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2 years ago

Find the hypotenuse of a right triangle whose sides are 12 and 16.

Mathematics

1 answer:

elena55 [62]2 years ago

4 0

Answer: 20

Step-by-step explanation:

a^2+b^2=c^2 (pythagorean theorem where c is hypotenuse)

12^2+16^2=c^2

144+256=c^2

400=c^2

square root of 400=20

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Given: ABCD trapezoid BC=1.2m, AD=1.8m AB=1.5m, CD=1.2m AB∩CD=K Find: BK and CK

stepladder [879]

Answer:

The value of BK is 3m and the value of CK is 2.4m.

Step-by-step explanation:

Given information: ABCD trapezoid

, BC=1.2m, AD=1.8m

, AB=1.5m, CD=1.2m

, AB∩CD=K.

Using the given information draw a figure.

Two sides of a trapezoid are parallel.

Since AB∩CD=K, therefore AB and CD are not parallel, because parallel line never intersect.

$AD\parallelBC$

$\angle KBC=\angle KAD$ (Corresponding angles)

$\angle KCB=\angle KDA$ (Corresponding angles)

By AA rule of similarity

$\triangle KBC\sim \triangle KAD$

Corresponding sides of similar triangles are proportional.

$\frac{KB}{KA}=\frac{KC}{KD}=\frac{BC}{AD}$

$\frac{x}{x+1.5}=\frac{y}{y+1.2}=\frac{1.2}{1.8}$

$\frac{x}{x+1.5}=\frac{1.2}{1.8}$

$\frac{x}{x+1.5}=\frac{2}{3}$

$3x=2x+3$

$x=3$

The length of BK is 3 m.

$\frac{y}{y+1.2}=\frac{1.2}{1.8}$

$\frac{y}{y+1.2}=\frac{2}{3}$

$3y=2y+2.4$

$y=2.4$

The length of CK is 2.4 m.

5 0

2 years ago

Read 2 more answers

A hovercraft takes off from a platform.

lubasha [3.4K]

Answer:

81 meters.

Step-by-step explanation:

The height (in meters), h(x) of a hovercraft x seconds after takeoff, is modeled by:

$h(x)=-3(x-3)^2+108$

We are to determine its height at the time of takeoff.

Now, at the time of takeoff, x=0.

We substitute x=0 to solve for h.

$h(0)=-3(0-3)^2+108\\=-3(-3)^2+108\\=-3(9)+108\\=-27+108\\=81$ meters$

The height of the hovercraft at takeoff is 81 meters.

7 0

3 years ago

Read 2 more answers

line segment AB has endpoints A (7.5,4.2) and B (2.3,5.4). Find the coordinates of the point that divides the line segment direc

Marrrta [24]

9514 1404 393

Answer:

(6.2, 4.5)

Step-by-step explanation:

We want, for some point P, ...

(P -A) / (B -P) = 1 / 3

3(P -A) = (B - P) . . . . . multiply by 3

4P = B +3A . . . . . . . . add P+3A

P = (B +3A)/4 . . . . . . .divide by 4

Filling in the coordinate values, we can find P to be ...

P = ((2.3, 5.4) +3(7.5, 4.2))/4 = (2.3+22.5, 5.4+12.6)/4

P = (6.2, 4.5)

5 0

3 years ago

Which expression and diagram represent “three times a number”?

kozerog [31]

Answer:

You've picked the right one! It's the one you've marked in the picture!

Step-by-step explanation:

Multiplication is just like addition; you're just doing it multiple times instead of once. 3x is equal to x + x + x. That's exactly what the option you chose in the image shows. Great job! You've got this!

6 0

3 years ago

Read 2 more answers

Age(years) Total( frequency)

xxTIMURxx [149]

Answer:

Step-by-step explanation:

7 0

3 years ago