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3 years ago

The expression (x-5)^2 is equivalent to...

Mathematics

1 answer:

liq [111]3 years ago

5 0

Answer:

option a x²-25

Step-by-step explanation:

(x-5)²

x²-25

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Luke puts $35 in his savings account every month. Use a calculator to find how much money he will save in a year.

irina1246 [14]

£35 X 12(months) = £420 per year he saves.

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3 years ago

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The results of a poll show that the percent of people who want a new restaurant is in the interval (24%, 38%) . There are 112,48

iris [78.8K]

Change the percents to decimals (by moving the decimal 2places to the left)
(.24, .38)

Multiply each by 112,483.
(.24x112483, .38x112483)
(26,996, 42,744). You can’t have decimals because people are whole numbers. So round to the nearest whole number

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3 years ago

Find all points on the curve x=4cos(t),y=4sin(t) that have the slope of 12.

Marianna [84]

Answer:

$\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )$ .

Step-by-step explanation:

We need to find all the points on the curve x=4cos(t),y=4sin(t) that have the slope of 1/2.

$x=4cos (t)$

$\dfrac{dx}{dt}=-4sin (t)$

$y=4sin (t)$

$\dfrac{dy}{dt}=4cos (t)$

Now,

$\dfrac{dy}{dx}=\dfrac{dy}{dt}\times \dfrac{dt}{dx}$

$\dfrac{dy}{dx}=4cos (t)\times \dfrac{1}{-4sin (t)}$

$\dfrac{dy}{dx}=-\cot t$

So, slope of the curve is $-\cot t$ .

$-\cot t=\dfrac{1}{2}$

$-\tan t=2$

$\tan t=-2$ ...(1)

Using $\sec^2t=1+\tan^2t$ , we get

$\sec^2t=1+(-2)^2$

$\sec^2t=1+4$

$\sec t=\pm \sqrt{5}$

$\cos t=\pm \dfrac{1}{\sqrt{5}}$

Now,

$\sin^2t=1-cos^2t$

$\sin t=\pm \sqrt{1-\dfrac{1}{5}}$

$\sin t=\pm \sqrt{\dfrac{4}{5}}$

$\sin t=\pm \dfrac{2}{\sqrt{5}}$

It equation (1), tan(t) is negative. So, sin and cos have different signs.

If $\sin t= \dfrac{2}{\sqrt{5}}$ , then $\cos t=- \dfrac{1}{\sqrt{5}}$ .

$x=4cos (t)=-\dfrac{4}{\sqrt{5}}$

$y=4sin (t)=\dfrac{8}{\sqrt{5}}$

If $\sin t=- \dfrac{2}{\sqrt{5}}$ , then $\cos t= \dfrac{1}{\sqrt{5}}$ .

$x=4cos (t)=\dfrac{4}{\sqrt{5}}$

$y=4sin (t)=-\dfrac{8}{\sqrt{5}}$

Therefore, the two points are $\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )$ .

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3 years ago

Help on thishwwhejjddjhdhddhdhdj

QveST [7]

The answer is D.
The first one says you add -4 each time in the sequence.
The second says you add -2 each time in the sequence.
The third says you multiply by -2 each time in the sequence.
The fourth says you multiply by -4 each time in the sequence.
-2*-4=8
8*-4=-32

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3 years ago

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What is b2*b5*b3 simplified?

Valentin [98]

Answer:

B10

Step-by-step explanation:

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3 years ago