Select the values that make the inequality -g > -6 true.
Then write an equalivalent inequality, in terms of g.
(Numbers written in order from least to greatest going across.)

Answer:

A

Step-by-step explanation:

Arc length is given by the formula:

\(\displaystyle s=2\pi r\frac{\theta}{360^\circ}\)

Where r is the radius and θ is the central angle, in degrees.

The windshield wiper has a radius of 20 inches and a central angle of 150°. Hence:

\(\displaystyle s=2\pi (20)\left(\frac{150}{360}\right)\)

Use a calculator:

\(\displaystyle s=\frac{50}{3}\pi \approx52.36\text{ inches}\)

Our answer is A.

The expression sin²x/(1+cosx) can be simplified to 1-cosθ

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Recall that sin²x = 1 - cos²x. Thus, we have:

sin²x/(1+cosx) = (1-cos²x) / (1+cosx)

                      = (1²-cos²x) / (1+cosx)

                      = (1+cosx)(1-cosx) / (1+cosx)

                      = 1-cosx

                      = 1-cosθ        (If x = θ)

Note: Using difference of two squares, 1²-cos²x = (1+cosx)(1-cosx)

Therefore, the expression sin²x/(1+cosx) can be simplified to 1-cosθ

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Answer:

The table is a quadratic function

Step-by-step explanation:

Given

The attached table

Required

Tell if it is a quadratic function

The difference in the x values are uniform (i.e. difference of 1), so the following method can be applied.

(1) Subtract adjacent y values.

\(d_1=2 - 16 = -14\)

\(d_2=-2 - 2 = -4\)

\(d_3 = 4--2 = 6\)

\(d_4 = 20 - 4 = 16\)

(2) Subtract adjacent differences in (1) above

\(d_5 = d_2 - d_1 = -4 --14 = 10\)

\(d_6 = d_3 - d_2 = 6 --4 = 10\)

\(d_7 = d_4 - d_3 = 16 -6 = 10\)

Notice the calculated differences in (2) are the same.

Hence, the table is a quadratic function

Answer:

7 square miles

Step-by-step explanation:

Answer:

I think its the right shape being the trapezoid

Step-by-step explanation:

the triangle looks like a triangle but then the reason why I said I think it's the on the right is because the acute angle makes it look like a trapezoid but then on the other side it has a right angle but I think its the right side.

Answer:

41 meters

Step-by-step explanation:

\(\frac{31}{64}\) = \(\frac{19.8}{x}\)

31x = (19.8)(64)

31x = 1267.2  Divide both sides by 31 and round

x = 41

Answer:

85 square inches

Step-by-step explanation:

The surface area is the area of all the sides and the bottom

The area of the bottom is

A = s^2  since it is a square

A = 5^2 = 25 in^2

The sides are triangles

A = 1/2 bh  where b is the base and h is the height

A = 1/2 ( 5)(6)

A = 15 in^2

We have 4 sides

The area of the 4 sides

4*15 = 60 in^2

Add the area of the side to the bottom

25+60 = 85 in^2

Answer:

Step-by-step explanation:

We have given that,this net can be folded to make a square pyramid.

we have to find the value of the surface area of this pyramid.

The surface area of this pyramid is the sum of all sides of it.

Atfirst the area of the bottom part,as it is a square,

Area=side^2

So,Area of the bottom. part=5^2=25 square inch.

NOW we have to find the value of the side areas of this pyramid.

As these parts are a triangle

Area of triangle=1/2×bh

where

so,Area=

But in this pyramid, it has 4 triangular sides.

So,Area of all triangular side=4×15=60 square inch.

The surface area =60+25=85 square inch

Answer:

the value of the expression is 22

Step-by-step explanation:

a2 + 12 + b

- input numbers..

(-2)2 + 12 + 14

-4 + 12 + 14

8 + 14

22

final answer 22

Answer:

18 (see picture for detailed explanation)

Step-by-step explanation:

Plato/Edmentum

Answer:

2

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. You have the following multiplication given in the problem above:

(x/3)(6/x)

2. Multiply the numerators and the denominators:

(x/3)(6/x) = 6x/3x

3. You can simplify the expression. Then, you have:

6x/3x = 2

Answer:

2

Step-by-step explanation:

1) simplify x

x/x = 1

2) simplify 6 with 3

6/3 = 2

3) multiply the two numbers

2*1 = 2

The given function is continuous at  x = 3,  RHL = LHL = F(2)

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  =  (x²-9)/(x² - x -6)(x² + 6x +9)

