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1 year ago

a direct variation function contains the points ( -8, -6 ) and (12,9 ) . Which equation represents the function ?

Mathematics

1 answer:

9966 [12]1 year ago

8 0

Answer:

y = $\frac{3}{4}$ x

Step-by-step explanation:

Given that the quantities vary directly then the equation relating them is

y = kx ← k is the constant of variation

To find k use either of the 2 given points

Using (12, 9), that is x = 12 when y = 9, then

k = $\frac{y}{x}$ = $\frac{9}{12}$ = $\frac{3}{4}$

y = $\frac{3}{4}$ x ← equation of variation

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A dog has dug holes in diagonally-opposite corners of a rectangular yard. One length of the yard is 8 meters and the distance be

LUCKY_DIMON [66]

For a better understanding of the solution provided please go through the diagram in the file attached.

Let ABCD be the rectangular yard. The diagonal d=17 meters. AD=8 meters. Therefore, the length of DC can be found by applying the Pythagorean theorem in the right triangle $\Delta ADC$ as:

$DC=\sqrt{17^2-8^2}=\sqrt{(AC)^2-(AD)^2}=\sqrt{225} =15$ meters.

6 0

2 years ago

A mouse traveled a total distance of 3/24 of a mile in a maze over the past three hours the mouse travel the same distance each

alexgriva [62]

Answer:

Total distance mouse traveled in 3 hours = $\frac{3}{24}$ of a mile

The mouse traveled the same distance in each hour. So in order to find the distance covered in 1 hour we have to divide the distance covered in 3 hours by 3. This will give us the distance that the mouse traveled in one hour.

So, the distance traveled in one hour will be = $\frac{3}{24} \div 3 = \frac{3}{24} \times \frac{1}{3} =\frac{1}{24}$ of a mile

The error which Matt made was that he divided only the denominator of the expression by 3, this probably was a calculation error.

Correct conclusion will be: Mouse travel 1/24 of a mile each hour

8 0

2 years ago

A rectangular prism is 3 units high, 2 units wide, and 5 units long. What is its surface area

andrew11 [14]

Answer:

62 square units

Step-by-step explanation:

Surface area of a rectangular prism = 2 ( wl + hl + hw)

Where,

w = width = 2 units

h = height = 3 units

l = length = 5 units

Surface area of a rectangular prism = 2 ( wl + hl + hw)

= 2 (2*5 + 3*5 + 3*2)

= 2 (10 + 15 + 6)

= 2 (31)

= 62 square units

Surface area of the rectangular prism = 62 square units

8 0

2 years ago

Solve the following multiplication and division problems. a. 8 T. 1,398 lb. 14 oz. × 6 b. 349 lb. 6 oz. ÷ 130 c. 6 T. 294 lb. ÷

tester [92]

Answer: a) 278382 oz

b) 43 oz

c) 64.1 oz

Step-by-step explanation:

a) 8 T. 1,398 lb. 14 oz. × 6

First we need to change it in 'oz'.

As we know that

$1\ ton=32000\ oz\\\\1\ lb=16\ oz$

so, it becomes,

$8\times 32000+1398\times 16+14\ oz\\\\=278382\ oz$

8 T. 1,398 lb. 14 oz. × 6 becomes

$278382\times 6\\\\=1670292\ oz$

b) 349 lb. 6 oz. ÷ 130

It becomes,

$349\times 16+6\ oz\\\\=5590\ oz\\\\\text{ at last it becomes}\\\\=\frac{5590}{130}\\\\=43\ oz$

c) 6 T. 294 lb. ÷ 3,071

First it becomes,

$6\times 32000+294\times 16\ oz\\\\=196704\ oz$

At last it becomes,

$\frac{196704}{3071}\\\\=64.1\ oz$

Hence, a) 278382 oz

b) 43 oz

c) 64.1 oz

6 0

2 years ago

Read 2 more answers

Sarah received \$55$55dollar sign, 55 for her birthday. She used some of that money to buy 333 shirts priced at mmm dollars each

satela [25.4K]

Answer:

$(55-3m) is the amount of money she has left

Step-by-step explanation:

In this question, we are asked to give an expression to represent how much money was left after Sarah had bought some certain stuffs at some prices using the money she received at her birthday.

Firstly, we identify that the total amount of money she has to spend is $55.

Now let’s project her total spendings. She bought 3 shirts with each shirt costing $m.

The total amount spent on the shirts is thus; 3 * $m = $3m

The amount of money she has left is the difference.

Mathematically, this is equal to $55 - $3m

4 0

1 year ago

Read 2 more answers