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3 years ago

Two thirds of a number is 3 1/2 more than three eights of a number. find the number

1 answer:

6 0

2/3x = 3.5 + 3/8x
8 • (2/3x) = 3.5 + 3 • (3/8)

16/24 X = 3.5 + 9/24 X
16/24x - 9/24x = 3.5
7/24 X = 3.5
7x/24 = 3.5
24 • (7x/24) = 3.5 • 24
7x = 84
7x/7 = 84/7
X = 12.

The number is 12.

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What is the length side of a triangle that has vertices at (-5, -1), (-5, 5), and (3, -1)?

Rasek [7]

The side lengths of triangle are 6 units, 8 units and 10 units.

<u>SOLUTION: </u>

Given that, we have to find what is the length side of a triangle that has vertices at (-5, -1), (-5, 5), and (3, -1)

We know that, distance between two points $P\left(x_{1}, y_{1}\right) \text { and } Q\left(x_{2}, y_{2}\right)$ is given by

$P Q=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

Now,

$\begin{array}{l}{\text { Distance between }(-5,-1) \text { and }(-5,5)=\sqrt{(-5-(-5))^{2}+(5-(-1))^{2}}} \\\\ {\qquad \begin{array}{l}{=\sqrt{(-5-(-5))^{2}+(5-(-1))^{2}}} \\\\ {=\sqrt{(0)^{2}+(5+1)^{2}}=\sqrt{(6)^{2}}=6} \\\\ {=\sqrt{(-5)^{2}+(5+1)^{2}+(5-(-1))^{2}}} \\\\ {=\sqrt{(-8)^{2}+(5+1)^{2}}=\sqrt{64+36}=\sqrt{100}=10} \\\\ {=\sqrt{(3-1)^{2}+(-1-(-1))^{2}}} \\\\ {=\sqrt{(5+3)^{2}+(0)^{2}}=\sqrt{(8)^{2}}=8}\end{array}}\end{array}$

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3 years ago

Suppose that during one period extreme cold,the average daily temperature decreased 1 1/2 F each day. How many days did it take

Alenkasestr [34]

We have been given that during one period extreme cold, the average daily temperature decreased $1\frac{1}{2}$ degree F each day. We are asked to find number of days it will take for the temperature to decrease by 9 degree F.

First of all we will convert our mixed fraction into improper fraction.

$1\frac{1}{2}=\frac{3}{2}$

Now we will divide total temperature change (9) by average daily temperature change ( $\frac{3}{2}$ ) to find number of days.

$9\div\frac{3}{2}$

Dividing a number by a fraction is same as multiplying the number by reciprocal of the fraction.

$9\cdot\frac{2}{3}$

$3\cdot2=6$

Therefore, it will take 6 days for the temperature to decrease by 9 degree F.

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2 years ago

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zimovet [89]

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3 years ago

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sweet [91]

Answer:

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Step-by-step explanation:

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3 years ago

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ArbitrLikvidat [17]

Answer:

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3 years ago