5
A line passes through the point (-4, -7) and has a slope of.
4
Write an equation in slope-intercept form for this line.
ロ=ロ
X
8
5

Answer:

(C) {-3, 2} is the correct answer.

The volume of the block of wood is 104.7634 cm³ and the total surface area is 186.4502 cm².

Volume is the measure of the amount of space occupied by a three-dimensional object. It is typically measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³).

The volume of the block of wood will be;

V = l x w x h = 4.55 cm x 9.1 cm x 2.54 cm

= 104.7634 cm³

Therefore, the volume of the block of wood is 104.7634 cm³.

The total surface area of the block of wood will be;

SA = 2lh + 2wh + 2lw

= 2(4.55 cm x 2.54 cm) + 2(9.1 cm x 2.54 cm) + 2(4.55 cm x 9.1 cm)

= 58.0094 cm² + 46.4314 cm² + 82.0094 cm²

= 186.4502 cm²

Therefore, the total surface area is 186.4502 cm².

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The ratio of the width to the length of the cell phone is 23/65.

Ratio is the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

To find the ratio of the width to the length of the cell phone, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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The figure that represent the triangle described in the question is option (C).

Triangle is a basic geometric shape that consists of three straight sides and three angles.

We can say triangle is a polygon with three sides and three vertices, and is one of the simplest and most fundamental shapes in geometry.

Class of Triangle based on sides

Class of Triangle based on their angles

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The shape resulting from a horizontal cross section, a vertical cross section, and an angled cross section of the cube are:

horizontal cross section: square.

vertical cross section: square.

angled cross section: rectangle.

In this exercise, you are required to use a graphing tool to investigate and determine the cross-sections of the given three-dimensional geometric object (cube), by passing different planes through them.

By critically observing the cross-sections of the three-dimensional geometric object (cube) I used, we can reasonably infer and logically deduce the following types of quadrilateral based on the cross-sections;

A horizontal cross section would produce a square.

A vertical cross section would produce a square.

An angled cross section would produce a rectangle.

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Answer:3/10

Step-by-step explanation:

Answer: The rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.

Step-by-step explanation:

Let's denote the volume of the cube as V and the length of each edge as x. Given that the volume of a cube is V = x^3, we can find the rate at which the length of each edge is changing.

We're given that the rate of change of the volume is dV/dt = 56 in³/sec. We want to find the rate of change of the length of each edge, which is dx/dt, when the length of each edge is 6 inches.

First, we differentiate the volume equation with respect to time t:

V = x^3

dV/dt = d(x^3)/dt

Using the chain rule:

dV/dt = 3x^2 * (dx/dt)

Now, we know that dV/dt = 56 in³/sec and x = 6 in. Plugging these values into the equation, we get:

56 = 3 * (6)^2 * (dx/dt)

Solving for dx/dt:

56 = 108 * (dx/dt)

dx/dt = 56 / 108

dx/dt ≈ 0.5185 in/sec (rounded to four decimal places)

So, the rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.

The slope of the line of best fit provides valuable information about the relationship between the two variables being plotted and can be used to make predictions about future data points or to identify patterns and trends in the data.

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

The slope of the line of best fit on a scatter plot represents the rate of change between the two variables being plotted.

In the case of Keilantra's math teacher, the slope of the line of best fit between student grades on weekly quizzes and the number of hours they say they study represents the change in grades for every additional hour of studying.

For example, if the slope is positive (i.e., the line slopes upward from left to right), it indicates that as the number of hours studied increases, the average grade on the quiz tends to increase as well.

On the other hand, if the slope is negative (i.e., the line slopes downward from left to right), it indicates that as the number of hours studied increases, the average grade on the quiz tends to decrease.

Therefore, the slope of the line of best fit provides valuable information about the relationship between the two variables being plotted and can be used to make predictions about future data points or to identify patterns and trends in the data.

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Karla will have approximately $11,149 in the account after 5 years, rounded to the nearest dollar.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that:

First, convert R as a percent to r as a decimal

r = R/100

r = 2.2/100

r = 0.022

Plug the given values into the above formula and solve for A.

A = P( 1 + r/n )^( n × t )

A = 10,000( 1 + 0.022/1 )^( 1 × 5 )

A = 10,000( 1 + 0.022 )^( 5 )

A = 10,000( 1.022 )^( 5 )

A = $11,149

Therefore, the accrued amount after 5 years is $11,149.

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The function that has a range of all real numbers is given as follows:

f(x) = -x + 2.

Hence the range for each function in the context of this problem is given as follows:

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The true statements include

Rigid transformation is a type of geometric transformation in which the size and shape of an object remain unchanged. Rigid transformations include

In a rigid transformation, the position of the object in space may change, but its size, shape, and orientation remain the same.

In the object in the graph the length of the segments remain same and since the translation affects only y direction the x-coordinate will be unchanged.

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If the loan is a total of $8,465 at 5.9% compounded monthly. at the end of the 12-month repayment period, the student will owe a total of $9246.35 on the loan.

   First, calculate the monthly interest rate by dividing the annual interest rate by 12:

Monthly interest rate = 5.9% / 12 = 0.004917

   Next, calculate the number of months in the repayment period, including the grace period:

Total repayment period = 12 + 6 = 18 months

   Use the formula for calculating the future value of a loan to find the total amount owed at the end of the repayment period:

   FV = PV x (1 + r)^n

   where:

   PV = the present value of the loan (i.e. the amount borrowed)

   r = the monthly interest rate

   n = the number of months in the repayment period

   Plugging in the numbers, we get:

FV = $8,465 x (1 + 0.004917)^18

FV = $9246.35

Therefore, the student will owe a total of $9246.35 on the loan.

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Felix has spent a total time of 11.4 hours (or 684 minutes) running this month.

we can calculate the total time Felix has spent running this month.

Given:

Warm-up time: 12 minutes

Running time: 20 minutes

Total exercise time in a month: 240 minutes

Step 1: Calculate the total time spent running

Let x be the total time spent running in minutes.

According to the given information, Felix spends 12 minutes on warm-up and 20 minutes on running.

So, the equation would be:

12 + 20x = 240

Step 2: Solve for x

Subtract 12 from both sides of the equation:

20x = 240 - 12

20x = 228

Divide both sides by 20:

x = 228 / 20

x = 11.4

So, Felix has spent a total of 11.4 hours (or 684 minutes) running this month.

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The statements that are always true regarding the diagram are:

m∠1 + m∠5 = 180°

m∠2 + m∠3 = m∠6

m∠3 + m∠4 + m∠5 = 180°

Explain the term diagram

It refers to a value or position that is higher or greater than another value or position. It is often used in comparisons or to describe the relative positions of objects or points on a graph or coordinate plane. The opposite of "above" is "below," which refers to a value or position that is lower or lesser.

According to the given information

We know that the sum of the measures of the three interior angles of a triangle is always 180°. Therefore, we have:

m∠2 + m∠3 + m∠5 = 180°

From the given information, we know that:

m∠2 + m∠1 = 180° (linear pair of angles)

m∠3 + m∠4 = 180° (linear pair of angles)

m∠5 + m∠6 = 180° (exterior angle theorem)

Rearranging these equations, we get:

m∠1 = 180° - m∠2

m∠4 = 180° - m∠3

m∠6 = 180° - m∠5

Substituting these expressions into the above equation for the sum of the interior angles, we get:

m∠2 + m∠3 + m∠5 = m∠2 + (180° - m∠1) + m∠5

m∠3 + m∠4 + m∠5 = (180° - m∠3) + m∠4 + m∠5

Simplifying these equations, we get:

m∠1 + m∠5 = 180°

m∠2 + m∠3 = m∠6

Therefore, the statements that are always true regarding the diagram are:

m∠1 + m∠5 = 180°

m∠2 + m∠3 = m∠6

m∠3 + m∠4 + m∠5 = 180° (which is equivalent to option 2)

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Answer: The answer is D

Answer:

-36

Step-by-step explanation:

To solve this problem, we need to integrate f'(x) to find f(x), and then evaluate f(3) and f(-1) to compute the expression f(3) - f(-1).

Integrating f'(x)=-4x - 5 with respect to x, we get:

f(x) = -2x^2 - 5x + C

Where C is the constant of integration.

To find the value of C, we can use the initial condition f(0) = 1. Substituting x = 0 and f(x) = 1 into the equation above, we get:

1 = -2(0)^2 - 5(0) + C

1 = C

So, we have:

f(x) = -2x^2 - 5x + 1

Now, we can evaluate f(3) and f(-1) and compute f(3) - f(-1):

f(3) = -2(3)^2 - 5(3) + 1 = -32

f(-1) = -2(-1)^2 - 5(-1) + 1 = 4

f(3) - f(-1) = (-32) - 4 = -36

Therefore, f(3) - f(-1) = -36.

Answer:

  -36

Step-by-step explanation:

You want F(3) -F(1) given f'(x) = -4x -5.

The desired difference is the definite integral ...

  [tex]\displaystyle \int_{-1}^3{(-4x-5)}\,dx=\left[-2x^2-5x\right]_{-1}^3=-2(9-1)-5(3+1)\\\\=\boxed{-36}[/tex]

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The inequality that would represent the possible values for the number of hours walking dogs is 9d + 8c ≥ 130

Inequalities in mathematics can be described as one that is been used in the expression of the relationship between two values that are not equal

It should be noted thed that Inequality  implies not equal with the symbol (≠)” symbols ≥ < > ≤. From the question , number of hours walking dogs (d) Let number of hours clearing tables  an be represented by( c) Hence the  appropriate inequality is 9d + 8c ≥ 130.

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The values of x, y and z are given as follows:

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The bases for the triangle in this problem are given as follows:

6 and 19.

Hence the segment x is obtained as follows:

x² = 6 x 19

x = sqrt(6 x 19)

x = 10.68.

Applying the Pythagorean Theorem, the value of y is given as follows:

y² = 6² + 10.68²

y = sqrt(6² + 10.68²)

y = 12.25.

The value of z is given as follows:

z² = 10.68² + 19²

z = sqrt(10.68² + 19²)

z = 21.8.

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Answer:

Step-by-step explanation:

We can simplify the given product using the properties of radicals:

√10x² √5x = √(10*5)x^(2+1) = √50x^3

We can further simplify the radical by factoring out the largest perfect square from 50, which is 25:

√50x^3 = √(25*2)x^3 = 5x√2

Therefore, the product √10x² √5x is equivalent to 5x√2, when x≥0.

To simplify the product √10x² √5x, we can combine the square roots and simplify:

√10x² √5x = √(10x² * 5x) = √(50x³) = √(25x² * 2x) = 5x√2x

Therefore, the choice that is equivalent to the original product when x≥0 is A. 5x√2x.

The height of the pole is approximately 10.2 yards tall.

Let's use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse (the longest side).

In this case, the pole is the vertical side of the right triangle, the ground is the horizontal side, and the rope is the hypotenuse. Let's call the height of the pole "h". Then we have:

h² + 11² = 15²

Simplifying:

h² + 121 = 225

Subtracting 121 from both sides:

h² = 104

Taking the square root of both sides:

h = √104

Simplifying:

h ≈ 10.2

Therefore, the pole is approximately 10.2 yards tall.

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Answer: The two numbers are 5 and 12

Step-by-step explanation:

As the least common multiple of two numbers is

60

, the two numbers are factors of

60

.

Factors of

60

are

{

1

,

2

,

3

,

4

,

5

,

6

,

10

,

12

,

15

,

20

,

30

,

60

}

As one of the numbers is

7

less than the other, the difference of two numbers is

7

Among

{

1

,

2

,

3

,

4

,

5

,

6

,

10

,

12

,

15

,

20

,

30

,

60

}

,

3

&

10

and

5

&

12

are the only two pair of numbers whose difference is

7

. But Least common multiple of

3

and

10

is

30

.

Hence, the two numbers are

5

and

12

.

The probability that all 3 children will be born with the disease is approximately 0.195 or 19.5%.

