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Tanya [424]
3 years ago
8

What is the solution to the system of equations below?

Mathematics
1 answer:
sattari [20]3 years ago
7 0

Answer:

<h2>x = 9, y = -36 → (9, -36)</h2>

Step-by-step explanation:

y=-3x-9\qquad(1)\\\\y=\dfrac{1}{3}x-39\qquad(2)\\\\\text{Substitute (1) to (2)}\\\\-3x-9=\dfrac{1}{3}x-39\qquad\text{multiply both sides by 3}\\\\-9x-27=x-117\qquad\text{add 27 to both sides}\\\\-9x=x-90\qquad\text{subtract}\ x\ \text{from both sides}\\\\-10x=-90\qquad\text{divide both sides by (-10)}\\\\x=9

\text{Put the value of x to (1):}\\\\y=-3(9)-9\\\\y=-27-9\\\\y=-36

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There are many theories and measurement for the speed of light. It is believed that light travels at 299,792 km per second.  In the earlier day philosopher Aristotle believed that light didn't travel but happens instantaneously.  Therefore, for Galileo and his assistant to be only 1km apart, I would have to agree with Aristotle theory of light traveling instantaneously.
8 0
3 years ago
Find the width of the rectangular prism when the surface area is 208 square centimeters.
ozzi
SA=2(lw+wh+lh) This is the formula for finding the surface area of a rectangular prism, where SA is surface area, l is length, w is width, and h is height.

208=2(lw+wh+lh)
104=lw+wh+lh Here, I divided both sides by 2 to get ride of the 2.

Now, I used prime factorization to find out all the prime factors of 104, which are 2, 2, 2, and 13. Since rectangular prisms only have 3 dimensions, I needed to combine two of the prime factors. In this case, I can either combine 2 of the 2s to get 2, 4, and 13 or I can combine 13 with one of the 2s to get 26, 2, and 2.

If my dimensions were 2, 4, and 13...
my surface area would be 172 sq cm.

If my dimensions were 2, 2, and 26...
my surface area would be 208 sq cm.

Hence, the width of the rectangular prism when the surface area is 208 square centimeters can be either 2 or 26.
7 0
3 years ago
Mary’s coffee shop borrowed $9,850 for new chairs and tables. The money was borrowed for 9 months at 9 ¼ % discounted rate, what
Greeley [361]
Let
M---------------> money borrowed -------------> <span>$9,850
r--------------> </span>discounted rate--------> <span>9 ¼=9.25-------> 0.0925
t---------------> time--------> </span><span>9 months=9*30=270 days
D-------------> </span><span>amount of the discount

we know that
D=M*r*t/360=(9850)*(0.0925)*(270/360)=683.34

the answer is $683.34</span>
6 0
3 years ago
One day, 148 copies of the student
Romashka-Z-Leto [24]

Answer:

312 copies

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40 + 60 = 100

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200 + 100 + 12 = 312 copies

6 0
2 years ago
Read 2 more answers
Please help whats a,h,k??
harina [27]

9514 1404 393

Answer:

  a = -2, h = 2, k = 1

Step-by-step explanation:

Compare the expressions. Match one pattern to the other.

  f(x)=-2|x-2|+1\\\\f(x)=\ \,\,a|x-h|+k \qquad\ a=-2,\ h=2,\ k=1

__

The transformations are ...

  Translation by (h, k) = (2, 1). That is, 2 units right and 1 unit up.

  Vertical scaling by "a", which is (i) reflection over the x-axis (because a < 0), and (ii) expansion by a factor of 2.

A table and graph are shown in the attachment.

5 0
2 years ago
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