Mathematics College

The functions f(x) and g(x) are shown on the graph.f(x)=x^2What is g(x)?A. g(x)=(x+3)^2B. g(x)=(x-3)^2C. g(x)=(1/3x)^2D. g(x)=3x^2

Answers

Answer 1

Given:

[tex]f(x)=x^2[/tex]

Let's find g(x).

From the given graph, we can see the graph of g(x) is compressed horizontally from f(x).

Thus, to find g(x) aply the transformation rules for function.

We have:

Horizontal compression of b units ==> f(bx)

Given the point on g(x):

(x, y) ==> (2, 12)

Let's solve for the value of the compressed factor.

We have:

[tex]\begin{gathered} 12=b(2)^2 \\ \\ 12=b4 \\ \\ \text{Divide both sides by 4:} \\ \frac{12}{4}=\frac{b4}{4} \\ \\ 3=b \\ \\ b=3 \end{gathered}[/tex]

This means the graph of f(x) was compressed horizontally by a factor of 3 to get g(x).

Thus, to write the function for g(x), we have:

[tex]g(x)=3x^2[/tex]

ANSWER:

[tex]D\text{.}g(x)=3x^2[/tex]

Related Questions

In parallelogram PQRS, diagonals PR and QS intersect at point T.Which statement would prove PQRS is a rhombus?PT > QTPT QTPR QSSTQT

Answers

We can have more arguments to prove that PQRS is a rhombus, but, the argument that we will use here is:

Let's look at the first statement, we have

[tex]PT>QT[/tex]

That's not correct, it would just prove that QR/2 > PS/2,

[tex]PR=QS[/tex]

This statement implies

[tex]\begin{gathered} PR^2=QS^2 \\ \\ PS^2+SR^2=PQ^2+QR^2 \end{gathered}[/tex]

We cannot conclude that

[tex]PS=SR=PQ=QR[/tex]

The next statement is

[tex]PT=QT[/tex]

A rhombus can have different diagonals, and in fact they have. Then let's go to the next one

[tex]ST=QT[/tex]

That also not exactly says it's a rhombus, it's a pallelogram property.

[tex]\angle SPT=\angle QPT[/tex]

By doing that we have that the diagonal bissects the angle

That implies that the angle b is also bissect.

The last statment is

[tex]\angle PTQ=\angle STR[/tex]

That's literally the vertex angle, it's true always, not only in that case, therefore the only possible answer is

[tex]\angle SPT=\angle QPT[/tex]

Pro

What is special about a unit circle? How does this help us when finding the six trigonometric ratios?

Answers

Answer:

A circle is a closed geometric figure without any sides or angles. The unit circle has all the properties of a circle, and its equation is also derived from the equation of a circle. Further, a unit circle is useful to derive the standard angle values of all the trigonometric ratios.

Step-by-step explanation:

Help me pleaseeee quicklyyyyy

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∠6 and ∠5 are alternative interior angle thus the measure of angles ∠5 = 45° , ∠6 = 45° ,∠7 = 45° and ∠8 = 135°.

What is an angle?

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

Angles 1,2,7 are the interior angles of a triangle and we know that the sum of all interior angles inside a triangle is 180°.

Therefore, ∠1 + ∠2 + ∠7 = 180°

Given, ∠1 = 70° and ∠2 = 65°

∠7 = 180° - (70 + 65) = 45°

Now, ∠8 = 180 - ∠7 ⇒ ∠8 = 135°

Now, ∠7 = ∠6 (vertical opposite angle) so ∠6 = 45°

∠6 = ∠5 (alternative interior angle) so ∠5 = 45°

Hence "∠6 and ∠5 are alternative interior angle thus the measure of angles ∠5 = 45° , ∠6 = 45° ,∠7 = 45° and ∠8 = 135°".

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Writing the equation of the line through two given points(1,-3) (5,-1). y=mx+b form

Answers

Given points (1,-3) and (5,-1).

Since the slope of the line passing through two points

[tex](x_1,y_1)(x_2,y_2)[/tex]

The slope of the equation is

[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-1-(-3)}{5-1} \\ m=\frac{2}{4} \\ m=\frac{1}{2} \end{gathered}[/tex]

Therefore, the slope of the line is 1/2.

