Find the value of each angle.​

{x | x < -12 or x > -6}

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Explanation:

Let's solve the first inequality for x.

(-2/3)x > 8

-2x > 8*3

-2x > 24

x < 24/(-2)

x < -12

The inequality sign flips when we divide both sides by a negative value.

Let's do the same for the second inequality.

(-2/3)x < 4

-2x < 4*3

-2x < 12

x > 12/(-2)

x > -6

The conclusion of each section is that x < -12 or x > -6 which points us to choice C as the final answer.

Side note: The intervals x < -12 and x > -6 do not overlap in any way. There's a gap between the two pieces. We consider these intervals to be disjoint. The number line graph is below.

Answer: 4/3 of a mile

Step-by-step explanation:

To find the distance that Pepe and Paula ran in 60 minutes, we need to first determine their individual pace in miles per minute. Pepe ran 2/3 of a mile in 5 minutes, so his pace was 2/3 / 5 = 2/15 of a mile per minute. Paula ran 1/4 of a mile in 2 minutes, so her pace was 1/4 / 2 = 1/8 of a mile per minute.

We can now use these values to determine the distance that each of them ran in 60 minutes. Pepe ran at a pace of 2/15 of a mile per minute, so he ran 2/15 * 60 = 8/15 of a mile in 60 minutes. Paula ran at a pace of 1/8 of a mile per minute, so she ran 1/8 * 60 = 3/8 of a mile in 60 minutes.

To find the total distance that Pepe and Paula ran in 60 minutes, we can add their individual distances: 8/15 + 3/8 = 35/60 + 45/60 = 80/60 = 4/3 of a mile. Therefore, Pepe and Paula cumulatively ran a total of 4/3 of a mile on their 60-minute training run.

The amount of the investment after 8 years will be, $4,357.64

Given, $500 is invested in an account earning 7% interest compounded quarterly.

We have to find the value of the invested amount after 8 years,

as, Amount = P(1 + r/100)^t

where, P is the amount of money invested, r is the rate of interest and t is the amount of time

Amount = 500(1 + 7/100)^(8×4)

Amount = 500(1.07)^32

Amount = 500×8.715

Amount = 4,357.635

So, the amount of the investment after 8 years will be, $4,357.64

Hence, the amount of the investment after 8 years will be, $4,357.64

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To find the exact value of (7π/6) using the unit circle, locate the angle (π/6) on the unit circle in the second quadrant, determine the coordinates, and adjust the y-coordinate to be negative. The final answer is (√3/2, -1/2). This answer is obtained by understanding the reference angle and using the coordinates of the point where the angle intersects the unit circle.

To find the exact value of (7π/6) using the unit circle, follow these steps:

1. Start by understanding the reference angle. The reference angle for (7π/6) is (π/6).

2. Locate the angle (π/6) on the unit circle. This angle lies in the second quadrant.

3. Determine the coordinates of the point where the angle intersects the unit circle. For (π/6), the x-coordinate is √3/2 and the y-coordinate is 1/2.

4. Since (7π/6) lies in the second quadrant, the x-coordinate will remain the same, but the y-coordinate will be negative. Therefore, the coordinates for (7π/6) are (√3/2, -1/2).

5. The exact value of (7π/6) is (√3/2, -1/2).

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Answer:

1 Mile per hour = 1.60934 kilometers per hour = 0.44704 meters per second (SI base unit). 1 mph = 0.447 04 m/s.

Step-by-step explanation:

1 Miles Per Minute to Miles Per Hour = 60 70 Miles Per Minute to Miles Per Hour = 4200

We have to use the "double distributive" property to solve the product

Then, we reduce like terms

Additionally, using the box method, we have the following

The required missing number is 51.02

Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar2, ar3, ar4, ar5, .....

Given here the numbers 140,100,71.4, ,36.44

clearly 140/100=100/71.4=1.4

Thus the given set of numbers form a geometric progression with common ratio 1.4

Therefore the complete set of numbers are 140,100,71.4,51.02,36.44

Hence, the required numbers is 51.02

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The required work done is 62400 J.

work done to lift a 1500 N object from the ground to the top of a 40 m building if the cable weighs 3 N per m

work done, is define as the product of force and displacement.

since,
work done to lift 1500N to height of 40 m is:
W= FS
   =  1500 x 40 = 60000J
now work done for rope
  is given by
w = mgΔx(40-x)
w= \(\int _0^{40}\left mg(40-x\right)dx\)
w=\(3\int _0^{40}\left(40-x\right)dx\)
w= 3\([40x-x^2/2]\left \{ {{40} \atop {0}} \right.\)
w= 3[1600-800]
w = 2400
Total work done for lifting 1500N to 40m height
= 6000+2400=62400J

Thus the required work done to lift 1500N weight to 40m is 62400J.

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Answer:

A, B, E

Step-by-step explanation:

Notice that A, B, and E all maintain their common ratios, while C and D do not.

By conducting mathematical operations, we know that John's gross pay will be $1,012 if he works 44 hours a week.

A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.

The supplied operands or integers must adhere to a set of predefined rules that are connected to the symbol of the math operator.

The order of operations refers to the rules that specify how to solve an expression including many operations.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).

So, we know that:

John earns $22 per hour for the first 40 hours of a week.

After every additional hour, he earns 1.5 times $22 each hour.

22 * 1.5 = $33

So, John's gross pay if he worked 44 hours will be:

22*40 + 33*4

880 + 132

$1,012

Therefore, by conducting mathematical operations, we know that John's gross pay will be $1,012 if he works 44 hours a week.

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Total amount of money in the account will be $456.

Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest.

The formula for simple interest is: Simple Interest = Principal × Rate × Time

Principal (P) is $300

Rate (R) is 6.5%

Time (T) is 8 years.

Simple Interest = $300 × 0.065 × 8

Simple Interest = $156

Total Amount = Principal + Simple Interest

Total Amount = $300 + $156

Total Amount = $456.

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Answer:

the slope intercept form is   y = (1/2)x - 1

Step-by-step explanation:

The slope-intercept form is, y = mx + b

We see from looking at the graph that,

at x = 0, y = -1

So, from this we find that b = -1

at x = 2, y = 0,

now, we find the slope m,

using,

\(m = \frac{y_{2} -y_1}{x_2-x_1}\)

Using x_2 = 2, y_2 = 0,

x_1 = 0, y_1 = -1, we get,

m = (0-(-1))/(2-0)

m = 1/2

So, the slope intercept form is,

y = (1/2)x - 1

Answer:

4.125 in decimal.

4 1/8 in fraction.

Step-by-step explanation:

First, let's simplify these fractions.  2 3/4=2.75 and 1 1/2=1.5  It says that Lucia walks 1.5 times farther on Tuesday, so just multiply 2.75 by 1.5 which comes to 4.125 miles.  Hope it helps

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Work Shown:

A = probability 1st satellite sends weak signal

A = 3/7

B = probability 2nd satellite sends weak signal, assuming event A happens earlier

B = 2/6 = 1/3

C = probability both A and B happen at the same time

C = A*B

C = (3/7)*(1/3)

C = 3/21

C = 1/7

Note: The fraction 3/7 has both numerator and denominator decrease by 1, to get 2/6, due to the "no replacement" condition.

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let the solution be \( ax + by - c = 0 \)

let the solutions be a = 3, b = 1

\( 3x + y = 0 \) is the equation with consistent value.

Answer:

the answer is -1

Step-by-step explanation:

im just tyna get my points thats all

Answer: 18

Step-by-step explanation:

\(\triangle HJK \cong \triangle HLK\) by HL. Therefore, \(JK=2\) by CPCTC.

Using the segment addition postulate, \(GK=9\).

Furthermore, \(\triangle HGK \cong \triangle HMK\) by HL. This means that \(MK=9\) by CPCTC.

Using the segment addition postulate again, \(GM=9+9=18\).

Given:

Required:

Solve for x

Explanation:

We have

multiply bot side with 3 and er get

Final answer:

Answer:

-320000

Step-by-step explanation:

Given

Lost Land = 80,000 acres yearly

Duration 4 years

Required

The total change

Represent the total change with y;

y is calculated as thus;

\(y = Lost\ Land * Duration\)

\(y = -80,000 acres * 4\)

\(y = -320000\ acres\)

Hence, a total of 320000 acres were lost during the period

Answer:

6 + (d * 2)

Step-by-step explanation:

You are adding 6 to the equation after the amount d times 2. In that case, a parentheses is required to round up d * 2.

The value of x is 6

A line segment can be defined as the partition formed by end points of a line.

From the information given, we have that line JL is the line with segments JK, KL and JL and K and the midpoint between J and L

This can be represented as;

JK + KL = JL

Where;

Substitute the values into the formula, we have;

5x -8 + 7x - 12 = 52

Now, collect like terms

12x = 52 + 20

Add like terms

12x = 72

Make 'x' the subject of formula

x = 72/12

x = 6

Thus, the value of x is 6

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Step-by-step explanation:

The ONE  solution to this system of two lines is the point where the two lines cross   at   (1,4)

Answer:

slope: -1/2

Y-intercept: -1

Step-by-step explanation:

Get Y by itself by subtracting x on both sides

2y= -x -2

Now divide both sides by 2 to cancel the two connected to the y:

Y = -1/2x -2/2

So y= -1/2x -1

Y=mx+b so m is the slope and b represents the y-intercept

Answer: no she dosen't

Step-by-step explanation:

If you were to add up all three numbers

49.95+19.95+21.95=91.85

Which means she is $1.85 short to buy all of the items

The area of the shaded region is = area of the sector - the area of the right angle triangle. so the area is \(9\pi /4 -9/2\)

Area of circle formula = \(\pi r^{2}\). The area of a circle is \(\pi\) multiplied by the square of the radius. The area of a circle when the radius 'r' is given is \(\pi r^{2}\)

The area of a circle when the diameter 'd' is known is \(\pi d\frac{2}{4}\). π is approx. \(3.14 or \frac{22}7}\). Area(A) could also be found using the formulas A = \((\frac{\pi}{4} )*d^{2}\), where 'd' is the radius and A= \(\frac{c^{2} }{4\pi }\), where 'C' is the given circumference.

According to the given information

The area of the shaded region is = area of the sector - the area of the right angle triangle.

A = \(9\pi /4 -9/2\)

Therefore the area of the shaded region is = area of the sector - the area of the right angle triangle. so the area is \(9\pi /4 -9/2\)

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Answer:

Step-by-step explanation:

This problem is on the mensuration of solids, a cylinder and a cone combined (a frustum)

We are required to solve for the total curve surface areas both solids

hence the curve surface area (henceforth CSA) of a cylinder is given as

\(CSA-cylinder=2\pi rh\)

\(CSA-cone= \pi rl\)

\(Total CSA= 2\pi rh+\pi rl\)

Given data

diameter d= 20

radius = d/2= 20/2= 10

height of cylinder h= 9

slant height of cone l= 16

substituting our data into the expression we have

\(Total -CSA= 2*\pi *10*9+\pi *10*16\\\\Total -CSA= 565.56+502.72\\\Total -CSA= 1068.28\)

Answer:

x=31

Step-by-step explanation:

2x+1=63 [Vertically opposite angles]

2x=63-1

x=62/2

x=31

Answer:

They each get 1/6

Step-by-step explanation:

Answer:

Option B is correct. the required domain of the function will be expressed as[-5, 3) U (3, ∞)

Step-by-step explanation: