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3 years ago

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

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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 $13\%\ of\ 215$

⇒ $13\%\ of\ 215$

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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 .

Given :-

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

To Prove :-

• $\sf\implies cos2A =\dfrac{\sqrt3}{2}$

Proof :-

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 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.

3 + -3 + 2z = 9 + -3

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

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