suppose f(x)=x^2 and g(x)=(1/5x)^2. Which statement best compares the graph of g(x) with the graph of f(x)?

Answer:

1. Count the total number of items. In this chart the total is

2. Divide the count (the frequency) by the total number.

3. Then, convert it to a percent.

Answer:

$11.67

Step-by-step explanation:

14 (the price he sold it for) = x + 1/5(x) (how much he upped the price)

14 = 6/5x

x = 11.67

To check find 20% of 11.67 which is 2.33 and add them together, which equals  $14, so it checks out.

Answer:

Step-by-step explanation:

A motorcycle dealer paid a certain price for a motorcycle

certain price = x

And marked it up by 1/5 of the price he paid.

marked price = 6/5x

Because x + 1/5x = 6/5x

Later, he sold it for $14.

6/5x = 14

1/5x = 14/6

x = 14/6 * 5

14 * 5 = 70

70/6 = 35/3

x = 35/3

x = 35/3 = $11.666666667

Substitute this back in to check it's right.

11.666666667 * 6/5 = 14

QUESTION 1

If f(x)=1-x² and g(x)=1-x,

Then,

(f-g)(x)=f(x)-g(x)

This implies that,

[tex]( f - g)(x) = 1 - {x}^{2} - (1 - x)[/tex]

[tex]( f - g)(x) = 1 - {x}^{2} - 1 + x[/tex]

We simplify to get,

[tex]( f - g)(x) = - {x}^{2} + x[/tex]

The correct choice is B.

QUESTION 2

Given:

f(x)=3+x

and

[tex]g(x) = {x}^{2} + 1[/tex]

[tex](f\circ g)(x)=f(g(x))[/tex]

[tex](f\circ g)(x)=f( {x}^{2} + 1 )[/tex]

[tex](f\circ g)(x)=3 + {x}^{2} + 1[/tex]

[tex](f\circ g)(x)= {x}^{2} +4[/tex]

Also,

[tex](g\circ f)(x)=g(f(x))[/tex]

[tex](g\circ f)(x)=g( 3+ x)[/tex]

[tex](g\circ f)(x)= {(3 + x)}^{2} + 1[/tex]

[tex](g\circ f)(x)= 9 + 6x + {x}^{2} + 1[/tex]

[tex](g\circ f)(x)= {x}^{2} + 6x + 10[/tex]

Laura has a $5,500 liability because that's what she owes and she is liable for it. She hasn't paid for it fully so the car has not become an asset. The answer is C.

Hope this helps

Answer:

I think th answer is A

Explanation:

Asset is a valuable or useful thing. The car is worth 18,000 so it is the asset. Liability is being responsible for things like debt, or something you own by law. She is responsible for the $5,500 she owes, so that is the liability. Hope this helps!

The unit price of one pencil is $0.60.

The cost of one pencil (the unit price) can be found by dividing the total cost by the number of pencils. In this case, we have $3.60 divided by 6. This gives us a unit price of $0.60 per pencil.

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Answer:um i belevie it is 300

Step-by-step explanation:

hope this helps

Answer:

281 is already a whole number

Step-by-step explanation:

There is no decimal point

Hope your day is great!

[tex]\bf \textit{exponential form of a logarithm} \\\\ \log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies \log_a b=y \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ln(x)=4\implies log_e(x)=4\implies e^4=x \\\\\\ e^8=y\implies log_e(y)=8\implies ln(y)=8[/tex]

The function could be used to model this situation is D. y = 2ˣ.

The function that could be used to model the situation where the number of bacteria, y, in a certain area doubles every hour, x, is: D. y = 2ˣ

This function represents exponential growth, where the number of bacteria doubles every hour.

The variable x represents the number of hours, and 2^x represents the doubling of the bacteria population over time.

Answer:

g(x) = 4/5 x² - 4

Step-by-step explanation:

∵ f(x) = 2/5 x² - 2

∵ f(x) stretched vertically by scale factor 2

∴ g(x) = 2[f(x)]

∴ g(x) = 2[2/5 x² - 2] = 4/5 x² - 4

The resulting function is g(x) = [tex]\( \frac{4}{5} x^2 - 4 \).[/tex].

Given the function f(x) = [tex]\( \frac{2}{5}x^2 - 2 \)[/tex] and the function g(x) representing a vertical stretch of f(x) by a factor of 2, we need to find the equation of g(x).

