Find (a) PQ to the nearest tenth and (b) the coordinates of the midpoint of PQ.
P(5,-4), Q(6,-5)
(a) PQ=(Round to the nearest tenth as needed.)

[tex]\\ \rm\rightarrowtail 2-sin^2x=2cos^2\left(\dfrac{x}{2}\right)[/tex]

[tex]\\ \rm\rightarrowtail 1+1-sin^2x=2cos^2\left(\dfrac{x}{2}\right)[/tex]

[tex]\\ \rm\rightarrowtail 1+cos^2x=2cos^2\left(\dfrac{x}{2}\right)[/tex]

[tex]\\ \rm\rightarrowtail cos^2x=2cos^2\left(\dfrac{x}{2}\right)-1[/tex]

[tex]\\ \rm\rightarrowtail cos^2x=cosx[/tex]

[tex]\\ \rm\rightarrowtail cosx=1[/tex]

[tex]\\ \rm\rightarrowtail x=n\pi[/tex]

As x lies in between 0 and 2π

Answer:

[tex]x=0,\dfrac{\pi}{2}, \dfrac{3\pi}{2},2\pi[/tex]

Step-by-step explanation:

Given equation:

[tex]2-\sin^2x=2 \cos^2(\frac{x}{2})[/tex]

Subtract [tex]2 \cos^2(\frac{x}{2})[/tex] from both sides:

[tex]\implies 2-\sin^2x-2 \cos^2(\frac{x}{2})=0[/tex]

Pythagorean identity

[tex]\sin^2x+\cos^2x =1[/tex]  

[tex]\implies \sin^2x =1-\cos^2x[/tex]

Substituting into the equation:

[tex]\implies 2-(1-\cos^2x)-2 \cos^2(\frac{x}{2})=0[/tex]

[tex]\implies 1+\cos^2x-2 \cos^2(\frac{x}{2})=0[/tex]

Cosine double angle identity:

[tex]\cos(2x)=2 \cos^2x-1[/tex]

[tex]\implies 2 \cos^2x=\cos(2x)+1[/tex]

Substituting [tex]\frac{x}{2}[/tex] for [tex]x[/tex]:

[tex]\implies 2 \cos^2(\frac{x}{2})=\cos(2\cdot\frac{x}{2})+1[/tex]

[tex]\implies 2 \cos^2(\frac{x}{2})=\cos x+1[/tex]

Substituting into the equation:

[tex]\implies 1+\cos^2x- (\cos x +1)=0[/tex]

[tex]\implies \cos^2x- \cos x =0[/tex]

Factoring:

[tex]\implies \cos x(\cos x- 1)=0[/tex]

Therefore,

[tex]\cos x=0[/tex]  

[tex]\implies x=\dfrac{\pi}{2}, \dfrac{3\pi}{2}[/tex]

and  [tex]\cos x-1=0[/tex]

[tex]\implies \cos x=1[/tex]

[tex]\implies x=0, 2\pi[/tex]

Answer:

5 terms

to the fourth degree

leading coeff of 1

3 turning points

end behavior (when x -> inf, y -> inf. When x -> - inf, y -> -inf)

x intercepts are (0,-4) (0,-2) (0,1) (0,3)

Relative min: (-3.193, -25) (2.193, 25)

Relative max: (-0.5, 27.563)

Step-by-step explanation:

The terms can be counted, seperated by the + and - in the equation given.

The highest exponent is your degree.

The number before the highest term is your leading coeff, if there is no number it is 1.

The turning points are where the graph goes from falling to increasing or vice versa.

End behaviour you have to look at what why does when x goes to -inf and inf.

X int are the points at which the graph crosses the x-axis.

The relative min and max are findable if you plug in the graph on desmos or a graphing calculator.

Answer:

y= -7x+26

Step-by-step explanation:

not sure how to explain... just followed order of operations

Answer:

-1/3

Step-by-step explanation:

2x + 6y = 5

6y = -2x + 5

y = -1/3x + 5/6

Representing the equation in slope intercept form, the slope of the line represented by the equation is - 1/3

Given the equation :

Slope intercept format :

2x + 6y = 5

6y = - 2x + 5

Divide both sides by 6 to isolate y

y = - 1/3x + 5/6

Hence, the value of slope, b in the equation is - 1/3

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the answer is b bc the way the other 2 are

Step-by-step explanation:

its the pattern.

Answer:

Hello! :) I hope I’m correct!!

Step-by-step explanation:

I think (C) 30 is not a perfect square.

(A) 1 = perfect square

(B) 25 = perfect square

(C) 30 = NOT a perfect square

(D) 36= perfect square

{Note: The square root of 30 is not an integer, so therefore 30 is not a square number}

Since the question is asking to find a number that is NOT a perfect square...

The answer would be (C) 30

Hope this helps! If you have any questions about this, feel free to ask! Have a wonderful day! ^-^

~By, BrainlyAnime~ <3

Answer:C.45

Step-by-step explanation:

                         [tex]\Huge\boxed{Your\;answer\;is\;45.}[/tex]

___________________________________________________________

                                                  [tex]\boxed{Explanation}[/tex]

So, we have the following equation...

[tex]5^2+20=(?)[/tex]

Remember, 5² also means 5x5.

Therefore, [tex]5x5=25\\25+20=45[/tex]

This means your final answer is 45.

___________________________________________________________

Glad to help!

Could i possibly get brainliest?

[tex]\huge\boxed{Thanks,\;Plip.}[/tex]

Answer:

a)  Shelton’s total pay before deduction: 10.25x

b)  To meet savings goal he'll have to work 827.415869 hours.

Step-by-step explanation:

Take-home pay:

  10.25x − 0.21(10.25x)

  10.25x − 2.1525x

  8.0975x

Save 25% for new laptop:

  .25(8.0975x) = 1675

     2.024375x = 1675

     x = 827.415869 hours

Answer:

D

Step-by-step explanation:

answer choices a/b can be eliminated because it's increasing, and answer choice c can be ruled out because its a dramatic increase!

hope this helps!<3

Answer:

i'd give you my insta

Step-by-step explanation:

Answer:

1 yard = 3 feet

40 × 3 = 120 feet

1 foot per 2 seconds

120 × 2 = 240

240 ÷ 60 = 4 minutes

it takes her 4 minutes to reach the surface

Answer:

6 minutes and 65 seconds

Step-by-step explanation:

The unit rate is: 1/2.

1/2 x 40 = 40/80

80/60 = 1.33

1.33 x 3   (Because every foot is a meter)

3.99 / .60

6.65.

Hope this helps! Have a good day.

(Also, nice Sans PFP, mine is Sans too ;>)

The amount of fabric needed = surface area of the rectangular prism (brick) = 146.5 cm²

The surface area of a rectangular prism is given as, A=2(wl+hl+hw).

The brick is a rectangular prism. Therefore, the amount of fabric needed to cover the brick would equal the surface area of the brick.

Given the following:

Plug in the values into the formula:

The surface area of the rectangular prism (brick) = 2(3.5 × 6 + 5.5 × 6 + 5.5 × 3.5) = 146.5 cm²

Learn more about surface area of rectangular prism on:

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Answer:

The Answer Is : 146.5

Step-by-step explanation:

I Just Took The Test And I Have Proof

Answer:

9

Step-by-step explanation:

1= 1x1x1 cubic

27=3x3x3 cubic

64=4x4x4 cubic

9 is not cubic

Answer:

Step-by-step explanation:

1x1x1=1³

3x3x3=27=3³

4x4x4=64=4³

Answer:

[tex]P(Red) = 0.125[/tex]

Step-by-step explanation:

Given

[tex]Red: 150[/tex]

[tex]White: 450[/tex]

[tex]Green: 225[/tex]

[tex]Blue: 375[/tex]

Required

Determine the probability of getting a red chair, next.

First, we nee the total number of chairs

[tex]Total = 150 + 450 + 225 + 375[/tex]

[tex]Total = 1200[/tex]

Probability of getting red is then calculated as thus;

[tex]P(Red) = Red/Total[/tex]

[tex]P(Red) = 150/1200[/tex]

[tex]P(Red) = 0.125[/tex]

Answer:

0.6

Step-by-step explanation:

We can get the answer by subtracting the decimal by one.

