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krok68 [10]
3 years ago
10

What is a. 11/12 - 7/12 b. 1/2 + 1/8 + 3/4 c. 3/4 - 1/6 ( all in simplified mode )

Mathematics
1 answer:
morpeh [17]3 years ago
5 0
A. when subtracting fractions with the same denominator, simply subtract the numerators and keep that number over the original denominator.  Thus 11/12-7/12 becomes 4/12.  But, this answer is not reduced because 4 is a factor of both the numerator and the denominator.  Thus, divide  4 by 4 and 12 by 4 to get the new numerator and denominator.  Your final fraction is 1/3.

b.  In this expression, the fractions do not all have the same denominator, so you cannot subtract them yet.  Your largest denominator is 8 but not all the other denominators are factors of 8.  So to make a common denominator with all the fractions, you need to find a number that all the denominators are factors of.  One example in this case is 24.  Each of these fractions must then be expressed in terms of this common denominator.  To do this, you need to find what can be multiplied by the original denominator to make 24.  In other words, divide 24 by the original denominator and multiply that answer by the original numerator.  In the case of 1/2, 24/2 is 12 and 12 x 1 is 12.  Thus, the new fraction is 12/24.  The second fraction is also done this way: 24/8=3 and 3x1 is 3 so the new fraction is 324.  The third fraction should be handled the same way: 24/4 is 6 and 6x3 is 18 so the new fraction is 18/24.  Finally, in 1/6, 24/6 is 4 and 4x1 is 4 so the new fraction is 4/24.  Then, like the previous problem, when you perform 12/24 + 3/24 + 18/24-4/24= 29/24.  Since 29 is larger than 24, this should be reduced.  Do this by subtracting the denominator from the numerator and keep the remaining fraction.  The final answer is 1 and 5/24.
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Anyone know this ? picture shown please help
valina [46]

They're just after some straightforward algebra starting from the Law of Cosine.  We don't have to evaluate any trig functions or anything like that.

c^2 = a^2 + b^2 - 2ab \cos C

We move the c² and the cosine term to their other sides,

2ab \cos C = a^2 + b^2- c^2

That's it for the algebra.  

a,b and c are the side lengths opposite A,B and C respectively.  So a=4, b=5, c=2.

We substitute:

2ab \cos C = 4^2 + 5^2- 2^2 = 16 + 25 - 4 = 37

Answer: A. 37

5 0
3 years ago
Activity Question 1 When designing a truss, a truss builder might know the base angle measurement and the length of the tie beam
laiz [17]

Answer:

36.87°  

Step-by-step explanation:

Assume the triangles are as in the diagram below.

∠BAC includes ∠DAE.

The measure of ∠BAE is 36.87°.

7 0
3 years ago
Phyllis invested 51000 dollars, a portion earning a simple interest rate of 4 percent per year and the rest earning a rate of 7
Liono4ka [1.6K]

Answer:

Phyllis invested $11,000 at a simple interest rate of 7 percent per year and $40,000 at a simple interest rate of 4 percent per year.

Step-by-step explanation:

From the information provided, you can write the following equations:

x+y=51000 (1)

0.04x+0.07y=2370 (2), where

x is the portion earning a simple interest rate of 4 percent per year

y is the portion earning a simple interest rate of 7 percent per year

First, you can isolate x in (1):

x=51000-y (3)

Now, you can replace (3) in (2) and solve for y:

0.04(51000-y)+0.07y=2370

2040-0.04y+0.07y=2370

0.03y=330

y=330/0.03

y=11000

Then, you can replace the value of y in (3) to find the value of x:

x=51000-11000

x=40000

According to this, the answer is that Phyllis invested $11,000 at a simple interest rate of 7 percent per year and $40,000 at a simple interest rate of 4 percent per year.

3 0
2 years ago
Find the gradient of the line segment between the points (-3,3) and (2,5).
BlackZzzverrR [31]

Answer:

2/5

Step-by-step explanation:

5-3/2-(-3)=2/5

7 0
3 years ago
PLEASE HEP ASAP!!!!!!! 30 POINTS!!!!!
anzhelika [568]

Answer:

a) 42°F < x < 176°F

b) The inequality graph is attached.

c) No, This is because at 20° F benzene would not be in liquid form but in solid form.

Step-by-step explanation:

According to the Question,

a) For the benzene to remain in liquid form, the temperature of benzene must be less than the boiling point and greater than the boiling point. Let x be the temperature of benzene, For benzene to remain as liquid, its temperature must be between:

42°F < x < 176°F

b) The inequality graph is attached. The graph shows that the temperature of benzene must be between 42°F and 176°F so that it would be a liquid. The Closed circles represent that it is greater than 2.

c) No, This is because at 20° F benzene would not be in liquid form but in solid form. Because the temperature cannot go below 42 before it freezes, she would not have been able to conduct her research .

5 0
2 years ago
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