The unit vector that is oppositely directed to v = (3, -4) and half its length is approximately u = (-0.5547, 0.8321).
How to find a unit vector that satisfies the given conditions?To find a unit vector that is oppositely directed to v = (3, -4) and half its length, we can follow these steps:
Find the length of vector v:
|v| = sqrt(3^2 + (-4)^2) = 5
Divide vector v by 2 to get a vector with half its length:
v/2 = (3/2, -2)
To get a vector that is oppositely directed to v, we can reverse the direction of v/2:
-(3/2, -2) = (-3/2, 2)
Finally, we can find the unit vector in the direction of (-3/2, 2) by dividing it by its length:
|(-3/2, 2)| = sqrt((-3/2)^2 + 2^2) = sqrt(13/4)
u = (-3/2, 2) / sqrt(13/4) = (-3/2) * (2/sqrt(13))/2 + (2/sqrt(13)) * (1/2)
Therefore, the unit vector that is oppositely directed to v = (3, -4) and half its length is approximately u = (-0.5547, 0.8321).
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A triangular prism has a net as shown below.
4m
5m
5m
3m
What is the surface area of this triangular prism?
20 points if you help me out!
Answer: 72 m²
Step-by-step explanation:
The data set is 12, 46, 32, 18, 26, 41, 46. the mean is 31.6 and the median is 32. if we add another 12, what affect does this have on the mean and median?
Adding another 12 to the data set would increase the sum of the values by 12, resulting in a new sum of 239. To find the new mean, we divide the new sum by the total number of values in the set, which is now 8. So the new mean would be 29.875, which is slightly lower than the original mean of 31.6.
To find the new median, we first need to rearrange the values in ascending order: 12, 18, 26, 32, 41, 46, 46, 12. Since there are now an even number of values, we take the average of the middle two, which in this case is (26 + 32) / 2 = 29. So the new median would be 29, which is lower than the original median of 32.
In summary, adding another 12 to the data set would slightly decrease the mean and lower the median.
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In a survey, the planning value for the population proportion is p* = 0.25. How large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.02? Round your answer up to the next whole number. How large a sample should be selected to provide a 95% confidence interval with a margin of error of 2? Assume that the population standard deviation is 30. Round your answer to next whole number.
The Sample size that is necessary for the selection is =7203
How to solveGiven that,
[tex]\hat p= 0.25[/tex]
[tex]1 - \hat p = 1 - 0.25 = 0.75[/tex]
margin of error = E = 0.01
At 95% confidence level the z is ,
\alpha = 1 - 95% = 1 - 0.95 = 0.05
[tex]\alpha / 2 = 0.05 / 2 = 0.025[/tex]
Z\alpha/2 = Z0.025 = 1.96 ( Using z table )
Sample size = n = [tex](Z\alpha/2 / E)2 * \hat p * (1 - \hat p)[/tex]
= (1.96 / 0.01)2 * 0.25 * 0.75
= 7203
Sample size =7203
In statistics, the sample size is the measure of the number of individual samples used in an experiment.
The size of the sample holds significant importance in any empirical study that aims to draw conclusions about a larger population based on a smaller sample.
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what dose y equal when the equation is negitive 5 y plus 4 is equal to negitive 11
Answer: y = 1.4
Step-by-step explanation:
if you write the equation it would be
-5y - 4 = -11
so first you would subtract 4 from -4 and -11 to cancel out the four.
so your equation would look like this -5y= -7
so now u would divide -5 by both sides to canceled out the -5
your equation should end up looking like
y=1.4
Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. sin lim 5 X400 :) X lim 5 X00 64--m-0 - sin)=(Type an exact answer)
Let's evaluate the limit using l'Hôpital's Rule when it is convenient and applicable:
The evaluated limit using l'Hôpital's Rule is 5.
Given limit,
lim (x -> 0) (sin(5x) / x)
Since both the numerator and denominator approach 0 as x approaches 0,
we can apply l'Hôpital's Rule.
Step 1: Differentiate the numerator and the denominator with respect to x.
- Derivative of sin(5x) with respect to x: 5*cos(5x)
- Derivative of x with respect to x: 1
Step 2: Apply l'Hôpital's Rule:
lim (x -> 0) (5*cos(5x) / 1)
Step 3: Evaluate the limit:
As x approaches 0, cos(5x) approaches cos(0) = 1.
