Answers
From this triangle we know:
THE AREA:
[tex]A=80cm^2[/tex]
THE HEIGHT:
[tex]H=B+12[/tex]
We know that the area, height, and base of a triangle are related according to the following formula:
[tex]A=\frac{BH}{2} \\ \\ Substituting \ H: \\ \\ A=\frac{B(B+12)}{2} \\ \\ Substituting \ A: \\ \\ 80=\frac{B(B+12)}{2} \\ \\ 2(80)=B(B+12) \\ \\ 160=B^2+12B \\ \\ B^2+12B-160=0[/tex]
Solving B by quadratic formula:
[tex]B_{12}=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ B_{12}=\frac{-12 \pm \sqrt{12^2-4(1)(-160)}}{2(1)} \\ \\ B_{12}=\frac{-12 \pm \sqrt{12^2-4(1)(-160)}}{2(1)} \\ \\ B_{1}=8 \ and \ B_{2}=-20[/tex]
Since we can’t have a negative value of the base, the correct option is:
[tex]B=8cm[/tex]
11) How long will it take the water balloon to hit the ground?We must use the formula:
[tex]h(t)=-5.2t^2+v_{0}t+h_{0}[/tex]
Since James drops the balloon from a height of 45m, then this is the initial height, so [tex]h_{0}=45m[/tex]. Moreover, at the very instant he drops the balloon the initial velocity is zero, so [tex]v_{0}=0[/tex]. When the ballon hit the ground [tex]h(t)=0[/tex]. Therefore:
[tex]0=-5.2t^2+45[/tex]
Solving this equation:
[tex]5.2t^2=45 \\ \\ t^2=\frac{45}{5.2} \\ \\ t^2=8.653 \\ \\ t=\sqrt{8.653} \\ \\ t=2.941s[/tex]
Rounding to the nearest tenth:
[tex]\boxed{t=2.9s}[/tex]
Finally, the water balloon will hit the ground after 2.9 seconds.
12) Height and initial velocityWe have the equation:
[tex]h(t)=-16t^2+32t+12[/tex]
But we know that this equation follows the form:
[tex]h(t)=-16t^2+v_{0}t+h_{0}[/tex]
According to this:
The height of the platform is [tex]h_{0}=12ft[/tex]
The initial velocity of the ball is [tex]v_{0}=32ft/s[/tex]
Related Questions
What is the slope of (-8, 2) and (1, -4).
Answers
Answer:
-2/3
Step-by-step explanation:
To find the slope of two points
m = (y2-y1)/ (x2-x1)
= (-4-2)/(1--8)
= (-4-2)/(1+8)
= -6/9
-2/3
Answer:
[tex]\large\boxed{\text{The slope}\ m=-\dfrac{2}{3}}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-8, 2) and (1, -4). Substitute:
[tex]m=\dfrac{-4-2}{1-(-8)}=\dfrac{-6}{9}=-\dfrac{6}{9}=-\dfrac{6:3}{9:3}=-\dfrac{2}{3}[/tex]
The function f(x) = -x^2 - 2x + 15 is shown on the graph. What are the domain and range of the function?
Answers
R; all quadratic functions are going to have ranges and domains of *ALL REAL NUMBERS* [(-∞, ∞)].
Answer: the domain is all real numbers. the range is {y|y ≤ 16}
Step-by-step explanation:
Don’t have trust issues
Helppp 1-7 pleaseee !!!!!
Answers
1.RT
2.QS
3.PS
4.T
5.QR
6.QSR
7.QRS
If correct mark best answer!
Which graph best represents the solution to the following pair of equations?
y = −2x + 13
y = 2x − 3
A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines having equations y is equal to negative 2 times x plus 13 and y is equal to 2 times x minus 3 are plotted. These 2 lines intersect at the ordered pair negative 4, negative 5.
A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines having equations y is equal to negative 2 times x plus 13 and y is equal to 2 times x minus 3 are plotted. These 2 lines intersect at the ordered pair 4, 5.
A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines having equations y is equal to negative 2 times x plus 13 and y is equal to 2 times x minus 3 are plotted. These 2 lines intersect at the ordered pair negative 4, 5.
A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines having equations y is equal to negative 2x plus 13 and y is equal to 2x minus 3 are plotted. These 2 lines intersect at the ordered pair 4, negative 5.
Answers
ANSWER
See attachment
EXPLANATION
The given equations are:
y = −2x + 13
y = 2x − 3
We equate the two equations to get
−2x + 13=2x − 3
Group similar terms:
-2x-2x=-3-13
-4x=-16
Divide both sides by -4,
x=4
Put x=4 into equation (2)
y=2(4)-3
y=5
The two graphs should intersect at:
(4,5)
Answer: The answer is (4, 5)
Step-by-step explanation:
What is the distance between the points (–4, –5) and (5, –1)?
