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3 years ago

What is 5.37 as a mixed number

Mathematics

2 answers:

Musya8 [376]3 years ago

6 0

5 37/100 5 is the whole part and you have 37 hundredths

melisa1 [442]3 years ago

3 0

5 37/100, there might be a more simplified answer idk though

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Given: AB || DE , AD bisects BE. Prove: ABC = DEC using the ASA postulate.

Ket [755]

Answer:

As per ASA postulate, the two triangles are congruent.

Step-by-step explanation:

We are given two triangles:

$\triangle ABC$ and $\triangle DEC$ .

AD bisects BE.

AB || DE.

Let us have a look at two properties.

1. When two lines are parallel and a line intersects both of them, then alternate angles are equal.

i.e. AB || ED and $\angle B$ and $\angle E$ are alternate angles $\Rightarrow$ $\angle B = \angle E$ .

2. When two lines are cutting each other, angles formed at the crossing of two, are known as Vertically opposite angles and they are are equal.

$\Rightarrow \angle ACB = \angle DCE$

Also, it is given that AD bisects BE.

i.e. EC = CB

1. $\angle B = \angle E$

2. EC = CB

3. $\angle ACB = \angle DCE$

So, we can in see that in $\triangle ABC$ and $\triangle DEC$ , two angles are equal and side between them is also equal to each other.

Hence, proved that $\triangle ABC$ $\cong$ $\triangle DEC$ .

8 0

3 years ago

Given the general form of the sinusoidal function, y = AsinB(x - C) + D, match the following items.

Jet001 [13]

Answer:

$\Delta y = A$ (Amplitude) (Correct answer: 1)

$\omega = B$ (Angular frequency) (Correct answer: 2)

$x_{o} = C$ (Phase shift) (Correct answer: 3)

$y_{o} = D$ (Vertical shift) (Correct answer: 4)

$\frac{2\pi}{\omega} = \frac{2\pi}{B}$ (Period) (Correct answer: 5)

Step-by-step explanation:

The general form of a sinusoidal function is represented by the following characteristics:

$y = \Delta y \cdot \sin \omega\cdot (x- x_{o}) + y_{o}$ (1)

Where:

$\Delta y$ - Amplitude.

$\omega$ - Angular frequency.

$x_{o}$ - Phase shift.

$y_{o}$ - Vertical shift.

$x$ - Independent variable.

$y$ - Dependent variable.

In addition, we know that the period associated with the sinusoidal function ( $T$ ) is:

$T = \frac{2\pi}{\omega}$

By direct comparison, we get the following conclusions:

$\Delta y = A$ (Amplitude) (Correct answer: 1)

$\omega = B$ (Angular frequency) (Correct answer: 2)

$x_{o} = C$ (Phase shift) (Correct answer: 3)

$y_{o} = D$ (Vertical shift) (Correct answer: 4)

$\frac{2\pi}{\omega} = \frac{2\pi}{B}$ (Period) (Correct answer: 5)

6 0

3 years ago

The fourth grade class at hart school is having a Valentine’s Day party. Each student will receive an 8-oz.cup of juice. If ther

avanturin [10]

Answer:

6 bottles of juice

Step-by-step explanation:

1. find the total amount of juice needed (number of students multiplied by the amount of juice): 48*8 = 384

2. find the number of bottles needed (total amount of juice divided by amount in each bottle): 384/64 = 6

8 0

3 years ago

The formula for the slant height of a cone is , where S is surface area of the cone. Use the formula to find the slant height, l

liq [111]

we know that

The formula of the surface area of the cone is equal to

$SA=\pi r^{2}+\pi rl$

where

SA is the surface area

r is the radius of the cone

l is the slant height

in this problem we have

$SA=500\pi\ ft^{2}\\r=15\ ft\\l=?$

Solve the formula for l

$SA=\pi r^{2}+\pi rl\\ \\\pi rl=SA-\pi r^{2} \\ \\l=\frac{SA-\pi r^{2} }{\pi r}$

substitute the values

$l=\frac{500\pi -\pi 15^{2} }{\pi15}\\ \\l=\frac{275}{15}\ ft\\ \\l=\frac{55}{3}\ ft\\ \\l=18\frac{1}{3}\ ft$

therefore

the answer is

The slant height is $18\frac{1}{3}\ ft$

7 0

4 years ago

Read 2 more answers

Lisa's shop sells 5 quarts of ice cream each day. How much is this in pints?

Sergeeva-Olga [200]

Answer:

Step-by-step explanation:

We know there are 5 quarts.

There are 2 pints for each quart.

This can be though of as a ratio of:

2 : 1

There are 5 quarts, which is 5 times bigger than the ratio of 1.

So this means we need to mutliply both sides of the ratio by 5, to make the quarts equivelent to 5:

2*5 : 1*5

10 : 5

So for every 5 quarts there are 10 pints.

Hope this helps!

8 0

3 years ago