Therefore, the limit is: 5*1 = 5
So, the evaluated limit using l'Hôpital's Rule is 5
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A researcher is studying life expectancy in different parts of the world using birth and death records she randomly selects a sample of 20 people from town a and a samle of 20 people form town b and records their lifespans in years.
mean lifespan in years standard deviation
town a 78.5 11.2
town b 74.4 12.3
the researhers wants to test the claim that there is a significant differnce in lifepan for people in the two towns. what are the null and alternative hypotheses that should be used to test this claim?
a. null: mu1 - mu2 is not equal to 0; alternative: mu1 - mu2 > 0 <---- a
b. null: mu1 - mu2 = 0; alternative: p1 - p2 is not equal to 0 <---- b
c. null: mu1 - mu2 = 0; alternative: mu1 - mu2 is not equal to 0 <---- c
d. null: p1 - p2 = 0; alternative: p1 - p2 < 0 <---- d
The correct answer is: c. null: mu1 - mu2 = 0; alternative: mu1 - mu2 is not equal to 0
The null hypothesis states that there is no significant difference in the mean lifespan of people in the two towns, while the alternative hypothesis states that there is a significant difference in the mean lifespan of people in the two towns.
Since we are comparing the means of two populations, we use the difference between the means as the test statistic. Therefore, the null hypothesis is mu1 - mu2 = 0 (there is no difference between the means) and the alternative hypothesis is mu1 - mu2 is not equal to 0 (there is a difference between the means).
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Find the most important variable in the problem.
If a company hired an additional 12 employees, and every employee needed a
phone, it would require 8 more phones. How many phones does the company
have available now?
OA. the number of employees hired
OB. the money required to purchase phones
OC. the number of phones available
In order for a triangle to be acute, what relationship must c2 have with a2 + b2?
group of answer choices
c2>a2+b2
c2
c2=a2+b2
In order for a triangle to be acute, the relationship that c² must have with a² + b² is c² < a² + b².
An acute triangle is a triangle in which all three angles are acute angles, which means they are less than 90 degrees. In other words, an acute triangle is a triangle with three acute angles.
To understand why the relationship between c^2 (the square of the longest side) and a^2 + b^2 (the sum of the squares of the other two sides) is important in determining whether a triangle is acute, we need to delve into the concept of the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Mathematically, it can be expressed as c^2 = a^2 + b^2, where c represents the hypotenuse, and a and b represent the other two sides.
In an acute triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side.
This can be visualized as follows: If we were to draw a right triangle with the shorter sides represented by segments a and b, and the longest side represented by segment c, the acute triangle would be formed by making the length of segment c shorter than the length determined by the Pythagorean theorem. This ensures that the angle opposite to the longest side remains acute.
On the other hand, if c^2 were equal to a^2 + b^2, we would have a right triangle, not an acute triangle. If c^2 were greater than a^2 + b^2, we would have an obtuse triangle since the angle opposite to the longest side would be greater than 90 degrees.
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50 POINTS ASAP Triangle 1 and triangle 2 are similar right triangles formed from a ladder leaning against a building.
Triangle 1 Triangle 2
The distance, along the ground, from the bottom of the ladder to the building is 12 feet. The distance from the bottom of the building to the point where the ladder is touching the building is 18 feet. The distance, along the ground, from the bottom of the ladder to the building is 8 feet. The distance from the bottom of the building to the point where the ladder is touching the building is unknown.
Determine the distance from the bottom of the building to the point where the ladder is touching the building for triangle 2.
27 feet
18 feet
12 feet
5 feet
The distance where the ladder is touching the building for triangle 2 is 12 ft
Determining the distance from the bottom of the building to the pointFrom the question, we have the following parameters that can be used in our computation:
Ladder 1
Distance along the ground = 12 ft
Distance touching the ladder = 8 ft
Ladder 2
Distance along the ground = 18 ft
Distance touching the ladder = x
Using proportion of similar triangles, we have
x : 18 = 8 : 12
Express as fraction
x/18 = 8/12
So, we have
x = 18 * 8/12
Evaluate
x = 12
Hence, the distance where the ladder is touching the building for triangle 2 is 12 ft
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Answer:
12?
