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Using the Factor Theorem, the quadratic equation is given by:

[tex]f(x) = 6(x^2 + 10x + 24)[/tex]

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

In this problem, we have a quadratic function, meaning that it has two roots, and it passes through (-6,0) and (-4,0), hence the roots are [tex]x_1 = -4, x_2 = -6[/tex], thus:

[tex]f(x) = a(x + 4)(x + 6)[/tex]

[tex]f(x) = a(x^2 + 10x + 24)[/tex]

Considering that it passes through (-3, -18), we can find a, hence:

[tex]18 = a[(-3)^2 + 10(-3) + 24][/tex]

[tex]3a = 18[/tex]

[tex]a = 6[/tex]

Hence the equation is:

[tex]f(x) = 6(x^2 + 10x + 24)[/tex]

More can be learned about the Factor Theorem at https://brainly.com/question/24380382

Answer:

Sailing end at 3:15 AM

Step-by-step explanation:

Connor did archery and sailing before dinner (in that order).

He started at 12:00 PM

We know that:

In archery, Connor spent 1 hour and 15 minutes

In sailing, Connor spent 2 hours.

The total time spent is:

1 hour + 15 minutes + 2 hours

3 hours + 15 minutes.

Then sailing end 3 hours and 15 minutes after 12:00 pm = 0:00 am, this is:

3:15 AM

Sailing end at 3:15 AM

Answer:

102

Step-by-step explanation:

170*(60%) = 170 *0.6= 102

60% of the entire part is also 0.6

Answer:

y = -7/3x + 10

Step-by-step explanation:

Step 1: Find the slope of the perpendicular line

Do this by taking the negative inverse of the first line

m = -7/3

Step 2: Find b

y = mx + b

y = -7/3x + b

3 = -7/3(3) + b

3 = -7 + b

b = 10

Answer:

I inch per hour for 2 hours = 2 inches

2 inches per hour for 6 hours = 6*2 = 12 inches

1 inch per hour for 1 hour = 1 inch

2+12+1 = 15 inches of snow total

Step-by-step explanation:

credit to: musiclover10045

Answer:

4186.67 cubic inches

Step-by-step explanation:

Volume of a sphere = 4/3 π r³

π = 3.14

Diameter = 20 inches

Radius = r = Diameter/2 = 20 inches/2 = 10 inches

Volume of the sphere = 4/3 × 3.14 × (10 inches)³

Volume of the sphere = 12560 ÷ 3

= 4186.6666667 cubic inches

Approximately to the nearest hundredth = 4186.67 cubic inches

Therefore, the volume of the ball is 4186.67 cubic inches.

Answer:

Step-by-step explanation:

according to the question equation is

5x+8+3x=26+6x

8x+8=26+6x

8x-6x=26-8

2x=18

x=18/2

x=9

Answer:

x=9

Step-by-step explanation:

Answer:

696.96 million acres of land

Step-by-step explanation:

Acres not federally owned = Percentage of acres not federally owned x total acres of land

Percentage of acres not federally owned = 100% - percentage of acres federally owned

100% - 82% = 18%

0.18 x 3872 = 696.96 million acres of land

Answer:

9

Step-by-step explanation:

x = 3^2

x = 3*3

x = 9

Answer: . 9

Step-by-step explanation:

Simplify both sides of the equation.

Answer and Step-by-step explanation:

The answer would be A.

This is because we don't know how many students correctly answered 29 questions, but we do know how many students correctly answered 20-29 questions on the test.

As for the other answers, it asks about the full range and not a specific number.

#teamtrees #PAW (Plant And Water)

Hi there! We can find the value of x by using this equation.

[tex] \large \boxed{tanx = \frac{19}{23} }[/tex]

If you remember, tanx = opposite/adjacent. We focus on the angle x currently.

Now that you might wanna ask if there is a value of x that makes 19/23. The answer is yes but in decimal.

[tex] \large{arctan( \frac{19}{23} )} = x[/tex]

You might wanna put arctan(19/23) in a calculator since it's not really possible to get the square root like value by yourself.

arctan(19/23) is 0.69

Then we round up and get 0.7

Hence, the value of x ≈ 0.7

Answer

Questions can be asked through comment.

