21. Find the measure of angle A.
40
20
80
160
160°

Answer:

  the numbers are 3, 5, 4

Step-by-step explanation:

The given relations can be written as a system of equations. These are conveniently solved using elimination.

Let the three numbers be represented by x, y, z. The given relations are ...

  x +y +z = 12

  x -y +z = 2

  x +y -z = 4

Subtracting the second equation from the first gives ...

  (x +y +z) -(x -y +z) = (12) -(2)

  2y = 10 . . . . . . . . . simplify

  y = 5 . . . . . . . . divide by 2

Subtracting the third equation from the first gives ...

  (x +y +z) -(x +y -z) = (12) -(4)

  2z = 8 . . . . . . . . . simplify

  z = 4 . . . . . . . . divide by 2

Using these values of y and z in the first equation lets us find x:

  x +5 +4 = 12

  x = 3 . . . . . . . . . subtract 9

The numbers, in order, are (3, 5, 4).

The graph is shown in the attached image.

The required value of δ = 1/4.  

0< |x-1| < δ
| f(x) - 4 | < 1/2 where f(x) = 6 - 2x

Inequality can be define as the relation of equation contains the symbol of ( ≤, ≥, <, >) instead of equal sign in an equation

now

| f(x) - 4 | < 1/2
|6 - 2x - 4 | <1/2
| 2-2x | < 1/2
| 1 - x | < 1/4
| x - 1 | < 1/4
since modulus function always give positive values.
0 < | x - 1 | < 1 /4

The required value of δ = 1/4.

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The equation that represents the given problem is (n-30) + n = 210. The correct option is the first option (n-30) + n = 210

From the question, we are to write an equation for the given problem

From the given information,

n = Tom's weight in pounds

If Jim weighs 30 pounds less than Tom

Then,

Jim weighs (n - 30)

Thus,

The sum of their weight is

(n-30) + n

∴ (n-30) + n = 210

Hence, the equation that represents the given problem is (n-30) + n = 210. The correct option is the first option (n-30) + n = 210

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Step-by-step explanation:

1825%

and percentage means 100

so 1825/100=73/4

Answer:

Step-by-step explanation:

To find the total perimeter of the parallelogram we must add 200+200+150+150

This equals 700. Then, since squares have side lengths that are all equal, we have to divide by 4.

700 / 4 = 175

So, the length of a side of a square having this perimeter would be 175mm

Hope this helps!

Answer:

248.00

Step-by-step explanation:

A = P(1 + rt)

A = the future value

P = the initial principal

r = annual interest rate (decimal)

t = the time in years

A=200(1+0.2*12)

Using the x-intercept concept, the function has x-intercept of 4 when c = -2.

The x-intercepts of a function are the values of x when y = 0.

In this problem, the function is:

cx - 5y + 8 = 0.

When y = 0, we have that:

cx + 8 = 0

x = 4, hence:

4c = -8

c = -2.

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Answer:

9/20

Step-by-step explanation:

Total number of candies =60

Number of Green candies, n(G)=36

Number of candies with caramel, n(C)=45

Since the events are independent, the probability of selecting two candies where the first is green and the second has caramel is given by:

P(GC)=P(G) X P(C)

\begin{gathered}=\dfrac{n(G)}{n(S)} X \dfrac{n(C)}{n(S)} \\=\dfrac{36}{60} X \dfrac{45}{60}\\ =\dfrac{9}{20}\end{gathered}=n(S)n(G)Xn(S)n(C)=6036X6045=209

The probability in its lowest form is 9/20.

Using the disk method, the volume of the solid is

[tex]\displaystyle \pi \int_3^8 \left(\dfrac1{2x-1}\right)^2 \, dx = \pi \int_3^8 \frac{dx}{(2x-1)^2}[/tex]

Substitute [tex]u = 2x-1[/tex] and [tex]du=2\,dx[/tex].

