Is this correct?
Or please provide an explanation.

Answer:

(10, -3)

Step-by-step explanation:

[tex]-\frac{7}{2}x+32=\frac{4}{5}x-11 \\ \\ -35x+320=8x-110 \\ \\ -43x=-430 \\ \\ x=10 \\ \\ \therefore y=-\frac{7}{2}(10)+32=-3[/tex]

Answer:

[tex]y-6=-\dfrac{1}{8}(x-10)[/tex]

Step-by-step explanation:

To find the equation of a line that passes through two points, first find its slope by substituting the given points into the slope formula.

Define the points:

Substitute the points into the slope formula:

[tex]\implies m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-6}{2-10}=\dfrac{1}{-8}=-\dfrac{1}{8}[/tex]

Therefore, the slope of the line is -¹/₈.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

To find the equation in point-slope form, simply substitute the found slope and one of the given points into the point-slope formula:

[tex]\implies y-6=-\dfrac{1}{8}(x-10)[/tex]

Part A

The dimensions of the shape shown are given as

length, l = 12 in

breadth (b) = width, w = 4 in

The area of the shape is given as;

Therefore, the area of the shape is 48 square inches.

Part B

The perimeter of a shape is the sum of all the outer sides enclosing the shape

From the above shape, we add all four sides together

Consequently, we can get the perimeter using formula method as well

Therefore, the perimeter of the shape is 32 inches.

Part C

From the dimension given in the question, since the shape has a length and width, and the length and width are not equal, then the shape is a rectangle.

The shape, therefore, is a rectangle.

To determine in how many pices of 2/3ft can a 9ft long ribbon be cut, you have to divide 9 by 2/3:

To divide both fractions, first turn the 9 into a fraction by adding 1 as a denominator

Now you have to invert the fraction that is the denominator of the division

And multiply it by the first fraction

She can divide the ribbon in 13 pieces of 2/3ft each

Given the equation (x + y)³ + 1 , we can assume we have two terms here. These are (x + y)³ and 1. Since both terms are perfect cubes, we can use the sum of cubes formula which is:

where a = (x+y) and b = 1.

Therefore, the factors of (x + y)³ + 1 is:

The factor of (x + y)³ + 1 is (x + y + 1)(x² + 2xy + y² - x - y +1).

Then x=36.

Find the inverse of:

The variable x can take any real value and the function f(x) exists. This means

the domain of f(x) is (-∞, +∞).

Now find the inverse function.

Swapping letters, we get the inverse function:

For each value of x, we get two values of y, thus this is not a function.

The domain of the inverse is restricted to values of x that make the square root exist, thus the domain is x ≥ 0, or [0, +∞)

The range of the inverse is the domain of the original function, that is, (-∞, +∞)

Function: No

Domain: [0, +∞)

Range: (-∞, +∞)

The choice to select is shown below.

To determine the width of the statue:

A local park has a length (L), width (W), and height (H) (all in feet)

Solve equation 1 and 2 simultaneously,

Solve equation 3 & 4 simultaneously, make W the subject of formular

Therefore the value of width of the statue = 12 feet

In general, an inverse variation relation has the form shown below

It is given that x=16, then y=5/4; thus,

Therefore, the equation is y=20/x

2) Set x=4 in the equation above; then

When x=4, y=5.

The volume of the cone is 45.28 cubic inches.

The amount of sand inside the cone is measured by its volume.

Based on the numbers for the radius and height, the cone's volume is 45.28 cubic inches.

The volume of a cone is the measure of how much space a cone takes up. Cone height and base radius both affect how much space the cone takes up.

The volume of the cone is given by V = [tex]\frac{1}{3}\pi r^{2} h[/tex]

The value of the radius is r = [tex]3\frac{1}{23} = \frac{70}{23}[/tex]

The value of Height is h = [tex]3\frac{5}{3} = \frac{14}{3}[/tex]

So, the Volume of the cone =[tex]V =\frac{1}{3}\pi r^{2} h[/tex]

[tex]V =\frac{1}{3}\pi r^{2} h\\\\V = \frac{1}{3}\pi (\frac{70}{23}) ^{2} \frac{14}{3} \\\\V = 45.28[/tex]

The volume of the cone is 45.28 cubic. inches

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18) the best estimate will be 75 square feet (option G)

18) radius = 10ft

let π = 3.14

We are told the deck will have 1/4 the area of a circle. We need to first find the area of a circle.

Area of circle = πr²

Next, we will divide the area by 4:

From the options, the one close to the result we got is 75 square feet

Hence, the best estimate will be 75 square feet (option G)

we have

C -----> total charge

b -----> number of buckets of balls

Remmeber that

the equation of the line in slope intercept form is equal to

y=mx+b

where

m is the slope and b is the initial value or y-intercept

In this problem

m=$1.50 per buckey

b=$5

therefore

y=1.50x+5

or

C=1.50b+5

38

1) Starting from the first equation

3x +6 = 18 Subtract 6 from both sides

3x = 18 -6

3x = 12 Divide both sides by 3

x =4

2) Since x =4, let's plug that into the second expression 10x -2 to find out "what is 10x -2"

10x -2 Replace x, by 4

10(4) -2 Effectuate the multiplication

40 -2

38

Hence, the answer is 38

Aye itz just me, this is the solution:

Initial balance = $ 37.99

Purchase 1 = ($ 26.29)

Purchase 2 = ($ 22.98)

Overdraft fee = ($ 25.00)

Deposit = $ 55.07

______________________

New balance = 37.99 - 26.29 - 22.98 - 25 + 55.07

New balance = $ 18.82

Given:

Each of these halves is to be cut into fourths.

So:.

A pizza is to be cut into halves

since half is represented by 1/2.

