All categories

2 years ago

An angle measures 2° less than the measure of its complementary angle. What is the measure of each angle?

Mathematics

1 answer:

Ahat [919]2 years ago

6 0

Answer:

angle: 44°

complementary angle: 46°

Step-by-step explanation:

Complementary angles have a sum of 90°. We can use this relation and the one given to write equations for the angles of interest.

<h3>setup</h3>

Let 'a' and 'c' represent the angle and its complement, respectively.

a = c -2 . . . . . an angle is 2° less than its complement

a +c = 90 . . . . complementary angles total 90°

<h3>solution</h3>

Using the first equation to substitute for 'a' in the second, we have ...

(c -2) +c = 90

2c = 92 . . . . . . add 2, collect terms

c = 46 . . . . . . . divide by 2

a = 46 -2 = 44 . . . . find 'a' using the first equation

The angle is 44°; its complement is 46°.

You might be interested in

2x^3-x^2+x-2 factorize

bekas [8.4K]

Answer:

$(x-1)(2x^2+x+2)$

Step-by-step explanation:

Factorize:

$f(x)=2x^3-x^2+x-2$

<u>Factor Theorem</u>

If f(a) = 0 for a polynomial then (x - a) is a factor of the polynomial f(x).

Substitute x = 1 into the function:

$\implies f(1)=2(1)^3-1^2+1-2=0$

Therefore, (x - 1) is a factor.

As the polynomial is cubic:

$\implies f(x)=(x-1)(ax^2+bx+c)$

Expanding the brackets:

$\implies f(x)=ax^3+bx^2+cx-ax^2-bx-c$

$\implies f(x)=ax^3+(b-a)x^2+(c-b)x-c$

Comparing coefficients with the original polynomial:

$\implies ax^3=2x^3 \implies a=2$

$\implies (b-a)x^2=-x^2 \implies b-2=-1 \implies b=1$

$\implies -c=-2 \implies c=2$

Therefore:

$\implies f(x)=(x-1)(2x^2+x+2)$

Cannot be factored any further.

4 0

2 years ago

Read 2 more answers

Someone who creates new ideas for profit is called

Airida [17]

The correct answer is D. An Entrepreneur.

I hope this helps. :)

And have a great day.

7 0

2 years ago

If a chicken lays 16 eggs every 40 days, what is the average number of eggs she lays per day?

Basile [38]

Answer:

40 / 16 = 2.5

Step-by-step explanation: ur telling me this is highschool math? lol. im in middle school but took this stuff in third grade.

5 0

2 years ago

Read 2 more answers

Unit 3, Lesson 7

aksik [14]

Answer:

Find the complete table in attached file.

Step-by-step explanation:

Find the Incomplete table in attached file

Given:

A car travels 55 miles per hour for 2 hours.

So the speed of the car 55 miles per hour is constant for 2 hours.

Using speed formula.

$Speed=\frac{distance}{time}$

Second row.

From the second row of the table $time = \frac{1}{2}=0.5\ sec$ and speed is constant $speed = 55\ mi/hr$ , so we need to find only distance.

$Speed=\frac{distance}{time}$

$55=\frac{distance}{0.5}$

$distance = 55\times 0.5$

$distance = 27.5\ mi$

Third row.

From the third row of the table $time =1\frac{1}{2}=\frac{3}{2} = 1.5\ sec$ and speed is constant $speed = 55\ mi/hr$ , so we need to find only distance.

$Speed=\frac{distance}{time}$

$55=\frac{distance}{1.5}$

$distance = 55\times 1.5$

$distance = 82.5\ mi$

Fourth row.

From the fourth row of the table $distance =110\ miles$ and speed is constant $speed = 55\ mi/hr$ , so we need to find time.

$Speed=\frac{distance}{time}$

$time=\frac{distance}{speed}$

$time=\frac{110}{55}$

$time = 2\ sec$

Therefore we complete the table from the above calculation.

8 0

3 years ago

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unkno

spin [16.1K]

The other endpoint is (1, -17).

The midpoint formula is:

$m=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Using our midpoint and endpoint, we have:
$(6, -11) = (\frac{11+x_2}{2}, \frac{-5+y_2}{2})
\\
\\6=\frac{11+x_2}{2} \text{ and } -11=\frac{-5+y_2}{2}
$

For the first equation (to find the x-coordinate) we will multiply both sides by 2:
$6\times2=\frac{11+x_2}{2}\times 2
\\
\\12=11+x_2$

Subtract 11 from both sides:
12 - 11 = 11+x₂ - 11
1 = x₂

For the second equation (the y-coordinate) we multiply both sides by 2:
$-11\times2=\frac{-5+y_2}{2}\times 2
\\
\\-22=-5+y_2$

Add 5 to both sides:
-22+5 = -5+y₂ + 5
-17 = y₂

This means that (x₂, y₂) is at (1, -17).

4 0

3 years ago