Simplify:
(a^-2)^-3 divided by (a^5)^-1

Answer:

Step-by-step explanation:

Sum of interior angles is 180

Sum of interior angles is 180

Vertical angles are same, the sum of remaining angles is same for both triangles:

Exterior angle is same as the sum of non-adjacent interior angles:

identicalAnswer:

1) 64, 2) 6, 3) 26, 4) 33

Step-by-step explanation:

#1

Sum of interior angles is 180

70 + 46 + x = 180

116 + x = 180

x = 64

#2

Sum of interior angles is 180

84 + 7x + 1 + 9x - 1 = 84

16x + 84 = 180

16x = 96

x = 6

#3

Vertical angles are identical, the sum of remaining angles is the same for both triangles:

35 + 25 = 34 + x

60 = 34 + x

x = 60 - 34

x = 26

#4

The exterior angle is the same as the sum of non-adjacent interior angles:

5x - 7 + 6x + 3 = 84

11x - 4 = 84

11x = 88

x = 8

m∠G = 5x - 7 = 5*8 - 7 = 40 - 7 = 33

Answer:

  (b)  {-8, 2}

Step-by-step explanation:

The given equation

  x³ +6x -16 = 0

cannot be factored in integers. It has one irrational real root near x=1.759, and two complex roots.

__

Perhaps you want to factor ...

  x² +6x -16 = 0

  (x +8)(x -2) = 0

This has solutions x = -8 and x = 2 that make the factors be zero.

_____

Additional comment

"Cubed" refers to an exponent of 3.

Answer:

Option b] (2,-8)

Step-by-step explanation:

⇒ x³ + 6x - 16 = 0

♦ the value of one root is irrational and other two are complex roots.

⇒ x² + 6x - 16 = 0

⇒ (x + 8)(x - 2) = 0

⇒ x = 2 , -8

Answer:

40 i think

Step-by-step explanation:

we have: ∠P + ∠Q + ∠R = 180°

<=> (4x – 14)º + (5x + 6)° + (x - 2)° = 180°

<=> 4x – 14 + 5x + 6 + x - 2 = 180°

<=> 10x - 10 = 180°

<=> 10x = 190

<=> x = 19°

So: ∠R = (x - 2)° = (19 - 2)° = 17°

ok done. Thank to me :>

Answer:

Answer:

N(h) = 17.5h + 15

Step-by-step explanation:

N(h) = 8.75h + 15              | write original equation

N(h) = 8.75(2) + 15            | multiply the original hourly fee by 2

N(h) = 17.5 + 15                 | solve

Stay healthy and happy <3.

Hope this helped.

The required function represents the new fees is given as N(h) = 17.5h + 15.

Given that,
An administrative assistant works from home and originally charged her clients $8.75 per hour for any clerical work plus a set fee of $15, or C(h) = 8.75h + 15. She decided to double her hourly fee but keeps her set fee the same.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given function,
C(h) = 8.75h + 15.
Now,
According to the question,
N(h) = 2× 8.75h + 15.
N(h) = 17.5h + 15.

Thus, the required function represents the new fees is given as N(h) = 17.5h + 15.

Learn more about simplification here:

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Answer:

\mathrm{X\:Intercepts}:\:\left(-\frac{431}{26},\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:43.1\right)

Step-by-step explanation:

Answer:

16 m

Step-by-step explanation:

12² + b² = 20²

I hope this helps!

Answer:

b = 16 m

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

b² + 12² = 20²

b² + 144 = 400 ( subtract 144 from both sides )

b² = 256 ( take square root of both sides )

b = [tex]\sqrt{256}[/tex] = 16 m

Answer:

Step-by-step explanation:

Dilation does not affect angles or the direction of lines. The lines of a dilated figure will be parallel to the original, unless they go through the center of dilation.

Line CD does not go through P, so C'D' is distinct and parallel to it (True).

Angles B and B' are congruent. (True)

Answer:

Each movie costs 3.99

Step-by-step explanation:

If every month he is paying $7.99 initially for the service, you take $19.96 and subtract the initial cost ($7.99) then your left with $11.97 and since he bought 3 movies then you divide $11.97 by 3 and your left with $3.99 which is your final answer!

Hope this makes sense!

Given that £ 42 is distributed among 3 friends.

So, each will get

Answer:

1,015

Step-by-step explanation:

7 pounds of honey equals 1 pound of wax

So if we have 145 pounds of was, we multiply 145 by 7

145x7= 1,015

Answer:

a. (10,10)

Step-by-step explanation:

This was by accident the first answer is right

Answer:

8

Step-by-step explanation:

Substitute the given values into the expression

[tex]\frac{1}{2}[/tex] xy²

= [tex]\frac{1}{2}[/tex] × 4 × (- 2)²

= 2 × 4

= 8

Answer:

85

Step-by-step explanation:

Write the numbers in order

66, 72, 74, 80, 83, 87, 91, 95, 98, 99

Find the middle number

83 and 87 are in the middle, so find the mean of them. 83+87= 170

170/2 = 85.

