All categories

2 years ago

<1 and <2 are supplementary. m<1=4x and m<2 =92 what is the value of x

Mathematics

1 answer:

monitta2 years ago

7 0

Answer:

x=22

Step-by-step explanation:

Supplementary means that the two angles that are supplementary equal 180 degrees. 180-m<2=m<1

180-92=88 (m<2=92)

m<1=88

m<1=4x

4x=88

x=22

You might be interested in

Bo and Erica are yoga instructors. Between the two of them, they teach 45 yoga classes each week. If Erica teaches 15 fewer than

Solnce55 [7]

Answer:

20 and 25.

Step-by-step explanation:

Given:

They both teach total 45 yoga classes each week.

Erica teaches 15 fewer than twice as many as Bo.

To find:

How many classes does each instructor teach per week = ?

Solution:

Let number of classes are taken by Bo = $x$

Then number of classes are taken by Erica = $2x - 15$ (given)

Total number of classes are taken by both = 45 (given)

According to the question.

$x$ + $2x - 15$ = 45

$3x - 15 = 45$

By adding both side by 15

$3x = 60\\$

By dividing both side by 3

$x = 20$

number of classes are taken by Bo = $x$ = 20

number of classes are taken by Erica = $2x - 15$

= $2\times20 - 15 = 40- 15 = 25\\$

Therefore, number of classes are taken by Bo and Erica is 20 and 25.

6 0

2 years ago

Integrate 1 - x / x(x2 + 1) d x by partial fractions.

solniwko [45]

Answer:

$log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x$

Step-by-step explanation:

step 1:- by using partial fractions

$[tex]\frac{1-x}{x(x^{2}+1) } =\frac{A(x^{2}+1)+(Bx+C)(x }{x(x^{2}+1) }$ ......(1)

step 2:-

solving on both sides

$1-x=A(x^{2} +1)+(Bx+C)x......(2)$

substitute x =0 value in equation (2)

1=A(1)+0

A=1

comparing x^2 co-efficient on both sides (in equation 2)

0 = A+B

0 = 1+B

B=-1

comparing x co-efficient on both sides (in equation 2)

-1 = C

step 3:-

substitute A,B,C values in equation (1)

now

$\\\int\limits^ {} \, \frac{1-x}{x(x^{2}+1) } d x =\int\limits^ {} \frac{1}{x} d x +\int\limits^ {} \frac{-x}{x^{2}+1 } d x -\int\limits \frac{1}{x^{2}+1 } d x$

by using integration formulas

i) by using $\int\limits \frac{1}{x} d x =log x+c........(a)\\\int\limits \frac{f^{1}(x) }{f(x)} d x= log(f(x)+c\\$ .....(b)

$\int\limits tan^{-1}x dx =\frac{1}{1+x^{2} } +C$ .....(c)

step 4:-

by using above integration formulas (a,b,and c)

we get answer is

$log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x$

6 0

2 years ago

Sally bought a car for 35000 in 2017. If the car loses 5.5% semiannually, what will the value of the value of the car be at the

kumpel [21]

The value of the year at the end of 2025 will be given by:
A=P(1+r/100)^n
where:
A=future value
P=principle
r=rate
n=number of terms
hence for the data given;
p=35000
R=5.5
n=(2025-2017)*2=16
Thus
A=35000(1+5.5/100)^16
A=$82, 434. 20

5 0

2 years ago

A bus travels two different routes: the Green Route and the Blue Route.

Alex17521 [72]

Answer:4.5

Step-by-step explanation: Check the file for my explanation