Make up an equation for a quadratic function whose graph satisfies the given condition. Use whatever form is most convenient. i. Has a vertex at (−2,−5). ii. Has a y-intercept at (0, 6). iii. Has x-intercepts at and (3, 0) and (5, 0). iv. Has x-intercepts at the origin and (4, 0). v. Goes through the points (4, 2) and (1, 2).

The required function is [tex]y = -\frac{3}{2} x -36[/tex] having domain and range as R and y-intercept is -36.

Given function

y=f(x) = [tex]-\frac{2}{3} x -24[/tex]

An inverse function is a function that returns the original value for which a function has given the output. If f(x) is a function that gives output y, then the inverse function of y, i.e. f-1(y) will return the value x.

In order to get inverse function [tex]f^-1x[/tex] let us arrange the given function

[tex]y+24 = -\frac{2}{3} x[/tex]

[tex]x = -\frac{3}{2} y-36[/tex]

Now, replace x with y and vice versa.

[tex]y = -\frac{3}{2} x -36[/tex]........(1)

or, [tex]f^-1x = -\frac{3}{2} x -36[/tex]

(1) will be the inverse function of the given function.

For x-intercept put y = 0 and for y-intercept put x=0 in eq(1)

x-intercept = -24

y-intercept = -36

The domain and range of f⁻¹x = set of all real numbers since f⁻¹x is a straight line equation, domain, and range of which is set of all real numbers.

Therefore, the required function is [tex]y = -\frac{3}{2} x -36[/tex] having domain and range as R and y-intercept is -36.

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Answer:

d and e

Step-by-step explanation:

did the test

Answer:

(1, 3) depending if it counts as 1 2 3 4 5... not 1...5...10

Step-by-step explanation:

so i think the solution was where the two lines cross?

Answer:

(-1,3)

Step-by-step explanation:

The solution to the system of equations is where the two graphs intersect.

The two lines intersect at x=-1  and y = 3

(-1,3)

Answer:

30,000 square yards

Step-by-step explanation:

Answer:

Answer:

(x+12) (x+2)

Step-by-step explanation:

x^2+14x+24

24x^2. factors= +12, +2

(x+12) (x+2)

Answer:

-2.8

Step-by-step explanation:

[tex] \frac{ - 3.5}{1.25} = - 2.8[/tex]

Answer:

A

Step-by-step explanation:

the sides s of a cube are congruent

the volume (V) of a cube is calculated as

V = s³ = 2³ = 8 ft³

Answers: 0.125, 1, 8, 64, 512

Step-by-step explanation: Hope this helps! :)

[tex]8^{-1} = 0.125[/tex]

[tex]8^{0} = 1[/tex]

[tex]8^{1} = 8[/tex]

[tex]8^{2} = 64[/tex]

[tex]8^{3} = 512[/tex]

Answer:

Straightforward: 70 + 48 or 72 + 46

With other ways: below ↓

Make a ratio and increase.

6:4

Find the least common multiples.

72:48

Next, take these 2 out of ratio form and add them together.

72

+48

120

Since the closest we get is 120...

We must change the LCM'S to get the true number. Either way, it will work if you reduce 48 by 2, or 72 by 2. Same answer.

[tex]120-2=118dollars\\72 - 2\\48 - 2[/tex]

Therefore,

Our problem answer can be seen as the original ratio, but modified, 72:48 or simply 70 + 48. For the ratio to be correct, you would have to factorize the least common multiples and re-add. I would not recommend this.

Answer:

The sine of an angle is equal to the cosine of its complementary angle, and the cosine of an angle is equal to the sine of its complementary angle.

Step-by-step explanation:

so the answer is D.

Step-by-step explanation:

it's simply going to be total time divided by the time to was one pot

Answer:

24, 12, 6, 3, 1.5, 0.75,0.375, 0.1875, 0.09375

The BOLD number is your answer, and the other ones are the sequence. oof, that was a lot of calculating!

Thanks!

Answer:

0.046875

Step-by-step explanation:

Each number is being divided in half each time.

24 / 2 = 12

12 / 2 = 6

6 / 2 = 3

3 / 2 = 1.5

1/5 / 2 = 0.75

0.75 / 2 = 0.375

0.375 / 2 = 0.1875

0.1875 / 2 = 0.09375

0.09375 / 2 = 0.046875 <--- This is the ninth term of the sequence.

Answer:

Step-by-step explanation:

maggie should get 37 candles in order for the 37 birthday

Answer:

The discount is $18.20 which changes the price of the jeans to $27.30.

Answer:

  y = √(5x+34)

Step-by-step explanation:

The regression formula that matches a square root function to these points can be worked out by a suitable calculator. The attachments shows the points are matched exactly by the function ...

  y = √(5x+34)

__

If you would like to work this by hand, you can put the (x, y) point values into the proposed equation and see what the coefficients need to be:

  y = √(ax +b)

  7 = √(3a +b)   ⇒   49 = 3a +b

  8 = √(6a +b)   ⇒   64 = 6a +b

Subtracting the first equation from the second, gives ...

