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3 years ago

Write the equation of a line perpendicular to 9xplus7yequals6 that passes through the point (9,negative 7).

Mathematics

1 answer:

andrew11 [14]3 years ago

7 0

$k:\ y=m_1x+b_1\\\\l:\ y=m_2x+b_2\\\\k\ ||\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1$

We have:

$k:\ 9x+7y=6\ \ \ |-9x\\\\7y=-9x+6\ \ \ \ |:7\\\\y=-\dfrac{9}{7}x+\dfrac{6}{9}\to m_1=-\dfrac{9}{7}\\\\l:\ y=m_2x+b\\\\l\ \perp\ k\iff-\dfrac{9}{7}m_2=-1\ \ \ \ |\cdot\left(-\dfrac{7}{9}\right)\\\\m_2=\dfrac{7}{9}\to\ l:\ y=\dfrac{7}{9}x+b$

We know. The line <em>l</em> passes throught the point (9, -7). Substitute the coordinates of the poin to the equation of line<em> l </em>:

$-7=\dfrac{7}{9}\cdot9+b\\\\-7=7+b\ \ \ \ |-7\\\\b=-14$

$y=\dfrac{7}{9}x-14\ \ \ \ |\cdot9\\\\9y=7x-126\ \ \ \ |-9y\ |+126\\\\7x-9y=126$

Answer: $y=\dfrac{7}{9}x-14\to7x-9y=126$

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(b) The area of a rectangular pool is 5488 m\2 If the length of the pool is 98 m, what is its width?

mrs_skeptik [129]

Answer:

Step-by-step explanation:

To find the area of a rectangle we have the foruma A=WxL.

But we already have the area and length so we can plug that in

5488=Wx98

Now its an algebreic expression.

SInce its multiplying we do the opposite, so we divide 98 on both sides.

98/98 crosses itself out so now its 5488/98. Which equals 56. So now our expression is W=56. To fact check we put the numbers 56 and 98 into the formula to see if we get 5488.

A=56x98

A=5488

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1 year ago

Choose the correct answer to 7,215 divided by 34 with a remainder

Vsevolod [243]

7,215: 34 = 0,212205882352941

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2 years ago

How are pairs of alternate interior angles related to one another? How are pairs of alternate exterior angles related to one ano

eduard

Answer:Each pair of alternate interior angles is congruent, and each pair of alternate exterior angles is congruent.

Step-by-step explanation:

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2 years ago

Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. Thi

Dovator [93]

Complete question:

Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby this mention is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect so the probability of a girl is 0.5. Assume that the group consists of 36 couples.

A) Find the mean and standard deviation for the number of girls in groups of 36 births.

B) Use the range rule of thumb to find the values separating results that are significantly low and significantly high.

C) Is the result of 33 girls significantly high? A result of 33 girls would suggest the method is effective or is not effective?

Answer:

a) mean = 18

Standard deviation =3

b) low range = 12

High range = 24

c) The result of 33 girls is significantly high. Yes, the method is effective.

Step-by-step explanation:

Given:

p = 0.5

n = 36

a) The mean is the product of n and p

Mean u = np

u = 36 * 0.5 = 18

The standard deviation is the square root of the product of n and p&q.

S.d ó = $\sqrt{npq}$

$= \sqrt{np(1-p)}$

$= \sqrt{36(0.5)(1-0.5)} = \sqrt{9} = 3$

b) To find the range rule of thumb:

• For low range

Low range = u - 2ó

= 18 - (2 * 3)

= 12

• High range

= u + 2ó

= 18 + (2*3)

= 24

c) The result is significantly high, because 33 is greater than 24 girls.

A result of 33 girls would prove the method as effective.

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3 years ago

Mr. Cresta spends $6.00 for every $3.00 he saves. Write a ratio equivalent to Mr. Cresta's spending

Andrei [34K]

Answer:

12:6 or $12 for every $6 he saves

Step-by-step explanation:

If he spends $6.00 for every $3.00, he would save $6 if he spends $12. In this case you could multiple or divide 6 by any number, and do the same to 3 to get an equivalent ratio. Ex. Multiple 6 times 2 to get $12 and 3 times 2 to get $6.

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3 years ago

Write the equation of a line perpendicular to 9xplus7yequals6 that passes through the point ​(9​,negative 7​).

Write the equation of a line perpendicular to 9xplus7yequals6 that passes through the point (9,negative 7).