A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 2 tables is $22. The total cost to rent 5 chairs and 6 tables is $60. What is the cost to rent each chair and each table?

Answers

Answer 1

Answer:

The cost to rent each chair and each table are $1.5 and $8.75 respectively

Step-by-step explanation:

Let x represent 1 chair

Let y represent 1 table

Therefore

3x + 2y = 22   ------------(1)

5x + 6y = 60   ------------(2)

Multiply (1) by 5 and (2) by 3

15x + 10y = 110   ----------(3)

15x + 18y = 180  ------------(4)

Subtract (3) from (4)

8y = 70

Divide through by 8

y = $8.75

Substitute y = 8.75 in (1)

3x + 2y = 22

3x + 2(8.75) = 22

3x + 17.5 = 22

Collect like terms

3x = 22 - 17.5

3x = 4.5

Divide through by 3

x =$1.5

Answer 2

Final answer:

By setting up a system of linear equations based on the given information and solving it, we determined that the cost to rent each chair is $1.50 and the cost to rent each table is $8.75.

Explanation:

To find the cost to rent each chair and each table from the party rental company, we set up a system of linear equations based on the information given:

3 chairs and 2 tables cost $22.5 chairs and 6 tables cost $60.

Let C be the cost of one chair and T be the cost of one table. We can write the following equations:

3C + 2T = $225C + 6T = $60

Solving this system of equations, we can find the values of C and T. First, multiply the first equation by 3 to eliminate T:

(3C + 2T) * 3 = 22 * 39C + 6T = $66

Now we can subtract the second equation from the modified first equation:

9C + 6T - (5C + 6T) = $66 - $604C = $6C = $1.50

With the cost of a chair known, we can substitute back into either equation to find the cost of a table:

3(1.50) + 2T = $224.50 + 2T = $222T = $22 - 4.502T = $17.50T = $8.75

The cost to rent each chair is $1.50 and the cost to rent each table is $8.75.


Related Questions

-f(x) = 2x + 6 Find f(-4)

Answers

The answer is 1 Bcuz u have to first plug in -4 for f then solve the equation by adding like terms and dividing

Divide the following polynomials, then place the answer in the proper location on the grid. Use synthetic division. Write the answer in descending powers of x.

(3x2 + 7x - 18) (x - 3)

Answers

The answer for the given polynomial by synthetic division is 3x+16+(30/(x-3)).

Step-by-step explanation:

The given polynomial is (3x^2 +7x -18) divided by (x - 3)

Take (x-3)=0, then x=3

    3  |  3        7       -18  

                    9        48

           3       16       30

step 1: write the coefficients of x^2, x and constant in first row. The divisor 3 is written separately on outside.

step 2: Write down the coefficient of x^2= 3 in the answer row as it is without any change.

step 3: Multiply each number in the answer row with the divisor and fill the answers in the second row.

step 4: The final step is to add the first row and second row. After addition, the answers are written in answer row and the last number in the answer row is the Remainder.

step 5: The remainder is written by dividing it with the divisor (x-3). The answer in the descending powers of x is 3x + 16 + (30/(x-3)).

Final answer:

The result of the division (3x^2 + 7x - 18) by (x - 3) using synthetic division is obtained as (3x + 16 + 30/(x - 3)).

Explanation:

To perform the synthetic division, the divisor (x - 3) is represented by its root '3'. Write down the coefficients from the dividend polynomial (3, 7, -18) at the top of your division setup. Write '3' to the left, leave some space, and then write down '3', '7', -18.

Then, perform the synthetic division: step one, bring the first coefficient (3) straight down. Step two, multiply this number by the root of the divisor (3), which is also 3. Write this product (9) underneath the next coefficient (7). Add these two numbers (7 + 9) to get 16. Write this number under the line. Now, repeat the previous step by multiplying 16 by the root, 3, to get 48. Write this under -18, add to get 30.

The quotient of the division is the polynomials received from the synthetic division which is 3x + 16 with a remainder of 30. So, the result of division (3x^2 + 7x - 18) by (x - 3) is (3x + 16 + 30/(x - 3)).

