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Crank
3 years ago
15

Directions - solve the liner system. enter your answer as an ordered pair. 2x + 3y = 31 y = x + 7

Mathematics
1 answer:
Leya [2.2K]3 years ago
8 0

(1) 2x + 3y = 31 y

(2) 2x + 3y = x + 7

(3) 31y = x + 7

(3) x = 31y - 7

(2) 2(31y - 7) + 3y = 31y - 7 + 7 ; 62y - 14 + 3y = 31y ; 34y = 14 ; y = 14/34 ; y = 7/17

(3) x = 31y - 7 ; x = 31*(7/17) - 7 ; x = (217 - 119)/17 = 98/17

x = 98/17 ≈ 5.76

y = 7/17 ≈ 0.41

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Please help thank you!!!
rusak2 [61]

Answer:

K' (-1,10)

L'(0,4)

M'(2,2)

Step-by-step explanation:

To use the mapping rule, substitute x and y with the original values

The coordinates of K are x=-4, and y=5.

Using the mapping rule, x of K' = -4+3 = -1

Using the mapping rule y of K' = 2x5=10

So K' is at the coordinate (-1,10)

The coordinates of L are x =-3, and y =2.

Using the mapping rule, x of L' = -3+3=0

Using the mapping rule y of L' = 2x2=4

So L' is at the coordinate (0,4)

The coorindates of M are x=-1 and y=1

Using the mapping rule, x of M' = -1+3=2

Using the mapping rule, y of M' = 2x1 = 2

So M' is at the coordinate (2,2).

8 0
3 years ago
Any number that is divisible by 4 is also divisible by 8. Find a counterexample to show that the conjecture is false. 12 40 26 2
mariarad [96]

12 as 12 is divisible by 4 but not divisible by 8


5 0
3 years ago
Please help! Here's the question. I really need it.
Korvikt [17]
Let’s first cut/separate this figure into two shapes: rectangle and a triangle

The area of the rectangle: 9 • 2 = 18
The area of the triangle: 1/2 • 8 • 4 = 16
The total area: 18 + 16 = 34
He needs 34 m square of grass
5 0
3 years ago
The Loft Theater has a center seating section with 3c + 8 rows and 4c-1 seats in each row. Write an expression for the total num
yulyashka [42]

If there are n rows

And if each row has m seats.

Then the total number of seats shall be n × m.

Here

Number of rows = (c+8)

And number of seats in each row = (4c-1)

Using the concept

Total number of seats

= (c+8)(4c-1)

FOILing or Distributing we get

= c(4c) + c (-1) + 8(4c) +8 (-1)

= 4c² - c + 32 c -8

Combining like terms

=4c² +31c - 8

The expression for total number of seats = 4c² + 31c -8

4 0
3 years ago
Solve the inequality. Enter any fractions as reduced improper fractions. 4x ≤ -2/5(6x + 6) The solution is _____​
Deffense [45]

Answer:

x≤ -3/8

Step-by-step explanation:

4x\le \:-\frac{2}{5}\left(6x+6\right)\\

Expand ;

\mathrm{Expand\:}-\frac{2}{5}\left(6x+6\right):\quad -\frac{12}{5}x-\frac{12}{5}

4x\le \:-\frac{12}{5}x-\frac{12}{5}\\\\\mathrm{Add\:}\frac{12}{5}x\mathrm{\:to\:both\:sides}\\\\4x+\frac{12}{5}x\le \:-\frac{12}{5}x-\frac{12}{5}+\frac{12}{5}x

Simplify

\frac{32}{5}x\le \:-\frac{12}{5}\\\\Multiply \:both\:sides\:by\:5\\5\times\frac{32}{5}x\le \:5\left(-\frac{12}{5}\right)\\\\Simplify\\32x\le \:-12\\\\Divide \:both\:sides\:by\:32\\\frac{32x}{32}\le \frac{-12}{32}\\\\Simplify\\x\le \:-\frac{3}{8}

6 0
4 years ago
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