Help please! What is the length of the highlighted side? (Show work)

Answer: See the attached image below

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Explanation:

Part A

The rule for a 180 degree rotation about the origin is

[tex](x,y) \to (-x,-y)\\\\[/tex]

The x and y values flip in sign from positive to negative, or vice versa.

A point like P(1,-1) will move to P ' (-1, 1) as shown in the first diagram. Points Q and R follow the same idea.

Side note: It doesn't matter if we rotate clockwise or counterclockwise. We'll end up at the same result. This only works for 180 degree rotations.

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Part B

When we apply an x-axis reflection, we apply this rule

[tex](x,y) \to (x,-y)\\\\[/tex]

This rule is nearly the same as the previous rule, but this time the x coordinate stays the same.

For example, the point P(1,-1) moves to P ' (1, 1)

The same applies to points Q and R as shown in the second diagram.

Answer:

9 and 18

Step-by-step explanation:

Let the integers be a and 2a (since one is twice the other).

The reciprocals are 1/a and 1/(2a) respectively.

Difference means tk subtract.

So we have 1/a-1/(2a)=1/18

Multiply both sides by 18:.

18a/a-18a/(2a)=18a/18

Simplify:

18-9=a

Simplify:

9=a

If a=9, then 2a=18

The integers are 9 and 18.

Test:

1/9-1/18

2/18-1/18

1/18

Golden!

Answer:

0.5 < x < 3

or (0.5, 3)

Step-by-step explanation:

-16t² + 56t + 2 = 26

Subtract both sides by 26

-16t² + 56t + 2 = 26

                 -26   -26

-16t² + 56t - 24 = 0

Divide both sides by -8 to simplify

(-16t² + 56t - 24)/8 = 0/8

2t² - 7t + 3 = 0

Factor

(x - 3)(2x - 1) = 0

Do this to find the x's

x - 3 = 0

 + 3  +3

x = 3

2x - 1 = 0

    + 1  + 1

2x = 1

2x/2 = 1/2

x = 0.5

0.5 < x < 3

This means the intervals will have to be between 0.5 and 3 seconds

Well this could be incredibly easy, by just saying [tex]m=0[/tex] and [tex]n=-3x[/tex].

This is a completely valid case but nevertheless seems too easy. The requirements are probably that n and m are integers or natural numbers but since that was not specified such probable requirement ought not to be followed.

Hope this helps :)

Answer:

(1, -1/2)

Step-by-step explanation:

Find the midpoint by finding the averages of the x coordinates and y coordinates:

(-5 + 7) / 2

2 / 2 = 1 (x coordinate)

(4 - 5) / 2

-1 / 2 = -1/2 (y coordinate)

So, the midpoint is (1, -1/2)

Answer: Student ticket cost $2 and an adult ticket cost $3.

257 kids total attended

Step-by-step explanation:

Answer:

x=-5

Step-by-step explanation:

First create a ratio -18/3 = 30/x

Cross multiply -18x=90

90/-18=-5

x=-5

Answer:

The decimal 0.6 is a rational number. It is the decimal form of the fraction 6/10.

Answer:

Yes. 0.6 is a rational number.

Answer:

3 is the value I guess because with seven it becomes 15 where as with 10 it become 12 so there is 3 numbers gap

I don't know exactly so I just try

Answer:

13 is the answer

Step-by-step explanation:

9514 1404 393

Answer:

  g(x) = 1/2

Step-by-step explanation:

The applicable relations are ...

  [tex]\log_b(x)=a\ \Longleftrightarrow\ b^a=x\\\\\log_b(x^a)=a\cdot\log_b(x)\\\\\log_b(b)=1[/tex]

__

We want to find logb(x) for x = b^(1/2). Using the first relation, we see ...

  g(x) = logb(x)

  b^(g(x)) = b^(1/2) . . . . . using g(x) = a

  g(x) = 1/2 . . . . . equating exponents

__

Alternatively, using the last two relations, we have x = b^(1/2), so ...

  g(b^(1/2)) = logb(b^(1/2)) = (1/2)logb(b) = (1/2)(1)

  g(x) = 1/2

_____

Additional comment

I find it useful to remember that a logarithm is an exponent. The first applicable relation shown above is a statement to that effect.

