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3 years ago

Write this equation in standard form 9x^2-4y^2-24y-72=0

1 answer:

4 0

$9x^2-4y^2-24y-72=0\\
\\
9x^2-4y^2-24y=72\\
\\
9x^2-(4y^2+24y+36)=72-36\\
\\
9x^2-4(y+3)^2=36\\
\\
\frac{9x^2}{36}-\frac{4(y+3)^2}{36}=\frac{36}{36}\\
\\
\boxed{\frac{x^2}{4}-\frac{(y+3)^2}{9}=1}$

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2 years ago

What is the equation of the line that is paralle to y=3x-8 and passes thur the point (4,-5)

Brrunno [24]

⊰_________________________________________________________⊱

Answer:

The equation is-: y=3x

Step-by-step explanation:

$\large\displaystyle\text{$\begin{gathered} \sf{Substitute \ the \ values \ into \ the \ formula \ y-y_1=m(x-x_1)} \\ \sf {parallel \ lines \ have \ same \ slopes, \ thus} \\ \sf{slope \ of \ the \ 2nd \ line = 3}\\ \sf{now \ substitute \ the \ values} \\ \sf {y-(-5)=3(x-4)}\\ \sf{y+5=3(x-4) (It's \ Point-Slope\;Form, \ see \ below \ for \ slope-intercept)}\\ \sf {y+5=3x-12} \\ \sf{y=3x-12-5} \\ \sf{y-3x-17} \end{gathered}$}}$

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4 0

2 years ago

Rafael want to buy the same number of gifts bags and bows gifts bags are sold in packs of 6. Bows are sold in packs of 9. What i

GenaCL600 [577]

Answer:

Rafael should buy 9 gift bags and 6 bows packet so, that she can have SAME NUMBER OF ITEMS, i.e 54.

Step-by-step explanation:

The gift bags are sold in the packs of 6.

So, the number of gift bags in 1 packet = 6 gift bags

The number of gift bags in 2 packet = 6 x 2 gift bags = 12 gift bags

The number of gift bags in 3 packet = 6 x 3 gift bags = 18 gift bags

And continuing similarly, we get

The number of gift bags in 9 packet = 6 x 9 gift bags = 54 gift bags.. (1)

The bows are sold in the pack of 9.

So, the number of bows in 1 packet = 9 bows

The number of bows in 2 packet = 9 x 2 bows = 18 bows

The number of bows in 3 packet = 9 x 3 bows = 27 bows

And continuing similarly, we get

The number of bows in 6 packet = 9 x 6 bows = 54 bows... (2)

Here, comparing both equations (1) and (2) , we get

The number of gift bags = 54 = The number of bows.

Hence, Rafael should buy 9 gift bags and 6 packet of bows so, that she can have SAME NUMBER OF ITEMS, i.e 54.

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3 years ago

Suppose a random sample of 50 college students are asked to measure the length of their right foot in centimeters. A 95% confide

hichkok12 [17]

Answer:

A 99% confidence interval will be wider than a 95% confidence interval

Step-by-step explanation:

From the question we are told that

The 95% confidence interval for for the mean foot length for students at the college is found to be 21.709 to 25.091 cm

Generally the width of a confidence interval is dependent on the margin of error.

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} }$

From the above equation we see that

$E \ \ \alpha \ \ Z_{\frac{\alpha }{2} }$

Here $Z_{\frac{\alpha }{2} }$ is the critical value of the half of the level of significance and this value increase as the confidence level increase

Now if a 99% confidence level is used , it then means that the value of

$Z_{\frac{\alpha }{2} }$ will increase, this in turn will increase the margin of error and in turn this will increase the width of the confidence interval

Hence a 99% confidence interval will be wider than a 95% confidence interval

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3 years ago

Elavter of using distuburting propties a. 17×102<br> b. 477×1035 -477×35

V125BC [204]

Answer: a. 1734 b. 477000

Step-by-step explanation:

We know that,

Distributive property : a(b+c) = ab+ac

a. 17 x 102

= 17 (100+2)

= 17 x 100 + 17 x 2 [Distributive property ]

= 1700+34

= 1734

b. 477×1035 -477×35

= 477 (1035-35) [Distributive property ]

= 477 (1000)

= 477000

3 0

3 years ago