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Dmitrij [34]
3 years ago
9

A useful rule of thumb called the "rule of 70" states that if something grows at a constant rate of z percent per year, it doubl

es in size approximately every __________ years.
a. z/70
b. 70/z
c. 70 - z
d. 70 × (z/100)
Mathematics
1 answer:
vesna_86 [32]3 years ago
4 0
<span>The answer is b. (70/z). If I put $100 into a savings account and the annual growth rate is 10%, the 70/10%= 7 years that the initial $100 would take to double.</span>
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Area of rectangle with diagonal of 5 in but length not given
sergij07 [2.7K]

Draw a rectangle with diagonal 5 in. Inside this rect. are 2 acute triangles of hypotenuse 5. Note that 3^2 + 4^2 = 5^2; thus the width of the rect. is 3 and the length is 4, with the result that the hypo. is sqrt(3^2+4^2), as expected.




3 0
3 years ago
what is the polynomial function of lowest degree with leading coefficient of 1 and roots 2 and 1 + square root2
Marta_Voda [28]
If the roots to such a polynomial are 2 and 1+\sqrt2, then we can write it as

(x-2)(x-(1+\sqrt2))

courtesy of the fundamental theorem of algebra. Now expanding yields

(x-2)(x-1-\sqrt2)=x^2-2x-(1+\sqrt2)x+2(1+\sqrt2)=x^2-(3+\sqrt2)x+2+2\sqrt2

which would be the correct answer, but clearly this option is not listed. Which is silly, because none of the offered solutions are *the* polynomial of lowest degree and leading coefficient 1.

So this makes me think you're expected to increase the multiplicity of one of the given roots, or you're expected to pull another root out of thin air. Judging by the choices, I think it's the latter, and that you're somehow supposed to know to use 1-\sqrt2 as a root. In this case, that would make our polynomial

(x-2)(x-(1+\sqrt2))(x-(1-\sqrt2))=x^3-4x^2+3x+2

so that the answer is (probably) the third choice.

Whoever originally wrote this question should reevaluate their word choice...
5 0
3 years ago
A function follows the rule y = -75 - 5 x . When the function's output is 25, the equation is 25 = -75 - 5 x .
Alex787 [66]

Answer:

The function's input = x = -20

Step-by-step explanation:

Given the function

y = -75 - 5x

Given that the output = y = 25

substituting the value y=25 and solve to find the input 'x'

25 = -75 - 5x

5x = -75-25

5x = -100

Divide bothe side by 5

x = -20

Thus, the function's input = x = -20

5 0
3 years ago
The perimeter of the trapezoid-shaped window frame is 23.59 feet. Write and solve an equation to find the unknown side length x
krok68 [10]

Answer:

5.62 + 3.65 + 5.62 + x = 23.59

x = 8.7 ft

Step-by-step explanation:

Perimeter of the trapezoid-shaped window = sum of all the sides of the window frame

Thus, the equation to find the unknown side length, x, would be:

✔️5.62 + 3.65 + 5.62 + x = 23.59

Solve for x

14.89 + x = 23.59

Subtract 14.89 from each side

14.89 + x - 14.89 = 23.59 - 14.89

✔️x = 8.7 ft

4 0
3 years ago
Will mark brainliest if correct :)
Finger [1]

Answer:

d = 12

c = 4

so I think d > c

Step-by-step explanation:

1 x 12 = 12

0.75 x 4 = 3

12 + 3 = 15

8 0
3 years ago
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