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2 years ago

Find the measure of each missing angle.

Mathematics

1 answer:

nadya68 [22]2 years ago

5 0

Answer:

Step-by-step explanation:

Angle sum property of triangle: Sum of all the angles of a triangle is 180

Alternate interior angles: When two parallel lines are intersected by a transversal, the pair of angles on the inner side of each of these lines but on the opposite side of the transversal are called alternate interior angles

In ΔABC,

∠1 + 90 + 38 = 180 {angle sum property of triangle}

∠1 + 128 = 180

∠1 = 180 - 128

$\sf \boxed{\bf \angle 1 = 52^ \°}$

AB // CD and AC is transversal.

$\sf \boxed{\bf \angle 3 = 38^\circ}$ {Alternate interior angles are equal}

In ΔACD,

∠2 + ∠3 + 63 = 180 {angle sum property of triangle}

∠2 + 38 +63 = 180

∠2 + 101 =180

∠2 = 180 - 101

$\sf \boxed{\bf \angle 2 = 79^ \°}$

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Lulu tells her little brother, Jack, that she is holding 20 coins, all of which are either dimes or quarters. They have a value

RSB [31]

Given :

Lulu tells her little brother, Jack, that she is holding 20 coins, all of which are either dimes or quarters.

They have a value of $4.10. She says she will give him the coins if he can tell her how many of each she is holding.

To Find :

How many dimes and quarters in Lulu holding?

Solution :

4.10 dollar = 410 cents

Let, number of dimes and quarter are x and y.

So, x + y = 20 ...1)

Also, 10x + 25y = 410 ...2)

Putting value of 1) in equation 2), we get :

10x + 25( 20 - x ) = 410

10x + 500 - 25x = 410

15x = 90

x = 6

y = 14

Therefore, number of dimes and quarters are 6 and 14 respectively.

Hence, this is the required solution.

3 0

3 years ago

A retangular prism has a length of 20 in. a width of 2 in., and a height of 3 1/4 in. The prism is filled with cubes that have e

ira [324]

Answer: 8320 cubes.

Step-by-step explanation:

1. Calculate the volume of the rectangular prism:

$V_1=l*w*h$

Where l is the lenght, w is the width and h is the height.

Substitute values.

(You can convert 3 1/4 to decimal by dividing the numerator by the denominator of the fraction and add this to the whole part: 3+0.25=3.25)

Then:

$V_1=20in*2in*3.25in=130in^{3}$

2. Calculate the volume of a cube:

$V_2=s^{3}$

Where s is the lenght of any side.

Then:

$V_2=(\frac{1}{4}in)^{3}=\frac{1}{64}in^{3}=0.0156in^{3}$

3. To calculate the number of cubes that are needed to fill the rectangular prism (which you can call n) , you must divide the volume of the prism by the volume of a cube. Then:

$n=\frac{V_1}{V_2}=\frac{130in^{3}}{0.0156in^{3}}=8320$ cubes