Given the functions:
f(x) = 2x^2
g(x) = 3x - 2
h(x)= -4x+5

Evaluate: f(g(h(2)))

A 162
B. 242
C. -44
D -123

A) Check the graph below, please. B) Horizontal translation to the left in 2 units. C) Vertical shift 4 units

1) Given that we have the function h(x) = |x+2| and g(x)= |x| + 4

A) Let's set a pair of tables, and pick 3 arbitrary values for x and then plug into each one

h(x) = |x+2|

x | y = |x+2|

-1 | 1 y =|-1 +2| = |1| = 1

0 | 2 y =|0+2| = |2| = 2

1 | 3 y =|1+2| = |1| = 1

g(x) =|x| + 4

x | y

-1 | 5

0 | 4

1 | 5

Let's plot those absolute value functions:

B) Considering the parent function f(x) =|x| we can notice that h(x) is a translation to the left, in two units. This we can see better this way:

Note that f(x) is in red, and h(x) in pink or light red.

C) Considering that f(x) = |x| we can see that g(x) = is a vertical shift 4 units up.

To find the numerical value of the expression, we have to replace the variables for their given values. This way:

The numerical value of the expression is 85.

1 .

Notice that 3/7 is close to 1/2 and 5/9 is also close to 1/2.

Therefore, an estimate for 3/7 + 5/9 is 1/2 + 1/2 = 1.

To estimate fractions using mental math, start by simplifying the fraction to the lowest possible denominator. Then, look at the fraction and round it to the nearest fraction that you feel comfortable working with which could be ¼, ⅓, ½, ¾, or even 1.

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ANSWER

Atlanta is 20.62 miles away from the starting point

EXPLANATION

This is a diagram of this problem

We're looking for the hypotenuse of this right triangle. Using the Pythagorean theorem:

Part a

Remember that the ordinate is the y-coordinate and the abscisa is the x-coordinate

so

(x, 2x+1)

y=2x+1

Part b

x=(1/2)y^2

Part c

x^2+y^2=25

Part e

y=2

Part f

x=7

Part g

x=y

Part h

Part i

3 per thousand?

10000 ------------------------- 1000

x ------------------------ 3

x = (3 x 10000)/1000

x = 30000/1000

x = 30

The answer is 30

ANSWER

The system has no solution

EXPLANATION

We want to find the solution to the system of equations given:

From the first equation, make x the subject of the formula:

Substitute that into the second equation and simplify:

As we can see, the two sides of the equality sign have two different values.

This implies that the system of equations has no solution.

Given:

Commutative law of addition.

2 only is the correct answer.

Answer: Balloon B

Step-by-step explanation:

The distance, in feet, is always four times the time, in seconds.

The root mean square velocity of Neon, in m/s as required in the task content is; 18.45 m/s.

It follows from the task content that the root mean square velocity of Neon is to be determined.

Since the molar mass of Neon is; 20 while the gas constant, R = 8.314 and T = 273K.

It follows from the root mean square velocity formula that we have;

R.M.S = √(3RT/M)

R.M.S = √{(3×8.314×273)/20}

R.M.S = √340.46

R.M.S = 18.45 m/s.

Hence, the root mean square velocity of Neon, Ne under the given condition is; 18.45 m/s.

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Let's rewrite it the first one

When we apply, log on both sides. We have the logarithm of a power equal to its exponent that is why we have y on the left side.

Rewriting the second one:

Since the Natural Logarithm is log in the base "e" we can say that x is equal to e raised to 9

X₁: science GPA for those who left their profession after graduation

X₂ science GPA for those who remained in their profession after graduation.

The working hypothesis is that the GPA of those who stayed is higher than those who left.

Which is the same as saying that the GPa of those who left is less than those who stayed.

μ₁ represents the population mean of the science GPA of those who left.

μ₂ represents the population mean of the science GPA of those who remained.

Part one

You can express the working hypothesis as follows:

The hypothesis does not include the equal sign, so this hypothesis can be considered as the alternative hypothesis.

The null hypothesis of this test will be the complement of the alternative hypothesis, and always carries the equal sign within. So if the alternative hypothesis states that "the mean of the leavers is less than the mean of the stayers", then the null hypothesis will be that "the mean of the leavers is greater than or equal to the mean of the stayers" you can symbolize this as:

Since the null hypothesis carries the equal sign you can also write it as:

Both options are equally valid.

