F(x)=2x+7 and g(x)=3x^2+2

Answer: A.-20

Step-by-step explanation:

Since x=4

substitute in and solve

h(4)=-5(4)

h(4)=-20

Answer:

Step-by-step explanation:

when x=4, then h(x)=-5 * 4=-20

Therefore, choose A

Answer:

$1

Step-by-step explanation:

To find the unit cost per DVD, you need to calculate the total cost of producing 1 million DVDs and divide that by the number of DVDs produced.

First, you need to find the cost of producing 1 DVD. You can do this by dividing the cost of building the factory by the number of DVDs produced per dollar spent on the factory:

cost of 1 DVD = $80,000 / (20 DVDs/$3) = $1

Then, you can multiply this cost by the number of DVDs produced to find the total cost of producing 1 million DVDs:

total cost = (cost of 1 DVD) * (number of DVDs) = $1/DVD * 1,000,000 DVDs = $1,000,000

Finally, you can divide the total cost by the number of DVDs produced to find the unit cost per DVD:

unit cost per DVD = total cost / number of DVDs = $1,000,000 / 1,000,000 DVDs = $1/DVD.

So, the unit cost of producing 1 DVD is $1.

Answer:

Step-by-step explanation:

I think you should divide

The probability that you first choose a green marble and then a blue marble is, P(green then blue) = 1/5.

What is probability?

Simply put, probability measures how likely something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Given:

A bag contains 2 blue, 1 red, and 3 green marbles.

So, the total marbles are 2 + 1 + 3 = 6

The probability of selecting a green marble is:

P(Green) = 3/6

Now, there are 5 marbles left.

The probability of selecting a blue marble is:

P(Blue) = 2/5

The required probability is:

P = 3/6 * 2/5 = 6/30 = 1/5

Hence, the probability that you first choose a green marble and then a blue marble is, P(green then blue) = 1/5.

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The solution of the quadratic equation 2x² - 5x = - 3 will be 3/2 and 1. Then the correct option is B.

Let the equation be ax² + bx + c = 0.

Then the roots of the equation will be

[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}[/tex]

The quadratic equation is given below.

2x² - 5x = - 3

Simplify the equation, then we have

2x² - 5x + 3 = 0

Then the roots of the equation are given as,

x = [-(-5) ± √((-5)² - 4 × 2 × 3)] / (2 × 2)

x = [5 ± √(25 - 24)] / 4

x = (5 ± 1) / 4

x = (5 + 1) / 4, (5 - 1) / 4

x = 6 / 4, 4 / 4

x = 3/2 and 1

The solution of the quadratic equation 2x² - 5x = - 3 will be 3/2 and 1. Then the correct option is B.

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Answer:

$150

Step-by-step explanation:

Let's call the cost price of the watch C. The salesperson sells the watch at 90% of the cost price, so they sell the watch for 0.9 * C dollars.

We know that 0.9 * C = 108 dollars, so C = 108 / 0.9 = <<108/0.9=120>>120 dollars.

The salesperson wants to make a profit of $30, so they need to sell the watch for 120 + 30 = <<120+30=150>>150 dollars.

Answer:220%

Step-by-step explanation:

The required interest as calculated from the given data equals $48.3 .

Given,

A $1,000 TR Global bond at an interest rate of 80.5 pays 6%.

A bond price of 90 on a $1,000 bond indicates that the bond will sell for $900, or 90% of $1,000.

Because we provided a $1,000 TR Global bond at 80.5 pays

means that 80% of $1,000 is used to fund the bond.

80.5% of $1,000 is equal to frac80.5100*1000=805.

The true cost is $805.

Currently, actual interest is 6%.

6% of $805= 6*100*805*0.06*805

=48.3

Final interest equals $48.3

Interest is calculated as Interest Rate * Balance or Principal.

Choosing the appropriate interest rate is frequently the more challenging part of calculating interest. The APR is typically used to denote the interest rate, which is frequently stated as a percentage.

The APR, however, frequently does not take compounding into account.

The actual rate of interest to be paid is expressed instead using the effective yearly rate.

To determine the appropriate interest earned over a specific period, an annual rate must frequently be converted.

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x=5/3

x=-4

This is simple just rearrange and sub into quadratic formula. The formula will spit out two answers and those are your final answers. Enjoy!

Both equations relate dimensions in feet with dimensions in inches (one is the inverse of the other) so the correct option is C.

Mai and Noah tried to find an equation that relates dimensions in feet to equivalent dimensions inches.

