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PIT_PIT [208]
3 years ago
13

Solve for p and simplify

Mathematics
2 answers:
nadezda [96]3 years ago
7 0

Answer:

8

Step-by-step explanation:

-\dfrac{1}{2} + p = \dfrac{5}{8}

Add 1/2 to both sides.

-\dfrac{1}{2} + p + \dfrac{1}{2} = \dfrac{5}{8} + \dfrac{1}{2}

p = \dfrac{5}{8} + \dfrac{4}{8}

p = \dfrac{9}{8}

dedylja [7]3 years ago
3 0

Given : \dfrac{-1}{2} + p = \dfrac{5}{8}

\implies p = \dfrac{1}{2} + \dfrac{5}{8}

\implies p = \dfrac{4 + 5}{8}

\implies p = \dfrac{9}{8}

The Question Mark should be Replaced with 8

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The mass of the particles that a river can transport is proportional to the sixth power of the speed of the river. A certain riv
kari74 [83]
The river flows at 2 miles per hour. This is the speed of the current, or the speed at which the water itself is moving.

The mass of the particles moving in river is proportional to the sixth power of 2, or 2^6 = 64 miles per hour. So, if x is the mass of the particle, then the speed is modeled by an inverse relationship x * 2^6 = k, for some constant k. 

For particles that are 15 times the usual mass, the speed of the river itself must increase for the particles to travel at the same speed as before. The mass of the particles is still proportional to the sixth power of the speed of the river, but the speed of the river can no longer be 2 miles per hour. It is some speed y, which we are solving for.

So, the key here is proportional. We can set up two proportions and cross multiply.

\dfrac{x}{2^6} =  \dfrac{15x}{y^6}  \\ (x)(y^6)=(2^6)(15x)

Cancelling our x's (because we don't need to solve for them), we have

y^6 = 15(2^6) = 15(64)=960

To solve for y, we must take the sixth root of both sides, or raise both sides to the one-sixth power.

\sqrt[6]{y^6} =  \sqrt[6]{960}

Using a calculator, we see that \sqrt[6]{960} = 3.14 \ miles \ per \ hour.
6 0
3 years ago
Evaluate -x^2-2x+5 when x=-10
kvv77 [185]
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6 0
3 years ago
Write a recursive rule for the sequence 4,10,16,22
Phantasy [73]

Answer:

a_{n+1} = a_{n} + 6

Step-by-step explanation:

The terms have a common difference d between consecutive terms, that is

10 - 4 = 16 - 10 = 22 - 16 = 6

To obtain the next term add 6 to the previous term ( recursive rule ), thus

a_{n+1} = a_{n} + 6 with a₁ = 4

8 0
3 years ago
Help please :D<br> this is a maps test so this is higher than my level
Citrus2011 [14]

Answer:

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Step-by-step explanation:

5 0
3 years ago
PLEASE HELP!!! I have no clue how to find the perimeter of MNP
vladimir1956 [14]

Answer:

130

Step-by-step explanation:

Triangle MNP is twice the size of triangle SRP. So 2(x+4)=5x-34.

Distribute: 2x+8=5x-34

Add 34 on both sides: 2x+42=5x

Subract 2x on both sides: 42=3x

Divide both sides by 3: 14=x

If x=14, then 5x-34

is 5(14)-34=70-34=36.

The perimeter of the triangle MNP is

MN+NP+PM.

MN is 36

NP is doubled the 22 because triangle MNP is twice the size of triangle MQS. So NP is 44.

PM is doubled the 25 because triangle MNP is twice the size of triangle QNR. So PM is 50.

The perimeter of the triangle MNP is

MN+NP+PM

=36+44+50

=130

3 0
3 years ago
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