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1 year ago

The sum of five consecutive positive integers is 2020. Find the largets of these numbers.

Mathematics

1 answer:

Alona [7]1 year ago

4 0

Answer:

406

Step-by-step explanation:

let the 5 consecutive positive integers be

n , n + 1 , n + 2 , n + 3 , n + 4 , then

n + n + 1 + n + 2 + n + 3 + n + 4 = 2020

5n + 10 = 2020 ( subtract 10 from both sides )

5n = 2010 ( divide both sides by 5 )

n = 402

then

largest integer = n + 4 = 402 + 4 = 406

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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

3 years ago

Read 2 more answers

If f(x)=3x+2,find f(f^-1(14)).

lisov135 [29]

Answer: 14

<u>Step-by-step explanation:</u>

f(x) = 3x + 2

To find f⁻¹, swap the x's and y's and solve for y --> Note: f(x) is y

x = 3y + 2

x - 2 = 3y

$\dfrac{x-2}{3}=y$

$\implies f^{-1}(x)=\dfrac{x-2}{3}$

$\implies f^{-1}(14)=\dfrac{14-2}{3}$

$\implies f^{-1}(14)=\dfrac{12}{3}$

$\implies f^{-1}(14)=4$

f(f⁻¹(14)) = f(4)

f(4) = 3(4) + 2

= 12 + 2

= 14

NOTE: the simplified version is .... f and f⁻¹ cancel out, leaving you with 14

4 0

3 years ago

What is the sum of 21 and 5 times a number f is 61

sukhopar [10]

Answer:

Answer is below

Step-by-step explanation:

21 + 5f = 61 Turn the words into an equation

-21 - 21 Subtract 21 from both sides

5f = 40 Divide both sides by 5

f = 8

If this answer is correct, please make me Brainliest!

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2 years ago

Read 2 more answers

Are lines of symmetry also diagonals in a polygon? Explain.

Vaselesa [24]

Well not all lines are lines of symmerty, because if you draw a let's say a rectangle on a piece of paper and draw a diagonal line through it, well the two sides don't really lie perfectly on one another!!

3 0

2 years ago

Can u pls help I don’t understand I’ll give u 15 points

Juliette [100K]

Answer: $\frac{4}{3}$

Step-by-step explanation:

This is a multiplication problem. You are multiplying $\frac{1}{3}$ by 4. This also means 4 divided by 3. They are both the same.

4 0

3 years ago