Remember that the relation between inches and feet is:

1 feet = 12 inches.

Then, the number in inches in x feet, is 12 times that amount, so:

y = 12*x

That is the equation for Mai.

While the number of feet in x inches, is given by:

y = x/12

That is Noah's equation.

So, technically, both of them are correct. Both of their equations relate dimensions in feet with equivalent dimensions in inches.

So the correct option is C.

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Answer:

y = - 3x - 28

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 )

y = [tex]\frac{1}{3}[/tex] x + 12 ← is in slope- intercept form

with slope m = [tex]\frac{1}{3}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3 , then

y = - 3x + c ← is the partial equation

to find c substitute (- 9, - 1 ) into the partial equation

- 1 = 27 + c ⇒ c = - 1 - 27 = - 28

y = - 3x - 28 ← equation of perpendicular line

The inequality that would represent this situation is 70+10x≥320 where x is the number of sales for Shane and the value of x will be ≥ 25.

According to the question,

We have the following information:

As a salesperson, Shane is paid $70 per week, plus $10 per sale. This week Shane want to make at least $320.

Let's take the number of sales needed to be made to be x.

Now, the following inequality will be used to represent this situation:

70+10x≥320

Now, subtracting 70 from both sides:

10x ≥ 320-70

10x ≥ 250

Dividing by 10:

x ≥ 25

Hence, the inequality that would represent this situation is 70+10x≥320 where x is the number of sales for Shane and the value of x will be ≥ 25.

Here is the complete question:

As a salesperson, Shane is paid $70 per week, plus $10 per sale. This week Shane want to make at least $320. Write the inequality to represent this situation and find the number of sales accordingly.

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When Sebatian has 379.33 buttons, Zoey has 2688.73 buttons, and Valeria has 1344.36 buttons, there will be a total of 4412.42 buttons.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here,

Let Sebastian have x button and Zoey have y button and Valeria have z button.

x+y=3068

x+z=2103

z=y/2

x+y=3068

x+y/2=2103

4x+y=4206

x+y=3068

3x=4206-3068

3x=1138

x=1138/3  

x=379.33

x+y=3068

379.33+y=3068

y=3068-379.33

y=2688.73

z=y/2

z=2688.73/2

z=1344.36

x+y+z=379.33+2688.73+1344.36

Total number of button=4412.42 buttons

The total number of buttons will be 4412.42 buttons when Sebatian have 379.33 buttons, Zoey have 2688.73 buttons, Valeria have 1344.36 buttons.

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Answer:91

Step-by-step explanation:

Formula for average is: (Unit 1 + Unit 2 + Unit 3) / 3

If we plug the values in we get

(91 + 88 + x) / 3 = 90

(179 + x) / 3 = 90

               *3    *3

179 + x = 270

x = 91

The value of function f (x) will be;

⇒ [tex]f (x) = - 2 x^{1/2} * 2 + 3x - 4[/tex]



Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division



Given that;

The value of function is,

⇒ [tex]f '' (x) = \frac{1}{x^{3/2} }[/tex]

And, f ' (4) = 2 , f (4) = 0

Now,

Since, The value of function is,

⇒ [tex]f '' (x) = \frac{1}{x^{3/2} }[/tex]

After integration we get;

⇒ [tex]f '(x) = - 2 x^{- 1/2} + c[/tex]

Here, f ' (4) = 2

Put x = 4 in above function, we get;

⇒ [tex]f '(x) = - 2 x^{- 1/2} + c\\2 = - 2 * 4^{- 1/2} + c\\ 2 = - 2/2 + c\\c = 3[/tex]

Hence, We get;

⇒ [tex]f'(x) = - 2x^{- 1/2} + 3[/tex]

Again integrating, we get;

[tex]f (x) = - 2 x^{1/2} * 2 + 3x + b\\f (x) = - 4 x^{1/2} + 3x + b[/tex]

Here, f (4) = 0

Put x = 4 in above function, we get;

[tex]f (4) = - 4 * 4^{1/2} + 3*4 + b\\0 = - 4 * 2 + 12 + b\\b = - 4[/tex]

So, We get;

⇒ [tex]f (x) = - 2 x^{1/2} * 2 + 3x - 4[/tex]

Thus, The value of function f (x) is,

⇒ [tex]f (x) = - 2 x^{1/2} * 2 + 3x - 4[/tex]



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The required linear function to model the amount of money in Iri's account at any time t using the simple interest formula is 185 + 5.55t.

An expense associated with borrowing money or other assets is interest.

