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Zielflug [23.3K]
3 years ago
5

Here is a system of linear equations: y= x+4 y= -3x-8

Mathematics
1 answer:
ipn [44]3 years ago
5 0

Answer:

  • A) (-3,1)

Step-by-step explanation:

<u>Given system of linear equations: </u>

  • y= x+4
  • y= -3x-8

---

  • x + 4 = -3x - 8
  • x + 3x = - 8 - 4
  • 4x = -12
  • x = -3

Then

  • y =-3 + 4 = 1

Solution is (-3, 1)

Correct option is A

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Find the length of the segment that joins the points (-5, 4) and (6,-3).
Helen [10]

Answer:

\boxed {\boxed {\sf d=\sqrt{170} \ or \  d\approx 13.04}}}

Step-by-step explanation:

We are asked to find the length of a segment or the <em>distance</em> between the 2 points. The formula for distance is:

d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2

where (x₁ y₁) and (x₂, y₂) are the points. We are given the points ( -5, 4) and (6, -3). If we match the number and the corresponding variable, it is:

  • x₁= -5
  • y₁= 4
  • x₂= 6
  • y₂ = -3

Substitute the values into the formula.

d= \sqrt{(6--5)^2+(-3-4)^2

Solve inside the parentheses.

  • 6--5 (Back to back negative signs become a positive)= 6+5 =11
  • -3-4= -7

d= \sqrt{(11)^2+(-7)^2

Solve the exponents.

  • (11)²= 11*11= 121
  • (-7)²= -7*-7= 49

d= \sqrt {(121)+(49)

Add.

d= \sqrt {170}

d=13.0384048104

Even though it's not specified, we could round to the nearest hundredth to make the answer more concise. The 8 in the thousandth place tells us to round the 3 to a 4 in the hundredth place.

  • 13.03<u>8</u>4048104

d\approx 13.04

The length of the segment is <u>√170</u> or approximately <u>13.04. </u>

7 0
2 years ago
Find the average rate of change over the given interval f(x)=3^x,[1,4]
nexus9112 [7]

Answer:

26

Step-by-step explanation:

Thus, f(b)−f(a)b−a=3(4)−(3(1))4−(1)=26.

7 0
3 years ago
Estimate the sum for 1,537 times 242 then find the sum
Furkat [3]
It says to estimate first 1,537 turns to 2,000 because the 5 is 5 or more so the 1 becomes 2 and everything else is zeros. Now multiply 2000x 242=484,000 is the Estimation. Now find the correct product for 1,537x242=371,954
5 0
2 years ago
Read 2 more answers
Nate has 6 3/5 of fabric. He uses 3 1/2 yards of fabric to make a pillow. How much fabric dose he left
NNADVOKAT [17]

Answer:

3 and 1/2  minus 2/3  minus 1/3 =

7/2 minus 2/3 minus 1/3 =

21/6 minus 4/6 minus 2/6 =

17/6 - 2/6 =

15/6 =    5/2 = 2 and 1/2

Optionally, you can think of it this way:

He used 2/3 yards for the pillow and 1/3 yard for the scarf.

So he used 1 yard

3 and 1/2 minus 1 = 2 and 1/2 = 5/2

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
The incline of a roller coaster is 2 times as long as its elevation, and the horizontal length of the roller coaster is 11 m mor
Gelneren [198K]
Let 
x-------> t<span>he horizontal length of the roller coaster
y------> </span>the elevation of the roller coaster
c------> t<span>he incline of a roller coaster
</span>
we know that
applying the Pythagoras theorem
c²=x²+y²-----> equation 1
c=2y-----> equation 2
x=11+y----> equation 3

substitute equation 2 and equation 3 in equation 1
[2y]²=(11+y)²+y²
4y²=11²+22y+y²+y²
2y²-22y-121=0

using a graph tool-----> to resolve the second order equation
see the attached figure

the solution is 
y=15.026 m

c=2*y-----> c=2*15.026----> c=30.052 m

the answer is
30.05 m


7 0
3 years ago
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