Answer:

[tex] - 22 + ( - 16) = - 22 - 16 = -3 8[/tex]

I hope I helped you^_^

Answer:

-38

Step-by-step explanation:

A good trick is to add it normally and just apply the sign

Answer:

qualitative

Step-by-step explanation:

Breed of dog does not involve numbers: it's qualitative since dogs can have categories like "poodle" or "dachshund."

Answer:

The Federal Reserve System, the central bank of the United States, was founded by Congress to provide a safe, flexible and stable monetary and financial system.

Answer:

21

Step-by-step explanation:

Answer:

They add up to equal 90 degrees.

Divide through everything by b :

[tex]\dfrac{a+c}{b+d} = \dfrac{\dfrac ab + \dfrac cb}{1 + \dfrac db}[/tex]

Since a/b < c/d, it follows that

[tex]\dfrac{a+c}{b+d} < \dfrac{\dfrac cd+\dfrac cb}{1 + \dfrac db}[/tex]

Multiply through everything on the right side by b/d to get

[tex]\dfrac{a+c}{b+d} < \dfrac{\dfrac{bc}{d^2}+\dfrac cd}{\dfrac bd+1} = \dfrac{\dfrac cd\left(\dfrac bd+1\right)}{\dfrac bd+1} = \dfrac cd[/tex]

and so (a + c)/(b + d) < c/d.

For the other side, you can do something similar and divide through everything by d :

[tex]\dfrac{a+c}{b+d} = \dfrac{\dfrac ad + \dfrac cd}{\dfrac bd + 1}[/tex]

and a/b < c/d tells us that

[tex]\dfrac{a+c}{b+d} > \dfrac{\dfrac ad + \dfrac ab}{\dfrac bd + 1}[/tex]

Then

[tex]\dfrac{a+c}{b+d} > \dfrac{\dfrac ab + \dfrac{ad}{b^2}}{1 + \dfrac db} = \dfrac{\dfrac ab\left(1+\dfrac db\right)}{1 + \dfrac db} = \dfrac ab[/tex]

and so (a + c)/(b + d) > a/b.

Then together we get the desired inequality.

Answer:

Assuming you just want it simplifies, the answer would be m+5

Step-by-step explanation:

4m+5-3m -------> combining like factors

m+5

Answer:

first piece: 2in

second piece: 8in

third piece: 10in

Step-by-step explanation:

We have

first piece + second piece + third piece = 20

second piece = 4 * first piece = 4x

third piece = 5 * first piece = 5x

x + second piece + third piece = 20

plug 4x in for the second piece, 5x in for the third

x + 4x + 5x = 20

combine like terms

10x = 20

divide both sides by 10 to isolate x

x = 2

second piece = 4x = 8

third piece = 5x = 10

Answer:

yes

Step-by-step explanation:

Answer:

Same makings on the lines and angles indicate they are congruent (have same measure).

As per drawing:

Answer:

731 and 164 rounded off to the nearest tens is 730 and 160.

the difference is 570

570. rounded off to the nearest hundred is 600

Answer:

9 used books

Step-by-step explanation:

there are 9 used books

solution:11-3=9

so therefore the answer is 9

Answer:

A

Step-by-step explanation:

The answer is the median because it shows how data are being scattered

Answer:

5/12

Step-by-step explanation:

tan=opposite/adjacent

tan30=5/12

Answer:

Tanθ = opposite/adjacent

[tex] \tan(30) = \frac{5}{12} [/tex]

I hope I helped you^_^

Answer:

5+12+5×2

5+12+10

27

According to BODMAS Rule the ans is 27

Answer:

27

Step-by-step explanation:

25÷5+ 12+5×2

=5+12+5x2

=5+12+10

=17+10

=27

Hope this helps! Thanks.

300000000000000000000000

Answer:

BODMAS

the answer is 3,729,000

Have a good day !