Rewrite [tex]x^4y^2-3x^3y^3[/tex] using a common factor.
A) [tex]3xy(x^3y-x^2y)[/tex]
B) [tex]3xy^2(x2-x^2y)[/tex]
C) [tex]x^2y(xy-3xy^2)[/tex]
D) [tex]x^2y^2(x^2-3xy)[/tex]
option d
The selling price of an item is $600. It is marked down by 10% , but this sale price is still marked up from the cost of $450. Find the markup from
cost to sale price.
$135 is markup price when cost is $450.
What is the cost price and an example?
Cost price, for instance, equals selling price plus profit ( when selling price and profit is given ) Cost is equal to Selling price plus Loss ( when selling price and loss is given ) Cost price = 100 Selling Price + 100 + Profit (where the Selling Price and Profit Percentage are supplied)selling price of item = $600
cost = $450
10%×$650=$585
$585-$450=$135
$135 is markup price .
Learn more about cost price
brainly.com/question/17716968
#SPJ1
A 60 inch board is to be cut into three pieces so that the second piece is four times as long as the first piece and the third piece is five times as long as the first piece if X represents the length of the first piece find length of all three pieces
The length of the first piece is 6 inches.
The length of the second piece is 24 inches.
The length of the third piece is 30 inches.
What is the length of each piece?The length of the first piece = x
The length of the second piece = 4 ×x = 4c
The length of the third piece = 5 × x = 5x
Total length of the board = 60
Sum of the length of the three pieces = total length of the board
x + 4x + 5x = 60
10x = 60
x = 60 / 10
x = 6
The length of the second piece = 4 ×6 = 24
The length of the third piece = 5 × 6 = 30
To learn more about how to calculate length, please check: https://brainly.com/question/11349306
#SPJ1
answer the question in the screenshot please?
The value of x and y in the vector matrix are 2 and 5
What is a vector Matrix?If a matrix has only one row or only one column it is called a vector.
A matrix having only one row is called a row vector.
A matrix having only one column is called a column vector.
The matrix for two equations
3 - x/4 = 5/2 ---------------------1
8 - 12/4 = y ----------------------2
From equation 1,
collect like terms
x/4 = 3-5/2
x/4 = 1/2
cross multiply
2x = 4
x = 4/2
x = 2
From equation 2,
8 - 3 = y
y = 5
In conclusion, the value of x = 2 and the value of y = 5
Learn more about vector matrices: https://brainly.com/question/22363471
#SPJ1
Simplify the expression.
the linear expression quantity negative 1 over 4 times r minus 8 minus 5 over 7 times r end quantity minus the linear expression quantity negative 3 over 4 times r plus 9 end quantity
negative 48 over 28 times r minus 1
negative 3 over 14 times r plus negative 17
negative 3 over 14 times r minus 1
9 over 28 times r plus negative 17
The value of the linear expression quantity negative 1 over 4 times r minus 8 minus 5 over 7 times r end quantity minus the linear expression quantity negative 3 over 4 times r plus 9 end quantity is B. negative 3 over 14 times r plus negative 17
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Based on the information given, the expression will be:
= (-1/4r - 8 - 5/7r) - (-3/4r + 9)
Collect like terms
-1/4r - 5/7r + 3/4r - 8 - 9.
= - 3/14r - 17
In conclusion, the correct option is B.
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
Answer:
Step-by-step explanation:
b
What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3? m
The y-coordinate of the point that divides the directed line segment from J to K into a ratio of is 5.
The coordinates of point that divides the line segment into m:n ratio can be obtained as follows,
Coordinates of point = [tex](\frac{mx_{2}+ nx_{1} }{m+n} \frac{my_{2}+ ny_{1}}{m+n} )[/tex]
The coordinate of point J is (-3,1)
The coordinate of point K is (-8,11)
Consider the point that divides the line segment into 2:3 ratio as P(x,y).
The coordinates of point that divides the line segment into 2:3 ratio can be calculated as follows,
[tex]Coordinates of P = (\frac{3(-3)+2(-8)}{2+3}, \frac{3(1)+2(11)}{2+3} )[/tex]
[tex]= (\frac{-9-16}{5}, \frac{3+22}{5} )\\\\= (\frac{-25}{5} \frac{25}{5} )[/tex]
= (-5,5)
Hence the answer is The y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3 is 5.
