A restaurant needs to plan seating for a party of 150 people. Large tables seat 10 people and small tables
seat 6. Let x represent the number of large tables and y represent the number of small tables. The
expression 10A +6B, which represents the total number of people you can seat using a large tables and
B small tables, is called a linear combination. For instance, 150 people could be seated using 3 large
tables and 20 small tables. Use that expression to enter an equation in standard form that models all the
different combinations of tables the restaurant could use. Then identify at least one possible combination
of tables other than (3, 20).
The equation is
Another possible combination is
).

Given:

Number of passengers seated in the roller coaster = 21

Empty seats = 3

Number of cars in roller coaster = 4 (each with the same number of seats)

To find:

An equation that can be used to determine the number of seats in each car.

Solution:

Let s be the number of seats in each car.

Total number of seats in 4 cars = 4s

Using the given information,

Total number of seats = Occupied seated + Empty seats

                                   = 21 + 3

                                   = 24

Now, the required equation is

[tex]4s=24[/tex]

Therefore, the required equation is [tex]4s=24[/tex].

Divide both sides by 4.

[tex]s=\dfrac{24}{4}[/tex]

[tex]s=6[/tex]

Therefore, the number of seats in each car is 6.

The line segment congruent to line HF will be  DF. The correct option is C.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.

Given that there are three triangles and these three triangles are connected to each other at the center's A, B, and C.

The diameter of the three circles is HF, DF, and DH. The three diameters are similar in shape and are also equal to each other.

Therefore, the line segment congruent to line HF will be  DF. The correct option is C.

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Answer:

Step-by-step explanation:

Domain : Set of all possible input values (x-values) on a graph

Codomain : Set of all possible out values for the input values (y-values) on the graph

Range : Actual output values for the input values (x-values) given on the graph.

Therefore, for the given graph,

Domain : (-∞, ∞)

Codomain : (-∞, 2]  

Range : (-∞, 2]

From the given graph every input value there is a image or output value.

Therefore, the given function is onto.

Answer:

160

Step-by-step explanation:

Just add lol fjfjfjfjjd

Answer:

Step-by-step explanation:

y - 2 = 2(x - 6)

y - 2 = 2x - 12

y = 2x - 10

Answer:

Step-by-step explanation:

1) a-2b+3c

2) 2a+(6+3)²

Answer:

$225

Step-by-step explanation:

A quarter is made up of 4 months,

If auto insurance is $900 per quarter, the monthly expense would be $900 / 4 = $225

Answer:

X = - 7/2 or -6

Step-by-step explanation:

2x^2 + 19x + 40 = -2

2x^2 +19x + 40+2 = 0

2x^2 + 12x +7x+42= 0

2x(x+6) 7(x+6) =0

(2x+7) (x+6) = 0

2x+7 = 0

2x = -7

2x÷2=-7÷2

X= -7÷2 and

X+6=0

X=-6

Answer: 16,000,000 years

Step-by-step explanation:

The question already states the formula for time so

1600/0.0001= 16,000,000

Answer:

Step-by-step explanation:

(3/4)(5/8) = 15/32

Answer:

d = [tex]\sqrt{26}[/tex] or d = 5.1

Step-by-step explanation:

[tex]d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d= \sqrt{(-5-0)^2+(-1-(-2))^2}\\d= \sqrt{(-5)^2+(1)^2}\\d= \sqrt{25+1}\\d= \sqrt{26}[/tex]

Answer:

x = 0.5 or [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

7+3x-12x=3x+1

  -3x      =-3x     cross out 3x

[tex]7-12x=1[/tex]  subtract 7 on both sides

-7          =-7

[tex]-12x=-6[/tex] divide -12 into both sides

[tex]\frac{-12x}{-12} = \frac{-6}{-12}[/tex]  cross out -12 and divide -6/-12 = 0.5

To check

7+3(0.5)=8.5 - 12(0.5)=2.5

3(0.5)=1.5+1= 2.5

Answer:

x=6

Step-by-step explanation:

I hope this helps you

Answer:

32-8 + 3x = 7x

24 + 3x = 7x

Then subtract the 3x and move it to the other side

24 = 4x

Then divide both side by 4

24/4 = 4x/4

The answer is

x = 6

Answer:

Perimeter: 42cm

Area: 66cm^2

Step-by-step explanation:

Answer:

P42 cm - P26 cm = 16 cm + 13 cm = P = 26 cm

Step-by-step explanation:

Those are two rectangles. One total and deduct the missing piece.

