Use the Law of Cosines. Find x to the nearest tenth.
B
15
24
16

The piecewise-defined function that gives the cost C(n) for a museum visitor who is n years old is C(n) = 0 for  0≤ n ≤ 12

Cn) = 3 for 12 ≤ n ≤ 17

C(n) = 8 for 18 ≤ n ≤ 64

C(n) = 4 for 65 ≤ n

The range of the function is {0, 3, 4, 8}.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Children under 12: free

Kids aged 12-17: $3

Adults aged 18-64: $8

Senior citizens 65 and over: $4

The function for the above can be written as,

C(n) = 0 for 0≤ n ≤ 12

Cn) = 3 for 12 ≤ n ≤ 17

C(n) = 8 for 18 ≤ n ≤ 64

C(n) = 4 for 65 ≤ n

The range of the function  C(x) is {0, 3, 4, 8}

Thus,

The piecewise-defined function that gives the cost C(n) for a museum visitor who is n years old is C(n) = 0 for  0≤ n ≤ 12

Cn) = 3 for 12 ≤ n ≤ 17

C(n) = 8 for 18 ≤ n ≤ 64

C(n) = 4 for 65 ≤ n

The range of the function is {0, 3, 4, 8}.

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Answer:

Step-by-step explanation:

Ok: It me again!

1. Since Greg earned 53$ for washing cars, he said he earned twice as much than mowing as a equation that would be:

2*m=53$ he made in total

So:

2. Answer: 2m=53$

The market price of the watch after a discount of 10% is  $3500   .

In the question ,

it is given that

the price at which the trader sold the wrist watch = $3150

the amount of discount given by trader = 10% ,

we need to find the market price of the watch ,

let the market price of the watch be "x" .

so , the formula that can be used to calculate the market price is

selling price = market price - (discount percent)×(market price)

Substituting the values , we get

3150 = x - 10% of x

3150 = x - 0.10x          ....because 10% = 0.10

(1 - 0.10)x = 3150

0.90x = 3150

Dividing both sides by 0.90 , we get

x = 3150/0.90

x = 3500

market price is $3500  .

Therefore , The market price of the watch after a discount of 10% is  $3500   .

The given question is incomplete , the complete question is

A trader sold a wrist watch for $3150 after giving a 10% discount. Find the marked price of the watch ?

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The angles x of the right angle triangle is 36.87 degrees.

A right angle triangle is a triangle that has one angle as 90 degrees. The angles of a right angle triangle can be found using trigonometric ratios.

Therefore, let's find the angle M(x)

sin x = opposite / hypotenuse

where

Therefore,

sin x = 6 / 10

sin x = 0.6

x = sin⁻¹ 0.6

x = 36.8698976458

x = 36.87 degrees.

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Answer:

5m-19

Step-by-step explanation:

distribute

4(2m-1)-3(m+5)

8m-4-3m-15

Combine like terms

8m-3m-4-15

5m-19

Hopes this helps please mark brainliest

Answer:

5m-19

Step-by-step explanation:

thank me later :)

Steps to Solving:

1) Distribute

2) Distribute the products again

3) Subtract the numbers

4) Combine like terms

Using scientific notation, the number can be expressed as 1.73 * 10⁻²

Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form. As we know, the whole numbers can be extended till infinity, but we cannot write such huge numbers on a piece of paper. Also, the numbers which are present at the millions place after the decimal needed to be represented in a simpler form. Thus, it is difficult to represent a few numbers in their expanded form. Hence, we use scientific notations.

Scientific notation helps us to represent the numbers which are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent. The exponent is positive if the number is very large and it is negative if the number is very small.

When the scientific notation of any large numbers is expressed, then we use positive exponents for base 10. For example:

20000 = 2 x 10⁴, where 4 is the positive exponent.

When the scientific notation of any small numbers is expressed, then we use negative exponents for base 10. For example:

0.0002 = 2 x 10⁻⁴, where -4 is the negative exponent.

From the above, we can now approach the problem and convert 0.0173 into scientific notation.

This will result into a negative exponent and can be expressed as

0.0173 = 1.73 * 10⁻²

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The equation which best shows the relationship between Davis' savings, y and the number of months passed, x is; y = 20 + 5x.

It follows from the task content that the equation which represents the relationship between Davis' savings and the number of months passed be determined.

According to the task content;

Davis has $20 in his savings account, and he adds $5 every month.

Therefore, we have;

y = 20 + 5x

This follows from the fact that the amount added after each month is $5.

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Answer: When you are simplifying exponential terms raised to another exponent, the way to simplify them is to multiply the exponents together.

