The sum of two numbers is 71. If their difference is 57, find both numbers.

There are (53)2 ⋅ 50 hens in a bird enclosure. What is the total number of hens in the enclosure?

Lisa [10]

I got 5,300. I’m not sure if that’s what you meant for “d”.

3 0

3 years ago

Read 2 more answers

Find the solution for the variable X. 2x = 12

Zina [86]

Answer:

x = 6

Step-by-step explanation:

12 / 2

= 6

2 x 6

=12

hope this was helpful! c:

4 0

3 years ago

If m∠a=47°, what is m∠b, m∠c, and m∠d? Explain how you know the measures are correct.

avanturin [10]

m ∠b = 133°, m ∠c = 47°, and m ∠d = 133°.

<h3>Further explanation</h3>

Follow the attached picture. I sincerely hope that's precisely a correct illustration.

We will use a graph of two intersecting straight lines.

Note that m ∠a and m ∠c are vertical angles. Since vertical angles share the same measures, in other words always congruent, we see $\boxed{ \ m \ \angle{c} = m \ \angle{a} \ } \rightarrow \boxed{\boxed{ \ m \ \angle{c} = 47^0 \ }}$

We continue to determine m ∠b and m ∠d.

Note that m ∠b and m ∠d represent supplementary angles. Recall that supplementary angles add up to 180°.

Let us see the following steps.

$\boxed{ \ m \ \angle{a} + m \ \angle{b} = 180^0. \ }$

$\boxed{ \ m \ 47^0 + m \ \angle{b} = 180^0. \ }$

Both sides subtracted by 47°.

$\boxed{ \ m \ \angle{b} = 180^0 - 47^0. \ }$

Thus $\boxed{\boxed{ \ m \ \angle{b} = 133^0. \ }}$

Finally, note that m ∠b and m ∠d are vertical angles. Accordingly, $\boxed{ \ m \ \angle{d} = m \ \angle{b} \ } \rightarrow \boxed{\boxed{ \ m \ \angle{d} = 133^0 \ }}$

<u>Conclusion:</u>

m ∠a = 47°
m ∠b = 133°
m ∠c = 47°
m ∠d = 133°

<u>Notes:</u>

Supplementary angles are two angles when they add up to 180°. $\boxed{ \ example: \angle{a} + \angle{b} = 180^0 \ }$
Vertical angles are the angles opposite each other when two lines cross. Note that vertical angles are always congruent, or of equal measure. $\boxed{ \ example: \angle{a} = \angle{c} \ }$

<h3>Learn more</h3>

About the measure of the central angle brainly.com/question/2115496
Undefined terms needed to define angles brainly.com/question/3717797
Find out the measures of the two angles in a right triangle brainly.com/question/4302397

Keywords: m∠a = 47°, m∠b, m∠c, and m∠d, 133°, vertical angles, supplementary, 180°, congruent

7 0

4 years ago

Read 2 more answers

The perimeter of a rectangle is 48 centimeters. The relationship between the length, the width, and the perimeter of the rectang

Evgesh-ka [11]

Answer:

The length in centimeters is (24-x) centimeters

Step-by-step explanation:

Mathematically, we are told that the equation linking the length, width and perimeter is as follows;

2(length) + 2(width) = 48

But in this case, we are told that the width is x centimeters

2(length) + 2(x) = 48

2(length) = 48-2x

length = (48-2x)/2

length = 24 - x

4 0

3 years ago

A rectangle is 5 meters longer than its width. If the length is shortened by 2 meters and width is increased by 1 meter, the are

Katarina [22]

Answer: Area = 6m²

Smaller number = 16

Hours = 9.6 h

Step-by-step explanation:

A rectangle is 5 meters longer than its width. If the length is shortened by 2 meters and width is increased by 1 meter, the area remains the same. Find the area of the rectangle.

1) w = x m 2) w = x + 1 m

l = x + 5 m l = x + 5 - 2 = x + 3 m

A₁ = A₂

A = w*l

A₁ = x(x+5) = x² + 5x

A₂ = (x+1)(x+2) = x² + x + 2x + 2 = x² + 3x + 2

A₁ = A₂

x² + 5x = x² + 3x + 2

5x - 3x = 2

2x = 2

x = 1

A₁ = x(x+5) = 1.6 = 6 m²

The ratio of two numbers is 2:5. If the larger number is 40, what is the smaller number.

5 40

5x = 80

x = 80/5 = 16

Sixteen construction workers can finish cementing a floor of a building in 3 hours. On a certain day, only 5 construction workers are available for the job. How long will it take the 5 construction workers to do the cementing job?

workers hours

16 3

5 x

↑ ↓ inversely proportional

16 x

5x = 16*3

5x = 48

x = 48/5

x = 9.6 h

6 0

3 years ago