Solve By Substitution

The senior classes at High School A and High School B planned separate trips to the water park. The senior class
at High School A rented and filled 14 vans and 16 busses with 1086 students. High School Brented and filled 10
vans and 13 busses with 870 students. Every van had the same number of students in it as did the busses. Find
the number of students in each van and in each bus.​

Answer:

√2 or 1.414

Step-by-step explanation:

the distance between two points

Answer:

No.

Step-by-step explanation:

1/4 is equivalent to 2/8, but not with 1/8.

Answer:

No.

Step-by-step explanation:

To find equivalent fractions, multiply the numerator and denominator by the same number.

Start with 1/4.

Multiply the numerator and denominator by 2.

You get 2/8.

2/8 is an equivalent fraction to 1/4.

2/8 and 1/8 are not equivalent.

Answer: No.

Answer:

Okay, here's the method I'm going to use.

If you drive north 6 miles, and then drive east 19 miles, you are technically making a triangle.

                    19 miles

           l_______________

6 milesl

           l

You are just missing the last side of the triangle: the straight line stretching from across your starting point to the ending point. You can find this by using the Pythagorean theorem.

a^2 + b^2 = c^2

6^2 + 19^2 = c^2

36 + 361 = c

397 = c

[tex]\sqrt{397}[/tex] = 19.924859

Rounded to the nearest tenth, your answer is

19.9 miles

Answer:

75

Step-by-step explanation:

an arc is half a circle

Answer: 3/4 of a mile

Step-by-step explanation:

Answer:

1.844

Step-by-step explanation:

easyy

Answer:

17=x

Step-by-step explanation:

In this case, we need to use Vertical Angles Theorem to solve this problem. Basically, because of the position of the angles, they are congruent.

68-x = 3x

Add x to both sides

68=4x

Divide by 4

17=x

Hope this helps!

Answer:

The value of 'x' is: 17°

Step-by-step explanation:

From what is being shown, there are two angles that are given:

(68 - x)°

3x°

Since they are congruent angles, meaning they are equal to each other, they will be put into a(n) equation such like shown below:

(68 - x)° = 3x°

(Then remove the parenthesis)

68° - x° = 3x°

     + x°=+3x°

------------------

68° = 4x°

------------------

(Divide both sides by 4)

[tex]\frac{68}{4} = \frac{4x}{4}[/tex]

------------------

17° = x

------------------

Your value of 'x' is 17.

Answer:

Step-by-step explanation:

y-y1 = m (x-x1), where (x1,y1) is the point the line passes through and m is the slope

y-(-1) = 2 (x-3)

y+1 = 2x - 6

Step-by-step explanation:

Find the slopes of the lines and compare. The lines intersect if slopes are different.

Slopes are

Slopes are same, lines are parallel

Slopes are

Lines intersect as slopes are different

Slopes must not be equal to get intersection

#1

For first line

For second

No,Parallel

#2

First

Second

Yes, Intersect

Answer:

235 miles per hour and 2,115 miles in 9 hours

Step-by-step explanation:

First determine how many miles the jet files in one hour:

470/2 =235 miles/hour

We want to know how many hours the jet could fly in 9 hours, so we multiply this value by 9.

235 x 9 = 2115 miles

Therefore, the jet could fly 2115 miles in 9 hours.

Answer:

1000 tiles required.

explanation:

Tiles dimension:

Floor dimension:

Area of floor:

Length * Width

50 * 40

2000 m²

Area of each tile:

Length * Width

1 * 2

2 m²

Number of tiles required = Area of floor ÷ Area of each tile

→ tiles = 2000/2

→ tiles = 1000

See below.

1000

area of rectangle = width x length

Given: width of floor = 40 m length of floor = 50 m ⇒ area of floor = 40 x 50 = 2000 m²

width of tile = 1 m length of tile = 2 m ⇒ area of tile = 1 x 2 = 2 m² Number of tiles needed = area of floor ÷ area of one tile                                        = 2000 ÷ 2                                        = 1000

I tried.

Answer:

m∠JTS = 104° ⇒ (A)

Step-by-step explanation:

The measure of an exterior angle of a triangle at one of its vertices equals the sum of the measures of the opposite interior angles.

Let us use this fact to solve the question

In ΔTSR

∵ T ∈ ray RJ

∴ ∠JTS is an exterior angle of ΔTSR

→ By using the fact above

∴ ∠TSR and ∠TRS are the opposite interior angles to ∠JTS

∴ m∠JTS = m∠TSR + m∠TRS

∵ m∠JTS = 27x - 4

∵ m∠ TSR = 30°

∵ m∠TRS = 18x + 2

→ Substitute their values in the equation above

∴ 27x - 4 = 30 + 18x + 2

→ Add the like terms in the right side

∴ 27x - 4 = 18x + 32

→ Add 4 to both sides

∴ 27x = 18x + 36

→ Subtract 18x from both sides

∴ 9x = 36

→ Divide both sides by 9

∴ x = 4

→ To find m∠JTS substitute x by 4 in its measure

∴ m∠JTS = 27(4) - 4 = 108 - 4

∴ m∠JTS = 104°

Area of triangle = 1/2 x base x height

Area of the triangle = 1/2 x 22 x 18 = 198 square m.

Area of semi circle = 1/2 x PI x r^2

Area of semi circle = 1/2 x 3.14 x 11^2 = 189.97 square m.

Total area = 198 + 189.97 = 387.97 square m.

Round up to 388 square m.

So first we have to find equation form angles.

Statement :- The measure of the second angle of a triangle is 20 more than the measure of the first.

Equation :-

second angle = 20 + x

{ Remember people get's confused when to multiply and when to add. when ever there "more than" then we will add and when there is ,"times" we will multiply}

Statement :-

the third angle is 10 less than three times the first

Now just see first less means we have to subtract 10 from 3 times the first means 3 × first angle.

