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4 years ago

Find the square of x^2+8^x+1 (please show work)

Mathematics

1 answer:

malfutka [58]4 years ago

8 0

Answer:

x^2 + 2^3x + 1

Step-by-step explanation:

In order to factor an integer, we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5...).

The number of times that each prime divides the original integer becomes its exponent in the final result.

In our example,

Prime number 2 to the power of 3 equals 8 .

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Please answer this question fast in two minutes

ahrayia [7]

Answer:

(7, 8)

Step-by-step explanation:

Midpoint Formula: $(\frac{x1+x2}{2}, \frac{y1+y2}{2})$

Simply set our midpoint and given point equal into a formula to find the other endpoint:

4 = (1 + x)/2

8 = 1 + x

x = 7

6 = (4 + y)/2

12 = 4 + y

y = 8

4 0

4 years ago

What is 15% of 60 draw a tape diagram

masha68 [24]

The 15% of 60 is 9 and a tape diagram, also known as a bar model, is a pictorial representation of ratios. In mathematics education, it is used to solve word problems.

7 0

4 years ago

A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2

Artemon [7]

Answer:

a) The height decreases at a rate of $\frac{7}{12}$ ft/sec.

b) The area increases at a rate of $\frac{527}{24}$ ft^2/sec

c) The angle is increasing at a rate of $\frac{1}{12}$ rad/sec

Step-by-step explanation:

Attached you will find a sketch of the situation. The ladder forms a triangle of base b and height h with the house. The key to any type of problem is to identify the formula we want to differentiate, by having in mind the rules of differentiation.

a) Using pythagorean theorem, we have that $25^2 = h^2+b^2$ . From here, we have that

$h^2 = 25^2-b^2$

if we differentiate with respecto to t (t is time), by implicit differentiation we get

$2h \frac{dh}{dt} = -2b\frac{db}{dt}$

Then,

$\frac{dh}{dt} = -\frac{b}{h}\frac{db}{dt}$ .

We are told that the base is increasing at a rate of 2 ft/s (that is the value of db/dt). Using the pythagorean theorem, when b = 7, then h = 24. So,

$\frac{dh}{dt} = -\frac{2\cdot 7}{24}= \frac{-7}{12}$

b) The area of the triangle is given by

$A = \frac{1}{2}bh$

By differentiating with respect to t, using the product formula we get

$\frac{dA}{dt} = \frac{1}{2} (\frac{db}{dt}h+b\frac{dh}{dt})$

when b=7, we know that h=24 and dh/dt = -1/12. Then

$\frac{dA}{dt} = \frac{1}{2}(2\cdot 24- 7\frac{7}{12}) = \frac{527}{24}$

c) Based on the drawing, we have that

$\sin(\theta)= \frac{b}{25}$

If we differentiate with respect of t, and recalling that the derivative of sine is cosine, we get

$\cos(\theta)\frac{d\theta}{dt}=\frac{1}{25}\frac{db}{dt}$ or, by replacing the value of db/dt

$\frac{d\theta}{dt}=\frac{2}{25\cos(\theta)}$

when b = 7, we have that h = 24, then $\cos(\theta) = \frac{24}{25}$ , then

$\frac{d\theta}{dt} = \frac{2}{25\frac{24}{25}} = \frac{2}{24} = \frac{1}{12}$

7 0

3 years ago

5/8 as a decimal and a percentage

Usimov [2.4K]

Answer:

5/8 as decimal is 0.625 and 62.5 percent

Step-by-step explanation:

Multiply 5 by 12.5 then divide by 100 and once you get the decimal multiply by 100.

4 0

3 years ago

One factor of f (x ) = 5 x cubed 5 x squared minus 170 x 280 is (x 7). what are all the roots of the function? use the remainder

olga2289 [7]

The roots of the function f(x) = 5x³ + 5x² - 170x + 280 are 2, 4 and -7

<h3>How to determine the roots of the function?</h3>

The function is given as:

f(x) = 5x³ + 5x² - 170x + 280

Factor out 5 in the function

f(x) = 5(x³ + x² - 34x + 56)

One of the roots is x + 7.

So, we have:

f(x)/(x + 7) = 5(x³ + x² - 34x + 56)/(x + 7)

Factor the expression on the right-hand side

f(x)/(x + 7) = 5((x - 2)(x - 4)(x + 7))/(x + 7)

Cancel out the common factors

f(x) = 5((x - 2)(x - 4)(x + 7)

Set the function to 0

5((x - 2)(x - 4)(x + 7) = 0

Divide through by 5

(x - 2)(x - 4)(x + 7) = 0

Expand

x - 2 = 0 or x - 4 = 0 or x + 7 = 0

Solve for x

x = 2, or x = 4 or x = -7

Hence, the roots of the function f(x) are 2, 4 and -7