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3 years ago

multiplication is defined as repeated addition.use the word repeated to define exponential form.justify your reasoning.

1 answer:

4 0

Exponential form is when a certain number is raised to the power of a certain number or also known as exponents. Exponents signifies that the base or the number that is being raised to a certain powers will be multiplied a number of times, based on the exponents).

Exponential form is defined as repeated multiplication of the base.

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One of the roots of the quadratic equation dx^2+cx+p=0 is twice the other, find the relationship between d, c and p

scZoUnD [109]

Answer:

$c^2 = 9dp$

Step-by-step explanation:

Given

$dx^2 + cx + p = 0$

Let the roots be $\alpha$ and $\beta$

So:

$\alpha = 2\beta$

Required

Determine the relationship between d, c and p

$dx^2 + cx + p = 0$

Divide through by d

$\frac{dx^2}{d} + \frac{cx}{d} + \frac{p}{d} = 0$

$x^2 + \frac{c}{d}x + \frac{p}{d} = 0$

A quadratic equation has the form:

$x^2 - (\alpha + \beta)x + \alpha \beta = 0$

So:

$x^2 - (2\beta+ \beta)x + \beta*\beta = 0$

$x^2 - (3\beta)x + \beta^2 = 0$

So, we have:

$\frac{c}{d} = -3\beta$ -- (1)

and

$\frac{p}{d} = \beta^2$ -- (2)

Make $\beta$ the subject in (1)

$\frac{c}{d} = -3\beta$

$\beta = -\frac{c}{3d}$

Substitute $\beta = -\frac{c}{3d}$ in (2)

$\frac{p}{d} = (-\frac{c}{3d})^2$

$\frac{p}{d} = \frac{c^2}{9d^2}$

Multiply both sides by d

$d * \frac{p}{d} = \frac{c^2}{9d^2}*d$

$p = \frac{c^2}{9d}$

Cross Multiply

$9dp = c^2$

$c^2 = 9dp$

Hence, the relationship between d, c and p is: $c^2 = 9dp$

8 0

2 years ago

Find the exact length of the third side.<br> 40<br> 9

Nutka1998 [239]

Answer:

Step-by-step explanation:

3 0

3 years ago

About how far apart do aesha and Josh live

Vesnalui [34]

Answer:

D. about 8.5 mi

Step-by-step explanation:

To go from Aesha to Josh, you go 6 units right and 6 units up.

Each unit is a mile, so you go 6 miles right and 6 miles up.

Think of each 6 mile distance as a leg of a right triangle, and the direct distance from one place to the other as the hypotenuse of the right triangle. Use the Pythagorean theorem to find the length of the hypotenuse.

a^2 + b^2 = c^2

The 6-mile legs are a and b. c is the hypotenuse.

(6 mi)^2 + (6 mi)^2 = c^2

c^2 = 36 mi^2 + 36 mi^2

c^2 = 72 mi^2

c = sqrt(72) mi

c = sqrt(36 * 2) mi

c = 6sqrt(2) mi

c = 6(1.4142) mi

c = 8.5 mi

8 0

3 years ago

While Jane was visiting her sister in Winchester, she bought a wooden bench that was marked down 25% from an original price of $

Anna007 [38]

Answer:

Step-by-step explanation:

The total cost of the bench would be $72 after the markdown being 10% from the orginal proce which was $80.

4 0

2 years ago

In the xy-plane, the line determined by the points (2,k) and (k, 32) passes through the origin. Which of the following could be

alexgriva [62]

1) Considering that those points (2,k) and (k,32) determines one same line, within the plane. Therefore we can say that

2) Considering that since they pass through the origin then their x -coordinate is equal to zero, and their y coordinate as well so

3) We can state that as a matter of fact (2, k) and (K, 32) can be rewritten as (2,0) and (0,32)

k=0

6 0

1 year ago