To learn more about coordinates click here https://brainly.com/question/17206319
#SPJ9
X1. A restaurant owner keeps track of the food
prepared for guests for several days. Based on this
data, what is the constant of proportionality, if any
for this scenario? Show or explain how you know.
Vegetables Guests
Prepared
(Pounds)
Friday 15
Saturday 35
Sunday 25
Day
(number)
12
28
20
The constant of proportionality is the ratio of the number of guests to the food prepared is 0.8.
What are the ratio and proportion?
The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given table,
Suppose the number of guest ∝ food prepared.
Take the first data,
12 ∝ 15
12 = k(15)
k = 12/15 = 0.8
Hence "The constant of proportionality is the ratio of the number of guests to the food prepared is 0.8".
To learn more about ratios and proportions, click here https://brainly.com/question/12024093
#SPJ9
You go out to dinner and tip the waiter 21%. If your bill was $86.20, then what was your bill after
tipping 21%? Round to the nearest hundredth.
Answer:
The bill after tipping 21 percent would be $104.30.
Step-by-step explanation:
$86.20 x 0.21 = $18.102
$86.20 + $18.102 = $104.302
$104.302 ≈ 104.30
Hope my answer helped! Have a great afternoon.
The (i,j) minor of a matrix A is the matrix Aij obtained by deleting row i and column j from A.
The (i,j) minor of a matrix A is the matrix Aij obtained by deleting row i and column j from A it is true.
The (i,j) minor of a matrix A is the matrix Aij obtained by deleting row i and column j from A. A determinant of an n×n matrix can be defined as a sum of multiples of determinants of (n−1)×(n−1) sub matrices.
This is done by deleting the row and column which the elements belong and then finding the determinant by considering the remaining elements. Then find the co factor of the elements. It is done by multiplying the minor of the element with -1i+j. If Mij is the minor, then co factor, [tex]c_{ij}[/tex] [tex]= -1^{i+j}[/tex] + [tex]m_{ij}[/tex].
Each element in a square matrix has its own minor. The minor is the value of the determinant of the matrix that results from crossing out the row and column of the element .
Learn more about the minor of the matrix here:
https://brainly.com/question/26231126
#SPJ4
You work a basic week of 40 hours and your basic rate is $19.50 per hour. A rival company offers you an annual salary is $36.000. Except for the pay, everything is identical between the conpanies. Do you accept or reject the rival company's offer, and why ?
I will have to reject the offer of the rival company since it's lesser than $40560.
How to calculate the amountFrom the information, the person works a basic week of 40 hours and the basic rate is $19.50 per hour. It should be noted that there are 52 weeks in a year. The total amount will be:
= 40 × 19.50 × 52
= $40560
The rival company offers you an annual salary is $36000.
I'll reject the rival company's offer since it's lower.
Learn more about salary on:
brainly.com/question/25273589
#SPJ1
1. Use substitution to solve each system of equations
y = -2
y = 3x - 20
Answer:
[tex]x=6, y=-2[/tex]
Step-by-step explanation:
[tex]-2=3x-20 \\ \\ 3x=18 \\ \\ x=6 \\ \\ \therefore x=6, y=-2[/tex]
Answer:
The answer is x = 6. If you want to solve the equation by inputting the x and y value, then take the x value and input it into the equation as well as the y value.
Step-by-step explanation:
To solve this equation, plug in the value equal to y and solve for x. The first thing you have to do is make the equation -2 = 4x - 20, since we already have the value for y which is given in the question. Then add 20 to both sides of the equation. We now have 18 = 3x, divide both sides by 3 and you have your answer.
Hence, X = 6.
A biologist uses a box-shaped fish trap that measures 1/4 meter by 2/3 meter by 3/5 meter. What is the volume of the trap in cubic meters?
Answer:
1/10 or 0.1 m^3
Step-by-step explanation:
V = 1/4 * 2/3 * 3/5 = 6/60 = 1/10 m^3 = 0.1 m^3
you receive a $60 gift card to a move theater. a ticket to an afternoon show costs $6 and a ticket to an evening show costs $10. the rules of the gift card state that you can only buy a maximum of 8 total tickets with the card. let x
The constraints for this situation in the form of a system of inequalities is 6x + 10 y = 60.
