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Solnce55 [7]
3 years ago
14

Find the equation of the line that passes through the point of intersection of x + 2y = 9 and 4x -2y = -4 and the point of inter

section of intersection of the lines 3x - 4y = 14 and 3x + 7y = -8.

Mathematics
1 answer:
Rudik [331]3 years ago
4 0

Answer:

y=-6x+10

Step-by-step explanation:

The point of intersection of

x+2y=9...eqn1


and


4x-2y=-4...eqn2

is the solution of the two equations.


We add equation (1) and equation(2) to get,

x+4x+2y-2y=9+-4


\Rightarrow 5x=5


\Rightarrow x=1

We put x=1 into equation (1) to get,

1+2y=9

\Rightarrow 2y=9-1

\Rightarrow 2y=8

\Rightarrow y=4


Therefore the line passes through the point, (1,4).


The line also passes through the point of intersection of

3x-4y=14...eqn(3)

and

3x+7y=-8...eqn(4)

We subtract equation (3) from equation (4) to obtain,

3x-3x+7y--4y=-8-14


\Rightarrow 11y=-22

\Rightarrow y=-2


We substitute this value into equation (4) to get,

3x+7(-2)=-8


3x-14=-8


3x=-8+14


3x=6

x=2

The line also passes through

(2,-2)



The slope of the line is

slope=\frac{4--2}{1-2} =\frac{6}{-1}=-6


The equation of the line is

y+2=-6(x-2)

y+2=-6x+12


y=-6x+10 is the required equation





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Explanation:

First, you need to add all of the numbers to find the total budget. The total budget is <u>$1,116.</u> Then, to find the percentages, you need to divide each sections' money by the budget. For example, for 'contributions', you will do $175.76/$1,116 and get 0.157. But, this is a decimal. To make it into a percentage, you move the decimal point 2 spaces to the right. .157 = 15.7% So, for the 'contributions' section, the answer is 15.7%. Another example. For the 'housing' section,  the amount was $350.84. Divide that by $1,116.

\frac{350.84}{1,116}=0.314

Move the decimal point <em>2 spaces to the right</em> -- 31.4%

<u>I hope you understand how I got these answers</u>

<em>Other Answers:</em>

Transportation: 4.5%

Clothing: 2.7%

Medical Expenses: 3.1%

Food: 17.9%

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Miscellaneous: 15.1%

8 0
3 years ago
How many cylindrical can of bottles 12 cm high and with 6 cm diameter could be filled from a tank containing 125 liters of deter
Orlov [11]

Answer:

368 cans.

Step-by-step explanation:

Volume of 1 can = π r^2 h.

Here h (height) = 12 and r (radius) = 1/2 * 6 = 3 cm.

So V =  π * 3^2 * 12

= 108π cm^3.

The tank hold 125 liters

=  125,000 cm^3, so:

Number of cans that could be filled = 125000/ 108 π

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4 0
3 years ago
Read 2 more answers
Sarah bought 18 boxes of 65 pens at $12 a box. She sold 378 of them at 3 for $1.00 and the rest at 4 for $1.00. Find her total p
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Answer:

$108

Step-by-step explanation:

1 box = $12

18 boxes = 12×18 = $216

Total = 18×65 = 1170 pens

Cost price, Cp = $216

3 = $1

378 = 378/3 = $126

1170-378= 792 pens remaining

4 = $1

792 = 792/4 = $198

Total selling price, sp = 126+198 = $324

Profit = Sp - Cp = 324 - 216 = $108

8 0
2 years ago
Find how many six-digit numbers can be formed from the digits 2, 3, 4, 5, 6 and 7 (with repetitions), if:
Goshia [24]

Answer:

case 1 = 2592

case 2 =  729

case 1 + case 2 =  2916

(this is not a direct adition, because case 1 and case 2 have some shared elements)

Step-by-step explanation:

Case 1)

6 digits numbers that can be divided by 25.

For the first four positions, we can use any of the 6 given numbers.

For the last two positions, we have that the only numbers that can be divided by 25 are numbers that end in 25, 50, 75 or 100.

The only two that we can create with the numbers given are 25 and 75.

So for the fifth position we have 2 options, 2 or 7,

and for the last position we have only one option, 5.

Then the total number of combinations is:

C = 6*6*6*6*2*1 = 2592

case 2)

The even numbers are 2,4 and 6

the odd numbers are 3, 5 and 7.

For the even positions we can only use odd numbers, we have 3 even positions and 3 odd numbers, so the combinations are:

3*3*3

For the odd positions we can only use even numbers, we have 3 even numbers, so the number of combinations is:

3*3*3

we can put those two togheter and get that the total number of combinations is:

C = 3*3*3*3*3*3 = 3^6 = 729

If we want to calculate the combinations togheter, we need to discard the cases where we use 2 in the fourth position and 5 in the sixt position (because those numbers are already counted in case 1) so we have 2 numbers for the fifth position and 2 numbers for the sixt position

Then the number of combinations is

C = 3*3*3*3*2*2 = 324

Case 1 + case 2 = 324 + 2592 = 2916

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The radius is 9 inches, and the diameter is 18 inches.

The volume of the box is 18 in x 18 in x 18 in or 5832 in.³.
4 0
3 years ago
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