Now, use the slope and the point (1,-3) to find the y-intercept.

[tex]\begin{gathered} y=mx+c \\ -3=\frac{1}{2}\times1+c \\ c=-3-\frac{1}{2} \\ c=-\frac{-7}{2} \end{gathered}[/tex]

Write the equation in slope-intercept form as

[tex]\begin{gathered} y=mx+c \\ y=\frac{1}{2}x-\frac{7}{2} \end{gathered}[/tex]

Which of the following sets of ordered pairs lies on the y-axis of a coordinate grid?

Answers

Solution

for this case the point that lies on the y axis need to satisfy that the x coordinate must be:

x= 0

then the best solution would be:

(0, -4)

I need help on this and no this isn't a quiz

Answers

Concept:

Parallel planes are planes in the same three-dimensional space that never meet.

Parallel Lines or parallel Segments are always the same distance apart, they will never meet.

skew lines are two lines that do not intersect and are not parallel.

Question: Name a plane parallel to plane PQR:

Answer: plane JKL

Question: Name a segment parallel to segment KP:

Answer: segment OJ

Question: Name a segment that is skew to OJ

Answer: segment SR

Speeds of Cars (in miles per hour)Intersection 1Intersection 2十十十十18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34• Part 1: Find the range of intersection 1 as a way to measure the variability of the data, showing your work. Remember, range isfound by taking the largest value minus the smallest value. (2 points)• Part 2: Find the range of intersection 2 as a way to measure the variability of the data, showing your work. Remember, range isfound by taking the largest value minus the smallest value. (2 points)

Answers

PART 1)

Range of intersection 1

(Max value - Min value )=

Largest value = 31 , Lowest value = 26

Then range1 is 31 - 26 = 5 miles /hour

Now PART 2:)

Maximum value= 27

Minimum value = 22

Then range2 is 27-22 = 5 miles/hour

Given the following piecewise function, determine the value of g(4) - 3g(3).

Answers

Piecewise Function

We are given the piecewise function shown in the figure.

We are required to calculate g(4) - 3g(3).

First, we calculate g(4). Since 4 is greater than 3, we use the second function:

[tex]g(4)=4^4+4^2+4-3=273[/tex]

Now we need to calculate g(3). We use the same function because 3 is greater or equal to 3:

[tex]g(3)=3^4+3^2+3-3=90[/tex]

Now we calculate:

g(4) - 3g(3) = 273 - 3*90 = 273 - 270 = 3

Answer: 3

hey can anyone help me on this im failing school xd

Answers

slope of line is -3 for points (1,0) and (0,3)

What is Slope of Line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From graph let us take two points (1, 0) and (0, 3)

x₁=1, x₂=0, y₁=0,y₂=3

Substitute these values in slope formula

m=3-0/0-1

m=3/-1

m=-3

Hence slope of line is -3.

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8 O 6 4. N Which function is graphed? 2. 4 6 8 -8 -6 -4 -2 0 -2 -6 O A. Y- (x² + 4, x=2 1-x+4,452 (x² + 4, x2 OD. V- x + 4, x32 1-x+4,4

Answers

The given curve is parabola and its last point is on the x axis at x = 2

So, the equation of curve is :

[tex]x^2+4,x<2[/tex]

In the equation of line,

The line start from x = 2 so, x ≥ 2

So, Equation of line is : -x + 4, x ≥ 2

Answer : B)

[tex]y=\begin{cases}x^2+4,x<2 \\ \square \\ -x+4,\text{ x}\ge2\end{cases}[/tex]

a teacher asks 15 students to estimate an answer to a question the answers or 1, 5, 5, 6, 7, 8, 10, 12 the correct estimate is 7 the teacher wants to calculate how far of the estimate were by finding the absolute value of the difference between each estimate and the answer which estimate was off by the most

Answers

We have the following estimations:

1, 5, 5, 6, 7, 8, 10, 12

The absolute value between each estimate and the answer is calculated as:

Estimate Absolute

Answer value

1 |1-7| = |-6| = 6

5 |5-7| = |-2| = 2

6 |6-7| = |-1| = 1

7 |7-7| = |0| = 0

8 |8-7| = |1| = 1

10 |10-7| = |3| = 3

12 |12-7| = |5| = 5

So, the estimated answer that was off by the most is 1.