Answers
Answer:
About 4.39.
Step-by-step explanation:
The distance formula is the square root of ( x2 − x1 ) squared + ( y2 − y1 ) squared. Plugging in our x and y values, you get 4.386342439892262, which rounds up to 4.39.
The answer is 4.39 and that’s the answer
What is the value of x?
Answers
Answer:
28
Step-by-step explanation:
Answer:
x = 14
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 6, hence
sum = 180° × 4 = 720°
Each exterior angle plus it's interior angle = 180°
Subtract each exterior angle from 180 to obtain interior angle
180 - 80 = 100, 180 - 56 = 124, 180 - 61 = 119, 180 - 43 = 137, 180 - 92 = 88
The 6 th interior angle is the sum of the 5 interior angles subtracted from 720
6 th angle = 720° - (100 + 124 + 119 + 137 + 88)° = 720° - 568° = 152°
The 6 th angle and 2x sum to 180 ( same reason as given above )
2x + 152 = 180 ( subtract 152 from both sides )
2x = 28 ( divide both sides by 2 )
x = 14
Share £747 in the ratio 2:7
Answers
Answer:
£166 : £581
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
2 + 7 = 9
747 ÷ 9 = 83
2 : 7
( × 83 both sides )
166 : 581
can you guys solve this lina is making jewelry.she has 7 beads and buys 4 additional packets of beads that each have the same number of beads.write an expression to show the total of beads that lina uses.1 the number of beads lina has 2 the total number of beads in the four packets 3 the total number of beads lina has
Answers
Answer:
4b+7
Step-by-step explanation:
7 beads= +7
4 packs= 4b
expression= 4b+7
The solution to the question "write an expression to show the total of beads that lina uses" is:
The number of beads Lina has = 7
The number of beads in the four packets = 4n
The total number of beads that Lina now has = 4n + 7
The number of beads Lina originally has = 7
The number of additional packets bought = 4
Let the number of beads in each packet be n
Total number of beads in the 4 packets = 4 x (number of beads in each packet)
Total number of beads in the 4 packets = 4n
The total number of beads that Lina now has = (The number of beads in the 4 packets) + (The number of beads she originally has)
The total number of beads that Lina now has = 4n + 7
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8.28÷0.72=115 can you please help me with this I'm struggling
Answers
Answer:
a
Step-by-step explanation:
Which of the following descriptions matches the sequence of events shown
in the tree diagram below?
Answers
The answer would be d- tossing s coin, tossing a second coin, and tossing a third coin
Option: D is the correct answer
D. Tossing a coin, tossing a second coin and tossing a third coin.
Step-by-step explanation:We know that when a coin is tossed then there are only two possible outcomes i.e. either a head or a tail.
Now, when a second coin is tossed then again we have two possible outcomes i.e. head and a tail.
and the total sample space of the two events is given by:
HH HT TT TH
Now, when a coin is tossed third time then in than two outcomes are possible on the coin i.e. a head and a tail.
Hence, the total number of outcomes are:
HHH HTH TTH THH
HHT HTT TTT THT
i.e. when a coin is tossed n times that the total possible outcomes are:
[tex]2^n[/tex]
Here the coin is tossed three times.
Hence, the total possible outcomes are: [tex]2^3=8[/tex]
Mr and mrs turner ate 3/4 of a pizza. They want to split the remaining part equally between their two sons how much of the pizza will each son recive
Answers
The remainder would be 1/4 of the pizza. 1/4 is equivalent to 2/8 of the pizza. This 2/8 can be easily divided for both sons. Therefore the answer would be each son would receive 1/8 of the pizza.
the radius of a cylinder is multiplied by 6 while the height is kept the same. what effect does this have in the volume of the cylinder
Answers
[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=\stackrel{\times 6}{6r} \end{cases}\implies V=\pi (6r)^2 h\implies V=\pi (6^2r^2) h \\\\\\ V=36~~\pi r^2 h\impliedby \textit{36 times the original volume}[/tex]
The effect that multiplying the radius by 6 would have on the volume of the cylinder is the volume would increase by a factor of 36
Calculating the volume of a cylinderFrom the question, we are to determine what effect multiplying radius by 6 would have on the cylinder
Using the formula for calculating the volume of a cylinder
V = πr²h
Where V is the volume of the cylinder
r is the radius
and h is the height
If the r is the radius and h is the height of the first cylinder,
Then, volume of the first cylinder will be
V = πr²h
For the new cylinder
radius = 6r
and h = h
Then, volume of the new cylinder will be
V₂ = π × (6r)² × h
V₂ = π × 36r² × h
V₂ = 36πr²h
The new volume is multiplied by a factor of 36
Hence, the effect that multiplying the radius by 6 would have on the volume of the cylinder is the volume would increase by a factor of 36.
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Statistics
1. What is the sum of all the results included in the sample divided by the number of observations. It is the average.
2. total data set
3. this is the collection, display, and analysis of the data
4. this is asking or inquiring people's opinion
5. this is the most frequently occurring element in a set
6. this measures the deviation between the scores and the mean, it mesures how dispersed the data is. the higher this is the more spread out the data is from each other.
7. the type of sample in which each member of the sample set or group has equal chance of being chosen
8. the spread of the middle 50% of the data
9. the middle term in a set of data. if the data set has an even number of terms this is the average of the two middle terms.
10. this is the process of gathering data from every member of a population
Answers
Answer:
1. mean
2. population
3. statistics
4. survey
5. mode
6. standard deviation
7. random
8. interquartile range
9. median
10. census
Step-by-step explanation:
The population of a town is 13,000. It decreases at a rate of 5% per year. In about how many years will the population be less than 12,000?
Answers
This is an exponential decay problem.
Using the equation Y = a *(1-rate)^time
where Y is the future value given as 12,000 and a is the starting value given as 13,000.
The rate is also given as 5%.
The equation becomes:
12,000 = 13,000(1-0.05)^x
12,000 = 13,000(0.95)^x
Divide each side by 13000:
12000/13000 = 0.95^x/13000
12/13 = 0.95^x
Use the natural log function:
x = ln(12/13) / ln(0.95)
x = 1.56 years. ( this will equal 12,000
Round to 2 years it will be less than 12000.
( 10 points) please help asap!!!
Answers
Answer:
f+5, g-10, 10-g, and 1/2p
Hope This Helps! Have A Nice Day!!
Answer:
A: F + 5
B: g - 10
C: 10 - g
D: P divided by 2
find the missing angle measures in the figure? A.) 103 degrees B. ) 93 degrees C.) 113 degrees D.) 83 degrees
Answers
I would think A. i just tried to figure it out on my own but forgive me if I'm wrong but I'm positive I'm right
What’s this answer to this question?
Answers
Answer:
Step-by-step explanation:
$20.00
Draw a 30° angle in standard position on the coordinate plane. Show the direction of rotation. Label the terminal side and the angle measure.
Answers
also the direction is anti clockwise
I hope it could help you :)
To draw a 30° angle in standard position on the coordinate plane, start by drawing the initial side of the angle which is the positive x-axis. Use a protractor to measure a 30° angle counterclockwise from the initial side. Then draw a line from the origin to the endpoint of the angle to represent the terminal side. Label the angle measure as 30° and label the terminal side accordingly. Indicate the direction of rotation by drawing an arrow showing the counterclockwise direction.
Explanation:To draw a 30° angle in standard position on the coordinate plane, follow these steps:
Start by drawing the initial side of the angle, which is the positive x-axis.Using a protractor, measure a 30° angle counterclockwise from the initial side.Draw a line from the origin to the endpoint of the angle to represent the terminal side.Label the angle measure as 30° and label the terminal side accordingly.Indicate the direction of rotation by drawing an arrow showing the counterclockwise direction.Learn more about Drawing a 30° angle on the coordinate plane here:https://brainly.com/question/31573620
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find the mean,median,and mode for the data.
114;120;115;114;118;117;114
pleassssseeee
thanks
:)
Answers
Answer:
Mean: 116
Median: 115
Mode: 115
Step-by-step explanation:
Mean is the average of the data set; it’s found by adding up all the numbers and dividing that sum by the number of numbers there are
(114 + 120 + 115 + 114 + 118 + 117 + 114)/7 = 812/7 = 116
Median is found out by ordering the given numbers from largest to smallest and finding the middle number; if there are an even number of given numbers, you add them up and divide by two.
In this case, you are lucky enough to be given an odd numbers of given numbers
Ordering (smallest to largest):
114, 114, 114, 115, 117, 118, 120
Median is 115
(this is the number in the middle of the data set)
Mode is the most frequently occurring number in the data set
In this case, the
Mode is 114
The mean of the data is 116, the median is 115, and the mode is 114. All three measures offer insights into the dataset's central tendencies.
To find the mean, median, and mode of the given data: 114, 120, 115, 114, 118, 117, 114, let's follow these steps:
Mean: Add all the numbers together and divide by the number of data points.
