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3 years ago

HELP ASAP!! 10 points!

Mathematics

1 answer:

masha68 [24]3 years ago

7 0

$\dfrac{5}{7}\ of\ 100:\\\\\dfrac{5}{7}\cdot100=\dfrac{5\cdot100}{7}=\dfrac{500}{7}=\dfrac{70+28+2}{7}=\dfrac{70}{7}+\dfrac{28}{7}+\dfrac{2}{7}\\\\=10+4+\dfrac{2}{7}=14\dfrac{2}{7}\\\\\dfrac{2}{7}\ \text{is smaller than}\ \dfrac{1}{2}.\ \text{Therefore}\ 14\dfrac{2}{7}\approx14\\\\Answer:\ \boxed{14}$

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8^-3 x 8^-2 x 8^5 a. 8^30 b. 1 c. 80 d. 24

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$8^{-3}\times8^{-2}\times8^5=8^{-3+(-2)+5}=8^{-5+5}=8^0=1$
b. 1

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4. A 12,000 kg truck is traveling down the road when it slams on its breaks. It travels 70 m before it slows to a

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3 years ago

2. Choose the graph that shows the solution of the inequality on the number line

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Answer:

Number line 3 also known as [C]

Step-by-step explanation:

Given that:

c ≤ -1

Knowing that:

≤ = Less than or equal to

Now substitute into the equation:

C less than or equal to -1

Thus, it going left on a number line.

The only number line with left is [A] and [C]

Since ≤ = Less than or equal to -1

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Thus, the answer is [C]

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1 year ago

A 12 foot ladder is placed against the side of the building. The base of the ladder is placed at an angle of 68° with the ground

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Step-by-step explanation:

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3 years ago

Rationalize the denominator of $\frac{5}{2+\sqrt{6}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where $A$, $B$, $C$

horrorfan [7]

Answer:

$A +B+C+D = 3$ is the correct answer.

Step-by-step explanation:

Given:

$\frac{5}{2+\sqrt{6}}$

To find:

$A+B+C+D = ?$ if given term is written as following:

$\frac{A\sqrt{B}+C}{D}$

Solution:

We can see that the resulting expression does not contain anything under $\sqrt$ (square root) so we need to rationalize the denominator to remove the square root from denominator.

The rule to rationalize is:

Any term having square root term in the denominator, multiply and divide with the expression by changing the sign of square root term of the denominator.

Applying this rule to rationalize the given expression:

$\dfrac{5}{2+\sqrt{6}} \times \dfrac{2-\sqrt6}{2-\sqrt6}\\\Rightarrow \dfrac{5 \times (2-\sqrt6)}{(2+\sqrt{6}) \times (2-\sqrt6)} \\\Rightarrow \dfrac{10-5\sqrt6}{2^2-(\sqrt6)^2}\ \ \ \ \ (\because \bold{(a+b)(a-b)=a^2-b^2})\\\Rightarrow \dfrac{10-5\sqrt6}{4-6}\\\Rightarrow \dfrac{10-5\sqrt6}{-2}\\\Rightarrow \dfrac{-5\sqrt6+10}{-2}\\\Rightarrow \dfrac{5\sqrt6-10}{2}$

Comparing the above expression with:

$\frac{A\sqrt{B}+C}{D}$

A = 5, B = 6 (Not divisible by square of any prime)

C = -10

D = 2 (positive)

GCD of A, C and D is 1.

So, $A +B+C+D = 5+6-10+2 = \bold3$

5 0

3 years ago