The table below represents a linear function f(x) and the equation represents a function g(x):

x f(x)
−1 −5
0 −1
1 3


g(x)

g(x) = 2x − 7

Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).

Part B: Which function has a greater y-intercept? Justify your answer.

Answer:

d. 36 sq. ft​

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh  where b is the base and h is the height

A = 1/2 (12) * 6

A = 36 ft^2

Answer:

f(n) = 2 + 3(n-1)

Step-by-step explanation:

Answer:

f(n) = 2 + 3(n-1)

Step-by-step explanation:

Hey there! :)

-4c + 3d = 8e ; solve for d.

In order to solve for d, you must isolate it (get it onto its own side). So, let's start off by adding 4c to both sides.

-4c + (-4c) + 3d = 8e + (-4c)

Simplify.

3d = 8e - 4c

Then, divide both sides by 3.

3d ÷ 3 = (8e - 4c) ÷ 3

Simplify.

d = 8/3e - 4/3c

Therefore, [tex]d = \frac{8}{3} e  -\frac{4}{3} c[/tex]

Answer:

[tex]\large\boxed{\dfrac{x+5}{x^2}-\dfrac{2}{5x}=\dfrac{3x+25}{5x^2}}[/tex]

Step-by-step explanation:

[tex]\dfrac{x+5}{x^2}-\dfrac{2}{5x}=\dfrac{5(x+5)}{5x^2}-\dfrac{2x}{5x^2}\qquad\text{use the distributive property}\\\\=\dfrac{5x+25}{5x^2}-\dfrac{2x}{5x^2}=\dfrac{5x+25-2x}{5x^2}=\dfrac{3x+25}{5x^2}[/tex]

The difference between the rational expressions below will be,[tex]\frac{3x+25}{5x^2}[/tex]

Arithmetic is an area of mathematics involving the study of numbers and the different operations that can be performed on them.

The difference in the rational expression is found as;

[tex]=\frac{x+5}{x^2} -\frac{2}{5x} \\\\=\frac{5(x+5)}{x^2} - \frac{2x}{5x^2} \\\\\ = \frac{5x+25}{5x^2} -\frac{2x}{5x^2 }\\\\\ = \frac{5x+25-2x}{5x^2} \\\\ = \frac{3x+25}{5x^2}[/tex]

The difference between the rational expressions below will be,[tex]\frac{3x+25}{5x^2}[/tex].

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Answer: B. 2=3x+10x^2

Step-by-step explanation:

The expression means the quadratic function equation.

B = 10x^2 + 3x -2 = 0

the equation is [-b ±√(b^2 -4ac)]/2a

b should be +3 to become -3 when it is plugged into the equation, and 'a' should be 10, and c should be -2.

Answer:B

Step-by-step explanation:

Ye you know me keep it a buck like 123 ye 2022 baby

Answer:

2p

Step-by-step explanation:

Take a trip back to simple division. What's 12/6? If you put 12 p's evenly into 6 piles, how many p's are in each pile?

2

Therefore, the answer is 2p.

For this case we have the expression:

"the square root of 4" is represented algebraically as:

[tex]\sqrt {4}[/tex]

Then, we can express the given statement as:

[tex]3 \sqrt {4} -2 \sqrt {4} =[/tex]

They are similar terms, we can subtract:

[tex]3 \sqrt {4} -2 \sqrt {4} = \sqrt {4} = \sqrt {2 ^ 2}[/tex]

By definition of power properties we have that:

[tex]\sqrt [n] {a ^ n} = a ^ {\frac {n} {n}} = a[/tex]

Then the expression is reduced to:

[tex]\sqrt {2 ^ 2} = 2[/tex]

Answer:

[tex]3 \sqrt {4} -2 \sqrt {4} = 2[/tex]

Answer:

What parabola tool?

Step-by-step explanation:

I went ahead and graphed the quadratic function however, you should learn how to graph it yourself the way they are asking you to using the "parabola tool", because I cant really show you my steps in graphing it since I don't know what your parabola tool is.

Sorry

Answer:

[tex]\large\boxed{y=-\dfrac{7}{3}x+4}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept (0, b)

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points:

(0, 4) → b = 4

and (3, -3)

Substitute:

[tex]m=\dfrac{-3-4}{3-0}=\dfrac{-7}{3}\\\\y=-\dfrac{7}{3}x+4[/tex]

Answer:

0.

Step-by-step explanation:

The nonpermissible replacement of the variable in an expression is the value of x that will make the denominator of the expression zero.

This problem will therefore be written as -5/3y≠0, and it can't be 0, so 0 is your non permissible replacement.

