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AnnZ [28]
3 years ago
12

How many times does the graph of 4x = 32 - x2 cross the x-axis ?

Mathematics
2 answers:
Alisiya [41]3 years ago
8 0

Answer:

Step-by-step explanation:

● 4x = 32 - x^2

Add x^2 to both sides

● 4x +x^2 = 32 -x^2+x^2

● x^2 +4x = 32

Substract 32 from both sides

● x^2+4x -32 =32-32

● x^2 +4x-32=0

That is a quadratic equation

We will use the determinant method

The determinant is b^2-4ac

● a = 1

● b = 4

● c = 32

● b^2-4ac = 4^2 -4×1×(-32) = 144

144 is positive so the parabola will cross the x-axis two times

● x = (-b -/+ √(b^2-4ac))/2a

● x = (-4 +/- 12) /2

● x = 8/2 or x= -16/2

● x = 4 or x =-8

The solutions are 4 and -8

Molodets [167]3 years ago
5 0

Answer:

x=4 orx=- 8

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

4

x

=

−

x

2

+

32

Step 2: Subtract -x^2+32 from both sides.

4

x

−

(

−

x

2

+

32

)

=

−

x

2

+

32

−

(

−

x

2

+

32

)

x

2

+

4

x

−

32

=

0

Step 3: Factor left side of equation.

(

x

−

4

)

(

x

+

8

)

=

0

Step 4: Set factors equal to 0.

x

−

4

=

0

or

x

+

8

=

0

x

=

4

or

x

=

−

8

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belka [17]

Answer:

g(x) = (-1/25)x + (203/25)

Step-by-step explanation:

The general equation for a line is slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept.

We know that perpendicular lines have opposite-signed, reciprocal slopes of the original line. Therefore, if the slope of f(x) is m = 25, the slope of g(x) must be m = (-1/25).

To find the y-intercept, we can use the newfound slope and the values from the given point to isolate "b".

g(x) = mx + b                                    <----- General equation

g(x) = (-1/25)x + b                             <----- Plug (-1/25) in "m"

8 = (-1/25)(3) + b                               <----- Plug in "x" and "y" from point

8 = (-3/25) + b                                  <----- Multiply (1/25) and 3

200/25 = (-3/25) + b                       <----- Covert 8 to a fraction

203/25 = b                                      <----- Add (3/25) to both sides

Now that we know both the values of the slope and y-intercept, we can construct the equation of g(x).

g(x) = (-1/25)x + (203/25)

4 0
2 years ago
Can someone solve and explain it to me please
lys-0071 [83]

Answer is C) 6

36 + 3(4x - 9) = 6(2x + 1)

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3 0
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A graduated commission employee makes 3.5% interest on the first $50,000 in sales and 6.5% interest on all sales over $50,000. W
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Step-by-step explanation:

6 0
3 years ago
What is the following product? Assume b&gt;0
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I’m sorry, need more information
6 0
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The ratio of runners to swimmers was 3:2. When 28 runners dropped out of the competition, the ratio became 5:6. How many total s
xz_007 [3.2K]

The total of 42 swimmers are competing

Step-by-step explanation:

The given is:

  • The ratio of runners to swimmers was 3 : 2
  • When 28 runners dropped out of the competition, the ratio became 5 : 6

We need to find how many total swimmers are competing

∵ The ratio of runners to swimmers was 3 : 2

- Multiply each term of the ratio by x

∴ There are 3x runners and 2x swimmers

∵ 28 runners dropped out of the competition

∴ The number of runners who complete = 3x - 28

∵ The ratio became 5 : 6

- Equate the ratio between the new number of runners and the

   number of swimmers by 5 : 6

∵ The new number of runners = 3x - 28

∵ The number of swimmers = 2x

∴ \frac{3x-28}{2x}=\frac{5}{6}

- By using cross multiplication

∴ 6(3x - 28) = 5(2x)

- Simplify both sides

∴ 18x - 168 = 10x

- Add 168 to both sides

∴ 18x = 10x + 168

- Subtract 10x from both sides

∴ 8x = 168

- Divide both sides by 8

∴ x = 21

∵ The number of swimmers is 2x

∵ x = 21

∴ The number of swimmers = 2(21) = 42

The total of 42 swimmers are competing

Learn more:

You can learn more about the ratio in brainly.com/question/2707032

#LearnwithBrainly

7 0
3 years ago
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