32. Find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round answer to the nearest whole number.

By observing the graphs, the equation of each line include the following:

a. y = 0.4x - 0.2

b. y = -x + 2

c. y = 4x - 2

d. y = 0.5x

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

Part a.

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 0)/(3 - 0.5)

Slope (m) = 1/2.5

Slope (m) = 0.4

At data point (0.5, 0) and a slope of 0.4, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 0 = 0.4(x - 0.5)  

y = 0.4x - 0.2

Part b.

We would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-2 - 2)/(4 - 0)

Slope (m) = -4/4

Slope (m) = -1

At data point (0, 2) and a slope of -1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = -1(x - 0)  

y = -x + 2

Part c.

We would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-2 - 2)/(0 - 1)

Slope (m) = -4/-1

Slope (m) = 4

At data point (0, -2) and a slope of 4, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 2 = 4(x - 0)  

y = 4x - 2

Part d.

Since the line passes through the origin (0, 0), it represents a proportional relationship;

y = kx

k = y/x

k = 2.5/5

k = 0.5

Therefore, the equation of this line is given by;

y = 0.5x

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Complete Question:

Observe the graphs and write in your notebook the equation of each line.

Let f(x)=-3x+2, g(x)=5 h(x) = -2x+9, and j(x) = 5-x. Find each value or expression.

1. (f +j)(3) = -5

3. (h + g)(-5) = 10

5. (f + g)(2) = 1

7. (g f)(-5) = 22

9. f((5)) = -11

1. (f + j)(3) = f(3) + j(3) = (-3(3)+2) + (5-3) = -7 + 2 = -5

3. To find the value of (h + g)(-5), we need to first add the functions h(x) and g(x), then evaluate the result at x = -5.

h(x) = -2x + 9

g(x) = 5

h(x) + g(x) = -2x + 9 + 5 = -2x + 14

So, (h + g)(-5) = -2(-5) + 14 = 10.

The answer is 10.

5. To find the value of (f + g)(2), we need to first add the functions f(x) and g(x), then evaluate the result at x = 2.

f(x) = -3x + 2

g(x) = 5

f(x) + g(x) = -3x + 2 + 5 = -3x + 7

So, (f + g)(2) = -3(2) + 7 = 1.

The answer is 1

7. (To find the value of (g + f)(-5), we need to first add the functions g(x) and f(x), then evaluate the result at x = -5.

f(x) = -3x + 2

g(x) = 5

f(x) + g(x) = -3x + 2 + 5 = -3x + 7

So, (g + f)(-5) = -3(-5) + 7 = 22.

The answer is 22

9. f(5) = -3(5) + 2 = -13 + 2 = -11

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Answer:

y=28/5

Step-by-step explanation:

Okay so for this we can use cross- multiplication. Basically, the product of the numerator of the first number and the denominator of the second is equal to the product of the denominator of the first and the numerator of the second.

What I mean is: 4*7=5*y

so,

28=5y

y=28/5

An equation to represent this situation is y = 60x

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, we can logically deduce that the cheetah was clocked running 60 miles per hour over a 50-yard distance. This ultimately implies that, an equation that models this situation is given by:

y = 60x

Where:

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Answer:

15 square units.

Step-by-step explanation:

To find the area, we must find the width and length of the rectangle. To find the width and length, we need to find the length of AB and the length of BC. We use the distance formula.

AB: A(-8, 3); B(-3, 3).

\(\sqrt{(-8-(-3))^2+(3-3)^2}\)

= \(\sqrt{(-8+3)^2+0^2}\)

= \(\sqrt{(-5)^2+0}\)

= \(\sqrt{25 }\)

= 5

BC: B(-3, 3); C(-3, 6).

\(\sqrt{(-3-(-3))^2+(3-6)^2}\)

= \(\sqrt{(-3 + 3)^2+(-3)^2}\)

= \(\sqrt{(0)^2+9}\)

= \(\sqrt{0+9}\)

= \(\sqrt{9}\)

= 3

Now that we have both the width and the length, we can solve for the area using A = lw, where A is the area, l is the length, and w is the width. In this case, l = 5 and w = 3.

A = lw

A = 5 * 3

A = 15

So, the area of the rectangle is 15 square units.