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What is the algebraic equation for this math trick

Pick a number
Add 2
Multiply by 3
Subtract 3
Divide by 3
Subtract the original number

Answers

Answer:

it will always be 1

Step-by-step explanation:

lets make an equation

pick a number : x

add 2 : x+2

multiply by 3 : (x+2)*3

subtract 3 : (x+2)*3-3

divide by 3 : ((x+2)*3-3)/3

if you simplify, you will get 1

step by step simplification

(x+2)*3 = 3x+6

3x+6-3=3x+3

(3x+3)/3 = x+1

x+1-x=1

Final answer:

The algebraic equation for the given math trick is: (((((x + 2) * 3) - 3) / 3) - x).

Explanation:

To represent the math trick you described algebraically, we can use the variable x to represent the initial number you pick. Following the steps you provided, the algebraic equation would be: ((((x + 2) * 3) - 3) / 3) - x. Let's break down each step:

Start with the initial number x.Add 2: x + 2.Multiply by 3: (x + 2) * 3.Subtract 3: ((x + 2) * 3) - 3.Divide by 3: (((x + 2) * 3) - 3) / 3.Subtract the original number x: ((((x + 2) * 3) - 3) / 3) - x.

what is the solution to this system of equations?

5x-3y=10
3x+3y=3​

Answers

Answer:

y = 5/2 , x= 7/2

Step-by-step explanation:

5x - 3y = 10…....(1)

3x + 3y = 3......(2)

solving by elimination, we subtract equation (2) from equation (1)

so, 2x = 7

dividing both sides by 2

x= 7/2

substitute x=7/2 for the value of y in equation (1)

5(7/2) - 3y = 10

multiply both sides by 2

35 - 6y = 20

rearranging

-6y = -15

dividing both sides by -6

y = 5/2

To determine the best fit undergraduate program, a high school senior researches the majors offered at the universities he is considering for admissions. The internet search reports that Arizona State University lists nine of their most popular majors and the percent of student population enrolled in the programs.
_______________________________________________
Popular Majors Percent of Student Body
Biology 8%
Business Marketing 20%
Communications/Journalism 6%
Education 5%
Engineering 7%
Interdisciplinary Studies 6%
Psychology 6%
Social Sciences 10%
Visual and Performing Arts 8%
----------------------------------------------------------
The university’s enrollment is expected to reach at least 20,000 students for the fall semester.
The minimum number of students who are expected to be working towards a Social Sciences degree is
The university requires that any student who is studying Visual and Performing Arts or Communications/Journalism must perform in one of the student productions before graduation. At least 20,000 students will be performing in the university’s student productions before graduation.
In the fall semester, % of the student population will be enrolled in a degree program not listed as one of the university’s most popular.
The most popular degree offered at Arizona State University is
For the fall semester, the university should expect that students will enroll in one of the two most popular

Answers

Final answer:

At least 2,000 students are expected to pursue a Social Sciences degree at Arizona State University. The most popular degree is Business Marketing, and about 6,000 students are estimated to enroll in the top two most popular programs (Business Marketing and Social Sciences) in the fall semester.

Explanation:

Based on the information provided about

Arizona State University's

most popular majors and their respective percentages, you can determine the minimum number of students expected to be working towards a Social Sciences degree. The

Social Sciences

program makes up 10% of the student body. Therefore, if the enrollment is expected to reach at least 20,000 students, you can expect that at least 2,000 students (10% of 20,000) will be working towards a

Social Sciences

degree. As for the most popular degree, Business Marketing is listed as comprising 20% of the student body, making it the most popular degree. The two most popular programs, Business Marketing and Social Sciences, make up 30% of the student body. So the university might expect that at least 6,000 students (30% of 20,000) will enroll in one of the two most popular programs in the fall semester.

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There are 1,198 souvenir paperweights that need to be packed in boxes. Each box will hold 12 paperweights. How many boxes will be needed?

Answers

Answer:

100 boxes

Step-by-step explanation:

Divide 1,198 with 12 because if there are 1,198 paperweights and each box holds 12 then how many boxes can hold these paperweights. Answer us 100 boxes

The main road in Belleville is 7 3/10 Miles long so far 2 3/4 miles have been repaved. How many miles have not been repaved

Answers

Answer:

4 11/20

Step-by-step explanation:

The length of road unpaved is 7 3/10 less 2 3/4 miles  The LCD of the fractions is 20 (both 10 and 4 divide evenly into 20).