So, the second answer is null hypothesis.

Part two

Considering that we are studying the population means of two normal variables and that we know the population standard deviation for both populations, the test statistic to use is the standard normal for the difference of means which is defined as follows:

Subindex 1 indicates the values corresponding to the "leavers":

X₁bar= 3.16

n₁= 103

σ₁= 0.52 → σ₁²= 0.2704

Subindex 2 indicates the values corresponding to the "stayers":

X₂bar= 3.28

n₂= 225

σ₂= 0.46 → σ₂²= 0.2116

Under the null hypothesis both population means are equal, which means that their difference is equal to zero:

If μ₁ = μ₂, then μ₁ - μ₂ = 0

Replace all values on the formula to determine the Z-value under the null hypothesis, i.e. the test statistic:

SOLUTIONS

The parallel line will be of form

the equation of the line that passes through the point (1/7,1) and is parallel to the line −4y−3x=−3

The equation of the line parallel to point(1/7 , 1)

Step 1:

Write the given vectors

Step 2

Resultant vector = [ 10 + (-6) , 9 + (-2) ]

= ( 4 , 7 )

Resultant vector = 4i + 7j

Step 3

Step 4:

Answer:

3x^5y^8

Step-by-step explanation:

so the cube root of 27 is 3

to find the cube root of x^15 divide the exponent by 3 which gets you x^5

do the same thing for y^24 and that gets you y^8

mhm and i think thats right

The heighth of the cylinder if the surface area is 942 square feet is 25 feet.

From the information given, the S = 2π(25) + 2π(5h). We are to find the heighth of the cylinder if the surface area is 942 square feet.

This will be:

S = 2π(25) + 2π(5h).

2π(25) + 2π(5h) = 942

50π + 10πh = 942

(50 × 3.14) + (10 × 3.14 × h) = 942

157 + 31.4h = 942

Collect like terms

31.4h = 942 - 157

31.4h = 785

h = 785/31.4

h = 25

The height of the cylinder is 25 feet

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Answer:

47/68

Step-by-step explanation:

total candies=136

not red candies=94

94/136=47/68

The equation for the given summation is:

   [tex]\sum_{n=1}^4 u_n = u_1 + u_2 + u_3 + u_4[/tex]

Here we have a summation of unknown terms of the form:

uₙ

That summation goes between n = 1 and n = 4, this means that we will have a sum of 4 terms, such that:

[tex]\sum_{n=1}^4 u_n[/tex]

Means that we need to sum the terms u₁, u₂, u₃, and u₄, then we can write the equation:

[tex]\sum_{n=1}^4 u_n = u_1 + u_2 + u_3 + u_4[/tex]

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Input data

Graph

Procedure

y-intercept

Y-Intercept of a Straight Line. Where a line crosses the y-axis of a graph.

(0, -6)

x-intercept

The x-intercept is the point where a line crosses the x-axis

(-8,0)

We have the next information

Let X be the number of customer purchased coffee

Let Y be the number of customer pwho urchased donuts

X∩Y Then is the number of customers who purchased both coffee and donuts

X∪Y is the number of customers who purchased both coffee or donuts

The number of customers who purchase only coffee is

48 customers purchased only coffee

The number of customers who purchase only donuts is

22 customers purchased only donuts

In order to know how many customers did not purchase either of these items

First we will calculate the customers that purchase something

then we know that the total number of customers is 110

21 customers did not purchase either of these items

The speed of the cyclist in miles per hour is 7.5 miles per hour. The distance covered by the cyclist in 5 hours is 30 miles.

According to the question,

We have the following information:

A cyclist rides his bike at the speed of 11 ft per second.

Now, it is given that we have to use 1 mile = 5280 ft.

So, we have:

1 ft = 1/5280 miles

We know that there 3600 seconds in 1 hour.

1 seconds = 1/3600 hour

So, we  have the speed in miles per hour:

11*(1/5280)/(1/3600)

(11*3600)/5280

7.5 miles per hour

Time taken = 5 hours

Speed = 7.5 miles per hour

Distance = speed*time

Distance = 7.5*5

Distance = 30 miles

Hence, the speed of the cyclist in miles per hour is 7.5 miles per hour. The distance covered by the cyclist in 5 hours is 30 miles.