Given:
you receive a $60 gift card to a move theater. a ticket to an afternoon show costs $6 and a ticket to an evening show costs $10. the rules of the gift card state that you can only buy a maximum of 8 total tickets with the card.
x = the number of afternoon tickets and y = the number of evening tickets.
6x ≤ 60
10y ≤ 60.
so
6x + 10 y = 60.
Therefore the constraints for this situation in the form of a system of inequalities is 6x + 10 y = 60.
Learn more about the inequalities here:
https://brainly.com/question/28823603
#SPJ4
X1. A restaurant owner keeps track of the food
prepared for guests for several days. Based on this
data, what is the constant of proportionality, if any
for this scenario? Show or explain how you know.
Vegetables Guests
Prepared
(Pounds)
Friday 15
Saturday 35
Sunday 25
Day
(number)
12
28
20
The constant of proportionality is the ratio of the number of guests to the food prepared is 0.8.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given tabel,
Suppose the number of guest ∝ food prepared.
Take the first data,
12 ∝ 15
12 = k(15)
k = 12/15 = 0.8
Hence "The constant of proportionality is the ratio of the number of guests to the food prepared is 0.8".
For more information about ratios and proportions,
brainly.com/question/26974513
#SPJ1
The given question is incomplete, the complete question follows,
What value of x is in the solution set of the inequality 4x - 12 ≤ 16 + 8x?
O-10
997
-9
-8
O-7
Answer:
-7
Step-by-step explanation:
Given inequality:
[tex]4x - 12 \leq 16 + 8x[/tex]
Subtract 4x from both sides:
[tex]\implies 4x - 12-4x \leq 16 + 8x -4x[/tex]
[tex]\implies -12\leq 16+4x[/tex]
Subtract 16 from both sides:
[tex]\implies -12-16\leq 16+4x-16[/tex]
[tex]\implies -28\leq 4x[/tex]
[tex]\implies 4x \geq -28[/tex]
Divide both sides by 4:
[tex]\implies 4x \div 4 \geq -28 \div 4[/tex]
[tex]\implies x \geq -7[/tex]
This means that x is equal to or greater than -7.
Therefore, the value of x that is in the solution set of the inequality is -7 as -10, -9 and -8 are all less than -7.
Answer:
x ≥ -7
Step-by-step explanation:
Given inequation,
→ 4x - 12 ≤ 16 + 8x
Then the value of x will be,
→ 4x - 12 ≤ 16 + 8x
→ 4x - 8x ≤ 16 + 12
→ -4x ≤ 28
→ x ≥ 28/-4
→ [ x ≥ -7 ]
Hence, the value of x is -7.
[tex]\frac{2\sqrt{3 }-1 }{3\sqrt{3}+4 }[/tex]
A bowling alley charges a flat fee to rent shoes. There is an additional fee for each game played. The function y=2. 5x+3 represents the cost y of bowling x games. Interpret the parameters of the function.
The number that represents the shoe rental charge is $3 and the price per game is $2.5.
Given:
The function y=2.5x+3 represents the cost y of bowling x games.
y = 2.5x+3
In the equation the 2.5 represents additional fee.
For 1 game = 2.5*1 = 2.5
For 2 games = 2.5 * 2
= 5
3 is the flat fee for renting the shoes.
Therefore the number that represents the shoe rental charge is $3 and the price per game is $2.5.
Learn more about the rental charge here:
https://brainly.com/question/16809318
#SPJ4
1. The floor of a building is 120 feet long
and 80 feet wide. A scale model of the
building has a length of 24 inches. What
is the width of the model?
Step-by-step explanation:
120 ft relate to 24 inches.
120/80 must be the same ratio as 24/model width.
120/80 = 3/2
so,
24/width = 3/2
48/width = 3
48 = 3width
width = 48/3 = 16 inches
8: fatuma's frower Garden is a Squase. If the enlarge it by increasing the Width by 1 m the length by 3m the area will be 19 square meters morethan the Present area.
A,find the length of the side of original garden B,What is the width of the new garden?
C,what is the length of the new garden?
D,find the area of the new garden?
