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3 years ago

8

Given thatx x=time (hours) and y=distance (miles),find the rate of change: (2,70) (5,175)

1 answer:

djverab [1.8K]3 years ago

3 0

The rate of change is 72

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What type of solution does 11x - 2 + 15 = 8 + 7 + 9x have?

sergiy2304 [10]

Given equation is : 11x - 2 + 15 = 8 + 7 + 9x

Solving this by grouping like terms on one side.

$11x-9x=8+7-15+2$

$2x=17-15$

$2x=2$

$x=1$

Hence, this equation has one solution.

4 0

2 years ago

What does "of" mean in a persent question

kykrilka [37]

Answer:

existing or occurring now

7 0

3 years ago

THe question asked what is 0.35 written as a ratio?

Masja [62]

Step 1: 0.35 = 35⁄100
Step 2: Simplify 35⁄100 = 7⁄20
answer: 7/20

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3 years ago

The hypotenuse of a right triangle is 1 centimeter longer than one side and 4 centimeters longer than three times the other side

snow_tiger [21]

Answer:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

Step-by-step explanation:

Represent:

The opposite with a
The adjacent with b
The hypotenuse with c

Given that:

$c = 1 + a$

$c = 4 + 3b$

Required

Solve for a, b and c

$c = c$

So, we have:

$1 + a = 4 + 3b$

Subtract 1 from both sides

$a = 4 -1 + 3b$

$a = 3 + 3b$

Apply Pythagoras Theorem

$c^2 = a^2 + b^2$

Substitute 3 + 3b for a and 4 + 3b for c

$(4 + 3b)^2 = (3 + 3b)^2 + b^2$

Open brackets

$16 + 12b+12b+9b^2 = 9 + 9b+9b+9b^2 +b^2$

$16 + 24b+9b^2 = 9 + 18b+10b^2$

Collect Like Terms

$10b^2 - 9b^2 + 18b - 24b + 9 - 16 = 0$

$b^2 - 6b -7 = 0$

Expand

$b^2 +b-7b-7=0$

Factorize:

$b(b+1)-7(b+1) =0$

$(b-7)(b+1) = 0$

Split:

$b - 7 = 0\ or\ b+1=0$

$b = 7\ or\ b=-1$

But the adjacent of a triangle can't have a negative measurement.

So:

$b = 7$

Recall that:

$c = 4 + 3b$

$a = 3 + 3b$

Substitute 7 for b in the above expressions

$c = 4 + 3 * 7$

$c = 4 + 21$

$c = 25$

$a = 3 + 3 * 7$

$a = 3 + 21$

$a = 24$

Hence, the dimensions of the triangle are:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

5 0

2 years ago

If a logo of 6 ft and he needs a quart of paint for every 22 square ft how many quarte will he need for the whole logo

bulgar [2K]

Complete Question

If a logo has dimensions of 6 ft and 11ft, he needs a quart of paint for every 22 square ft. How many quarts will he need for the whole logo?

Answer:

3 quarts of paint

Step-by-step explanation:

The Logo is rectangular in shape, hence:

The area of a rectangle = Length × Width

The logo has dimensions of 6 ft and 11ft.

Area of the Logo = 6ft × 11ft = 66ft²

He needs a quart of paint for every 22 square ft

Hence:

22 ft² = 1 quart of paint

66ft² = x

Cross Multiply

22 ft² × x = 66 ft² × 1 quart

x = 66 ft² × 1 quart/22 ft²

x = 3 quarts of paint

Therefore, he will need 3 quarts of paint for the whole logo.

7 0

2 years ago