Hope this helps!

Answer:

ya the equation divides y as a function of x

The probability of observing 35 or fewer heads from 100 coin tosses assuming the coin is fair is approximately 0.13%. Assuming the coin is fair, the probability of observing a head on a single coin toss is 0.5, and the probability of observing a tail is also 0.5.

We can use the normal approximation to the binomial distribution to find the probability of observing 35 or fewer heads from 100 coin tosses. The mean of the binomial distribution is np = 100 x 0.5 = 50, and the standard deviation is the square root of np(1-p) = sqrt(100 x 0.5 x 0.5) = 5.

We can standardize the distribution by subtracting the mean and dividing by the standard deviation:

z = (35 - 50) / 5 = -3

Using a standard normal distribution table or calculator, the probability of observing a z-score of -3 or less is approximately 0.0013.

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The probability that the company will have to refund money to a customer is approximately 0.5276

A subfield of statistics known as probability studies random events and their likelihood of happening. It is used to anticipate the future and calculate the likelihood of events by dividing the number of positive outcomes by the total number of possible outcomes.

The probability that the dishwasher will last at least 6 years is the probability that it will not fail in the first 6 years, which can be calculated as:

\(P(X \geq 6) = e^{(-\frac{6}{8} )}\) = 0.4724

Therefore, the probability that the company will have to refund money to a customer is the complement of this probability, which can be calculated as:

P(refund) = 1 - P(X ≥ 6) = (1 - 0.4724) = 0.5276

So, the probability that the company will have to refund money to a customer is approximately 0.5276, assuming that the expected lifetime of the dishwasher is 8 years and the probability of failure in any given year is constant and independent of other years.

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The probability that the company will have to refund money to a customer, you would need information about the failure rate of the dishwasher over a six-year period.

If that information is available, you can calculate the probability. If it's not provided, then it's impossible to determine the probability accurately.

Without more information about the reliability of the dishwasher and the likelihood of it breaking down within the warranty period, it is difficult to determine the exact probability of the company having to refund money to a customer. However, assuming the company has reliable and durable products, the probability of them having to refund money may be low.

It is important to note that warranties typically have terms and conditions that must be met in order to qualify for a refund, so it is always best to read and understand the warranty before making a purchase.

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Answer:

x ≈ 12.5 units

Step-by-step explanation:

\(\frac{11}{x}\) = cos 28° ⇒ x = \(\frac{11}{cos 28^{0} }\)

cos 28° ≈ 0.883

x ≈ 12.5 units

Answer:

Mercury, Venus, Earth, Mars, and Uranus

Step-by-step explanation:

Calculate the escape velocity for each planet, using the equation v = √(2gR).

\(\left[\begin{array}{cccc}Planet&R(m)&g(m/s^{2})&v(m/s)\\Mercury&2.43\times10^{6}&3.61&4190\\Venus&6.07\times10^{6}&8.83&10400\\Earth&6.37\times10^{6}&9.80&11200\\Mars&3.38\times10^{6}&3.75&5030\\Jupiter&6.98\times10^{7}&26.0&60200\\Saturn&5.82\times10^{7}&11.2&36100\\Uranus&2.35\times10^{7}&10.5&22200\\Neptune&2.27\times10^{7}&13.3&24600\end{array}\right]\)

The rocket's maximum velocity is double the Earth's escape velocity, or 22,400 m/s.  So the planets the rocket can escape from are Mercury, Venus, Earth, Mars, and Uranus.

Answer:

1/6

Step-by-step explanation:

There is only one side of the die with a number 4, and 6 possible outcomes. Therefore the answer is 1/6

Answer:

3

Step-by-step explanation:

Numbers between 21 and 30 divisible by 3 are 24 and 27. so you get the HCF of the two.

\(\frac{2}{7}= \frac{3.5}{x} => 2x=3.5(7)= 24.5 => x=\frac{24.5}{2} = 12.25\)

ok done. Thank to me :>

Apply Thales theorem

Answer:

D

Step-by-step explanation:

Khan Academy

Answer: the awnser is B

Answer:

continuous

rain does not fall in specific units like 1 inch , 2 inches etc... but 1.23456 etc..

