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dmitriy555 [2]
3 years ago
15

What is the solution to the system of equations? {x+2y=10y=12x+3

Mathematics
1 answer:
Marianna [84]3 years ago
5 0

The solution to given system of equations are (x,y) = (\frac{4}{25} , \frac{123}{25})

<em><u>Solution:</u></em>

Given that we have to find solution to the system of equations

<em><u>Given equations are:</u></em>

x + 2y = 10  ------ eqn 1

y = 12x + 3 ------ eqn 2

We can solve the above equations by substitution method

<em><u>Substitute eqn 2 in eqn 1</u></em>

x + 2(12x + 3) = 10

x + 24x + 6 = 10

25x = 10 - 6

25x = 4

x = \frac{4}{25}

<em><u>Substitute the above value of x in eqn 2</u></em>

y = 12(\frac{4}{25}) + 3\\\\y = \frac{48}{25} + 3\\\\y = \frac{48+75}{25}\\\\y = \frac{123}{25}

Thus the solution to given system of equations are (x,y) = (\frac{4}{25} , \frac{123}{25})

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How do you solve this? r^2+32=12r
Andre45 [30]

Answer:

r = {-8, -4}

Step-by-step explanation:

Simplifying

r2 = -32 + -12r

Solving

r2 = -32 + -12r

Solving for variable 'r'.

Reorder the terms:

32 + 12r + r2 = -32 + -12r + 32 + 12r

Reorder the terms:

32 + 12r + r2 = -32 + 32 + -12r + 12r

Combine like terms: -32 + 32 = 0

32 + 12r + r2 = 0 + -12r + 12r

32 + 12r + r2 = -12r + 12r

Combine like terms: -12r + 12r = 0

32 + 12r + r2 = 0

Factor a trinomial.

(8 + r)(4 + r) = 0

Subproblem 1

Set the factor '(8 + r)' equal to zero and attempt to solve:

Simplifying

8 + r = 0

Solving

8 + r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-8' to each side of the equation.

8 + -8 + r = 0 + -8

Combine like terms: 8 + -8 = 0

0 + r = 0 + -8

r = 0 + -8

Combine like terms: 0 + -8 = -8

r = -8

Simplifying

r = -8

Subproblem 2

Set the factor '(4 + r)' equal to zero and attempt to solve:

Simplifying

4 + r = 0

Solving

4 + r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-4' to each side of the equation.

4 + -4 + r = 0 + -4

Combine like terms: 4 + -4 = 0

0 + r = 0 + -4

r = 0 + -4

Combine like terms: 0 + -4 = -4

r = -4

Simplifying

r = -4

Solution

r = {-8, -4}

3 0
3 years ago
Can anyone help me with this Midterm Advanced Algebra problem. (DONT ANSWER IF YOUR NOT SURE)
Viktor [21]

Answer:

6

Step-by-step explanation:

divide

4 0
3 years ago
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What is the area of triangle pqr on the grid? a triangle pqr is shown on a grid. the vertex p is on ordered pair 7 and 6, vertex
horsena [70]

P(7,6), Q(1,6), R(4,2)

We have PQ parallel to the x axis. We'll call that the base,

b = 7 - 1 = 6

The altitude is then the y difference h = 6 - 2 = 4

The area is \frac 1 2 bh = \frac 1 2 (6)(4) = 12

Answer: 12 square units


In general we can use the shoelace formula for the area of any polygon given coordinates. We write the points like this:

(7,6), (1,6), (4,2)

(1,6), (4,2), (7,6)

The area is then half the absolute value of the sum of the cross products:

A = \frac 1 2 | 7(6)-6(1) + 1(2)-6(4) + 4(6)-2(7) | = \frac 1 2 |24| = 12


6 0
3 years ago
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Sarah hiked a path that took her from 34 feet below sea level to 52 feet above sea level . What was the change in her elevation?
Ugo [173]

Answer:

86 ft

Step-by-step explanation:

<em>First method: Logical thinking</em>

Think of the position 34 ft below sea level as -34.

The position above sea level is 52.

You need to find the distance between -34 and 52.

You go from 34 ft below sea level, -34 to 0. That is 34 ft.

Then you go from sea level, 0 ft, to 52 ft above sea level. That is 52 ft.

The total is 34 ft + 52 ft = 86 ft

Answer: 86 ft

<em>Second method: Calculate a distance in math</em>

The distance between two points on a number line is the absolute value of the difference of their coordinates. The coordinates are -34 and 52. Subtract the numbers in either order, and take the absolute value of the difference.

|-34 - 52| = |-86| = 86

If you did it in the other order, you'd get the same answer.

|52 - (-34)| = |52 + 34| = |86| = 86

Answer: 86 ft

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2 years ago
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Alexus [3.1K]

Answer:

a)6

b)v^2-u^2/2a

Step-by-step explanation:

a)Given that,

u=12

a= -6

s=9

We know that,

v^2=u^2+2as

or, v^2=(12)^2+2×(-6)×9

or,v^2=144-108

or,v^2=36

or, v=√36

∴v=6

         (Ans)

b)If ,v^2=u^2+2as

then, u^2+2as=v^2

or,2as=v^2-u^2

or, s=v^2-u^2/2a

∴s=v^2-u^2/2a

Hope ya find it helpful.. Thanks a lot...

6 0
3 years ago
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