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3 years ago

Question 2: Please help I do not understand this question.

Mathematics

1 answer:

Svetradugi [14.3K]3 years ago

5 0

The measurement of AB is 16.23.

Solution:

Given ACB is a right angled triangle.

AC = 10, ∠C = 90° and ∠A = 52°.

cos θ ≈ 0.616

Here AC is the base and AB is Hypotenuse.

To find the length of AB:

$$\cos\theta=\frac{\text{Base}}{\text{Hypotenuse}}$

$$\cos 52^\circ=\frac{10}{AB}$

$$0.616=\frac{10}{AB}$

Do cross multiplication, we get

$$AB=\frac{10}{0.616}$

AB = 16.23

Hence the measurement of AB is 16.23.

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A person invests $2,740 in an account that earns 4.3% annual interest. Find when the value of the investment reaches $7,000. If

Juli2301 [7.4K]

So, to set up your equation is the hardest part. If you remember the basic format, you're set.

I(t) = P * (1+r%)^t

t= time and this will be our variable

Initial amount P = $2740

Rate = 4.3% which converts numerically into .043

I(t) = 7000

Before we get to find out how to find how many years it takes to get to $7000, set up the basic equation by plugging in what we know.

I(t) = $2740(1+4.3%)^t

I(t)=2740(1.043)^t

Now plug in for $7000 for I(t)

7000=2740(1.043)^t Divide both sides by 2740

7000/2740 = 2740/2740(1.043)^t

2.55474453=(1.043)^t

Now you can solve for t in two ways. You can either use the natural log or graph it on your graphing calculate and see when the two equations meet.

In your calculator you can set up:

ln(2.55474453)/ln(1.043) = t which is the method I prefer since it's much simpler

t=22.278528

but you can also graph it in your ti-84

with

y1=2.55474453

y2=(1.043)^x

and find where they intersect on the graph.

either way it'll be the same answer

3 0

3 years ago

Can someone help me with this problem

Naily [24]

<h3>Answer: Choice A</h3><h3>The point Z ' is at (8,4)</h3><h3>The point Y ' is at (0,4)</h3>

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Explanation:

The key thing here is that point Z does not move. Why not? Because this is where the center of dilation occurs. The center point is fixed. Everything around the center will expand away from, or contract toward, the center.

In this case, the scale factor is 4/5 = 0.8 which is less than 1. So points will contract toward the center. The old pre-image shrinks to make the image smaller.

Note how point Y = (-2,4) is 10 units away from point Z. You can count out the spaces or subtract the x coordinates. Use an absolute value to make sure the result is positive

|x1-x2| = |-2-8| = |-10| = 10

|x2-x1| = |8-(-2)| = |8+2| = |10| = 10

So 0.8 times this distance is therefore 0.8*10 = 8 meaning that point Y' is going to be 8 units away from point Z' or Z.

Subtract 8 from the x coordinate of point Z to get x-8 = 8-8 = 0.

The y coordinate stays the same at y = 4 the whole time.

----------------------------------------

In short, point Y starts at (-2,4) and moves to (0,4)

Distance from Y to Z is 10 units

Distance from Y' to Z' is 8 units

8/10 = 4/5 = 0.8 is the scale factor

Point Z does not move. So Z and Z' are at the same location.

5 0