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eimsori [14]
3 years ago
9

Factoring with Diagrams

Mathematics
1 answer:
Finger [1]3 years ago
7 0

Answer:

(x - 7)(x - 4)(x + 4).            

Step-by-step explanation:

A(x) = x3 – 7x² – 16x +112

Dividing by x-7:

      x^2  - 16               <-------- Quotient

     -----------------------------

x-7)x^3 - 7x^2 - 16x + 112

     x^3 - 7x^2

                    0 - 16x + 112

                        - 16x + 112

                          ..............

so A(x) = (x - 7)(x^2 - 16)       x^2 - 16 is the difference of 2 squares so we have:

(x - 7)(x - 4)(x + 4).

Checking by expanding the brackets:  

(x - 7)(x - 4)(x + 4)

= x(x - 4)(x + 4) - 7(x - 4)(x + 4)

= x(x^2 - 16) - 7(x^2 - 16)

= x^3 - 16x - 7x^2 + 114

= x^3 - 7x^2 - 16x + 112          

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Step-by-step explanation:

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Identify, graph, and state the symmetries for the polar equation r=2+2sintheta.
IRINA_888 [86]

Answer:

Graph = Cardioid

Axis of symmetry = y-axis

Critical points= \frac{\pi}{2} , \frac{3\pi }{2}

Step-by-step explanation:

General equation for this type of cardioid is:

a ± b sinθ

Condition for a cardioid = \frac{a}{b} = 1

Axis of symmerty according to the graph of 2 + 2 sinθ is along y-axis.

Critical points:

r = 2 + 2 sinθ  ⇒ r = 2(1 + sinθ) ⇒ r' = 2 cosθ  

 ∵derivative of 1 + sinθ = cosθ

For finding critical point the derivative is equal to zero,

2 cosθ = 0    ⇒    cosθ = 0

the value of cosθ is equal to zero at intervals: \frac{\pi}{2} , \frac{3\pi }{2}

So, critical points = \frac{\pi}{2} , \frac{3\pi }{2}

3 0
3 years ago
Deja is training for a race on Saturday. On Sunday, she runs 1/6 of a mile. On Monday she runs 1/5 of a mile. On Tuesday she run
maksim [4K]

Answer:

49/20 miles or 2.45 miles

Step-by-step explanation:

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10/60+12/60+15/60+20/60+30/60+60/60=147/60=49/60 or 2.45

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Describe the graph of the Celsius-Fahrenheit relationship
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Using linear function concepts, the graph of the Celsius-Fahrenheit relationship is linear with an intercept of 32 and slope of 1.8.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

From the table, we have that:

  • When the input is of 0, the output is of 32, hence the intercept is of 32.
  • When the input changes by 10, the output changes by 18, hence the slope is of 18/10 = 1.8.

Thus, the graph of the Celsius-Fahrenheit relationship is linear with an intercept of 32 and slope of 1.8.

More can be learned about linear functions at brainly.com/question/24808124

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