Hope this helps!

Answer:

Because the negative in the front cancels out the other neg.

Step-by-step explanation:

Answer:

-(3 - 2x ) = -3 + 2x = 2x - 3

Step-by-step explanation:

If you expand the brackets in -(3 - 2x) by multiplying all numbers by -1 (the negative symbol in front of the brackets represents negative 1 just without the 1)

Thus you get -3 + 2x.

Then rearranging the equation by swapping the 2x with the -3 you get 2x - 3.

Answer:

m(h) = 5.25h

$11.81 for 2 hours and 15 minutes

Step-by-step explanation:

Answer:

[tex]\frac{16x^2+48x}{8x} = 2x+6\\\frac{56x^2-14x}{7x} = 8x-2\\\frac{18x^2+15x}{3x}=6x+5\\\frac{20x^2-32x}{4x}=5x-8[/tex]

Step-by-step explanation:

We will solve the division one by one:

[tex]\frac{16x^2+48x}{8x} = \frac{8x(2x+6)}{8x} = 2x+6\\\frac{56x^2-14x}{7x}=\frac{7x(8x+2)}{7x}=8x+2\\\frac{18x^2+15x}{3x} =\frac{3x(6x+5)}{3x} = 6x+5\\\frac{20x^2-32x}{4x}=\frac{4x(5x-8)}{4x}=5x-8[/tex]

a)

[tex]\dfrac{16x^2+48x}{8x}[/tex]

Since, both the terms in the numerator have a common factor as: 8x.

Hence, we take out common 8x from the numerator term and hence it could be written as:

[tex]\dfrac{8x(2x+6)}{8x}[/tex]

i.e.

[tex]=2x+6[/tex]

b)

[tex]\dfrac{56x^2-14x}{7x}[/tex]

Since, both the terms in the numerator have a common factor as: 14x.

Hence, we take out common 14x from the numerator term and hence it could be written as:

[tex]=\dfrac{14x(4x-1)}{7x}\\\\=2(4x-1)\\\\=8x-2[/tex]

c)

[tex]\dfrac{(18x^2+15x)}{3x}[/tex]

Since, both the terms in the numerator have a common factor as: 3x.

Hence, we take out common 3x from the numerator term and hence it could be written as:

[tex]=\dfrac{3x(6x+5)}{3x}\\\\=6x+5[/tex]

d)

[tex]\dfrac{20x^2-32x}{4x}[/tex]

Since, both the terms in the numerator have a common factor as: 4x.

Hence, we take out common 4x from the numerator term and hence it could be written as:

[tex]=\dfrac{4x(5x-8)}{4x}\\\\=5x-8[/tex]

Answer:

-6x^2 y^3 = B

Step-by-step explanation:

42x^5y^4=(-7x^3y)(B)​

Solve for B

Divide by -7

42x^5y^4/-7=(-7x^3y)(B)/-7

-6 x^5 y^4 = x^3 y B

Divide by x^3

-6 x^5 y^4/x^3 = x^3 y B​/x^3

-6 x^5/x^3 y^4 = By

-6 x^2 y^4

Divide by y

-6x^2 y^4/y = By/y

-6x^2 y^3 = B

Answer:  A) 7 o---------------→

Step-by-step explanation:

[tex]\dfrac{2}{9}x+3>4\dfrac{5}{9}\\\\\\\text{Subtract 3 from both sides:}\\\\\dfrac{2}{9}x>1\dfrac{5}{9}\\\\\\\text{Convert the mixed number into an improper fraction:}\\\\\dfrac{2}{9}x>\dfrac{14}{9}\\\\\\\text{Multiply both sides by }\dfrac{9}{2}\text{ to isolate x:}\\\\x>\dfrac{14}{9}\times \dfrac{9}{2}\\\\\\\text{Simplify (cancel out the 9's and factor out a 2:}\\\\x>7[/tex]

The graph will have an open dot at 7 and the arrow will point to the right.

7 o--------->

Answer:

A

Step-by-step explanation:

EDGE 23

Answer:

2y + 3x = 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 3x + 2y = - 4 into this form

Subtract 3x from both sides

2y = - 3x - 4 ( divide all terms by 2 )

y = - [tex]\frac{3}{2}[/tex] x - 2 ← in slope- intercept form

with slope m = - [tex]\frac{3}{2}[/tex]

• Parallel lines have equal slopes, thus

y = - [tex]\frac{3}{2}[/tex] x + c ← partial equation of parallel line

To find c substitute (4, - 1) into the partial equation

- 1 = - 6 + c ⇒ c = - 1 + 6 = 5

y = - [tex]\frac{3}{2}[/tex] x + 5 ← in slope- intercept form

Multiply through by 2

2y = - 3x + 10 ( add 3x to both sides )

3x + 2y = 10 ← in standard form

The equation of the line parallel to 3x+2y= -4 goes through the point (4,-1).

The general equation of a straight line exists y = mx + c, where m is the gradient, and y = c exists the value where the line cuts the y-axis. This number c is named the intercept on the y-axis. The equation of a straight line with gradient m and intercept c on the y-axis stands y = mx + c.

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 3x + 2y = - 4 into this form

Subtract 3x from both sides

2y = - 3x - 4 ( divide all terms by 2 )

y = -  x - 2 ← in slope- intercept form

with slope m = -

• Parallel lines have equal slopes, thus

y = -  x + c ← partial equation of parallel line

To find c substitute (4, - 1) into the partial equation

- 1 = - 6 + c ⇒ c = - 1 + 6 = 5

y = -  x + 5 ← in slope- intercept form

Multiply through by 2

2y = - 3x + 10 ( add 3x to both sides )

3x + 2y = 10 ← in standard form.

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Answer:

[tex]y=-\frac{4}{3}x[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

step 1

Find the value of k

we have

the point (9,-12)

x=9, y=-12

[tex]k=y/x[/tex]

substitute

[tex]k=-12/9=-4/3[/tex]

step 2

Find the equation

[tex]y=kx[/tex]

so

[tex]y=-\frac{4}{3}x[/tex]

Answer:

-4/3

Step-by-step explanation:

If the lines are parallel, they have the same slope.

Since the red line has a slope of -4/3, the green line will have a slope of -4/3

Answer:

[tex]\frac{1}{2}[/tex] , or the first option

Step-by-step explanation:

The formula to find the slope of a line is [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]. It doesn't matter which set of coordinates is (x₁,y₁), as long as you make sure you put them in the right places.

(x₁,y₁) = (1,2)

(x₂,y₂) = (5,4)

[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]   Plug in your numbers

[tex]\frac{4 - 2}{5 - 1}[/tex]   Simplify

[tex]\frac{2}{4}[/tex]   Simplify

[tex]\frac{1}{2}[/tex]

Answer:

slope = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (5, 4)

m = [tex]\frac{4-2}{5-1}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

Answer:

24

-560

Step-by-step explanation:

(1) (-2) * 3 * (-4)

A negative time a negative is a positive

2*3*4 = 24

(iv) 8 x 7*(-10)

This result will be negative since there are positive times negative

8*7 =56* 10 = 560

8*7* (-10) = -560

ANSWER

[tex]x = - 3[/tex]

EXPLANATION

When a quadratic equation is in the vertex form,

[tex]f(x) = a {(x - h)}^{2} + k[/tex]

the equation of axis of symmetry is simply

[tex]x = h[/tex]

The given quadratic equation is

[tex]f(x) = {(x + 3)}^{2} - 8[/tex]

We can rewrite this as

[tex]f(x) = {(x - - 3)}^{2} - 8[/tex]

We now compare to

[tex]f(x) = a {(x - h)}^{2} + k[/tex]

We have

[tex]h = - 3 \: \: \: and \: \: k = - 8[/tex]

Therefore equation of axis of symmetry is:

[tex]x = - 3[/tex]

The correct option that shows the values of the two 3s in the price $3,435 is D) 3,000; 30

In the given price, $3,435, the first 3 represent the thousand place value, while the second 3 represents the one's place value.

The comma in option D indicates the separation of thousands, so it correctly represents the first 3 as part of the thousands place value.

The number 30 in option D represents the second 3 as part of the one's place value.

Therefore, option D) 3,000; 30 is the choice that correctly shows the values of the two 3s in the price $3,435.

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[tex]\dfrac{16}{7x+4}+A=\dfrac{49x^2}{7x+4}\\\\A=\dfrac{49x^2}{7x+4}-\dfrac{16}{7x+4}\\\\A=\dfrac{49x^2-16}{7x+4}\\\\A=\dfrac{(7x-4)(7x+4)}{7x+4}\\\\A=7x-4[/tex]

[tex]\bf \stackrel{~~~~~~~~\textit{is equivalent}}{\cfrac{16}{7x+4}+A~~=~~\cfrac{49x^2}{7x+4}}\implies \stackrel{\textit{cross-multiplying}}{\cfrac{16~~\begin{matrix} (7x+4) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 7x+4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}+A(7x+4)=49x^2} \\\\\\ 16+A(7x+4)=49x^2\implies A(7x+4)=49x^2-16\implies A=\cfrac{49x^2-16}{7x+4}[/tex]

[tex]\bf A=\cfrac{7^2x^2-4^2}{7x+4}\implies A=\cfrac{\stackrel{\textit{difference of squares}}{(7x)^2-4^2}}{7x+4}\implies A=\cfrac{(7x-4)~~\begin{matrix} (7x+4) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 7x+4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A=7x-4~\hfill[/tex]

Answer:

B) {-5x + 4y = 8

{-x + 5y = 10

Step-by-step explanation:

Add like it said, and you will see your answer.

Answer:

Option B

[tex]-5x+4y=8[/tex]

[tex]-x+5y=10[/tex]

Step-by-step explanation:

We are given that

System of equations

[tex]-5x+4y=8[/tex]

[tex]4x+y=2[/tex]

We have to find an equivalent system of equations using sum of system and first equations

Sum of system of equations

[tex]-5x+4y+4x+y=8+2[/tex]

[tex]-x+5y=10[/tex]

Therefore, option B is true.

Answer: 2x^2-y^2+5xy-2y

a. There is four terms in the simplified expression.

b. Two terms in the simplified expression are negative.

Step-by-step explanation:

Write the expression like an addition/ subtraction problem.

-3x²+2y²+5xy-2y

+5x²-3y²

_________

This makes it easier to identify what to combine for like terms.

Final answer:

The simplified expression is 2x² - y² + 5xy - 2y. There are two negative terms in the simplified expression: -y² and -2y.

Explanation:

To simplify the expression -3x² + 2y² + 5xy - 2y + 5x² - 3y², we need to combine like terms. The like terms are the ones that contain the same variables to the same power. Here’s a step-by-step explanation:

The simplified expression is 2x² - y² + 5xy - 2y.

Now, to answer the question about the number of negative terms: in the simplified expression, there are two negative terms, which are -y² and -2y. A term is considered negative if it has a minus sign in front of it, indicating that it is less than zero when all other variables are considered to be positive.

ANSWER

[tex]y = \frac{1}{4}x+1[/tex]

EXPLANATION

The slope-intercept equation of a straight line is of the form

[tex]y = mx + b[/tex]

Where 'm' is the slope and 'b' is the y-intercept.

From the question we have slope to be

[tex]m = \frac{1}{4} [/tex]

We substitute the slope into the slope-intercept equation and obtain:

[tex]y = \frac{1}{4}x + b[/tex]

To find the value of 'b' we plug in the point (-8,-1) into our current equation.

[tex] - 1= \frac{1}{4}( - 8)+ b[/tex]

[tex] - 1= - 2+ b[/tex]

[tex] - 1 + 2 = b[/tex]

[tex]1 = b[/tex]

[tex]b =1 [/tex]

The complete equation is

[tex]y = \frac{1}{4}x + 1[/tex]

Answer:

The solutions are: x=6. x=-4 and x=-8.

Step-by-step explanation:

The solution to the system of the equation is going to be given by the points where the graphs of:

y = x3 + 6x2 - 40x AND y = 192 intercept.

By looking at the graph, we can deduce they intercept at three points:

(-8, 192), (-4, 192) and (6, 192).

Another way to verify this, is by solving the following system of equations:

x3 + 6x2 - 40x - 192 = 0

Factorizing, we get:

(x-6)(x+4)(x+8) = 0

Where we can clearly see that the solutions are: x=6. x=-4 and x=-8.

Answer:

A -8

B -4

D 6

Step-by-step explanation:

Correct on EDGE

Answer:

Step-by-step explanation:

When you find the sum of a number you are adding two or more numbers together. therefore the only answer that you could use to get a sum of 5 when your first term is 12 would be -7

Answer:

Volume = 784*pi

Step-by-step explanation:

We are given the height and radius of cylinder

So,

Radius = r = 7

Height = h = 16

The formula for finding volume of cylinder is:

[tex]Volume=\pi r^{2} h\\Putting\ in\ the\ values\ of\ r\ and\ h\\Volume=\pi *(7)^{2}*16\\V=\pi *49*16\\V=784\pi [/tex]

Answer:

Volume of cylinder = 784 cubic units

Step-by-step explanation:

Points to remember

Volume of cylinder =  πr²h

Where r - Radius of cylinder and

h - Height of cylinder

To find the volume of cylinder

It is given that,

radius r = 7 units and height h = 16 units

Volume of cylinder =  πr²h

 = π * 7² * 16

 = 784 cubic units

Therefore Volume of cylinder = 784 cubic units