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SpyIntel [72]
1 year ago
11

The sum of three times a number and a second number is five. two times the first number added to the second number is 10. find t

he two numbers.
Mathematics
1 answer:
Aneli [31]1 year ago
7 0

Answer:

-5 , 20

Step-by-step explanation:

<h3>Forming system of linear equations and solving:</h3>

Let x and y be the first and second number respectively.

3x + y = 5 -------------(i)

       y = 5 - 3x

2x + y = 10 -------------(ii)

Method used for solving: substitution method.

Substitute y = 5 - 3x in equation (ii)

   2x + 5 - 3x = 10

   2x - 3x + 5 = 10

Combine like terms,

        -x + 5  = 10

Subtract 5 from both sides,

               -x = 10 - 5

                -x = 5

Multiply the entire equation by (-1)

                \sf \boxed{\bf x = -5}

y = 5 - 3*(-5)

 = 5 + 15

\sf \boxed{\bf y =20}

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Jessica has 84.5 of fabric to make curtain
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Answer:

10.8\ yd

Step-by-step explanation:

<u><em>The complete question is</em></u>

Jessica has 84.5 yards of fabric to make curtains. She makes 6 identical curtains and has 19.7 of fabric remaining. How many yards of fabric does Jessica use per curtain?

Let

x-------> amount of yards of fabric that Jessica used per curtain

we know that

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The linear equation that represent this situation is

Solve for x

6x=84.5-19.7\\6x=64.8\\x=10.8\ yd

3 0
2 years ago
F divides HJ in the ratio 3:1. If H = (-11,7) and J = (5,3), what are the<br> coordinates of F?
Hatshy [7]

Answer:

The coordinates of HF are (1, 4)

Step-by-step explanation:

The parameters of the line are;

The coordinate of the end points are H = (-11, 7), and J = (5, 3)

The ratio by which the point F divides the line = 3:1

The segments in the line are HF, and FJ

Therefore;

The fraction of the length of HJ that is represented by HF = 3/(3 + 1) × HJ = 3/4 × HJ

HF = 3/4 × HJ

Which gives the coordinates of the point F as follows;

Coordinate of F = (-11 +(5 - (-11))×3/4, 7 + (3 - 7)×3/4) =  (1, 4)

The coordinates of F are (1, 4)

We check the length of HF, from the equation for the length to of a line to get;

l = \sqrt{\left (y_{2}-y_{1}  \right )^{2}+\left (x_{2}-x_{1}  \right )^{2}}

l_{HF} = \sqrt{\left (4-7  \right )^{2}+\left (1-(-11)  \right )^{2}} = \sqrt{\left (-3  \right )^{2}+\left (12  \right )^{2}} = 3\cdot \sqrt{17}

Similarly, we check the length of HJ, to get;

l_{HF} = \sqrt{\left (3-7  \right )^{2}+\left (5-(-11)  \right )^{2}} = \sqrt{\left (-4  \right )^{2}+\left (16  \right )^{2}} = 4\cdot \sqrt{17}

The length of HF = 3·√(17)

The length of HJ = 4·√(17)

Therefore, from HF = 3/4× HJ, we have;

HF = 3/4 × 4·√(17) = 3·√(17)

Therefore, the coordinates of HF are (1, 4)

7 0
3 years ago
15/8 + (-3 4/7) plz help me.
givi [52]
I think it’s -1.69642857143
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3 years ago
Ranger says the expression is not in its simplest form. He thinks the two terms need to be combined. Is Ranger right that 8x − 2
ladessa [460]

Answer:

4(2x - 5)

Step-by-step explanation:

Rewrite "20" as 4 * 5

Rewrite "8" as 4 * 2

=4 * 2x - 4 * 5

Factor out common term "4"

=4(2x - 5) <------ Your answer.

5 0
2 years ago
Read 2 more answers
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