Need help finding the answer.

Write and solve a real world problem that can be represented by the expression (-3)(5)+10

ryzh [129]

Answer:

-5

Step-by-step explanation:

(-3)(5) =-15 +10 =-5

8 0

3 years ago

Read 2 more answers

The following integral requires a preliminary step such as long division or a change of variables before using the method of par

shtirl [24]

Division yields

$\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}$

Now for partial fractions: you're looking for constants a, b, and c such that

$\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}$

$\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a$

which gives a + b = 2, c = 0, and 2a = -7, so that a = -7/2 and b = 11/2. Then

$\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}$

Now, in the integral we get

$\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx$

The first two terms are trivial to integrate. For the third, substitute y = x ² + 2 and dy = 2x dx to get

$\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}$

7 0

2 years ago

The diagram below shows an Isosceles triangle. Label the base angles and the vertex

Dmitry [639]

The base angles of an isosceles triangle are equal

The base angles are 15 degrees, while the vertex angle is 150 degrees

The base angles are given as:

Base = (6a- 3) and (a + 12)

So, we have:

$\mathbf{6a -3 =a + 12}$

Collect like terms

$\mathbf{6a -a =3 + 12}$

$\mathbf{5a = 15}$

Divide both sides by 5

$\mathbf{a = 3}$

Substitute 3 for a in Base = (6a- 3),

$\mathbf{Base = 6 \times 3 - 3}$

$\mathbf{Base = 18 - 3}\\$

$\mathbf{Base = 15}$

So, the base angle is 15 degrees.

The vertex angle is calculated using:

$\mathbf{Vertex=180 -2 \times Base}$

So, we have:

$\mathbf{Vertex=180 -2 \times 15}$

$\mathbf{Vertex=150 }$

Hence, the vertex angle is 150 degrees

Read more about isosceles triangles at:

brainly.com/question/25739654

6 0

1 year ago

Which statement correctly compares the spreads of the distributions?

swat32

Answer:

b. the ranges of penguin heights are the same.

Step-by-step explanation:

Hello!

Statements:

Which statement correctly compares the spreads of the distributions?

a. the mode of penguin heights at county side zoo is greater than the mode at city view zoo.

b. the ranges of penguin heights are the same.

c. the range of penguin heights is greater at city view zoo than at county side zoo.

d. the range of penguin heights is greater at county side zoo than at city view zoo.

The mode and mean are measurements of central tendency, these indicate the position of a data set but don't show any information concerning the distribution of said data.

The range on the other had is a measurement of variance, it shows the difference between the maximum and minimum values of the data set and indicates its total dispersion.

City view Zoo R= 44-37= 7 cm

County side Zoo: R= 45-38= 7 cm

Both ranges are the same.

I hope this helps!

7 0

3 years ago

A colony of 40 bacteria doubles in size every 309 minutes. What will the population be 618 minutes from now?

andreev551 [17]

It will be 69 because 68 is wrong and 69 is right

7 0

2 years ago