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Kamila [148]
2 years ago
6

Find the equation of the line with slope m=1/4 that contains the point (4,5).

Mathematics
1 answer:
sladkih [1.3K]2 years ago
7 0

Answer: x - 4y = -16

Step-by-step explanation: Since we're given a point and a slope, we can write the equation of this line using the point-slope formula.

<h2>y  -  y₁  =  m(x  -  x₁)</h2><h2 />

The given point, (4, 5), represents (x₁, y₁).

So if we plug all our given information into the formula,

including our slope of 1/4, we get y - 5 = 1/4(x - 4).

To put our equation in standard form, first, distribute

the 1/4 through the parentheses.

So we get y - 5 = 1/4x - 1.

Remember that standard form cannot have any fractions in it so our next step is to multiply both sides of the equation by 4 to get rid of the fraction.

That gives us 4y - 20 = x - 4.

Now moves the -20 to the right side by adding 20 to both sides.

So we get 4y = x + 16.

Now subtract x from both sides to get -x + 4y = 16.

Finally, our coefficient on our x term must be positive so we

divide both sides by -1 to get x - 4y = -16.

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A rocket is launched straight up from the ground with an initial velocity of 192 feet per second. The equation for the height of
Ivenika [448]

The equation for the height of the rocket at time t given

h= -16t^2+192t

We have to find the time t, when the rocket reaches 560 feet.

That means we have to find t when h = 560 ft. we will place 560 in the place of h to find t now.

h= -16t^2+192t

560 = -16t^2+192t

In the right side, we can check -16 is the common factor. So we will take out -16 from the rigbht side.

560 = -16(t^2 - 12t)

To get rid of -16 from the right side and move it to left side, we will divide both sides by -16.

560/-16 = -16(t^2-12t)/-16

-35 = t^2 -12t

Now we will move -35 to the righ side by adding 35 to both sides.

-35+35 = t^2-12t+35

0 = t^2 -12t+35

t^2-12t+35 = 0

We will factorize thee left side to find the values of t now. We need to find a pair of factors of 35 that by adding them we will get -12.

The pair of factors of 35 are -5 and -7 and by adding -5-7 we will get -12.

t^2-12t+35 =0

(t-5)(t-7) =0

So by using zero product property we will get

t-5 =0

t-5+5 = 0+5

t=5

Also t-7 =0

t-7+7 = 0+7

t=7

So we have got the rocket reaches at 560ft when t = 5 seconds and also when t = 7 seconds.

Now part b.

When the rocket completes its trajectory and hits the ground then the height or h = 0. So we will place h = 0 there in the equation.

h= -16t^2+192t

0= -16t^2 + 192 t

0 = -16(t^2-12t)

-16(t^2-12t) = 0

We will move -16 to the other side by dividing it to both sides.

-16(t^2-12t)/-16 = 0/-16

t^2-12t = 0

We will take out the common factor t from the left side. By taking out t we will get,

t(t-12) = 0

We will use zero product property now. By using that we will get,

t = 0

ans also t-12 = 0

t-12+12 = 0+12

t = 12

When the rocket completes its trajectory and hits the ground the time t can not be 0. When t =0, the rocket starts the trajectory.

So when the rocket completes its trajectory and hits the ground ,

then t = 12seconds.

So we have got the required answers.

6 0
2 years ago
Steven put together 981 pieces of a puzzle. About how many pieces did he put together? Round to the nearest thousand. Use what y
Colt1911 [192]
About 1,000 puzzle pieces
3 0
2 years ago
Please help me. It’s geometry
Verizon [17]

Option 3:

m∠ABC = 66°

Solution:

Given \overline {F A D} \| \overline {E H C} and ABH is a transversal line.

m∠FAB = 48° and m∠ECB = 18°

m∠ECB = m∠HCB = 18°

<u>Property of parallel lines: </u>

<em>If two parallel lines cut by a transversal, then the alternate interior angles are equal.</em>

m∠FAB = m∠BHC

48° = m∠BHC

m∠BHC = 48°

<u>Exterior angle of a triangle theorem: </u>

<em>An exterior angle of a triangle is equal to the sum of the opposite interior angles.</em>

m∠ABC = m∠BHC + m∠HCB

m∠ABC = 48° + 18°

m∠ABC = 66°

Option 3 is the correct answer.

4 0
3 years ago
One year, a farmer harvested 50,000 bushels of wheat on her family farm.
Zanzabum
The answer is C, hope this helps
4 0
3 years ago
Help Plez 20 Points Due Today
Jobisdone [24]

Answer:6.25

Step-by-step explanation :  ratio of areas = one half :two point five in a half        

=1.0:6.25

8 0
3 years ago
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