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3 years ago

6

Write a function rule for “The output is 6 more than five times the input.” Use x for the independent variable and y for the dep

endent variable. y=

1 answer:

Svetradugi [14.3K]3 years ago

6 0

Answer:

y=5x+6

Step-by-step explanation:

+6 is six more than.

5x is five times the input.

For example, let's say x=3. you gotta multiply first so you can get the five times out of the way. 3×5=15. Now we got to add six because "6 more than" means to add six. so, 15+6=21. I plugged in 21 for y to check and I got x=3, so this works.

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A and ∠B are complementary angles. If m∠A is 35LaTeX: ^\circ∘, what is the measure of B?

ipn [44]

Since they are complementary, they both add up to 90 degrees. So, 90-35=55 degrees.

The measure of angle B is 55 degrees.

5 0

3 years ago

Read 2 more answers

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

mash [69]

Answer:

8

Step-by-step explanation:

Because you left one pence then it is 9-1=8

3 0

4 years ago

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On circle O below, the measure of SV is 120°.<br><br><br>What is the measure of VU?<br>

DochEvi [55]

Answer: Angle VU is 44 degrees

Step-by-step explanation:

7 0

3 years ago

In what time will Rs. 5600 amount to Rs. 6720 at 8% per annum?

Leona [35]

Answer: 2 years

Step-by-step explanation:

If Interest= Principal x rate x time/100; then time is (100 × Interest)/(Principal × Rate)

From the question, old Principal is 5600, new principal =6720, the difference is the interest accrued.

Interest = 6720 - 5600 = Rs 1120

Rate = 8% = 8 ÷ 100 = 0.08

Time = x

Then, slot the values into the formula

Time= 100 x 1120 / 6720 x 8

= 112000/53760

=2.08

Time= 2years

I hope this helps

8 0

4 years ago