MATHEMATICS HIGH SCHOOL

Solve for
a. 7a-2b = 5a b

Answers

Answer 1
Answer:

For this case we have the following expression:

From here, we must clear the value of a.

We then have the following steps:

Place the terms that depend on a on the same side of the equation:

Do common factor "a":

Clear the value of "a" by dividing the factor within the parenthesis:

Answer:

The clear expression for "a" is given by:
Answer 2
Answer:

Answer:  The required value of a is (2b)/(7-5b).

Step-by-step explanation:  We are given to solve the following equation for the value of a:

7a-2b=5ab~~~~~~~~~~~~~~~~~~~~~(i)

Since there are two unknowns and only one equation , so the value of a will definitely contain the value of b.

The solution of equation (i) for a is as follows:

7a-2b=5ab\n\n\Rightarrow 7a-5ab=2b\n\n\Rightarrow a(7-5b)=2b\n\n\Rightarrow a=(2b)/(7-5b).

Thus, the required value of a is (2b)/(7-5b).

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John has a total of 13 coins in his pocket. Of the 13 coins, they are all either quarters or dimes. The total value of the coins is $2.50. How many quarters does John have in his pocket?
A polynomial has one root that equals 5-7i. Name one other root of this polynomial
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The 2020 Election is shaping up to be the largest one yet! They estimate that there are 240,000,000 eligible voters in the United States this year. So far, 70,000,000 have voted, and experts estimate that upwards of 150,000,000 people will vote in total this year. What percentage of eligible voters will participate in this year's election?

Is the mean always a more accurate measure of center than the median

Answers

No, because in a set of data with outliers, the median would not be affected by the mean would be. 

The product of two integers is 50. one integer is twice the other. find the integers.

Answers

(1) -5*(-10)=50
(2) 5*10=50
use what they are telling. 

a*b=50 (one integer times the other give you a product of 50. we're randomly calling these integers "a" and "b")

2a=b (one integer is twice the amount of the other. we're randomly selecting "b" to be twice the amount of "a")

plug in what we know 

a*(2a)=50 (we replaced "b" with "2a" because we know from the info they gave us that b=2a)

now solve for "a"

a*2a=50
2a²=50
a²=50/2
a²=25
√a²=√25
a=5

which because 2a=b we know that b=10 

A student raises her grade average from a 75 to a 90. What was the percent of increase in the student’s grade average? Round your answer to the nearest tenth of a percent, if necessary.

Answers

=(new-old)/old *100%
=(90-75)/75 *100%
=20%
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In how many ways can 12 students sit in two rows each row having 6 "srudents"

Answers

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A fruit stand has to decide what to charge for their produce. They need \$5.30$5.30dollar sign, 5, point, 30 for 111 apple and 111 orange. They also need \$7.30$7.30dollar sign, 7, point, 30 for 111 apple and 222 oranges. We put this information into a system of linear equations.

Answers

Answer:

111 apples cost $3.30 and 111 oranges cost $2 (1 apple costs nearly $0.03 and 1 orange costs nearly $0.02)

Step-by-step explanation:

Let the price of 111 apples be $x and the price of 111 oranges be $y.

1. 111 apples and 111 oranges cost $5.30, thus

x+y=5.30

2. 111 apples and 222 oranges cost $7.30, then

x+2y=7.30

Subtract the first equation from the second:

x+2y-x-y=7.30-5.30

y=2

Substitute it into the first equation:

x+2=5.30

x=3.30

111 apples cost $3.30 and 111 oranges cost $2 (1 apple costs nearly $0.03 and 1 orange costs nearly $0.02)

Answer:

3.30 for apple and 2.00 for an orange

Step-by-step explanation:

A hummingbird is flying toward a large tree that has a radius of 6 feet. When it is 33 feet from the center of the tree, its lines of sight form two tangents. What is the measure of the arc on the tree that the hummingbird can see?

Answers

Answer:

Length of the arc = 5.25017 feet

Step-by-step explanation:

The line from the middle of the tree to the tip of the tangent lines is 33 ft and from the circumference of the tree its 27ft. One of the right angle triangles is picked and the angle is determined using SOHCAHTOA

Hence Tan X = 6/27

X = Tan-1 (6/27) = 12.52880770915o

Hence both sum of angles where tangent lines meet = 2 x 12.52880770915o = 25.05761541830o

Angle of the arc inside the circle = 50.115o

Length of the arc = 50.115/360 x (2x22/7 x 6) = 5.25017040025ft
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