Solve for x in the diagram below.

Solve For X In The Diagram Below.

Answers

Answer 1

Answer:

x = 20

Step-by-step explanation:

2x°

(x + 10)°

little box on the bottom left means this is a right angle which is 90°

add up all the angles and make it equal to 90°

( x° + 2x° + (x + 10)° ) = 90°

4x + 10 = 90

4x = 80

x = 20

Answer 2
Step-1: Understanding the Diagram

Since we can see the "square" at the bottom left corner of the angle, the square indicates that the angle is a right angle (which measures 90°).

We can also see three smaller angles forming the right angle. Therefore, the sum of the measure of the smaller angles = 90°.

According to the diagram, the measures of the smaller angles are x°, 2x°, and (x + 10)° respectively. Then we get the following equation:

[tex]\implies x + 2x + (x + 10) = 90\°[/tex]

Step-2: Solving the equation obtained in step-1

Here, we had the equation: [tex]\underline{x + 2x + (x + 10) = 90\°}[/tex]

[tex]\implies x + 2x + x + 10 = 90\°[/tex]              [tex]\text{(Ope} \text{ning the parentheses)}[/tex]

[tex]\implies 4x + 10 = 90\°[/tex]                             [tex]\text{(Combining like terms)}[/tex]

[tex]\implies 4x + 10 - 10 = 90 - 10[/tex]          [tex]\text{(Subtracting 10 on both sides)}[/tex]

[tex]\implies 4x = 80[/tex]                                    [tex]\text{(Simplifying both sides)}[/tex]

[tex]\implies \dfrac{4x}{4} = \dfrac{80}{4} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{(Dividing 4 on both sides)}[/tex]                            

[tex]\implies \boxed{x = 20}[/tex]                                      [tex]\text{(Simplifying both sides)}[/tex]

Therefore, the value of x, in the diagram provided, is 20.


Related Questions

 What property is used to do…
-2y + 15 = -23

Answers

Answer:

-2y= -23-15

-2y=-38

-y= -38/2

-y=19 proved

PLEASE HELP IM STUCK

Answers

Answer:

y = 7.25 + 0.65x

Step-by-step explanation:

y = total cost

x = each mile

it starts at 7.25

any mile after that is an extra $0.65

y = 7.25 + 0.65x

If someone can help with this that would be great

Answers

Answer:

p ≈ 7.3 m

Step-by-step explanation:

using the Sine Rule in the triangle

[tex]\frac{p}{sinP}[/tex] = [tex]\frac{r}{sinR}[/tex] ( substitute values )

[tex]\frac{p}{sin40}[/tex] = [tex]\frac{10}{sin62}[/tex] ( cross- multiply )

p × sin62° = 10 × sin40° ( divide both sides by sin62° )

p = [tex]\frac{10sin40}{sin62}[/tex] ≈ 7.3 m ( to the nearest tenth )

Answer:

[tex]\fbox {p = 7.3 m}[/tex]

Step-by-step explanation:

Applying the Law of Sines :

[tex]\boxed {\frac{sin R}{PS} = \frac{sin P}{RS}}[/tex]

Substitute the values :

sin 62° / 10 = sin 40° / pp = sin 40° × 10 / sin 62°p = 0.64278761 × 10 / 0.882947593p = 7.3 m (nearest tenth)

1. what are the peaks of a periodic function?
a. the highest points of the graph
b. the lowest points of the graph
c. the extremes of the graph
d. the x-intercepts of the graph

Answers

Answer:

A. The Highest Points Of The Graph

Step-by-step explanation:

A nonperiodic function is one that generates a graph without a regular recurring pattern over a fixed time interval. A repeating section of a graph is called the period.

The probability of winning on an arcade game is 0.568. If you play the arcade game 22 times, what is the probability of winning more than 15 times

Answers

The probability of winning 15 out of the 22 games is [tex]P = 0.099[/tex]

what is the probability of winning more than 15 times?

We know that the probability of winning on the arcade game is 0.568.

