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2 years ago

What is the solution to this equation? −1/4(x+1 2/3)=−2 1/5

Mathematics

1 answer:

pogonyaev2 years ago

7 0

Answer:

x = 107/15

Step-by-step explanation:

Our first step should be to turn all of the mixed fractions into improper fractions. So, 1 2/3 becomes 5/3, and -2 1/5 becomes -11/5. We now get -1/4(x + 5/3) = -11/5. Now we should divide both sides by -1/4, and we get x + 5/3 = -11/5 x -4 = 44/5. So x + 5/3 = 44/5. We want the denominator to be equal on both sides so a common denominator could be 15. 5(5)/3(5) = 25/15. 44(3)/5(3) = 132/15. So now we have x + 25/15 = 132/15. We subtract both sides by 25/15 and we get x = 107/15.

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1. The diagonal of a quadrilateral

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Consider the length of diagonal is 8.5 cm instead of 8.5 m because length of perpendiculars are in cm.

Given:

Length of the diagonal of a quadrilateral = 8.5 cm

Lengths of the perpendiculars dropped on it from the remaining opposite vertices are 3.5 cm and 4.5 cm.

To find:

The area of the quadrilateral.

Solution:

Diagonal divides the quadrilateral in 2 triangles. If diagonal is the base of both triangles then the lengths of the perpendiculars dropped on it from the remaining opposite vertices are heights of those triangles.

According to the question,

Triangle 1 : Base = 8.5 cm and Height = 3.5 cm

Triangle 2 : Base = 8.5 cm and Height = 4.5 cm

Area of a triangle is

$Area=\dfrac{1}{2}\times base \times height$

Using this formula, we get

$Area(\Delta 1)=\dfrac{1}{2}\times 8.5\times 3.5$

$Area(\Delta 1)=14.875$

and

$Area(\Delta 2)=\dfrac{1}{2}\times 8.5\times 4.5$

$Area(\Delta 2)=19.125$

Now, area of the quadrilateral is

$Area=Area(\Delta 1)+Area(\Delta 2)$

$Area=14.875+19.125$

$Area=34$

Therefore, the area of the quadrilateral is 34 cm².

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2 years ago

How to simplify -2(x-6)

klasskru [66]

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Can you help me with this question please!

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Answer:

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Step-by-step explanation:

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In New York State, the minimum wage has grownexponentially. In 1966, the minimum wage was$1.25 an hour and in 2015, it was $8.75

Alona [7]

The Solution.

In 1966, which is the initial year(t); t = 0, and minimum wage(y), y = $1.25

Similarly.

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The rate of growth to the nearest percent is

$\text{Rate of growth =}\frac{y_2-y_1}{t_2-t_1}\times100$ $\begin{gathered} \text{Where y}_2=8.75,t_2=49\text{ years} \\ y_1=\text{ \$1.25},t_1=0 \end{gathered}$

Substituting into the formula above, we get

$\text{Rate of growth =}\frac{8.75-1.25}{49-0}\times100$ $\text{Rate of growth = }\frac{7.5}{49}\times100=15.31\approx15\text{ \%}$

Hence, the correct answer is 15%

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1 year ago

Jesse has 5 and 3/4 dozen eggs. How many eggs does Jesse have?

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