Solve the system using addition. Use pencil and paper. Explain why the addition method is a good choice for solving the system. If you wanted to solve for x first, is the addition method still a good choice? Explain. X-4.6y = - 8.8 -x+2.9y = 3.7 The solution is. (Type an order

Answers

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Which value of x proves that the two triangles above are similar? 42.7 ft 26.7 ft 10 ft 25.6 ft

Answers

[tex]x=26.7\text{ ft}[/tex]

Explanation

Step 1

we have two triangles

ACE and BCD

if the triangles are similar, then the ratio of the sides must be the same:

[tex]\begin{gathered} \frac{\text{red line}}{purple\text{ line}}=\frac{blue\text{ line}}{\text{green line}} \\ \text{replacing} \\ \frac{16+x}{32}=\frac{x}{20} \end{gathered}[/tex]

Step 2

solve for x

[tex]\begin{gathered} \frac{16+x}{32}=\frac{x}{20} \\ \text{cross multiply} \\ 20(16+x)=32\cdot x \\ 320+20x=32x \\ \text{subtrac 20x in both sides} \\ 320+20x-20x=32x-20x \\ 320=12x \\ \text{divide both sides y 12} \\ \frac{320}{12}=\frac{12x}{12} \\ \text{ x=26.66} \end{gathered}[/tex]

rounded

[tex]x=26.7\text{ }[/tex]

I hope this helps you

west high schools population is 250 students fewer than twice the population of east high school. the two schools have a total of 2858 students. how many students attend east high school?

Answers

From properties of linear equation, 1036 students attend east high school.

What is linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

Let east high school have x students

West high school have 2x - 250

Total count of students from both the schools are 2858 students.

Then we get

x + 2x-250 = 2858

=> 3x - 250 = 2858

=> 3x = 2858 + 250

=> 3x = 3108

=> x = 3108/3

=> x = 1036

Therefore, 1036 students attend east high school.

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jamals lawn is shaped like a square with an area of 224.9ft2 .which measurement is closest to the side length of his lawn in feet

Answers

We use the formula for the area "A" of a square with equal sides of length "l":

[tex]A=l^2[/tex]

Since we know the value of the area is:

[tex]A=224.9ft^2[/tex]

We substitute that value into the formula for the area:

[tex]224.9ft^2=l^2[/tex]

Next, we take the square root of both sides of the equation:

[tex]\sqrt[]{224.9ft^2}=\sqrt[]{l^2}[/tex]

On the right side, the exponent and the square root will cancel, and we will get "l", and on the left side, we calculate the square root:

[tex]14.99ft=l[/tex]

Which can be rounded to the closest value, that is 15 ft.

Answer: 15 feet

Make a tree diagram, Please complete number 18.Please be quick, I am in a hurry.

Answers

Explanation:

The question wants us to list out all the possible outcomes in question 18

From the question

We have a spinner that has 5 possible outcomes

[tex]\mleft\lbrace\text{Red, Orange, Green, Purple, Yellow}\mright\rbrace[/tex]

The outcomes of flipping a coin are

[tex]\begin{gathered} \mleft\lbrace\text{Head, Tail}\mright\rbrace\text{ } \\ \text{which can be written as} \\ \mleft\lbrace H,T\mright\rbrace \end{gathered}[/tex]

Thus, to get the possible outcomes, we will have

Mr. Ocana drove 15 miles to go to work last week. Due to construction on the road, this week he drove 21 miles to go to work. What is the percent increase in the number of miles he drove to work this week? О 40% 50% ООО 60% O 70%

Answers

ANSWER:

40%

STEP-BY-STEP EXPLANATION:

In this case, what we must do is calculate the percentage that represents 21 miles, assuming that 100% is 15 miles, like this

[tex]21\cdot\frac{100}{15}=140\text{\%}[/tex]

Now we subtract 100% from this value, like this:

[tex]140\text{\%}-100\text{\%}=40\text{\%}[/tex]

18. The surface area of a cone is 12611 square meters. The diameter of the 5 points cone's circular base is 22 meters. What is the lateral area of the cone? Round your answer to the hundredths place value. * A 1 5 7 1 +/- B 5 -- C С 3 2 6 7 3 +/- D 1 4 7 0 2 7 +/-

Answers

data

Area = 126pi m^2

diameter = 22

TA = pi r h + pir^2

126pi = LA + pi(11)^2

LA = 126pi - 121pi

LA = 5pi

Letter B.