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In order to solve the expression:

We operate inn such a manner that x is left alone, that is:

We have our expression 9 - 2x = 35.

In order to solve for x, we try and leave x alone, that is, we sustract 9 from both sides of the operation:

9 - 9 - 2x = 35 -9 => -2x =26

Now that we have this, we proceed to eliminate -2 from the side of x, for that we divide both sides by -2, that is:

(-2/-2)x=(26/-2) => x = -13

Lin says that about 6.2 x 10^5 more people live in San Jose than in Atlanta. To find if she is right you substract the population of Atlanta from the population in San Jose:

Substraction of numbers in scientific notation:

1. Turn the numbers to get the same power of base 10.

You move to the left the decimal to increase the power of base 10 and move to the right to g

6 bracelets Eva can make with the yarn she has left with .

The equation is [tex]\frac{3n}{2}=9[/tex]

Algebra is a branch of mathematics that helps translate real-world situations or problems into mathematical truths. Mathematical operations like addition, subtraction, multiplication, and division are needed in addition to variables like x, y, and z to construct a meaningful mathematical expression. All branches of mathematics, such as calculus, trigonometry, and coordinate geometry, employ algebra. A fundamental algebraic expression is 2x + 4 = 8, which results from operations like addition, subtraction, multiplication, and division on variables and constants. Algebraic expressions are obtained as the mathematical statement.

Eva has 11 meters of yarn and she gives 2 meters of the yarn to her friend

Now she left with 11 -2 = 9

As Each bracelet uses [tex]\frac{3}{2}[/tex] meters of yarn

n braclet = [tex]\frac{3n}{2}[/tex]

9= [tex]\frac{3n}{2}[/tex]

n = [tex]\frac{18}{3}[/tex]

=6

6 bracelets Eva can make with the yarn she has left with .

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The first equation is increasing at highest rate.

Which function has highest increasing rate?

We can know which function has the highest rate of increase by looking at its slope. The function with the highest slope will have the highest rate.

In equation first m = 2 and is highest among every slope.

12x - 6y = -24

-6y = -12x -24

y = 2x +4

m = 2 (increasing)

In second equation m = 1

m = (-4 + 5)/(2-1) = 1

for a straight line function , the slope is given by

m = ( y₂ -y₁)/(x₂-x₁)

m = ( -3 -3)/(2- (-1)) = -6 /3 = -2

Therefore the function is decreasing

8,0) (0,-4)

m = (-4 -0) /(0-8) = 4/8 = 1/2

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Isosceles triangle have 2 equal lengths

Square or Rectangle have 4 equal teiangles

Isosceles trapezoid also divides

Then answer is

Isosceles trapezoid. Option A)

Given:

Given the diagram

Required: The measure of angles 1, 2 and 3.

Explanation:

The sum of interior angles of a triangle is 180 degrees. So,

The angles x and 1 are supplementary angles, that is, the sum of angles 1 and x gives 180 degrees.

The angle 2 is the opposite angle of 55 degrees. Hence angle 2 equals 55 degrees, that is,

Angle y and 150 degrees are supplementary angles. So,

The sum of the interior angles of a triangle equals 180 degrees.

Final Answer:

Answer:

1018.3

Step-by-step explanation:

The volume of a cylinder=πr2h

=22\7*6*6*9

=1018.3

therefore, the of the cylinder is 1018.3

The domain of a function is the set of x values the function uses as inputs; from a graph the domain is the x-values that the graph take on the x-axis; in this case, since we have an infinite amount of x-valeus the function uses we will write the domain as an interval. The domain is:

Similarly, the range is the set of values the function takes on the y-axis, from the graph we notice that the range is:

The equation to describe the relationship between the height of the plant and the number of weeks is

y = x + 5

Given,

The height of the plant = x

The number of weeks = y

The height of plant at 6th week = 11 inches

The height of plant at 8th week = 13 inches

The height of plant at 10th week = 15 inches

We have to find the equation to describe the relationship between the height of the plant and the number of weeks.

Lets see,

x = 6 and y = 11, y – x = 11 – 6 = 5

x = 8 and y = 13, y – x = 13 – 8 = 5

x = 10 and y = 15, y – x = 15 – 10 = 5

That is,

y – x = 5.

y = x + 5

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