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3 years ago

Use the distributive property and combine like terms to write an equivalent expression: 5(3x + 2) - 8(x +1)

2 answers:

6 0

5(3x+2)-8(x+1)
= 15x + 10 - 8x - 8 (open parenthesis. first one multiple each term by 5. second one, multiply each term by -8)
= 7x + 2 (subtract like terms)

bixtya [17]3 years ago

4 0

Answer:

7x + 8

Step-by-step explanation:

15x + 10 - 8x + 8

combine like terms

7x + 8

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A sequence is defined by the recursive function f(n + 1) = one-halff(n). If f(3) = 9 , what is f(1) ? 1 3 27 81

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Answer:

Step-by-step explanation:

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3 years ago

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Brandy plays a hockey video game. She earns 2 stars for every goal she scores

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-8 stars

Step-by-step explanation:

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3 years ago

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The 11th term of an progression is 25 and the sum of the first 4 terms is 49. The nth term of the progression is 49

KIM [24]

Answer:

For 1: The first term is 10 and the common difference is $\frac{3}{2}$

For 2: The value of n is 27

Step-by-step explanation:

The n-th term of the progression is given as:

$a_n=a_1+(n-1)d$

where,

$a_1$ is the first term, n is the number of terms and d is the common difference

The sum of n-th terms of the progression is given as:

$S_n=\frac{n}{2}[2a_1+(n-1)d]$

where,

$S_n$ is the sum of nth terms

For (1):

The 11th term of the progression:

$25=a_1+10d$ .......(1)

Sum of first 4 numbers:

$49=\frac{4}{2}[2a_1+3d$ ......(2)

Forming equations:

$98=8a_1+12d$

$25=a_1+10d$ ( × 8)

The equations become:

$98=8a_1+12d$

$200=8a_1+80d$

Solving above equations, we get:

$102=68d\\\\d=\frac{102}{68}=\frac{3}{2}$

Putting value in equation (1):

$25=a_1+10\frac{3}{2}\\\\a_1=[25-15]=10$

Hence, the first term is 10 and the common difference is $\frac{3}{2}$

For 2:

The nth term is given as:

$49=10+(n-1)\frac{3}{2}$

Solving the above equation:

$39=(n-1)\frac{3}{2}\\\\n-1=26\\\\n=27$

Hence, the value of n is 27

3 0

3 years ago

Deon rolled a susided die 40 times. The number 4, appears 15 times. Find the

dedylja [7]

Answer:

The experimental probability of rolling a 4 in the next trial is $\frac{1}{6}$ .

Step-by-step explanation:

The experimental probability is the ratio of the favorable outcomes to the total number of outcomes.

That is, the probability of an event E is:

$P(E)=\frac{n(E)}{N}$

Here,

n (E) = favorable outcomes

N = total number of outcomes

It is provided that Deon rolled a six-sided die 40 times.

And in these 40 rolls, the number 4 appeared 15 times.

A six-sided die has an equal probability of landing on any of the six numbers.

The rolling a die is an independent event experiment, i.e. the result of the previous roll does not affect the result of next roll.

Let X = number on the face of the die

Compute the probability of rolling a 4 in the next trial as follows:

P (Rolling a 4) = P (X = 4)

$=\frac{n(X=4)}{N}\\=\frac{1}{6}\\$

Thus, the experimental probability of rolling a 4 in the next trial is $\frac{1}{6}$ .

8 0

4 years ago

A bank loaned out $17,500, part of it at the rate of 10% annual interest, and the rest at 14% annual interest. The total interes

Gennadij [26K]

Answer:

$7 000 was loaned at 10 % and

$10 500 was loaned at 14 %

Step-by-step explanation:

Let x = amount loaned at 10 %

Then 17 500 - x = amount loaned at 14 %

0.10x = interest on 10 % loan

0.14(17 500 - x) = interest on 14 % loan

2170.00 = total interest

$\begin{array}{rcl}0.10x + 0.14(17 500 - x) & = & 2170.00\\0.10x + 2450 - 0.14x & = & 2170.00\\2450 - 0.04x & = & 2170.00\\-0.04x & = & -280\\\\x & = & \dfrac{-280}{-0.04}\\\\x & = & \mathbf{7000}\\\\\end{array}$

$7000 was loaned at 10 % and

$10 500 was loaned at 14 %

Check:

\ $\begin{array}{rcl}0.10\times 7000 + 0.14(17 500 - 7000) & = & 2170\\700 + 0.14(10 500) & = & 2170\\700 + 1470 & = & 2170\\2170 & = & 2170\\\end{array}$

OK.

3 0

4 years ago