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cestrela7 [59]
3 years ago
5

Follow the directions to solve the system of equations by elimination. 8x + 7y = 39 4x – 14y = –68 Multiply the first equation t

o enable the elimination of the y-term. Add the equations to eliminate the y-terms. Solve the new equation for the x-value. Substitute the x-value back into either original equation to find the y-value. Check the solution. The solution to the system of equations is
Mathematics
2 answers:
Viefleur [7K]3 years ago
10 0
(1/2 ,5) hope this helped
PolarNik [594]3 years ago
5 0

Answer:

1/2,5

Step-by-step explanation:

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50
ozzi

Answer:

90 km, N 46° E

Step-by-step explanation:

<em>A jet flies due North for a distance of 50 km and then on a bearing of N 70° E for a further 60 km. Find the distance and bearing of the jet from its starting point.</em>

Look at the diagram I drew of this scenario. You can see the jet flies North for 50 km, and then turns at a 70° angle to fly another 60 km. We want to find the distance from the starting point, SP, to angle C (labeled).

This will be the jet's distance from its starting point.

In order to find the bearing of the jet from its starting point, we will need to find the angle formed between distances b and c, labeled angle A.

The <u>Law of Cosines</u> will allow us to use two known sides and one known angle to solve for the sides opposite of the known angle.

In this case, the known angle is 110° (angle B) so we will use the <u>Law of Cosines</u> respective to B.

  • b² = a² + c² - 2ac cosB

Substitute the known values into the equation and solve for b, the distance from the starting point (A) to the endpoint (C).

  • b² = (60)² + (50)² - 2(60)(50) cos(110°)
  • b² = 6100 -(-2052.12086)
  • b² = 8152.12086
  • b = 90.28909602
  • b ≈ 90 km

The distance of the jet from its starting point is 90 km. Now we can use this b value in order to calculate angle A, the bearing of the jet.

The <u>Law of Cosines</u> with respect to A:

  • a² = b² + c² - 2bc cosA

Substitute the known values into the equation and solve for A, the bearing from the starting point (clockwise of North).

  • (60)² = (90.28909602)² + (50)² - 2(90.28909602)(50) cosA
  • 3600 = 8152.12086 - 6528.909602 cosA
  • -4552.12086 = -6528.909602 cosA
  • 0.6972252853 = cosA
  • A = cos⁻¹(0.6972252853)
  • A = 45.79519
  • A ≈ 46°

The bearing of the jet from its starting point is N 46° E. This means that it is facing northeast at an angle of 46° clockwise from the North.

7 0
2 years ago
What is (f + g)(x)? <br><br> f(x)=x^3−x<br><br> g(x)=x^3+2x^2−10
Leya [2.2K]
(f+g)(x)=f(x)+g(x) = x³-x +x³ +2x²-10=2x³ + 2x²-x-10
(f+g)(x)=2x³ + 2x²-x-10
4 0
3 years ago
Please explain how you got the answer. No links I will report you. Show your work.
tekilochka [14]

Answer:

x = 6

Step-by-step explanation:

5 sides all the same length

s = 22.5/5

s = 4.5

--------------------

x - 1.5 = 4.5

Add 1.5 to both sides

x = 6

4 0
3 years ago
Read 2 more answers
What does the word partial mean.
levacccp [35]
Not completely or not the full thing

hope this helps ! and hope you pass !
5 0
3 years ago
Read 2 more answers
A computer software vendor claims that a new version of its operating system will crash fewer than 10 times per year on average.
Oksana_A [137]

Answer:

Step-by-step explanation:

The hypothesis is written as follows

For the null hypothesis,

µd ≤ 10

For the alternative hypothesis,

µ > 10

This is a right tailed test

Since no population standard deviation is given, the distribution is a student's t.

Since n = 97

Degrees of freedom, df = n - 1 = 97 - 1 = 96

t = (x - µ)/(s/√n)

Where

x = sample mean = 8.9

µ = population mean = 10

s = samples standard deviation = 3.6

t = (8.9 - 10)/(3.6/√97) = - 3

We would determine the p value using the t test calculator. It becomes

p = 0.00172

Since alpha, 0.01 > than the p value, 0.00172, then we would reject the null hypothesis. Therefore, At a 1% level of significance, there is enough evidence that the data do not support the vendor’s claim.

3 0
3 years ago
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