Solve the equation for all real solutions.

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Explanation:

Vertex form in general is

y = a(x-h)^2 + k

The given vertex is at (3,6) meaning (h, k) = (3, 6)

So h = 3 and k = 6 are plugged into the first equation shown above

y = a(x-h)^2 + k

y = a(x-3)^2 + 6

Now plug in x = 1 and y = 42, which is from (x,y) = (1,42).

So we get,

y = a(x-3)^2 + 6

42 = a(1-3)^2 + 6

At this point, we have one variable and we can isolate it like so:

42 = a(1-3)^2 + 6

42 = a(-2)^2 + 6

42 = a(4)

42 = 4a+6

4a+6 = 42

4a = 42-6

4a = 36

a = 36/4

a = 9 is the final answer

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Extra info (optional section):

This means the y = a(x-h)^2 + k becomes y = 9(x-3)^2 + 6

Let's expand that out and get it into standard form

y = 9(x-3)^2 + 6

y = 9(x^2-6x+9) + 6

y = 9x^2-54x+81+6

y = 9x^2 - 54x + 87

The last equation is in the form y = ax^2+bx+c where,

a = 9

b = -54

c = 87

Answer:

He's correct its 432

Step-by-step explanation:

Answer: 470

Step-by-step explanation: I need One more brainliest for next rank I’d appreciate it

Answer:

40%

HOPE THIS HELPS

- Todo ❤️

Step-by-step explanation:

Is/of=%/100

8/20=%/100

8*100=800

800/20=40

Answer:

40%

Step-by-step explanation:

8 percent of 20=

8/20=0.4

0.4×100=40%

Answer:

D. y = sin (7.59x)

Step-by-step explanation:

I calculated it logically

Answer:

112.5

Step-by-step explanation:

He should expect 112.5 hits if he bats 450 times during the season.

In mathematics, Multiplication operations perform Multiplying values on either side of the operator.

For example 4×2 = 8

A baseball player's batting average is 0.250, which implies he hits 25% of the time he bats.

Here,

batting average = 0.250

number of times batting = 450

According to the given situation, the required solution would be as follows:

The number of hits = batting average × number of times batting

The number of hits = 0.250 × 450

Apply the multiplication operation, and we get

The number of hits = 112.5

Therefore, he should expect 112.5 hits to get.

Learn more about Multiplication operations here:

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tan is really sin/cos and cot is really cos/sin so just put what they really mean in their place to make it ----> sin 0/cos 0 + cos0/sin 0 = sec 0 csc 0 then sec 0 is really 1/sin 0 and csc 0 is really 1/cos 0 so you just sove by cross multiply and multiply bottom together to get sin^2 0 + cos^2 0/sin 0 cos 0 then simplify to get 1/sin 0 cos 0 which is really 1/sin 0 1/cos 0 = sec 0 csc 0.  ㄒɦĄŊĸ ĦØφĒ ĮŤ ɧėŁP ♡✧♡

Answer:

The probability that a car chosen at random is not red is 75%.

Step-by-step explanation:

Given that a used car dealer sells SUVs and cars, and of all the vehicles, 60% are cars, and of all the vehicles, 15% are red cars, to determine what is the probability that a car chosen at random is not red you must perform the following calculation:

60 = 100

15 = X

15 x 100/60 = X

25 = X

100 - 25 = 75

Therefore, the probability that a car chosen at random is not red is 75%.

Answer:

C) 31.2

Step-by-step explanation:

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hope it helps...

have a great day!

Answer:

A

Step-by-step explanation:

The requried simplified value of x in the intersection of two lines is 6.

Opposite angles are a pair of angles that are formed when two lines intersect. The two angles are located on opposite sides of the point where the two lines intersect.

Opposite angles are also called vertical angles, and they have equal measures. This means that if we know the measure of one opposite angle, we can find the measure of the other opposite angle by setting them equal to each other.

Here,
When two lines intersect, opposite angles are equal. So, we can set the two opposite angles equal to each other and solve for x.

Given that the opposite angles are 3x + 2 and 20 degrees, we have:

3x + 2 = 20

Subtracting 2 from both sides, we get:

3x = 18

Dividing both sides by 3, we get:

x = 6

Therefore, the value of x is 6.

Learn more about opposite angles here:

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Answer:

[tex] \displaystyle 702[/tex]

Step-by-step explanation:

we are given a exponential function

[tex] \displaystyle f(x) = {3}^{x + 1} - 22[/tex]

where x represents the number and f(x) represents the amount

we are also given that when x is 3 then f(x) is 59 likewise when x is 6 then f(x) is 2165

to figure out the average rate of change between 3 and 6 we can consider the average rate of change formula given by

[tex] \displaystyle m = \frac{ f(x)_ {2} - f(x)_{1} }{ x_{2} - x_{1} } [/tex]

substitute what we have:

[tex] \displaystyle m = \frac{ 2165 - 59 }{6 - 3 } [/tex]

simplify substitution:

[tex] \displaystyle m = \frac{2106 }{3 } [/tex]

simplify division:

[tex] \displaystyle m = 702[/tex]

hence, the average rate of change between 3 and 6 is 702

Answer:

1

Step-by-step explanation:

Multiply all(3) given lengths to get your volume.