A vertical stretch of a function f(x) by a factor of k means multiplying the function by k. Here the factor k is 2.

So, the equation of g(x) will be:

Substitute f(x) into the equation:

Distribute the 2:

Therefore, the equation for g(x) after a vertical stretch by a factor of 2 is g(x) = [tex]\( \frac{4}{5} x^2 - 4 \)[/tex].

Answer:

3^9

Step-by-step explanation:

We we multiply exponents with the same base, we can add the exponents

a^b * a*c = a^(b+c)

3^5 * 3^4

3^(5+4)

3^9

To feed 58 people at the party there should be 10 cakes.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Desmond knows that 2 cakes will feed 11 people. If he is inviting 58 people to his parent's anniversary party.

The number of cakes for 58 people will be calculated as,

11 people = 2 cakes

1 person = 2 / 11

58 people = ( 58 x 2 ) / 11

58 people = 10 cakes

To know more about an expression follow

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ANSWER

[tex]V_{cone}=\frac{1}{3} \pi t^2k[/tex]

EXPLANATION

The volume of a cylinder is given by

[tex]V_{cylinder}=\pi r^2h[/tex]

The radius of the given cylinder is r=t.

The height of the cylinder is h=k.

The volume of the given cylinder is

[tex]V_{cylinder}=\pi t^2k[/tex]

The volume of a cone with the same base radius and height is

[tex]V_{cone}= \frac{1}{3} \pi t^2k[/tex]

Answer:

The correct answer is Option 2

1/3 πt²k

Step-by-step explanation:

points to remember

Volume of cone = 1/3 πr²h

Where r - Radius of cone and

h - Height of cone

To find the volume of given cone

Here radius of cone r = t and

Height of cone h = k

Therefore we can write,

volume of cone =  1/3 πr²h =  1/3 πt²k

Therefore the correct answer is option 2

Answer:

Trapezoid

Step-by-step explanation:

The points are shown in the attached graph.

You can clearly see from the picture that it is a "Trapezoid".

Trapezoid is basically a quadrilateral (4 sided-figure) that has 1/2 pair of parallel sides.

On the other hand, a parallelogram has 2 pair of parallel sides.

Thus, a parallelogram is a special type of trapezoid where there are 2 pair of parallel sides. But trapezoid need not be a parallelogram.

The picture shows 1 pair of parallel sides, hence it is a trapezoid.

Answer: [tex]8x+36[/tex]

Step-by-step explanation:

To simplify the expression you must apply the Distributive property.

Keep on mind that:

- According to the Distributive property, the product of the difference is equal to the difference of the products:

[tex]a(b-c)=ab-ac[/tex]

- Remember the multiplication of signs:

(-)(-)=+

(+)(+)=+

(-)(+)=-

Then, you obtain the following:

[tex](-2x-9)(-4)=8x+36[/tex]

Answer: The correct answer is 8x - 36.

Step-by-step explanation: I am 98% sure.

Answer:

Stacy

Step-by-step explanation:

4.23 < 4.3

Stacy is 0.07 feet taller than Erik, as of the given conditions.

Given that,
Erik is 4.23 feet tall. Stacy is 4.3 feet tall.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Heights
Stacy = 4.3 feet
Erik = 4.23 feet
Difference = 4.3 - 4.23 = 0.07 feet

Thus, Stacy is 0.07 feet taller than Erik, as of the given conditions.

Learn more about arithmetic here:

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zoom out a little i cant see it that well

Answer:

First Option

Step-by-step explanation:

The number of solutions is given by the values in which the equation of the circumference is equal to the equation of the line.

In other passwords the number of solutions is equal to the number of times the line intersects or touches the circumference.

Notice in the graph that the line does not touch the circumference.

Therefore for this case there are no solution

Answer:

The answer is A (no solution)

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

Definitions of parallelogram and rectangle:

A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.

A rectangle is a parallelogram with four right angles.

This gives us that each rectangle is a parallelogram.

But an arbitrary parallelogram can have angles that are not necessarily right (for example, 60°, 120°, 60°, 120°). Thus, there are a lot of parallelograms that are not rectangles.

The correct answer is B.

Hope this helps.

Answer:

San Fransisco

Step-by-step explanation:

If Geneva is 12°C colder than her hometown, this means that her hometown is 12°C warmer than -3°C.

