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Alla [95]
3 years ago
12

which inequality represents the following situation 3/5 times 5 less than a number is no more than 27

Mathematics
1 answer:
andrey2020 [161]3 years ago
6 0

The answer is \frac{3}{5}(x-5) \leq 27


Let's build the expression piece by piece, translating sentences into formulas:


"3/5 times..." \to \frac{3}{5} \times \ldots


"5 less than a number..." \to x-5 \ldots


So, the first block becomes


"3/5 times 5 less than a number..." \to \frac{3}{5}(x-5) \ldots


"...is no more than 27" \ldots \leq 27


So, putting the pieces together, you have the answer



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3 years ago
Assume that in October of a particular year about 215 billion text messages were sent or received in the US, and the prediction
Julli [10]

Answer:

There will be 243 billion messages sent or received in November.

Step-by-step explanation:

Given.

Number of text messages sent or received =215 billion.

Increment on the very next month =13\%=\frac{13}{100}=0.13

Lets find what is 13\%\ of\ 215

 ⇒13\%\ of\ 215

 ⇒0.13\times 215=27.95

So we will add this value to our previous months data.

Now

Number of text messages sent in the month of November =(27.5+215)=242.95 billion.

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5 0
3 years ago
If sinA=√3-1/2√2,then prove that cos2A=√3/2 prove that
Ivan

Answer:

\boxed{\sf cos2A =\dfrac{\sqrt3}{2}}

Step-by-step explanation:

Here we are given that the value of sinA is √3-1/2√2 , and we need to prove that the value of cos2A is √3/2 .

<u>Given</u><u> </u><u>:</u><u>-</u>

• \sf\implies sinA =\dfrac{\sqrt3-1}{2\sqrt2}

<u>To</u><u> </u><u>Prove</u><u> </u><u>:</u><u>-</u><u> </u>

•\sf\implies cos2A =\dfrac{\sqrt3}{2}

<u>Proof </u><u>:</u><u>-</u><u> </u>

We know that ,

\sf\implies cos2A = 1 - 2sin^2A

Therefore , here substituting the value of sinA , we have ,

\sf\implies cos2A = 1 - 2\bigg( \dfrac{\sqrt3-1}{2\sqrt2}\bigg)^2

Simplify the whole square ,

\sf\implies cos2A = 1 -2\times \dfrac{ 3 +1-2\sqrt3}{8}

Add the numbers in numerator ,

\sf\implies cos2A =  1-2\times \dfrac{4-2\sqrt3}{8}

Multiply it by 2 ,

\sf\implies cos2A = 1 - \dfrac{ 4-2\sqrt3}{4}

Take out 2 common from the numerator ,

\sf\implies cos2A = 1-\dfrac{2(2-\sqrt3)}{4}

Simplify ,

\sf\implies cos2A =  1 -\dfrac{ 2-\sqrt3}{2}

Subtract the numbers ,

\sf\implies cos2A = \dfrac{ 2-2+\sqrt3}{2}

Simplify,

\sf\implies \boxed{\pink{\sf cos2A =\dfrac{\sqrt3}{2}} }

Hence Proved !

8 0
3 years ago
Solve the following equation <br> 6x-3=4z+9
Pie

Answer:

z=1.5

Step-by-step explanation:

Simplifying

6z + 3 + -4z = 9

Reorder the terms:

3 + 6z + -4z = 9

Combine like terms: 6z + -4z = 2z

3 + 2z = 9

Solving

3 + 2z = 9

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '-3' to each side of the equation.

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Combine like terms: 3 + -3 = 0

0 + 2z = 9 + -3

2z = 9 + -3

Combine like terms: 9 + -3 = 6

2z = 6

Divide each side by '2'.

z = 3

Simplifying

z = 3

8 0
3 years ago
Read 2 more answers
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