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kramer
3 years ago
14

Find the remainder of the division of

Mathematics
2 answers:
Naily [24]3 years ago
7 0

Answer:

C) 77

Step-by-step explanation:

Using remainder theorem:

x = 7

7³ - 5(7)² - 4(7) + 7

77

katen-ka-za [31]3 years ago
6 0
<h3>Answer: C) 77</h3>

Remainder theorem: If p(x) is divided by (x-k), then the remainder is p(k)

In our case, p(x) = x^3-5x^2-4x+7 and k = 7

p(x) = x^3-5x^2-4x+7

p(7) = (7)^3-5(7)^2-4(7)+7

p(7) = 77

The remainder is 77

Side note: The nonzero remainder means x-7 is not a factor of x^3-5x^2-4x+7.

You can also use polynomial long division (see figure 1) or synthetic division (see figure 2). The figures are attached in the image below.

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700/10 equals 70, so the answer is 70.
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What is the constant of proportionality in the equation?<br>y=5x<br>0<br>1<br>4 or <br>5
Ann [662]

Answer:

hope it helps...

Step-by-step explanation:

The value of the constant of proportionality is k=5k=5

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=ky/x=k or y=kxy=kx

The value of the constant k is equal to the value of the slope

In this problem we have

y=5xy=5x ------> is a linear direct variation

The slope is m=5m=5

therefore

The value of the constant of proportionality is k=5k=5

4 0
3 years ago
What is the area of the sector? Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter
n200080 [17]

Question:

What is the area of the sector? Either enter an exact answer in terms of π or use 3.14 and enter your answer as a decimal rounded to the nearest hundredth.

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete as the values of radius and central angle are not given.

However, I'll answer the question using the attached figure.

From the attached figure, the radius is 3 unit and the central angle is 120 degrees

The area of a sector is calculated as thus;

Area = \frac{\alpha }{360} * \pi r^2

Where \alpha represents the central angle and r represents the radius

By substituting \alpha = 120 and r = 3

Area = \frac{\alpha }{360} * \pi r^2 becomes

Area = \frac{120}{360} * \pi * 3^2

Area = \frac{1}{3} * \pi * 9

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Area = 3\pi square units

Solving further to leave answer as a decimal; we have to substitute 3.14 for \pi

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Hence, the area of the sector in the attached figure is 3\pi or 9.42 square units

8 0
3 years ago
The width of a rectangle is the length minus 2 units. the area of the rectangle is 35 units
Mariana [72]

Answer:

Length=7units\\\\Width=5units

Step-by-step explanation:

Width=(Length-2) units

W=(L-2) units

Area of the rectangle= 35 square units

Area = length* Width

35= L*(L-2)\\\\35=L^2-2L

Subtracting 35 both sides:

L^2-2L-35=0

Solving the quadratic equation for 'L' ;

Using factorization:

L^2+5L-7L-35=0

Taking common from the equation :

L(L+5)-7(L+5)=0\\\\(L+5)(L-7)=0\\\\L+5=0\\\\L=-5

OR

L-7=0\\\\L=7

The length cannot be negative, therefore Length(L)= 7

Width=Length-2\\\\=7-2\\\\=5 units

Length=7units\\\\Width=5units

8 0
3 years ago
Use the discriminant to determine the nature of the roots of the following questions
soldier1979 [14.2K]

Answer:

the function has two distinct real roots.

Step-by-step explanation:

D=b²-4ac    

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D=0 One real root

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Since D is > than 0, the function has two distinct real roots.

6 0
3 years ago
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