1. Graph the system of equations.2. What are all the values for x for which f(x)=g(x)?

Whole numbers are the numbers 0, 1, 2, 3, 4, etc. (the natural numbers and zero). Negative numbers are not considered whole numbers. All natural numbers are whole numbers, but not all whole numbers are natural numbers since zero is a whole number but not a natural number.

For example.

- 2, - 10

The Growth rate is 3/4 ft/year

What is Growth rate ?

Growth rates are computed by dividing the difference between the ending and starting values for the period being analyzed and dividing that by the starting value. Formula is,  Growth rate = Absolute change / Previous value.

growth rate = (12-9)/(8-4)

                    = 3/4 ft/year

Therefore, The Growth rate is 3/4 ft/year

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We have the following:

Answer: 2(3x^2-5x-1) or 6x^2-10x-2

Step-by-step explanation: combine like terms, and then factor by grouping :)

Answer:

Explanation:

Given the below equation;

To solve for x, the 1st step is to subtract 2x from both sides of the equation;

The 2nd step is to add 7 to both sides of the equation;

The final step is to divide both sides of the equation by 3;

Answer:

see my photo bro. hope it can help.

Answer:

[tex]\textsf{(a)} \quad \overline{v}=-8t-4h-2[/tex]

[tex]\textsf{(b)} \quad v(t)=-8t-2[/tex]

[tex]\textsf{(c)} \quad L(t)=-26t+41[/tex]  

(d)  See attachment.

Step-by-step explanation:

Given equation for displacement:

[tex]s(t)=-4t^2-2t+5[/tex]

Average velocity formula:

[tex]\boxed{\overline{v}=\dfrac{s(t_2)-s(t_1)}{t_2-t_1}}[/tex]

where:

To find the average velocity of s(t) between the inputs t and t+h:

Find expressions for s(t) at t₁ and t₂:

[tex]\implies s(t_1)=s(t)=-4t^2-2t+5[/tex]

[tex]\begin{aligned}\implies s(t_2)=s(t+h)&=-4(t+h)^2-2(t+h)+5\\&=-4(t^2+2th+h^2)-2t-2h+5\\&=-4t^2-8th-4h^2-2t-2h+5\end{aligned}[/tex]

Substitute the found values into the average velocity formula:

[tex]\begin{aligned}\implies \overline{v} =\dfrac{s(t_2)-s(t_1)}{t_2-t_1}}&=\dfrac{(-4t^2-8th-4h^2-2t-2h+5)-(-4t^2-2t+5)}{(t+h)-t}}\\\\&=\dfrac{-4t^2-8th-4h^2-2t-2h+5+4t^2+2t-5}{t+h-t}\\\\&=\dfrac{-8th-4h^2-2h}{h}\\\\ &=-8t-4h-2\\\\ \end{aligned}[/tex]

Therefore, the average velocity between the inputs t and t+h is:

[tex]\boxed{\overline{v}=-8t-4h-2}[/tex]

To find the equation for instantaneous velocity v(t), differentiate the equation for displacement:

[tex]\begin{aligned}\implies v(t)&=s'(t)\\&=2 \cdot -4t^{(2-1)}-1 \cdot 2t^{(1-1)}+0\\&=-8t-2\end{aligned}[/tex]

Find the value of s when t = 3:

[tex]\begin{aligned}\implies s(3)&=-4(3)^2-2(3)+5\\&=-4(9)-6+5\\&=-36-6+5\\&=-42+5\\&=-37\end{aligned}[/tex]

To find the gradient of s(t) at t = 3, substitute t = 3 into the differentiated function:

[tex]\begin{aligned}\implies s'(3)=v(3)&=-8(3)-2\\&=-24-2\\&=-26\end{aligned}[/tex]

Substitute the found gradient and found point (3, -37) into the point-slope form of a linear equation to find the equation of the tangent line L(t):

[tex]\begin{aligned}\implies s-s_1&=m(t-t_1)\\s-(-37)&=-26(t-3)\\s+37&=-26t+78\\s&=-26t+41\\\implies L(t)&=-26t+41\end{aligned}[/tex]

See attachment.

distribute the parentheses

substract 32.8 on both sides

The simple interest formula is:

where P is the principal, r is the interest rate and t is the time.

In this case the principal is $1800, the interest rate is 0.035 (in decimal form) and t is 2. then the interest he pays is:

Therefore in total he will pay $1926

We have here two sets of numbers, and we have to find the value for one of the operations of sets, that is, the intersection operation.