Thus, the problem becomes 7 6/20 - 2 15/20.

We have to borrow 1 from that 7 because 15/20 is larger than 6/20.  This results in

6 26/20 - 2 15/20, or

4 11/20  

The total length of the main road in Belleville is [tex]7^{(3/10)}[/tex] miles. So far, [tex]2^{3/4}[/tex] miles have been repaved, leaving [tex]7^{(3/10)}[/tex] - [tex]2^{3/4}[/tex] miles that have not been repaved.

1. The total length of the main road is given as [tex]7^{(3/10)}[/tex] miles. In mathematical notation, [tex]7^{(3/10)}[/tex] represents the cube root of 7, which is then raised to the power of 3. So, the total length of the road is the cube root of 7, and then that result is cubed.

2. The length of the repaved portion is given as [tex]2^{3/4}[/tex] miles. In mathematical notation, [tex]2^{3/4}[/tex] represents the fourth root of 2, which is then raised to the power of 3. So, the repaved length is the fourth root of 2, and then that result is cubed.

3. To find the remaining length that has not been repaved, we simply subtract the repaved length from the total length:

  Remaining length = [tex]7^{(3/10)}[/tex] - [tex]2^{3/4}[/tex]

Calculating the values, the total length is approximately 2.262 miles (rounded to three decimal places) and the repaved length is approximately 1.682 miles (rounded to three decimal places). Now, subtracting the repaved length from the total length, we get approximately 0.580 miles (rounded to three decimal places) as the length that has not been repaved.

Therefore, the remaining length that has not been repaved is approximately 0.580 miles (rounded to three decimal places).

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help please 10 points !!images below

Answers

Answer for Question 1 is option 2  

Answer for Question 2 is option 3  

Answer for Question 3 is option 3  

Step-by-step explanation:  

For question 1 by plotting the two points we get the coordinates as (-2, 3) and (2, 1) where the x values are -2, 2 and the y values are 3, 1 respectively.  By substituting values of x in the formula given we get that equation 2 satisfies the values of y as in the graph.  

For question 2 the plotted line is split into two parts where one half is for values of x <2 and the other half is for values of x>2. By finding out the coordinates we get them as (2,-2), (1,-2.5) and (0,-3) for x<2 and by substituting the values of x in the formula we get option 3 as our answer.  

For question 3 we need to find the value of y when x=3 and the first condition is only for values greater than 3 so we take the second condition and substitute the value of x=3 and we get the value of y as 5 so the answer is option 3  

               

Solve v^2-7v-33=0 by factoring

Answers

this is not factorable. find a solution via the quadratic formula!

If f(x) = 5x + 4, which of the following is the inverse of f(x)

Answers

Answer:

f^-1 (x)=1/5x-4/5

Step-by-step explanation:

y=5x+4

x=5y+4

5y=x-4

y=1/5x-4/5

Answer:

I WOULD SAY THAT THE ANSWER IS C

Step-by-step explanation:

I GOT IT FROM A

                          P

                          E

                          X

GIVING BRAINLIEST NEED HELP PLZ!!!!
Simplify ( x - 2) - (6 x - 9)

Answers

Answer:

Subtracting polynomials is simply subtracting the like terms

(x-2)-(6x-9)

First you want to subtract your x from 6x

x-6x= -5x

Than you would subtract -2 and -9

-2- -9=7

-2+9=7

Your final answer would be

-5x+7

Hope this helps ;)

Step-by-step explanation:

Please help I need your it please
The following graph, made by the manager of the basketball team, compares the free throw percentages for various players.
Which statement best describes why this graph could be misleading?

A.The graph does not indicate if the free throws were made at home or away.

B.The color of the bar for Player H is different from the color of the other bars in the graph.

C.The graph is missing the scale on the y-axis, making it unclear as to how much higher the free throw percentage is for one player than for another.

D.We don't know if all of the people on the team are included in the graph.

