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2 years ago

Ethan is a farmer. He spends 50 hours each week working on

Mathematics

1 answer:

Ne4ueva [31]2 years ago

6 0

2/9 of 50 = 11.1
Ethan spends 11.1 hours feeding the animals every week

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Write the equation of a line that contains (2,−2) and perpendicular to another line with slope −1. (20 POINTS)

Kay [80]

Y=mx+b or -2=-1 x 2+b, b= -2(-1)(2) b=0

Therefore the equation of the line is

y=-1x

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3 years ago

51 less than the 8 times an unknown number is equal to 53.

Anton [14]

Let, Unknown number = x

8x-51 = 53

8x = 53+51

x = 104/8

x = 13

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3 years ago

Solve The Equation <br> 4x×9y=7<br> 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:

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

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

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

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3 years ago

Gary wants to buy a bicycle that usually sells for $74.99. The store is having a sale and all merchandise is discounted by 25%.

NeX [460]

Answer:

B. $56.24

Step-by-step explanation:

74.99 x 7.5%=5.62425

5.62425 x 10= 56.24

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2 years ago

If you horizontally stretch the quadratic parent function, f(x) = x2, by a factor of 4, what is the equation of the new function

navik [9.2K]

Please write x^2, not x2.

If you stretch the graph of y=x^2 vertically by a factor of 4, the resulting graph represents the quadratic function y = 4x^2. It's still a parabola, but appears to be thinner.

This particular question is about horizontal stretching, however. Stretching the graph horizontally by a factor of 4 results in the new function g(x) = (x/4)^2. Try graphing x^2 and also (x/4)^2 on the same set of axes to observe this phenomenon.

3 0

3 years ago

Read 2 more answers