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2 years ago

What is the area of this shape?

Mathematics

1 answer:

Dovator [93]2 years ago

3 0

Answer:

The area of this shape equals $30cm^{2}$

Step-by-step explanation:

From the diagram, we can see that this shape is a parallelogram (since opposite sides are equal to each other). The formula for the area of the parallerlogram is as follows:

$Area = bh$ (where "b" is the base, and "h" is the height).

And so we get...

$Area = bh = (10)(3) = 30cm^{2}$

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Solve The Equation 4x×9y=7 4x-9y=9

hoa [83]

Answer:

$\large\boxed{x=\dfrac{9}{8}-\dfrac{\sqrt{109}}{8},\ y=-\dfrac{1}{2}-\dfrac{\sqrt{109}}{18}}\\or\\\boxed{x=\dfrac{9}{8}+\dfrac{\sqrt{109}}{2},\ y=-\dfrac{1}{2}+\dfrac{\sqrt{109}}{18}}$

Step-by-step explanation:

$\left\{\begin{array}{ccc}4x\times9y=7&(1)\\4x-9y=9&(2)\end{array}\right\\\\(2)\\4x-9y=9\qquad\text{subtract}\ 4x\ \text{from both sides}\\-9y=-4x+9\qquad\text{change the signs}\\9y=4x-9\qquad\text{substitute it to (1)}\\\\4x(4x-9)=7\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\(4x)(4x)+(4x)(-9)=7\\(4x)^2-36x=7\\(4x)^2-2(4x)(4.5)=7\qquad\text{add}\ 4.5^2\ \text{to both sides}\\(4x)^2-2(4x)(4.5)+4.5^2=7+4.5^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2$

$(4x-4.5)^2=7+20.25\\(4x-4.5)=27.25\to 4x-4.5=\pm\sqrt{27.25}\\\\4x-\dfrac{45}{10}=\pm\sqrt{\dfrac{2725}{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{2725}}{\sqrt{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25\cdot109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25}\cdot\sqrt{109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{5\sqrt{109}}{10}\qquad\text{add}\ \dfrac{45}{10}\ \text{to both sides}\\\\4x=\dfrac{45}{10}\pm\dfrac{5\sqrt{109}}{10}$

$4x=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 4}\\\\x=\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\\\\\text{Put the values of}\ x\ \text{to (2):}\\\\9y=4\left(\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\right)-9\\\\9y=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}-\dfrac{18}{2}\\\\9y=-\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 9}\\\\y=-\dfrac{1}{2}\pm\dfrac{\sqrt{109}}{18}$

8 0

3 years ago

1: Ken earned $176 from his part-time job this summer. He spent 25% of his money on games. He is going to donate 14 of the rema

tatiyna

The charity will receive $ 11

<h3>Solution:</h3>

Ken earned $176 from his part-time job this summer

Amount earned = $ 176

He spent 25% of his money on games

Therefore,

Money spent on games = 176 - 25 % of 176

$\text{Money spent on games } = 176 - \frac{25}{100} \times 176\\\\\text{Money spent on games } = 176 - 0.25 \times 176\\\\\text{Money spent on games } = 176 - 44\\\\\text{Money spent on games } = 132$

He is going to donate 1/4 of the remaining money to charity

Reamining amount = 176 - 132 = 44

Therefore,

$Money\ given\ to\ charity = \frac{1}{4} \times 44 = 11$

Thus he gave $ 11 to charity

8 0

3 years ago

Jess owns 4 red shirts, 5 blue shirts, and 3 white shirts. She chooses a shirt to wear at random. What is the probability that s

Gelneren [198K]

3 out of 12 she will choose white

5 0

3 years ago

Read 2 more answers

in science class 2/3 of the students have a sister. Of the students who have a sister 1/2 have a brother which model shows the f

faust18 [17]

Answer:

1/3

Step-by-step explanation:

4 0

3 years ago

An airplane travels 290 km between Austin and Dallas in 1 h 15 min. What is it’s average speed?

aniked [119]

The average speed of the plane between Austin and Dallas is 232 kmph

Solution:

Given that,

Total distance traveled by airplane = 290 km

Time taken for travel between Austin and Dallas = 1 hour 15 minute

Let us convert the time taken to hours

$\begin{array}{l}{1 \text { minute }=\frac{1}{60} \text { hours }} \\\\ {15 \text { minutes }=\frac{15}{60}=\frac{1}{4}} \\\\ {\text { 1 hour } 15 \text { minutes }=1 \frac{1}{4} \text { hours }=\frac{1 \times 4+1}{4}=\frac{5}{4} \text { hours }}\end{array}$

The average speed is given as:

$\text { Average speed }=\frac{\text { total distance }}{\text { total time taken }}$

Plugging in the values, we get,

$\text { Average speed }=\frac{290}{\frac{5}{4}}=\frac{290}{5} \times 4=232$

Hence the average speed is 232 kmph

6 0

3 years ago