Answers

Answer: C

Step-by-step explanation:

to be a good graph the x axis and y axis need labeled

Final answer:

The graph could be misleading because it does not indicate if the free throws were made at home or away, it is missing the scale on the y-axis, and it doesn't specify if all team members are included.

Explanation:

The statement that best describes why this graph could be misleading is A. The graph does not indicate if the free throws were made at home or away. The graph may show higher or lower percentages for certain players based on the location of the game. For example, a player may have a higher free throw percentage when playing at home compared to playing away.

Additionally, statement C is also correct. The graph is missing the scale on the y-axis, which makes it unclear how much higher or lower the free throw percentages are for each player.

Lastly, statement D is another reason why the graph could be misleading. Without knowing if all the people on the team are included, the graph may not provide an accurate representation of the overall free throw percentages of the team.

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Factor and solve the equation x^3-x^2-30x=0

Answers

Answer:

Step-by-step explanation:

The ratio of boys to girls is 7:12. If there are 76 children how many are girls?

Answers

Answer:

Step-by-step explanation:

I need help

Answer:

28 girls

Step-by-step explanation:

Given girls : boys ===> 7 : 12

i.e.

fraction all children who are girls = 7 / (7 + 12) = 7 / 19

fraction all children who are boys = 12 / (7 + 12) = 12 / 19

given that there are 76 children

number of girls = fraction of all children who are girls x total number of children

= 7/19   x   76

= 28 girls

Hugo took these steps to solve the system of equations.

2 x minus 3 y = negative 11. 3 x + 2 y = negative 5.

Step 1 4 x minus 6 y = negative 11. 9 x + 6 y = negative 15.
Step 2 13 x = negative 26
Step 3 x = negative 2
Step 4 3 (negative 2) + 2 y = negative 5. Negative 6 + 2 y = negative 5. 2 y = 1. y = one-half.
Step 5 The solution is (Negative 2, one-half).

Is Hugo’s solution to the system of equations correct? Explain why or why not.
Yes, Hugo’s solution is correct.
No, Hugo should have gotten positive 2 in step three.
No, Hugo forgot to multiply both sides of the first equation in step one.
No, Hugo should have subtracted the equations instead of adding them in step 2.

Answers

Answer:

C

Step-by-step explanation:

Answer:  C ) No, Hugo forgot to multiply both sides of the first equation in step one.

Step-by-step explanation:

The graphs of f(x) and g(x) are shown below.

On a coordinate plane, a straight line with a positive slope represents f (x) = x minus 3. The line goes through (0, negative 3) and (3, 0). On a coordinate plane, a straight line with a negative slope represents g (x) = negative 0.5 x. The line goes through (negative 4, 2), (0, 0), and (4, negative 2)

For what interval is the value of (f – g)(x) negative?
(negative infinity, negative 1)
(negative infinity, 2)
(0, 3)
(2, infinity)

Answers

Answer:

(negative infinity, 2)

Step-by-step explanation:

The two functions are given by f(x) = x - 3 and g(x) = - 0.5x

So, (f - g)(x) = x - 3 - ( - 0.5x) = 1.5x - 3

Then, for (f - g)(x) to be negative (1.5x - 3) < 0

⇒ 1.5x < 3

x < 2

Therefore, the interval will be (negative infinity, 2) for which the function (f - g)(x) will be negative. (Answer)

Answer:

negative infinity 2

Step-by-step explanation:

just did the test

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 4 large boxes and 8 small boxes has a total weight of 197 kilograms. A delivery of 2 large boxes and 3 small boxes has a total weight of 83 kilograms. How much does each type of box weigh?

Answers

A large box of fruit weighs 18.25 kilograms and a small box weighs 15.5 kilograms.

Step-by-step explanation:

Let,

Weight of large box = x

Weight of small box = y

According to given statement;

4x+8y=197      Eqn 1

2x+3y=83       Eqn 2

Multiplying Eqn 2 by 2

[tex]2(2x+3y=83)\\4x+6y=166\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 1

[tex](4x+8y)-(4x+6y)=197-166\\4x+8y-4x-6y=31\\2y=31[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{31}{2}\\y=15.5[/tex]

Putting y=15.5 in Eqn 2

[tex]2x+3(15.5)=83\\2x+46.5=83 \\2x=83-46.5\\2x=36.5[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{36.5}{2}\\x=18.25[/tex]

A large box of fruit weighs 18.25 kilograms and a small box weighs 15.5 kilograms.