Step-by-step explanation:

Answer: X = 1.12

Y = 1.75

Step-by-step explanation:

8/10 = 5/X +5

5(10) = 8(X + 5)

CROSS MULTIPLY AND DIVIDE

50 - 40 = 8X + 40 -40

10 = 8X

10/8 = 8X/8

1.25 = X

8/10 = 7/7 +Y

CRPSS MULTIPLY AND DIVIDE

7(10) = 8(7 +Y)

70 = 56 + 8Y

70 -56 = 56 -56 + 8Y

14 = 8Y

14/8 = 8Y/8

1,75 = Y

The equation for S, in terms of t, is S = 18 - 2t

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The initial value is 18 inches,

The rate of change is -1.5 inches per hour,

t is the number of hours.

S = 18 - 2t

Number of Hours after the                      Depth of Snow on Hudson's Lawn

Storm                                                                           (Inches)

0                                                                                        18

1                                                                                          16

2                                                                                         14

3                                                                                         12

Therefore, the equation for S, in terms of t is S = 18 - 2t.

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Answer: You can find a right degree angle of a triangle when it’s a 90 degrees or if you can see it makes like a square.

Answer:

r=-40

Step-by-step explanation:

[tex]\frac{-0.4r}{-0.4} = \frac{16}{-0.4}[/tex]

r=-40

The height is 31.51 inches.

From the question, we have

Let height= h

width = h+6

diagonal = 49 inches

Using Pythagoras Theorem

49²  = h²  + (h+6)²

2401 = h² +h² +36+12h

2401 = 2h² +36+12h

2h²+12h-2365 = 0

Solving this, we get

h=−3+1/2√4766

h=31.51 inches

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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The average rate of change of the function over the range 4≤ x ≤7 using the function defined in the table is -1.

Given that,

We have to find the Find the average rate of change of the function over the range 4≤ x ≤7 using the function defined in the table below.

x           f(x)

1           90

4           87

7           84

10          81

We have to find the slope of the 2 points.

The points are (4,87) and (7,84)

The slope point is rise/run

Rise is y₂-y₁

Run is x₂-x₁

So,

Slope = (84-87)/(7-4)

Slope = (-3)/(3)

Slope = -1

Therefore, The average rate of change of the function over the range 4≤ x ≤7 using the function defined in the table is -1.

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Based on the mentioned information, each birthday card costs $2.2.

Forming the equation based on the mentioned variables. The equation will be formed as -

Cost of birthday cards × number of cards + cost of thank-you notes × number of notes = total cost

Equation for package a

3x + 2y = 9.60 : Equation 1

Equation for package b

8x + 6y = 26.60 : Equation 2

Multiplying equation 1 with 3

9x + 6y = 28.8 : Equation 4

Now subtracting equation 2 from equation 4

9x + 6y = 28.8

-8x (-)+ 6y = (-) 26.60

The result will be :

x = 2.2

Thus, the cost of birthday card is $2.2

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The quadrilateral with the given vertices is a Rhombus , the correct option is (C) .

In the question ,

it is given that ,

the vertices of the quadrilateral are (0,2), (6,0), (0,-2), (-6,0)

let us rename , the coordinates as A(0,2) , B(6,0) , C(0,-2) , D(-6,0) .

the distance between two points (x₁,y₁) and (x₂,y₂) can be calculated using the formula

d = √(x₂ - x₁)² + (y₂ - y₁)²

distance between A(0,2) and B(6,0) is

AB = √(6 - 0)² + (0 - 2)²

AB = √(6² + (-2)²)

AB = √(36+4)

AB = √40

distance between B(6,0) and C(0,-2) is

BC = √(0 - 6)² + (-2 - 0)²

BC = √((-6)² + (-2)²)

BC = √(36+4)

BC = √40

distance between C(0,-2) and D(-6,0) is

CD = √(-6 - 0)² + (0 - 2)²

CD = √((-6)² + (-2)²)

CD = √(36+4)

CD = √40

distance between D(-6,0) and A(0,2) is

DA = √(0 -(-6))² + (2 - 0)²

DA = √(6² + 2²)

DA = √(36+4)

DA = √40

we see that the length of all the sides  is √40 ,

all the sides are same in Square and Rhombus ,

But from the graph below, we see that the quadrilateral formed is in the shape of the Rhombus .

Therefore , The quadrilateral with the given vertices is a Rhombus .

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Wyatt has to drive more than 50 miles to save his earnings after spending it.

Given,

The cost for training and license = $500

The cost for gas and insurance = $4 per mile

The amount paid for the first delivery = $400 + $6 per miles

We have to find the total cost he spends and earns;

Here,

x be the distance he drives in mile

Then,

The amount he spends = $500 + $4x

The earnings of him = $400 + $6

Then,

Equate this;

500 + 4x ≥ 400 + 6x

500 - 400 ≥ 6x - 4x

100 ≥ 2x

x ≥ 100/2

x ≥ 50

That is,

Wyatt has to drive more than 50 miles to save his earnings after spending it.

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The cost of the hotel for 1 night is $130 using the ratio concept.

If b is not equal to 0, an ordered pair of real numbers a and b, represented as a / b, is a ratio. An equation that balances two ratios is called a proportion. For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 male and 3 girls. The formula a: b or a/b can be used to compare any two values.

However, the percentage formula is represented as a:b::c:d or a:b=cd.

There are three types of proportion. They are:

1) Direct Proportion.

2) Inverse Proportion.

3) Compound Proportion.

4) Continued Proportion

Given,

Cost for four rental nights = $520

The cost for one rental night is given by

x = 520/4

x = $130 per night

Therefore, the cost of the hotel for 1 night is $130.

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Their down payment of $22,500 is 15% of the purchase​ price.

A $7500 down payment​ is 5% of the purchase​ price.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A family buys a studio apartment for 150,000.

They pay a down payment of $22,500.

∴ Their down payment is (22500/150000)×100% of the purchase​ price which is,

= 15% of the purchase​ price.

Let x be the percentage of $7500 downpayment in a purchase of 150000.

∴ (x/100)×150000 = 7500.

1500x = 7500.

x = 75/15.

x = 5%

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Using World problem : work and time,

Himari will take 13 hour and 12 minutes to complete the job alone.

We have given that

Time taken by Even to do a job = 11 hours

let "x hours" be the time taken by humari to do this job alone .

Even'rate to do a job = 1/11 per hour

Himari and Even work together and do the job in 6 hours .

rate at which both are working together and do the job = 1/6 per hour.

Himari' rate to do job = 1/x hours per day

Now , using the formula "together work "

Even'rate + Himari'rate = rate of together work

=> 1/11 + 1/x = 1/6

we solve the above equation and find out the value of x

multiple both sides with 66x we get,

=> 6x + 66 = 11x

=> 5x = 66

=> x = 66/5 = 13 hours and 12 minute

Hence, Himari will take 13 hour and 12 minutes to do job alone .

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The approximate difference between the maximum and minimum distances of the Earth from the Sun in thousands of kilometers, considering the graph, in thousands of kilometers, is of:

50.

The approximate difference between the maximum and minimum distances of the Earth from the Sun in thousands of kilometers, is obtained by the subtraction of the maximum value and the minimum value of the graph.

From the graph shown at the end of the answer, these parameters are presented as follows:

Hence the difference between these two values is obtained as follows:

25,000 - (-25,000) = 25,000 + 25,000 = 2 x 25,000 = 50,000 km.

In thousands of km, the difference is:

50000/1000 = 50.

The graph is given by the image shown at the end of the answer.

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4 shirts ∝ 31

4 = 31k

7 shirts ∝ 54.25

7 = 54.25k

Where k is the constant of proportionality

The constant of proportionality is k = 0.13.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Timberlee buys 4 shirts for $31 and Riley buys 7 shirts for $54.25.

In proportionality terms, we can write as,

4 shirts ∝ 31 _____(1)

7 shirts ∝ 54.25 _____(2)

(1) can be written as,

4 shirts = 31K

7 shirts = 54.24k

Where k is the constant of proportionality.

Now,

The value of k.

From (1)

4 = 31k

k = 4/31

k = 0.13

From (2)

7 = 54.24k

k = 7/54.24

k = 0.13

Thus,

The constant of proportionality is k = 0.13.

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The measure of angle (12x + 18)° is 102 degrees and the measure of angle (8x +10) ° is 66 degrees.

An equation is an expression that shows the relationship between two or more numbers and variables.

We have been given the angles as;

(12x + 18)° and (8x +10)

We need to solve the value of x by an alternate interior angle;

(12x + 18)° = (8x +10)

Solving;

(12x - 18)° = (8x +10)

(12x - 8x)° = (18 +10)

4x = 28

x = 7

The value of x is 7.

Thus, (12x + 18)° = 102 degree

(8x +10) = 66 degree

Hence, the measure of angle (12x + 18)° is 102 degrees and the measure of angle (8x +10) ° is 66 degrees.