A. The length of the side of original garden is 4 m
B. The width of the new garden is 5m
C. The length of the new garden is 7m
D. The area of the new garden is 35 m²
Let the side of the garden = x m.
area = x² m²
From the question, we have
The new length is (x+3) m and the new width is (x+1) m.
Then the new area = (x+3)(x+1) m².
(x+3)(x+1)=x²+19
⇒ x²+3x+x+3=x²+19
⇒ 4x+3=19
⇒ 4x=19-3
⇒ 4x=16
⇒ x = 4 m
The length of the side of original garden is 4 m
new length = (x+3) m = (4+3)m = 7 m
new width = (x+1) = (4+1) = 5 m
new area = (x+3)(x+1) m² = 7*5 = 35 m²
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.
To learn more about multiplication visit: https://brainly.com/question/5992872
#SPJ1
Please help me please
Answer:
x = 2
Step-by-step explanation:
The image shows a large rectangle with a similar, smaller triangle inside of it. The small leg on the small rectangle is 4, and the small leg on the large rectangle is 12. This tells me that the scale factor is 3.
If the scale factor is 3, then
[tex]6*3=6+6x[/tex]
Simplify
[tex]18=6+6x\\12=6x\\x=2\\[/tex]
This scale drawing shows a parking lot with an actual length of 315 meters. What is the width of the actual parking lot?
The width of the actual parking lot, given the length of the scale drawing and the actual length, is 235 m
How to find the width?The scale is given in the question to be 1 cm : 50 m. This means that for every 1 cm on the scale drawing, the actual dimensions are 50m.
Given that the width of the parking lot on a scale drawing is 4. 7 cm, the width of the actual parking lot will be:
= Width of parking lot on scale drawing x Number of meters per centimeter in drawing
= 4. 7 x 50
= 235 m
Find out more on scale at https://brainly.com/question/24693076
#SPJ1
(a) 11³ x 11=11
11³
||³ + x = || 2
Step-by-step explanation:
I suspect you mean
11³ × 11 = ?
11³ ÷ 11 = ?
11³ × 11 = 11⁴
11³ ÷ 11 = 11²
why ?
11³ = 11×11×11
11³ × 11 = 11×11×11 × 11 = 11×11×11×11 = 11⁴
11³ ÷ 11 = 11×11×11 / 11 = 11×11 × 1 = 11×11 = 11²
Find the slope of the line shown of the graph to the right
The slope will be 1, for the right.
What is the slope of line?
Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.
We know that formula two find the slope of the line joining two points which is
m = (4-3)/(4-3)
m = 1
Hence the slope of the line is shown in the graph is 1.
Learn more about Slope, by the following link
https://brainly.com/question/3493733
#SPJ1
What is the value of q in the solution to this system of equations?
2m - 5q = 8
4m + 2q = 64
Answer:
q = 4
Step-by-step explanation:
Step 1: Set up the equation
The system of equations can be solved algebraically by substitution or elimination.For substitution, solve one of the equations for m and plug it into the other equation in order to solve for q.For elimination, cancel the m terms in order to solve for q.Step 2: Solve for q
Substitution:2m - 5q = 84m + 2q = 644m = 64 - 2qm = [tex]\frac{64-2q}{2}[/tex]m = 16 - [tex]\frac{1}{2}[/tex]q2(16 - [tex]\frac{1}{2}[/tex]q) - 5q = 832 - q - 5q = 8-6q = -24q = 4Elimination:2m - 5q = 8 (multiply whole equation by -2 in order cancel m terms)4m + 2q = 64-2(2m - 5q = 8)-4m + 10q = -164m + 2q = 6412q = 48q = 4Emily's family loves to work together in the garden. They have a slight preference for flowers, as 60\%60%60, percent of their plants are flowers and 40\%40%40, percent are vegetables. They have 505050 plants growing in the garden.
How many vegetable plants do they have?
If Emily's family loves to work together in the garden . The number of vegetable plants they have is :20.
How to determine the number of vegetable plants?Using this formula to determine the number of vegetable plants
Number of vegetable plants = Percentage of vegetable plants × Number of plants
Let plug in the formula
Number of vegetable plants = 40% × 50
Number of vegetable plants = 20
Therefore we can conclude that the number of vegetable plants is 20.
