A. 7/3 B. 3/7 C. -3/7 D. -7/3

Complete this proof.

Alja [10]

Answer:

1) distributive property

2) subtraction property of equality

3) division property of equality

Step-by-step explanation:

Given : If $\frac{1}{2}(8x+14)=39$ , then x=8

To complete the proof :

Solution :

Following are the complete steps or proof of solving the given expression,

$\frac{1}{2}(8x+14)=39$ is given

$4x + 7 = 39$ - distributive property

$4x = 32$ - subtraction property of equality

$x = 8$ - division property of equality

3 0

3 years ago

Read 2 more answers

How many integers between 10 and 60, inclusive, can be evenly divided by neither 2 nor 3?

erastovalidia [21]

Find total number of integers.

$a_1=10,a_n=60,d=1 \\a_n=a_1+(n-1)d \\60=10+(n-1)1 \\n-1=50 \\n=51$

Find how many integers is divisible by 2.

$a_1=10,a_n=60,d=2
\\a_n=a_1+(n-1)d
\\60=10+(n-1)2
\\2(n-1)=50
\\n-1=25
\\n=26$

Eliminate even numbers.

11, 13, 15,..., 57, 59

This array contains 51 - 26 = 25 numbers.

Eliminate numbers before the first number divisible by 3 and after the last number divisible by 3.

15, 17, 19,..., 55, 57

This array contains 25 - 3 = 22 numbers.

Now we should eliminate numbers divisible by 3: 15, 21, 27...

$a_1=15,a_n=57,d=6,n=?
\\a_n=a_1+(n-1)d
\\57=15+(n-1)6
\\6(n-1)=42
\\n-1=7
\\n=8$

There are 8 such numbers.

Therefore, there are 25 - 8 = 17 numbers that can be evenly divided by neither 2 nor 3

6 0

3 years ago

I need help solving this

pentagon [3]

Y=mx+b where m=slope=(dy/dx) and b=y-intercept (value of y when x=0)

You have two points...(1,-2),(3,2) so

m=(y2-y1)/(x2-x1)=(2--2)/(3-1)

m=4/2=2 now that you have the slope...

y=2x+b, you can use either point to solve for the y-intercept, I'll use (3,2)

2=2(3)+b

2=6+b

b=-4 so the line is:

y=2x-4

5 0

3 years ago

Please Help me. Also if you could show your work thatd be great.

Over [174]

Answer:

3) $all \: real \: numbers$ , $( - \infty , \infty )$ , or $- \infty \leqslant x \leqslant \infty$ (same thing)

4) $- \infty < y < 0$ or $( - \infty ,0)$ (same thing)

5) $-2$ or $(0, -2)$ (same thing)

Step-by-step explanation:

3) Domain represents the amount of $x$ -values in a function. The image shows that the function's arrows point in both directions (right and left), infinitely, so the domain would be $all \: real \: numbers$ , $( - \infty , \infty )$ , or $- \infty \leqslant x \leqslant \infty$ (same thing).

4) Range represents the amount of $y$ -values in a function. The function goes downward forever ( $- \infty < y$ ) by the indication of an arrow and halts just under the y-axis ( $y < 0$ ). After combining these two inequalities, you see that the range is $- \infty < y < 0$ or $( - \infty ,0)$ (same thing).