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nikdorinn [45]
3 years ago
6

A system of linear equations includes the line that is created by the equation y = x+ 3, graphed below, and the line through the

points (3, 1) and (4, 3).
On a coordinate plane, a line goes through (0, 3) and (2, 5).

What is the solution to the system of equations?

(–1, 2)

(1, 3)

(8, 11)

(9, 12)

i really dont get this at all can someone help me and explain

Mathematics
1 answer:
ad-work [718]3 years ago
7 0

Answer:

(8,11)

Step-by-step explanation:

1st line

y = x+ 3

We need to find the equation of the other line

We have two points (3, 1) and (4, 3)

Slope

m = (y2-y1)/(x2-x1)

   = ( 3-1)/(4-3)

   = 2/1 = 2

The slope intercept form is y = mx+b where m is the slope and b is the y intercept

y =2x+b

Using the point (4,3)

3 = 2(4)+b

3 = 8+b

3-8=b

-5 =b

y = 2x-5

We have 2 lines

y =x+3 and y = 2x-5

Setting them equal to each other

x+3 = 2x-5

Subtract x from each side

x+3-x = 2x-5-x

3 = x-5

Add 5 to each side

3+5 =x-5+5

8=x

Now we can find y

y =x+3

y = 8+3

y=11

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it costs $20 for 4 play tickets and $35 for 7 play tickets. Is cost per ticket constant? why or why not?
KonstantinChe [14]

Answer:

The cost per ticket is<u> constant</u>.

Step-by-step explanation:

Given:

It costs $20 for 4 play tickets and $35 for 7 play tickets.

Now, to get whether cost per ticket is constant or not.

So, if the cost per ticket is constant that means the cost of ticket for a play or more is fixed, non-varying and it does not change.

Now, we check it:

4 play tickets costs  = $20.

1 play tickets costs  = $20 ÷ 4 = $5.

So, 7 play tickets costs = $5 × 7 = $35.

Thus, the cost of ticket for play is not changing and it is constant.

So the cost per ticket is constant.

Therefore, the cost per ticket is constant.

4 0
3 years ago
Eights rooks are placed randomly on a chess board. What is the probability that none of the rooks can capture any of the other r
erastova [34]

Answer:

The probability is \frac{56!}{64!}

Step-by-step explanation:

We can divide the amount of favourable cases by the total amount of cases.

The total amount of cases is the total amount of ways to put 8 rooks on a chessboard. Since a chessboard has 64 squares, this number is the combinatorial number of 64 with 8, 64 \choose 8 .

For a favourable case, you need one rook on each column, and for each column the correspondent rook should be in a diferent row than the rest of the rooks. A favourable case can be represented by a bijective function  f : A \rightarrow A , with A = {1,2,3,4,5,6,7,8}. f(i) = j represents that the rook located in the column i is located in the row j.

Thus, the total of favourable cases is equal to the total amount of bijective functions between a set of 8 elements. This amount is 8!, because we have 8 possibilities for the first column, 7 for the second one, 6 on the third one, and so on.

We can conclude that the probability for 8 rooks not being able to capture themselves is

\frac{8!}{64 \choose 8} = \frac{8!}{\frac{64!}{8!56!}} = \frac{56!}{64!}

7 0
3 years ago
Solve the math problem
luda_lava [24]

Answer: a) y=-29x-20 b) y=3/5x-18

Step-by-step explanation:

a) m = (-49-38)/(1 - (-2)) = -87/3 = -29

y=-29x+b --> Substitute (1,-49) as a point

(-49)=-29(1)+b

-49=-29+b

-b=-29+49

b=-20

Therefore, the equation of the line is y=-29x-20

b) m = (-18-(-9)/(0-15)) = -9/-15 = 3/5

The y-intercept is (0,-18) as it's where the line intersects the y-axis and x equals 0

Therefore, the equation of the line is y=3/5x-18

4 0
3 years ago
Show that the equation 2x + 3 cos x + e ^ x = 0 has a root on the interval [- 1, 0]
ExtremeBDS [4]

If <em>x</em> = -1, you have

2(-1) + 3 cos(-1) + <em>e</em> ⁻¹ ≈ -0.0112136 < 0

and if <em>x</em> = 0, you have

2(0) + 3 cos(0) + <em>e</em> ⁰ = 4 > 0

The function <em>f(x)</em> = 2<em>x</em> + 3 cos(<em>x</em>) + <em>eˣ</em> is continuous over the real numbers, so the intermediate value theorem applies, and it says that there is some -1 < <em>c</em> < 0 such that <em>f(c)</em> = 0.

5 0
3 years ago
Class 6 MATHS is this correct? ​
Rashid [163]

Answer:

yes ur right

Step-by-step explanation:

6 0
2 years ago
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