Learn more about number of vegetable plants here: brainly.com/question/13048369
#SPJ1
The correct question is :
Emily's family loves to work together in the garden. They have a slight preference for flowers, as 60 percent of their plants are flowers and 40 percent are vegetables. They have 50 plants growing in the garden.
How many vegetable plants do they have?
Which situation cannot be represented by the equation 8−x=3?
Responses
ASAP PLEASE
Responses
Sunnyville had 3 fewer inches of rain than Pleasantville. Pleasantville had 8 inches of rain. What is x, the amount of rain in Sunnyville?
Jackson walked 8 dogs. Henry walked 3. What is x, the number of dogs the boys walked all together?
Joe had $8 and bought a piece of pizza. He had $3 left over. What is x, the cost of the pizza?
The difference between Amal's score and Katie's score was 3. Amal had 8 points, but Katie had fewer. What is x, the amount of Katie's score?
Project: Chef for a DayImagine you are the pastry chef at your favorite restaurant. The manager has just told you that you have a large crowd coming in for lunch tomorrow and you need to prepare. This project includes a recipe for chocolate chip cookies. You are expecting 60 people, but the recipe does not serve that many people, so you will need to adjust the ingredients so there will be enough.
Chocolate Chip Cookies (makes 12 servings)
1 ¼ cups all-purpose flour
½ teaspoon baking soda
¼ teaspoon salt
¾ cup sugar
1 egg
2 tablespoons milk
1 ¾ cup chocolate chips
Read each question below carefully and provide complete answers.
1. This recipe serves 12 people, but you need to serve 60 people. What number will you need to multiply the amount of each ingredient by to adjust the recipe? How did you determine this number?
2. Show the steps involved in finding out how much flour you will need to make 60 servings of chocolate chip cookies, as if you were teaching someone how to multiply with fractions. Please do not use decimals in your work or in your final answer.
3. Show the steps involved in finding out how much baking soda you will need to make 60 servings of chocolate chip cookies, as if you were teaching someone how to multiply with fractions. Please do not use decimals in your work or in your final answer.
4. Rewrite the rest of the chocolate chip cookie recipe for 60 servings. Be sure to show your work for each ingredient and express each amount as a fraction.
_____teaspoons salt
_____cups sugar
_____eggs
tablespoons milk
_____ cups chocolate chips
5. How many more eggs do you need for 60 servings than you need for 12 servings? How did you obtain this number?
6. If you wanted to make exactly 78 servings of chocolate chip cookies, what number would you need to multiply the original amount of each ingredient by to adjust the recipe? How did you determine this number?
7. Consider you make a mistake with the salt and multiply wrong which adds more salt then needed. Your cupcakes might not taste the greatest. Another mistake might be you incorrectly find the wrong amount to make. You make too little or not enough. What we do after the mistake is the important part. These mistakes are really not a big deal but in some instance in life we make bigger mistakes that weigh heavy on us. God is a loving and forgiving God. Isaiah 41:10 Fear not, for I am with you; be not dismayed, for I am your God; I will strengthen you, I will help you, I will uphold you with my righteous right hand.
Reflect on a time when you made a mistake. It can be a big mistake, a small mistake, or somewhere in between. Please don’t go into specifics but talk about how you handled the situation with God’s help and how you felt after. Please write a paragraph of at least 5 sentences.
NEED HELP FAST ITS A PROJECT!
The number needed to multiply the amount of each ingredient by to adjust the recipe is 5. It's determined by dividing the number of people that needs to be served by the number of people the provided ingredients will serve.
The steps involved in finding out how much all-purpose flour needed to make 60 servings of chocolate chip cookies is multiplying Quantity of flour provided by number needed to multiply each ingredients with.The steps involved in finding out how much baking soda needed to make 60 servings of chocolate chip cookies is multiplying Quantity of baking soda provided by number needed to multiply each ingredients with.Quantity of other ingredients needed expressed as a fraction:1 ¼ teaspoons salt
3 ¾ cups sugar
5 eggs
10 tablespoons milk
10 ½ cups chocolate chips
The number of eggs needed for 60 servings than 12 servings is 4 eggs. This is obtained by subtracting eggs needed for 12 servings from eggs needed for 60 servingsThe number needed to multiply the amount of each ingredient by to adjust the recipe to 78 servimgs is 6 ½. It's determined by dividing the number of people that needs to be served by the number of people the provided ingredients will serve.How to adjust given ingredients to the required number of servingsThe ingredients provided serves = 12 peopleNumber of people that needs to be served = 60 people1. Number needed to multiply the amount of each ingredient by to adjust the recipe = Number of people that needs to be served ÷ The ingredients provided serves
