In quadrilateral ABCD, \angle A=5x+20,\angle B=3x-30,\angle C=2x+10,and\angle D=8x.∠A=5x+20,∠B=3x−30,∠C=2x+10,and∠D=8x. Find the value of Angle B.

Equation:
x=
angle b=

Answer:

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

Step-by-step explanation:

first we distribute the a to the 2x and -3

2ax -3a=bx+5

we move the -3a over by adding 3a

2ax=bx+5+3a

then we move the bx over

2ax-bx=5+3a

we can now group the left side like this

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

to find x all we must do is divide both sides by (2a-b)

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

Answer:

Length = [tex]5\ \text{ft}[/tex]

Breadth = [tex]5\ \text{ft}[/tex]

Step-by-step explanation:

Let [tex]x[/tex] be the length of the garden

and [tex]y[/tex] be the width of the garden

From the details of the cost in the question we get

[tex]20x+2\times (10y)=200\\\Rightarrow 20x+20y=200\\\Rightarrow x+y=\dfrac{200}{20}\\\Rightarrow x+y=10\\\Rightarrow y=10-x[/tex]

Now area of the garden is

[tex]A=xy\\\Rightarrow A=x(10-x)\\\Rightarrow A=10x-x^2[/tex]

Differentiating with respect to x we get

[tex]\dfrac{dA}{dx}=10-2x[/tex]

Equating with 0

[tex]0=10-2x\\\Rightarrow x=\dfrac{-10}{-2}\\\Rightarrow x=5[/tex]

Double derivative of the area is

[tex]\dfrac{d^2A}{dx^2}=-2<0[/tex]

So, area is maximum at [tex]x=5[/tex]

[tex]y=10-x=10-5\\\Rightarrow y=5[/tex]

So, the length and breadth of the rectangle is [tex]5\ \text{ft}[/tex].

Answer:

9944

Step-by-step explanation:

Calculator. Was there anything else you needed help on while I'm at it?

Answer:

9944

Explaination:

Typed it into a calculator

Answer:

(-2x^3)+(9x^2)

Step-by-step explanation:

Answer is above. Hope it helps!

Answer:

A) False

B) False

Step-by-step explanation:

A. Two angles whose measures add up to 90° are said to be complementary, while two angles are adjacent when formed beside each other. So, adjacent angles might be complementary or supplementary. Thus, the answer to the first part of the question is false.

B. When two angles share a side, they are said to be adjacent to each other. But supplementary angles add up to [tex]180^{o}[/tex]. Since adjacent angles might be complementary or supplementary, then the answer to the second part of the question is false.

Answer: No because BC is not perpendicular to AB.

Step-by-step explanation:

Yes, rhombus ABCD is a square as all four angles of the rhombus are right angles.

A square is a special type of rhombus where all four sides have the same length and all four angles are right angles.

In this case, we can see that all four sides of the rhombus have the same length by calculating the distance between each pair of vertices. For example, the distance between A and B is:

distance = [tex]\sqrt{[/tex] [tex]((-8 - (-1))^2[/tex] + [tex](11 - (-13))^2[/tex])

distance = [tex]\sqrt{[/tex] ([tex]7^2[/tex] + [tex]24^2[/tex])

distance = [tex]\sqrt{[/tex] (625) = 25

The distance between each other pair of vertices is also 25, so all four sides of the rhombus have the same length.

We can also see that all four angles of the rhombus are right angles by calculating the angles between each pair of adjacent sides. For example, the angle between sides AB and BC is:

angle = arctan((13 - (-13))/(-8 - (-1)))

angle = arctan(26/7)

angle = 78.6°

The angle between each other pair of adjacent sides is also 78.6°, so all four angles of the rhombus are right angles.

Therefore, rhombus ABCD is a square.

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Answer:

a = 1 ; b = - 8

Step-by-step explanation:

x² + 2x - 7 = (x² + 2x + 1) - 1 - 7 = (x + 1)² - 8

a = 1

b = - 8

Answer:

a = 1 , b = -8

Step-by-step explanation:

(x+1)^2 = x^2+2x+1

x^2+2x+1-8 = x^2+2x-7

Answer:

136

Step-by-step explanation:

the two base pairs angles add up to equal 44

subtract 44 from 180 to get the missing angle

you get 136

Answer:

c

Step-by-step explanation:

Answer:

104 feet

Step-by-step explanation:

Answer:

104

Step-by-step explanation:

Step-by-step explanation:

hope this helps, happy learning

Two vertical asymptotes exist. The leftmost one's equation is, x = -6, and the rightmost one's equation is, x = 6.