Step-by-step explanation:
Not too sure! I am in the middle of taking the test right now though
Solve for x: √8x + 4 = 6
The solution to the equation √8x + 4 = 6 is x = 0.5.
What is the value of x?An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.
Given the equation in the question:
√8x + 4 = 6
To solve for x in the equation, isolate the term containing the variable x.
Subtract 4 from both sides of the equation:
√8x + 4 - 4 = 6 - 4
√8x = 6 - 4
√8x = 2
Square both sides of the equation:
( √8x )² = 2²
8x = 4
Divide both sides of the equation by 8:
x = 4/8
x = 1/2
x = 0.5
Therefore, the value of x is 0.5.
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Aura builds model airplanes. Her first model airplane is 4
feet long
She wants her next model airplane to be
4
as long as the first
How long will her next modhi airplane be?
1
ft
12
B
1
4
12
ft
7
4
12
ft
D
17
ft
The next model airplane will be 16 feet long.
How long will Aura's next model airplane be if she wants it to be four times as long as her first model airplane which is 4 feet long?To find the length of Aura's next model airplane, we need to multiply the length of her first model airplane by 4, since she wants the next one to be 4 times as long as the first. Therefore, the length of her next model airplane would be:
4 feet (length of first model airplane) x 4 = 16 feet
So, the length of her next model airplane would be 16 feet.
Note that this assumes that Aura's first model airplane is the baseline for measurement and that the "4" in the question refers to a factor of 4, not an additional 4 feet. If the question were interpreted differently, the answer may be different.
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7 women and 7 men are on the faculty in the mathematics department at a school. how many ways are there to select a committee of five members of the department if at least one woman must be on the committee?
In 1981 number of ways a committee of five members of the department if at least one woman must be on the committee.
By choosing some items from a set and creating subsets, permutation and combination are two approaches to express a collection of things. It outlines the numerous configurations for a certain set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.
The number of ways of picking 5 from 14 is what the question is actualy asking minus combinations of 5 from 7 , because there must be 1 woman
so 5 from 14 is given by :
= [tex]\frac{14*13*12*11*10}{5*4*3*2*1}[/tex]
which is :
14 x 13 x 11 = 2002
combinations of 5 from 7 is :
(9x8x7x6x5) / (5x4x3x2x1)
[tex]\frac{7*6*5*4*3}{5*4*3*2*1}[/tex]
which is :
7 x 3= 21
so the final answer is 2002 - 21 = 1981.
Therefore, in 1981 ways a committee of five members of the department if at least one woman must be on the committee.
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Una carretera recta forma un angulo de 22° con la horizontal dde cierto punto Q en ella el angulo de elevacion del avion en el punto A 57 en el mismo instante dde otro punto Q a 100 m adelante del primero el angulo de elevacion 63 los puntos P Q A quedan en el plano vertical calcule la distancia de P al avion
The distance from P to the airplane is y = x + 100 ≈ 628.38 m.
What is the triangle?A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
From a certain point Q on a straight road, which forms an angle of 22° with the horizontal, the angle of elevation of an airplane at point A is 57°. At the same instant from another point Q, 100 meters ahead of the first point, the angle of elevation of the airplane is 63°. The points P, Q, and A are in the same vertical plane. Find the distance from P to the airplane.
To solve the problem, we can use the concept of similar triangles. Let's call H the height of the airplane and x the distance from Q to the airplane. Then, the distance from P to the airplane is given by y = x + 100.
From triangle QA1H, we have:
tan(57°) = H / x
From triangle QA2H, we have:
tan(63°) = H / (x + 100)
Dividing these two equations, we get:
tan(57°) / tan(63°) = x / (x + 100)
Solving for x, we get:
x = 100 * tan(63°) / (tan(63°) - tan(57°)) ≈ 528.38 m
Therefore, the distance from P to the airplane is:
y = x + 100 ≈ 628.38 m.
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Bilquis is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 29 meters from the building. The angle of elevation from her eyes to the roof (point A) is 17°, and the angle of elevation from her eyes to the top of the antenna (point B) is 31º. If her eyes are 1. 51 meters from the ground, find the heigh[of the antenna (the distance from point A to point B). Round your answer to the nearest meter if necessary.