P=2(l+w)

First: Total 12 by 9 rectangles = P42 cm

Second: Lengths = 12 -5 = 7 and 9-3 = 6 = P=26

Thirs: add the missing lengts! 7 + 6 cm

Answer:

25272 to the 10 power

Step-by-step explanation:

Answer:

-2 or -14/7 (they're the same)

Step-by-step explanation:

I hope this helps!

Answer:

Step-by-step explanation:

-3 ²/₇ - ( - ⁵/₇)

- 23 / 7  + 5 / 7

_  23 + 5

       7

_ 18

    7

- 2 ⁴/₇  

Solving for w by making w the subject of the formula, we would have: D. w = (P - 2l)/2.

To make a variable a subject of the formula, we solve for the variable.

Given the equation, P=2l + 2w, we are required to solve for w.

Thus:

P = 2l + 2w

Subtract both sides by 2l

P - 2l = 2w

Divide both sides by 2

(P - 2l)/2 = w

w = (P - 2l)/2

Therefore, solving for w by making w the subject of the formula, we would have: D. w = (P - 2l)/2.

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Answer:

-4

Step-by-step explanation:

thats the answer

Answer:

X= -4

Step-by-step explanation:

X+8=4 this is a one step equation first, you subtract 8 on both sides that gives you

x=-4

thats your answer

Answer:

√8 and √23

Step-by-step explanation:

The appropriate square root are √7 and √20.

Given that, each number graphed is the square root of a whole number that is not a perfect square.

We need to write the appropriate square root in each box.

The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.

Now, we can see the decimal numbers marked on the number line are 2.7 and 4.39.

So, 2.62²=6.8644≈7

Then the square root of number is √7

4.39²=19.2721

Then the square root of number is √20

Therefore, the appropriate square root are √7 and √20.

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Answer:

[tex]x=1[/tex]

Step-by-step explanation:

Start with:

[tex]5x+2=3x+4(2x-1)[/tex]

Distribute the [tex]4[/tex] into [tex](2x-1)[/tex]:

[tex]5x+2=3x+8x-4[/tex]

Combine like terms:

[tex]5x+2=11x-4[/tex]

Add [tex]4[/tex] to both sides of the equation:

[tex]5x+6=11x[/tex]

Subtract [tex]5x[/tex] from both sides of the equation:

[tex]6=6x[/tex]

Divide both sides of the equation by the coefficient of [tex]x[/tex], which is [tex]6[/tex]:

[tex]1=x[/tex]

or

[tex]x=1[/tex]

Answer:

see explanation

Step-by-step explanation:

Given the points (a, c ) and (b, c )

Since the y- coordinates are equal the distance formula simplifies to

d = [tex]\sqrt{(x_{2}-x_{1})^2 }[/tex]

with x₁ = a and x₂ = b

d = [tex]\sqrt{(b-a)^2}[/tex] = b- a

Answer:

work is attached and shown

The coordinates of the midpoint will be (4,5).

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

A midpoint is a point that lies on a line connecting two other locations and is in the middle of the line. Given that the midpoint of AB is M(-2,2) and the coordinates of A are (-8, -1).

The midpoint will be calculated by using the formula below:-

( -8 + x ) / 2 = -2

( -8 + x ) = -4

x = -4 + 8 = 4

( -1 + y ) / 2 = 2

( -1 + y ) = 4 = 1 + 4 = 5

Therefore, the coordinates of the midpoint will be (4,5).

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Answer:

a = 1

Step-by-step explanation:

Step 1: Write equation

a - 2(4 - a) = 7a - 12

Step 2: Solve for a

Distribute -2: a - 8 + 2a = 7a - 12

Combine like terms: 3a - 8 = 7a - 12

Subtract 3a on both sides: -8 = 4a - 12

Add 12 on both sides: 4 = 4a

Divide both sides by 4: a = 1

Step 3: Check

Plug in x to verify if it's a solution.

1 - 2(4 - 1) = 7(1) - 12

1 - 2(3) = 7 - 12

1 - 6 = -5

-5 = -5

Answer:

Step-by-step explanation:

equation given:   a - 2(4 - a) = 7a - 12

distribute and expand the equation

a - 8 + 2a = 7a - 12

combine similar terms:

a + 2a - 7a = -12 + 8

simplify:

-4a = -4

a = -4 / -4

proof that a = 1

a - 2(4 - a) = 7a - 12

1 - 2(4 - 1) = 7(1) - 12

1 - 2(3) = 7 - 12

1 - 6 = -5

-5 = -5  therefore, the a = 1 is correct.

Answer:

3/7

Step-by-step explanation:

Answer:

D

Step-by-step explanation: