Find the length of the unknown side of the triangle.
The length of the unknown side of the triangle is​

Answer:

  a² = b² -w² +2wx

Step-by-step explanation:

The algebra is pretty straightforward. Expand the expression in parentheses and add x².

  b² -(w -x)² = e² = a² -x²

  b² -(w² -2wx +x²) = a² -x² . . . . . expand the square

  b² -w² +2wx -x² = a² -x² . . . . . . distribute the minus sign

  b² -w² +2wx = a² . . . . . . . . . . . . add x²

Answer:

-3, 0, 3

Step-by-step explanation:

Given, [tex] y = -\frac{4}{3}x + 2 [/tex], the set of x values that will make Kayda not to get y values that are not fraction are -3, 0, 3.

This is so, because,

when x = -3, [tex] y = -\frac{4}{3}(-3) + 2 = \frac{12}{3} + 2 = 4 + 2 = 6 [/tex]

when x = 0, [tex] y = -\frac{4}{3}(0) + 2 = -0 + 2 = 2 [/tex]

when x = 3, [tex] y = -\frac{4}{3}(3) + 2 = \frac{-12}{3} + 2 = -4 + 2 = -2 [/tex]

The correct response is -3, 0, 3

Answer:

D

Step-by-step explanation:

If the number is positive, the absolute value is the same as the number. If the number is negative, the absolute value is just a positive version of that number. So the absolute value of 0 is 0, -18 is 18, -31 is 31, and -44 is 44. Out if these, D has the greatest absolute value, so it would be D

Answer:

D. -44.

Step-by-step explanation:

Absolute value of -44:

= |-44| = 44

Answer:

34

Step-by-step explanation:

The dead bodies are still in the room.

Answer:

9.5

Step-by-step explanation:

5/(a+3)=3/(a-2)

5(a-2)=3(a+3)

5a-10=3a+9

5a-3a=9+10

2a=19

a=9.5

M

Answer:

a)

{FVVV,FFVV,VFVV,VVVV,FVFV,FFFV,VFFV,VVFV,FVVF,FFVF,VFVF,VVVF,FVFF,FFFF,VFFF,VVFF}

b)

{FFFV,FFVF,FVFF,VFFF}

c)

{FFFF,VVVV}

d)

{FFFV,FFVF,FVFF,FFFF,VFFF}

e)

{FFFV,FFVF,FVFF,FFFF,VFFF,VVVV}

{FFFF}

f)

{FFFV,FFVF,FVFF,VFFF,FFFF,VVVV}

{ }

Step-by-step explanation:

a)

The 16 outcomes for a sample of four home mortgages classified as fixed and variable rate are

Sr.No Outcomes

1          FVVV

2         FFVV

3         VFVV

4         VVVV

5         FVFV

6         FFFV

7         VFFV

8         VVFV

9         FVVF

10        FFVF

11         VFVF

12        VVVF

13        FVFF

14        FFFF

15        VFFF

16        VVFF

b)

Let A be the event that exactly three are fixed rate. Thus, event A consists of following outcomes

A={FFFV,FFVF,FVFF,VFFF}

c)

Let B be the event that all four are of same type. The event B consists of either all fixed rate or all variable rate. Thus, event B consists of following outcomes

B={FFFF,VVVV}

d)

Let C be the event that at most one of four is variable rate. The event C consists of less than and equal to one variable rate. Thus, event C consists of following outcomes

C={FFFV,FFVF,FVFF,FFFF,VFFF}

e)

Let union of part(c) and part(d) can be represented as BUC. The union represents all the outcomes in event B and event C.

B∪C={FFFF,VVVV}∪{FFFV,FFVF,FVFF,FFFF,VFFF}

B∪C={FFFV,FFVF,FVFF,FFFF,VFFF,VVVV}

Let intersection of part(c) and part(d) can be represented as B∩C. The intersection represents the common outcomes in event B and event C.

B∩C={FFFF,VVVV}∩{FFFV,FFVF,FVFF,FFFF,VFFF}

B∩C={FFFF}

f)

Let union of part(b) and part(c) can be represented as AUB. The union represents all the outcomes in event A and event B.

A∪B={FFFV,FFVF,FVFF,VFFF}∪{FFFF,VVVV}

A∪B={FFFV,FFVF,FVFF,VFFF,FFFF,VVVV}

Let intersection of part(b) and part(c) can be represented as A∩B. The intersection represents the common outcomes in event A and event B.

A∩B={FFFV,FFVF,FVFF,VFFF}∩{FFFF,VVVV}

A∩B={ }

So intersection of part(b) and part(c) is an empty set as there is no common outcome in these two sets.

Sample of four homes.

The sample of 4 homes is on a mortgage and has been classified as a fixed rate of F and a variable rate of V. The mortgage is thus an agreement between the lender of the money and the borrower. The lender has the right to take away the property.

Thus answer is given below.

Learn more about the sample of four homes.

brainly.com/question/14565659.

Answer:

point B

Step-by-step explanation:

the lines intersect at that point

Answer:

  33, 11, 24 feet

Step-by-step explanation:

Let s represent the length of the second side. Then the length of the first side is 3s and the length of the third side is s+13. The perimeter is the sum of side lengths:

  (3s) +(s) +(s +13) = 68

  5s = 55 . . . . . subtract 13

  s = 11 . . . . . . . divide by 5

The side lengths are ...

  33, 11, 24 feet

Answer:

2²⁰ bytes

Step-by-step explanation:

Given

[tex]Phone\ Storage = 2^{20}\ bytes[/tex]

[tex]App\ Storage = 4^4\ megabytes[/tex] of phone storage space

Required

Determine the storage space of the app in bytes

To answer this, we simply multiply the app storage by the phone storage

This gives:

[tex]Total = 2^{20} * 4 ^4[/tex]

Express 4 as 2²

[tex]Total = 2^{20} * 2^2^* ^4[/tex]

[tex]Total = 2^{20} * 2^8[/tex]

Apply Laws of Indices

[tex]Total = 2^{20+8}[/tex]

[tex]Total = 2^{28}[/tex]

Hence, the storage space of the app is 2²⁰ bytes

Answer:

$34,230

Step-by-step explanation:

Total Salary = Base Salary + Increase

Total Salary = 32600 + (32600)(0.05)

Total Salary = $34,230

I hope I helped you

Step-by-step explanation:

First you solve: 25:5=?

After: the number you find×8=?

And:?+5=?

The number -2

Answer:

0.3

Step-by-step explanation:

There are:

Total marbles:

Then:

Answer is: the probability of not draw a blue marble is 0.3

Answer:

10x

Step-by-step explanation:

3x + 7x

= 10x

Answer:

Your process is indeed correct!

The full solution is:

[tex]\displaystyle \int\frac{\sin ^3 x}{\sqrt{\cos x}}\, dx= \frac{2}{5} \cos^{{}^{5}\!/\!{}_{2}} x - 2\cos ^{{}^{1}\!/\!{}_{2}}x + C[/tex]

Step-by-step explanation:

We want to evaluate the integral:

[tex]\displaystyle \int \frac{\sin^3(x)}{\sqrt{\cos(x)}}\, dx[/tex]

As you had done, we can rewrite our integral as:

[tex]\displaystyle =\int \frac{\sin(x)(\sin^2(x))}{\sqrt{\cos(x)}}\, dx[/tex]

Using the Pythagorean Identity, this is:

[tex]\displaystyle =\int \frac{\sin(x)(1-\cos^2(x))}{\sqrt{\cos(x)}}\, dx[/tex]

Now, we can make a substitution. Let u = cos(x). Then:

[tex]\displaystyle du = - \sin x \, dx[/tex]

Substitute:

[tex]\displaystyle = \int\frac{1-u^2}{\sqrt{u}} \, \left(- du\right)[/tex]

Simplify:

[tex]\displaystyle = -\int \frac{1}{\sqrt{u}} - \frac{u^2}{\sqrt{u}}\, du[/tex]

Rewrite:

[tex]\displaystyle = -\int u^{{}^{-1}\!/\!{}_{2}} - u^{{}^{3}\!/\!{}_{2}}\, du[/tex]

By the Reverse Power Rule:

[tex]\displaystyle = -\left(2u^{{}^{1}\!/\!{}_{2}} - \frac{2}{5} u^{{}^{5}\!/\!{}_{2}}\right) + C[/tex]

Simplify:

[tex]\displaystyle = \frac{2}{5} u^{{}^{5}\!/\!{}_{2}}-2u^{{}^{1}\!/\!{}_{2}} + C[/tex]

Back-substitute:

[tex]\displaystyle = \frac{2}{5} \cos^{{}^{5}\!/\!{}_{2}} x - 2\cos ^{{}^{1}\!/\!{}_{2}}x + C[/tex]

Answer:

=  - 2 [tex]\sqrt{cos(x)}[/tex] + 2 cos⁵/₂ (x)  + C

                          5

Step-by-step explanation:

∫ sin³ (x)    dx

  [tex]\sqrt{cos(x)}[/tex]

= ∫ sin² (x) sin (x)    dx

   [tex]\sqrt{cos(x)}[/tex]

= ∫ (1 - cos² (x) sin (x)  dx

   [tex]\sqrt{cos(x)}[/tex]

= ∫ - 1 - u²   du

        √u

= ∫ -   1    +  u³/₂   du

        √u

= - ∫   1    du  +  ∫ u³/₂   du

        √u

substitute it back

=  - 2 √u + 2 cos⁵/₂ (x)

                 5

add constant, therefore

=  - 2 [tex]\sqrt{cos(x)}[/tex] + 2 cos⁵/₂ (x)  + C

                         5

Answer:

y = 8x-40

Step-by-step explanation:

The slope intercept form of a line is

y= mx+b  where m is the slope and b is the y intercept

We know the slope is 8 and the x intercept is 5 ( 5,0)

y = 8x +b

Substitute the point into the equation

0 = 8(5)+b

0 = 40+b

b=-40

The equation is

y = 8x-40

Answer:

if its fractions then 1/4 if its percentage then 25%

Step-by-step explanation:

Answer:

4 1/8hours ÷ 2 3/4

Step-by-step explanation:

Answer:

y= -1/2(x) +8

gradient= -1/2

Intercept= 8

Step-by-step explanation:

Let's transform the equation to y -intercept form first

6x - 3y - 15= 0

-3y= -6x+15

Y= -6/-3(x) +(15/-3)

Y= 2x -5

Intercept c= -5

Gradient m =2

Rule of perpendicularity

mm'= -1

m'= -1/m

m' = -1/2

Equation of line of the point (4, 6)

(Y-Y1)/(x-x1)=m'

(Y-6)/(x-4)= -1/2

2(y-6)= -1(x-4)

2y -12 = -x +4

2y= -x +4+12

2y= -x+16

y= -1/2(x) +8

gradient= -1/2

Intercept= 8

Answer: x=4

Step-by-step explanation:

 -8-x=x-4x

  -8-x=-3x

-x+3x=8

    2x=8

      x=4

Answer:

he would need about 16 weeks

Answer:

1-72: Estimate- 15 weeks

        Actual- $125/$7.75= 16.13 weeks.

1-73: 3 feet long=36 inch board

        6 feet long=72 inch board

        12 feet long = 144 inch board

1-74: a. 100, 50, 60, 40, 20, 0

        b. 75, 60, 45, 30, 15, 0

        c. 125, 100, 75, 50, 25, 0

        d. 250, 200, 150, 100, 0

Answer:

9 1/6

Step-by-step explanation:

Add the whole numbers: 5+8

Combine the fractions by making their denominator the same: 7/6

Add 6/6 = 1 so add to the whole numbers to make this a mixed fraction.

Answer:

9 1/6

Step-by-step explanation:

5 2/3 + 3 1/2 =

We need to get a common denominator of 6

5 2/3 *2/2 = 5 4/6

3 1/2 *3/3 = 3 3/6

5 4/6 + 3 3/6

8 7/6

8+ 6/6 + 1/6

8 + 1 + 1/6

9 1/6

Answer:

The angle from the centre of Ann's slice is 60 degrees.

Step-by-step explanation:

If the size of the slices is proportional to the ages of the children eating the cake, then the sum of their ages equal to 360 degrees (since the cake is a circle).

So to work out the angle of Ann's portion, we find a fraction for Ann's age over the total of all of their ages. So:

5/(5 + 10 + 15) = 5/30

Now since we know their ages are proportional to the slices of cake, we can find the same value for the fraction 5/30 that is out of 360 to work out the angle. Let's call the angle representing Ann's slice x. So know we can create an equation:

5/30 = x/ 360

5/30 * 360 = x

x = 60

Answer:

60 degrees.

Step-by-step explanation:

Answer:

Hope it helped u if yes mark me BRAINLIEST pzllzllzl

Answer:

176

Step-by-step explanation:

14x12 = 168 + 8 = 176

There are 176 inches in 14 feet, 8 inches.

To find the total number of inches in 14 feet, 8 inches, we need to convert the feet to inches and then add the inches.

So, 14 feet =  14 x 12

= 168 inches.

Adding the extra 8 inches, the total is:

= 168 inches + 8 inches

= 176 inches.

Therefore, there are 176 inches in 14 feet, 8 inches.

Learn more about Unit Conversion here:

https://brainly.com/question/28600662

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Answer:

i think it should be no solution

Answer:

X=5/2

Step-by-step explanation:

Multiply both sides by 12 since it is the lcm

[tex] 4 \times 2x - 6x = 5 \\ 2x = 5 \\ x = \frac{5}{2} [/tex]

Answer:

12.385; (10.0, 14.7)

Step-by-step explanation:

Given the following information :

Temperature, x 72 85 91 90 88 98 75 100 80

Number of absences, y 3 7 10 10 8 15 4 15 5

The obtained regression equation:

y= 0.449x - 30.27

Where y = predicted variable ; x = independent variable ; - 30.27 = intercept and slope = 0.449

Constructing a 95% prediction interval for y:

x = 95°

Inputting x = 95 into the regression equation :

y= 0.449(95) - 30.27

y = 42.655−30.27 = 12.385

Prediction interval = y ± error margin

To save computing time, error margin (E) can be obtained using the online error margin calculator.

Obtained error margin (E) value = 2.3398

(12.385 - 2.3398, 12.385 + 2.3398)

(10.0452, 14.7248)

(10.0, 14.7)