The principal is the amount borrowed, and the interest is calculated as a percentage of the principal for a specific period of time.

If someone borrowed $1,000 at 2% interest and accumulated $100 in interest, the interest for that year would be $22.

It's because interest is paid on a total of $1100, which includes the principal ($1000) and accrued interest ($100). 2% of $1100 is $22.

So, in this situation, the checking account offers simple interest at a rate of 3% annually. Her account has $185 in it.

The total balance of the account will always be:

= 185 + (PRT/100)

P = principal

R = rate

T = time

Then,

= 185 + [(185 × 3 × t)/100]

= 185 + 5.55t

185 + 5.55t is the function.

Therefore, the required linear function to model the amount of money in Iri's account at any time t using the interest formula is 185 + 5.55t.

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Correct question:
Iris's checking account pays simple interest at 3% per year. She has $185 in

her account. Write a linear function to model the amount of money in her

checking account at any time t.

Answer:

See below.

Step-by-step explanation:

1) Combine Like Terms

-8w + 16x + 20w – 40x

= -24x + 12w

2) Apply the distributive property to simplify

the expression

8(12x – 20)

= 96x - 160

3) Add 7w – 12 and -15w + 60

= -8w + 48

4) Subtract 2w + 4 from 3w – 6

= 3w - 6 - (2w + 4)

= 3w - 6 - 2w - 4

w - 10

5) Solve for x:

7.2 + x = 18.1

x = 10.9

6) Solve for x:

x – 25 = -3

x = 22

Answer:

Step-by-step explanation:

1. Combine Like Terms

[tex]\tt -8w + 16x + 20w - 40x[/tex]

[tex]\tt 12w+16x-40x[/tex]

[tex]\boxed{\tt 12w-24x}[/tex]

2) Apply the distributive property to simplify:-

[tex]\tt 8\left(12x-20\right)[/tex]

[tex]\tt 8\times \:12x-8\times \:20[/tex]

[tex]\boxed{\tt 96x-160}[/tex]

3. Add 7w – 12 and -15w + 60:-

[tex]\tt 7w-12+ (-15)w+60[/tex]

[tex]\tt 7w-15w-12+60[/tex]

[tex]\tt -8w-12+60[/tex]

[tex]\boxed{\tt -8w+48}[/tex]

4. Subtract 2w + 4 from 3w – 6:-

[tex]\tt 2w+4-3w-6[/tex]

[tex]\tt 2w-3w+4-6[/tex]

[tex]\tt -w+4-6[/tex]

[tex]\boxed{\tt -w-2}[/tex]

5. Solve for x:-

[tex]\tt 7.2+x=18.1[/tex]

[tex]\tt x+7.2=18.1[/tex]

[tex]\tt x+7.2-7.2=18.1-7.2[/tex]

[tex]\boxed{\tt x=10.9}[/tex]

6) Solve for x:

[tex]\tt x - 25 = -3[/tex]

[tex]\tt x=-3+25[/tex]

[tex]\boxed{\tt x=22}[/tex]

_________________

Hope this helps you!

Have a nice day!

The equation of the inequality graph with dashed line

The equation of the inequality graph with solid line

Using the slope intercept form of the straight line which is of the form

y = mx + c

The slope, m is the ratio of the change in the output to the change in the input. This is given by the formula

m = (y₀ - y₁) / (x₀ - x₁)

Slope calculation using the points (0, -4) and  (2, 0)

m = (-4 - 0) / (0 - 2)

m = 2

y intercept, c from the graph

c = -4

applying inequality representations

shading above the line is greater than and dotted lines means it does not have equal to

hence y > 2x - 4

for the solid line graph

the slope, m calculating using the points on the graph (0, 4) and  (4, 0)

m = (4 - 0) / (0 - 4)

m = (4) / (-4)

m = -1

y intercept, c from the graph

c = 4

The equation of the line is y = -x + 4

Solid lines indicate an equality in the inequality, while shading over the line indicates a greater than

hence y ≥ -x + 4

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The measure of angle ∠C = 35°, 2x = 50° and x = 25°.

In Euclidean geometry, an angle is made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively.

Angles can be formed by two rays in the plane where they are placed.

Additionally, when two planes overlap, angles are created.

Dihedral angles are what they are called.

So, m∠ABC:

We know that ∠C in triangle ABC = 180 - 145 = 35°

Now, the measure of  m∠ABC:

95 + 35 + 2x = 180

130 + 2x = 180

2x = 180 - 130

2x = 50°

x = 50/2

x = 25°

Therefore, the measure of angle ∠C = 35°, 2x = 50° and x = 25°.

