Answer:
Account C will give George at least a 4% annual yield.
Step-by-step explanation:
This problem can be solved by using simple maths formula given below
Year rate = (1+i)^n-1
where i = compounding rate and n = interval period
Now checking annual rate for each option using above formula
Account A)
Yr = 3.8% ( n= 12 and i= 3.75/12)
Account B)
Yr = 3.9 % ( n= 4 and i= 3.85/4)
Account C)
Yr = 4 % ( n= 365 and i= 3.95/365)
Tomas is at least 7 years older than Larry. If Tomas is 16 years old, how old is Larry
Answer:
Larry is about 9 years old
Step-by-step explanation:
Subtract
plz explain and help me answer this question
Answer:
-637
Step-by-step explanation:
What number divide by -7 gives you 91
if a b and c are three different numbers which of the following equations has exactly one solution?
A:ax+b=ax+b
B:ax=bx+c
C:ax+b=ax+c
Option B is correct.
Step-by-step explanation:
We need to identify which of the following equations has exactly one solution.
We will solve each equation to find the answer
A. [tex]ax+b=ax+b[/tex]
Solving and finding value of x:
[tex]ax+b=ax+b\\ax-ax=b-b\\0=0[/tex]
This equation has infinite number of solutions because both sides are equal to 0
B. [tex]ax=bx+c[/tex]
Solving and finding value of x:
[tex]ax=bx+c\\ax-bx=c\\x(a-b)=c\\x=\frac{c}{a-b}[/tex]
This equation has exactly one solution
C. [tex]ax+b=ax+c[/tex]
[tex]ax+b=ax+c\\ax-ax=c-b\\0=c-b[/tex]
This equation has no solution because both sides are not equal.
So, Option B is correct.
Keywords: Solving Equations
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Does Anyone know the answer to this?
Exact form: x= NEGATIVE 6/7
janet is going to hire a makeup artist for a fashion show and is comparing prices. Austin charges $54 as a booking fee and an additional $80 per hour. Brad charges $69 per hour, plus a booking fee of $65. Depending on the length of the show, the cost could end up being the same for either artist. How long would the show be? What would the cost be?
Step-by-step explanationF(t)= 24 + 36*t
G(t) = 22 + 38*t
They are the same when 24 + 36t = 22 + 38t
Everything to right side: 0 = 22 + 38t - 24 - 36t
0 = 2t - 2
2 = 2t
t=1
THey are the same at one hour.
Longer than 1 hour, the first one is cheaper.
Here's the table to compare them side by side
t 24 + 36 t 22 + 38t
1/2 42 41
1 60 60
2 96 98
3 132 136
The fashion show needs to be 1 hour long for the cost of hiring either makeup artist Austin or Brad to be the same.
To determine how long the fashion show would need to be for the costs of hiring makeup artists Austin and Brad to be the same, we can set up an equation based on their respective fees. Austin charges a booking fee of $54 plus $80 per hour, while Brad charges a $65 booking fee plus $69 per hour.
Let's let 'h' be the number of hours for which the fashion show will run. For Austin, the total cost will be $54 + $80h. For Brad, the cost will be $65 + $69h. To find the number of hours where the costs are equal, we set the two expressions equal to each other:
54 + 80h = 65 + 69h
Now we solve for 'h':
Subtract 69h from both sides: 54 + 11h = 65
Subtract 54 from both sides: 11h = 11
Divide both sides by 11: h = 1
So, the fashion show needs to be 1 hour long for the cost of hiring either makeup artist to be the same, which would be $134.
Janet's paycheck was $248.60. She put 1/4 of her paycheck into a checking account and 1/5 of what was left to buy dinner for her family. How much money does she have remaining from her paycheck? Show Work!
Janet has remaining $ 149.16 in her paycheck
Solution:Given that Janet's paycheck was $248.60
She put 1/4 of her paycheck into a checking account
Therefore amount put into checking account is given as:
[tex]\text {amount put into checking account }=\frac{1}{4} \times 248.60=62.15[/tex]
So she spent $ 62.15 into checking account
Now the remaining paycheck amount left is:
remaining paycheck amount left = 248.60 - 62.15 = 186.45
Therefore remaining paycheck amount left is $ 186.45
Now she spent 1/5 of what was left to buy dinner for her family
[tex]\text { Amount spend on dinner }= \frac{1}{5} \times 186.45 = 37.29[/tex]
So she spent $ 37.29 on dinner
Now the remaining paycheck amount left is:
remaining paycheck amount left = 186.45 - 37.29 = 149.16
Thus Janet has remaining $ 149.16 in her paycheck
26. Higher Order Thinking A mother
manatee, pictured to the right, is three
times as long as her baby manatee.
a. How long is her baby manatee? Write
and solve an equation.