= 60/12
= 5
2. Steps involved in finding out how much flour you will need to make 60 servings of chocolate chip cookies.
Quantity of flour provided = 1 ¼ cups
Flour needed for 60 servings = Quantity of flour provided × number needed to multiply each ingredients with
= 1 ¼ × 5
= 5/4 × 5
= 25/4
= 6 ¼
3. Steps involved in finding out how much baking soda you will need to make 60 servings of chocolate chip cookies
baking soda needed for 60 servings = Quantity of baking soda provided × number needed to multiply each ingredients with
= ½ × 5
= 5/2
= 2 ½
4. Teaspoons salt = ¼ × 5 = 5/4 = 1 ¼
Cups sugar = ¾ × 5 = 15/4 = 3 ¾
Eggs = 1 × 5 = 5
tablespoons milk = 2 × 5 = 10
Cups chocolate chips = 1 ¾ × 6 = 7/4 × 6 = 42/4 = 10 ½
5. The number of eggs needed for 60 servings than 12 servings = eggs needed for 60 servings - ieggs needed for 60 servings
= 5 - 1
= 4
6. Number needed to multiply the amount of each ingredient by to adjust the recipe to 78 servings = Number of people that needs to be served ÷ The ingredients provided serves
= 78/12
= 6 ½
7. One time I made a mistake of keeping bad company, it really affected my studies because I lost concentration in school. My parents were disappointed in me but they helped me get back on the right track.
Read more on recipes and ingredients:
https://brainly.com/question/2985210
#SPJ1
triangle with side of 8 and 11 and angle of 38
The area of the triangle is 43.81 square units
The side a = 8 units
The side b = 11 units
The perimeter of the triangle = 32 units
First we have to find the third side of the triangle
a + b + c = 32
Substitute the values in the equation
8 + 11 + c = 32
19 + c = 32
c = 32 - 19
c = 13 units
Then the area of the triangle = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
The value of s = (a + b + c) / 2
= (8 + 11 + 13) / 2
= 32/2
= 16
Substitute the values in the equation
The area of the triangle = [tex]\sqrt{16(16-8)(16-11)(16-13)}[/tex]
Subtract the terms
= [tex]\sqrt{(16)(8)(5)(3)}[/tex]
= [tex]\sqrt{1920}[/tex]
= 43.81 square units
Hence, the area of the triangle is 43.81 square units
The complete question is:
Find the area of a triangle , two sides of which are 8 cm and 11 cm and the perimeter is 32 cm.
Learn more about area of triangle here
brainly.com/question/19305981
#SPJ9
Find the measures of the numbered angles.
Answer: <1=104 degrees, <2=76 degrees, <4=104 degrees, <5=104 degrees, <6= 76 degrees, <7= 76 degrees, <8= 104 degrees
Step-by-step explanation:
<76 & < 2 are vertical angles, which means they are congruent. <1 & <2 are supplements, meaning when you add them up they equal 180 degrees (180-76=104 degrees). <1 & <4 are vertical angles. Using the Alternating Exterior Angles Theorem (AIA), <2 & <7 are congurent. Using the same theorem, <1 & < 8 are congruent. <7 & <5 are supplements, and so is <8 & <6.
A television can be purchased cash for $1800 or on hire purchase for a deposit of 20% and 18 monthly payments of $90. If taken on hire purchase calculate:
A) the deposit
B) the hire purchase price
C) Hence, the amount saved if the television is bought for cash.
The sum of 2 numbers is 27. One half of the first number plus one third of the
second number is 11. Find the numbers.
Answer:
x = 12, y = 15
Step-by-step explanation:
x + y = 27
1 / 2 x + 1 / 3 y = 11
y = 27 - x
1 / 2 x + (27 - x) / 3 = 11
1 / 2 x + 9 - 1 / 3 x = 11
1 / 6 x = 2
x = 12
12 + y = 27
y = 15