The result of this operation is the values that are common to both sets.

If we saw set A and set B, we will have:

Both sets have five elements. However, they have no common elements (or nothing in common). Therefore, the result will be the empty set:

That means both sets have no common elements ---> empty set.

In summary, we have that:

The area of triangle DEF = 4 ( area of triangle QRP) which is determined that by comparing the expression for the lengths of PR and QR.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

According to the data provided,

Triangle ΔDEF is an isosceles triangle having DE, EF, and FD sides.

Since DE = EF and P,R, and Q are the midpoints of the sides DF, EF, and DE,

We know from isosceles triangle theorems that the area of a triangle formed by uniting the midpoints of two isosceles triangles is one-fourth the area of the isosceles triangle.

As evidence, consider the following:

Because point Q is the halfway of DE, its coordinates are (a, b). (Because the midpoint of a line segment always has coordinates that are half the total of the coordinates of the end points.)

Because point R is the midpoint of FE, its coordinates are (3a,b).

The length of the base, DF, in triangle DEF is 4a and the height is 2b. As a result, its area is 4ab. (Because the area of a triangle equals 1/2 its base × height.)

The length of the base, QR, of the triangle QRP is 2a, while the height is b.

As a result, its area is ab.

Therefore, the area of triangle DEF is four times that of triangle QRP.

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Combining the three different transformations—rotations, reflections, and translations—will result in congruent shapes. Actually, any pair of congruent shapes can be matched to one another using a combination of one or more of these three transformations.

There are four possible transformations of a point, line, or geometric figure, each of which changes the object's shape and/or location. Pre-Image denotes the shape of the object before transformation, while Image denotes the final position and shape of the object.

Given Data

We now know that during rigid transformations, the size and shape of the figures are maintained (reflections, translations, and rotations). The pre-image and the image are always in agreement.

Matt has the following transformational abilities:

Reflection (Flip)

A reflection keeps its original shape because the comparable points from the pre-image to the image stay at the same distance from the line of reflection.

Rotations as a Congruence Transformation

A figure twists when it rotates. The figurine looks to have fallen over, although being the same size and shape. A great illustration of a rotation in the actual world is a clock. The connecting arms of a clock rotate around its axis every hour or every day. A rotation is defined by its degree; common rotations include 90 degrees, 180 degrees, and 270 degrees. The figure completes a full 360-degree rotation before returning to its starting point. The direction of a rotation, whether it be in a clockwise or counterclockwise counterclockwise. This information can be used to calculate the degree, quantity, and direction of a revolution.

Translational congruence transformation

We refer to a movement as a translation when an object or shape is moved from one place to another without changing its size, shape, or orientation. Every point on an item or shape is moved by the same amount and in the same direction during a translation, sometimes referred to as a slide.

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BISECTRIZ: Divide the interior or exterior angle of each vertex into two congruent angles. Then we have that the angle that ES starts and that shares the 2 right triangles is the same:

As we can see, both triangles share the angle and the hypotenuse, that is, their height is also the same, so the height of PC is equal to 8

First write the equation in the form y=mx+c

[tex] \frac{3y}{3} = \frac{6x}{3} + \frac{12}{3} \\ y = 2x + 4[/tex]

YOU CAN SEE THAT NOW THE SLOPE OF THE LINE IS 2 TO GET THW Y INTERCEPT WE KNOW THAT AT THE Y-AXIS x=0

PLUG IN 0 IN THE PLACE OF X TO GET Y IN THE EQUATION OF THE LINE.

[tex]y = 2(0) + 4 \\ y = 4[/tex]

THE Y-INTERCEPT IS (0,4)

THEREFORE THE LINE HAS A SLOPE 2 AND A Y INTERCEPT (0,4)

FIRST OPTION IS THE ANSWER.

The average rate of change f(x) on the interval -6 ≤ x ≥ 2 is; 5

Average rate of change is a measure of how much the function changed per unit, on average, over that interval. This is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.

Now, the formula for the average rate of change over the interval (a, b) is;

f'(x) = [f(b) - f(a)]/(b - a)

Now, we are given the interval as -6 ≤ x ≥ 2.