Keywords: linear equation, elimination method

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From 2003 onward, the number of daily visitors to a website increased by 200% every two years. So, for example, the number of visitors in 2011 was 200% more than the number of visitors in 2009.

In what year was the number of daily visitors $800\%$ more than the number of daily visitors in 2003?

Answers

It takes 4 years for number of daily visitors to be 800% more than the number of daily visitors in 2003

Solution:

Let the number of visitors in 2003 be 100

From 2003 onward, the number of daily visitors to a website increased by 200% every two years

Therefore, Number of visitors in 2005 is given as:

Visitors in 2005 = 100 + 200 % of 100

[tex]Visitors\ in\ 2005 = 100 + \frac{200}{100} \times 100\\[/tex]

Visitors in 2005 is 300

Similarly, in 2007, the number of visitors is given as:

Visitors in 2007 = 300 + 200 % of 300

Visitors in 2007 = 300 + 600

Visitors in 2007 = 900

Now find the percentgae increase from 2003 to 2007

[tex]\text { Percentage increase }=\frac{\text {visitors in } 2007-\text {visitors in } 2003}{\text {visitors in } 2003} \times 100[/tex]

[tex]\text{percentgae increase} = \frac{900 - 100}{100} \times 100\\\\\text{percentgae increase} = 800[/tex]

Thus it is a 800 % increase

Number of years = 2007 - 2003 = 4 years

Thus it takes 4 years for number of daily visitors to be 800% more than the number of daily visitors in 2003

If a number increases by $200\%$, then this means that $2$ times the number is added to the original number. The result is $3$ times the original number. So, the information given in the problem means that the number of daily visitors to the website tripled every two years.

For the number of daily visitors to increase by $800\%$, it must become $9$ times its original value (that's $8$ times the original number added onto the original number). This is equivalent to tripling and then tripling again.

Relative to its value in $2003$, the number of daily visitors to the website tripled by $2005$, then tripled again by $2007$. So, $\boxed{2007}$ is the year in which this number reached $800\%$ more than its value in $2003$.

Miguel and Molly are cyclists. The graph shows the distance Miguel biked one day. Molly biked at a rate of 0.15 mile per minute. Which statement about their speed is true? Why

Answers

Answer:

Miguel traveled 0.2 mile per minute.

Step-by-step explanation:

3÷15=0.2

Final answer:

Speed can be interpreted from a graph's slope in a distance versus time plot. Comparing this to Molly's speed of 0.15 mile per minute, we could establish who is faster or slower. However, without the actual graph of Miguel's bicycling, we can't make a specific comparison.

Explanation:

This question relates to graph interpretation and the concept of speed. Here, we're trying to compare the cycling speed of Miguel and Molly. Molly's speed is given as 0.15 mile per minute. Without the graph available, we cannot definitively compare their speeds. But let's briefly explain what we'd look for.

If we had Miguel's graph, we'd specifically examine the slope of the graph. In a distance vs. time plot, speed is represented by the slope of the graph. Therefore, if the slope of Miguel's graph indicated a value higher than 0.15 mile per minute (steep slope), Miguel was going faster. Conversely, if it showed a lesser value (gentle slope), Miguel was going slower.

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If you place a 89-foot ladder against the top of a 80-foot building, how many feet will
the bottom of the ladder be from the bottom of the building?

Answers

Answer:

[tex]\large \boxed{\text{39 ft}}[/tex]

Step-by-step explanation:

Let x be the distance from the foot of the ladder to the base of the building.

We have a right triangle, so we can use Pythagoras' Theorem.

