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Advocard [28]
3 years ago
12

Solve the system of equations using substitution. y = x + 6 y = –2x – 3

Mathematics
2 answers:
telo118 [61]3 years ago
5 0

Answer:

x = -3

y= 3

Step-by-step explanation:

y =  x + 6 -----------------------(I)

y = -2x - 3 ---------------------(II)

Substitute y =x +6 in equation (II)

x + 6  = -2x - 3

Add 2x to both sides

x + 2x +6 = -3

Combine like terms

3x + 6 = - 3

Subtract 6 from both sides

3x = - 3 - 6

3x = -9

Divide both sides by 3

x = -9/3

x = -3

Plug in s = -3 in equation (I)

y = -3 + 6

y = 3

Assoli18 [71]3 years ago
4 0
Hope this helps! feel free to clarify

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Coach Shaw is buying baseball equipment for his team. He gets a reduced rate if he buys 8 baseballs for every 3 batting helmets.
Natalija [7]

Answer:

Helmets-12

Baseballs-32

Step-by-step explanation:

Given the tax rate as 6% and the reduced prices as $2.25/baseball and $22.50/helmet and that the budget is $400:

The new prices are reduced price plus tax:

Baseball \ Price =2.25\times (1.06\%)=2.39\\\\Helmet \ Price= 22.50\times (1.06\%)=23.85

Let x be the number of groups of 8 baseballs as well as the number of groups of 3 helmets,therefore:

8x(2.39)+3x(23.85)=400\\\\19.12x+71.55x=400\\\\x=4.4116\\\\x\approx 4

Substitute for x=4 to find the highest number of baseballs and helmets:

Helmets=4x3=12

Baseball=4x8=32

#Price cost will be 12x23.85+32x2.39=362.68 (balance=37.32)

Hence, Shaw can buy 12 helmets and 32 baseballs and still remain with $37.32

3 0
3 years ago
What is the equation of the line parallel to 3x + 5y = 11 that passes through the point (15, 4)?
soldier1979 [14.2K]

Answer:

The answer is

<h2>y =  -  \frac{3}{5} x + 13</h2>

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the parallel line we must first find the slope of the original line

The original line is 3x + 5y = 11

We must first write the equation in the general equation above

So we have

5y = - 3x + 11

Divide both sides by 5

<h3>y =  -  \frac{ 3}{5} x +  \frac{11}{5}</h3>

Comparing with the general equation above

Slope = - 3/5

Since the lines are parallel their slope are also the same

Slope of parallel line = - 3/5

So the equation of the line using point

(15, 4) and slope - 3/5 is

<h3>y - 4 =  -  \frac{3}{5} (x - 15) \\y - 4 =  -  \frac{3}{5} x + 9 \\ y =  -  \frac{3}{5} x + 9 + 4</h3>

We have the final answer as

<h3>y =  -  \frac{3}{5} x + 13</h3>

Hope this helps you

8 0
3 years ago
PLEASE HELP ILL GIVE BRAINLIEST
natka813 [3]

Answer:

It is a right triangle.

Step-by-step explanation:

Right triangles will always have a right angle equalling 90 degrees. The other two angles will always be 45 degrees.

5 0
3 years ago
Read 2 more answers
Given angle YMC = 170 degrees, find the measure of angle AMC.
makkiz [27]

Answer:

i think 10 because in triangle there is 180 and 180-170 = 10

5 0
2 years ago
Read 2 more answers
A ball is launched straight up in the air from a height of 6 feet. Its velocity (feet/second) t seconds after launch is given by
german

Step-by-step explanation:

A ball is launched straight up in the air from a height of 6 feet. The velocity as a function of time t is given by :

f(t) = -32 t+285

Height of the ball is :

h(t)=\int\limits{f(t){\cdot} dt}\\\\h(t)=\int\limits{(-32t+285){\cdot} dt}\\\\h(t)=-16t^2+285t+C

C is constant. Here the ball is launched from a height of 6 feet. So,

h(t)=-16t^2+285t+6

At t = 2 s, h(t)=-16(2)^2+285(2)+6=512\ m

At t = 9 s, h(t)=-16(9)^2+285(9)+6=1275\ m

Between 2 s and 9 s, the ball's height changed is : 1275 - 512 = 763 m.

6 0
4 years ago
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