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Bad White [126]
3 years ago
13

Make g the Subject of the formula 3e + 4g = 7 + 9eg

Mathematics
1 answer:
Keith_Richards [23]3 years ago
3 0

g can be written as \frac{7-3e}{4-9e}

<u>Explanation:</u>

Given:

3e + 4g = 7 + 9eg

We have to make g as the subject.

So,

Shifting g variable to left hand side and the rest to the right hand side.

4g - 9eg = 7 - 3e

g( 4 - 9e ) = 7 - 3e

g = \frac{7-3e}{4 - 9e}

Therefore, g can be written as \frac{7-3e}{4-9e}

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What is the slope of the line that passes through (3,-7) and (-1,1)
Anna [14]

Answer:

-2

Step-by-step explanation:

slope formula is (y2-y1)/(x2-x1)

1 - -7 / -1 - 3

8 / -4

-2

5 0
2 years ago
I need the answers plz
garik1379 [7]

Answer:

These problems are an example of equations with two unknowns. The way these equations are solved is that we write these equations one under the another.

If both equations have, such is the case here, same parts, we can simply cancel the same parts out and subtract the rest of equatuons. That way, we are left with only one unknown (the other one was eliminated), which makes it easy to solve.

After we have found the value of an unknown, we just plug it back into any of the starting equations and solve for the second unknown.

2. Adult ticket costs $12 and child ticket costs $14.

3. Adult ticket costs $10 and child ticket costs $5.

4. One daylily costs $9 and one bush of ornamental grass costs $2.

5. A van can carry 15 and a bus can carry 56 students.

Step-by-step explanation:

2. If we mark the price of one adult ticket with x and the price of one child ticket with y, we get that:

- first day: 7x + 12y = $252

- second day: 7x + 10y = $224

Now, we can make a system:

7x + 12y = 252

7x + 10y = 224

We can now subtract these two equations and 7x will cancel out, so we get:

12y - 10y = 252 - 224

2y = 28

y = 14

Now, we can plug the value of y into any of the two equations:

7x + 10y = 224

7x + 140 = 224

7x = 84

x = 12

3. Similarly, if we mark the price of one adult ticket with x and the price of one child tickey with y, we'll get a system:

x + 12y = 70

x + 9y = 55

Again, if we subtract these two, x will cancel out, so we have:

12y - 9y = 70 - 55

3y = 15

y = 5

Now, we plug the value of y into any of the two equations, and we get:

x + 9y = 55

x + 45 = 55

x = 10

4. Using the same principle, we can mark the price of one daylily with x and the price of one bunch of ornamental grass with y, we'll get a system:

12x + 11y = 130

12x + 12y = 132

Again, we subtract so that 12x cancel out and we get:

11y - 12y = 130 - 132

-y = -2

If we get minuses on both sides, we can simply multiply both sides with -1 and we get:

y = 2

Again, we plug y:

12x + 12y = 132

12x + 24 = 132

12x = 108

x = 9

5. If we mark number of students in a van with x and the number of students in a bus with y, we get a system:

2x + 12y = 702

2x + y = 86

As you've probably already noticed the pattern, we subtract equations and cancel 2x out to get:

12y - y = 702 - 86

11y = 616

y = 56

Once again, we plug the value of y into any equation:

2x + y = 86

2x + 56 = 86

2x = 30

x = 15

4 0
3 years ago
Share $420 in the ratio of 2:5:7
arsen [322]

Answer:

If you split it up it would be 60, 150, 210

4 0
2 years ago
Given: angle 2 and angle 3 form a linear pair, angle 1 and angle 3 are vertical angles, and m angle 1, m angle 4, and m angle 5
Volgvan

Answer:

Step-by-step explanation:

<1 + <2 = 180 degrees (straight angle)

<3 + <5 + <4 = 180 degrees (straight angle)

<1 = <3 (vertical angles)

<1+<2 = <3+<4+<5 (straight angles)

<2 = (<3-<1)+<4+<5 (<3 - <1 = 0)

<2 = <4 + <5

5 0
3 years ago
A real estate agent is showing homes to a prospective buyer. There are ten homes in the desired price range listed in the area.
Citrus2011 [14]

Answer:

0.48% probability that all four are new

Step-by-step explanation:

The homes are chosen "without replacement", which means that after a home is visited, it is not elegible to be visited again. So we use the hypergeometric distribution to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

In this question:

Total of 10 homes, so N = 10.

We want 4 new, so x = 4.

In total, there are 4 new, so k = 4.

Sample of four homes, so n = 4.

Then

P(X = 4) = h(4,10,4,4) = \frac{C_{4,4}*C_{6,0}}{C_{10,4}} = 0.0048

0.48% probability that all four are new

6 0
3 years ago
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