The height of the antenna is approximately 17 meters.
To solve for the height of the antenna, we need to use trigonometry. Let's call the height of the antenna "h".
First, we need to find the distance from point A to point B. We can use the angle of elevation from her eyes to the roof (17°) and the horizontal distance from the building (29m) to find the height of the building.
tan(17°) = height of building / 29m
height of building = 29m * tan(17°)
height of building = 8.20m
Now we can use the height of the building and the angle of elevation from her eyes to the top of the antenna (31°) to find the distance from point A to point B.
tan(31°) = h / 29m + 8.20m
h = (29m + 8.20m) * tan(31°)
h = 15.51m
Finally, we need to add the height of Bilquis' eyes to the height of the antenna to find the total height.
total height = h + 1.51m
total height = 17.02m
Therefore, the height of the antenna is approximately 17 meters.
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Jose conducted an experiment to measure the rate of minerals dissolving in water and changed the temperature of the water for each trial.
What is the independent variable in this experiment?
A: number of trials being tested
B: temperature of the water
C: type of minerals used for each trial
D: rate the minerals dissolved
The independent variable in the study is the temperature of the water
What is the independent variable?The variable that the experimenter consciously modifies or changes is known as the independent variable.
The variable that is supposed to have an impact on the dependent variable is this one. After then, the dependent variable is assessed and recorded to see if it changes as a result of the independent variable's manipulation.
The temperature was changed before each trial hence the temperature was manipulated and that is the independent variable.
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What is the multiplicity of the zero of the polynomial function that represents the volume of a sphere with radius x+5
The graph of the function will touch the x-axis at x = -5, but not cross it, and the behavior of the graph near x = -5 will be determined by the degree of the zero (which is 3 in this case).
The polynomial function that represents the volume of a sphere with radius x+5 is given by:
[tex]V(x) = (4/3)\pi (x+5)^3[/tex]
To find the multiplicity of the zero, we need to factor out the (x+5) term from the polynomial:
V(x) = (4/3)π(x+5)(x+5)(x+5)
We can see that the zero is x = -5, and it has a multiplicity of 3, since there are three factors of (x+5) in the polynomial.
This means that the graph of the function will touch the x-axis at x = -5, but not cross it, and the behavior of the graph near x = -5 will be determined by the degree of the zero (which is 3 in this case).
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You are at the beach with your friends. You have brought some supplies to make sand castles. These supplies include a pail that has a base with a circumference of 87 inches, is 12 inches tall, and has an opening on top that is twice the diameter of the base. You also have a plastic pyramid mold that has a square base with an edge that measures 6 inches and is 7 inches tall, and an empty soup can with a diameter of 5. 25 inches and is 6. 5 inches tall
The opening of the pail has a diameter of approximately 55.4 inches (since it's twice the diameter of the base).
Based on the information you provided, it sounds like you have some great supplies for making sand castles at the beach with your friends.
Firstly, let's take a look at the pail. You mentioned that it has a base with a circumference of 87 inches, which means that the diameter of the base is approximately 27.7 inches (since circumference = pi x diameter). The pail is also 12 inches tall and has an opening on top that is twice the diameter of the base. Therefore, the opening has a diameter of approximately 55.4 inches (since it's twice the diameter of the base). With these measurements, you can use the pail to make some pretty big sand castles!
Next, you mentioned a plastic pyramid mold that has a square base with an edge that measures 6 inches and is 7 inches tall. This mold should be perfect for making pyramid-shaped sand castles. Just fill it with sand, pack it down, and carefully remove the mold to reveal your pyramid!
Finally, you mentioned an empty soup can with a diameter of 5.25 inches and is 6.5 inches tall. This can could be used to make cylindrical shapes in your sand castles. Simply pack sand around the can, press down firmly, and carefully remove the can to reveal your cylinder.
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Can someone help me asap? It’s due today
Step-by-step explanation:
the answer will be "15" according to the question.
