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zepelin [54]
2 years ago
14

5. The length of a rectangle is 3 inches less than its width. If the

Mathematics
1 answer:
artcher [175]2 years ago
5 0

Answer:

length is 17 in, width is 20

Step-by-step explanation:

let's shape this as an algebraic equation, where x= the length of one side.

since the width is 3 inches longer than the length, x will be the length and x+3 will be the width.

the perimeter is 74 in, and the perimeter is the added length of all sides. in a rectangle, 2 sides are the length and 2 sides are the width, so:

74 = 2x + 2(x + 3)

let's distribute the 2.

74 = 2x + 2x + 6

now, we combine the x's.

74 = 4x + 6

after this step, subtract 6 from the right to add it to the left side.

68 = 4x

finally, divide both sides by 4.

17 = x

perfect! now that we know the length, we just have to add 3 to find the width.

17 + 3 = 20

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15.
alekssr [168]

Answer:

  15. y = 6x

  16. x = 11

Step-by-step explanation:

15. A direct variation equation is of the form ...

  y = kx

Solving for k, we find ...

  k = y/x = 42/7 = 6

The equation is y = 6x.

__

16. Filling in the given values, we have ...

  66 = 6x

  11 = x . . . . . . . divide by 6

7 0
2 years ago
What should the following equation be multiplied by in order to eliminate the fractions? x/2 + x/3 = 25/3
tatuchka [14]

Answer:

6

Step-by-step explanation:

4 0
3 years ago
Verify that -5, 1/2, and 3/4 are the zeroes of the cubic polynomial 4x^3+20x^2+2x-3. Also verify the relationship between the ze
Finger [1]

Solution:

we have been asked to verify that -5, 1/2, and 3/4 are the zeroes of the cubic polynomial 4x^3+20x^2+2x-3

To verify that whether the given values are zeros or not we will substitute the values in the given Polynomial, if it will returns zero, it mean that value is Zero of the polynomial. But if it return any thing other than zeros it mean that value is not the zero of the polynomial.

Let f(x)=4x^3+20x^2+2x-3\\\\\text{when x=-5}\\\\f(-5)=4(-5)^3+20(-5)^2+2(-5)-3=-13\\\\\text{when x=}\frac{1}{2}\\

f( \frac{1}{2} ) = 4 ( \frac{1}{2} )^3+20(\frac{1}{2})^2+2(\frac{1}{2})-3=\frac{7}{2}\\\\

\text{when x=}\frac{3}{4}\\\\

f( \frac{3}{4} ) = 4 ( \frac{3}{4} )^3+20(\frac{3}{4})^2+2(\frac{3}{4})-3=\frac{183}{16}\\

Hence -5, 1/2, and 3/4 are not the zeroes of the given Polynomial.

Since sum of roots=\frac{-b}{a}= \frac{-20}{4}=-5\\

But -5+\frac{1}{2}+\frac{3}{4}=  \frac{-15}{4}\neq-5

Hence we do not find any relation between the coefficients and zeros.

Anyway if the given values doesn't represents the zeros then those given values will not have any relation with the coefficients of the p[polynomial.

6 0
3 years ago
What is the solution to the inequality x - 2 < -2?
7nadin3 [17]
Well the solution to this problem is x < -4
3 0
3 years ago
Question and choices Are below
Vika [28.1K]

Answer:

9ft

Step-by-step explanation:

Use the pythagorean theorem.

15^2 = 12^2 + x^2

solve for x

x^2 = 81

x = 9

7 0
3 years ago
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