12 feet
b. If a blue whale is 9 times as long as the
manatee shown, how much longer is
a blue whale than the manatee? Write
and solve equations.
Answer:
a) Hence the Baby Manatee is 4 feet long.
b) Hence the Length of blue whale is 108 feet.
Step-by-step explanation:
Given:
Length of Mother manatee = 12 feet.
Now given that:
A mother manatee is three times as long as her baby manatee.
Let the length of baby manatee be 'x'.
So equation can be framed as
[tex]3x=12[/tex]
hence the equation is [tex]3x=12[/tex].
Solving the equation we get;
Dividing both side by 3 using Division property of equality we get;
[tex]\frac{3x}{3}=\frac{12}{3}\\ \\x=4\ feet[/tex]
a) Hence the Baby Manatee is 4 feet long.
Solving for part b we get;
Given:
If a blue whale is 9 times as long as the mother manatee
Hence equation can be framed as;
Length of blue whale is = [tex]9 \times \textrm{Length of Mother manatee}[/tex]
Length of blue whale is = [tex]9\times 12 =108\ feet[/tex]
b) Hence the Length of blue whale is 108 feet.
Determine the product, h (x), of the linear and quadratic factors.
f(x) = (8x – 3)
and
g(x) = (x - 1)2
h(x)=_______
[tex]h(x) =8x^3-19x^2+14x-3[/tex]
Step-by-step explanation:
Given functions are:
[tex]f(x) = 8x-3\\g(x) = (x-1)^2[/tex]
h(x) is the product of g(x) and f(x)
[tex]h(x) = f(x) * g(x)\\= (8x-3)(x-1)^2\\= (8x-3)(x^2-2x+1)\\= 8x(x^2-2x+1)-3(x^2-2x+1)\\= 8x^3-16x^2+8x-3x^2+6x-3[/tex]
Combining like terms
[tex]=8x^3-16x^2-3x^2+8x+6x-3\\=8x^3-19x^2+14x-3[/tex]
Hence,
[tex]h(x) =8x^3-19x^2+14x-3[/tex]
Keywords: Functions, product
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Using only the numbers 1 through 14. Add the numbers to get 28 (using 4 numbers), 14 (using 3 numbers), 30 (using 4 numbers), and 33 (using 3 numbers)
Answer:
10 + 9 + 7 + 2 = 28 (Getting 28 using 4 numbers from 1 to 14)8 + 5 + 1 = 14 (Getting 14 using 3 numbers from 1 to 14)11 + 12 + 4 + 3 = 30 (Getting 30 using 4 numbers from 1 to 14)14 + 13 + 6 = 33 (Getting 33 using 3 numbers from 1 to 14)Step-by-step explanation:
The given numbers:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
Getting the number 28 (using 4 numbers):
If we add the following 4 numbers from 1 to 14, we would get 28.
10 + 9 + 7 + 2 = 28
Getting the number 14 (using 3 numbers):
If we add the following 3 numbers from 1 to 14, we would get 14.
8 + 5 + 1 = 14
Getting the number 30 (using 4 numbers):
If we add the following 4 numbers from 1 to 14, we would get 30.
11 + 12 + 4 + 3 = 30
Getting the number 33 (using 3 numbers):
If we add the following 3 numbers from 1 to 14, we would get 33.
14 + 13 + 6 = 33
Keywords: addition, number
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David made a scale drawing of a mural he is going to paint. He used a scale of 1 cm=4ft. If the actual mural will be 16 feet long, how long is the mural in David’s drawing
Answer:
The mural in David's drawing is 4 cm long.
Step-by-step explanation:
Given:
David made a scale drawing of a mural he is going to paint.
He used a scale of 1 cm=4ft.
If the actual mural will be 16 feet long.
Now, to find how long is the mural in David's drawing.
