Given the graphs of f(x) and g(z) below, find the composition of functions f(g(-1)).

Answer:

x = 2 - 5[tex]\sqrt{3}[/tex], x = 2 + 5[tex]\sqrt{3}[/tex]

Step-by-step explanation:

x² - 4x = 71

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 2)x + 4 = 71 + 4

(x - 2)² = 75 ( take the square root of both sides )

x - 2 = ± [tex]\sqrt{75}[/tex] = ± 5[tex]\sqrt{3}[/tex] ( add 2 to both sides )

x = 2 ± 5[tex]\sqrt{3}[/tex]

then

x = 2 - 5[tex]\sqrt{3}[/tex] , x = 2 + 5[tex]\sqrt{3}[/tex]

The number sentence is 5 - 7 and temperature at midnight is equal to -2°F .

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.

The temperatures are given at different time of a day. It is given that the final temperature was the temperature that existed at midnight. Firstly temperature rise between 6 AM and 3PM by 11° from - 6 °F at 6 AM and then between 3PM and midnight it fell by 7°.

So , we can show these variations as follows :

At 6AM temperature = - 6 °F

Between 6AM and 3 PM temperature rose by 11° , so temperature at 3 PM will be :

= - 6 + 11

= 5 °F

Between 3PM and midnight the temperature fell by 7° , so the number sentence will be :

= 5 - 7

And the temperature at midnight will be :

= -2°F

Therefore , the number sentence is 5 - 7 and temperature at midnight is equal to -2°F .

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A number in which value of 3 is ten times greater than the value of 3 is 375,786.

Here,

We have to find a number in which the value of the 3 is ten times greater than the value of the 3 in 135,864.

What is Place value?

Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

Now,

The value of 3 in 135,864 is 30,000.

And, We want to write a number that is ten times greater than 30,000.

Hence, We have to write any other number in which the value of 3 is 300,000.

Since, There are infinitely many numbers that we can write.

Some numbers are:

375,786

2,345,576

9,387,988  ........  and so on.

Therefore, A number in which value of 3 is ten times greater than the value of 3 is 375,786.

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Answer:

15-(6+7)

Step-by-step explanation:

Answer:

15 - (6+7)

Step-by-step explanation:

Answer:

Answer for this question is C because, 1 input has 2 outputs. And that's why C doesn't represent a function.

Error: They failed to account for when x-5 is negative.

Solution:

[tex]|x-5|<20 \\ \\ -20<x-5<20 \\ \\ \boxed{-15<x<25}[/tex]

Over the course of three weeks, she practiced for 609 minutes to become ready. The constant of proportionality is k=203.

Given that,

Rochelle planned out additional practice because she was getting ready for a big swim meet.

Over the course of three weeks, she practiced for 609 minutes to become ready. Every week she practiced for the same amount of time.

We have to find the constant of proportionality (k) between Rochelle's weekly practice time (w) and the number of minutes she practiced each week (m).

3 week =609 minutes

3w=609m

1w=609m/3

1w=203m

For 1 week she practiced 203 minutes.

Now,

Constant of proportionality is

m=kw

203=k(1)

k=203

Therefore, the constant of proportionality is k=203.

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By using multiplication, we get that the number of pounds of rice will be 19.8 pounds.

We are given that:

1 kg of rice = 2.2 pounds of rice.

We need to find the number of pounds of rice in 9 kg of rice.

So, we will use the operation of multiplication to covert the units from kg into pounds.

So, we get that:

9 kg of rice = 2.2 × 9 pounds of rice

9 kg of rice = 19.8 pounds of rice.

Therefore, by using multiplication, we get that the number of pounds of rice will be 19.8 pounds.

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The coordinates of the midpoint M of the line segment VW are M = (5, 6)

In this question,

We have been given a line segment having endpoints V(7, 2) and W(3, 10)

We need to find the coordinates of the midpoint M of the line segment VW.

We know that the midpoint of points (x1, y1) and (x2, y2) is

M = (x1 + x2 / 2, y1 + y2 / 2)

Using midpoint formula,

M = ((7 + 3) / 2, (2 + 10) / 2)

M = (10/2, 12/2)

M = (5, 6)

Therefore, the coordinates of the midpoint M of the line segment VW are M = (5, 6)

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Answer:

Yes, 14 × 216 = 3024

Step-by-step explanation:

Answer:

18/5 which also equals 3 3/5 would be the answer

One person took a loan A monthly payment is $530.65. An interest rate is 5.90%. APR is over 29 years. The present value of a loan is 100.69.

Given that,

One person took a loan

A monthly payment is $530.65

An interest rate is 5.90%

APR is over 29 years.

We have to find the present value of a loan

The formula for present value of a loan is

The present value (PV) formula is used in finance to determine the present worth of money received in the future. The compound interest formula serves as the foundation for the present value formula (PV formula). The formula for compound interest is,

PV = [tex]\frac{FV}{(1+\frac{r}{n)} ^{nt}}[/tex]

Where,

PV=present value

FV=future value

r= rate of interest

n=When frequently the amount compounds

t=time

Given FV=$530.65

r= 5.90% =0.059

t=29 years

n=1(Due to the amount's annual compounding).