Domain: ,(-∞, -6) U (-6, 6) U (6, ∞)

There are two vertical asymptotes on the f(x) graph. The leftmost one's equation is:

x = -6

and the equation of the rightmost one is:

x = 6

Part B

The vertical asymptotes at x=-6 and x=6 define the domain of f as follows:

(-∞, -6) U (-6, 6) U (6, ∞)

Therefore, Two vertical asymptotes exist. The leftmost one's equation is x = -6, whereas the rightmost one's equation is x = 6.

The complete question is:

Identify any vertical, horizontal, or oblique asymptotes in the graph of y=f(x). State the domain of f. Identify any vertical asymptotes. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. OA. There is only one vertical asymptote. Its equation is (Type an equation.)OB. There are two vertical asymptotes. The equation of the leftmost one is and the equation of the rightmost one is (Type an equation.)OC. There are no vertical asymptotes.

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Answer:

I just know additional

Step-by-step explanation:

Answer: $9.25 an hour

Step-by-step explanation:

Answer:

7x-21

Solution:

7 times x and 7 times negative 3

Answer:

[tex]\huge\boxed{\sf{7x-21}}[/tex]

Step-by-step explanation:

Hello.

The Distributive property states that

a(b+c)=ab+ac

Where

a, b, and c = variables/constants

Now, simplify the expression:

7(x-3)

Multiply x and 3 times 7 and subtract the products:

7x-21

I hope it helps & have an outstanding day.

[tex]\boxed{imperturbability}[/tex]

Answer:  0.92 feet (choice B)

You're close but not quite there. To get the answer, you divide 29.44 over 32

If you had 32 feet of banner and 32 students, then each student would get 32/32 = 1 foot. Since the length of the banner is smaller than the number of students, this means each student only gets a fraction of a foot. This fraction value is fairly close to 1 because 29.44 is close to 32.

Answer:

B: 0.92

Step-by-step explanation:

Divide the banner length by the amount of students

[tex]\frac{29.44}{32}[/tex]

Answer:

Step-by-step explanation:

Find the diagram attached. From the diagram, we can see that;

<USW = <TSR (vertically opposite angles)

Given

<USW = 7x-34

<TSR = 4x+29

Equate

7x-34 = 4x+29

7x-4x = 29+34

3x = 63

x = 63/3

x = 21°

Find <USW

<USW =7x-34

<USW =7(21)-34

<USW = 147-34

<USW = 113°

Hence the measure of <USW is 113°

Answer:

I'll try my best in explaining the steps.

Considering both signs are greater than and less than sign, its an open circle.

For the first equation, you would have an open circle, basically one that isn't colored in, on 8 on the number line. The arrow would be pointing to the left because the equation is telling us numbers that are less than 8.

For the second equation, you would have an open circle, basically one that isn't colored in, on -1 on the number line. The arrow would be pointing to the right because the equation is telling us numbers that are greater than -1.

Step-by-step explanation:

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete as what is required of the question is not stated.

However, since the question is only limited to distance, a likely question could be to calculate the distance from Bayville to Colleyville.

Represent the distance from Atlanta to Colleyville with AC

Represent the distance from Atlanta to Bayville with AB

Represent the distance from Bayville to Colleyville with BC

So, we have that:

[tex]AC = 25.5\ miles[/tex]

[tex]AB = 10\frac{2}{3}\ miles[/tex]

The relationship between AB, AC and BC is:

[tex]AC = AB + BC[/tex]

Make BC the subject of formula:

[tex]BC = AC - AB[/tex]

[tex]BC = 25.5 - 10\frac{2}{3}[/tex]

Convert fraction to decimal

[tex]BC = 25.5 - 10.7[/tex]

[tex]BC = 14.8[/tex]

Hence, the distance from Bayville to Colleyville is 14.8 miles

The rate of flow of water through a pipe is gallons per day is 3.333%.

Given that, water flows through a pipe at a rate of 4 quarts per month.

We need to express this rate of flow in gallons per day.

4 quarts will make a gallon.

Now, according to the question, 1 gallon of water flows through a pipe per month.

We know that number of days in a month is equal to 30 days.

Per day=1 gallon of water/Number of days in a month

=1/30 gallons of water.

The rate of flow in gallons per day=1/30 × 100

=3.3333%≈3.333%

Therefore, the rate of flow of water through a pipe is gallons per day is 3.333%.