  (64) -(49) = (6a +b) -(3a +b)

  15 = 3a   ⇒   a = 5

  49 = 3(5) +b   ⇒   b = 34

Answer:

137/11 or approx. 12.45

Step-by-step explanation:

Answer:

M = 20

Step-by-step explanation:

given M is directly proportional to r³ then the equation relating them is

M = kr³ ← k is the constant of proportion

to find k use the condition when r = 4, M = 160 , then

160 = k × 4³ = 64k ( divide both sides by 64 )

[tex]\frac{160}{64}[/tex] = k , then

k = 2.5

M = 2.5r³ ← equation of proportion

when r = 2 , then

M = 2.5 × 2³ = 2.5 × 8 = 20

Answer:

It would be 8 cups of flour.

Answer:

8 cups

Step-by-step explanation:

Answer:

○ [tex]\displaystyle x^2 + 4x + 13[/tex]

Step-by-step explanation:

Sinse this expression is unfactourable with rational quantities, use the Quadratic Formula:

[tex]\displaystyle -B ± \frac{\sqrt{B^2 - 4AC}}{2A} = x\\ \\ -4 ± \frac{\sqrt{[-4]^2 - 4[1][13]}}{2[1]} = x \hookrightarrow -4 ± \frac{\sqrt{16 - 52}}{2} = x \hookrightarrow -4 ± \frac{\sqrt{-36}}{2} = x \hookrightarrow \frac{-4 ± 6i}{2} = x \\ \\ \boxed{-2 - 3i, -2 + 3i = x}[/tex]

I am joyous to assist you at any time.

Step-by-step explanation:

Speed is independent and distance is dependent

Distance depends on the speed

Speed influences the distance

Answer:

that looks hard

Step-by-step explanation:

thx for the points

Answer:

The method used in solving the example above is called the elimination method, because we eliminate one variable first, to get a linear equation in one variable. In the example above, we eliminated y. We could also have eliminated x. Try doing it that way. 2. You could also have used the substitution, or graphical method, to solve this problem. Try doing so, and see which method is more convenient.

First multiply both the equations by some suitable non-zero constants to make the coefficients of one variable (either x or y) numerically equal. Step 2: Then add or subtract one equation from the other so that one variable gets eliminated. If you get an equation in one variable, go to Step 3. If in

we obtain a true statement involving no variable, then the original equations has infinitely many solutions. If in Step 2, we obtain a false statement involving no variable, then the original pair of equations has no solution, i.e., it is inconsistent.

Solve the equation in one variable (x or y) so obtained to get its value.

Substitute this value of x (or y) either of the original equations to get the value of the other variable.

Step-by-step explanation:

Answer:

85 Square Units

Step-by-step explanation:

We need to start by finding the area of the triangle:

(base*height)/2

[tex]\frac{17*10}{2} =85[/tex]

Then we find the area of the rectangle:

Height*Width= 170

Then we finally take the area of the rectangle (170) and subtract the area of the triangle (85) and we get the answer of 85.

Answer:

I'm not 100% sure but i think its a  

Step-by-step explanation:

Both have 2 heads and 2 tails so that's 4 and it's a fair game and b is wrong and you will eliminate c.

The game is fair because there is an equal chance of winning an losing the game.

Probability is simply how likely something is to happen.

[tex]P(E )=\frac{Number\ of \ favorable\ outcomes }{Total\ number \ of outcomes}[/tex]

Where,

P(E) is the probability of an event.

A fair game is the game in which there is an equal chance of wining or losing.

According to the given question.

Two coins are tossed.

[tex]\implies sample\ space= \{ HH, HT, TH, TT\}[/tex]

[tex]\implies total\ number \ of outcomes = 4[/tex]

Therefore,

The probability that you win is given by

[tex]P(E_{1} )=\frac{Number\ of \ favorable\ outcomes }{Total\ number \ of outcomes}[/tex]

[tex]\implies P(E_{1} )= \frac{1}{4}[/tex]                            (getting HH is a favorable outcome)

[tex]\implies probability\ of\ losing\ the\ game = 1-\frac{1}{4} =\frac{3}{4}[/tex]

And, the probability that your friend wins the game is given by

[tex]P(E_{2}) = \frac{Total\ number\ of\ favorable\ outcomes\ }{Total\ number\ of\ outcomes}[/tex]

[tex]\implies P(E_{2} )=\frac{1}{4}[/tex]                    (getting TT is the favorable outcome)

[tex]\implies probability\ of\ losing\ the\ game = 1-\frac{1}{4} =\frac{3}{4}[/tex]

Hence, the game is fair because there is an equal chance of winning an losing the game.

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Answer:

Step-by-step explanation:She can bowl 8 games and what I did was subtract the $4.25 from the $25and thethen divide the rest by the 2.52.50

Answer:

The next 3 steps are:
#1: [tex]\sqrt{ (x+2)^{2}} =\sqrt{10}[/tex] -- Using the square root method, we're going to find the square root of both sides.

#2: [tex]x+2 = \frac{+}{} \sqrt{ 10 }[/tex] -- When finding the square root of 10 it has to be + and minus.

#3: [tex]x + 2 = \frac{+}{}\sqrt{10} \\ -2 \ \ \ \ \ \ \ -2\\[/tex] -- Subtract 2 on both sides

#4 (solution): [tex]x = -2 \frac{+}{} \sqrt{10}[/tex]

Answer: 1.4

Step-by-step explanation: