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Natalka [10]
3 years ago
8

The measures of two complementary angles are (3y − 1)° and (4y + 7)°. Determine the value of y. (Type number only)

Mathematics
1 answer:
blondinia [14]3 years ago
5 0

Answer:

y = 12

Step-by-step explanation:

Complementary angles sum to 90 , so

3y - 1 + 4y + 7 = 90

7y + 6 = 90 ( subtract 6 from both sides )

7y = 84 ( divide both sides by 7 )

y = 12

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Which of the following equations is an example of inverse variation between the variables x and y
Sonbull [250]

Answer:

The answer is y = 6/x ⇒ answer A

Step-by-step explanation:

* Lets revise what is the meaning of the inverse variation

- It is a mathematical relationship between two variables

- It can be expressed by an equation in which the product of two

 variables is equal to a constant

- If y is in inverse variation with x

∴ y ∝ 1/x

- Change this relation to equation

∴ y = k/x, where k is the constant of the variation

- We can write it by another way

∵ y ∝ 1/x

∴ y = k/x ⇒ by using cross multiplication

∴ yx = k

* Now lets solve the problem

∵ There is an inverse variation between the two variables x and y

∴ y ∝ 1/x

∴ y = k/x

- Look to the answer

# We will chose A because

∵ y = 6/x  ⇒ use the cross multiplication

∴ yx = 6 ⇒ and 6 is a constant

∴ k = 6

* The answer is y = 6/x

5 0
3 years ago
A box with no top is to be constructed from a piece of cardboard whose length measures 12 inches more than its width. The box is
MAXImum [283]

Answer:

Width is 12 inches and height is 4 inches.

Step-by-step explanation:

Let the width of the piece of cardboard be = w inches

Then length is = w+12 inches

As given, 4 inch squares are cut from each corner;

So, the width is = w-8 inches

Length is = w+12-8=w+4 inches

When we are folding the cut portion, that gives the height as = 4 inches

The volume is given by : length x width x height

And volume is given as 256 cubic inches

So, 256=(w+4)(w-8)(4)

=> 256=(w^{2}-4w-32)4

=> 64=(w^{2}-4w-32)

=> w^{2} -4w=96

or w^{2} -4w-96=0

=> w^{2} -12w+8w-96=0

=> w(w-12)+8(w-12)=0

We get , (w+8)=0 ; w = -8(neglect the negative value)

(w-12)=0 ; w = 12 inches

And length = 12+12=24 inches

Hence, dimensions are : L = 24 inches ; w = 12 inches and h = 4 inches

We can check by putting these values in equation : 256=(w+4)(w-8)(4)

256=(12+4)(12-8)(4)

=> 256=(16)(4)(4)

=> 256=256

5 0
3 years ago
A frying pan has a radius of 14 centimeters. What is the circumference of the frying pan? Use 22 over 7 for 3.14
katen-ka-za [31]
To find the circumference calculate pi x the diameter of the circle.
Since the radius is 14, the diameter is 28. 3.14 x 28 = about 87.96
3 0
3 years ago
Chip and dale are driving in a toy engine around the Christmas tree at a speed of 300 miles/hour. how many minutes will it take
Deffense [45]

Using proportions, it is found that it will take them 0.00248548 minutes to do one loop.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, according to their speed, in 60 minutes, they drive 300 miles. In how many minutes will they drive 20 m = 0,0124274 miles?

The <em>rule of three</em> is:

60 min - 300 miles

x min - 0.0124274 miles

Applying cross multiplication:

300x = 60 \times 0.0124274

x = \frac{60 \times 0.0124274}{300}

x = 0.00248548

It will take them 0.00248548 minutes to do one loop.

More can be learned about proportions at brainly.com/question/24372153

7 0
2 years ago
Which statements can be used to justify the fact that two right angles are supplementary? Select two options.
agasfer [191]

Answer:

A right angle measures 90°.

A supplementary angle is twice the measure of a complementary angle.

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
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