Find the line of tangency to the circle defined by (x-3)^2 + (y-7)^2 = 169 at the point (15,2).
first off, let's look at the equation of the circle
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{}{h}~~,~~\underset{}{k})}\qquad \stackrel{radius}{\underset{}{r}} \\\\[-0.35em] ~\dotfill\\\\ (x-\stackrel{h}{3})^2+(y-\stackrel{k}{7})=169\implies (x-\stackrel{h}{3})^2+(y-\stackrel{k}{7})=\stackrel{ r }{13^2}[/tex]
so we have a circle centered at (3 , 7) with a radius of 13, Check the picture below.
so the line we want is the line in purple, which is tangential to the circle and therefore perpendicular to the blue line.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the blue line
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{3}}} \implies \cfrac{ -5 }{ 12 } \implies - \cfrac{5 }{ 12 } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-5}{12}} ~\hfill \stackrel{reciprocal}{\cfrac{12}{-5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{12}{-5} \implies \cfrac{12}{ 5 }}}[/tex]
so we're really looking for the equation of a line whose slope is 12/5 and it passes through (15 , 2)
[tex](\stackrel{x_1}{15}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{12}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{12}{5}}(x-\stackrel{x_1}{15}) \\\\\\ y-2=\cfrac{12}{5}x-36\implies {\Large \begin{array}{llll} y=\cfrac{12}{5}x-34 \end{array}}[/tex]
PLS HELP! and actually answer the question please
Step-by-step explanation:
First start with the graph of y = | x|
then shift it RIGHT one unit
| x -1 |
then shift it DOWN one unit
y= |x-1| -1
The Integral ∫55dx/√86x - x^2 can converges to
The integral ∫(5/5)dx/√[86(x^2 - x^2)] converges to 5 since the denominator becomes 0 at x=0, which is not in the interval of integration [5,5].
We can start by simplifying the integrand
∫(5/5)dx/√[86(x^2 - x^2)]
Using the identity a^2 - b^2 = (a + b)(a - b), we can rewrite the denominator as
√[86(x^2 - x^2)] = √[86(x + x)(x - x)] = √[86] * √[x + x] * √[x - x] = √[86] * √[2x] * √[0] = 0
Therefore, the integrand is undefined when x = 0. Since the interval of integration is [5,5], which does not include 0, the integral is well-defined and converges to 5.
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If a person drives his car at the speed of 50 miles per hour, how far can he cover in 2.5 hours?
6 Evaluate without using calculators. -4(-2)+(-12)÷(+3)+-20+(+4)+(-6
Answer:
Its 12
Step-by-step explanation:
1. Following PEMDAS, we first solve the equation inside the parentheses.
-4(-2) = 8
-12 ÷ 3 = -4
-20 + 4 = -16
2. Now, we have the following expression:
8 + (-4) + (-16)
3. Again, following PEMDAS, we solve the equation inside the parentheses first.
8 + (-4) + (-16) = 8 - 4 - 16
4. Finally, we solve the equation from left to right.
8 - 4 - 16 = 8 - (4 + 16)
8 - (20) = -12
Therefore, the value of the expression is -12.
Create a table of values for the function y=x² - 4x + 12 for the domain {-2,-1,0,1}. What is the value of f¹(12)?
Answer:
f¹(12) = 20
Step-by-step explanation:
f(-2) = 24
f(-1) = 17
f(0) = 12
f(1) = 9
f¹(x) = 2x - 4
f¹(12) = 20
HELPPPPP FAST PLEASEEEE
Answer:
AEC is similar to BDC in terms of the type of triangle
That's all I can really say
I hope this helps :)
determine the ordered pairs of....