Answer:

I added a little extra in case! Mark me brainleast

Step-by-step explanation:

Mean          84.5

Median           85

Mode         83, 80, 91, 74, 66, 99, 87, 72, 95, 98.

Range         33

Minimum         66

Maximum 99

Answer:

A & D

Step-by-step explanation:

Both use SSS to prove triangles congruent.

Therefore, if all three sides of two triangles are the same, then the triangles are said to be congruent. If we have a side, an angle between the sides, and then another side that is congruent, we know they are congruent. In other words, side, angle, side.

"If and only if the following two conditions are met, two triangles are congruent.

Three corresponding sides have the same value.

The measurements of the three related angles are all equal."

given instance,

Think about the triangles PQR and ABC.

If A = P, B = Q, and C = R

AB = PQ, BC = QR, and AC = PR as well.

If ABC and PQR are congruent triangles, then ABC PQR is the way to write it.

As a result, the following are true statements concerning congruent triangles:

The length of each of the three pairs of corresponding sides is the same.

The three pairs of comparable angles in each case are all of the same size.

To learn more about Congruent triangle refer to:

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Answer:

y = 1

Step-by-step explanation:

To find the Horizontal Asymptote, you have to look at the degree of the numerator and denominator.

[tex]h(x) = \frac{x^n}{x^m}[/tex]

The angles, 60°, [tex]\displaystyle \frac{\pi}{4}[/tex] and [tex]\displaystyle \frac{\pi}{6}[/tex] are special angles that have known trigonometric ratio values.

First part;

Second part;

Third part;

Reasons:

First Part;

Considering a unit circle with the center at the origin of the graph, we have;

The sine of the angle, θ, rotated by the radius is the vertical distance of a point P on the circle which is the location of the radius, from the horizontal axis.

The cosine of the angle, θ, is the horizontal distance of P from the vertical axis, such that we have;

The coordinates of point P = (cos(θ), sin(θ))

In the four quadrant, we have;

First Quadrant; All trigonometric ratios are positive

Second Quadrant; sine is positive

Third Quadrant; Tan is positive

Fourth Quadrant; Cosine is positive

Second part;

We have; At 120°, the point P is the same elevation from the horizontal axis, therefore;

sin(60°) = sin(120°) = 0.5·√3

However, the x-coordinate of the point P is in the negative direction, therefore, we get;

cos(120°) = -cos(60°) = -0.5

Similarly from the quadrant relationship, we have;

240° is in the third quadrant, and it is 60° below the negative horizontal line, therefore;

sin(240°) = -sin(60°) = -0.5·√3

cos(240°) = -cos(60°) = -0.5

300° is in the fourth quadrant, and it is 60° below the positive x-axis, therefore;

sin(300°) is negative and cos(300°) is positive

Which gives;

sin(300°) = -sin(60°) =  -0.5·√3

cos(300°) =  cos(60°) = 0.5

Third part;

[tex]\displaystyle \frac{\pi}{4} =45^{\circ}[/tex]

[tex]\displaystyle \frac{\pi}{6} =30^{\circ}[/tex]

The sine and cosine of 45° can be used to find the sine and cosine of (180° + 45°) = 225°, (360° - 45°) = 315°

Also, due to the mid location of the angle 45° on the quadrant, we have;

Another angles is the sines and cosine of (90° + 45°) = 135°

Therefore, [tex]\displaystyle \frac{\pi}{4}[/tex], can be used to find the sine and cosine of 135°, 225°, and 315°

[tex]\displaystyle 135^{\circ} = \mathbf{\frac{3 \cdot \pi}{4}}[/tex], [tex]\displaystyle 225^{\circ} = \frac{5 \cdot \pi}{4}[/tex], [tex]\displaystyle 315^{\circ} = \frac{7 \cdot \pi}{4}[/tex]

Therefore,

[tex]\displaystyle \frac{\pi}{4}[/tex] can be used to find the sine and cosine of [tex]\displaystyle \mathbf{\frac{3 \cdot \pi}{4}}[/tex], [tex]\displaystyle \mathbf{\frac{5 \cdot \pi}{4}}[/tex], and [tex]\displaystyle \mathbf{ \frac{7 \cdot \pi}{4}}[/tex]

Similarly, the sine and cosine of, [tex]\displaystyle \frac{\pi}{6}[/tex]  = 30° can be used to find the sine and cosine of 150°,  210°, and 330°.

[tex]\displaystyle 150^{\circ} = \frac{5 \cdot \pi}{6}[/tex], [tex]\displaystyle 210^{\circ} = \frac{7 \cdot \pi}{6}[/tex], and [tex]\displaystyle 330^{\circ} = \frac{11 \cdot \pi}{6}[/tex]

[tex]\displaystyle \frac{\pi}{6}[/tex], can be used to find the sine and cosine of [tex]\displaystyle \mathbf{ \frac{5 \cdot \pi}{6}}[/tex], [tex]\displaystyle \mathbf{ \frac{7 \cdot \pi}{6}}[/tex], and [tex]\displaystyle \mathbf{\frac{11 \cdot \pi}{6}}[/tex]

Learn more about the sine and cosine of angles here:

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Answer:

Step-by-step explanation:

The cosine value of an angle is the x coordinate of the point the angle corresponds to on the unit circle, and the sine value of an angle is the y coordinate of that point. 120, 240, and 300 all form 60 degree reference angles which in turn forms 30-60-90 triangles which help to find the sine and cosine of these corresponding angles. Pi/4 radians converts to 45 degrees which forms a 45-45-90 special triangle on the unit circle which has its own known trigonometric ratio. Pi/6 radians converts to 30 degrees which forms a 30-60-90 triangle on the unit circle which also has a known trigonometric ratio. These ratios help find the sine and cosine of the angles on the unit circle which corresponds to a point on the coordinate plane.

Answer:

Step-by-step explanation:

Determine which climbed at a constant rate

A constant rate would produce a straight line.  The slope is the same for all the data for that climber.  We can either calculate the slope between the first and last intervals and see if the slope changes.  Or we can graph the points, which I chose to do.  See the attachment.

Note that Joe's rate is not constant.  It appears as though he's wearing down.  Both Zas and Stephon have constant slopes, so their climbing rates are constant over the period measured.

The slope is the climbing rate:

Joe:           Not Constant

Zas:            2.5 feet/sec

Stephon:     4.0 feet/sec

Time to Reach 30 feet

Joe:           Unknown - he's slowing down at an unpredictable rate.

For Zas and Stephen, use their slopes in the expression:

Use m for slope (ft/sec):  y = m(t) where t is time in seconds

Zas:            2.5 feet/sec:  y = 2.5(t)  Time to reach 30 is 30/2.5 or 12 sec.

Stephon:     4.0 feet/sec:  y = 4.0(t)  Time to reach 30 is 30/4.0 or 7.5 sec.

Answer:

yes

Step-by-step explanation:

Answer:

35 dimes and 60 nickels

Step-by-step explanation:

let d = # of dimes and n = # of nickels

We know that Timmy has a total of 95 coins, consisting of dimes and nickels

So d + n = 95

The total value of his bank is $6.50

A dime is worth $0.10 and a nickel is work $0.05

So 0.10d + 0.05n = $6.50

Note that we've just created a system of equations that we can solve

We have the two equations

0.10d + 0.05n = 6.50 and d + n = 95

There are many different methods we can use to solve this system but the easiest way in this situation is probably going to be the substitution method.

First we are going to want to rearrange the terms of the second equations so that one of the variables are defined.

d + n = 95

- subtract d from both sides -

n = 95 - d

We now defined "n"

Now that we have defined one of the variables we can plug in ( or substitute ) the value of it into the other equation. Once we substitute it we can solve for the other variable.

0.10d + 0.05n = 6.50

n = 95 - d

0.10d + 0.05(95 - d) = 6.50

we now solve for d

0.10d + 0.05(95 - d) = 6.50

step 1 distribute the 0.05

0.05 * 95 = 4.75 and 0.05 * -d = -0.05d

0.10d + 4.75 - 0.05d = 6.50

step 2 combine like terms 0.10d  - 0.05d = 0.05d

0.05d + 4.75 = 6.50

step 3 subtract 4.75 from both sides

0.05d = 1.75

step 4 divide both sides by 0.05

0.05d / 0.05 = d and 1.75 / 0.05 = 35

d = 35

Now that we have found the value of one variable we can plug it into one of the equations and solve for the other variable ( note that the equation that we use does not matter, we will acquire the same answer )

d + n = 95

d = 35

35 + n = 95

subtract 35 from both sides

n = 60

We can conclude that he has 35 dimes and 60 nickels

Answer:

The domain of the graph is all real numbers less than or equal to 0.

Hope this helps! :D

Answer:

1332.25 yd²

Step-by-step explanation:

To find the area, you do length times width. Since it is a square and each side is 36.5, you do 36.5 * 36.5 to find the area.

36.5 * 36.5=1332.25

Answer:

answer 215 nickels

Step-by-step explanation: