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velikii [3]
3 years ago
14

WILL MARK BRAINLEIST!! Each figure is composed of large squares and small squares. The side length of the

Mathematics
1 answer:
julsineya [31]3 years ago
5 0

9514 1404 393

Answer:

  A. x² -4

  B. 2x² +8

Step-by-step explanation:

The area of a square is the square of the side lengths. That means the area of each large square is x², since it has a side length of x.

__

A. The area of 4 small squares is subtracted from the area of the large square to find the shaded area:

  x² -4×1² = x² -4 . . . area of Figure A

__

B. The area of two small squares is added to the area of two large squares to find the shaded area:

  2x² +2×2² = 2x² +8 . . . area of Figure B

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Is this generalization true? All triangles have at least 2 acute angles
Airida [17]
Yes
if you had less than 2, the lines wouldn't cross each other and wouldn't form a triangle
3 0
3 years ago
Read 2 more answers
Find the vertex of the graph of f(x)=-4(x-1)(x+5)
madreJ [45]

The vertex of the graph is (h, k) = (- 2, 36).

<h3>How to find analytically the vertex of a quadratic equation</h3>

In this question we have a quadratic equation of the form f(x) = a · (x - r₁) · (x - r₂) and we need to transform the expression into its vertex form of determine the coordinates of the vertex. First, we need to exprand the expression:

f(x) = - 4  · (x - 1) · (x + 5)

f(x) = - 4 · (x² + 4 · x - 5)

f(x) = - 4 · x² - 16 · x + 20

Now we proceed to complete the square:

f(x) = - (4 · x² + 16 · x - 20)

- f(x) = 4 · x² + 16 · x - 20

- f(x) = (2 · x)² + 8 · (2 · x) - 20

- f(x) + 36 = (2 · x)² + 8 · (2 · x) + 16

- f(x) + 36 = (2 · x + 4)²

- f(x) + 36 = 4 · (x + 2)²

f(x) - 36 = - 4 · (x + 2)²

The vertex of the graph is (h, k) = (- 2, 36).

To learn more on quadratic equations: brainly.com/question/17177510

#SPJ1

7 0
1 year ago
When x = 3 and y = 5, what is the value of 3x2 - 2y?​
Mumz [18]

Answer:

8

Step-by-step explanation:

3 times 3 is 9

2 yimes 5 is 10

9 times 2 is 18

18-10 is 8

4 0
4 years ago
Read 2 more answers
A simple random sample from a population with a normal distribution of 99 body temperatures has xbar = 99.10°F and s = 0.64°F. C
motikmotik

The general formula for the margin of error is e = (zs)/√n, when the sample size is 30 or more (otherwise, we'd need to to a t-interval).

Since we're needing a 99% confidence interval, we need to know what the positive z-score associated with this two-tailed area under the normal curve is.  This can be a little tricky if you're using a standard normal table.  What you want is a two-tailed interval that has an area of .99.  What this means is that the remaining 0.01 is divided into 0.005 on each end.  This then means that, to the right of the mean (which is 0), the area is 0.005 less than the total right-half area of 0.5, or 0.495.  The total cumulative area, then, includes this plus the left half of .5, or 0.5 + 0.495 = .0995.

Then, if all we have to go on is a cumulative standard normal table, then we need to find the area closest to 0.995 and find the corresponding z-score.  This z-score is 2.58.

Now that we have the z-score, we can now plug in all the values into the formula.  

e = (2.58 · 0.66)/√102 = 0.1686.

So the 99% confidence interval will be that far above and below the mean (which is 98.8).  So the lower limit is 98.8 - 0.1686 = 98.631, and the upper limit is 98.8 + 0.1686 = 98.967.

The TI-84 method:

This is much easier, if you're allowed to use this technology.  You begin with the STAT button, and then move over to the TESTS menu.  Then select ZInterval.  We have summary stats rather than data in this problem, so we select Stats as the input.  For the standard deviation, we put 0.66, for x-bar 98.8, for n 102, and for C-level 0.99.  Then select Calculate, and it will provide the interval at the top of the screen (98.632, 98.968).  Note that the lower limit is slightly different by this method.  This is because, when doing it by hand, we had to approximate the z-score.  This created a rounding error, albeit  a small one.

4 0
3 years ago
If b is the midpoint of ac, ac=cd, ab=3x+4, ac=11x-17, and ce=49, find de
IrinaK [193]

First, we draw our line.

 

|------------------------------------------------------------------------------------|

a                                                                                                            e

 

 

Next, break up this line into segments using the information.

 

|----------------------|----------------------|--------------------|------------------|

a                            b                            c                         d                      e

 

 

The entire line is 29.

 

ab + bc + cd + de = ae

ab + bc + cd + de = 29

 

You also know that

 

bd = bc + cd

 

 

Due to midpoint theorem,

 

ab = bc

cd = de

 

 

Then,

 

2ab + 2cd = 29

 

 

The equations we will use are

 

bd = bc + cd                       eq1

2bc + 2cd = 29                   eq2

 

 

Dividing both sides of the equation in eq2 yields

 

bc + cd = 14.5

 

bd = bc + cd

bd = 14.5

5 0
3 years ago
Read 2 more answers
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