Let the length of mural in David's drawing be [tex]x\ cm[/tex].
So, as given 1 cm = 4 ft.
1 cm is equivalent to 4 ft.
Thus, [tex]x\ cm[/tex] is equivalent to 16 feet.
Now, to get the length of mural in David's drawing by using the cross multiplication method:
[tex]\frac{1}{4} =\frac{x}{16}[/tex]
By cross multiplication:
[tex]16=4x[/tex]
Dividing both sides by 4 we get:
[tex]4=x[/tex]
[tex]x=4\ cm.[/tex]
Therefore, the mural in David's drawing is 4 cm long.
A block has a volume of 0.07M^3 and a density of 3500 KG/m^3 . What’s the force of gravity acting on the block(and weight) in the air
The force of gravity acting on the block(and weight) in the air is 2403.45 newton
Step-by-step explanation:
Density of an object is defined as the ratio of mass to volume
So we can write it as:
[tex]d = \frac{m}{V}[/tex]
And the force is given by:
[tex]F_g = mg[/tex]
We know that
d = 3500 kg/m^2
V = 0.07 m^3
g = 9.81 ms^-2
So we will calculate the mass first
[tex]d = \frac{m}{V}\\3500 = \frac{m}{0.07}\\m = 3500*0.07\\m = 245\ kg[/tex]
Now,
[tex]F_g = 245 * 9.81\\= 2403.45\ N[/tex]
The force of gravity acting on the block(and weight) in the air is 2403.45 newton
Keywords: Force, gravity
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Help Needed!!!..............................
Answer:
I think D.
Step-by-step explanation
Answer:
Part(B) is the correct answer
Step-by-step explanation:
Given functions are
f(x) = [tex]4x^3+5[/tex] and g(x) = [tex]\sqrt[3]{x-5/4}[/tex]
So both are inverse of each other
Since Definition of inverse function is
If a function f(x) is mapping from x to y , then the inverse function of f(x) maps
y back to x.
Solution
suppose
y = f(x)
y = [tex]4x^3+5[/tex]
in order to find inverse of f(x)
interchange the variables x and y
x = [tex]4y^3+5[/tex]
Now solve for y
Subtract 5 from both sides we get
[tex]4y^3[/tex] = x-5
Divide both sides by 4 we get
[tex]y^3[/tex] = (x-5)/4
[tex]y = \sqrt[3]{x-5/4}[/tex]
so this is the inverse of the f(x) and also from this we see that is [tex]g(x) = \sqrt[3]{x-5/4}[/tex]
This is Answer.
Blueberries cost $4.00 per pound. How many pounds of blueberries can u buy for $1.00
Answer:
Step-by-step explanation:
Blueberries cost $4.00 for 1 pound. The number of blueberries that can be bought $1.00 = (1×1)/4 pounds
= 1/4 pounds
who can solve this exercises pleaseeee i have a exam
Answer:
Step-by-step explanation:
1) Two angles supplementary. So sum of two angles is 180
One angle = x
Other angle = 2x
x + 2x = 180
3x = 180
x = 180/3 = 60
The angles are 60, 120
2)Two angles complementary. So sum of two angles is 90
one angle = x
Other angle = x + 20
x +x +20 = 90
2x + 20 = 90
2x = 90- 20
2x = 70
x = 70/2 = 35
The angles are 35,55
3) one angle =x
Other angle = 3x - 20
x + 3x - 20 = 120
4x = 120 + 20
4x = 140
x = 140/4 = 35
The angles are 35,85
5) x + 4x -20 = 180
5x = 180 + 20
5x = 200
x = 200/5 = 40
x = 40
6) This sum is not clear only half is visible
An artist needs to purchase jars of paint. The table shows Which quantity container is the better buy?
different sizes of paint jars and their prices.
2-oz jar
4-oz jar
Paints
Total Price
4OZ jar
8-oz jar
2-oz jar
$1.50
16-oz jar
4-oz jar
$2.92
8-oz jar
$5.68
16-ozjar
$11.62
Answer:8-oz jar
First, we have to find out what is the unit rate of the 2-oz jar. $1.50÷2 is $.75.
Second, we have to find the unit rate of the 4-oz jar. $2.92÷4=$73.
Third, we have to find the unit rate of the 8-oz jar. $5.68=$.71.