Answer: 1 ft3 I think is the answer

Step-by-step explanation: :)

Answer:

$9.45

Step-by-step explanation:

1 - 0.12 = 0.88

12.60 * 0.88 = 9.45

You save $3.15

Answer:

The third equation, [tex]7\frac{1}{2} +m = 4\frac{2}{3}[/tex].

Step-by-step explanation:

In this question, we have to solve the equation for each of the options and after doing so we will see that the only option that will have m equal a positive number is the third option. Here is how we solve that equation:

[tex]7\frac{1}{2} +m = 4\frac{2}{3} \\m = 4\frac{2}{3} - 7\frac{1}{2}\\m = -2\frac{5}{6}[/tex]  

Answer:

Major Arc

Step-by-step explanation:

A major arc is the larger angle between two points of a circle -- greater than 180 degrees of rotation, whereas minor arcs are the smaller of the two possible arcs, arcs that are less than 180 degrees.

Answer:

(5,3)

Step-by-step explanation:

add the equations to eliminate to x's and get 8y=24

divide both sides by 8 to get y=3

then substitute in -2x+3(3)=-1 to solve for x

so x=5 so the solution is (5,3)

Answer:

[tex]x=5 \\y=3[/tex]

Step-by-step explanation:

[tex]-2x+3y=-1\\2x+5y=25[/tex]

Add these equations to eliminate x:

[tex]8y=24[/tex]

Then, solve [tex]8y=24[/tex] for y:

[tex]8y=24[/tex]

[tex]\frac{8y}{8} =\frac{24}{8}[/tex] (divide both sides by 8)

[tex]y=3[/tex]

Now let's find the value of x:

Substitute 3 for y in [tex]-2x+3y=-1[/tex]

[tex]-2x+(3)(3)=-1[/tex]

[tex]-2x+9=-1[/tex] (simplify both sides of the equation)

[tex]-2x+9+-9=-1+-9[/tex] (add both sides by -9)

[tex]-2x=-10[/tex]

[tex]\frac{-2x}{-2} =\frac{-10}{-2}[/tex]  (divide both sides by -2)

[tex]x=5[/tex]

Therefore, the value of x = 5 and y = 3

Answer:

16

Step-by-step explanation:

Answer:the answer is 16

Step-by-step explanation:

JUST ADD

Answer:

1/4

Step-by-step explanation:

5/20= 1/4

Answer:

1/5th of them are dogs

Step-by-step explanation:

5+20= 25

5/25 can be reduced to 1/5

Answer: 27

Step-by-step explanation:

9*3

Answer:

Population of fish in

{[12 ÷ 4] + [16 ÷ 8 (7 – 5)]} – 1.

{[3] + [2(2)]} – 1.

{[3] + [4]} – 1.

7-1

6

Answer:

Step-by-step explanation:

Remark

Let the shorter base = x

Let the longer base = 3x

h = 5

Area = 60

Formula

Area = (b1 + b2)*h /2

Solution

60 = (x + 3x)*5 / 2                Multiply both sides by 2

2*60 = (x + 3x)*5                  Combine like terms

120 = 4x *5

120 = 20x                             Divide by 20

120/20 = x

x = 6

Therefore the two bases are

x = 6

3x = 18

Answer:

C

Step-by-step explanation:

Answer:

A function R x that models the total revenue per game is as follows:

Rx = 87,5000 + 3,750x – 500x^2.

Step-by-step explanation:

Based on the information in the question, we have:

Rx = Total revenue per game

x = Number of $0.25 increases in the price of a hot dog

Average sales of hot dogs = 35,000

Effect of each 25 cent increase in the price on average sales = 35,000 - 2000x

Effect of each 25 cent increase in the price on selling price = 2.5 + 0.25x

Therefore, we have:

Rx = (35,000 - 2000x)(2.5 + 0.25x)

This can be solved further by opening the brackets as follows:

Rx = 87,5000 + 8,750x - 5,000x - 500x^2

Rx = 87,5000 + 3,750x – 500x^2

Therefore, a function R x that models the total revenue per game is Rx = 87,5000 + 3,750x – 500x^2.

Answer:

14

Step-by-step explanation:

If we take Gabrielle's age as 2x and Mikhail's age as x, it equals to 3x. Divide 42 by 3, multiply by 1, you get 14.