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Anna35 [415]
2 years ago
12

What is the simplified form of the difference shown below? (3a^2-6a-1)-(5a^2-2a+3)

Mathematics
1 answer:
kodGreya [7K]2 years ago
8 0

Answer:

(3a^2-6a-1)-(5a^2-2a+3)

= 3a²-6a-1 -5a²+2a-3

=3a²-5a²-6a+2a-1-3

= -2a²-4a-4

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Bronwyn equals to 12
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And Carl is 24
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Write a fraction to a decimal
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1/2 = 0.5

1/4 = 0.25

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4X-3 (x²+2x)<br> Find (f-g) (4)
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Answer:

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assuming 4x-3 = f(x) and the other equation = g(x)

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Read 2 more answers
Help me jim! geometry homework
Maksim231197 [3]

Question 1

The angles 52 degrees match up. So if the sides are in proportion, then the triangles are similar.

Notice how 8/12 = 18/27 is a true equation. So the sides are in proportion to one another.

Therefore, the triangles <u>are similar</u>. I used the <u>SAS similarity theorem</u>.

================================================================

Question 2

Let's find the missing angle of the triangle on the right. For now, make that missing angle to be x.

Rule: For any triangle, the three angles always add up to 180

x+70+32 = 180

x+102 = 180

x = 180-102

x = 78

The missing angle of the triangle on the left is 78 degrees

Repeat for the other triangle as well

y+78+32 = 180

y+110 = 180

y = 180-110

y = 70

Both triangles have the angles 32, 70, 78 in whatever order you wish.

Since the angles match up like this, <u>the triangles are similar</u> because of the <u>AA Similarity theorem</u>

Technically, we only need 2 pairs of congruent angles at minimum. But having 3 congruent pairs doesn't hurt either.

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Question 3

We have a pair of congruent 54 degree angles shown. There's another pair of angles at the very top that overlap (aka shared angles).

Since we have two pairs of congruent angles, <u>the two triangles are similar</u>.

This time we use the <u>AA Similarity theorem</u>

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Question 4

Let's divide the longest side of the bottom triangle by the longest side of the triangle on top

48/32 = 1.5

Now let's divide the shortest sides of each triangle in the same order

36/24 = 1.5

Repeat for the middle-most sides

45/30 = 1.5

We get the same linear scale factor 1.5 each time. Therefore, <u>the triangles are similar</u> due to the <u>SSS Similarity theorem</u>

================================================================

Question 5

Any angle is equal to itself due to the <u>reflexive property</u>. So that will go for reason number 2.

Reason 3 is <u>SAS similarity</u> because we have the sides in proportion (statement 1) and the angles are congruent (statement 2).

3 0
2 years ago
A recent study asked U. S. Adults to name 10 historic events that occurred during their lifetime that have had the greatest impa
Nadusha1986 [10]

Using the z-distribution, as we are working with a proportion, it is found that the 99% confidence interval for the proportion of all U. S. Adults who would include the 9/11 attacks on their list of 10 historic events is (0.7458, 0.7942). It means that we are 99% sure that the true proportion for all U.S. adults is between these two bounds.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which:

  • \pi is the sample proportion.
  • z is the critical value.
  • n is the sample size.

In this problem, the parameters are:

z = 2.575, n = 2000, \pi = 0.77

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 - 2.575\sqrt{\frac{0.77(0.23)}{2000}} = 0.7458

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 + 2.575\sqrt{\frac{0.77(0.23)}{2000}} = 0.7942

The 99% confidence interval for the proportion of all U. S. Adults who would include the 9/11 attacks on their list of 10 historic events is (0.7458, 0.7942). It means that we are 99% sure that the true proportion for all U.S. adults is between these two bounds.

More can be learned about the z-distribution at brainly.com/question/25890103

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