Sum: 114 + 120 + 115 + 114 + 118 + 117 + 114 = 812Number of data points: 7Mean: 812 / 7 = 116Median: Arrange the numbers in ascending order and find the middle value. If there is an even number of observations, calculate the average of the two middle values.
Ordered data: 114, 114, 114, 115, 117, 118, 120Since n = 7 (an odd number), the median is the 4th value which is 115Mode: The most frequently occurring value in the dataset.
Mode: 114 (appears 3 times)Thus, the mean is 116, the median is 115, and the mode is 114.
-6n+21 =12n-15 I need help solving the equation
Answers
Answer:
n = 2
Step-by-step explanation:
Given
- 6n + 21 = 12n - 15 ( collect terms in n on the left and numbers on the right )
Subtract 12n from both sides
- 18n + 21 = - 15 ( subtract 21 from both sides )
- 18n = - 36 ( divide both sides by - 18 )
n = 2
The fulcrum of a lever is the point on which it turns. Based on the function, how many pounds of force are needed to lift the rock if the distance from the fulcrum is 6 feet?
Answers
Answer: 10 pounds of force
Answer:
10 lb of force are needed to lift the rock if the distance from the fulcrum is 6 feet.
Step-by-step explanation:
From the given graph it is clear the curve passing through the point (1.5,40), (2,30), (2.5,24), (3,20) and (4,15).
These points satisfy by the equation
[tex]y=\frac{60}{x}[/tex]
where, x is the distance in feet from the fulcrum and y is needed force in pounds.
Put x=6 in this equation,
[tex]y=\frac{60}{6}=10[/tex]
Therefore, 10 lb of force are needed to lift the rock if the distance from the fulcrum is 6 feet.
can you simplify before multiplying 14×25/27
Answers
Answer:
No.
Step-by-step explanation:
You can not simplify this expression before multiplying it, because no whole numbers go into both 14 and 27, and also no whole numbers go into both, 25 and 27. This is the correct answer to this question.
Hope this helps!!!
Kyle.
Before multiplying in the expression 14×25/27, try to simplify. Simplify 25/27 first, which gives an approximate decimal 0.9259. Multiply the approximation by 14, which gives the approximately 12.9626.
Explanation:Yes, you can simplify before multiplying in the given expression, 14×25/27. This follows the mathematic principle of simplifying terms prior to engaging in the operation. Here's how you can do it:
First let's simplify 25/27. This cannot be simplified further and will result in an approximation when decimalized, around 0.9259.Then, multiply the simplified fraction or its decimal approximation by 14. So, multiplying 14 by 0.9259 gives approximately 12.9626.Learn more about Simplification here:https://brainly.com/question/33857870
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What is the LCM of 5,13 and 10
Answers
1 because 13 is not divisible buy anything other than 1
The LCM of 5, 13 and 10 is 130.
What is the LCM of 5,13 and 10?The LCM (Least Common Multiple) of two numbers is the smallest number that is a multiple of both numbers.
The LCM is the smallest number that is a multiple of 5, 13, and 10. To find the LCM, we can use the following steps:
1. Find the prime factorization of each number.
2. Find the highest power of each prime factor.
3. Multiply the prime factors together, using the highest power of each factor.
The prime factorization of 5 is 5.
The prime factorization of 13 is 13.
The prime factorization of 10 is 2 * 5.
The highest power of 2 is 1.
The highest power of 5 is 1.
The highest power of 13 is 1.
Therefore, the LCM of 5, 13, and 10 is:
2 * 5 * 13 = 130
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A cone has a radius of 4 units and a height of 6 units. Its volume is (A. 96 / B. 100.48 / C. 301.44 / D. 401.92) cubic units. If a cylinder has the same radius and the same height as the cone, then its volume is (A. 66.99 / B. 288 C. / 301.44 / D. 904.32) cubic units.
Answers
Answer:
A cone: B. V = 100.48 cubic unitsA cylinder: C. V = 301.44 cubic unitsStep-by-step explanation:
The formula of a volume of a cone:
[tex]V=\dfrac{1}{3}\pi r^2H[/tex]
r - radius
H - height
We have r = 4 u and H = 6 u. Substitute:
[tex]V=\dfrac{1}{3}\pi(4^2)(6)=\dfrac{1}{3}\pi(16)(6)=\dfrac{1}{3}\pi(96)=32\pi\ u^3[/tex]
[tex]\pi\approx3.14\to V\approx(32)(3.14)=100.48\ u^3[/tex]
If the cylinder has the same radius and height as a cone, then the volume of the cylinder is three times larger than the volume of the cone.
Therefore, the volume of acylinder:
[tex]V\approx3(100.48)=301.44\ u^3[/tex]
Why?
