The teachers had to transport 165 students by bus on a field trip. Each bus holds 64 students. How many buses do they need to order?

Answer:  See below.

Step-by-step explanation:

We'll assume the top and bottom lines are parallel.  That means angles 4 and 5 are 90 degrees since the line coming down is perpendicular to the parallel line.  The sum of angles 1 and 2 is also 90°.  The interior angles of a triangle must add to 180°. So far we have two:  90° and 60°.  The third must therefore be 30°(angle 2).  Angle 3 must be 120° since it shares a straight line with the 60° angle and the straight line is 180° from one side to the other.  Angle 1 must be (90°- angle 2), which makes it 60°.  

1.  60°

2. 30°

3.  120°

4.  60°

5.  90°

Answer:

Than the other one is a good idea for the angle measured

Measures of angles 3 and 6 is 60°

Parallel lines are those straight lines that are always the same distance apart from each other.

Given that, line m is parallel to line n and m ∠ 3 = (7x-10) and m ∠ 6=(5x+10)

Since m ║ n then

m ∠ 3 = m ∠ 6

(7x-10) = (5x+10)

2x = 20

x = 10

m ∠ 3 = 7x-10 = 7*10 - 10 = 60°

m ∠ 6 = (5x+10) = 5*10 + 10 = 60°

Hence, Measures of angles 3 and 6 is 60°

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Answer:

In an hour, Alex can wash 14 windows.

Step-by-step explanation:

10 1/2 windows per 3/4 hour

per usually means a / sign because you are finding the unit rate

10.5/0.75 (I just converted everything into a fraction to make it easier)

solve:

10.5/0.75 = 14

Another way to solve:

10 1/2 / 3/4

= 21/2 * 4/3

= 21*4/2*3

= 84/6

= 14

Check:

If Alex washes 14 windows per hour, you can check by multiplying 14 by 3/4 of an hour

14*3/4

=42/4

=10.5

10.5 is the same as 10 1/2

Answer:

16.95

Step-by-step explanation:

because when you add 14.95 and 2 together you get 16.95

Answer:

Step-by-step explanation:

Area of  Big circle = πr² = 3.14 * 6.5*6.5  = 132.67 cm²

Area of small circle = 3.14 * 2.3*2.3 = 16.61 cm²

Area of shaded region = area of big circle - area of small circle

         = 132.67 - 16.61  = 116.06 cm²

Answer:

X = 2/3 and Y = 3

Step-by-step explanation:

Matrix: 3 -1 -1

-3 5 13

Main determinant:

| 3 -1 |

| -3 5| = 12

Dx: |-1 -1|

|13. 5| = 8

X = 8/12 = 2/3

Determinant y:

|3 -1|

|-3 13| = 36

Y = 36/12 = 3

Answer:

Step-by-step explanation:

Given,

Area of the triangle

[tex] = {105m}^{2} [/tex]

Base of the triangle

= 15m

Let,

Height of the the triangle be h

Therefore,

By the problem,

[tex] = > \frac{1}{2} \times base \times height = 105[/tex]

[tex] = > \frac{1}{2} \times 15 \times h = 105[/tex]

[tex] = > h = \frac{105 \times 2}{15} [/tex]

=> h = 7 × 2

=> h = 14m

Hence,

The req. height of the triangle is 14 m (Ans)

Answer:

The answer is 14 m.

Step-by-step explanation:

Area = [tex]105^{2}[/tex]

Base = 15 m.

Height = ?

The formula for finding the area of triangle is

[tex]A = \frac{h_{b}b}{2}[/tex]

Put the values in the formula

[tex]105 = \frac{h_{b}15 }{2}[/tex]

Use MPE or Multiplication Property of Equality

210 = 15[tex]h_{b}[/tex]

Now use DPE or Division Property of Equality

[tex]\frac{210}{15} = \frac{15_{hb} }{15}[/tex]

14 = [tex]h_{b}[/tex]

The height of the triangle is 14 m.

To check, multiply the height and base to get the area.

14 * 15 = 105 [tex]m^{2}[/tex]

Answer:

3x - y = -1

Step-by-step explanation:

Standard form of equation is Ax + By = C

y - y1 = m (x -x1)

y - 7 = 3 (x - 2)

y - 7 = 3x - 6

3x - y = -7 +6

3x - y = -1

Answer:  [tex]y-3x=1[/tex]

Step-by-step explanation:

Standard form :

Ax+By=C

We have a linear function y=kx+b ;

we also know its slope k=3 ; and that it passes through the point (2 ; 7 )

Then:

[tex]y=3x+1[/tex]

now substitute the knowledge of the coordinates of the point

[tex]3\cdot 2+b=7 \\\\ b=7-6\\\\ \underline{b=1\ \ \ \ \ }[/tex]

Then we get the function:

[tex]y=3x+1[/tex]

Standard form :

[tex]y-3x=1[/tex]

Answer:

80

Step-by-step explanation:

80%

Answer:

40

Step-by-step explanation:

Let the number be y

-1/2 × y = -20

y = -20 ÷ -1/2

y = 20 × 2

y = 40

Answer:

See below:

Step-by-step explanation:

Hello! My name is Galaxy and I will be helping you today!

We can solve this problem in two steps, one being comprehension and another being solving. I'll start off with comprehension.

Comprehension

We can start to solve this problem by looking at it.

We can see that there is a right angle, therefore the angles that are in it are Complementary (Add up to 90).

That means that 30+3x=90.

We can now begin solving.

Solving

We can start solving by setting up an equation.

[tex]30+3x=90[/tex]

We can do this because we know due to the law of complementary angles that 30 and 3x MUST equal to 90.

[tex]3x=60\\x=20[/tex]

We can do basic algebra, we can find out that x is equal to 20 degrees. Let's now check our answer.

[tex]30+3(20)=90?\\30+60=90?\\90=90[/tex]

Therefore the answer is x=20 degrees

Cheers!

Answer:

#1 is A   #2 is C   #3 is D   #4 is D   #5 is D   #6 is A

Step-by-step explanation:

I might be wrong for number 5 or the others but hope this works for you.

:)

Answer:

$160.16

Step-by-step explanation:

Well first you need to find 12% of 143.

100%=143

10%=14.3

2%=2.86

12%=17.16

Now we add 17.16 to 143 to get 160.16. This means he pays $160.16.

Answer:

Step-by-step explanation:

Answer:

(2 , -3)

Step-by-step explanation:

7x +2y = 8

-5x - 2  = -12

The only method that uses addition/subtraction is elimination

5(7x + 2y = 8)

7(-5x = 10) I am getting x coefficient to be the same, LCF of 7 and 5 is 35)

(multiply it out and now we can get ready to subtract) *I got 10 by adding 2 to -12*

35x + 10y = 40

-35x = 70

10y = -30

y = -3

substitute y into original equation

7x + 2 (-3) = 8

7x - 6 = 8

7x = 14

x = 2

(2 , -3 )

Answer:

Step-by-step explanation:

Add 5x to both sides to isolate -2:

-5x + 5x - 2 = -12 + 5x

-2 = -12 + 5x

Add 12 to both sides to isolate the 5x:

-2 + 12 = -12 + 12 + 5x

10 = 5x

Divide both sides by 5:

[tex]\frac{5x}{5} = 10 \div 5\\[/tex]

x = 2

Substitute this value into the first equation:

7x + 2y = 8

7(2) + 2y = 8

14 + 2y = 8

Subtract 14 from both sides:

14 - 14 + 2y = 8 - 14

2y = -6

Divide both sides by 2:

2y ÷ 2 = -6 ÷ 2

y = -3

So the coordinate set is:

(2, -3)

Hope this helps!

Answer:

-128, 512

Step-by-step explanation:

-8/2 = -4, 32/-8 = -4, so the ratio r = -4. 32*-4 = -128, -128*-4 = 512

Answer:

96ft^3 (The third option)

Step-by-step explanation:

The volume of a prism is derived by the formula length*width*height. This is also known as the base*height. The base here is 6*4, but since it's a triangle, we divide by 2 to get 12 as the base. the height is 8, so 12*8=96 ft^3. Hope this helps!

Answer:

B) (-8, -6, 1)

There are a lot of steps and I don't want to spend the time writing it all out... sorry. :')

Hope this helps :)

Answer:

Step-by-step explanation:

You want to simplify ? or just find the value ?

Answer:

The top is the inches and the bottom is the cm.

Step-by-step explanation:

I might not be correct but I hope this works

Answer:

83.3

Step-by-step explanation:

Alright so

She can write 500 words per hour

An hour is 60 minutes

500 divided by 6 (because 6x10= 60)

so you get est. 83 words per 10 mins.

To double check, do 83x6= 498, which is because the 83, is 83.3 (repeating)

Answer:

What would best describe the universal set U?

positive integers less than 10

What would best describe set A?

prime numbers in U

What would best describe A ∪ B?

numbers in U that are prime or even

What would best describe A ⋂ B?

even prime numbers in U

Hope it helps!

The universal set is the set of all natural numbers less than or equal to 9

The sets are given as:

A = {2, 3, 7, 5}

B = {2, 6, 8, 4}

Number 1 and 9 are outside the circles.

The universal set is the collection of all elements in the set.

i.e.

U = {1,2,3,4......9}

Hence, the universal set is the set of all natural numbers less than or equal to 9

We have:

A = {2, 3, 7, 5}

The elements of set A are prime numbers between 2 and 7 (inclusive)

Hence, the set A is the set of all prime numbers from 2 to 7

We have:

A = {2, 3, 7, 5}

B = {2, 6, 8, 4}

The elements of set A u B is all elements in both sets.

So, we have:

A u B = {2,3,4,5,6,7,8}

Hence, the set A u B is the set of all natural numbers from 2 to 8

We have:

A = {2, 3, 7, 5}

B = {2, 6, 8, 4}

The elements of set A n B is the common elements in both sets.

So, we have:

A n B = {2}

Hence, the set A n B is 2

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Answer:

po 989r9  vcmc cohol,j

Step-by-step explanation:

Answer:

x=17

Step-by-step explanation:

ok so since lines PR and RQ are congruent (we know because of the lines on them), that means angles P and Q are also equal.

now we can set up the equation to find x like this:

29+29+(8x-14)=180 (180 because the three angles of a triangle always equal 180)

x=17

Answer:

$3.50 for 1 bag

Step-by-step explanation:

To Find How much is for 1 bag of Doritos Divided $7.00 by 2

Which gives you 3.50

Therefore for 1 bag of Doritos = $3.50

Answer: y=9x+8

Step-by-step explanation:

y=mx+b

y=(slope)x+(y int)

just plug in

y=9x+8

slope^ ^y intercept

Answer:

Your y intercept is 1.

Step-by-step explanation:

slope is y2-y1 over x2-x1, or 2.

slope intercept formula is y=mx+b, and if you plug values into formula you get 3=2(1)+b

and if you solve that, 2x1=2, 3-2=1.

then you get 1 as your y intercept.

Answer:

11.0833333

5 1/4

5.83

11.08

Answer:

11.08

Step-by-step explanation:

Because the 3’s are repeating we don’t need to put all of them

Answer:

k = 4

Step-by-step explanation:

Calculate the slope m using the slope formula, then equate to - 1

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, k ) and (x₂, y₂ ) = (2, 0 )

m = [tex]\frac{0-k}{2-(-2)}[/tex] = [tex]\frac{-k}{2+2}[/tex] = [tex]\frac{-k}{4}[/tex] , then

[tex]\frac{-k}{4}[/tex] = - 1 ( multiply both sides by 4 )

- k = - 4 ( multiply both sides by - 1 )

k = 4