Determine whether the figure is a parallelogram using the distance formula.

Q\left(-10,-2\right),R\left(1,-1\right),S\left(1,-7\right),T\left(-11,-8\right)Q(−10,−2),R(1,−1),S(1,−7),T(−11,−8)

The composite functions and their domains are listed as follows:

a) (f ∘ g)(x) = sin(2x/(x + 5)), domain is all real values except x = -5.

b) (g ∘ f)(x) = sin(2x)/(sin(2x) + 5), domain is all real values except x = -5 and the values of x for which sin(2x) + 5 = 0.

c) (f ∘ f)(x) = sin(sin(2x)), domain is all real values.

d) (g ∘ g)(x) = x/(6x + 5), domain is all real values except x = -5 and x = -5/6.

The composite functions are found applying the inner function as the input to the outer function, according to the rule presented as follows:

(f ∘ g)(x) = f(g(x)).

The domain is the set of values that respect all the input constraints of the inner function, of the outer function, and of the composite function.

For this problem, the functions are given as follows:

For item a, the inner function g is applied as the input to the outer function f, hence:

f(g(x)) = sin(2x/(x + 5))

The sine has no constrains, the fraction cannot have a denominator zero, hence the domain is composed by all real values except x = -5.

The other composite functions are listed as follows:

[tex]g(g(x)) = \frac{\frac{x}{x + 5}}{\frac{x}{x + 5} + 5} = \frac{x}{6x + 5}[/tex]

Domain is all real values except:

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Answer: y = 11

Step-by-step explanation:

Our problem: 72y - 126 = 522 + 144

1. Simplify 552 + 144 to 666

72y - 126 = 666

2. Add 126 to both sides

72y = 666 + 126

3. Simplify 666 + 126 to 792

72y = 792

4. Divide both sides by 72

y = [tex]\frac{792}{72}[/tex]

5. Simplify [tex]\frac{792}{72}[/tex] to 11

y = 11

a) The maximum height of the ball is 100 feet.

b) The velocity of the ball on its way up is +16 feet per second.

c) The velocity of the ball on its way down is - 16 feet per second.

A free fall is an uniformly accelerated motion experimented by a particle due to the effects of gravity. The position of the ball (s) in time (t), in seconds, is described by a quadratic equation.

a) First, we find the maximum height reached by the ball:

s(t) = 80 · t - 16 · t²

16 · t² - 80 · t + s(t) = 0

Then, by using the discriminant:

(- 80)² - 4 · 16 · s(t) = 0

64 · s(t) = (- 80)²

s(t) = 100 ft

b) Second, find the function velocity by derivatives:

v(t) = 80 - 32 · t

Third, find the time related to the position s(t) = 96 ft:

s(t) = 80 · t - 16 · t²

100 = 80 · t - 16 · t²

16 · t² - 80 · t + 96 = 0

Then, by quadratic equation:

t = 3 s or t = 2 s.

Fourth, evaluate the function velocity:

v(2) = 80 - 32 · 2

v(2) = 16

v(3) = 80 - 32 · 3

v(3) = - 16

The velocity of the ball when s(t) = 96 ft on its way up is 16 feet per second.

c) The velocity of the ball when s(t) = 96 ft on its way down is - 16 feet per second.

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The points on the graph of the given function at the value f(x)=3 would be x=5.0971 and x=1.5695.

What is a graph of a function?

A function's graph is the set of all points in the plane of the form (x, f(x)). The graph of f could also be defined as the graph of the equation y = f(x).

The given function is

                               [tex]f(x)=\frac{8-x}{x^2-7x+12}\\\\\[/tex]

Now we put f(x) = 3, we get

                             [tex]3=\frac{8-x}{x^2-7x+12}\\\\\\\3x^2-21x+36=8-x\\3x^2-20x+24=0\\[/tex]

Solving we get

                                x=5.09717

                                 x=1.5695

So the points on the graph of the given function at the value f(x)=3 would be x=5.0971 and x=1.5695.

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The distance it should take my classmate to ride the bicycle at each speed to burn 575 calories would be = 13.2m for first speed and 11.3m for the second speed.

A fitness program is defined as the program that is adequately organised for the purpose of maintaining proper healthy calories.

The period he plans to ride the bicycle for a day = 60minutes.

For the first speed,

8 cal/ min = 11mph

To convert to hour,

8 × 60 =480

He burns 480cal per hour in 11mph speed

If 480cal = 11 mph

575 cal = X

make X the subject of formula;

X = 575×11/480

X = 6325/480

X = 13.2 m

For the second speed;

12.75 cal/ min = 15mph

To convert to hour,

12.75 × 60 =765cal

He burns 765cal per hour in 11mph speed.

If 765cal = 15mph

575 cal = y

make y the subject of formula;

y = 575 × 15/765

y = 8625/765

y = 11.3 m

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The coordinates of T' are, T'(-3, -1).

What is rotation?

A rotation is a transformation in which each point of a preimage is turned through a predetermined angle and direction around a fixed point. The center of rotation is the fixed point. The term for the amount of rotation is the angle of rotation, and it is expressed in degrees. Measure the specified angle in the anticlockwise direction using a protractor.

Given: Triangle RST has vertices R(1, 1), S(1, 4), and T(3, 1).

We have to find the coordinates of T' after counterclockwise rotation of 180°.

Since, The rule for a rotation by 180° about the origin is (x, y) → (−x, −y).

So, the coordinates R(1, 1), S(1, 4) and T(3, 1) changes to R'(-1, -1), S'(-1, -4) and T'(-3, -1).

Therefore, the coordinates of T' are T'(-3, -1).

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The length of i will be 531.3 inch when h is 300 inch and ∠G is 30° and ∠H is 29°.

When two straight lines or rays intersect at a shared terminal, an angle is generated. An angle's vertex is the common point of contact. The difference in direction between two lines or surfaces is defined as an angle. Angles are expressed in degrees. From a same point, the two hands draw separate sets of lines. Angle refers to these groups of lines that originate from a common point. Every minute, the two hands create various angles. In real life, one example of an angle is a clock.

Here,

∠I=180-(30+29)

=180-59

∠I=121°

h/sin H=i/sin I

300/sin 29=i/sin 121

i=300*sin 121/sin 29

i=531.3 inch

When h is 300 inches, G is 30 degrees, and H is 29 degrees, the length of I is 531.3 inches.

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The point estimate for the lifetime of a certain type of battery is 120.1 hours.

Let X represent the battery's lifetime. X has a normal distribution with a standard deviation of 20 hours. The sample size is 50, and the average lifetime is 120.1 hours.

Calculating the mean of a sample drawn from the population yields a point estimate of the population's mean. The mean is calculated as the sum of all sample values divided by the number of values.

A single value estimate of a parameter is referred to as a point estimate. A sample mean, for example, is a point estimate of the population mean. An interval estimate provides a range of values within which the parameter is expected to fall. The population mean point estimate is sample mean and this is 120.1 hours.

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Complete question

The lifetime of a certain type of battery is known to be normally distributed with standard deviation =σ17 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 95% confidence interval for the mean lifetime for this type of battery. What is the point estimated?

The expected value of their repair costs is $41.50.

Given the probability of failure as 0.5%, this can be illustrated as 0.005.

The cost of repair is given as $300.

The expected value of the company will be:

= Earnings - [(Cost × P(failure)]

= 43 - (300 × 0.005)

= 43 - 1.50

= 41.5

The value is $41.50.

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Complete question

company estimates that 0.5% of their products will fail after the original warranty period but within 2 years of the purchase, with a repair cost of $300. The company offers an extended two-year warranty.

If a consumer does not purchase the extended warranty, then the consumer will need to pay $43 for any necessary repairs. What is the expected value of their repair costs?

Answer:

70

Step-by-step explanation:

8 - 1 = 7

7 x 10 = 70

He used 70 sheets.

The area of the semicircle is A = 1187.9 cm².

The area of a circle with a radius of r is A = πr².

Given that, the diameter of the semicircle is 55 cm.

The radius of the semicircle is,

r = 55/2

The area of a semicircle is given by,

A = (1/2)πr²

Substitute the values,

A = (1/2)π(55/2)²

A = 1187.9

Hence, the area of the semicircle is A = 1187.9 cm².

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Unit rate of (1 /5 barrel) / (1/2hour) is equals to (2/5) barrels /hour.

What is unit rate?

"Unit rate is defined as the representation of the ratio of the two different units with value of the denominator equals to 1."

According to the question,

Given,

1/5 barrel/1/2 barrel

⇒ (1/2) hour = (1/5) barrel

⇒ 1 hour = (2/5) barallel

⇒ (2/5) barrel per one hour.

Therefore,

Unit  rate of given value is rewritten as

2/5 barrel/hour

hence option b is correct.

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Your question is incomplete. Please find the missing content below.

Rewrite 1/5 barrel 1/2 hour as a unit rate.

A. 2 1/2 barrel/hour

B. 2/5 barrel/hour

C. 10 barrels/hour

D. 1/10 barre./hour

True statement are:

A. This graph is not a function because the value x = 3 is assigned to

more than one y-value.

D. This graph is a function because the value of x is the same for

every value of y.

Given,

In the question:

To see the graph :

Mark all the statement that are true.

Now, According to the question:

From the graph,

Equations are expressions of two mathematical expressions t such as two numbers, functions. An equality between quantities and operations, usually with an equal sign "=".

Functions is a correspondences between two sets that are not empty each element in the set of input values can corresponds to a element in a set of output values that is unique.

Hence, True statement are:

A. This graph is not a function because the value x = 3 is assigned to

more than one y-value.

D. This graph is a function because the value of x is the same for

every value of y.

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Answer:

y(3xy-2x+1)

Step-by-step explanation:

I'm pretty sure it'd be y(3xy-2x+1).

Answer:

3xy²-2xy +y

Step-by-step explanation:

15x²y³-10x²y² +5xy² = 5xy(3xy²-2xy +y)

then

5xy(3xy²-2xy +y) / 5xy = 3xy²-2xy +y

the answer is a, -π/8

Answer:

x = 1

Step-by-step explanation:

Given:

g(x) = 4x - 4

To Find:

x when g(x) = 0

[tex] \rm \implies 4x - 4 = 0 \\ \\ \rm \implies 4x - 4 + 4 = 0 + 4 \\ \\ \rm \implies 4x = 4 \\ \\ \rm \implies \cancel{\frac{4}{4}} x = \cancel{ \frac{4}{4} } \\ \\ \rm \implies x = 1[/tex]

If Clara lives 12 floors above Darren, Clara lives on the 16 floor while Darren lives on the 4 floors.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

Given that Darren and Clara reside in a towering structure, this is expected. Twelve stories above Darren, Clara resides. One day, Darren climbed the stairs from his apartment to Clara's and went to see her. He was halfway up, on the eighth floor.

Suppose Darren and Clara live on x and y number of floor respectively.

If Clara lives 12 floors above Darren.

x-y=12

If in halfway he is on the 8th floor the total number of floors in the building will be 16.

As a result, we can say that Clara lives on the 16 floors while Darren lives on the 4 floor.

Thus, if Clara lives 12 floors above Darren, Clara lives on the 16 floors while Darren lives on the 4 floors.

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Answer:

exterior angle = 139°

(I'm using "X" instead of "2")

to find the exterior angle, find the interior angle first and then use the straight line.

interior angle = 180° therefore,

75° + 64° + X = 180

139° + X = 180°

X = 180° - 139°

X = 41° (not the answer)

a straight line = 180°

X = 41°

Y - the exterior angle

41° + Y = 180°

Y = 180° + 41°

Y = 139°

hope this is clear :)

Answer:

(2x+1)(3x+4)

Step-by-step explanation:

6x² + 11x + 4

multiply the first and last term

i.e (6x²)(4) = 24x²

find two terms that multiplies to give 24x² and when added would give 11x

¶ 8x and 3x

Therefore; 6x² + 11x + 4

6x² + 8x + 3x + 4

2x(3x + 4) + 1(3x + 4)

Answer; (2x + 1)(3x + 4)

The dimensions of the rectangular paint of perimeter 104.09 inches are given as follows:

The perimeter of any polygon, including a rectangle, is given by the sum of all the lengths of the outer edges of the figure.

Hence, for a rectangle of height h and width w, the perimeter is given by twice the sum of these dimensions, hence it is given as follows:

P = 2(h + w).

In this problem, the perimeter has the value given as follows:

P = 104.09 inches.

Hence:

2(h + w) = 104.09

h + w = 104.09/2

h + w = 52.045 inches.

The painting is 5.72 inches taller than it is​ wide, hence:

h = 5.72 + w.

Then the height is obtained as follows:

5.72 + w + w = 52.045

2w = (52.045 - 5.72)

w = (52.045 - 5.72)/2

w = 23.16 inches.

Then the height of the rectangular painting is given as follows:

h = 5.72 + w = 5.72 + 23.16 = 28.88 inches.

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The value of h in the parallelogram is 4 feet

The area of the parallelogram = b × h

Where b is the base of the parallelogram

h is the height of the parallelogram

One side of the parallelogram = 6 feet

The second side of the parallelogram = 8 feet

If the base of the parallelogram is 6 feet

The area = 6 × h

If the base of the parallelogram is 8 feet

Then the area of the parallelogram = 8 × 3

= 24 square feet

In both cases the area will be equal, then the equation will be

6h = 24

h = 24 / 6

h = 4 feet

Hence, the value of h in the parallelogram is 4 feet

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Answer:

$235.20

Step-by-step explanation:

the tax :

[tex] \frac{12}{100} \times 210 = 25.20[/tex]

total cost :

$210 + $25.20 = $235.20

Answer:

Either 15 or -1 see below

Step-by-step explanation:

I am not sure if you menat n = 2 or n = -2

n= 2

4n + 7  Subtitute in 2 for n

4(2) + 7

8 + 7

15

n = -2

4n + 7y

4(-2) + 7

-8 + 7

-1

Answer:123

Step-by-step explanation:

31231231232131

The quantity of items tha must be made for supply to equal demand is 2050 items

Demand simply means a consumer's desire to buy goods and services without any hesitation and pay the price for it.

To calculate the unit of quantity Q that must be made for demand to be equal to supply, we equate the demand and supply equation.

From the question,

For Demand

From Supply,

When supply is equal to demand

Solve for P

Substitute the values of P into equation 1

Hence, the quantity of items tha must be made 2050 items.

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Answer:

Step-by-step explanation:

the correct answer is A.

because if Kay has 5 pencils and it is given to Merry 1, it means that Kay still has 4 pencils.

Answer:

Step-by-step explanation:

They're both linear graphs, so they both follow the formula y = mx + b.

The y-intercept is when the graph crosses the y-intercept, so when x = 0.

First graph:

Slope(m): [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{-3-(-1)}{-3-0} =\frac{-2}{-3} =\frac{2}{3}[/tex]

y-intercept(b): (0, -1)

Second graph:

Slope(m): [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{-4-2}{-3-0} =\frac{-6}{-3} =2\\[/tex]

y-intercept(b): (0, 2)