To check whether it is continuous at x = 2

First taking LHL,

\(\lim_{h \to \ 0}\)  ((2-h)²-9)/((2-h)² - (2-h) -6)((2-h)² + 6(2-h) +9)

⇒  -5/(-4x25)

⇒   1/20

Now, taking RHL

\(\lim_{h \to \ 0}\)  ((2+h)²-9)/((2+h)² - (2+h) -6)((2+h)² + 6(2+h) +9)

⇒  -5/(-4x25)

⇒   1/20

The value at x = 3

F(3)  =   ((2)²-9)/((2)² - (2) -6)((2)² + 6(2) +9)

       =  -5/(-4x25)

       =   1/20

Hence Proved,   RHL = LHL = F(2)

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Hey there!

You would use the distributive property. ( * = multiplication)

5(x - 2) = (5 * x) - (5 * 2) = 5x - 10

Hope it helps and have an amazing day!

Since the samples of the study are independent, the condition for inference have been met

The body mass index for adults in the United States = 26.8

BMI stands for Body Mass Index

Body mass index of marathon runners = less than 26.8

The random samples = 35

The body mass index of the random samples = 22.7

Standard deviation = 3.1

Then the researchers will conduct a one sample t test for a population mean.

The one sample t-test is is defined as the hypothesis test that check whether the unknow population mean is different from the specific value

Here the samples are independent

Therefore, the condition for inference have been met

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Answer:

Step-by-step explanation:

f(x) is simply another way of saying y

We are told that y = 15, so we set the equation 18x² + 15x - 10 equal to 15.

Add 10

18x² + 15x = 25

18x² + 15x + 25 = 0

Factor

(6x − 5) (3x + 5) = 0

Find both solutions for x

6x - 5 = 0

6x = 5

x = 5/6

Now, for the other solution.

3x + 5 = 0

3x = -5

x = -5/3

The height of the largest photo is 16 inches.

Sydney's senior picture package includes several sizes of portraits. The smallest photo is a 1.5-inch wide and 2 inch tall rectangle.

The largest photo is 12 inches wide and is similar to the smallest photo.

Let's assume that the largest photo's height is h, then we can say the ratio of the largest photo to the smallest photo is given as:\[\frac{h}{2}=\frac{12}{1.5}\]

Simplify the ratio:\[\frac{h}{2}=8\]

Multiplying each side by 2:\[h = 16\]

Therefore, the height of the largest photo is 16 inches.

Hence, the answer is 16.

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The length of side x is approximately 24.87, rounded to the nearest hundredth.

how can we find side of the triangle?

To find the length of side x, we can use the sine function, which relates the opposite side to an angle to the hypotenuse:

sin(11°) = opposite side/hypotenuse

Rearranging this equation, we get:

opposite side = sin(11°) * hypotenuse

We know that the hypotenuse has a length of 130, so we can substitute that in:

opposite = sin(11°) * 130

Using a calculator, we can evaluate sin(11°) to be approximately 0.1919, so we can substitute that in as well:

opposite = 0.1919 * 130

Simplifying this expression, we get:

opposite ≈ 24.87

Therefore, the length of side x is approximately 24.87, rounded to the nearest hundredth.

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The length and width of the rectangle are 5 inches and 1 inches respectively.

The length and width of the rectangle can be found as follows;

l = 3 + 2w

area of a rectangle = lw

where

Therefore,

5 = lw

5 = (3 + 2w)w

5 = 3w + 2w²

2w² + 3w - 5 = 0

Hence,

2w² + 3w - 5 = 0

Therefore,

w = 1  and w = - 5 / 2

width = 1 inches

length =  3 + 2(1) = 5 inches

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The best prediction for the number votes Pierre should expect to receive is 40 votes

From the question, we are determine the best prediction for the number of votes Pierre should expect to receive

From the given information,

He takes a poll of 34 random students and finds that 5 said they would vote for him

Then, we can assume that,

Out of every 34 random students, 5 would vote for him

The total number of students that will vote = 272

There are eight 34s in 272

NOTE: 272 ÷ 34 = 8

Then, he should expect 8 × 5 votes

8 × 5 votes = 40 votes

Hence, the best prediction for the number votes Pierre should expect to receive is 40 votes

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Answer:

y = x + 60

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (20, 80) and (x₂, y₂ ) = (40, 100) ← 2 points on the line

m = \(\frac{100-80}{40-20}\) = \(\frac{20}{20}\) = 1

the line crosses the y- axis at (0, 60 ) ⇒ c = 60

y = x + 60 ← equation of line

Answer: 85 units

Step-by-step explanation:

x^2 +35x + 35 = 10235

-10235 on both sides

x^2 + 35x -10200

Now Factor

( x - 85 ) ( x + 120 )

Now plug in for x using 85 or -120

(85)^2 + 35(85) + 35

7225 + 2975 + 35 = 10235

So 85 is the right answer

Answer:

D= [-4,-1) U (2,4)

R = [-3,5)

Answer:

it is inequalities

- thank you

Answer:

24:26 and 36:39 are two ratios that are equivalent to 12:13.