[tex]\begin{array}{rcl}80^{2} + x^{2}& = & 89^{2} \\6400+ x^{2} & = & 7921\\x^{2} & = & 1521\\x & = & \sqrt{1521}\\& = &\mathbf{39}\\\end{array}\\\text{The foot of the ladder will be $\large \boxed{\textbf{39 ft}}$ from the base of the building,}[/tex]

how do i find the mid point in A(-3,13) B(15,7) and C(-3,11)​

Answers

Answer:

Midpoint of AB=(6,10) ,Midpoint of BC=(6,9) and Midpoint of CA=(-3,12)

Step-by-step explanation:

Given that the points are A(-3,13), B(15,7) and C(-3,11)​

To find the mid points :

To find midpoint of AB

Let [tex](x_1,y_1) and (x_2,y_2)[/tex] be the points A(-3,13),B(15,7) respectively

Midpoint of AB[tex]=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

[tex]=(\frac{-3+15}{2},\frac{13+7}{2})[/tex]

[tex]=(\frac{12}{2},\frac{20}{2})[/tex]

[tex]=(6,10)[/tex]

Midpoint of AB=(6,10)

To find midpoint of BC

Let [tex](x_1,y_1) and (x_2,y_2)[/tex] be the points B(15,7),C(-3,11) respectively

Midpoint of BC[tex]=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

[tex]=(\frac{15-3}{2},\frac{7+11}{2})[/tex]

[tex]=(\frac{12}{2},\frac{18}{2})[/tex]

[tex]=(6,9)[/tex]

Midpoint of BC=(6,9)

To find midpoint of CA

Let [tex](x_1,y_1) and (x_2,y_2)[/tex] be the points C(-3,11),A(-3,13),respectively

Midpoint of CA[tex]=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

[tex]=(\frac{-3-3}{2},\frac{11+13}{2})[/tex]

[tex]=(\frac{-6}{2},\frac{24}{2})[/tex]

[tex]=(-3,12)[/tex]

Midpoint of CA=(-3,12)

Therefore Midpoint of AB=(6,10) ,Midpoint of BC=(6,9) and Midpoint of CA=(-3,12)

Approximately how many ounces are equivalent to 1 kilogram?

Answers

Answer: 35.27 oz

The answer is: The change of 1 kg ( kilogram ) unit for a weight and mass measure equals = into 35.27 oz ( ounce ) as per its equivalent weight and mass unit type measure often used.

Final answer:

Approximately, 1 kilogram is equivalent to 35.3 ounces. This calculation is achieved by starting with the knowledge that 1 kilogram is 1000 grams, then converting this measurement to ounces knowing that 1 gram equals 0.0353 ounces.

Explanation:

The topic at hand is the conversion between weight metrics, specifically how many ounces are approximately equivalent to a kilogram. It's important to note that 1 kilogram is approximately equivalent to 35.274 ounces. Here's why:

We understand from the given information that 1 ounce is produced by a mass of 28.35 grams (abbreviated as g). Given that 1 kilogram (kg) is equal to 1000 grams, to find the equivalent of a kilogram in ounces, we need to convert 1000 grams to ounces:

Step-by-Step Calculation

Start with 1 kilogram, which is equivalent to 1000 grams.Knowing that 1g equals to 0.0353 ounces, multiply 1000 grams by 0.0353 oz/g. This gives us 35.3 ounces.

So, 1 kilogram is approximately equivalent to 35.3 ounces.

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Select all true statements.

Answers

Answer:

A) Sin A  + Sin B  =  1.2 Sin C  

D) Sin C =  2.5 Sin A  = 1.25 Sin B

E)  Sin A  + Sin C  =  1.75 B

Step-by-step explanation:

Here, in the given triangle ABC

Base AC = 16 units, AB  = 2 units, and BC  = 8 units

Now, by Trigonometric Functions:

[tex]\frac{Sin A}{8} = \frac{Sin B}{16} =\frac{Sin C}{20}[/tex]

Comparing first two terms, we get:

[tex]\frac{Sin A}{8} = \frac{Sin B}{16} \\\implies 2Sin A = Sin B[/tex]                 ........... (1)

Also,

[tex]\frac{Sin B}{16} = \frac{Sin C}{20} \\\implies Sin C = 1.25 Sin B[/tex]   ....... (2)

Comparing first and last  terms, we get:

[tex]\frac{Sin C}{20} = \frac{Sin A}{8} \\\implies SinC = 2.5 Sin A[/tex]      ..........  (D)

Also, Sin A  = 0.5 Sin B

So, the given statement Sin A  = 2 Sin B is FALSE

⇒ 2.5 Sin A  = 1.25 Sin B   .......... (D)

Also,  Sin B  = 2 Sin A

⇒ Sin A  + Sin B =  Sin A + 2 Sin A =  3 Sin A

Also, Sin A  = 0.4 Sin C

⇒3 Sin A = 3 x (0.4) Sin C  = 1.2 Sin C  ..