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[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-6)}}} \implies \cfrac{4 +5}{6 +6} \implies \cfrac{ 9 }{ 12 } \implies \cfrac{3 }{ 4 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{ \cfrac{3 }{ 4 }}(x-\stackrel{x_1}{(-6)}) \implies y +5 = \cfrac{3 }{ 4 } ( x +6) \\\\\\ y+5=\cfrac{3 }{ 4 }x+\cfrac{9}{2}\implies y=\cfrac{3 }{ 4 }x+\cfrac{9}{2}-5\implies {\Large \begin{array}{llll} y=\cfrac{3 }{ 4 }x-\cfrac{1}{2} \end{array}}[/tex]

Answer:

[tex]\displaystyle \boxed{ y=\frac{3}{4}x-\frac{1}{2} }[/tex]

Step-by-step explanation:

      First, we will find the slope. This is done by finding the change in y over the change in x.

[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }= \frac{4--5}{6--6} =\frac{4+5}{6+6}=\frac{9}{12}=\frac{3}{4}[/tex]

      Next, we will find the equation. We will create a point-slope equation and simplify into slope-intercept form.

y - 4 = [tex]\frac{3}{4}[/tex](x - 6)

y = [tex]\frac{3}{4}[/tex]x - [tex]\frac{9}{2}[/tex] + 4

y = [tex]\frac{3}{4}[/tex]x - [tex]\frac{1}{2}[/tex]

Answer: Yes. The answer is -1.

Step-by-step explanation:

2x+3y=4, y=2

Would look like this: 2x+3(2)=4.

1. Multiply 3 x 2 = 6

2) 2x + 6 =4

3) Subtract 6 from both sides

4) Will look like this: 2x = -2

5) -2 / 2 = -1

Answer: -1

Equation: 2x+3(2)=4.

Answer:

x= -1

Step-by-step explanation:

2x + 3y = 4

2x + 3(2) = 4

2x + 6 = 4

2x = 4 - 6

2x = -2

x = -2/2

x = -1

The  interpretation of the y-intercept is that the sales made in Year 2 is 20 million

A graph y-axis and x-axis. The y-axis is the vertical axis while x-axis is the horizontal axis. In this case, the y-axis is the Sales and the x-axis is the Year

The y-intercept is the point where the graph touches the y-axis. In this case, the y-intercept is 20. If you trace to the x-axis (Year), the value there is 2. The interpretation is that the sales made in Year 2 is 20 million

The point can be interpreted as the sales made in Year 8 is 40 million

The output value of this graph when the input value is 4 i.e. Year 4. The output value is the sales made in Year 4 which is 30 million (it is approximately halfway between 20 and 40)

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Answer:

length: 20m. width: 15m

Step-by-step explanation:

70/2 = 35

35         35

+5          -5

40         30

40/2     30/2

20         15

The total charge for this job is $12131.04.

Charge per square yard to remove old carpet = $5.99

Charge per square yard to install the new carpet = $4.50

Charge for carpet and pad they selected per square yard = $16.99 and $3.00

Dimension of the living room = 17 1/2 by 20 feet

⇒ 35/2 by 20 feet

Dimension of the hall = 4 by 12 feet

The living room and the hall is in the shape of rectangular.

The formula of the area of the rectangle is

A= length x width

the total area of the living room and the hall is

⇒ (35/2) x 20 + (4 x 12)  

⇒ 398 square feet.

The total cost is

⇒ 5.99 + 4.50 + 16.99 + 3. 00

⇒30.48

Thus, the total charge for this job is

⇒398 x 30.48

⇒$12131.04

Total cost (TC) in that is the overall economic cost of production and is made of variable cost, which varies in step with the amount of a terrific produced and includes inputs together with exertions and raw materials, plus fixed cost, which is unbiased of the quantity of an amazing produced and includes inputs that cannot be various in the brief term including homes and machinery, which include probably sunk prices.

Total cost in economics includes the full possibility price (blessings received from the next-nice alternative) of every issue of production as part of its constant or variable prices.

The additional total cost of one additional unit of manufacturing is known as marginal cost.

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The graph's curve "moves to the left/right/up/down," "expands or compresses," or "reflects" when a function is transformed. f(x) = 3x+8

A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output. Every function has a domain and a codomain, as well as a range.

The graph's curve "moves to the left/right/up/down," "expands or compresses," or "reflects" when a function is transformed. For example, the graph of the function f(x) = x2 + 3 is generated by simply pushing the graph of the function g(x) = x2 up by 3 units.

Therefore,

f(x) = |x|

y = f(x) + C C < 0 moves it down

y = |x| 8  for  shifting down 8

y = f(x + C) C > 0 moves it left

y = Cf(x)  C > 1 stretches it in the y-direction

y = 3x+8  to stretch it 2 vertically

y = −f(x)  Reflects it about x-axis

y = 3x+8

Hence, The graph's curve "moves to the left/right/up/down," "expands or compresses," or "reflects" when a function is transformed. f(x) = 3x+8

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