14. Find (f +g)(x) if f(x)=4 x²-5x and g(x)=3x²+6x-4.
(f +g)(x)=-x²+11x-4
(f +g)(x)=7x²+x-4
(f +g)(x)=x²-11x+4
(f +g)(x)=-x²-x⁴

10 - a + b = 2

We know that a = 3 and b = 14, so lets substitute this in.

10 - 3 + 14 = 2

7 + 14 = 2

21 = 2

This is incorrect.

This means that a \(\neq\) 3 and b \(\neq\) 14

I hope this helps! :)

Answer:

r = 7 mm

Step-by-step explanation:

given:

A cone that has volume 1026.25mm^3 and height 20mm.

Find:

the radius of the cone

solution:

volume of a cone = 1/3 π r² h

where

vol = 1026.25 mm³

h = 20 mm

plugin values into the formula:

vol. = 1/3 π r² h

1026.25 = 1/3 π r² (20)

r² =    1026.25  

        1/3 π  (20)

r = \(\sqrt{49}\)

r = 7 mm

therefore,

the radius of the cone = 7 mm

Answer:

7 mm

Step-by-step explanation:

volume = 1026.25mm^3

height 20mm.

vol. = 1/3 π r² h

1026.25 = 1/3 π r² (20)

r² =    1026.25 / (1/3 π  (20) )

r = 7 mm

radius of the cone = 7 mm

Answer:

11.8 =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj/ hyp

cos 25 = x/ 13

13 cos 25 =x

11.78200123 =x

11.8 =x

Answer:

C - 11.8

Step-by-step explanation:

Answer:

To determine the amount of engine oil needed, we need to find 5% of 3.8 gallons:

0.05 x 3.8 = 0.19

So, 0.19 gallons of engine oil should be added to the jerry can.

Answer:

9000

Step-by-step explanation:

Subtract the $9 from the total then divide by 2:

38-9 = 29

29/2 = 14.50

Answer: $14.50 each

Subtract the $9 from the total then divide by 2

38-9 = 29

29/2 = $14.50

              ^

For Rob Herndon to achieve his goal of paying off $430,000 in 10 years, he needs to make $34,186.97 at 5% compounded annually.

A future value refers to a value on a future date based on an assumed growth rate of interest over some period.

The future value can be determined using the FV formula or table.

We can also compute the future value using an online finance calculator as follows:

N (# of periods) = 10 years

I/Y (Interest per year) = 5%

PV (Present Value) = $0

FV (Future Value) = $430,000

Results:

PMT = $34,186.97

Sum of all periodic payments = $341,869.70

Total Interest= $88,130.30

Thus, for Rob Herndon to achieve his goal of paying off $430,000 in 10 years, he needs to make $34,186.97 at 5% compounded annually.

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Answer:

  -4

Step-by-step explanation:

If you multiply out the square, you can see ...

  (x +p)^2 = q

  x^2 +2px +p^2 = q

The coefficient of the x-term is 2p, so ...

  2p = -8

  p = -8/2 = -4

For given triangle, x is 4√5 using Pythagorean theorem.

What is Pythagorean Theorem?

Pythagoras Theorem (also known as Pythagorean Theorem) is a mathematical concept that explains the relationship between the sides of a right-angled triangle. The sides of a right triangle are also referred to as Pythagorean triples. This theorem's formula and proof are discussed with examples here.

The Pythagorean theorem is used to calculate the length of an unknown side and the angle of a triangle. We can deduce the base, perpendicular, and hypotenuse formulae from this theorem.

The Pythagoras Theorem formula is presented in the definition as:

Perpendicular² + Base² = Hypotenuse²

c² = a² + b²

Now,

Given that perpendicular =19

Hypotenuse=21

then Base²=21²-19²  using Pythagoras theorem

Base=√441-361

=√80

=4√5

Hence,

          x is 4√5

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60 inches²

A₁ = l×w = 15 in²

A₂ = 2l×2w = 4lw

replace lw

A₂ = 4×lw = 4×15in² = 60 inches²

The area after dilation is 60 sq.inches.

The area of rectangle for a rectangle of length L and width W is given by

                                               A =  L* W

It is measured in square units.

The area of a rectangle is 15 sq.inches

The rectangle is dilated by a scale factor of 2.

If the length and width of the rectangle is L and W.

The new length = 2L

The new width = 2W

The new area = 2L * 2W

Area = 4 * LW

Area = 4 * 15

Area = 60 sq.inches

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The given options, the only value greater than 1 is 1.003. Therefore 0.886, which is less than 1 and makes the inequality true.

The given number sentence is 5.3 × > 5.3, where we need to find the scaling factor that makes the inequality true. To do this, we can divide both sides of the inequality by 5.3. This gives us:

5.3 × x > 5.3 ÷ 5.3 × k

We need to find the value of k that makes the inequality true. Simplifying the right-hand side of the equation, we get:

5.3 ÷ 5.3 × k = k × 1 = k

Substituting this into our equation, we get:

5.3 × x > k

We know that 5.3 × 1 = 5.3, which means that k must be greater than 1 to satisfy the inequality. Among the given options, the only value greater than 1 is 1.003. However, this value would make the inequality too large, so it is not the correct answer.

The correct answer is therefore 0.886, which is less than 1 and makes the inequality true.

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Answer:

A. The theoretical probability of spinning any one of the five colors is 20%.

C. The theoretical probability of spinning green is equal to the experimental probability of spinning green.

E. If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.

These are the answers on edg 2020, just took the test.

Step-by-step explanation:

Answer:

a, c, e,

Step-by-step explanation:

:)

Answer:

x = 80

Step-by-step explanation:

supplementary angles sum to 180°

sum the 2 angles and equate to 180

x + 40 + x - 20 = 180

2x + 20 = 180 ( subtract 20 from both sides )

2x = 160 ( divide both sides by 2 )

x = 80

Answer:

Step-by-step explanation:

Set up an equation:

7x + 10x + 13x = 100000 and solve for x:

30x = 100000 so

x = 3333.33

Anna gets 7(3333.33) = 23333.31

Louise gets 10(3333.33) = 33333.33

Lacey gets 13(3333.33) = 43333.29

Answer:

1008.5 cans

Step-by-step explanation:

2019/2=1008.5

if you wanted per day, 1008.5/365=2017/730

Answer:

3rd option is the amswer

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Step-by-step explanation:

\( {a}^{2} + {b}^{2} = {c}^{2} \\ {9}^{2} + {40}^{2} = {41}^{2} \\ 81 + 1600 = 1681 \\ 1681 = 1681\)

Step-by-step explanation:

you draw a circle ⭕ then you do lines inside the circle the you write the numbers aside

The linear program shows that there are different attainable arrangements that accomplish the same ideal objective function value..

Based on the given data, since the objective function values at the five corner points are diverse, able to conclude that there's no one-of-a-kind ideal arrangement for this linear program.

The reality that there are numerous distinctive objective function values at the corner points suggests that there are numerous ideal arrangements or that the objective work isn't maximized or minimized at any of the corner points.

In this case, the linear program may have numerous ideal arrangements, showing that there are different attainable arrangements that accomplish the same ideal objective function value.

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It is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in
the graph intersecting the x- or y-axis at a different point.

Function is an operation that takes an input, performs some processing on it, and returns a result. It is a set of instructions that performs a specific task. Functions are typically used to perform repetitive tasks, like finding the sum of two numbers, adding two strings together, or finding the maximum of a list of numbers. Functions are essential to programming and can be used to make code more organized, reusable, and efficient.


The function f(x) = x is the parent function for linear equations. This equation is generally used to graph a line with a slope of 1 and a y-intercept of (0, 0). In order to translate this parent function, different transformations are applied to it.

A vertical translation down 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function down 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, -4).

A horizontal translation right 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function right 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (4, 0).

A horizontal translation left 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function left 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (-4, 0).

Finally, a vertical translation up 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function up 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, 4).

In conclusion, it is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in the graph intersecting the x- or y-axis at a different point.

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The inequalities which satisfy the number line shown is x>2 and x>=2.

We are given that;

The number line showing inequality

Now,

x>2 satisfies the equation by the given number line

x>=2 satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

Therefore, by the number line the answer will be x>2 and x>=2 .

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7) The  probability that the two numbers have an even sum is: 0.5

8) The probability that the two are even is: 0.25

7) We want to find the probability that the two numbers have an even sum.

The only combinations that produces an even sum are:

(1, 3), (3, 1), (1, 1), (2, 2), (2, 4), (4, 2), (4, 4), (3, 3)

The other combinations of numbers are:

(1, 2), (1, 4), (2, 1), (4, 1), (2, 3), (3, 2), (3, 4), (4, 3)

Thus, we have a total of 16 combinations and the  probability that the two numbers have an even sum is:

P(two numbers with even sum) = 8/16 = 0.5

8) The probability that the two are even is:

4/16 = 1/4

= 0.25

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according to the question the volume of the right rectangular prism is 67.5 cubic inches.

Volume is characterized as the space involved inside the limits of an article in three-layered space. The capacity of the object is another name for it.

A right rectangular prism's volume can be calculated by multiplying its lengths, width, and height. The prism's measurements are 3, 3/4, 5, & 4 1/2 inches.

First, we need to convert 4 1/2 to an improper fraction:

4 1/2 = (4 x 2 + 1)/2 = 9/2

Now, we can multiply the dimensions together to find the volume:

Volume = length x width x height

Volume = 3 x 3/4 x 5 x 9/2

Volume = 67.5 cubic inches

Hence, the bottom rectangular prism has a 67.5 cubic inch volume.

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Answer:

79/9 or 8.4 or 8 4/9

Step-by-step explanation:

Answer:

Well, parallel lines have the same slope so I think the second option is the answer

From the histogram, we get that 30.88% of students scored between 50 and 70 points on the exam.

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

From the histogram:

\(\frac{21}{68} = 0.3088\)

0.3088 x 100% = 30.88%

30.88% of students scored between 50 and 70 points on the exam.

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Answer:

Solution given:

< 1+ 83°= 180 [co- interior angle]

<1=180-83=97°

<1=97° is your answer

The image of the labeled spinner isn't attached

Answer:

Kindly check explanation

Step-by-step explanation:

Answering hypothetically ;

First create a sample space using the label of the two spinners ;

Each space will be the sum of the possible number that shows up on each turn of the spinner.

From the sample space, count the number of spaces where, the sun is greater than 4, that is the required outcome ; = x

Then the total number of samples in the sole space = total possible outcomes = y

Hence,

P(obtaining a sum greater than 4) = required outcome / Total possible outcomes

= x / y