[tex]\displaystyle \pi \int_3^8 \frac{dx}{(2x-1)^2} = \frac\pi2 \int_5^{15} \frac{du}{u^2} \\\\ ~~~~~~~~ = -\frac\pi2 \frac1u \bigg|_5^{15} \\\\ ~~~~~~~~ = -\frac\pi2 \left(\frac1{15} - \frac15\right) = \boxed{\frac\pi{15}}[/tex]

The amount of paper that are needed to line the bottom of 3 drawers with paper is equal to 2,160 square inches.

First of all, we would calculate the area of the bottom of each drawer as follows:

Area = length × width

Area = 36 × 20

Area = 720 square inches.

Next, we would multiply this area by 3:

Total area = 720 × 3

Total area = 2,160 square inches.

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Complete Question:

A decorator wants to line the bottom of 3 drawers with paper. If the bottom of each drawer measures 36 inches by 20 inches, how many square inches of paper are needed?

A. 1,040

B. 1,080

C. 2,040

D. 2,160

The measure of angle A is 144.3 degrees and the angle to cut the molding is 54.3 degrees

Start by solving the acute part of angle A using the following sine function

sin(Ax) = (30 - 4)/32

Evaluate the quotient

sin(Ax) = 0.8125

Take the arc sin of both sides

Ax = 54.3

The measure of angle A is then calculated as:

A = 90 + Ax

This gives

A = 90 + 54.3

Evaluate

A = 144.3

Hence, the measure of angle A is 144.3 degrees

In (a), we have:

Ax = 54.3

This represents the angle where the molding would be cut

Hence, the angle to cut the molding is 54.3 degrees

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See the graph in the attached image.

Answer:

20

Step-by-step explanation:

According to Euclidian theorem:

h^2 = AD*CD (h is the height, DB in this case)

rewrite the equation by using given values

10^2 = 5*CD find the square value of 10

100 = 5*CD divide both sides by 5

20 = CD

Answer:

19/20

Step-by-step explanation:

He got 4 incorrect, meaning he got 80-4 correct.

80-4 = 76.

Fraction = 76/80 = 38/40 = 19/20.

Answer:

19/20

Step-by-step explanation:

[tex]\frac{80-4}{80} =\frac{76}{80} =\frac{19}{20}[/tex]

Hope this helps

Answer:

to find the value of x

x=(8x28)÷4

Answer: x=56

x/y 28/4=x/8

reduce 28/4 to 7/1

7/1 = x/8

cross multiply

x=56

Step-by-step explanation:

The 8% of us states have names that start with the letter w the answer is 8%.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

The complete question is:

Of the 50 us states 4 have names that start with the letter w what percentage of us states have names that start with the letter w.

The percentage of the US states that have names that start with the letter W can be calculated:

Percentage = (No of US states starting with W/Total no of US states)×100

Percentage = (4/50)×100

Percentage = 8%

Thus, the 8% of us states have names that start with the letter w the answer is 8%.

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Answer:

$9.66 isb15% of $64.40

Step-by-step explanation:

64.40×15%

Answer:

54y+78

Step-by-step explanation:

6*3y+ 18y

6*7=42

4*9=36

4*9y=36y

18y+36y+42+36= 54y+78

Answer:

48000

Step-by-step explanation:

After rounding each number to the criteria stated, we get the question 800 * 60. Multiply the 8 and the 6 and add the same number of zeros that are there right now. this is 48 + "000" so 48000.

The interest you will earn from the loan of 500 dollars at rate of 6% and 6 months is $15.

He borrowed $500 and she will pay at the end of 6 months.

The interest rate is 6%.

Therefore,

I = prt / 100

where

Therefore,

I = 500 × 6 × 0.5 / 100

I = 1500 / 100

I = $15

Therefore, the interest you will earn from the loan is $15.

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Answer:

(y - x)/(y + x)

Step-by-step explanation:

(1/x - 1/y)/(1/x + 1/y) =

= (1/x - 1/y)/(1/x + 1/y) × (xy)/(xy)

= (y - x)/(y + x)

The required value of function F(x), when x=18 is -2

A line of best fit is f(x) ≈ −0.86x + 13.5 for the set of points in the table
x     = 2   3   5   6  7  8  9
F(x) = 21  10 10  8  9  5  6

What is line?
line, is curve showing the shortest distance between 2 points.

