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3 years ago

find the point, M, that divides segment AB into a ratio of 5:2 if A is at (1,2) and B is at (8, 16).

Mathematics

1 answer:

Paha777 [63]3 years ago

7 0

Answer:

Step-by-step explanation:

A(1,2) ---->(x1,y1)

B(8,16) ----->(x2,y2)

m:n = 5:2

$M(\frac{x_{2}m+x_{1}}{m+n},y_{2}m+y_{1}}{m+n})\\\\=M(\frac{5*8+2*1}{5+2},\frac{5*16+2*2}{5+2})\\\\=M(\frac{40+2}{7},\frac{80+4}{7})\\\\=M(\frac{42}{7}{,\frac{84}{7})\\\\=M(6,12)$

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A baker bakes 50 muffins. 1/5 of the muffins are chocolate chip. 1/2 of the muffins are blueberry. The rest are cinnamon. How ma

vitfil [10]

Answer:

15 muffins are cinnamon.

Step-by-step explanation:

Given that:

Number of muffins baked = 50 muffins

Chocolate chip muffins = 1/5 of 50 = $\frac{1}{5}*50$

Chocolate chip muffins = 10 muffins

Blueberry muffins = 1/2 of 50 = $\frac{1}{2}*50$

Blueberry muffins = 25

Cinnamon muffins = Muffins baked - chocolate chip muffins - blueberry muffins

Cinnamon muffins = 50 - 10 - 25

Cinnamon muffins = 50 - 35 = 15

Hence,

15 muffins are cinnamon.

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3 years ago

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.

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3 years ago

Write the expression in standard form: 5(3a) + 8(-5b) + (4 * c * 6) * = Multiplication symbol

scoray [572]

Answer:

use photomath and your welcome :)))

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2 years ago

A rectangle is 40 yards long and 30 yards wide. What is the length of the diagonal that cuts through the center?

choli [55]

Answer:

it should be 50

Step-by-step explanation:

Using the pythagorean theorem c = $\sqrt{a^{2} +b^{2} }$ we get 50

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3 years ago

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skelet666 [1.2K]

Answer:

Step-by-step explanation:

x^2 + 6x - 2x - 3

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3 years ago

find the point, M, that divides segment AB into a ratio of 5:2 if A is at (1,2) and B is at (8, 16).​

find the point, M, that divides segment AB into a ratio of 5:2 if A is at (1,2) and B is at (8, 16).