Then the probability of losing is:

P = 1 - 0.568 = 0.432

The probability of winning 15 out of 22 games is given by the equation:

[tex]P = C(22, 15)*(0.568)^{15}*(0.432)^{7}[/tex]

Where C(22, 15) is the number of combinations of 15 elements that we can make with a set of 22 elements, given by:

[tex]C(22, 15) = \frac{22!}{(22 - 15)!*15!} = \frac{22!}{7!*15!} = \frac{22*21*20*19*18*17*16}{7*6*5*4*3*2*1} = 170,544[/tex]

Then the probability is:

[tex]P = 170,544*(0.568)^{15}*(0.432)^7 = 0.099[/tex]

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It took an hour to now a lawn using a mower with 14 inches blade. How long will it take using a mower with 12 inches wide

Answers

If the time taken by 14 inches wide is one hour then the blade of 12 inches wide will take 1 hour 17 minutes to mow a lawn.

What is width?

The width of something is the measurement of one side of a body. It is generally less than length of that body or shape.

How to calculate time?

We have been given time of 1 hour if blade is 14 inches wide and we have to calculate time taken by 12 inches wide blade:

It will be as 14/12* 1 hour

=14/12

=1.167

=1.17 hour

Hence the time taken by the blade of 12 inches wide will be 1 hour and 17 minutes.

Answer:

70 mins

Step-by-step explanation:

This is called inverse proportion.

1hr : 14in

x hr : 12in

Ask yourself, what do you do to 14 to get 12? To find this out, we do:

14 / 12 = 1.16666667

Since the blade is smaller, it will take longer. So, we times 1hr by 1.16666667 to get

1.16666667 hrs =

1.17 hours (rounded)

This is 70.2 mins, or 1hr 10 mins

Hope this helps!

What make 6 6 6 6=9 true

Answers

Answer:

Step-by-step explanation:

6^0 + 6^0 + 6^0 + 6

= 1+1+1+6

= 9.

Which of these statements is true for f(x)=(1/10)^x

A. the range of f(x) is y>1/10

B. it is always increasing

C. the graph contains (1, 1/10)

D. the domain of f(x) is x>0

Answers

Answer: C. the graph contains (1, 1/10)

Step-by-step explanation:

When x=1, [tex]y=(1/10)^1=1/10[/tex].

A scientist observes the bacteria’s growth. In the first observation, there were 12 bacteria, 24 in the second observation, 48 in the third and so on. How many bacteria will be there in the 8th observation? Use the explicit formula.

1,536
28
126
27

Answers

Answer:

Step-by-step explanation:96 in the fourth since they are adding the answer itself two times before you get the other like 12 bacteria and then 24 so that means 12 + 12 is 24 and the third one 48 so 24 +24 =48

fourth 48 + 48=96

 fifth 96+96=192

sixth  192+192=384

seventh 384+384=768

last but not least 768+768 = 1536

so your answer is 1,536

Work out the area of the triangle.

Answers

Answer:

555.75m²

Step-by-step explanation:

Triangle Area = 1/2b*h

1/2 57 * 19.5 =

28.5 * 19.5 =

555.75m²

Three friends owe 18 dollars to another friend for gas if they plan to split the cost evenly which of the following expressions could they use to find how much they each owe

Answers

If they plan to split the cost evenly, the expression that could be used to find how much they each owe is 18/3

How to determine the amount paid by each?

The given parameters are:

Total amount owed = 18 dollars

Number of friend = 3

If they plan to split the cost evenly, the expression that could be used to find how much they each owe is represented as:

Amount = Total/Friends

This gives

Amount = 18/3

Hence, the expression is 18/3

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There are 26 prize tickets in a bowl, labeled A to Z. What is the probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen? Does this represent an independent or dependent event? Explain.

Answers

Using it's concept, there is a 0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For the first ticket, since 5 out of 26 letters are vogal, the probability is:

5/26.

For the second ticket, since there is no replacement, the probability is:

4/25.

The probability of both tickets is:

[tex]p = \frac{5}{26} \times \frac{4}{25} = 0.0308[/tex]

0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.

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A procedure for using sample data to find the estimated regression equation is _____. Group of answer choices point estimation interval estimation the least squares method extrapolation

Answers

c. the least squares method.

Regression equation:

In simple linear regression, the predicted value of the dependent variable is given by the equation = b0 + b1x. The values of b0 and b1 are calculated from the data so that the line = b0 + b1X minimizes the total sum of squared errors (error is the difference between the predicted value and the actual value of y).

Least squares method:

The least squares method is a statistical procedure to find the best fit for a set of data points by minimizing the sum of the offsets or residuals of points from the plotted curve.

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The measure of one angle of an octagon is twice the measure of one of the other seven congruent angles. What is the measure of each angle?

Answers

Each one of the smaller angles  x = 120 degrees and the larger angle = 2x = 2 × 120 = 240 degrees

How to find the angle of octagon?

The angle of an octagon can be found as follows;

An octagon is a polygon that has 8 sides.

The sum of angles in an octagon is 1080 degrees.

Therefore,

x + x + x + x + x + x + x + 2x = 1080

Hence,

9x = 1080

divide both sides by 9

x = 1080 / 9

x = 120

Therefore, each one of the smaller angles  x = 120 degrees and the larger angle = 2x = 2 × 120 = 240 degrees

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a jet bomber traveling 500 mph arrived over its Target at the same time as its fighter jet escorted which left the same fate 2.5 hours after the bomb took off how many hours did the bomber take to reach the target of the fighter jet travel at 60 miles per hour ​

Answers

Since the jet bomber arrived over its Target at the same time as its fighter jet escorted, it took the jet bomber 0.34 h to reach the target.

To find the number of hours, we need to solve simultaneous equations.

What are simultaneous equations?

Simultaneous equations are pair of equations which contain two unknowns.

How to calculate the number of hours the bomber jet took off?

Let

D = distance travelled by both bomber jet and fighter jet.t = time bomber jet took off v = speed of bomber jet. T = time fighter jet took off and V = speed of fighter jet.

So, D = vt

D = 500t  (1)

Also, D = VT

D = 60T  (2)

Since  jet bomber traveling 500 mph arrived over its Target at the same time as its fighter jet escorted which left the same fate 2.5 hours after the bomb took off.

T = t + 2.5

So, D = 60(t + 2.5)  (3)

The required simultaneous equations

D = 500t  (1)

D = 60(t + 2.5)  (3)

Equating equations (1) and (3), we have

500t = 60(t + 2.5)

500t = 60t + 150

500t - 60t = 150

440t = 150

t = 150/440

t = 15/44

t = 0.34 h

So, it took the jet bomber 0.34 hours to reach the target.

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Determine the unknown length or angle measurement. Round each answer to the nearest whole number

Answers

(a) The value of the unknown length, a, is 18 cm
(b) The value of the unknown angle measurement, θ, is 39°

Law of sines

From the question, we are to determine the unknown length and angle measurement

(a)

A + B + C = 180° (Sum of angles in a triangle)

A = 180° - (B + C)

A = 180° -(68° + 59°)

A = 53°

Using the law of sines

[tex]\frac{a}{sin A}=\frac{c}{sin C}[/tex]

[tex]\frac{a}{sin 53^\circ}=\frac{19.5}{sin 59^\circ}[/tex]
[tex]a=\frac{19.5 \times sin 53^\circ}{sin 59^\circ}[/tex]

[tex]a= 18.168[/tex]

[tex]a \approx 18 cm[/tex]

(b)

[tex]\frac{sin A}{a}=\frac{sin B}{b}[/tex]

[tex]\frac{sin \theta}{15}=\frac{sin 57^\circ}{20}[/tex]

[tex]sin \theta=\frac{15 \times sin 57^\circ}{20}[/tex]

[tex]sin \theta=0.6290[/tex]

[tex]\theta=sin ^{-1} (0.6290)[/tex]

[tex]\theta=38.976 ^\circ[/tex]

[tex]\theta \approx 39^\circ[/tex]

Hence, the value of the unknown length, a, is 18 cm
The value of the unknown angle measurement, θ, is 39°

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WILL MAKE BRAINLIEST!!
Complete the congruence statement for the figure below.

Answers

Triangle TRS is the correct option ……..

Calculate how long it would take for an investment of R9000 to double if the simple interest rate is 11% per annum.​

Answers

Answer:

9.09 years

Step-by-step explanation:

Use the simple interest formula

A=P(1+rt)

18000=9000(1+.11*t), solve for t

t = 9.0909

You have 1 blue suit, 2 black suits, and 1 brown suit, You also have 2 blue ties, 3 red ties, and 3 pink ties. What is the probability that you pick a striped shirt AND a blue suit AND a pink tie

Answers

The probability that you pick a striped shirt AND a blue suit  is 1/4 AND a pink tie is 3/8.

