consider the parent function f(x)=x^2. a. graph y=f(x). b. write an equation for f(1/2x). Then sketch a graph of y=f(1/2x) and describe the transformation. c.write an equation for f(3x). Then sketch a graph of y=f(3x) and describe the transformation.

From that diagram that is drawn above, C is the midpoint of the line AB:

AC = 17

AB = 5x - 6

Since C is the midpoint of AB;

AB = 2AC = 2CB:

5x - 6 = 2(17)

5x - 6 = 34

5x = 34 + 6

5x = 40

x = 40/5

x = 8

2 + m > 10

substituting with m = 7, we get:

2 + 7 > 10

9 > 10

which is false, because 9 is less than 10

Step 1:

Choose either Substitution or elimination method to solve system of equation.

Step 2:

If you choose substitution,

firstly, name the equation

3x + y = 4 .............................1

2x + y = 0 ..............................2

secondly, choose one of the equation and make one of the varable subject of the relation

2x + y = 0 .......................1

y = -2x

Step3

substitute y in equation 2

3x + (-2x) = 4

3x - 2x = 4

x = 4

Step 4:

find y from y = -2x

y = -2(4)

y = -8

( 4 ), ( -8 )

Answer:

x = 4

y = - 8

Step-by-step explanation:

3x + y = 4

2x + y = 0

(3x + y ) (-1 ) = 4 ( - 1 )

2x + y = 0

- ( 3x + y ) = - 4

2x + y = 0

The distance between Joey and his home was such that joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters is 6 1/12 meters.

To subtract in mathematics is to take something away from a group or a number of objects.

The group's total number of items decreases or becomes lower when we subtract from it.

It is known that East and West are the opposite of each other.

So, 15 2/3 towards the east let's take it positively.

And 21 3/4 towards left let's consider it negative.

So, the distance from the home

⇒ | ( 15 + 2/3) - (21 +3/4) |

⇒ | 15 -21 + 2/3 - 3/4 |

⇒ | -6 + (8 - 9)/12 |

⇒ | -6 - 1/12 |

⇒ | -(6 +1/12) |

⇒ 6 1/12

Hence "The distance between Joey and his home was such that joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters is 6 1/12 meters".

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Given:

A standard tire has 10/32 inches of tread.

The tire needs to be replaced when only 2/32 inches of tread remains left.

Here the tire is needed to be replaced after 40,000 miles.

To find:

The thickness of tire rubber lost every 1,000 miles.

Step-by-step solution:

According to the question,

The tire is replaced when only 2/32 inches of tread remain left.

The new tire has 10/32 inches of tread.

Thus tire needs to loose:

10/32 - 2/32 = 8/32 inches of tread.

This means upon traveling for 40,000 miles, 8/32 inches of tread is lost.

So their ratio equals:

40,000 = k (8/32)

k = 40,000 × 32 / 8

k = 40,000 × 4

k = 1,60,000

So to calculate for 1000 miles:

1000/x = 1,60,000

1/x = 1,60,000 / 1000

1/x = 160

x = 1 / 160 inches

Thus we can say for every 1000 miles, 1 / 160 inches of tread is lost.

Since we want to express 48.001 to the hundredths, let's look at the places of the digits after the decimal point:

Therefore, 48.001 to the hundredths is 48.00

The figure formed will be hexagonal

Answer:

Step-by-step explanation:

Use the order of operations.

PEMDAS stands for:

Do exponents first.

[tex]\sf{y^3=-125}[/tex]

[tex]\sf{x=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\dfrac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\dfrac{-1+\sqrt{3}i}{2}}}[/tex]

[tex]\rightarrow \sf{y=\sqrt[3]{-125},\:y=\sqrt[3]{-125}\dfrac{-1+\sqrt{3}i}{2},\:y=\sqrt[3]{-125}\dfrac{-1-\sqrt{3}i}{2}}[/tex]

[tex]\sf{\sqrt[3]{-125}=\boxed{\sf{-5}}}[/tex]

Therefore, the correct answer is y=-5.

I hope this helps, let me know if you have any questions.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{y^3 = -125}[/tex]

[tex]\large\text{Solve/take the cube root}[/tex]

[tex]\mathsf{(-125)^{^\dfrac{1}{3}}}\mathsf{ = y}[/tex]

[tex]\mathsf{y = (-125)^{^\dfrac{1}{3}}}[/tex]

[tex]\large\text{Simplify it}[/tex]

[tex]\mathsf{y = -5}[/tex]

[tex]\huge\text{Therefore, your answer is: \boxed{\mathsf{y = -5\ (\rm \bold{O}ption\ A.)}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

24,500 meters

Step-by-step explanation:

Using mathematical operations of addition, multiplication, division, and subtraction, the final score was:

The basic mathematical operations for getting mathematical results from numbers, values, and variables include addition, multiplication, division, and subtraction.