Since warmer means a higher number, we find 12 + -3, which is 9°C.

The town that is 9°C is San Fransisco.

Answer:

The slope of Function A is greater than the slope of function B  while the y-intercept of Function  B is greater than the y-intercept of function A.

Step-by-step explanation:

Function A is f(x) = 5x + 2

The slope is 5 and the y-intercept is (0, 2).

Function B. The slope is  (5-2) / (0- -1) = 3.

also (8-5) / (1 - 0) = 3

The slope is 3.

The y-intercept is at (0, 5) because one point on the graph is (0, 5).

Answer:

Their slopes are equal but y-intercepts are not equal.

Step-by-step explanation:

Its simple arithmatics

Answer:

A

Step-by-step explanation:

With this question, its actually way easier than you think. If you want to find corresponding angles, you have to find a way to make the shapes overlap to be exactly the same. If they cannot be exactly the same, there will not be corresponding angles. For this, if you rotate quadrilateral 90 degrees counter-clockwise, you will see that the shapes look the same. Then you can just match up the angles that have the same degree measure (or just look the same for simplicity) and you have your answer. The answer is actually in the question too. ABCD=JKLM, but each letter is actually in the right place. A=J B=K C=L D=M.

Hope this helped! ^-^

Answer:B

Step-by-step explanation:Probably not A

B,C,D are probably the ones

but i think its b

Answer:

[tex]f(7)=\frac{-5}{3}[/tex] or [tex]f(7)=-1.67[/tex]

Step-by-step explanation:

We are given the following function of x and we are to find the value of [tex] f ( 7 ) [/tex]:

[tex] f ( x ) = \frac { 3 } { x + 2 } - \sqrt { x - 3 } [/tex]

Substituting the given value (7) in the above function to get:

[tex]f(x)=\frac{3}{x+2}-\sqrt{x-3}[/tex]

[tex] f ( 7 )= \ frac{3}{7+2}-\sqrt{7-3}[/tex]

[tex] f(7) = \frac { 3 } { 9 } - \sqrt { 4 } [/tex]

[tex]f(7)=\frac{1}{3}-2[/tex]

[tex]f(7)=\frac{1}{3}-\frac{6}{3}[/tex]

[tex]f(7)=\frac{-5}{3}[/tex] or [tex]f(7)=-1.67[/tex]

Answer:

C

Step-by-step explanation:

Each of the tables is a linear relationship. Linear relationships increase or decrease steadily by adding or subtracting a constant. Table A increases by 5. Table B decreases by 2. Table C doesn't change. Table D increase by 4.

A "no change" means the y values never change. The constant is 0 and is a horizontal line. Table C is the solution.

Answer:

Option C.

Step-by-step explanation:

Linear relationship : If the relation between variables is represent by a non vertical straight line, then it is called a  linear relationship.

Horizontal line is a special case of linear relationship. It is know as no change linear relationship. It means the output value remains same for each input value.

In option C, the given table is  

x      y

14    12

20   12

26   12

32   12  

Only in option C, the y-values are constant. So, it represents no change linear relationship.

Therefore the correct option is C.

Answer:  a. 1

Step-by-step explanation:

[tex]\sqrt{2x+7}+1=\sqrt{2x+14}\\\\(\sqrt{2x+7}+1)^2=(\sqrt{2x+14})^2\\\\2x+7+2\sqrt{2x+7}+1=2x+14\\\\2x+8+2\sqrt{2x+7}=2x+14\\\\2\sqrt{2x+7}=6\\\\\sqrt{2x+7}=3\\\\(\sqrt{2x+7})^2=(3)^2\\\\2x+7=9\\\\2x=2\\\\x=1\\\\\\Check:\\\sqrt{2(1)+7}+1=\sqrt{2(1)+14}\\\\\sqrt9+1=\sqrt16\\\\3+1=4\ \checkmark[/tex]

Answer:

We shall use the method of splitting the middle term

To factorize

3x² - 10 x + 8

We need two numbers which add to give -10 and multiply to give 3 × 8 = 24

The numbers are -6 & -4

(-6)+(-4) = -10

(-6)(-4) = 24

So we shall split -10x as -6x - 4x

We get

3x² -10x + 8

= 3x² -6x -4x+8

Taking out 3x common from first two terms & -4 from the lest two terms we get

= 3x(x-2)-4(x-2)

Taking out (x-2) common we get

= (x-2)(3x-4)

So

3x² - 10x + 8 = (x-2)(3x-4)

Answer:

2 and 3

Step-by-step explanation:

on EDGE 2021

Answer:

545454

Step-by-step explanation:

This is a ratio.  you take 666/333 = x/272727.  Basically tis says 666 cm to 333 m is equal to some number of centimeters to 272727 meters.  Then just solve for x.  272727(666/333) = 545454.