Fourth, we have to find the unit rate of the 16-oz jar. The division for this one may be tricky. From dividing $11.62 by 16, is stopped at the 3rd number I got from dividing. I got $.726. This is not a value of cents and the value can't go in the thousandths place. So, I rounded .726. I got $.73. So $11.62÷16=$.73.
Lastly, you have to compare the amounts.
The lowest amount or better buy, is $.71 or 8-oz jar.
Answer:
8-oz
Step-by-step explanation:
had the same question on the same assignment:)
Does anyone know how to rationalise the denominator ???
Answer:
Multiply the entire expression by the radical denominator. This keeps the expression equal and makes the denominator 3, a whole number.
Step-by-step explanation:
The denominator is irrational because it is a radical number, √3.
To rationalize the denominator, multiply the entire expression by √3. The denominator will become a whole number. This works because you multiply top and bottom by the same value.
[tex]\frac{3 + \sqrt{2} }{\sqrt{3}}[/tex]
[tex]= \frac{(\sqrt{3})(3 + \sqrt{2}) }{(\sqrt{3})(\sqrt{3})}[/tex]
[tex]= \frac{(\sqrt{3})(3 + \sqrt{2}) }{3}[/tex]
√3 X √3 = 3 because:
√3 X √3 = √3²
Squaring a number and also finding its square root are opposites, or reverse operations. They cancel out
You probably need to simplify the rest of the equation too.
[tex]\frac{(\sqrt{3})(3 + \sqrt{2}) }{3}[/tex]
[tex]= \frac{3(\sqrt{3}) + (\sqrt{2})(\sqrt{3})}{3}[/tex] Distribute over brackets
[tex]= \frac{3(\sqrt{3}) + \sqrt{2*3}}{3}[/tex] Simplify
[tex]= \frac{3(\sqrt{3}) + \sqrt{6}}{3}[/tex]
Some people use a more simplified version whether they simplify each term in the numerator:
[tex]\frac{3(\sqrt{3}) + \sqrt{6}}{3}[/tex] (3√3)÷3 = √3
[tex]\sqrt{3} + \frac{\sqrt{6}}{3}[/tex]
A group of friends are sharing 2 & 1/2 lbs of berries. If 5 friends are sharing the berries how many lbs does each friend get ??????
Please help, brainliest!!
Write an expression equivalent to 4(6x + 12), and state the property you used to write it.
Answer:
4(6x) + 4(12)
Distributive property
4(6x + 12) = 4(6x) + 4(12)
To see if the answer is correct, we can solve the equations
24x + 12 = 24x + 12
The expressions are equal, so the equivalent expression provided is correct
Hope this helps :)
Answer:
By applying the Distributive Property, I can generate these equivalent expressions: 24x + 48, 24(x + 2), and 12(2x + 4).
Circumcenter of triangle with coordinates of (1,1) (1,-3) (7,-3)
Answer:
Circumcenter of triangle [tex](4,-1)[/tex]
Step-by-step explanation:
Given coordinates are [tex](1,1)(1,-3)(7,-3)[/tex]
We will draw these points on the graph.
Let [tex]A(1,1)[/tex], [tex]B(1,-3)[/tex] and [tex]C(7,-3)[/tex]
We can see it is a right-angle triangle.
Let [tex]O[/tex] be the midpoint of line [tex]AC[/tex]
So, the coordinate of the point [tex]O[/tex] will be
[tex]A(1,1)\ C(7,-3)\\\\Midpoint\ O\ will\ be\\\\O=(\frac{1+7}{2},\frac{1+(-3)}{2})\\ \\O=(\frac{8}{2},\frac{-2}{2})\\\\O=(4,-1)[/tex]
Also, we know the coordinates of circumcenter of a right angle triangle will be midpoint of its hypotenuse.
So, coordinates of circumcenter is [tex](4,-1)[/tex]
I NEED HELP PLEASE!!
Answer:
t = 51°
Step-by-step explanation:
The total sum of a polygon's exterior angles is always 360°.
Add all of the given angles and equate it to 360°.
