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Helga [31]
3 years ago
13

How many solutions does the system of linear equations 6a + 3b = 12 and 6a - 3b = 12 have?

Mathematics
1 answer:
Olin [163]3 years ago
3 0

Answer:

One solution

Step-by-step explanation:

Lets solve it for b

3b= -6a+12

3b= 6a-12

Simplifying

b= -2a+4

b= 2a+4

Both have same slope and intercept hence both lines are going to intersect at one point. So the equations are having one solution.

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A city park employee collected 1,850 cents in nickels, dimes, and quarters at the bottom of a wishing well. There were 30 nickel
makvit [3.9K]

Answer: there are 70 dimes and 40 quarters.

Step-by-step explanation:

A dime is 10 cents

A nickel is 5 cents

A quarter is 25 cents

Let x represent the number of dimes at the bottom.

Let y represent the number of quarters at the bottom.

The city park employee collected 1,850 cents in nickels, dimes, and quarters at the bottom of a wishing well. If there were 30 nickels, it means that

10x + 25y + 30 × 5 = 1850

10x + 25y = 1850 - 150

10x + 25y = 1700- - - - - - - - -1

There is a combined total of 110 dimes and quarters. It means that

x + y = 110

Substituting x = 110 - y into equation 1, it becomes

10(110 - y) + 25y = 1700

1100 - 10y + 25y = 1700

1100 + 15y = 1700

15y = 1700 - 1100

15y = 600

y = 600/15

y = 40

x = 110 - y = 110 - 40

x = 70

4 0
3 years ago
2) find an equation of the line theough the given
Olenka [21]

Answer:

y = -2x + 2

Step-by-step explanation:

Given the following data;

Points on the x-axis (x1, x2) = (2, -1)

Points on the y-axis (y1, y2) = (-2, 4)

To find the equation of line in slope intercept form;

First of all, we would determine the slope of the line.

Mathematically, slope is given by the formula;

Slope = \frac{Change \; in \; y \; axis}{Change \; in \; x \; axis}

Slope, m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}}

Substituting into the equation, we have;

Slope, m = \frac {4 - (-2)}{-1 -2}

Slope, m = \frac {4 + 2}{-1 -2}

Slope, m = \frac {6}{-3}

Slope, m = -2

Next, we would use the following formula to find the equation of the line;

y - y1 = m(x - x1)

Substituting into the formula, we have;

y - (-2) = -2(x - 2)

y + 2 = -2x + 4

y = -2x + 4 - 2

y = -2x + 2 = mx + c

8 0
3 years ago
To measure the distance, a an Engineer locates points A, B, C, D, and E as shown. What is the length of DB to the nearest meter?
yarga [219]
I believe the answer should be DB = 10.
To find the missing side, you have to cross multiple the values on each side, and each value should be equal to each other.
3 0
3 years ago
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babunello [35]
I believe the answer is A. because the theory of continental drift and sea-floor spreading causes new rock to form and creates the old rock .. older
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Combine like terms: 80 + 50m + 65 + 40m​
Nuetrik [128]

Answer:

90m+145

Step-by-step explanation:

80 + 50m + 65 + 40m​

90m+145

3 0
3 years ago
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