Another way of looking at it is what did we multiply 333 by to get 666.  Answe is 2, so we do the same  for 272727.  2*272727 = 545454

If you wanted to you could have also converted units so everything was in either centimeters of meters, but as long as you keep things in the right order this works.  

Answer: the number of centimetres is 54cm

Step-by-step explanation:

Given that 6 centimeters represents 3meters.

The number of centimeters on the blue print that will represent an actual distance of 27meters will be Y

6 : Y = 3 : 27

That is

6/Y = 3/27 = 1/9

Cross multiply

Y = 54 cm

Answer: Madeline is 20 yrs old

Step-by-step explanation:

If Laura is 50 and she is 10 years older than Raena then Raena is 40 that would then make Madeline 20 years old.

Final answer:

To determine Madeline's age, we set up an equation based on the given relationship and solved it to find that Madeline is 20 years old.

Explanation:

To solve the question about Raeana, Madeline, and Laura's ages, we first define the variables. Let's denote Madeline's age as M. Since Raeana is twice as old as Madeline, Raeana's age would be 2M.

The problem states that Laura is 10 years older than Raeana, making Laura's age 2M + 10. Given that Laura is 50 years old, we can set up an equation: 2M + 10 = 50.

Now, we solve for M:
Subtract 10 from both sides of the equation to isolate the term with M on one side: 2M = 40.

Divide both sides by 2 to solve for M: M = 20.

Therefore, Madeline is 20 years old.

Answer:

[tex]\large\boxed{c.\ 7}[/tex]

Step-by-step explanation:

[tex]3x-6=21\qquad\text{divide both sides by 3}\\\\\dfrac{3x}{3}-\dfrac{6}{3}=\dfrac{21}{3}\\\\x-2=7[/tex]

Answer:

The answer is (b) ⇒[tex]\frac{d^{5} }{2\sqrt{c} }[/tex]

Step-by-step explanation:

∵ [tex]\frac{\sqrt{c^{2}d^{6}}}{\sqrt{4c^{3}d^{-4}}}[/tex]

∵ √x² = x ⇒ that means to cancel the square root divide

  the power by 2

∴ [tex]\sqrt{c^{2}d^{6}}=cd^{3}[/tex]

∵ √4 = 2 ⇒ √2×2 = √2² = 2

∵ √c³  = [tex]c^{\frac{3}{2}}[/tex]

∴ [tex]\sqrt{4c^{3}d^{-4}}=2c^{\frac{3}{2}}d^{-2}[/tex]

∴ [tex]\frac{cd^{3}}{2c^{\frac{3}{2}}d^{-2}}[/tex]

∵ In the same base with multiplication we add the power,

  in same base with division we subtract the power

∴ [tex]\frac{1}{2}c^{1-\frac{3}{2}}d^{3-(-2)}=\frac{1}{2}c^{\frac{-1}{2}}d^{5}=[/tex]

  [tex]\frac{d^{5}}{2c^{\frac{1}{2}}}=\frac{d^{5}}{2\sqrt{c}}[/tex] ⇒  [tex]c^{\frac{1}{2}}=\sqrt{c}[/tex]

∴ The answer is (b) ⇒ [tex]\frac{d^{5}}{2\sqrt{c}}[/tex]

Answer:

b. [tex]\frac{d^{5}}{2\sqrt{c} }[/tex]

Step-by-step explanation:

The given expression is

[tex]\frac{\sqrt{c^2d^6} }{\sqrt{4c^3d^{-4}} }[/tex]

We simplify the radicand using the property;  [tex]\frac{a^m}{a^n} =a^{m-n}[/tex]

[tex]\frac{\sqrt{d^{6--4}} }{\sqrt{4c^{3-2}} }[/tex]

[tex]\frac{\sqrt{d^{10}} }{\sqrt{4c^{1}} }[/tex]

[tex]\frac{d^{5}}{2\sqrt{c} }[/tex]