So each piece is now

If each of these halves is to be cut into fourths, then the fraction of final pieces is:

Answer:

1/8

Step-by-step explanation:

Fractions

We have 1/2

!/2 is to be cut in 1/4

1/2 * 1/4 = 1/8

The problem is;

-2(x-1) - 2 > 8 - 5x +4+ x

open the parenthesis

-2x + 2 -2 > 8- 5x + 4+ x

collect the like-term

-2x+5x-x > 8+4

2x > 12

divide both-side of the inequality by 2

x>6

The first mistake that was made is adding of the x-variables

It is 2x and not -6x

Answer:

Step-by-step explanation:

Solution:

Given that a value or quantity must not exceed ten, let x represent the value or quantity.

Since it must not exceed 10, this implies that

The second option is the correct answer.

Given:

Using a graphing calculator, we have the graph shown below:

The point of intersection of the equations represents the solution to the system.

Hence, the solution to the system is:

x = 0.216

y = 0.646

According to the given graph, we have the following:

1) The graph represents a plane descending.

2) The line is slanting downwards and therefore has a negative slope.

3) It takes the plane 15 seconds to touch the ground.

4) The plane starts at 3 kilometers in the sky.

5) Graph does not touch the origin (0,0).

The given graph shows a decreasing line, starting at y = 3, and reaching y = 0 when x = 15.

The answer of the given inequality is x < 16

Difference between equality and inequality equations

Both mathematical phrases, equations and inequalities, are created by connecting two expressions.The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols show that the two expressions in an inequality are not always equal: >, <, ≤ or ≥. Or in simple words the equation which has '=' sign is an equality equation while the inequality equation has the signs are >, <, ≤ or ≥.

The inequality expression is ,

(1 * x) /4  < 4  or x/4 < 4

=> x < 4 * 4

=> x < 16

Therefore, the answer is x < 16.

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Let's begin by listing out the given information:

A fair dice has 6 sides

The dice has its sides numbered from 1-6

The number of sides with even numbers (2, 4 & 6) equals 3

The number of sides with odd numbers (1, 3 & 5) equals 3

The probability of rolling an even number is given as shown below:

The probability of rolling an odd number is given as shown below:

The probability of rolling an even number followed by an odd number is obtained by the product of the probabilities above. We have:

Therefore, the probability of rolling an even number and then an odd number is 1/4

The derivative of the function y = -1/x-2 is 1/(x-2)².

Given, the function is y = -1/x-2

Differentiate the function with respect to x.

dy/dx = d/dx (-1/x-2)

the function is in the form of :

d/dx [f(x)g(x)] = f(x)d/dx((x)) + g(x)d/dx(f(x))

here d/dx [f(x)g(x)]  = d/dx [(-1)(1/x-2)]

therefore, d/dx [(-1)(1/x-2)] = (-1)d/dx(1/x-2) +(1/x-2)d/dx(-1)

⇒ d/dx [(-1)(1/x-2)] = (-1)(-1)(x-2)⁻¹⁻¹ + (1/x-2)d/dx(0)

⇒ d/dx [(-1)(1/x-2)] = 1(x-2)⁻² + 0

⇒  d/dx [(-1)(1/x-2)] = 1/(x-2)²

Hence the derivative of the function is 1/(x-2)²

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x > -8

Let the number be represented by x:

Three times the number = 3x

Six minus three times the number = 6 - 3x

Six minus three times the number is less than 30:

That can be interpreted mathematically as:

6 - 3x < 30

To find the value of x:

Step 1: Collect like terms

- 3x < 30 - 6

-3x < 24

Step 2: Divide both sides by 3:

-x < 8

Multiply both sides by (-1) and change the < sign to >

(-1) (-x) > 8 x(-1)

x > -8

Answer:

6/7

Step-by-step explanation:

24/28 they both are commonly divisible by 4,

making them 6/7

If we have:

To solve for l we can start by inverting the sides and substracting 2w from both sides so that the term with l becomes alone in the left side:

Now, we can divide both sides by 2 so thay the 2 in 2l gets canceled:

So, the answer we would get is

The line segment BD has a length of 18 units

The possible figure is added as an attachment

From the question, we have the following parameters:

The lengths BE and ED implies that the point E is between the endpoints B and D

Since the shape is a parallelogram, then the point E is halfway between the endpoints B and D

So, we have

BE = ED

Substitute the known values in the above equation

6x + 44 = -6x - 16

Evaluate the like terms

So, we have

12x = -60

Divide both sides by 12

x = -5

Substitute x = -5 in BE = 6x + 44

So, we have

BE = 6 x -5  + 44

Evaluate

BE = 14

The length is then calculated as

BD = 2 x BE

So, we have

BD = 2 x 14

Evaluate

BD = 18 units

Hence, the length of BD is 18 units

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Considering the given table, it is found that:

a. The exponential regression equation is: P(t) = 2408.80(1.059)^t.

b. The yearly percent increase is of 5.9%.

c. P(13) = 5075.

d. The population of the town after 13 years is of 5075.

The exponential regression equation is found inserting the points into a calculator.

The points are given as follows:

(0, 2400), (3, 2801.27), (7, 3608.71), (12, 4974.15), (14, 5426.17), (19, 6898.37).

Using a calculator, the function is:

2408.80(1.059)^t.

The yearly percent increase rate is calculated as follows:

1 + r = 1.059

r = 1.059 - 1

r = 0.059

r = 5.9%.

Then in 13 years, the population will be given as follows:

P(13) = 2408.80(1.059)^13 = 5075.

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$75 -----> 100%

x ---------> 20%

asnwer 1: they leave her $ 15

answer 2: the total cost of the meal is

$ 90