PV=[tex]\frac{530.65}{(1+\frac{0.059}{1})^{1\times29} }[/tex]

PV=[tex]\frac{530.65}{(1+0.059)^{29}}[/tex]

PV=[tex]\frac{530.65}{(1.059)^{29}}[/tex]

PV=[tex]\frac{530.65}{5.27}[/tex]

PV=100.69

Therefore, The present value of a loan is 100.69.

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The length of the rectangular wall of a barn is 7 and the width is 17 feet

Area of the rectangular wall of a barn = 119 square feet

Length of the wall of the barn = width of barn + 10 feet

Let the width of the wall of the barn be x feet

So, the length of the wall of the barn will be x + 10 feet

The area of the rectangular wall of the barn is given by:

Area of the rectangular wall of the barn = Length of the barn * Width of the barn

119 = x*(x+10)

119 = x^2 +10x

0 = x^2 +10x - 119

Using splitting the middle term method

0 = x^2 + 17x - 7x - 119

0 = x(x + 17) - 7(x + 17)

x = 17 or 7.

Since the width is 10 feet more than the length

Therefore, the length of the rectangular wall of a barn is 7 and the width is 17 feet

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The coordinate of B is (1,-3)

In coordinate system mid point is the point which is exactly at the middle

The coordinates of point A are (5,1)

The coordinate of  mid point M are (3,-1)

It is to be noted that mid point divides both sides in the ratio 1:1

We are required to find the coordinates of point B

Let the coordinates of B be (x,y)

For mid points, section  formula further simplifies to

m's x coordinate= (a's x coordinate + b's x coordinate)/2

m's y coordinate = (a's y coordinate + b's y coordinate)/2

therefore,

3 = (5+x)/2

6=5+x

x=6-5 =1

-1 = (1+y)/2

-2 =1+y

y=-3

Hence the coordinates of B are (x,y) which is (1,-3)

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The distance of Neptune from the sun than Mercury will be B. Subtract the distances by getting the same power of 10: (4.5 x 10^10) - (5.8 x 10^7)-(4.5 x 10^10)-(.0058 x 10^10) = 44.99 x 10/10km.

From the information, Mercury is 5.8 x 10^7 km from the sun and Neptune is 4.5 x 10^10 km from the sun.

It should be noted that since we want to find the difference, therefore, we've to subtract.

Therefore, distance of Neptune from the sun than Mercury will be Subtract the distances by getting the same power of 10: (4.5 x 10^10) - (5.8 x 10^7)-(4.5 x 10^10)-(.0058 x 10^10) = 44.99 x 10/10km.

In conclusion, the correct option is B.

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Answer:

[tex]A_{new}=(-3,0)\\B_{new}=(0,-1)\\C_{new}=(1,-4)\\D_{new}=(-3,-5)[/tex]

Step-by-step explanation:

Looking at the diagram, you can see and determine the following points, write them down:

A=(-1,4)

B=(2,3)

C=(3,0)

D=(-1,-1)

Translating 2 units left means x changes by (-2)

Translating 4 units down means y changes by (-4)

Old Point + Point Change = New Point

[tex]A_{old}+T=A_{new}\\A_{old}=(-1,4)\\T=Translation=(-2,-4)\\A_{old}+T=(-1,4)+(-2,-4) = A_{new}=(-3,0)[/tex]

[tex]B_{old}=(2,3)\\C_{old}=(3,0)\\D_{old}=(-1,-1)\\T=(-2,-4)\\B_{new}=(2,3)+(-2,-4)=(0,-1)\\C_{new}=(3,0)+(-2,-4)=(1,-4)\\D_{new}=(-1,-1)+(-2,-4)=(-3,-5)[/tex]

The solution set to the inequality m-7>-2(m+0.5) is all real numbers greater than -0.75.

Real numbers are the set of all rational and irrational numbers, which includes all positive and negative numbers, fractions, decimals, and integers. They are represented on the number line and are composed of an infinite amount of numbers between any two given numbers.

This can be represented graphically on a number line by selecting a ray starting at -0.75 and extending infinitely in the positive direction. The point on the ray at -0.75 represents the boundary between the solution set and the numbers not included in the solution set.

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Answer:

  10.770

Step-by-step explanation:

You want the distance between points (-12,20) and (-22,16) using the distance formula.

The distance formula gives you the distance (d) between points (x1, y1) and (x2, y2).

  d = √((x2 -x1)² +(y2 -y1)²)

For the given points, the distance is ...

  d = √((-22-(-12))² +(16 -20)²) = √((-10)² +(-4)²) = √(100+16)

  d = √116 = 2√29 ≈ 10.770330

The distance between the given points is about 10.77 units.

Answer:

B. Irrational

Step-by-step explanation:

The √14 = 3.74 recurring. This isn't an integer and therefore can't be written as a fraction. Therefore it's an irrational number.