From the given polynomial graph, we see that;

f(2) = 0 and f(-6) = 40

Thus;

f'(x) = [f(-6) - f(0)]/(2 - (-6))

f'(x) = (40 - 0)/8

f'(x) = 5

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the equation for the saved money is

195 = 8w + 35

here w = no. of weeks.

so the answer is 8w + 35 = 195

we have the sequence

1,790 2,555 3,320 4,085 4,850

so

a1=1,790 ----> first term

a2=2,555

a3=3,320

a4=4,085

a5=4,850

Find out the difference between consecutive terms

a2-a1=2,555-1,790=765

a3-a2=3,320-2,555=765

a4-a3=4,085-3,320=765

a5-a4=4,850-4,085=765

This is an arithmetic sequence

The common difference is d=765

so

we have

d=765

a1=1,790

substitute

Let:

The coordinates for the new figure will be given by:

Where:

O = Center of dilation at (a,b) = (3,2)

k = Scale factor = 0.1

So:

Since:

(2.8,2), (2.8,1.9), (2.9, 1.9) and (2.9,2) are much closer to the center of dilation we can conclude that the dilated figure is closer to the center of dilation.

Solution:

Given:

A polygon on a grid.

Question 2a:

The length of each side of the polygon on the grid is given by;

Question 2b:

Perimeter is the sum of the outer sides enclosing a shape.

Hence, the perimeter of the factory is;

Thus,

Therefore, the perimeter of the factory is 1000 feet.

The figures that have sides that to be perpendicular are figures A and E.

For the given question;

As we can see that the only in figures A and E, there are two lines making an angle of 90 degrees.

Thus, only figures A and E have the sides perpendicular to each other.

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The expression for the volume of the Prism is 1/3(Base area x Height)

In the given prism

Height = 10 mi

Base is in the shape of right angle triangle

Area of right angle triangle = 1/2 x Base x Height

Area of right angle triangle = 1/2 x 8 x 6

ARea of right angle triangle = 24

Area of base of the prism = 24mi².

Volume of the prism = 1/3 (Base area x Height)

Volume of the prism = 1/3 (24 x 10)

Volume of the prism = 1/3(240)

Volume of the prism = 80mi³.

The volume of prism is 80 mi³.

The dimensions that we must use in this problem, are the dimensions of the screen of a TV of 75 inches:

• W = width = 65.4" ,

• H = heigh = 36.8".

• The form of the TV is a rectangle, we compute the area A of the rectangle by the following formula:

• The aspect ratio r is given by the quotient of the width (W) by the height (H):

• The length of the TV diagonal L can be computed using Pitagoras Theorem:

Answer

• width = 65.4",

• heigh = 36.8",

• area = 2406.72in²,

• aspect ratio = 1.777

• length of the diagonal = 75.04in.

Let the commission sales = X

Salary Plan 1

salary per week = $400

commission sales = 2%

Salary Plan 2

salary per week = $300

commission sales = 18%

Becky's salary for both plans (inclusive of commission sales) would be:

Plan 1:

Plan 2:

In order to find how much Becky needs to make in sales for salary to be the same from both plans would be:

Therefore, the commission sales should be $625

The linear function passing through points (1,7) and (2.5, 1) is given by:

y = -4x + 11.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

y = mx + b

In which the coefficients are described as follows:

For this problem, the two points that form the function are given as follows:

(1,7) and (2.5, 1).

The slope is given by change in y divided by change in x, hence it is given by:

m = (1 - 7)/(2.5 - 1) = -4.

Then:

y = -4x + b.

When x = 1, y = 7, hence we can find the intercept b of the function as follows:

7 = -4(1) + b

b = 7 + 4

b = 11.

Hence the equation is:

y = -4x + 11.

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Answer:

It belongs to the sets of natural numbers, {1, 2, 3, 4, 5, …}.

It is a whole number because the set of whole numbers includes the natural numbers plus zero. It is an integer since it is both a natural and whole number.

Answer:  rational numbers if thats an answer

Step-by-step explanation:

Given the following expression:

a.) 8x - 1 = 3x + 4

Let's determine the value of x,

8x - 1 = 3x + 4

8x - 1 + 1 - 3x = 3x + 4 + 1 - 3x

8x - 3x = 4 + 1

5x = 5

5x/5 = 5/5

x = 1

Therefore, x = 1.

The total cheese used by Alan to make 6 batches of recipe is 3360 g

An equation is an expression that is used to show the relationship between two or more numbers and variables.

1 oz = 28 g

The recipe calls for 20 oz. of cheese for each batch. Hence:

Total cheese in gram for each recipe = 20 oz. * 28 g per oz. = 560 g

There are 8 batches, hence:

Total cheese = 560 g * 6 batches = 3360 g

The total cheese is 3360 g

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