2/5 = 0.4

1 - 0.4 = 0.6

Answer:

3.875

Step-By-Step-Explanation

3 2/8 + 5/8

Answer:

oranges $3.50 per Kg, bananas $3 per Kg

Step-by-step explanation:

let b represent cost of bananas and o represent cost of oranges , then

2b + 3o = 16.5 → (1)

o = b + 0.5 → (2)

substitute o = b + 0.5 into (1)

2b + 3(b + 0.5) = 16.5 ← distribute parenthesis on left side and simplify

2b + 3b + 1.5 = 16.5

5b + 1.5 = 16.5 ( subtract 1.5 from both sides )

5b = 15 ( divide both sides by 5 )

b = 3

substitute b = 3 into (2)

o = 3 + 0.5 = 3.5

cost of oranges = $3.50 and cost of bananas = $3

Answer: y = 3x + 5

............................

plz mark brainlest

Answer: I got these correct 100%.

Step-by-step explanation:

First page:

1. True

2. True

3. True

4. True

5. False

6. True

7. False

Second page:

1.False

2.False

3.False

4.False

5.False

6.True

7.True

8.True

Answer:

The answer to your question would be 20

Hope this helps!

Answer:

4x + 8y =12                        [inconsistent]

x + 2y = -3

x = 6                                   [inconsistent]

x = -2

2y = 5x + 6                          [inconsistent]

-10x + 4y = 8

x - 3y=2

4x - 12y = 8                          [dependent]

x+ 4y = 12                              [independent]

2x - 8y = 4

4x + 8y = -6                        [dependent]

6x + 12y = -9

4y - 2x = 6                            [inconsistent]

8y = 4x -12

y - x = 0                                [independent]

y = -x

2y - x = 4

1/2x - y = 2                            [inconsistent]

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

f(x) = 3x + k

f(4) = 10

f(4) = 3×4+k

10 = 12 + k

10-12 = k

k = -2

Answer: Mount Everest (8,848 m 29,029 ft) was first climbed, when the summit was reached by Edmund Percival Hillary

Answer:

27

Step-by-step explanation:

3*5=15+12=27]

Evaluation of 3x + 12 for x = 5 is 27.

Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.

Given expression,

3x + 12

And to solve for x= 5,

we substitute the value of x in given expression,

3(5)+ 12 = 15 + 12

             = 27

Therefore, evaluation of expression 3x + 12 for x = 5 is 27.

To learn more about the expression;

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Answer:

[tex]k=3[/tex]

Step-by-step explanation:

Given the following question:

[tex]\frac{9-2k}{3} =k-2[/tex]

To find the answer we need to isolate k, in order to do that we need to use inverse of operations to cancel out integers on each side of the expression.

[tex]\frac{9-2k}{3} =k-2[/tex]
[tex]3\times0=0[/tex]
[tex]2\times3=6[/tex]
[tex]9-2k=k\times3-6[/tex]
[tex]9-9=0[/tex]
[tex]-6-9=15[/tex]
[tex]k\times3=3k[/tex]
[tex]-2k=3k-15[/tex]
[tex]-2k-2k=0[/tex]
[tex]3k+-3k=-5k[/tex]
[tex]-5k=-15[/tex]
[tex]-5k\div-5=k[/tex]
[tex]-15\div-5=3[/tex]
[tex]k=3[/tex]

Your answer is "k =3."

Hope this helps.

Answer:

A=½bh

20=5x(½)

multiply by reciprocal both sides

40=5x

divide

8=x

Answer:

the gradient is -5/1 or -5 because it is a negative slope meaning you would go from top to bottom.

Step-by-step explanation:

mr clean

Answer:

-5

Step-by-step explanation:

The points through which the line passes are :-

(-1, 0) and (-2, 5)

Slope (m) = 5 - 0 / -2 + 1

= 5 / -1

= -5

Answer:

up and 2; down and 3

Step-by-step explanation:

hope this helps!! have an amazing day <3

The equation the function after the transformation is  g(x) = -4x² - 16

Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation.

here, we have,

to determine the transformation of the function:

The equation of the function is given as

f(x) = x²+2

The sequence of transformations is given as follows:

Translate up by 2 units

Reflection across the x-axis

Vertically stretched by a factor of 4

When the above transformations are combined, we have:

Translate up by 2 units: g(x) = f(x) + 2

Reflection across the x-axis: g(x) = -(f(x) + 2)

Vertically stretched by a factor of 4: g(x) = -4(f(x) + 2)

So, we have

g(x) = -4(x²+2 + 2)

Expand

g(x) = -4x² - 16

Hence, the function g(x) is g(x) = -4x² - 16

Read more about transformation at

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