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dem82 [27]
2 years ago
6

find three consecutive integers for which 3 times the sum of the first and third integers is -342? show step by step

Mathematics
1 answer:
Artyom0805 [142]2 years ago
3 0

Answer:

-58, -57, -56

Step-by-step explanation:

if the first integer is x,

the second integer must be x + 1 (because it's consecutive)

and the third must be x + 2

Therefore:

3 times the sum of the first and third integers is -342:

3 * (x + (x+2) ) = -342

Combine like terms in parentheses

3 * (2x + 2) = -342

Distribute the 3 to the 2x and the 2:

6x + 6 = -342

Subtract 6 on both sides

6x = -348

Divide by 6 on both sides

x = -58

x + 1 = -57

x + 2 = -56

-58, -57, -56

Check:

3 * (-58 + -56) = 3 * -114 = -342

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A trader had 30,500 eggs . He sold 12,680 of them to John and 16,570 to Peter. How many eggs he had left
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Answer:

C. 17,820

Step-by-step explanation:

30,500-12,680= 17,820

4 0
2 years ago
Quadrilateral ABCD is inscribed in a circle. What is the measure of angle A? Enter your answer in the box.
SashulF [63]

Answer:

135°

Step-by-step Explanation:

==>Given:

An inscribed quadrilateral ABCD with,

m<A = (3x +6)°

m<C = (x + 2)°

==>Required:

measure of angle A

==>Solution:

First, let's find the value of x.

Recall that the opposite angles in any inscribed quadrilateral in a circle are supplementary.

Therefore, this means m<A + m<C = 180°

Thus, (3x+6) + (x+2} = 180

3x + 6 + x + 2 = 180

Collect like terms:

3x + x + 6 + 2 = 180

4x + 8 = 180

Subtract 8 from both sides:

4x + 8 - 8 = 180 - 8

4x = 172

Divide both sides by 4:

4x/4 = 172/4

x = 43

We can now find m<A = (3x + 6)°

m<A = 3(43) + 6

= 129 + 6

measure of angle A = 135°

6 0
3 years ago
A triangular prism is 4 millimeters long. It has a triangular face with a base of 13 millimeters. The volume of the prism is 416
muminat

Answer:

16 millimeters

Step-by-step explanation:

  • Length of the Triangular Prism=4 millimeters
  • Base Length of One Triangular Face=13 millimeters.
  • Volume of the Prism =416 cubic millimeters.

Now:

Volume of a Prism=Base Area X Prism Length

Since we have a triangular base:

Volume of the Prism=(0.5 X Base X Height) X Prism Length

Substituting the given values, we obtain:

416=(0.5 X 13 X Height) X 4

416=26 X Height

Divide both sides by 26

Height of its triangular face=16 millimeters

4 0
3 years ago
Read 2 more answers
A line and the point (3,4) are graphed in the coordinate plane. what is the equation of the line that passes through the point (
oksano4ka [1.4K]

Answer:

B. y=1/4x+13/4

Step-by-step explanation:

3 0
2 years ago
Add three data values to the following data set so the mean increases by 10 but the median does not change. The numbers are 42 3
777dan777 [17]
In order the numbers are 20, 29, 32, 37, 42.
So that means the median is 32. In order for the median to stay the same one of the three data values must be 32 as well as adding a number to each side of the ends. One 32 or less another 32or more.
The mean right now is: 20+29+32+37+42=160 and there are 5 values.
Mean: 160/5=32
For it to increase by 10 it has to be 42.
extra 3 numbers I used were 31, 32, & 113 (those are your answer)
3 0
3 years ago
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