Whereas, if it was √16 which equals 4, the answer would be rational as it is an integer which can be written as a fraction such as 4/1 or 8/2 etc.

A line segment has two endpoints, whereas a ray has one endpoint and extends infinitely in the other direction, and a line extends infinitely in both directions.

Step-by-step explanation:

that's why it is so important to always write also the units a number represent.

and for a fully nice scientific notation you write also at least 1 digit after the decimal point.

(a) 6.0 × 10²⁴ kg

(b) 4.0 × 10² g

now,

1 kg = 1000 g ("kilo" means 1000)

so, in order to be able to compare the 2 numbers, you have to bring both numbers to the same unit. either both to kg or both to g.

6.0 × 10²⁴ kg = 6.0 × 10²⁴ × 1000 g = 6.0 × 10²⁷ g

or

4.0 × 10² g = 4.0 × 10² / 1000 kg = 4.0 × 10^-1 kg

once you have both showing the same unit, you can truly compare them.

The scientist should use 90 ounces of 35 percent solution and 120 ounces of water.

Percent is defined as the amount for a hundred units. Percentage is calculated by dividing the given amount by the total amount and multiplying by 100.

Let the scientist uses x ounces water.

Therefore the 35 percent solution is 210 - x.

Therefore the amount of salt in the 35 percent solution is 0.35 (210 - x )

The resulting mixture contains 15 percent salt.

Amount of salt = 15% of 210 =0.15 × 210 = 31.5 ounces.

Now 31.5 = 0.35 ( 210 - x )

or, 90 = 210 - x

or, x = 120 ounces

Therefore the 35 percent solution needed = 210 - 120 =90 ounces

Hence the scientist should use 90 ounces of 35 percent solution and 120 ounces of water.

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Answer:

x = -26

Step-by-step explanation:

[tex](f-g)(x)=\frac{4}{x-3}-\frac{3}{x+5}=\frac{3}{x^2 +2x-15} \\ \\ \frac{4(x+5)-3(x-3)}{x^2 +2x-15} \\ \\ =\frac{4x+20-3x+9}{x^2 +2x-15}=\frac{3}{x^2 +2x-15} \\ \\ \frac{x+29}{x^2 +2x-15}=\frac{3}{x^2+2x-15} \\ \\ x+29=3 \\ \\ x=-26[/tex]

This is in the domain of the equation, and is thus a solution.

Similar triangles are triangles which have the same corresponding angle measures and proportional side lengths. The value of x is 17.5.

Similar triangles are triangles which have the same corresponding angle measures and proportional side lengths.

Let PQ be the line between RS and RT.

Now PQR and RST are similar triangles.

RT/RP=RS/RQ

14/8=x/10

Use cross multiplication

14(10)=8x

140=8x

Divide both sides by 8.

17.5=x

Therefore x is 17.5.

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Answer:

when one of them is done

Step-by-step explanation:

you can't meet together because you don't run fast the

The standard deviation of the portfolio return is 3.14%

What is Sharpe ratio?

Sharpe ratio measures the by extent to which the risk of an investment portfolio is compensated as it indicates the return per unit of risk inherent in the portfolio whereas the standard deviation measures the risk of expected return of the portfolio.

It should be noted that the Sharpe ratio can be determined as the expected return of the portfolio minus the risk-free rate of return divided by the standard deviation of the portfolio.

Sharpe ratio=(expected return-risk-free rate)/standard deviation

Sharpe=2.99

expected return=12.9%

risk-free rate=3.5%

standard deviation=unknown(assume it is x)

2.99=(12.9%-3.5%)/x

2.99*x=9.40%

x=9.40%/2.99

x=3.14%

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The image of the transformation on the graph are (7, -7), (7, -2) and (-1, -14)

The graph represents the given parameter

On the graph, we have the coordinates of the triangle to be

(3, 1), (3, 6) and (-5, -6)

The transformation rule is given as

Translated 4 units to the right, and 8 units down.

Mathematically, the transformation rule is given as

(x, y) = (x + 4, y - 8)

When the above transformation rule is applied to the coordinates of the triangle, we have

(3 + 4, 1 - 8), (3 + 4, 6 - 8) and (-5 + 4, -6 - 8)

Evaluate the sum and the difference

So, we have

(7, -7), (7, -2) and (-1, -14)

Next, we plot the image of the transformation on the graph

See attachment for the image of the transformation of the triangle on the graph

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The two numbers that you would subtract to find the interquartile range (IQR) of the set of values are: A. 22 - 18.

The interquartile range (IQR) = Upper quartile (Q3) = lower quartile (Q1).

Given the data set, 17, 21, 19, 23, 16, 22, 19, 20, 24, 18, we have the following:

Upper quartile (Q3): 22 (center of the second half of the data)

Lower quartile (Q1): 18 (the middle/center of the first part of the data)

Interquartile range (IQR) = 22 - 18

Interquartile range (IQR) = 4

Therefore, the two numbers that you would subtract to find the interquartile range (IQR) of the set of values are: A. 22 - 18.

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