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Answer:

[tex] \huge A (n) = 5 ({2})^{n - 1} \\ [/tex]

Step-by-step explanation:

The nth term of a geometric sequence is given by

[tex]A(n) = a _ 1( {r})^{n - 1} [/tex]

a1 is the first term

r is the common ratio

From the question we have the final answer as

[tex]A (n) = 5 ({2})^{n - 1} [/tex]

Hope this helps you

Answer:

x^2+5x-14=0

Step-by-step explanation:

(x+7)(x-2)=0

x (x-2)+7 (x-2)=0

x^2-2x+7x-14=0

x^2+5x-14=0

Answer:

x = 8 is a solution for the equation

Answer:

Percentage increase= 37.5%

Step-by-step explanation:

Giving the following information:

Sales on weekdays (Q0)= 240 units

Sales on weekends (Q1)= 330 units

To calculate the percentage increase, we need to use the following formula:

Percentage increase= [(Q1/Q0) - 1]*100

Percentage increase= [(330/240) - 1]*100

Percentage increase= 37.5%

Answer:

x = 30          0  <= x < 2

Step-by-step explanation:

senx +3 + sex -3 = 1

2senx = 1

senx =1/2

x = arcsen(1/2)

x = 30

Answer:

a

[tex]P(X = 4 ) = 0.0677 [/tex]

b

[tex]P(X \ge 1  ) =   0.9424 [/tex]

Step-by-step explanation:

From the question we are told that

   The probability of a US household having an internet access in 2001 is  p = 0.51

   The sample size is  n = 4

Generally the distribution of the number of US household with internet access at 2001  follows a binomial distribution  

i.e  

         [tex]X  \~ \ \ \  B(n , p)[/tex]

and the probability distribution function for binomial  distribution is  

      [tex]P(X = x) =  ^{n}C_x *  p^x *  (1- p)^{n-x}[/tex]

Here C stands for combination hence we are going to be making use of the combination function in our calculators  

   Generally  the probability that all four had Internet access in 2001 is mathematically represented as

      [tex]P(X = 4 ) =  ^{4}C_4 *  (0.51)^4  (1- 0.51)^{4-4}[/tex]

=>  [tex]P(X = 4 ) = 0.0677 [/tex]

Generally  the probability that at least one of four randomly selected U.S. households had Internet access in 2001 is mathematically represented as

      [tex]P(X \ge 1  ) =  1 - P(X <  1 ) =  1-  P(X = 0 )[/tex]

=>   [tex]P(X \ge 1  ) =   1-  [^{4}C_0 *  (0.51 )^0 *  (1- 0.51 )^{4-0 } ][/tex]

=>   [tex]P(X \ge 1  ) =   1-  [1 *  1 *  (0.49 )^{4 } ][/tex]

=>   [tex]P(X \ge 1  ) =   0.9424 [/tex]

Answer:

2 gallons an hour

Step-by-step explanation:

This is a fraction equal to

2 gal ÷ 1 hours

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 1

2 gal

÷ 1

1 hours

÷ 1

=

2 gal

1 hour

=

2 gal

hour

= 2 gal per hour

Answer:

3/8

Step-by-step explanation:

1/4 ÷ 2/3 = 3/8

Answer: 3.971

Step-by-step explanation: first, you need to set up your addition problem. When adding decimals, you need to line up the decimal points. So you get something like this:

3.85

0.004

0.117

+————-

Then you add vertically and you get your answer of 3.971

Your welcome :)

The value of the given expression ( 3.85+0.004+0.117 ) is 3.971.

The process of increment of any number of quantities or the process of integrating small parts to make a big part is called summation.

first, you need to set up your addition problem. When adding decimals, you need to line up the decimal points. So you get something like this:

 3.850

 0.004

 0.117

+————-

3.971.

Then you add vertically and you get your answer of 3.971.

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Answer:

[tex]T_{10} = 0.05078125[/tex]

[tex]S_{18} = 51.9998016358[/tex]

Step-by-step explanation:

Given:

Sequence = 26, 13, 6.5 ....

Solving (a): The 10th term

The sequence is a geometric progression and the nth term will be solved using:

[tex]T_n = ar^{n-1}[/tex]

In this case:

[tex]n = 10[/tex]

[tex]r = \frac{T_2}{T_1}[/tex] --- Common Ratio

[tex]r = \frac{13}{26}[/tex]

[tex]r = 0.5[/tex]

[tex]a = 26[/tex] --- First term

So, [tex]T_n = ar^{n-1}[/tex] becomes

[tex]T_{10} = 26 * 0.5^{10-1}[/tex]

[tex]T_{10} = 26 * 0.5^{9}[/tex]

[tex]T_{10} = 26 * 0.001953125[/tex]

[tex]T_{10} = 0.05078125[/tex]

Solving (b): The sum of first 18 terms

This will be calculated using:

[tex]S_n = \frac{a(1 - r^n)}{1 - r}[/tex]

Substitute values for n, a and r

[tex]S_{18} = \frac{26 * (1 - 0.5^{18})}{1 - 0.5}[/tex]

[tex]S_{18} = \frac{25.9999008179}{0.5}[/tex]

[tex]S_{18} = 51.9998016358[/tex]

Hence, the sum of first 18 terms is 51.9998016358