40° + 34° + 34° + 46° + (2t - 50°) + (2t - 50°) + 2t = 360° Collect like terms
154° + 2t - 50° + 2t - 50° + 2t = 360° Remove brackets and collect like terms
54° + 6t = 360° Isolate t by doing reverse operations in reverse BEDMAS
6t = 360° - 54° Subtract 54° from both sides
6t = 306° Divide both sides by 6
t = 51° Answer
Please respond to the question below in your own words with proper explanations and use of math vocabulary. Here is a function.
What is the function equation in function notation?
Enter your answer in the box. Show your work. Explain how you found your numbers for the slope and y-intercept.
Answer:
Slope = - 3, y-intercept is 4 and the equation is y = - 3x + 4.
Step-by-step explanation:
Slope of a straight line passing through two given points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is given by the formula
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].
Now, the given graph of the straight line passes through the points (0,4) and (1,1) points.
Hence, the slope of the straight line will be = [tex]\frac{1 - 4}{1 - 0} = - 3[/tex]
Again, the straight line intersects the y-axis at point (0,4) point. hence, its y-intercept is 4.
Therefore, the straight line has equation
y = - 3x + 4 (Answer)
An electronics store makes a profit of $72.00 for every television sold and $90.00 for every computer sold. The manager’s target is to make at least $360.00 a day on sales from televisions and computers. Let x = the number of televisions sold. Let y = the number of computers sold. Which of the following represents three possible solutions to the problem?
A. 72x+90y>360 (5,2),(3,3) and (1,4)
B. 72x+90y<360 (4,0),(2,2) and (1,1)
C. 72x+90y>360 (3,1),(2,2) and (1,0)
D 72x+90y>360 (4,0),(3,3) and (1,4)
Answer:
Option A, C and D is the three possible solution.Step-by-step explanation:
Each Television earns $72 and each Computer earns $90.
The manager’s target is to make at least $360.00 a day.
It is not clarified the exact number of Televisions and Computers.
Hence, as per the given condition, [tex]72x + 90y \geq 360\\8x + 10y \geq 40\\4x + 5y \geq 20[/tex].
Now we just need to check the given options, whether they satisfy the above equation, or not.
Except the option B, each inequality indicates a value greater than 360.
Hence, option B can not be the possible solution.
To meet the profit target of 72x + 90y ≥ 360, the correct points are listed in Option A: (5, 2), (3, 3), and (1, 4). These points meet the required profit condition.
To solve this problem, we need to find the inequality that represents the manager's profit target and identify the solutions that meet this condition. Given:
The profit per television is $72 (x represents the number of televisions sold).The profit per computer is $90 (y represents the number of computers sold).The manager’s goal is to make at least $360. This can be represented by the equation: 72x + 90y ≥ 360.
We need to check which option lists points that satisfy this inequality. Let's test the points:
Option A: 72x + 90y > 360 (5, 2), (3, 3), and (1, 4)
(5, 2): 72(5) + 90(2) = 360 + 180 = 540 (satisfies ≥ 360)(3, 3): 72(3) + 90(3) = 216 + 270 = 486 (satisfies ≥ 360)(1, 4): 72(1) + 90(4) = 72 + 360 = 432 (satisfies ≥ 360)Option B: 72x + 90y < 360 (4, 0), (2, 2), and (1, 1)
(4, 0): 72(4) + 90(0) = 288 (does not satisfy ≥ 360)(2, 2): 72(2) + 90(2) = 144 + 180 = 324 (does not satisfy ≥ 360)(1, 1): 72(1) + 90(1) = 72 + 90 = 162 (does not satisfy ≥ 360)Option C: 72x + 90y > 360 (3, 1), (2, 2), and (1, 0)
(3, 1): 72(3) + 90(1) = 216 + 90 = 306 (does not satisfy ≥ 360)(2, 2): 72(2) + 90(2) = 144 + 180 = 324 (does not satisfy ≥ 360)(1, 0): 72(1) + 90(0) = 72 (does not satisfy ≥ 360)Option D: 72x + 90y > 360 (4, 0), (3, 3), and (1, 4)
(4, 0): 72(4) + 90(0) = 288 (does not satisfy ≥ 360)(3, 3): 72(3) + 90(3) = 216 + 270 = 486 (satisfies ≥ 360)(1, 4): 72(1) + 90(4) = 72 + 360 = 432 (satisfies ≥ 360)Only Option A lists points that all satisfy the inequality 72x + 90y ≥ 360. Therefore, Option A is the correct answer.
giselle is 4 years older than her brother marco. the sum of their ages is 30. Write and solve a system of equations to find their ages
Find x and y
x = ?
y = ?