Hope it helps, and Happy Learning! :)

Answer:

7 and 1/8 i think

Step-by-step explanation:

Answer:

y=-4(x,y)=(0,-4)

y=-3(x,y)=(2,-3)

y=-2(x,y)=(4,-2)

y=-1(x,y)=(6,-1)

y=0(x,y)=(8,0)

y=1(x,y)=(10,1)

Step-by-step explanation:

Answer:

Answer attached

Step-by-step explanation:

I think you can plot it in the graph.

Step-by-step explanation:

x= how many members are in the group

x= 100/x

x= 100/(x-5)

x(x-5)=100

x^2-5x=100

x^2-5x-100=0

and then use the quadratic formula (i can't type it srry)

Answer:

Step-by-step explanation:

Initial number of members:  x

Sum of money:  K£ 100

Each had to pay:  100/x

Five members less, each paid K£1 more, we get equation:

Multiply all terms by x(x - 5) and solve the quadratic equation:

The second root is ignored as negative.

Answer:

1

when using a quadratic ration 1 is the formatted answer

Step-by-step explanation:

Answer:

it says 5 points u baiting us?XD

Step-by-step explanation:

Answer:

Helloooo

Step-by-step explanation:

Its just 5 point but thanks :)

Answer:

See below.

Step-by-step explanation:

As the diameter is 5 inches, the radius “r” is 5/2 = 2.5 inches.

We calculate the volume of a sphere as follows: [tex]V = 4/3 \pi r^3[/tex]

As we have to use 3.14 for pi, we’ll use that instead of “true” pi.

The formula becomes:

[tex]V = 4/3*3.14*2.5^3 = 65.42[/tex]

The volume of the sphere is 65.42 cubic inches.

Answer:

A!

Step-by-step explanation:

Hope that helps have an amazing day! <3

Answer:

D

Step-by-step explanation:

V = 4.5 ×5 ×2.5 = 56.25

(D )

Answer:

56  1/4 cm^3

Step-by-step explanation:

To find the volume,

V = l*w*h

  = 2 1/2 * 4 1/2 * 5

Changing to improper fractions

   = 5/2 * 9/2 *5

   = 225/4

Changing back to a mixed number

56  1/4 cm^3

Answer:

Assuming each box = 1 unit, the answer is 7.2

Step-by-step explanation:

Answer:

32 oz per water bottle

$0.33 dollars per ounce

Step-by-step explanation:

We are already given 32 oz as the amount per water bottle, so all we need to do is calculate the dollars per ounce. We can do this by dividing the cost of the water bottle by the number of ounces.

$10.70 ÷ 32= 0.334375 ------> 0.33

Rounding to the hundredths place we get $0.33.

Answer:

[tex]area = 960cm^2[/tex]

Step-by-step explanation:

Perimeter = 2 x (length + width) ------(1)

Perimeter = 124cm

Let length be x

Given width is 2cm shorter than length , that width = x -2

    [tex]Perimeter = 2 (x + (x -2))\\\\124 = 2(x +x -2)\\\\62 = 2x -2 \\64 = 2x\\x = 32[/tex]

Length = 32cm

Width = 32 - 2 = 30cm

Area = length x width

  [tex]= 32 \times 30 = 960cm^2[/tex]

Answer:

2n.

Step-by-step explanation:

This an arithmetic sequence with a1 = 2 and d = 2

an = a1 + d(n - 1)

= 2 + 2(n - 1)

= 2n + 2 - 2

= 2n.

Answer:

Step-by-step explanation:

a. Width

We are given the area and the length so we can use this to find the width using the formula for rate:

Length * Width = Area

20 * w = 200

20w = 200

w = 200/20

w = 10 cm

b. Now that you have both the length and the width, the perimeter is:

= (2 * length) + (2 * width)

= (2 * 20) + (2 * 10)

= 40 + 20

= 60 cm

Answer:

11

Step-by-step explanation:

dont forget to five-star and heart!

If the digit after tenth is greater than or equal to 5, add 1 to tenth. Else remove the digit. Example

124.58

The first number of right of decimal point is 5

The second digit after decimal point is 8 which is greater than 5

So add 1 to 5

Result = 124.6

no answer just explanation,

Answer:

Step-by-step explanation:

v=3p(w-r)

v=3pw-3pr

v+3pr=3pw

(v+3pr)/3p=w