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Congruence is a property between two or more shapes that proves that they are equal in all respect. The required proof in the given question is shown below:

Two or more figures are said to be congruent if and only if they have equal length of sides, or measure of interior angles.

A triangle is a plane shape bounded by three straight sides, with three interior angles. The series properties can be used to classify the types of triangles with respect to their sides and angles. Some types of triangles are; equilateral, isosceles, right angled, acute angles scalene etc.

Thus to prove that: ΔADE ≅ Δ CDF

                               ΔBDE ≅ ΔBDF

AD ≅ DC (congruent property of similar figures)

AE ≅ CF (similarity property)

DE ≅ DF (congruent property of similar figures)

Thus,

ΔADE ≅ ΔCDF (SSS congruent property)

Also,

EB ≅ FB (congruent property of similar figures)

BD (common side of congruent figures)

DE ≅ DF (congruent property of similar figures)

So that,

ΔBDE ≅ ΔBDF (SSS congruent property)

This implies that,

i ΔADE + ΔBDE = ΔABD

ii. ΔCDF + ΔBDF = CBD

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The required parameters of a smaller surface area and a smaller amount of metal per can are a radius of 3.05 cm and a height of 6.09 cm.

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. A three-dimensional shape's surface area is the sum of all of its faces. Finding the area of each face and adding them together gives us the surface area of a form.

Here,

V=πr²h

178=πr²h

πrh=178/r

S=2πr²+2πrh

S=2πr²+2*(178/r)

S=2πr²+356/r

S'=4πr-356/r²

S'=0

4πr=356/r²

r³=356/4π

r³=28.343

r=3.05 cm

h=178/πr²

h=178/(3.14*3.05*3.05)

h=178/29.23

h=6.09 cm

The dimensions needed for less surface area so each can uses less metal is radius as 3.05 cm and height as 6.09 cm.

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Answer:

A

Step-by-step explanation:

Option A is the only Option with the correct domain.

Answer:

-----------------------------

Given three consecutive terms of a GP:

The middle term is the geometric mean of the other terms. Therefore:

The matching choice is D.

After the substitution 2(3y - 17) +3y = -7 is the answer of the system of equation.

One or many equation having same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given system of the equation,

x = 3y - 17      {equation 1}

2x + 3y = -7         {equation 2}

Substitute the value of x from the equation 1 to equation2,

2 (3y - 17) + 3y = -7

Therefore, after the substitution 2(3y - 17) +3y = -7 is the answer of the system of equation.

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The value of the given expression, 67π × 7, is 1473.4

From the question, we are to determine the value of the given expression.

From the given information,

The given expression is

67π × 7

To determine the value of the expression, we will evaluate the expression step-wisely.

Evaluate 67π

67π = 210.4867

Multiply by 7

210.4867 × 7

= 1473.4069

≈ 1473.4

Hence, the value is 1473.4

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Answer:

9.14 servings

Step-by-step explanation:

The question is asking how many servings of cereal does the box contain, or in other words, how many groups of 56 grams can you make from 512 grams.

To find out how many groups of 56 you can make, you need to divide 512 by 56:

512 ÷ 56 = 9.14

In the series of a value of a(4)=216

What do the terms sequence and series mean?

Mathematical sequence and series formulas pertain to several kinds of sequences and series. A series is the accumulation of the elements in a sequence, which is a group of arranged elements that follow a pattern. The formulas for the nth term and the sum are typically included in the sequence and series formulas.

Given that:

a(1) = 8

a(n)= 3a(n-1)

so a(4) = 3a(3) = 72*3 = 216

a(3)= 3a(2) = 24*3 = 72

a(2)= 3a(1) = 3*8 = 24

Hence a(4) = 216

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Answer:

[tex](2x-3)(4x^2+6x+9)[/tex]

Step-by-step explanation:

Given expression:

[tex]8x^3-27[/tex]

Rewrite 8 as 2³ and 27 as 3³:

[tex]\implies 2^3 \cdot x^3-3^3[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot c^b=(ac)^b[/tex]

[tex]\implies (2x)^3-3^3[/tex]

[tex]\boxed{\begin{minipage}{5cm}\underline{Difference of Cubes Formula}\\\\$a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)$\\\end{minipage}}[/tex]

Apply the Difference of Cubes Formula.

Therefore:

[tex]\implies (2x-3)((2x)^2+2x \cdot 3+3^2)[/tex]

[tex]\implies (2x-3)(4x^2+6x+9)[/tex]