Answer:
Part 1) [tex]x=1.25\ units[/tex]
Part 2) [tex]y=1.75\ units[/tex]
Step-by-step explanation:
In this problem
the triangles of the figure are similar by AA Similarity Theorem
Remember that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
Applying proportion
Find the value of x
[tex]\frac{5}{5+x}=\frac{8}{10}[/tex]
solve for x
[tex]5(10)=8(5+x)\\50=40+8x\\8x=50-40\\8x=10[/tex]
[tex]x=\frac{10}{8}=1.25\ units[/tex]
Find the value of y
[tex]\frac{7}{7+y}=\frac{8}{10}[/tex]
solve for y
[tex]7(10)=8(7+y)\\70=56+8y\\8y=70-56\\8y=14[/tex]
[tex]y=\frac{14}{8}=1.75\ units[/tex]
Paul and Cindy own different pizza shops. Paul makes 12 pizzas the first day and 6 pizzas each day after that. Cindy makes 16 pizzas the first day and 4 pizzas each day after that. Who will have made more pizzas after 9 days? How many pizzas will that person have made?
A . Paul. He has made 80 pizzas after 9 days.
B . Cindy. She has made 132 pizzas after 9 days.
C. Paul. He has made 60 pizzas after 9 days.
D . Cindy. She has made 48 pizzas after 9 days.
The right answer is Option C.
Step-by-step explanation:
Given,
Pizzas made by Paul on first day = 12
Pizzas made each day after that = 6
Let,
p represent the number of pizzas made after first day.
Total pizzas = 6p + 12
Number of days = 8 because first day 12 pizzas are made
Total pizzas = [tex]6(8)+12=60[/tex]
Pizzas made by Cindy on first day = 16
Pizzas made each day after that = 4
Total pizzas = 4p + 16
Total pizzas = [tex]4(8)+16=48[/tex]
Paul has made more pizzas after 9 days. He has made 60 pizzas.
The right answer is Option C.
Keywords: comparison, addition
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Answer:
C
Step-by-step explanation:
Please answer the question
A system of equations is shown below.
5x + 3y = -6
2x + y = -4.
Which statement about the ordered pair (-6, 8) is true? Show your work.
A. It is the only solution to the system
B. It is not a solution to either equation
C. It is one of many solutions to the system
D. It is a solution to the first but not the second equation
Answer:
Step-by-step explanation:
(-6,8)...x = -6 and y = 8
lets start subbing
5x + 3y = -6
5(-6) + 3(8) = -6
-30 + 24 = -6
-6 = -6
so (-6,8) IS a solution to this equation
2x + y = -4
2(-6) + 8 = -4
-12 + 8 = -4
-4 = -4
so (-6,8) IS a solution to this equation
A. It is the only solution to the system
Given f(x) = 14x + 42, find x when f(x) = 35.
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Form an equation:
14x + 42 = 35
-42
14x = -7
/14
x = -0.5
Have A Nice Day ❤
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Answer:
532
Step-by-step explanation:
14x + 42 = ?
14(35) + 42 = ?
14(35) + 42 =532
During a period of 80 minutes, a music station played 8 minutes of commercials. What is the ratio of music they played to commercials they played?
Answer:
Step-by-step explanation:
80 minutes.......8 minutes played commercials....that means (80 - 8) = 72 minutes played music
so the ratio of music to commercials is : 72/8 which reduces to 9/1...so the ratio is 9:1 <=== ur answer
** pay attention to the wording, because if it would have asked for the ratio of commercials to music, it would have been 8/72....ratio would be 1:9
please help me out will mark brainliest :)
Answer:
AOC
Step-by-step explanation:
Angle COX is formed at vertex O with two rays OC and OX.
Angle AOX is formed at vertex O with two rays OA and OX.
Ray OA lies between rays OC and OX.
All three rays have the common vertex O.
The angle addition postulate describes that putting two angles side by side with their vertices together creates a new angle whose measure equals the sum of the measures of the two original angles.
So,
[tex]m\angle AOX+m\angle AOC=m\angle COX[/tex]