According to the statement

Number of blue suit = 1

Number of black suit = 2

Number of brown suit = 1

Number of blue ties = 2

Number of red ties = 3

Number of pink ties = 3

Now we find the probability by its formula

Probability that picked suit is blue = blue suits/ total number of suits

Probability = 1/4

Now,

Probability that picked tie is pink = Pink tie / total number of ties

Probability = 3/8

So, The probability that you pick a striped shirt AND a blue suit  is 1/4 AND a pink tie is 3/8.

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A doctor asked a patient to reduce his medication by a regular number of tablets per week. The reduction plan begins one week after the visit to the doctor. If 10 weeks after the visit to the doctor the person is taking 40 tablets and 20 weeks after the visit the person is taking 30. Find the weekly reduction in his consumption of tablets.

Answers

1 tablet weekly reduction in his consumption of tablets.

What is an algebraic expression?

Algebraic expression is a set of variable, constant and algebraic operations like addition, subtraction, multiplication and division. for example 3x^2+2x+3=0

Tablet after 10 week of doctor visit = 40 tablet

Tablet after 20 week of doctor visit= 30

In 10 week there is a difference of (40-30) 10 tablets.

in 10 week there is reduction of 10 tablets its mean there is reduction of 1 tablet per week

so, the weekly reduction of 1 tablet per week.

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PLEASE HELP IM STUCK

Answers

Answer:

-70

Step-by-step explanation:

We are given this arithmetic sequence:

-2, -6, -10, -14, ...

And we want to find the 18th term in it.

The 18th term can be found using this formula:

1st term + common difference(desired term-1)

The desired term is the term that we are looking for. In this case, it would be the 18th term, so substitute 'desired term' with 18.

1st term + common difference(18-1)

So, let's find the first term and the common difference.

The 1st term is the first term (number) that appears in the sequence. In this case, that number would be -2.

The common difference can be found by doing second term minus first term.

Remember that we know that the first term is -2. The second term is the second number that appears in the sequence, which would be -6.

So, do -6 subtract -2.

-6 - - 2

-6 + 2

-4

The common difference is -4.

So, we can plug -2 and -4 into the formula.

-2 - 4(18-1)

Now, doing the order of operations, first, subtract 1 from 18.

-2-4(17)

Now multiply -4 and 17 together.

-2 -68

Subtract -68 from -2.

-70

The 18th term of the sequence is -70.

Using the formula: A=p(1+r)t
How much money will Mario have if he puts $1000 in a savings account earning 4% annually after 10 years?
Select one:
O a. $1004
O b. $1428.24
• c. $1000
© d. $2156.01

Answers

The amount of money Mario will have if he puts $1000 in a savings account earning 4% annually after 10 years is $1,480

Compound interest

A = p(1 + r)^t

p = $1000r = 4% = 0.04t = 10 years

A = p(1 + r)^t

= 1000(1 + 0.04)^10

= 1000(1.04)^10

= 1000(1.48)

A = $1,480

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Zoe went out to her garden and cut 19 roses from the first rose bush, 28 roses from the second rose bush, 37 roses from the third rose bush, and 46 roses from the fourth rose bush. What kind of sequence is this?

Answers

Based on the given scenario, the kind of sequence explained is an arithmetic sequence

Sequence

First bush = 19 rosesSecond bush = 28 rosesThird bush = 37 rosesFourth bush = 46

First term, a = 19

Second term, a + d

28 = 19 + d

28 - 19 = d

9 = d

Common difference, d = 9

Third term, a + 2d

= 19 + 2(9)

= 19 + 18

= 37

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The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.15 gallons. A previous study found that for an average family the variance is 3.61 gallons and the mean is 19.4 gallons per day. If they are using a 95% level of confidence, how large of a sample is required to estimate the mean usage of water

Answers

The minimum sample size required to estimate the mean usage of water = 2225.07

What is Standard deviation?

In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

We can find the minimum sample size required to estimate the mean usage of water as shown below:

Standard deviation [tex]\sigma =3.61[/tex]

Margin of error E=0.15

Critical value for 95% confidence interval = 1.96

Required minimum sample size: [tex]n=(\frac{Z_{\frac{\alpha}{2}}.\sigma }{E} )^2[/tex]

[tex]=(\frac{1.96\times 3.61}{0.15} )^2[/tex]

=2225.07

Hence, the minimum sample size required to estimate the mean usage of water = 2225.07

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Find the surface area of the pyramid. Round to the nearest tenth.