You spin the spinner once. What is P(2 or odd)?

Answers

Answer:

P(2 or odd)=1

Explanation:

The spinner has 3 parts.

The probability of spinning a 2:

[tex]P(2)=\frac{1}{3}[/tex]

The probability of spinning an odd number (1, 3):

[tex]P(\text{odd)}=\frac{2}{3}[/tex]

Therefore:

[tex]\begin{gathered} P(2\text{ or odd)=}\frac{1}{3}+\frac{2}{3} \\ =\frac{3}{3} \\ =1 \end{gathered}[/tex]

Which set can represent the side lengths of a right triangle?

Answers

The set that represents a right triangle has to satisfy Pythagorean's Theorem where the greatest side is the hypothenuse. Let's evaluate each of them until we get the right set.

[tex]\begin{gathered} 7^2=6^2+(\sqrt[]{21})^2 \\ 49=36+21 \\ 49=57 \end{gathered}[/tex][tex]\begin{gathered} (5\sqrt[]{3})^2=7^2+5^2 \\ 25\cdot3=49+25 \\ 75=74 \end{gathered}[/tex]

[tex]\begin{gathered} (2\sqrt[]{5})^2=4^2+2^2 \\ 4\cdot5=16+4 \\ 20=20 \end{gathered}[/tex]

As you can observe, set B satisfies the theorem.

Hence, B is the answer.

Given the following information, determine which lines, if any, are parallel. State the converse that justifies your answer.

Answers

1. angle j and k.

Due to the Converse of Corresponding Angles Postulate, j || k.

2. Angles 2 and 5 are the alternating inner angles of the lines j and k. Given that angle 2 = angle 5,

The Converse of Alternate Interior Angles Theorem states that j || k.

J || K converse alternative interior angles.

what are parallel angles?

similarly

3. angle 3 = angle 10 The exterior angles of the lines l and m, respectively, are angle 3 and angle 10. Since the Converse of Alternate Exterior Angles Theorem states that angle 3= angle 10, l || m.

converse alternative exterior angles l || m.

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Maria jogs 5 laps of a football field that
is 100 m by 50 m. How far does she jog?

Answers

Answer:

1500 m

Step-by-step explanation:

given that the field is 100m by 50m we can find that the perimeter of the field is 300m. if she jogged 300m 5 times she would have jogged 1500m

Hello. I would like help with problem. Quick answer is OK.Thank you

Answers

Answer:

not continuous, 2 holes. Option A is correct

Explanations;

For a function to be continuous, the left hand limit of a function must be equal to the right hand limit at the point x = a

From the graph shown you can see that the limit of the function from the left is not equal to the limit of the function from the right at x = 0. Therefore, we can conclude that there are discontinuities at x = 0.

You can also see that the function has 2 holes at (0, 0) and (0, -1).

Find the principal which amounts to #5,000 at simple interestin 5 years at 2% per annum

Answers

To answer this we have to apply the simple interest formula:

I =P x r x t

Where:

I= interest

P= Principal

R= Interest rate ( in decimal form)

t = time (years)

Replacing with the values given:

Interest= I

Principal = ?

Interest rate = 2/100 =0.02

time= 5 years

I = P x 0.02 x 5

I= 0.1P

Amount= P+I

A = P+0.1P

5,000= P+0.1P

5,000= 1.1P

5,000/1.1 =P

4,545.45 =P

Dan's dog walking job pays $15 per hour his job as a car wash attendant pays $400 each week Dan wants to know how many hours he needs to spend walking dogs to earn more than $520 in a week. Which three equalities can model this situation? select all the correct answers.

