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1 year ago

Solve the following system of equations.

Mathematics

1 answer:

Elan Coil [88]1 year ago

5 0

Answer:

(2,-3)

Step-by-step explanation:

I am not sure if you meant the first equation to be y or -y. I solved it as y.

y = x-5 -x -3y =7

I am going to take the second equation and write it as x =

-x - 3y = 7 Give equation

-x = 3y +7 Add 3y to both sides

x = -3y-7 Multiplied each term in the equation by -1 so that x could be positive

I am going to substitute -3y-7 for x in the first equation up above

y = x - 5

y = -3y -7 - 5 Substitute -3y-7 for x

y = -3y -12 Combined -7-5

4y = -12 Added 3y to both sides

y = -3 Divided both sides by 4.

I now know that y is -3, I will plug that into x = -3y-7 to solve for x

x = -3(-3) -7

x = 9-7 A negative times a negative is a positive

x = 2

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Kayla and he children went into a restaurant and she bought $63 worth of hotdogs and tacos. Each hotdog costs $3.50 and each tac

Diano4ka-milaya [45]

Answer:

Kayla bought 7 tacos and 10 hotdogs

Step-by-step explanation:

Let the number of hotdogs be x.

Let the number of tacos be y.

i) It is given that x = y + 3

ii) It is also given that 3.5x + 4y = 63, therefore 7x + 8y = 126

iii) substituting the value of x from i) in ii) we get 7(y + 3) + 8y = 126

therefore 15y + 21 = 126

therefore 15y = 105

therefore y = 7

Therfore Kayla bought 7 tacos

iv) Using the value of y from iii) in i) we x = 7 + 3 = 10

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2 years ago

A freight train leaves a station and travels north at 60 mph. 4 hours later, a passenger train leaves on a parallel track and t

harkovskaia [24]

Answer:

first do:

60mph * 4 hours= 240mi

Let D = the distance the passenger train has to

travel to catch the freight train

Start a stopwatch when the passenger train leaves

Let t = the time on the stopwatch when they meet

Equation for freight train:

d-240=60t

Equation for passenger train:

d=100t

all together:

100t-240=60t

we can do 100t-60t because they both have (t)= 40t

40t=240 *now divide 240 by 40= 6

THEN do:

D= 100mph x 6= 600mi

They will meet 600 mi from the station

to check:

d-240=60t x 6

600-240= 360

60 x 6= 360

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3 years ago

5^3 - 64/8 plus 10^2

Murljashka [212]

5^3 - 64/8 + 10^2=217

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3 years ago

Consider angle θ in Quadrant II, where sinθ = 4/5 . What is the value of cosθ?

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Answer:

3/5

Step-by-step explanation:

sin theta=opposite/hypotenuse

4/5=opposite/hypotenuse

therefore opposite=4 and hypotenuse=5

for adjacent

using pythagoras theorem

a^2+b^2=c^2

opposite^2 + adjacent^2 =hypotenuse^2

4^2 + adjacent^2 =5^2

16 + adjacent^2 =25

adjacent^2 =25-16

adjacent = $\sqrt{9$

adjacent=3

cos theta=adjacent/hypotenuse

=3/5

therefore the value of cos theta is 3/5

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