Answers

Answer:

279

Step-by-step explanation:

The area of the square base is 9² = 81.

The area of each triangular face is (1/2)(9)(11)=99/2.

So, the total surface area is 4(99/2)+81=279

Which of the following is equal to the expression below?

(4^-5)^3

A. -4^2

B. 1/4^15

C. -4^15

D. 1/4^2

Answers

Answer: B

Step-by-step explanation:

[tex](4^{-5})^3=4^{-15}=\frac{1}{4^{15}}[/tex]

please help with this.

Answers

Answer:

R = $2,120

Ticket price = $11

Step-by-step explanation:

Finding revenue when t = 10 :

R = -6(10)² + 132(10) + 1440R = 1400 + 1320 - 600R = 2720 - 600[tex]\fbox {Revenue = 2,120 dollars}[/tex]

The vertex of the graph will have the maximum revenue.

Vertex = (h, k)h = -b/2ah = -132/2(-6)h = 132/12h = 11

Hence, the revenue is maximum when the ticket price is $11.

please answer quickly

Answers

1a. 10. 24

1b. 125/243

2a. 0. 0048

2b. 32/3125

3a. 0. 64

3b. 0. 0031

4a. 2/5

4b. 48. 735

5a. 2. 36

5b. 1. 39

How to determine the values

1a. Given the values

(2/5)^2/(1/2)^6

Multiply both the numerator and denominator by the powers

⇒ [tex]\frac{\frac{4}{25} }{\frac{1}{64} }[/tex]

To find the common ration, multiply thus;

⇒ [tex]\frac{4}{25}[/tex] × [tex]\frac{64}{1}[/tex]

⇒ [tex]\frac{256}{25}[/tex]

= 10. 24

1b. (5/7)^2 × (5/7)^1

= [tex]\frac{25}{49}[/tex] × [tex]\frac{5}{7}[/tex]

= [tex]\frac{125}{343}[/tex]

= 125/243

2a. 0. 6^1  × 0. 2^3

= 0. 6 × 0. 008

= 0. 0048

2b. (2/5)^3 × (2/5)^2

= [tex]\frac{8}{125}[/tex] × [tex]\frac{4}{25}[/tex]

= [tex]\frac{32}{3125}[/tex]

= 32/ 3125

3a. 1^99 - 0. 6^2

= 1 - 0. 36

= 0. 64

3b. (0. 2 ) ^1 × (1/8)^2

= 0. 2 × 1/64

= 0. 2 × 0. 016

= 0. 0031

4a. (1/2)^2/ (5/8)^1

= [tex]\frac{\frac{1}{4} }{\frac{5}{8} }[/tex]

Take the inverse of the denominator

= [tex]\frac{1}{4}[/tex] × [tex]\frac{8}{5}[/tex]

= 2/5

4b. 7^2 - 0. 5^3

= 49 - 0. 125

= 48. 875

5a. 3^1 - 0. 8 ^2

= 3 - 0. 64

= 2. 36

5b. 0. 7^2 + 0. 9^1

= 0. 49 + 0. 9

= 1. 39

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x: -1/2

-6(x-2):

por favor necesito una respuesta

Answers

The value of the expression if x = -1/2 is 15

Function and values

Given the expression below shown;

f(x) = -6(x - 2)

If the value of x is -1/2, hence;

f(-1/2) = -6(-1/2 - 2)

Simplify

f(-1/2) = -6(-5/2)

f(-1/2) = 6 * 5/2

f(-1/2) = 3 * 5 = 15

Hence the value of the expression if x = -1/2 is 15

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Identify an equation in point slope form for the line parallel to y=-2/3×+8 that paases through (4,-5)

Answers

Answer:

y=-2/3x-7/3

Step-by-step explanation:

a parallel line has the same slope but different y intercept

so we need to solve for y=-2/3x+b

since it passes through 4,-5 we can plug it in for x and y

-5=-2/3(4)+b

-5=(-8/3)+b then add 8/3 to both sides

-5 is also -15/3

-7/3=b

so answer is y=-2/3x-7/3

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