In this situation, we apply these four basic mathematical operations.

Fizzy = 2 points

X = 5 points

Total scores = 93 points

The points in 8 Fizzys = 16 points (8 x 2)

The points in 5 Xs = 25 points (5 x 5)

The equation showing the total scores of K = total scores + 16 - 25

= (93 + 16 - 25)/2

= 42 points

The equation showing the total scores of W = total scores - 16 + 25

= (93 - 16 + 25)/2

= 51 points

Final scores are K = 42 and W = 51.

Thus, applying mathematical operations, the final score shows that K scored 42 points while W scored 51 points, totaling 93 points for the two teams.

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Answer:

Explanation:

Given A = (4, 6) B = (2, 8) C = (5, 10)

SImilarly, for A' = (2, 3) B' = (1, 4) C' = (2.5, 5)

Since it is a dilation, AB/A'B' should be the same as BC/B'C', but that is not the case here.

Solution

- The base is a regular hexagon. This implies that it can be divided into equal triangles.

- These equal triangles can be depicted below:

- If each triangle subtends an angle α at the center of the hexagon, it means that we can find the value of α since all the α angles are subtended at the center of the hexagon using the sum of angles at a point which is 360 degrees.

- That is,

- We also know that regular hexagon is made up of 6 equilateral triangles.

- Thus, the formula for finding the area of an equilateral triangle is:

- Thus, the area of the hexagon is:

- With the above formula we can find the length of the regular hexagon as follows:

- The formula for the volume of a hexagonal pyramid is:

- Thus, the volume of the pyramid is

1) is already written, so we start with the second line.

2)

JM is parallel to KL ----> Given

3) ∠KML = ∠JML ----> They are angles on two perpendicular lines, and Since JM bisects LK, they are equal.

4) ∠KJL=∠MKL ---> Since JM bisects ∠J, the angles KJL and MKL are equal

5) ∠JKM=∠JLM ----> Since 3) and 4), the angles JKM and JLM must also be equal so that the sum of internal angles of each triangle will be 180°

Thus: Triangle JMK is congruent to triangle JML

This problem provides the faces of a triangular prism, and we need to calculate the surface area.

The surface area of the prism is equal to the sum of the area of all individual faces. Three faces are rectangles, while two are triangles.

The area of a rectangle can be found by using the following expression:

While the area of a triangle can be found by using the following expression:

Two rectangles are equal, with measurements 2.25 cm by 8.5 cm, one rectangle has a measurement of 6.5 cm by 2.5 cm, and the two triangles are equal with a base equal to 6.5 cm and a height of 8.5 cm, therefore we have:

And the total area is:

The surface area of the prism is approximately 108 square centimeters.

We have an even 3 digits number whose sum lie is less than 9, has got 3 digits and less than 140.

We will establish the inequalities that satisfies the conditions given and then figure out the number.

From our last inequality, we can easily see that the number in question is 14 x 8 or 14 x 9. Any multiple of 7 that is even is also a multiple of 14.

From the above, it can be easily seen that 112 satisfies the conditions listed.

The number is 112

Divide the total amount of fabric by the amount needed to create a purse to find how many purses will she be able to make.

Since she has 10 yards of fabric and each purse requires 1/3 of a yard, then, divide 10 over 1/3:

Therefore, Angelina will be able to make 30 purses using 10 yards of fabric.

The given data points from the graph of the exponential function, f, and the, values from the table of the function g, gives the statement that correctly compares the two functions as the option;

The end behaviour of a function is the description of how the function behaves towards the boundaries of the x–axis.

The given points on the exponential function, f, are;

(-0.25, 10), (0, 6), (5, -2) and also the x–intercept (1, 0)

The points on the function g, obtained from the table of the values for g(x), expressed as ordered pairs are;

(-1, 15), (0, 3), (1, 0), (2, -34), (3, -16)

The coordinates of the x–intercept is given by the point where the y–value is zero.

The x–intercept for the exponential function, f, is therefore (1, 0)

Similarly, the x–intercept for the function, g, is (1, 0)

Therefore, both functions have the same x–intercept

However, the end behaviour of the function, f, as the x approaches infinity is that f(x) approaches negative infinity, while the end behaviour of the function, g, as the the value of x approaches infinity is g(x) is increasing towards positive infinity.

The correct option is therefore;

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Given two matrices

We will solve for the resultant matrix -B - 1/2A.