[tex]6x - y > - 3[/tex]
and
[tex]4x + 3y < 4[/tex]
The ordered pairs of the system of inequalities are (1, 0) and (0, -5)
Determining the ordered pairs of the system of inequalitiesFrom the question, we have the following parameters that can be used in our computation:
6x - y > -3
4x + 3y < 4
The above expression is a system of linear inequality
That implies that we graph the inequalites in the system on the same plane and write out ordered pairs from the region that represent the solution of the system
Next, we plot the graph
See attachment for the graph of the inequality
The ordered pairs are (1, 0), (0, -5) and other pairs
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Pls help me it’s due tmrw
Answer:
Problem 8:
Option C) DE = √21
Problem 9:
Option C) Perimeter = 30 cm
Step-by-step explanation:
1. Problem 8
Draw a line segment connecting the center of the circle, X, to A. This is the radius of the circle
The points ABX form a right triangle with AX as the hypotenuse and AB, BX as the legs of the right triangle
By the Pythagorean theorem
hypotenuse² = sum of the squares of the two legs
Plugging in line segment references
AX² = AB² + BX²
We are given AC = 8, BX = 3
Since the segment BX intersects AC at right angles, AB = BC = AC/2
So AB = 8/2= 4
Plugging these values into the Pythagorean formula
AX² = AB² + BX²
AX² = 4² +3²
AX² = 16 + 9
AX² = 25
Draw a line connecting X and D
The points DEX form a right triangle with DX as the hypotenuse and EX and DE as the legs
Again, by the Pythagorean theorem
DX² = DE² + EX²
But DX is the radius of the circle so it must be the same as AX
Substitute for DX in terms of AX
DX² = DE² + EX²
=> AX² = DE² + EX²
But AX² = 25 and EX = 2 giving EX² = 4
Therefore
AX² = DE² + EX² becomes
25 = DE² + 4
DE² = 25 - 4
DE² = 21
DE = √21
This is choice C
Problem 9
To find the perimeter, just add up the individual side lengths:
Perimeter = 10 + 8 + 7 + 5 = 30 cm
Option C
Aiden gave each member of his family a playlist of random songs to listen to and asked them to rate each song between 0 and 10. He compared his family’s ratings with the release year of each song and created the following scatterplot:
What would the linear equation be?
The linear equation from the given scatterplot will be y = -0.1x + 9.
On the given scatterplot we have the song released details on the x-axis and the average rating of the songs by the family members on the y-axis.
To get the linear equation from the given scatterplot we have to find the y-intercept of the equation.
The general form of the equation is y = mx + c
here, m is the slope and c is the y-intercept.
By, the given graph we can say that y is intercepting at the value '9'. So, the y-intercept is 9.
To find the slope we have to take two points,
Let's take two points as (1970, 7) and (1990, 5).
From the points slope = (5-7)/(1990-1970)
= -2/20 = -1/10 = -0.1
So, the equation from the given scatterplot is y = mx+c
So, y = -0.1x + 9.
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Rote tells the little monsters to do an overhead press every $12$ seconds and a squat every $30$ seconds. (For example, they should do their first squat $30$ seconds into the drill.)
How many times during the $200$ second drill should the little monsters do an overhead press and a squat at the same instant?
The number of times that the little monsters will do an overhead press and a squat at the same instant during the drill is: 3 times
How to solve Prime Factorization Problems?We are told that, Rote tells the little monsters to carry out an overhead press every 12 seconds and then also a squat every 30 seconds.
Thus, prime factorization of 12: 2² x 3.
Thus, prime factorization of 30: 2 x 3 x 5.
For us to get the least common multiple, we will have to find the highest power of each of the prime factors that show up in either factorization. Therefore, we can say that the smallest common multiple of 12 and 30 are: 2² x 3 x 5 = 60
This tells us that the little monsters will carry out an overhead press and then a squat at the same instant for every 60 seconds.
For us to find how many times this will occur during the 200-second drill, we will then divide 200 by 60:
200 ÷ 60 = 3 remainder 20
This tells us that there will exist 3 complete cycles of both of the exercises during the 200-second drill, with an additional 20 seconds left over.
Therefore, we can say that the little monsters will do an overhead press and a squat at the same instant 3 times during the drill.
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can someone please help will give brain
Answer:
y = 9
Step-by-step explanation:
• Parallel lines have equal slopes
calculate the slope m of TU using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = T(- 7, 4 ) and (x₂, y₂ ) = U(- 2, - 6 )
[tex]m_{TU}[/tex] = [tex]\frac{-6-4}{-2-(-7)}[/tex] = [tex]\frac{-10}{-2+7}[/tex] = [tex]\frac{-10}{5}[/tex] = - 2
now calculate the slope of VW and equate to - 2
with (x₁, y₁ ) = V(8, 7 ) and (x₂, y₂ ) = W(7, y )
[tex]m_{VW}[/tex] = [tex]\frac{y-7}{7-8}[/tex] = [tex]\frac{y-7}{-1}[/tex]
now equating gives
[tex]\frac{y-7}{-1}[/tex] = - 2 ( multiply both sides by - 1 to clear the fraction )
y - 7 = 2 ( add 7 to both sides )
y = 9