Write an equivalent expression without parentheses and combine terms if possible 7(y + 7) - 11y

Mathematics

2 answers:

Vesnalui [34]3 years ago

3 0

Answer:

-4y +49

Step-by-step explanation:

Use the distributive property to eliminate parentheses. Then combine like terms.

7(y +7) -11y

= 7y +7·7 -11y

= y(7 -11) +49

= -4y +49

AURORKA [14]3 years ago

3 0

7(y+7)-11y
7y+49-11y

18y+49

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Alvin is 8 years older than Elga. The sum of their ages is 78. What is Elga's age?

Mazyrski [523]

Answer:

Step-by-step explanation:

ok let's look at these old farts.

alvin is 8 years older than elga, so elga needs 8 more years to be as old as Alvin is. AKA,

Alvin = Elga + 8

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Alvin + Elga = 78

Now put the equations together,

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2 years ago

Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha

Pavel [41]

Answer:

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Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

$\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}$ .

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

$\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}$ .

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$\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right)$ .

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

$\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}$ .