All categories

3 years ago

Solve the system of equations using substitution -3x + 2y = 12 x = 2y - 8

Mathematics

1 answer:

SCORPION-xisa [38]3 years ago

5 0

Answer:

(-2, 3)

Step-by-step explanation:

Given the system of equations:

-3x + 2y = 12

x = 2y - 8

You can 'substitute' the expression '2y - 8' for the value of 'x' in the first equation and solve for 'y':

-3(2y - 8) + 2y = 12

Distribute: -6y + 24 + 2y = 12

Combine like terms: -4y + 24 = 12

Subtract 24 from both sides: -4y + 24 - 24 = 12 - 24 or -4y = -12

Divide both sides by -4: -4y/-4 = -12/-4 or y = 3

Use y = 3 to solve for 'x':

x = 2(3) - 8 or 6 - 8

x = -2

(-2, 3)

You might be interested in

One of Gemma's 5 friends is going to upgrade to a newer device soon. The average cost of their devices will then increase to $66

larisa [96]

Old value of 5 devices = 657
New value of 5 devices = 663

Increment cost of 5 devices
663 - 657
6

Therefore the increment for one device
6 / 5
1.2

8 0

3 years ago

The scale factor on a scale drawing of machine part is 15 1 /8. If the part is 3 7/8 inches long as the drawing, how long is the

Marta_Voda [28]

Answer:

Option D) 58 39/64 inches

Step-by-step explanation:

we know that

The scale drawing is

$15\frac{1}{8}$

convert to an improper fraction

$15\frac{1}{8}=\frac{15*8+1}{8}=\frac{121}{8}$

That means

121 in in the actual, represent 8 in on a scale drawing

To find how long is the actual part for 3 7/8 inches long as the drawing

Apply proportion

First convert to an improper fraction

$3\frac{7}{8}=\frac{3*8+7}{8}=\frac{31}{8}$

$\frac{121}{8}\frac{actual}{drawing} =\frac{x}{(31/8)}\frac{actual}{drawing}\\ \\x=121(31/8)/8\\ \\x=\frac{3,751}{64}\ in$

convert to mixed number

$\frac{3,751}{64}\ in=\frac{3,712}{64} +\frac{39}{64} =58\frac{39}{64}\ in$

7 0

3 years ago

Hi Need help ASAP please

solong [7]

it's 3/2 because it rises three and goes over two. hope this helps !!

7 0

2 years ago

I keep putting in the formula but I keep getting the answer wrong

Advocard [28]

Answer:

314 in² (nearest whole number)

Step-by-step explanation:

Radius of a regular polygon: The distance from the center of the polygon to any vertex. The radius of a hexagon is equal to the length of one side.

Therefore, from inspection of the given diagram:

radius = 11 in ⇒ side length = 11 in

To find the area of a regular polygon, we first need to calculate the apothem. The apothem is the line drawn from the center of the polygon to the midpoint of one of its sides.

$\textsf{Length of apothem (a)}=\dfrac{s}{2 \tan\left(\frac{180^{\circ}}{n}\right)}$

where:

s = length of one side
n = number of sides

Given:

s = 11 in
n = 6

Substitute the given values into the formula and solve for a:

$\implies \textsf{a}=\dfrac{11}{2 \tan\left(\frac{180^{\circ}}{6}\right)}=\dfrac{11\sqrt{3}}{2}$

Area of a Regular Polygon

$\textsf{A}=\dfrac{n\:s\:a}{2}$

where:

n = number of sides
s = length of one side
a = apothem

Given:

n = 6
s = 11

$\textsf{a}=\dfrac{11\sqrt{3}}{2}$

Substitute the given values into the formula and solve for A:

$\implies \sf A=\dfrac{6 \cdot 11 \cdot \dfrac{11\sqrt{3}}{2}}{2}$

$\implies \sf A=314.3672216...$

$\implies \sf A=314\:\:in^2\:\:(nearest\:whole\:number)$

8 0

1 year ago

No links please ASAP!!! Find the slope of the line that passes through (5,3) and (4,2).

hodyreva [135]

Answer:

Step-by-step explanation:

y2 - y1/ x2 - x1

3-2/ 5-4 = 1/1 = 1

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

5 0

2 years ago