MATHEMATICS HIGH SCHOOL

Which of these is a simplified form of the equation 7p 4 = − p 9 2p 3p? 13p = 13 3p = 5 7 = 4 11 = 15

Answers

Answer 1

Answer:

Answer:

$\boxed{\sf{3p=5}}$

Step-by-step explanation:

To find:

The value of p

Given:

7p + 4 = −p + 9 + 2p + 3p

$\sf{7p+4=-p+9+2p+3p}$

Isolate the term of p, from one side of the equation.

Combine like terms.

$\rightarrow \sf{7p+4=-p+2p+3p+9}$

Add the numbers from left to right.

-p+2p+3p=4p

7p+4=4p+9

Then, you subtract by 4 from both sides.

$\sf{7p+4-4=4p+9-4}$

Solve.

7p=4p+5

Subtract by 4p from both sides.

7p-4p=4p+5-4p

Solve.

$\boxed{\sf{3p=5}}$

Divide by 3 from both sides.

3p/3=5/3

Solve.

p=5/3

Divide is another option.

5/3=1.6666

So, the final answer is 3p=5.

I hope this helps, let me know if you have any questions.

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Round 45,122 to the nearest ten thousand

Answers

Rounded to the nearest 10,000, 45,122 is 50,000. This is because the 5 has been reached and so it is rounded up.

To round to the nearest ten thousand, we look at the last four digits. If these digits are 5000 or greater, then we round the thousands digit up, and if they are less than 5000, then we round down, keeping the ten thousand's digit the same.

The question is asking to Round 45,122 to the nearest ten thousand .

The last 4 digits are 5122.

This is greater than 5000.So we round up .

45,122 to the nearest ten thousand is 50,000.

The length of a rectangle is 7 mm longer than its width. Its perimeter is more than 62 mm. Let w equal the width of the rectangle. Write an expression for the length in terms of the width.
Use these expressions to write an inequality based on the given information.
Solve the inequality, clearly indicating the width of the rectangle

Answers

We know that the length (L) of the rectangle in question is 7mm longer than its width (W). Let's represent that as the following:
L=7+W

A rectangle's perimeter (the total sum of its sides) will be made my 2 sides representing the length (2L) and 2 sides representing the width (2W). We also know that this rectangle's perimeter is greater than 62. Since eventually we are solving for W, let's state all expressions in terms of W:
2L=2(7+W)
2(7+W)+2W>62
14+2W+2W>62
14+4W>62
4W>62-14
4W>48
W>48/4
W>12
If the rectangle's perimeter is greater than 62, then the width will be greater than 12. Let's confirm this:
Perimeter=2L+2W
P=2(7+12)+2(12)
P=14+24+24
P=62
So we can see that if the perimeter is to surpass 62, W needs to be greater than 12 and L ( which is also 7+W) needs to be greater than 19.

Final answer:

The length of the rectangle is expressed as w + 7 mm. The inequality for the perimeter is 2(w + w + 7) > 62. The solution for the inequality reveals that the width, w, must be more than 12mm.

Explanation:

The question is asking for an expression for the length of a rectangle in terms of the width and an inequality based on the perimeter. We are given that the length of the rectangle is 7 mm longer than its width, and its perimeter is more than 62 mm.

The width of the rectangle is defined as w. We can express the length as w + 7 mm, since it is 7 mm longer than the width.

The perimeter of a rectangle is calculated as 2 times the sum of its width and length, so we form the inequality: 2(w + w + 7) > 62.

To solve it, we simplify the left side: 4w + 14 > 62. We then subtract 14 from both sides, getting 4w > 48. Finally, we divide both sides by 4, which gives us w > 12. Therefore, the width of the rectangle must be more than 12 mm.

Learn more about Inequalities here:

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A soft drink manufacturer produces 3120 cans in an 8 hour day. Cans are packaged 24 to a case. How many cases are produced each week? Each month? (Assume one week is 40 hours and one month is four weeks )

Answers

Week: 3120 x 5 = 15,600 cans ÷ 24 = 650 cases

Month: 650 x 4 = 2,600 cases

Find the particular solution to y ' = 2sin(x) given the general solution is y = C - 2cos(x) and the initial condition y of pi over 2 equals 1 .-2cos(x)
2 - 2cos(x)
1 - 2cos(x)
-2 - 2cos(x)

I think it is option C. Thank you in advance!

Answers

Answer:

1 − 2 cos x

Step-by-step explanation:

y' = 2 sin x

y = C − 2 cos x

1 = C − 2 cos(π/2)

1 = C

y = 1 − 2 cos x

Use the following table of the function f(x) = x4 − 4x to answer this question: x f(x)
-2 24
-1 5
0 0
1 -3
2 8
What is the average rate of change from x = −1 to x = 2?
A. −3
B. −1
C. 1
D. 3