Now, putting x = 18 in f(x) ≈ −0.86x + 13.5
f(x) ≈ −0.86(18) + 13.5

= -1.98
≅ -2 (approximation)

Thus, the required values of x=18 in a line of best fit is -2.

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The test statistic z  is 2.33, the p-value corresponding to the test statistic z value is 0.0099.

Probability is the measure of the likeliness of happening of an event.

The mean of the data is 15.07 centimeters

The standard deviation of the data is 0.26 centimeters.

n = 75

Significance Level ∝ = 0.01

According to the null and alternative hypothesis

Hₐ : [tex]\rm \mu[/tex] ≤15  vs H₁ : [tex]\rm \mu[/tex] >15

The test statistic z  is given by

[tex]\rm Z = \dfrac{(X-\mu)}{\sigma/\sqrt{n}}[/tex]

Z = ( 15.07 -15)/(0.26/√75)

Z = 2.33

The p-value corresponding to z value is 0.0099

as p-value < significance level, therefore the H₁ : [tex]\rm \mu[/tex] >15 is acceptable.

No, significant evidence is not present to tell that the length of bolts is actually greater than the mean value at a significance level of 0.01.

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Using the quotient rule, the derivative of [tex]y[/tex] is

[tex]y' = \dfrac{(x^2-1) x' - x(x^2-1)'}{(x^2-1)^2} = \dfrac{(x^2-1) - x(2x)}{(x^2-1)^2} = -\dfrac{x^2+1}{(x^2-1)^2}[/tex]

as you're shown in the picture.

If [tex]y[/tex] has any local extrema, they occur at critical points where [tex]y'=0[/tex] or possibly when [tex]y'[/tex] is undefined.

In this case, [tex]y'[/tex] is undefined when [tex]x=1[/tex], but this is outside the domain of [tex]y[/tex] anyway, so we can ignore that.

That leaves us with the zero-case. For [tex]x\neq1[/tex], the denominator is always positive, so the numerator must be zero. But this never happens, since

[tex]-(x^2+1) = 0 \implies x^2 = -1[/tex]

but [tex]x^2\ge0[/tex] for all real [tex]x[/tex]. Therefore [tex]y[/tex] has no critical points and thus no extrema.

Answer:

1/2

Step-by-step explanation:

We are given the expression 3b²-c, and we want to evaluate it if b is 1/2 and c is 1/4.

Because b and c are given values, we can substitute them into the expression as so:

Replace b with 1/2 in the expression.

3(1/2)²-c

Now replace c with 1/4 in the expression.

3(1/2)²-1/4

Now to solve this, we need to use the order of operations, which is usually known as PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) in the United States, although other countries have different abbreviations.

Regardless, the order of operations tells us that we should start with what is inside parentheses (i.e. if we need to do anything, like multiplying or dividing any numbers that are inside parentheses).

In this case, we don't have anything. So, we should go next to exponents, and we do have an exponent here (1/2 is raised to the second power).

So let's evaluate that.

Raise 1/2 to the second power (multiply it by itself).

1/2 * 1/2 = 1/4

We can substitute (1/2)² with 1/4:

3(1/4) - 1/4

Next, we should take care of any multiplication / division, making sure that we should work left to right

There is one multiplication thing to do: the 3(1/4), which will be 3/4

Replace 3(1/4) with 3/4.

3/4 - 1/4

Now, we can subtract 1/4 from 3/4, as the final two things in PEMDAS are addition and subtraction (A and S). Note that even though while addition is written first, we should always be working left to right, so for example if we had 3 - 4 + 6, we should do 3 - 4 first, THEN add 6 to the result of that. The same is true for multiplication and division.  

3/4 - 1/4 = 2/4 = 1/2

Answer:

its 20, because I said it

Step-by-step explanation:

so 5+5=10

30-10=20

1) given

2) given

3) Definition of linear pair

4) If alternate interior angles are congruent, then the lines are parallel.