Step-by-step explanation:

Answer:

The speed of the helicopter is 160mph.

Step-by-step explanation:

The speed of the helicopter is 160mph.

Speed

Speed =Distance/Time

450miles/s-35mph = 702miles/s+35

450×s+35 = 702×s-35

450s+15,750 = 702s-24,570

Collect like terms

702s-450s = 15,750 + 24,570

252s= 40,320

Divide both side by 252s

s= 40,320/252

s= 160mph

Inconclusion the speed of the helicopter is 160mph.

5 "Always." Consecutive angles of a rectangle are always congruent.

6 "Never." A parallelogram is not always a square.

7 "Sometimes." In a rhombus, the diagonals are always perpendicular bisectors of each other, but they are not always congruent.

8 "Always." A rectangle has congruent sides, but not necessarily all four sides.

9 Given: ABCD is a parallelogram

To prove: AABC = ACDA

Proof:

AB || DC (definition of parallelogram)

AD || BC (definition of parallelogram)

∠ABC = ∠CDA (alternate interior angles)

AC = AC (reflexive property)

∠BCA = ∠DAC (alternate interior angles)

Therefore, AABC = ACDA (ASA congruence theorem)

10 Given: TRAP is an isosceles trapezoid

To prove: AAPR ARTA

TR = AP (definition of isosceles trapezoid)

∠APT = ∠ATR (alternate interior angles)

∠PAR = ∠RTA (alternate interior angles)

∠PAR = ∠APT (angles at a point)

Therefore, AAPR ARTA (AA congruence theorem)

Consecutive angles of a rectangle are always congruent. This is a property of rectangles that is true for every rectangle.

A square is a specific type of parallelogram that has all four sides congruent and all four angles right angles.

A rectangle has two pairs of opposite sides that are congruent, but the adjacent sides may have different lengths. This is a defining characteristic of rectangles, and it is always true for every rectangle.

The ASA congruence theorem states that two triangles are congruent if two angles and the included side of one triangle are congruent to the two angles and the included side of the other triangle. In this case, ∠ABC and ∠CDA are congruent by (3), AC is congruent by (4), and ∠BCA and ∠DAC are congruent by (5). Therefore, AABC = ACDA by the ASA congruence theorem.

The AA congruence theorem states that two triangles are congruent if two angles of one triangle are congruent to two angles of the other triangle, and the side between those angles is congruent in both triangles

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The equation that represents the total cost of electric service using Zap Electric company is y = $0.06r + $6.55

The equation that represents the total cost of electric service using Bolt Electric Company is y = $0.12r + $2.83

The equation that can be used to determine the total cost of electric service is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one. When drawn on a graph, a linear equation is usually a straight line.

The total cost is the sum of the monthly service fee and the total cost of the kilowatt used.

Total cost = service fee + (charge per kilowatt x number of kilowatts used)

Zap Electric company : $0.06r + $6.55

Bolt Electric Company : y = $0.12r + $2.83

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The inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

Inverse of a function can be calculated by following the steps mentioned below -

According to the question, the equation given is as follows

y = f(x) = 2x + 5

y = 2x + 5

Replace 'y' with 'x', we get -

x = 2y + 5

Now, solve for y -

2y = x - 5

y = (x/2) - (5/2)

Replace 'y' with f⁻¹(x) -

f⁻¹(x) = (x/2) - (5/2)

Hence, the inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

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Answer:

x = 11/2 = 5.5

Step-by-step explanation:

2x-6 = 5

2x = 11

x = 11/2 = 5.5

Answer:

54

Step-by-step explanation:

9x6=54

The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

A division is a process of splitting a specific amount into equal parts.

We have to find 3x³-2x²+7x+9 divided by x²-3x

3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.

The steps to solve this are given below.

Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next digit of the dividend (if present).

Step 5: Repeat the same process.

Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

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