The table below represents a linear function f(x), and the equation represents a function g(x): X) -1, 0, 1 F(x) -5, -1, 3 G(x)=4x+3

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

Part B which functions has greater y-intercept. Justify

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Answer:

1026

Step-by-step explanation:

Common difference = d = 2nd term  - first term

 d = -3 - (-11) = -3 +11 = 8

First term = a = -11

First we need to find the number of terms in this series

[tex]a_{n} = 125\\\\a + (n- 1)d = a_{n}\\\\[/tex]

-11 + (n- 1) * 8 = 125

 (n-1)*8 = 125 + 11

 (n-1) * 8 = 136

n -1 = 136/8

n -1 = 17

  n = 17+1

 n = 18

[tex]S_{n} =\frac{n}{2}(a+a_{n})\\\\S_{18} =\frac{18}{2}(-11+125)\\\\[/tex]

   = 9 * 114

   = 1026

1. Divide 240 by 10 = 24

2. Multiply 24 • 8 = 192

Michele will need 192 oz. of mayonnaise.

Answer:

192 oz

Step-by-step explanation:

Hi there!

1) Create a proportion

[tex]\frac{8 (oz)}{10(servings)} =\frac{x(mayo)}{240(servings)} \\\frac{8}{10} =\frac{x}{240}[/tex]

2) Solve for x

[tex]\frac{8}{10} =\frac{x}{240}[/tex]

Multiply both sides by 240

[tex]\frac{8}{10} *240=x\\192=x[/tex]

Therefore, Michele would need 192 oz of mayonnaise.

I hope this helps!

Answer:

Diameter = 14 units

Step-by-step explanation:

Volume ofa cylinder = πr²h

Volume of the cylinder = 245π cubic units

Height = 5 units

Volume of a cylinder = πr²h

245π = π × r² × 5

245π = 5r²π

Divide both sides by π

245π / π = 5r²π / π

245 = 5r²

r² = 245/5

= 49

r² = 49

r = √49

r = 7 units

Diameter = 2 × radius

= 2 × 7 units

= 14 units

Diameter = 14 units

Answer:

$1.70

Step-by-step explanation:

To figure out how much each apple costs, divide $1.50 by the quantity of apples (6). The answer to that is $0.25, so multiply it by the two apples to get $0.50.

For the oranges, divide $3 by 5. The answer for that is $0.60. Multiply that by the two oranges to get $1.20.

Then, add $0.50 to $1.20 to get a total of $1.70

Answer:

$1.70

Step-by-step explanation:

We know that you can buy 6 apples for $1.50 and 5 oranges for $3.00. So let's look at the cost for one individual apple first.

To find the amount/apple we can divide $1.50 by 6. Here's another way to look at it:

Assume A is cost per apple.

6A = $1.50

6A/6 = $1.50/6

A = $0.25

Now to find the amount for 2 apples, you want to multiply the amount it costs for one apple by 2, because you are multiplying the quantity by 2 as well.

A= $0.25

A *2 = $0.25 * 2

2A = $0.50

So for two apples, it is 50 cents.

We can use a similar process for oranges but with a different price and quantity.

Assume R is cost per orange.

5R = $3.00

5R/5 = $3.00/5

R = $0.60

To find the amount for two oranges we multiply the cost by two.

R = $0.60

R*2 = $0.60*2

2R = $1.20

Finally, we want the total amount for apples AND oranges so we find the sum.

$0.50 + $1.20 = $1.70

Answer:

358

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Probability is equal to the amount of desirable outcomes divided by the total amount of outcomes. Each coin has two sides, and there are three of them. This accounts for a total of 2^3 or 8 outcomes. Now, we need to find the amount of outcomes where two or more coins land on heads. We can start by listing those possibilities: THH, HTH, HHT, and HHH. Notice that the first three are just three ways of rearranging the same result. We can see that there are four desirable outcomes. This means the probability is 1/2.

Answer:

120

Step-by-step explanation:

5*4*3*2*1

Step-by-step explanation:

The second equation

[tex]2.4x = 1.2x + 15[/tex]

is the answer for the 1st picture.

2nd, solve for x.

[tex]1.2x = 15[/tex]

[tex]x = 12.5[/tex]

You cant create half a page so let lower it down to 12.

12 is the answer for the second answer.

Answer:

[tex]\displaystyle A = 12[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Area of a Region Formula:                                                                                     [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

y = x

Interval: x = 1 to x = 5

Step 2: Sort

Graph the function. See Attachment.

Bounds of Integration: [1, 5]

Step 3: Find Area

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Answer:

Their present ages are 12 years and 16 years.

Step-by-step explanation:

Given that,

Ages of Raju and Ravi are in the ratio 3:4 .Four years from now the ratio of their ages will be 4:5.

Let their present age is 3x and 4x.

Ages after four years from now will be:

[tex]\dfrac{3x+4}{4x+4}=\dfrac{4}{5}\\\\5(3x+4)=4(4x+4)\\\\15x+20=16x+16\\\\20-16=16x-15x\\\\x=4[/tex]

So,

Raju's present age is 3(4) = 12 years

Ravi's present age is 4(4) = 16 years

Answer:

Inverse sine

Step-by-step explanation:

Recall the three common trig ratios

Remember SohCahToa

Sine = Opposite over Hypotenuse (SOH)

Cosine = Adjacent over Hypotenuse (CAH)

Tangent = Opposite over Adjacent (TOA)

Now let's look back at the question

It asks us which inverse function would we use to solve for angle Z

Looking at angle Z, we are given it's opposite side length and the hypotenuse ( longest side ).

When dealing with the opposite side length and hypotenuse we use trig function sine.

When trying to find the angle we use inverse so we would use inverse sine to find the measure of angle A

Answer:

_____________________________

2 x 5 = 10

2 x 4 = 8

10 + 8 = 18

______________________________

5 + 4 = 9

_______________________________

_ 9 = 18

18 : 9 = 2

Answer:

[tex]m \angle A = m \angle C[/tex] by reason [tex]\overline{AB} \cong \overline{BC}[/tex] and [tex]m \angle B = m \angle M = m \angle P[/tex].

[tex]\triangle AMO \cong \triangle CPO[/tex] SAS Theorem

Step-by-step explanation:

We proceed to demonstrate the statement by Geometric means:

1) [tex]\overline{AB} \cong \overline{BC}[/tex], [tex]\overline {AM} \cong \overline {PC}[/tex], [tex]m\angle AMO = m\angle CPO[/tex] Given.

2) [tex]\frac{AM}{AB} = \frac{PC}{BC}[/tex] Proportionality.

3) [tex]\frac{AM}{AM + MB} = \frac{PC}{BP + PC}[/tex] Definition of line segments.

4) [tex]\frac{1}{1+\frac{MB}{AM} } = \frac{1}{\frac{BP}{PC}+1}[/tex] Algebra.

5) [tex]\frac{BP}{PC} + 1 = 1 +\frac{MB}{AM}[/tex] Algebra.

6) [tex]\frac{BP}{PC} = \frac{MB}{AM}[/tex] Algebra.

7) [tex]BP = BM[/tex] By 1)

8) [tex]m \angle B = m \angle M = m \angle P[/tex] By 1), 7)

9) [tex]\triangle AMO \sim \triangle ABC[/tex], [tex]\triangle CPO \sim \triangle ABC[/tex] By 1), 7), 8). Defintion of simmilarity.

10) [tex]\frac{AM}{MO} = \frac{AB}{BC}[/tex], [tex]\frac{PO}{PC} = \frac{AB}{BC}[/tex] Definition of proportionality.

11) [tex]\frac{AM}{MO} = \frac{PO}{PC}[/tex] Algebra.

12) [tex]AM^{2} = PO\cdot MO[/tex] Algebra.

13) [tex]PO = MO[/tex] By 12) and Algebra.

14) [tex]\overline{PO} \cong \overline{MO}[/tex] By 13).

15) [tex]\triangle AMO \cong \triangle CPO[/tex] SAS Theorem/Result.

Answer:

(0,-6)

Step-by-step explanation:

9x + 3y = -18

Solve for y to get equation in slope intercept form

( y = mx + b )

9x + 3y = -18

Subtract 9x from both sides

9x - 9x + 3y = -18 - 9x

3y = -9x - 18

Divide both sides by 3

3y/3 = y

-9x - 18 / 3 = -3x - 6

We're left with y = -3x - 6

The equation is now in y intercept form

y = mx + b where b = y intercept

-6 takes the spot of b therefore the y intercept would be at (0,-6)

Photo isn't clear.

And which number

Answer:

It is reflected in the y axis followed by a dilation by a factor of 1/2

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

If a point A(x, y) is reflected in the y axis, the new point is at A'(-x, y).

If a point A(x, y) is dilated by a factor of k, the new point would be at A'(kx, ky).

The vertices of rectangle WXYZ is at W(2, 4), X(6, 4), Y(6, 2) and Z(2, 2).

If the rectangle is reflected in the y axis, the new points are W'(-2, 4), X'(-6, 4), Y'(-6, 2) and Z'(-2, 2). If it is then dilated by a factor of 1/2, the new vertices is at W''(-1, 2), X''(-3, 2), Y''(-3, 1) and Z''(-1, 1).

Answer:

- 13

Step-by-step explanation:

Plug 3 in for x:

-5(3)+2

Simplify :

-15+2

=-13

Answer:

-13

Step-by-step explanation:

f(x) = -5x + 2

f(3) = -5(3) + 2

f(3) = -15 + 2

f(3) = -13

Answer:

Step-by-step explanation:

Hello there

I'm also a student so I'm not 100% sure on this one, but I think I know.

Usually when you have functions you just replace the letters for their value:

f = 11x

g = x² - 6x + 3

h = -x + 4

Th exercise is asking for (g * h) (x)

Since there are parenthesis, here's what we have:

[(x² - 6x + 3)(-x + 4)](x)

Use the left side of the equation:

[(x² - 6x + 3)(-x + 4)](x)

And solve it:

-x³ + 6x² -3x + 4x² - 24x + 12

That's equal to

-x³ + 10x² -27x + 12

Multiply all that by that x on the left:

-x^4 + 10x³ -27x² + 12x

No idea if that's right so please tell me

Answer:

C. Line

Is the correct answer

Answer:

no tHank you hope someone can help

Step-by-step explanation:

Answer:

The angle measures 25°; the complement measures 65°; the supplement measures 155°.

Step-by-step explanation:

The sum of the measures of two complementary angles is 90.

If the angles measure x and y, then x + y = 90.

Given angle x, then y = 90 - x.

The sum of the measures of two supplementary angles is 180.

If the angles measure x and y, then x + y = 180.

Given angle x, then y = 180 - x.

Let the angle be x.

Its complement is 90 - x.

Its supplement is 180 - x.

5(90 - x) = 2(180 - x) + 15

450 - 5x = 360 - 2x + 15

-3x = -75

Angle: x = 25

Complement: 90 - x = 90 - 25 = 65

Supplement: 180 - x = 180 - 25 = 155

Answer: The angle measures 25°.;, the complement measures 65°; the supplement measures 155°.

Answer:

beginning of march 4.1

beginning of jun      6.4

Step-by-step explanation:

Answer:

A. 25%

Step-by-step explanation:

50% = 1/2

1/2 of 1/2 = 1/2 * 1/2=

1/4 = 25%

Answer:

100%-50%=50% so the answer is B

Answer:

4.

Step-by-step explanation:

A line AB is perpendicular to the line CD.

As shown in the diagram, there are four angles which measures 90°.

Answer:

x = -72

Step-by-step explanation:

-72 + 8 = -64

The third square root of -64 is -4

Answer:

[tex]a_1 = 5[/tex]

[tex]a_n = a_{n-1} + 2[/tex]

Step-by-step explanation:

Given

[tex]a_n = 5 + (n - 1)2[/tex]

Required

The equivalent recursive function

The general explicit function is:

[tex]a_n = a_1+ (n - 1)d[/tex]

So, by comparison

[tex]a_1 = 5[/tex]

[tex]d = 2[/tex]

The recursion of an arithmetic sequence is:

[tex]a_n = a_{n-1} + d[/tex]

Substitute 2 for d

[tex]a_n = a_{n-1} + 2[/tex]

Hence: (a) is correct