MATHEMATICS MIDDLE SCHOOL

A truck can be rented from Company A for ​$80 a day plus ​$0.30 per mile. Company B charges ​$20 a day plus ​$0.50 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same

Answers

Answer 1
Answer:

Write equations for both companies:

Company A = 80 + 0.30x

Company B = 20 + 0.50x

X = number of miles.

Set the equations to equal and solve for x:


80 + 0.30x = 20 + 0.50x

Subtract 0.30x from both sides:

80 = 20 + 0.20x

Subtract 20 from both sides:

60 = 0.20x

Divide both sides by 0.20:

x = 60 / 0.20

x = 300


The answer is 300 miles.

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Math homework help (99 pt)

Answers

This implies that there will be infinitely many solutions. If you plug in any value for a, you will end up with an equation that is true.

For example, let's plug in a = 0.

(0-3)/(2) = (0-3)/(2) \n\n \boxed{\bf{(-3)/(2) = (-3)/(2) }}

We can even plug a bigger number like a = 100, and it will still work. That is because it has infinitely many solutions. It's like if you have an equation like:
x = x
Any value of x will equal to x. There are infinitely many solutions to it.

(101-3)/(2) = (101-3)/(2) \n\n (98)/(2) =(98)/(2)\n\n \boxed{\bf{49 =9 }}

Your final answer is infinitely many solutions.

Answer:

-6

Step-by-step explanation:

Find the surface area of the cylinder. Round your answer to the nearest tenth. (Open attachment to see image of the cylinder).

Answers

formula: SA = (2 × π(pie) × radius × height) + (2 × π(pie) × radius square.)
So the equation will be SA=( 2 × 3.14 × 2 × 4) + ( 2 × 3.14 × 2²)
Then, we will get                                     ↓                            ↓
                                           SA=      50.24               +         25.12
                                           SA =                   75.36 in²

Which is equivalent to (4xy – 3z)2, and what type of special product is it?16x2y2 + 9z2, the difference of squares

16x2y2 + 9z2, a perfect square trinomial

16x2y2 – 24xyz + 9z2, the difference of squares

16x2y2 – 24xyz + 9z2, a perfect square trinomial

Answers

Answer:

16x^2y^2-24xyz+9z^2

It is a perfect square trinomial.

Step-by-step explanation:

The given expression is (4xy-3z)^2

We can use the formula (a-b)^=a^2-2ab+b^2

Here, we have

a = 4xy, b = 3z

Using the formula, we have

(4xy-3z)^2\n=(4xy)^2-2(4xy)(3z)+(3z)^2\n\n16x^2y^2-24xyz+9z^2

Therefore, the equivalent expression is 16x^2y^2-24xyz+9z^2

It is a perfect square trinomial.
(4xy-3z)^(2) =(4xy)^(2) -2(4xy)(3z)+ (3z)^(2) =16 x^(2) y^(2) -24xyz+9 z^(2)
The type of special product is 'a perfect square trinomial'.

A triangular window is above the door to a cafe. The base of the window is 12 ft, and the height is 10 ft. What is the area of the window?

Answers

1/2 × 12 × 10

= 6 × 10

= 60 square feet

Hope this helps!
120 ft.

Hope that helped :)

Students in Miss Moseley's fourth grade class are learning multiplication, and they demonstrate mastery by passing assessments. Travis has passed 11 tests, and his classmate, Jenifer, has passed 2 tests. Going forward, Travis plans to pass 2 tests per week. Meanwhile, Jenifer plans to pass 5 tests per week. Eventually Jenifer will catch up to Travis. When the number of tests each student has passed are equal, how many tests will each student have passed and how many weeks will it take?

Answers

Answer:
Each will have passed 17 tests and it will take 3 weeks.

Explanation:
Let x be the number of weeks.
The number of tests Travis passes to begin with is 11.
We then add 2 tests per week, or 2x to that, giving us:
11+2x.

The number of tests Jenifer has passed to begin with is 2.
We then add 5 tests per week, or 5x to that, giving us:
2+5x.

Setting these equal, we have:
11+2x=2+5x.

Subtract 2x from each side:
11+2x-2x=2+5x-2x;
11=2+3x.

Subtract 2 from each side:
11-2=2+3x-2;
9=3x.

Divide both sides by 3:
(9)/(3) = (3x)/(3);
3=x.

It will take 3 weeks.
In 3 weeks,
Travis will have passed:
11+2*3 = 11+6 = 17 tests.
Jenifer will have passed the same number, since she catches up with him at this point.

Answer:

Each will pass 17 test after 3 weeks.

Step-by-step explanation:

Consider the provided information,

Let x is the number of weeks.

Travis has passed 11 tests and plans to pass 2 tests per week.

11+2x

Jenifer, has passed 2 tests and plans to pass 5 tests per week.

2+5x

Now equate them as shown.

11+2x=2+5x

11-2=5x-2x

9=3x

x=3

Hence, after 3 weeks both have passed the same number of test.

Substitute x=3 in 11+2x

11+2(3)=17

Hence, each will pass 17 test after 3 weeks.

Given: ∠H and ∠X are supplementary. Prove: l || n

Answers

I won't write out a formal proof; here's an outline.

H+X=180.  definition of supplementary
H+F=180   crossing lines
X=F           supplements of the same angle are equal, or just algebra          
l || n          When the alternate angles of a transverse line between two lines are congruent, the lines are parallel
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