Equation :-

third angle = 3x - 10

Now let's represent :-

We know sum of angles of triangle is equal to 180°

So :-

Measure of angles :-

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

Let the first angle be x

According to the question,

[ 2nd angle is 20 more than the first angle ]

[ 3rd angle is 10 less than thrice times the first angle ]

By using Angle sum property

That is,

[tex]\sf{ x + ( x + 20) + ( 3x - 10) = 180{\degree}}[/tex]

[tex]\sf{ x + x + 20 + 3x - 10 = 180{\degree}}[/tex]

[tex]\sf{ 5x + 10 = 180{\degree}}[/tex]

[tex]\sf{ 5x = 180 - 10}[/tex]

[tex]\sf{ 5x = 170}[/tex]

[tex]\sf{ x = }{\sf{\dfrac{ 170}{5}}}[/tex]

[tex]\sf{ x = }{\sf{\cancel{\dfrac{ 170}{5}}}}[/tex]

[tex]\bold{ x = 34{\degree}}[/tex]

Thus,

Hence, The three angles of the given triangle are 34° , 54° and 92°

[tex]\bold{\huge{\underline{ Verification }}}[/tex]

Here, we have

By using Angle sum property :-

[tex]\sf{ 34 + 54 + 92 = 180{\degree}}[/tex]

[tex]\sf{ 88 + 92 = 180{\degree}}[/tex]

[tex]\sf{ 180 = 180{\degree}}[/tex]

[tex]\bold{ LHS = RHS }[/tex]

Hence, Verified

Answer:

Step-by-step explanation:

Very simple, if the total was $12.65, and they included a 15% tip, so we do 12.65 *15%=1.8975

So we subtract that by 12.65 and our answer is approximately $10.75

Answer:

The Correct Answer Is : 11

Step-by-step explanation:

I Just Took The Test

Answer: 2+(-3/5) = 1.4

Step-by-step explanation: Remember work what is in the parentheses first!

Simplify the expression.

Exact Form: 7/4

Decimal Form: 1.4

Mixed Number Form: 1 2/5

Answer:

[tex]\frac{7}{5}[/tex]

Step-by-step explanation:

Equation: [tex]2-\frac{3}{5}[/tex]

1). Convert to fraction: [tex]\frac{2*5}{5}-\frac{3}{5}[/tex]

2). Same denominators = combine fractions

[tex]\frac{(2*5)-3}{5}=\frac{7}{5}[/tex]

hope this helps! sorry if it didnt

Answer:

[tex]\mathsf{\cos T=\dfrac{28}{53}}[/tex]

Step-by-step explanation:

[tex]\mathsf{\cos(\theta)=\dfrac{adjacent\ side}{hypotenuse}}[/tex]

[tex]\implies \mathsf{\cos T=\dfrac{28}{53}}[/tex]

Answer:

The answer is C.

Check the picture below, so the shaded area is really just the area of one quarter of a circle's area with a radius of 7, and a triangle whose base is 7 and height is 7, so let's simply sum both of them up.

[tex]\stackrel{\textit{\Large Areas}}{\stackrel{\textit{quarter of a circle}}{\cfrac{1}{4}(\pi)(7)^2}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(7)(7)}}\implies \cfrac{49\pi }{4}~~ + ~~\cfrac{49}{2}~~ \approx~~63.0[/tex]

Answer:

where's the question?

Step-by-step explanation:

carry on laern

Rate = distance / time

Rate = 21 miles / 3 hours

Rate = 7 miles / hour

The answer is choice A. Hope this helps.

The length of a rectangle is 5 more than twice the width. If the perimeter of the rectangle is 34 cm find the length?

In this question we are provided with the perimeter of the rectangle = 34 cm and it is given that the length of the rectangle is 5 more than the twice it's breadth and asked to find out the length of the rectangle.

[tex] \small \orange{ \underline{\rm \blue{length \: of \: a \: rectangle \: is \: 5 \: more \: than \: twice \: the \: width.}}}[/tex]

Let us assume breadth as x then length = 2x +5

We know,

[tex] \star \: \large\boxed{ \rm{ Perimeter_{(rectangle)} = 2(length + breadth)}}[/tex]

Substituting the values we get

34 = 2(2x +5 + x)

→ 34 = 2(3x + 5)

→ 34 = 6x + 10

→ 34 - 10 = 6x

→ 24 = 6x

→ [tex]\dfrac{24}{6}[/tex] = x

x = 4

Length = 2x + 5 = 2 × 4 + 5 = 8 + 5 = 13 cm

Breadth = x = 4cm

Length = 13 cm.

Given:

A race car game takes 6 points from a player each time the player hits a cone.

To find:

The integer which represents the change in total points if the player hits 10 cones.

Solution:

According to the given information,

1 hit = -6 points

Here, negative sign represents the reduction in points after hitting a cone.

If the player hits 10 cones.

(1 × 10) hit = (-6 × 10) points

10 hit = -60 points

So, the change in total points if the player hits 10 cones is -60.

Therefore, the required integer is -60.

Answer: 60

Step-by-step explanation:

based on the given conditions, formulate: 

 Calculate the product or quotient: 60

get the result Answer: 60

Good luck

Answer:

9

Step-by-step explanation:

5, 8, 9, 9, 9, 10

(9+9)/2=9

Answer:

3n

5,10,8,9,9,9

= 5 , 1 , 0

5-1=4 - 1 3

Answer:

d multiplication ‌ ‌ ‌ ‌ ‌

Answer: D. Subtraction property of equality

Step-by-step explanation:

They are subtracting 6 from both sides of the equality.