This operation is represented as

Let's simplify the matrices further based on scalar operations that can be done here. The B matrix will be multiplied by -1 while the A matrix will be multiplied by 1/2. We now have

Now, we apply the subtraction of matrices to the simplified matrix operation above. We have

Hence, the resulting matrix for the operation -B - 1/2A is

Substituting x = 0 into the function we get:

f(0) = 4(0) - 2

f(0) = 0 - 2

f(0) = -2

In a linear relationship, each step of x modifies the y value in the same way.

In the first table, when x = 1, y = 3 and when x = 2, y = 6. This is an increment of 3. If this is a linear relationship, we expect the next value of y to be the previous value plus 3, thus y = 9. But in the table shows x =3 and y = 12. We can rule out the first table.

With similar reasoning, in the second table, we see (1, 2) and (2, 5). This is an increase of the y value of 3. We expect the next value to be y = 8, but we see (3, 9). The second table is not a linear relationship.

In the third table, we see (1, -3) and (2, -5). This is a decrease of -2. We expect the next value of y to be y = -7, and we do see (3, -7). The next value should be y = -9, and the table shows (4, -9). Table 3 shows a linear relationship.

To be sure, let's see the 4th table. We see (1, -2) and (2, -4). This is a decrease of -2. The expected next value is y = -6, but the next point is (3, -2). Fourth table is not a linear relationship.

Thus, the correct answer is the top-right table.

[tex]15 + 0.10x = 0.15(60) + 0.15(x) \\ 15 + 0.10x = 9 + 0.15x \\ \\ 0.10x - 0.15x = 9 - 15 \\ - 0.05x = - 6 \\ \frac{ - 0.05x}{ - 0.05} = \frac{ - 6}{ - 0.05} \\ x = 120[/tex]

ATTACHED IS THE SOLUTION

For the given functions, the two compositions are:

(f o g)(x) =  9x² + 5

(g o f)(x) = 3*x² + 15

Here we have two functions which are:

f(x) = x² + 5

g(x) = 3x

Now we want to find the compositions:

(f o g)(x) = f( g(x) )

So we just need to evaluate f(x) in g(x), we will get:

f( g(x) ) = g(x)² + 5

f( g(x) ) = (3x)² + 5 = 9x² + 5

The other composition is:

(g o f)(x) = g(f(x))

And we can get this in a similar way:

g(f(x)) = 3*f(x)  = 3*(x² + 5) = 3*x² + 15

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Hello there. To solve this question, we have to remember some properties about polar coordinates.

Given a point (x, y) and we want to plot the graph for (r, theta) after making the transformation, the graph will be something like the following:

In this case, we want to graph the point (5, 3pi/4)

First, notice 3pi/4 = 75º, which is in the first quadrant.

Therefore the graph will indeed look like the one above:

Which is the option contained in the first answer.

Answer:

5) The midrange is 19.5ºF

6) The midrange is 67.5º

Explanation:

The problem tell us how to calculate the midrange.

In (5) the minimum and maximum values are given (-6ºF and 45ºF, respectively). Using the formula:

In (6), we need to find the minimum and maximum values from a list of them. We can see that the minimum is 58º and the maximum 77º

Then:

18) the best estimate will be 75 square feet (option G)

18) radius = 10ft

let π = 3.14

We are told the deck will have 1/4 the area of a circle. We need to first find the area of a circle.

Area of circle = πr²

Next, we will divide the area by 4:

From the options, the one close to the result we got is 75 square feet

Hence, the best estimate will be 75 square feet (option G)

The required exponential function f(x) = (4)(2)ˣ which is passes through the two points (-1,2) and (3,32).

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable

Let the formula for an exponential function would be as

⇒ f(x) = abˣ  

The exponential function passes through the two points (-1,2) and (3,32).

f(-1) = 2

f(3) = 32

2 = ab⁻¹

2b = a

32 = ab³

Substitute the value of a = 2b in the above equation,

32 = 2b×b³

32 = 2b⁴

b⁴ = 16

b⁴ = 2⁴

b = 2

Substitute the value of b = 2 in the equation a = 2b,

So a = 2×2 = 4

⇒ f(x) = (4)(2)ˣ  

Therefore, the required exponential function f(x) = (4)(2)ˣ  

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Explanation:

The equation is given below as

Step 1:

Collect similar terms, we will have

Hence,

The simplified form of the equation will be

Use a rule of three to find the amount of rooms wire with 3/62 rolls:

Answer:

Explanation:

Here, we want to simplfy the given expression

From what we have:

Substituting the values, we have it that:

Recall the following property of exponents:

Therefore:

Answer: Option A.