If -15 is added to a number, the sum will be 8 times the number. find the number

The restaurant is trying out a new menu. They asked 25 people if they liked the changes and 19 said they did. The restaurant had

Finger [1]

My best answer is B.) 173. 19/25 = ?/227. 25 times 9.08 = 227 so 9.08 times 19 = 172.52 1 which rounds up to 173

3 0

3 years ago

Use Pascal’s Triangle to expand the binomial. (8v+s)^5

il63 [147K]

Pascal 's triangle is

1
1,1
1,2,1
1,3,3,1
1,4,6,4,1
1,5,10,10,5,1

the row 1,5,10,10,5,1 is the one we need to expand (8v+s)⁵.

Given (a+b)⁵ each term of the row is the coefficient of akbt

with k goes form 5 to 0 and t goes from 0 to 5.

so (a+b)⁵=1a⁵b⁰+5a⁴b¹+10a³b²+10a²b³+5a¹b⁵+1a⁰b⁵

=a⁵+5a⁴b+10a³b²+10a²b³+5ab⁵+b⁵.

In the case of (8v+s)⁵:

a=8v
b=s

1(8v)⁵s⁰+5(8v)⁴s¹+10(8v)³s²+10(8v)²s³+5(8v)¹s⁵+1(8v)⁰s⁵

= (8v)⁵+5(8v)⁴s+10(8v)³s²+10(8v)²s³+5(8v)s⁵+s⁵=

= 8⁵v⁵+5⋅8⁴v⁴s+10⋅8³v³s²+10⋅8²v²s³+40vs⁵+s⁵=

= 32768v⁵+20480v⁴s+5120v³s²+640v²s³+40vs⁵+s⁵.

8 0

3 years ago

If the area A of a triangle is 72, and the height h is equal to the length of the base b, what is the length of the base?

alexgriva [62]

Answer:

option B

Step-by-step explanation:

let the height=x

base=x

Area=½bh

72=½x•x

72×2=x²

144=x²

x=√144=12

5 0

2 years ago

Read 2 more answers

4

yaroslaw [1]

Answer:

The expression that represents the given sequence is 5+6(n-1). Option C (not labeled).

Explanation:

Arithmetic Sequences

In an arithmetic sequence, each term can be obtained by adding or subtracting a fixed number to the previous term. That fixed number is called the common difference.

We are given the following sequence:

5, 11, 17, 23, 29, ...

Each term is located in a position starting from n=1. Let's test each option:

A For n=1 we should have the first term (5). Substituting n=1 into the general equation: 5+6(n+1) = 5+6(1+1) = 5+12 = 17. Since the resulting term is not 5, this option is incorrect.

B For n=1, 6+5(n+1)= 6+5(2)=16. This option is incorrect.

C (not labeled) For n=1, 5+6(n-1)=5+6(1-1)=5+0=5. The first term is correct. Let's test for the second term (n=2):

5+6(2-1)=5+6=11. Correct. For n=3

5+6(3-1)=5+12=17. Correct.

We can see the terms are increasing by 6, and the given sequence is also increasing by 6. Thus, This option is correct.

D For n=1, 6+5 (n-1)=6+0=6. This option is incorrect.

5 0

2 years ago

Int(1 \(1 + {e}^{x} )

Andreyy89

Answer:

$\begin{aligned}\int{\frac{1}{1 + e^{x}}\cdot dx}= x - \ln(1 + e^{x}) + C\end{aligned}$ .

Step-by-step explanation:

The first derivative of the denominator $1 + e^{x}$ is $e^{x}$ . Rewrite the fraction to obtain that expression on the numerator.

$\begin{aligned}\frac{1}{1 + e^{x}} &= \frac{1 + e^{x}}{1 + e^{x}} - \frac{e^{x}}{1+e^{x}}\\&=1-\frac{e^{x}}{1+e^{x}}\end{aligned}$ .

In other words,

$\begin{aligned}\int{\frac{1}{1 + e^{x}}\cdot dx} &= \int{dx} - \int{\frac{e^{x}}{1+e^{x}}\cdot dx}\end{aligned}$ .

Apply $u$ -substitution on the integral $\displaystyle \int{\frac{e^{x}}{1+e^{x}}\cdot dx}$ :

Let $u = 1 + e^{x}$ . $u > 1$ .

$du = e^{x}\cdot dx$ .

$\displaystyle \int{\frac{e^{x}}{1+e^{x}}\cdot dx} = \int{\frac{du}{u}} = \ln{|u|} = \ln{u} +C = \ln{(1+e^{x})}+C$ .

Therefore

$\begin{aligned}\int{\frac{1}{1 + e^{x}}\cdot dx} &= \int{dx} - \int{\frac{e^{x}}{1+e^{x}}\cdot dx}\\ & = x - \ln{(1 + e^{x})}+C\end{aligned}$ .

7 0

2 years ago