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3 years ago

Algebra applications: find the value of x and y

Mathematics

1 answer:

Inga [223]3 years ago

3 0

Answer : The value of x and y is 8 and 10 respectively.

Step-by-step explanation :

As we known that if two parallel lines are cut by a transversal line then consecutive interior angles are supplementary.

From the given figure we conclude that:

$5x-y+150=180$ ...........(1)

$5x-y=180-150$

$5x-y=30$ ............(2)

$5x+y+130=180$ ...........(3)

$5x+y=180-130$

$5x+y=50$ ...........(4)

Now we adding equation 2 and 4, we get the value of x.

$5x-y+5x+y=30+50$

$10x=80$

$x=8$

Now we are putting the value of x in 4, we get the value of y.

$5x+y=50$

$5(8)+y=50$

$y=50-40$

$y=10$

Therefore, the value of x and y is 8 and 10 respectively.

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3 years ago

Drew drives his car and Rachel drives her truck in the same direction on the highway at constant speeds for 3.25 hours. During t

never [62]

Answer:

After 4.5 hours of driving at the same constant speeds, Drew and Rachel are 6.5 miles apart.

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3 years ago

Help. Find the value of x to the nearest tenth

vodka [1.7K]

I will assume that line 4 bisect line x exactly in half. This means that if we solve the last side of the triangle like seen in the pic below we will know what half of line x is

To find the length of the last side of the triangle (let's call this y) you must use Pythagorean theorem

$a^{2} +b^{2}=c^{2}$

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = 4

b = y

c = 6

^^^Plug these numbers/variables into the theorem

$4^{2} +y^{2} =6^{2}$

solve for y

16 + $y^{2}$ = 36

$y^{2}$ = 20

x = √20

x ≈ 4.472

^^^This is only half of x so if you double it then it will get you the full length of x

4.472 * 2 = 8.944

8.9 (D)

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3 years ago

A group of employees is stranded on top of a 120 feet building because a fire occurred. Your goal is to throw a rope from a 60 f

Paul [167]

Step-by-step explanation:

-16t² + 64t + 60 = 120

this is a quadratic equation, and its points of f(t) = 0 can be calculated. there are usual 2 such solutions for a quadratic equation.

so, we need to bring it to a form that ends in "= 0".

-16t² + 64t - 60 = 0

that is also the same as

-4t² + 16t - 15 = 0

the formula for the solutions of such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

a = -4

b = 16

c = -15

so,

t = (-16 ± sqrt(256 - 4×-4×-15))/(2×-4) =

= (-16 ± sqrt(256 - 240))/-8 =

= (-16 ± sqrt(16))/-8 = (-16 ± 4)/-8

t1 = (-16 + 4)/-8 = -12/-8 = 3/2

t2 = (-16 - 4)/-8 = -20/-8 = 5/2

so, it depends on what the unit of time t is. let's assume seconds.

therefore, the rope will reach the top of the building while going up after 3/2 = 1 1/2 = 1.5 seconds.

and then, as the shot rope makes a curve and comes back down again (that is why we have 2 solutions : the rope will reach the height of 120ft during its flight path twice : once while still going up, and once when coming back down again) it will be at the height of the top of the building after 5/2 = 2 1/2 = 2.5 seconds.

so, it depends if the people there can grab it at the first chance, and if the path of the rope would allow them to grab it also again on its way back down. this we don't know.

I therefore guess, that your teacher is aiming for the first solution.

4 0

3 years ago

Algebra applications: find the value of x and y​

Algebra applications: find the value of x and y