide both sides by 18 )
x = 3
reposting this as a priority question worth 15 points help please ASAP
Answer:
3. f(x) = 5^x
4. f(x) = 3 (8)^x
Step-by-step explanation:
3. Which function represents the data 2=>25, 3=>125, 4 =>625
You just have to plug the values of x in the equations provided and see which one fit, you stop testing for a given equation when it doesn't match the data table.
f(x) = x^4 + 9 - NO
for x = 2, 2^4 + 9 = 16 + 9 = 25 YES
for x = 3, 3^4 + 9 = 81 + 9 = 90 NO, should be 125
f(x) = 4^x + 9 - NO
for x = 2, 4^2 + 9 = 16 + 9 = 25 YES
for x = 3, 4^3 + 9 = 64 + 9 = 73 NO, should be 125
f(x) = x^5 - NO
for x = 2, 2^5 = 32 NO, should be 25
f(x) = 5^x YES
for x = 2, 5^2 = 25 YES
for x = 3, 5^3 = 125 YES
for x = 4, 5^4 = 625 YES
4. Which of the options is equivalent to f(x) = 3(2)^(3x)
By property of the powers you can easily break down the 3x exponent into a much simpler way.
[tex](2)^{3x} = (2^{3} )^{x} = 8^{x}[/tex]
From (2)^(3x) we got to 8^x, so the equation can now be written:
f(x) = 3 (8)^x, which is the first choice.
You could easily verify it with x = 2 in each equation.
If some one is doing a 20 mile bike ride.He has cycled 11 miles so far.What percentage of the total distance has he cycled
if we take 20 to be the 100%, what is 11 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 20&100\\ 11&x \end{array}\implies \cfrac{20}{11}=\cfrac{100}{x}\implies 20x=1100 \\\\\\ x=\cfrac{1100}{20}\implies x=55[/tex]
A salesperson set a goal to earn $2,800 in October. He receives a base salary of $1,400 per month as well as a 8% commission for all sales in that month. How many dollars of merchandise will he have to sell to meet his goal?
Answer:
[tex]\$17,500[/tex]
Step-by-step explanation:
Let
x----> that month's sales
y----> October earnings
we know that
[tex]8\%=8/100=0.08[/tex]
[tex]y=0.08x+1,400[/tex] -----> equation A
[tex]y=2,800[/tex] -----> equation B
Equate equation A and equation B and solve for x
[tex]2,800=0.08x+1,400[/tex]
[tex]0.08x=2,800-1,400[/tex]
[tex]x=1,400/0.08[/tex]
[tex]x=\$17,500[/tex]
Final answer:
The salesperson needs to earn an additional $1,400 on top of the base salary to meet the goal, which means they need to sell $17,500 worth of merchandise with an 8% commission rate.
Explanation:
To calculate the amount of merchandise the salesperson must sell to meet the goal of $2,800, we need first to understand how much more money is needed beyond the base salary. The salesperson receives a base salary of $1,400. Since the goal is $2,800, the additional amount needed from commission is $2,800 - $1,400 = $1,400.
With an 8% commission rate, we can set up an equation where the amount of merchandise sold (let's call it x) times the commission rate (0.08) equals the additional amount needed ($1,400). The equation is: 0.08x = $1,400. To find x, divide both sides by 0.08, therefore x = $1,400 / 0.08, which equals $17,500.
So, the salesperson will need to sell $17,500 worth of merchandise to meet the goal of earning $2,800 in October.
Rewrite without absolute value for the given conditions, y=|x−5|+|x+5|, if x>5
Answer:
y=2x when x>5
Step-by-step explanation:
y=|x−5|+|x+5|
If x > 5 then x-5 is greater than 0 so we can remove the absolute value bars from the first term
x>5 then x+5 >0 so we do not need the absolute value bars on the second term
y = x-5 + x+5
Combine like terms
y = x+x-5+5
y = 2x
Let $a_1$, $a_2$, $\dots$, $a_{12}$ be twelve equally spaced points on a circle with radius 1. find\[(a_1 a_2)^2 + (a_1 a_3)^2 + \dots + (a_{11} a_{12})^2.\](the sum includes the square of the distance between any pair of points, so the sum includes $\binom{12}{2} = 66$ terms.)
The sum evaluates to 144. See the linked question in the comments for details.
Ramon wants to make a rectangular prism with 5 cubes. Can he do this? Explain. Draw cubes to show your answer.
Answer:
Place them in a line.
Step-by-step explanation:
Take the First cube and place it on the paper
Then place another cube behind that cube
Repeat with remaining cubes
Should end up with a line of cubes that create a rectangular prism.
Ramon cannot form a rectangular prism using exactly 5 cubes because a rectangular prism has 6 faces, which would each be formed by a cube. To create even the smallest possible rectangular prism, he would need at least 6 cubes.
Explanation:No, Ramon cannot make a rectangular prism using exactly 5 cubes. A rectangular prism is a three-dimensional figure with six faces that are rectangles. It would not be possible to form a rectangular prism using only 5 cubes because to form a rectangular prism you need at least 6 cubes.
Each cube would represent one face of the rectangular prism.
This is because a rectangular prism has 3 dimensions: length, width, and height. Even if you make the smallest possible rectangular prism, you would need a minimum of 6 cubes (1 cube length, 1 cube width, and 6 cubes high). If he has only 5 cubes, at least one dimension (length, width, or height) would be incomplete.
Learn more about Geometry here:https://brainly.com/question/31408211
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