Step-by-step explanation:

Answer: 20/12

Step-by-step explanation: In order to get a 12 in the denominator

of 5/3, we multiply top and bottom of 5/3 by 4 to get 20/12.

So 20/12 is an equivalent fraction.

Answer:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

Step-by-step explanation:

To solve this problem, we'll consider the velocities of the cruise ship and the Gulf Stream as vectors and calculate their components and resultant vector. Then we'll find the magnitude (resultant velocity) and direction (resultant direction) of the resultant vector.

Given:

Cruise ship velocity (south): 22 mph

Gulf Stream velocity (east): 4 mph

A) Vector component for the cruise ship:

The cruise ship is traveling south, so its velocity vector is (0, -22).

B) Vector component for the Gulf Stream:

The Gulf Stream is flowing east, so its velocity vector is (4, 0).

C) Resultant vector:

To find the resultant vector, we'll add the two velocity vectors together:

Resultant vector = Cruise ship velocity + Gulf Stream velocity

Resultant vector = (0, -22) + (4, 0)

Resultant vector = (0 + 4, -22 + 0)

Resultant vector = (4, -22)

D) Resultant velocity:

The magnitude of the resultant vector gives us the resultant velocity. We can use the Pythagorean theorem to calculate it:

Resultant velocity = sqrt((x-component)^2 + (y-component)^2)

Resultant velocity = sqrt((4)^2 + (-22)^2)

Resultant velocity = sqrt(16 + 484)

Resultant velocity = sqrt(500)

Resultant velocity ≈ 22.4 mph (rounded to the nearest tenth)

E) Resultant direction:

The direction of the resultant vector can be found using trigonometry. We'll use the inverse tangent function (arctan) to find the angle between the resultant vector and the positive x-axis.

Resultant direction = arctan(y-component / x-component)

Resultant direction = arctan(-22 / 4)

Resultant direction ≈ -1.405 radians or -80.5 degrees (rounded to the nearest tenth)

Therefore, the answers are:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

These two equations form a system that can be solved to find the values of x and y, representing the number of children and adults, respectively, who played on that day.

The correct system of equations to model this scenario is:

x + y = 414 (Equation 1)

9x + 12y = 3780 (Equation 2)

In this system, x represents the number of children and y represents the number of adults who played that day.

Equation 1 represents the total number of customers, which is 414. It states that the sum of the number of children (x) and the number of adults (y) is equal to 414.

Equation 2 represents the total cost of the games played. Since the cost for a child's game is $9 and the cost for an adult's game is $12, we multiply the number of children (x) by $9 and the number of adults (y) by $12. The equation states that the total cost, which is $3780, is equal to the sum of these individual costs.

Together, these two equations form a system that can be solved to find the values of x and y, representing the number of children and adults, respectively, who played on that day.

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Answer:

1 and 7

Step-by-step explanation:

supplementary means that they add up to 180º

1,3                    5,6              1,7          

2,4                   7,8              2,8

1,2                    5,7              3,5

3,4                   6,8              4,6

There are still some more but my hands are tired of typing.

Answer:

A: 1 and 7

Step-by-step explanation:

when 2 angles are put next to each other on a straight line with a line going through the middle those two angles always add to 180 since 180 is equal to a straight line.

supplementary angles are 2 angles that together make 180.

out of the options given, all of them except 1 and 7 are equal angles and as a result would not add to 180. if you put angles 1 and 7 on a straight line together, they do, thus the answer is A, aka 1 and 7.

Answer: 53

Step-by-step explanation:

rate * time = distance, or rt=d given, t=10 hours and d= 530 miles, r (10) = 530, or r= 530/10 = 53 miles/hour

Hope this helps ^^

sum is the answer to addition problem.

less than is subtraction and "times" is multiplication.

So we have

3x+2=5x-4

So the answer is C.

Also, i'm bored so imma solve it.

3x+2=5x-4

    -2      -2

3x=5x-6

-5x -5x

-2x=-6

/-2   /-2

x=3

---

hope it helps

Answer:

25 $ in 1 hour

Step-by-step explanation:

Answer:23.18

Step-by-step explanation:divide 510 by 22

The probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 8/25 or 0.32 (rounded to the nearest millionth).