Answers

Answer:

520<400+15x

15x>120

15x+400>520

Explanation:

Pay of Dan's car wash attendant job =$400 per week

The amount he earns per hour walking dogs = $15

Let the number of hours spent walking dogs in a week = x

Therefore, total earning for walking dogs =$15x

Since he wants to earn more than $520, we have that:

[tex]15x+400>520\text{ (Option F)}[/tex]

We can rewrite this as:

[tex]520<400+15x\text{ (Option B)}[/tex]

If we collect like terms, we have:

[tex]\begin{gathered} 520-400<15x \\ 120<15x \\ \implies15x>120\text{ (Option C)} \end{gathered}[/tex]

So the inequalities are:

0. 520<400+15x

1. 15x>120

2. 15x+400>520

Make a scatter plot of the data. Scale the x-axis by ones and the y-axis by twos.

Answers

Answer

Age of Car in years is represented as x

Avg. Miles per Gallon is represented as y

y = 0.97x + 1.214

Correlation Coefficient = 0.673

Explanation

Age of Car in years is represented as x

Avg. Miles per Gallon is represented as y

The datapoints are fed into a calculator and plotted with the datapoints also processed according to some formulas that'll be provided here

The first figure contains the data points and the regression data processed to be used to calaculate the required parameters.

The second attached image shows the plotted data and the line of best fit and the equation that best represents the relationship between the two parameters.

Then the last image shows the parameters used to calculate the equation of correlation and the correlation coefficient.

Hope this Helps!!!

Sketch the vectors u and w with angle θ between them and sketch the resultant.

Answers

Given:

Two vectors (u) and (w) and the angle between them θ

[tex]\begin{gathered} |u|=50 \\ |w|=12 \\ \theta=35\degree \end{gathered}[/tex]

the sketch of the vectors will be as shown in the following figure:

As shown, the resultant vector is the blue line segment

The vector R has a magnitude = 60.22

And the angle between u and R = 5.56°

Fido ran away from home at a speed of 5 mi/hour. He ran in a straight line. After a while he decided to go back home for dinner so turned around and walked home along the same path he had run on. He walked at 2 mi/hour. The walk home took one hour longer than the run did. How long did Fido run?

Answers

Distance = Speed x time

For the run; speed = 5 mi/hr, time = t

For the walk: speed= 2 mi/hr, time = t + 1

Since he walked on a straight line and he returned following the same path

Distance travelled for the run = distance travelled for the walk

Distance for run: 5 x t = 5t

Distance for walk : 2 (t + 1) =2t + 2

Thus , 5t = 2t + 2

5t - 2t = 2

3t = 2

t = 2/3 hour = 2/3 x 60 minutes = 2x 20 = 40 minutes

He took him 40 minutes to run

Little help here please

Answers

Step-by-step explanation:

as the intersection angles of parallel lines with a third line are the same for both parallel lines (and then vice versa for the other pair of parallel lines), we have a lot of equal angles here.

not to forget : the sum of all angles around a single point on one side of a line is always 180°.

51 = (y + z)

(6z + 9y) = x

x + (x + z) = x + 51 = 180°

x = 129°

we have now

y + z = 51

9y + 6z = 129

so,

z = 51 - y

9y + 6(51 - y) = 129

9y + 306 - 6y = 129

3y = -177

y = -59

z = 51 - y = 51 - -59 = 51 + 59 = 110

the value of z that makes j and k parallel is 110.

Fill in the gaps to factorise the expression.
2x^2+7x+3

Answers

The factorised form of the expression given in the task content is; 2x² + 7x + 3 is; (2x + 1) (x + 1).

Factorisation of quadratic expressions.

It follows from the task content that the factorised form of the expression is to be determined.

On this note, the factorised form of the expression is as follows;

2x² + 6x + x + 3.

By grouping terms; we have;

(2x² + 6x) + (x + 3).

Factorise two terms each at as follows;

2x(x + 1) + 1(x+3)

(2x + 1) (x + 1)

Therefore, the factorised form of the expression; 2x² + 7x + 3 is; (2x + 1) (x + 1).