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balandron [24]
3 years ago
6

Can someone help me with this math question

Mathematics
1 answer:
Lapatulllka [165]3 years ago
4 0

Answer:

(2, 1).

Step-by-step explanation:

Dilated by factor 3:

C = (6, 3) ----> C' would be (6 * 1/3, 3 *1.3) = (2, 1).

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If y=2x+3 find the value of y when x=5
Alex73 [517]
Y is 13 when you solve the problem
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What do you have to do to each side to solve 5x &lt; 20? <br> Solve 5x &lt; 20. ✏️Show your work
sergejj [24]

Answer:

x < 4

Step-by-step explanation:

Step 1: Write inequality

5x < 20

Step 2: Solve for <em>x</em>

  1. Divide both sides by 5: x < 4

Here we see that any number less than 4 will work. So numbers like 3, 0, or even -12587235897 would work.

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A _____ is the composition of a translation and a reflection across a line parallel to the direction of translation.
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A Glide Reflection is the composition of a translation and a reflection across a line parallel to the direction of translation. 
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Use the given zero to find the remaining zeros of each function f(x)=2x^4+5x^3+5x^2+20x-12 zero:-2i
frutty [35]

Answer:

1/2, 3

Step-by-step explanation:

This is a pretty involved problem, so I'm going to start by laying out two facts that our going to help us get there.

  1. The Fundamental Theorem of Algebra tells us that any polynomial has <em>as many zeroes as its degree</em>. Our function f(x) has a degree of 4, so we'll have 4 zeroes. Also,
  2. Complex zeroes come in pairs. Specifically, they come in <em>conjugate pairs</em>. If -2i is a zero, 2i must be a zero, too. The "why" is beyond the scope of this response, but this result is called the "complex conjugate root theorem".

In 2., I mentioned that both -2i and 2i must be zeroes of f(x). This means that both x-2i and x+2i are factors of f(x), and furthermore, their product, x^2+4, is <em>also</em> a factor. To see what's left after we factor out that product, we can use polynomial long division to find that

2x^4+5x^3+5x^2+20x-12=(x^2+4)(2x^2+5x-3)

I'll go through to steps to factor that second expression below:

2x^2+5x-3=2x^2+6x-x-3\\=2x(x+3)-(x+3)\\=(2x-1)(x+3)

Solving both of the expressions when f(x) = 0 gets us our final two zeroes:

2x-1=0\\2x=1\\x=1/2

x+3=0\\x=-3

So, the remaining zeroes are 1/2 and 3.

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3 years ago
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You are told that a 95% confidence interval for a population proportion is (0.3775, 0.6225) What was the sample proportion that
Maru [420]
The mean of the confidence interval is (0.3775 + 0.6225) / 2 = 0.5. Therefore, the standard deviation of the proportion would have been sqrt[0.5*(1 - 0.5) / n], where n is the sample size. This expression simplifies to sqrt(0.25/n).

A 95% CI has a corresponding z = 1.96, so since the distance from 0.5 to 0.3775 (or 0.6225 to 0.5) is equal to 0.1225. Therefore, if we divide 0.1225 / 1.96 = 0.0625, we get the value of the SD, and this should be equal to sqrt(0.25/n).

0.0625 = sqrt(0.25/n)
n = 64
This means that the proportion was 0.5 and the sample size was 64.
6 0
3 years ago
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