1. Calculate the total number of students on the Student Government Board by summing up the numbers in the table:

  Total Students = 2 + 2 + 2 + 4 + 0 + 3 + 4 + 2 = 19

2. Calculate the total number of graduate students on the Student Government Board:

  Total Graduate Students = 2 + 0 = 2

3. Calculate the total number of students living in on-campus housing:

  Total On-Campus Housing = 2 + 2 + 0 + 4 + 2 = 10

4. Calculate the probability of selecting a graduate student from the Student Government Board by dividing the total number of graduate students by the total number of students:

  Probability of Graduate Student = Total Graduate Students / Total Students = 2 / 19

5. Calculate the probability of selecting a student living in on-campus housing by dividing the total number of students in on-campus housing by the total number of students:

  Probability of On-Campus Housing = Total On-Campus Housing / Total Students = 10 / 19

6. Calculate the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing by summing up the probabilities from steps 4 and 5:

  Probability = Probability of Graduate Student + Probability of On-Campus Housing = 2 / 19 + 10 / 19

7. Simplify the fraction if necessary. In this case, the fraction cannot be simplified further, so the final probability is 2 / 19 + 10 / 19 = 12 / 19.

8. Convert the fraction to a decimal by dividing the numerator by the denominator: 12 / 19 ≈ 0.631578947, which rounds to 0.632 (rounded to the nearest thousandth).

9. Finally, express the probability as a fraction in lowest terms: 12 / 19 is already in lowest terms.

Therefore, the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 12/19 or approximately 0.632 (rounded to the nearest thousandth).

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Answer:

The dinner date

Step-by-step explanation:

Dividing the segments, it is found that:

----------------------------

\(K - J = \frac{1}{n}(J - L)\)

And this is the answer to option b.

----------------------------

Option a:

If \(\mathbf{n = 4}\), it has that:

\(K - J = \frac{1}{4}(J - L)\)

This is applied to find both the x-coordinate and the y-coordinate of K.

----------------------------

Thus:

\(K - J = \frac{1}{4}(J - L)\)

\(x - 4 = \frac{1}{4}(4 - 0)\)

\(x - 4 = 1\)

\(x = 5\)

----------------------------

Thus:

\(K - J = \frac{1}{4}(J - L)\)

\(y - (-5) = \frac{1}{4}(-5 - (-7))\)

\(y + 5 = \frac{2}{4}\)

\(y = \frac{1}{2} - 5\)

\(y = \frac{1}{2} - \frac{10}[2}\)

\(y = -\frac{9}{2}\)

The coordinates of K if n = 4 are \((5,-frac{9}{2})\)

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Answer:

Choose any two numbers from 82 to 99.

Step-by-step explanation:

The square of 9 is 81, since 9 × 9 = 81.

The square of 10 is 100, since 10 × 10 = 100.

Choose any two numbers from 82 to 99; their square roots must, therefore, fall between 9 and 10.

let the number of sweets with Angela be " x "

and , let the number of sweets with Sabrina be " 3x "

Then ,

\(\bold{x + 3x = 60} \\\\\bold{ 4x = 60} \\\\\bold{ x = \cancel \frac{60}{4}} \\ \\\fbox\pink{ x = 15}\)

Hence ,

number of sweets with Angela = 15

number of sweets with Sabrina = 3(15) = 45

hope helpful~

Answer:

To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.

Given:

Length = 36 inches

Width = 24 inches

Height = 18 inches

Converting the dimensions to feet:

Length = 36 inches / 12 inches/foot = 3 feet

Width = 24 inches / 12 inches/foot = 2 feet

Height = 18 inches / 12 inches/foot = 1.5 feet

Now, we can calculate the volume of the box by multiplying the length, width, and height:

Volume = Length * Width * Height

Volume = 3 feet * 2 feet * 1.5 feet

Volume = 9 cubic feet

Therefore, the shipping box can hold 9 cubic feet.

Step-by-step explanation:

First convert the units because it's asking for the cubic feet but they give us the measurements in inches.

To convert inches to feet we divide the number by 12.

36 ÷  12 = 3

24 ÷  12 = 2

18 ÷ 12 = 1.5

Now to find the volume, we multiply it all together.

3 × 2 × 1.5 = 9

It can hold 9 cubic feet.

Hope this helped!