The formula of a volume of a cone:
[tex]V_{cone}=\dfrac{1}{3}\pi r^2H[/tex]
The formula of a volume of a cylinder:
[tex]V_{cylinder}=\pi r^2H[/tex]
Therefore
[tex]V_{cone}=\dfrac{1}{3}V_{cylinder}\to V_{cylinder}=3V_{cone}[/tex]
If the radius and height are the same.
Answer:
A cone has a radius of 4 units and a height of 6 units.
Its volume is
[100.48]
cubic units. If a cylinder has the same radius and the same height as the cone, then its volume is
[301.44]
cubic units.
Step-by-step explanation:
Write parametric equations of the line -3x+4y=7
Answers
Answer:
x = 1 + t and y = 2.5 + 0.75t
Step-by-step explanation:
Parametric equations are the equations in which the all the variables of the equation are written in terms of a single variable. For example in 2-D plane, the equation of the line is given by y=mx+c, there x is the independent variable, y is the dependent variable, m is the slope, and c is the y-intercept. The equation of the given line is -3x + 4y = 7. The goal is to convert the variables x and y in terms of a single variable t. First of all, take two points which lie on the line. By taking x=1, y comes out to be 2.5 and by taking x=0, y comes out to be 2.5. The general form of the straight line is given by:
(x, y) = (x0, y0) + t(x1-x0, y1-y0), where (x, y) is the general point, (x0, y0) is the fixed point, t is the parametric variable, and (x1-x0, y1-y0) is the slope.
Let (x0, y0) = (1, 2.5) and (x1, y1) = (0, 1.75). Substituting in the general equation gives:
(x, y) = (1, 2.5) + t(1, 0.75). This implies that x = 1 + t and y = 2.5 + 0.75t!!!
Answer:
x=t, y=(3/4)t+(7/4)
Step-by-step explanation:
We start by changing the equation the slope-intercept form.
4y=3x+7
y=(3/4)x+(7/4)
then we set x equal to t
x=t
and substitute
y=(3/4)t+(7/4)
that's it.
Calculate the area of a circle with a radius of 8 feet
Answers
Answer:
201.06 square feet
Step-by-step explanation:
area of a circle is given by πr², where π = 3.1416
A = 3.1416 * 8²
A = 3.1416 * 64 = 201.0624 square feet
A = 201.06 square feet
What is the maximum value that the graph of y=cos x assumes?
Answers
Answer:
I am assuming you mean a normal cosine parent graph. The maximum a y=cos(x) graph can approach is one.
Answer:
1
Step-by-step explanation:
The square root of 73
Answers
8.5 is the answer to your question
The square root of 73 is approximately 8.544. It lies between the perfect squares of 64 and 81. The square root cannot be represented exactly as an integer or a simple fraction.
To find the square root of 73, we recognize that it is not a perfect square. Thus, the square root cannot be represented exactly as an integer or a simple fraction. We use approximation methods or a calculator to find it.
Steps to Find the Approximate Square Root of 73:
First, find the nearest perfect squares surrounding 73. We know that 64 (8²) and 81 (9²) are the closest.Next, since 73 is closer to 64, we can estimate that √{73} is slightly more than 8.Using a calculator, we find that the square root of 73 is approximately 8.544.So, the square root of 73 is about 8.544.
Stuck on geometric series question (in picture)
Answers
Answer:
The value of a7 is 128
Step-by-step explanation:
* Lets revise the rule of the geometric series
-There is a constant ratio between each two consecutive numbers
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
* General term (nth term) of a Geometric series:
# a1 = a , a2 = ar , a3 = ar2 , a4 = ar3 , a5 = ar4
# an = ar^n-1, where a is the first term , r is the constant ratio
between each two consecutive terms , and n is the position
of the term in the series
* Now lets solve the problem
∵ a = 2
∵ r = -2
* To find a7 put n = 7
∵ an = a (r)^n - 1
∴ a7 = 2 (-2)^(7 - 1) = 2 (-2)^6
∵ (-2)^6 = 64 ⇒ even power canceled the negative sign
∴ a7 = 2 (64) = 128
∴ The series is : 2 , -4 , 8 , -16 , 32 , -64 , 128 , ............
* The value of a7 is 128
which parent function is represented by the graph
Answers
Answer:
D. Reciprocal parent function
Step-by-step explanation:
The given function has the x-axis as the horizontal asymptote
The vertical asymptote is the line x=0, which is the y-axis.
This means that the function has x, in the denominator.
Therefore, the function represented by the graph is [tex]\frac{1}{x}[/tex].
This is the parent reciprocal function.
The correct choice is D