We have,

Assuming that the probability of a child being born with the disease is independent of whether or not their siblings are born with the disease, we can use the multiplication rule of probability:

P(all 3 children have the disease)

= P(first child has the disease) x P(second child has the disease) x P(third child has the disease)

Since each child has a 57% chance of being born with the disease:

P(all 3 children have the disease)

= 0.57 x 0.57 x 0.57

Now,

P(all 3 children have the disease)

= 0.195

Therefore,

The probability that all 3 children will be born with the disease is approximately 0.195 or 19.5%.

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The equations for which 8 is a solution:

are x minus 4 = 4

2 x = 4

StartFraction x Over 8 EndFraction = 1

x + 6 = 2

The equations for which 8 is a solution are:

x - 4 = 4 (if we substitute x=8, we get 8-4=4 which is true)

2x = 4 (if we substitute x=8, we get 2*8=16 which is true)

StartFraction x Over 2 EndFraction = 16 (if we substitute x=8, we get 8/2=4 which is not true)

StartFraction x Over 8 EndFraction = 1 (if we substitute x=8, we get 8/8=1 which is true)

So, the correct answers are:

x minus 4 = 4

2 x = 4

StartFraction x Over 8 EndFraction = 1

x + 6 = 2

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The amount that Marcus will receive when he redeems the CD at the end of the 19 years, which is described as the compounded future value, is $37,255.14.

The future value is the present investment or value compounded at an interest rate.

The future value can be determined using the FV formula or an online finance calculator as follows:

N (# of periods) = 228 months (19 years x 12)

I/Y (Interest per year) = 7.5%

PV (Present Value) = $9,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $37,255.14

Total Interest: $28,255.14

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The probability of selecting an elm or oak tree is 0.38.

The probability of selecting an elm or oak tree is the sum of the probabilities of selecting an elm and selecting an oak:

P(elm or oak) = P(elm) + P(oak)

P(elm) = 0.04

P(Oak) =0.34

Plug in these values

= 0.04 + 0.34

= 0.38

Therefore, the probability of selecting an elm or oak tree is 0.38.

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The missing values of function rule, Y for corresponding value of X= (-4 ) and (-2) will be 9 and 3 respectively.

                                              [tex]X|-4 |- 2|\\ Y|\quad9\; | \quad3\;|[/tex]

Now for the given fucntion ,

By substituting the values of x into the equation [tex]y = -3x - 3[/tex] and solving for y, we can determine the values of y for [tex]x = -4\; and -2[/tex].

[tex]For \;x = -4:\\y = -3(-4) - 3\\y = 12 - 3\\y = 9[/tex]

Hence, for x =(-4), y= 9

[tex]For\; x = -2:\\y = -3(-2) - 3\\y = 6 - 3\\y = 3[/tex]

Hence, for x =( -2), y = 3

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Correct Question:Fill in the table using this function rule. y = - 3x-3

[tex]X|-4 |- 2|\\ Y|\quad?\; | \quad?\;|[/tex]

The rectangle with largest area has length 3 and width 3/2, with an area of 9/2.

What is a rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral. Because the opposing sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

The equation for the area of a rectangle is length * width. For us here, it would be x * y. We can substitute the equation of the line for y and get

A = x * (6-x)/2

A = 3x - x2/2

To find the maximum of this equation, we first need to find a critical point. So we take the derivative and find the zeros:

A' = 3 - x = 0

x = 3

So we have a critical point at 3, which happens to be the maximum of the area equation. We plug this back into the line equation to get y:

y = (6 - 3)/2 = 3/2

So the rectangle with largest area has length 3 and width 3/2, with an area of 9/2.

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Therefore, the value of f(m-2) is 5/(m-2) + 2, and the value of function g(1/2) is 2.

In mathematics, a function is a rule or correspondence between two sets, where each input value from the first set (called the domain) corresponds to exactly one output value in the second set (called the range). A function is often represented by a formula, equation, or graph.

Here,

1. To find f(m-2), we substitute (m-2) for x in the expression for f(x):

f(m-2) = 5/(m-2) + 2

So the value of f(m-2) is 5/(m-2) + 2.

2. To find g(1/2), we substitute 1/2 for x in the expression for g(x):

g(1/2) = -2(1/2) + 3

So the value of g(1/2) is -1 + 3, which simplifies to 2.

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