Answer:
8x-6
Step-by-step explanation:
2.1 units and 8.7 units
2.3 units and 7.8 units
2.6 units and 6.6 units
The Law of Sines tells you
... sin(C)/c = sin(A)/a
... sin(C) = c·sin(A)/a . . . . multiply by c
... C = arcsin(c·sin(A)/a) . . take the inverse sine
Then
... sin(B)/b = sin(A)/a . . . . law of sines again
... b = a·sin(B)/sin(A) . . . . multiply by a·b/sin(A)
where B = 180° - A - C = 160° - C . . . . . . sum of angles in a triangle is 180°
Filling in the given values, we get
... C = arcsin(5.4·sin(20°)/3.3) ≈ 34.033° or 145.967°
Then
... B = 125.967° or 14.033°
and
... b = 3.3/sin(20°)·sin(125.967°) or 3.3/sin(20°)·sin(14.033°)
... b = 7.8 or 2.3 . . . units
The appropriate choice is
... 2.3 units and 7.8 units
Answer:
C)2.3 units and 7.8 units
Step-by-step explanation:
Part A Write an expression with two terms for the number of baskets that Kari makes. Explain how you found your expression.
Part B Write an expression with three terms for the number of baskets that Kari and Julie make in all. Explain how you found your expression.
Answer:
X= 2y - 3
Kari makes X tryouts. She also makes 3 less than twice as many as Julie which would be X= 2y - 3
Julie makes y tryouts and twice would be 2y.
Step-by-step explanation: hope this helps!!! :)
Answer:
X= 2y - 3
Kari makes X tryouts. She also makes 3 less than twice as many as Julie which would be X= 2y - 3
Julie makes y tryouts and twice would be 2y.
Step-by-step explanation:
The each bottle of juice cost $ 7.55 before tax .
Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
Grayson bought bag of popcorn (P)= $3.50
Five pack of juice bottles.
The total cost before tax was $11.05.
According to given question we have
Let the cost of the juice bottles be x.
P+ x= $11.05.
$3.50+x=$11.05
x=$11.05-$3.50
x=$ 7.55
Therefore, the each bottle of juice cost $ 7.55 before tax .
Learn more details about arithmetic here:
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The question is about finding the cost of each bottle of juice. The cost of the juices was found by subtracting the cost of popcorn from the total amount. Each bottle of juice cost $1.51.
To solve this problem, we need to first determine how much was spent on the juice. We know that Grayson spent $11.05 in total and that the popcorn cost $3.50. By subtracting the cost of the popcorn from the total spent, we will find out how much Grayson spent on the juice.
Step 1: Subtract the cost of the popcorn from the total amount spent: $11.05 - $3.50 = $7.55. This is how much was spent on the juice bottles.
Step 2: We know that there are five juice bottles in the pack. To find out the cost of each juice bottle (J), we divide the total cost of the juice by the number of bottles in the pack: $7.55 / 5 = $1.51.
So, the equation which determines J, the cost of each juice bottle, is $3.50 + 5J = $11.05. Solving this equation gives J = $1.51.
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Jon decides to renew and will now pay $11.72 monthly per thousand on his loan. You can ignore the small amount of principal that has been paid.
What is the amount of the old monthly payment? $ ____
What is the amount of the new monthly payment? $ ____
What is the percent of increase in his new monthly payment? ____ %
Remark
The first fact you need to know is that the bank has taken money from you and nothing has been reduced from the principle. Crafty people those bankers; you are going to pay off the interest before touching the principle. They're like you to refinance for the rest of your life at the rates you currently have.
Point. You started out with a 50k debt. You still have that same debt.
Solution
Givens
number of thousands (n) = 50000/1000 = 50
Amount paid per thousand (A) = 10.67
Total monthly payments (T) = ?
Part A
T = n * A
T = 50 * 10.67
T = 533.50 is the old monthly payment
Part B
T = n * A
T = 50 * 11.72
T = 586.00 new monthly payment.
Part C
This is a notes question. What have you been told in your notes on this question. You can find the raw amount just by subtracting 586 - 533.50 = 52.50
But how do you find the % increase. Which one of the payments do you use as your base?
In point of fact, you should be using the first number 533.5
What % will you get when you multiply that by 533.5 and get 52.50?
You are not trying to find 586. You are trying to find the number that you add to 533.5 to get to 586
The answer is (52.50 / 533.5)*100% = 9.84% is the % increase.
You are told to ignore the amount of principal paid, so you are apparently to assume the loan amount was for $50 thousand.
a) The old monthly payment was $10.67×50 = $533.50
b) The new monthly payment is $11.72×50 = $586.00
c) The increase in monthly payment is figured in the usual way:
... (new/old -1)×100% = (1.0984-1)×100% = 9.84%
_____
In reality, about 3% of the loan will have been paid at the end of 2 years. Thus, the original loan amount may have been near $51,500. This problem is telling you to ignore the difference.
Prove: Z2 = Z4
Step-by-step explanation:
we know about vertical angels that are equal
so <2=<4
(in fact they are congruent angles)
we found those only from the definition of vertical angles.
In geometry, vertical angles (like Z2 and Z4) formed by two intersecting lines are always equal. Therefore, if Z2 and Z4 are defined as vertical angles, they are equal in measurement. This is a fundamental concept of geometry.
In the field of Geometry, vertical angles are always congruent, which means they have the same measure in degrees. When you have two intersecting lines, they create vertical angles that are across from one another. Therefore, if Z2 and Z4 are defined as vertical angles, they must be equal in measurement.
Here is an explicit step-by-step explanation:
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