⇒Sin A  + Sin B  =  1.2 Sin C   ........ (A)

B)   Sin A  - Sin B  = 0.4 Sin C - 2 Sin A  =  0.4 Sin C - 2 (0.4 Sin C)  

= 0.4 Sin C  - 0.8 Sin C  = -0.4 Sin C

⇒Sin A  - Sin B  =  -0.4 Sin C   ........ (B)

So, the given statement is FALSE

E)   Sin A  + Sin C =  0.5 Sin B + 1.25 B =  1.75 B

⇒ Sin A  + Sin C  =  1.75 B  ....(E)

On a boat, a cabin's window is in the shape of an isosceles trapezoid, as shown below. What is the area of the window?

Answers

ANSWER: 182 inches

STEP-BY-STEP EXPLANATION:

Since, it is an isosceles trapezoid, then area of an isosceles triangle is given by: [tex]\frac{1 (a+b)}{2}[/tex] × h

where a and b are the two parallel sides of the triangle and h is the height of an isosceles triangle.

Now, a= 12 inches and b= 2+2+12=16 inches and h=13 inches.

[tex]\frac{1 (12+16)}{2}[/tex] × 13 = 182 inches

whats the square root of 49

Answers

Answer:

The square root of 49 is 7. 7*7=49

Hope this helps,

:)

What is the value of the expression when y = 2?
3(y + 2)

Answers

Answer:

12

Step-by-step explanation:

3[y+2]

2+2= 4

3 multiplied by 4 is 12

Answer: 12

Step-by-step explanation: Since y = +2, we simply plug a +2 in for y in the expression. So we have 3(2 + 2).

Following your order of operations, you should simplify what's inside the parentheses first so 2 + 2 simplifies to 4.

Bring down your 3 and you have 3(4) which equals 12.

x² - 6x – 40=0
Complete the square

Answers

Answer:

Step-by-step explanation:

x^2 - 6x - 40 = 0.....get the -40 to the other side

x^2 - 6x = 40....now take half of ur x term (6)....so its 3...then square it (3^2 = 9)...now add 9 to both sides

x^2 - 6x + 9 = 40 + 9

(x - 3)(x - 3) = 49

(x - 3)^2 = 49...take sqrt of both sides, eliminating the ^2

x - 3 = sqrt 49

x = 3 (+ - ) 7

x = 3 + 7 = 10 or x = 3 - 7 = -4

so x = 10 or x = -4

Write the polynomial function, in standard form, that has zeros -2, 5, and 0.

Answers

Answer:

f(x) = x³ - 3x² - 10x

Step-by-step explanation:

Given that the zeros are x = - 2, x = 5 and x = 0 then the factors are

(x + 2), (x - 5) and (x - 0) = x

The polynomial is the product of it's factors, thus

f(x) = x(x + 2)(x - 5) ← expand factors using FOIL

     = x(x² - 3x - 10) ← distribute parenthesis by x

     = x³ - 3x² - 10x

Find the x and y intercepts of -2x - 4y = -12

Answers

Answer: x-intercept(6,0) & y-intercept(0,3)

Step-by-step explanation: To find the x-intercept, subsitutue zero in for y and solve for x, and vice versa to solve for y.

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Now you know the answer as well as the formula. Hope this helps, have a BLESSED AND WONDERFUL DAY!

- Cutiepatutie ☺❀❤

Can someone plz help me with this problem?

Answers

Answer:

option (2)

Step-by-step explanation:

Given the area (A) of a circle is

A = πr² ← r is the radius ( divide both sides by π )

[tex]\frac{A}{\pi }[/tex] = r² ( take the square root of both sides )

[tex]\sqrt{\frac{A}{\pi } }[/tex] = r → option (2)

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