Point C is in the interior of ∠ABD, and ∠ABC ≅ ∠CBC. If m∠ABC = (5/8x + 18) and m∠CBD = (4x), what is m∠ABD?

Answers

Answer 1

Answer:

[tex]\angle ABD =42.4^{\circ}[/tex]

Step-by-step explanation:

We are given that Point C is in the interior of ∠ABD

We are also given that ∠ABC ≅ ∠CBD

Now ,

[tex]\angle ABC = (\frac{5}{8}x + 18)\\\angle CBD = (4x)[/tex]

Since we are given that ∠ABC ≅ ∠CBD

So, [tex]\frac{5}{8}x + 18=4x\\4x-\frac{5}{8}x=18\\\frac{32x-5x}{8}=18\\\frac{27x}{8}=18\\x=\frac{18 \times 8}{27}\\x=5.3[/tex]

[tex]\angle CBD = (4x)=4(5.3)=21.2^{\circ}[/tex]

[tex]\angle ABD = \angle CBD+\angle ABC=21.2+21.2=42.4^{\circ}[/tex]

Hence [tex]\angle ABD =42.4^{\circ}[/tex]


Related Questions


If it takes 930 kg of food to feed a pair
of elephants for 3 days, how much food
would you need to feed them for a week?

Answers

Answer:

2170

Step-by-step explanation:

930 divided be 3= 310

310 multiplied by 7=2170

what are factors of 7​

Answers

Answer:

1 and 7

Step-by-step explanation:

Please help me ...............,..

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Answer:

Angle A and H are Alternate exterior angles and they are congruent.

5 divided 5/6 helpabacon hair please

Answers

Answer:

what? expalint the question

Step-by-step explanation:

Based on the survey results from 300 selected students in the Burbank School District (BSD), the 98% confidence interval used to estimate the population proportion of all BSD students who have access to a working computer at home was computed to be 48% to 60%. The following 2 subquestions require a numeric input, no work is necessary. [2 points] What number of students (out of the 300 sampled) have access to a working computer at home

Answers

Answer:

follows are the solution to this question:

Step-by-step explanation:

Please find the correct question in the attached file:

The formula for calculating the Confidence interval of proportion:

[tex]\to CI=\hat{p} \pm Z_{\frac{\alpha}{2}} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\\to \hat{p}=\frac{\text{lower limit +upper limit}}{2}\\[/tex]

      [tex]=\frac{0.48+0.60}{2}\\\\=\frac{1.08}{2}\\\\=0.54[/tex]

The number of learners with access to working at home on a computer:

[tex]= 0.54 \times 300 \\\\=162[/tex]

Lower limit =0.48

upper limit = 0.60

[tex]\to margin \ error = \frac{\text{upper limit - lower limit}}{2}\\[/tex]

                          [tex]=\frac{0.60-0.48}{2}\\\\=\frac{0.12}{2}\\\\= 0.06[/tex]

20% of the days were sunny. How many days were sunny?

Answers

Answer:

73

Step-by-step explanation:

simple math, ez mne.

Answer:

73 days were sunny

Step-by-step explanation:

20% of 365 is 73.

Translate the sentence into an equation.
Seven times the sum of a number and 2 is 6.
Use the variable y for the unknown number.

Answers

Answer:

7(y+2)=6

Step-by-step explanation:

its right

If a roof has a pitch of 5 to 11, how high will the roof rise over a 33-foot run?
a.
3
C.
2
72 feet
1 feet
b. 15 feet
d.
20 feet

Answers

The answer is b. 15ft

plz help i need this quick consider the equation 9(x+4)=-27what value of x makes this statement true?

Answers

Answer:

x=-7

Step-by-step explanation:

janesa has 24 coins in her pocket worth exactly $1.00. she tells her younger brother jackson that he can have the coins if he correctly guesses how many of each coin she has. she gives him the hint that there are only nickels and pennies. complete the equation that represents the total value of the nickels and p pennies 5( blank ) + p = 100

Answers

Answer:

Number of Nickels = 19

Number of pennies = 5

Step-by-step explanation:

The type of coins that Janessa has = nickels and pennies.

Janessa has a total number of 24 coins

The sum of the nickels and pennies = $1.00

Let us represent the number of nickels as x

The number of pennies as y

Hence, our system of equations is :

x + y = 24..... Equation 1

x = 24 - y

A nickel is worth 5 cents.

1 nickel = $0.05

A penny is worth 1 cent.

1 penny = $0.01

Therefore,

$0.05× x + $0.01 × y= $1.00

0.05x + 0.01y = 1.00........Equation 2

Substitute 24 - y for x in Equation 1

0.05(24 - y) + 0.01y = 1

1.2 - 0.05y + 0.01y = 1

1.2 - 1 = 0.05y - 0.01y

0.2 = 0.04y

y = 0.2/0.04

y = 5

We have 5 pennies

x = 24 - y

x = 24 - 5

x = 19

We have 19 nickels

8 tomatoes for $2 unit rate
I don't have much so please 17

Answers

That would be 16 dollars I’m pretty sure dude

Michael exercises more than 35 minutes per day.
Use t to represent Michael's amount of exercise (in minutes per day).

Answers

Answer:

t>35

Step-by-step explanation:

Since Michael exercises more than 35 days, t is greater than 35. To express that in an inequality, the answer is t>35. Hope this helped!

A circle is inscribed in a square. If the perimeter of the square is 40, what is the area of the circle? Use 3.14 for pi.

Answers

Answer:

78.5

Step-by-step explanation:

We have the perimeter of the square, which is 40, and 40/4=10. In this picture, we see that the circle's diameter is the same as the length of one side of the square. Therefore, the diameter of the circle is 10. The are formula for circles is [tex]\pi r^{2}[/tex], where [tex]r[/tex] is the radius. The radius of the circle is just the diameter divided by 2, and 10/2=5. Now, [tex]5^2[/tex] is 25, and [tex]3.14\cdot25=78.5[/tex].

PLEASE HURRY!!!! WILL MARK BRAINLIST!!!!!!d. Using the equation for average rate above, determine the cheetah's average rate for the entire

trip.

Answers

Answer:

Average Rate = 55mph

Step-by-step explanation:

Now it’s time to tackle the original question. Going from point A to point B, the cheetah traveled at an average rate of 70 mph. Returning to point A, the cheetah traveled at an average rate of 40 mph.

Can we say that this cheetah’s average rate was 55 mph?

a.The average rate for the trip is equal to the total distance traveled divided by the total time traveled.

Average Rate = 70+ 40/2= 110/2 = 55mph

Yes the average rate of the cheetah is 55 mph

The following equations represent the distance traveled on each leg of the trip.

First leg of trip: td=r1 t1= 70*t

Second leg of trip: td=r2 t2= 40*t

Write an equation for the average rate for the trip. Remember, the cheetah runs from point A to point B and back to point A.

Total distance = r1 t1+ r2 t2

Average rate = Total distance / total time

                        =  r1 t1+ r2 t2/ t1+ t2

                        =70t+ 40t/ 2t

                         =110t/2t

                          = 55mph

                           

Answer:

the answer is 55 mph

Step-by-step explanation:

Average rate = Total distance / total time

                       =  r1 t1+ r2 t2/ t1+ t2

                       =70t+ 40t/ 2t

                        =110t/2t

what is the measure of each angle

Answers

Answer:

60 degrees

Step-by-step explanation:

60 degrees because all sides are equal and 180/3 is 60.

60 degrees because a triangle is 180 and there are 3 sides so all of them are equal

In order to receive credit for an English assignment, Alex must reflect on AT LEAST 5 out of 7 passages. In how many ways can this be done?

Answers

Answer:

expressionism I just took that test trust you got a workout and English and I'm miss that I hope we close at Johnny's and I'm miss that I hope we close again for the one that was a big deal for me to hit the road and I'm miss that I hope we close again for the one time of day or so he can come over for a lol you want to text cause I'm miss that I hope we close again for the one that was a if he can come over for a lol you want to text Leo and I'm miss that I hope we close again for the one that 5th to text cause I'm miss that I hope.

I think it’s 35 ways

I’LL MARK BRAINLEST! :)

Answers

Answer:

9.9

Step-by-step explanation:

7^2+7^2= c^2

c= 9.9

Answer:

the correct answer is 10.9

Step-by-step explanation:

I got this answer right.

PLEASE HELP!!!!!!! Which set of numbers is arranged in decreasing order?

Answers

Answer:

C

Step-by-step explanation:

 [tex]\bold{Hello!}\\\bold{Your~Answer~Is~Below!}[/tex]

______________________________

 [tex]\bold{Solutions~Steps:}[/tex]

[tex]1.)~Simplify~everything~into~decimal~form:[/tex]

[tex]\bold{2\pi}[/tex][tex]\bold{6.283185307}[/tex][tex]\bold{\sqrt{37}}[/tex][tex]\bold{6.08276253}[/tex][tex]\bold{\frac{55}{9}}[/tex][tex]\bold{6.111111111}[/tex]

[tex]2.)~Round~to~the~nearest~hundredth :[/tex]

[tex]\bold{2\pi:6.283185307=6.28}[/tex][tex]\bold{\sqrt{37}:6.08276253=6.08}[/tex][tex]\bold{\frac{55}{9}:6.111111111=6.11}[/tex]

[tex]3.)~Order~them~in~decreasing~order,~(Greatest~to~Least:)[/tex]

[tex]\bold{6.82}[/tex][tex]\bold{2\pi}[/tex][tex]\bold{\frac{55}{9}}[/tex][tex]\bold{\sqrt{37}}[/tex]

______________________________

 [tex]\bold{Answer:}[/tex]

[tex]\bold{The~correct~decreasing~order~is~\boxed{C.}}[/tex]

______________________________

 [tex]\bold{Hope~this~helps,}\\\bold{And~best~of~luck!}\\\\\bold{~~~~~-TotallyNotTrillex}[/tex]

A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 20 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight

Answers

Answer:

0.128rad/sec

Step-by-step explanation:

Let x represent the between the man and the point on the path

θ = the angle

dx/dt = 4 ft/s

dθ/dt = rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight

tan θ = x/20 ft

Cross Multiply

20tan θ = x

dx/dt = 20sec² θ dθ/dt

dθ/dt = 1/20 × cos² θ dx/dt

dθ/dt= 1/20 × cos² θ × 4

dθ/dt = 1/5 × cos² θ

Note : cos θ = 4/5

dθ/dt = 1/5 × (4/5)²

dθ/dt = 16/125

dθ/dt = 0.128rad/sec

Provide a) the **EQUATION** and b) the solution for the following:
During a charity drive, the senior class raised $85 more than twice the amount raised by the freshman class. The senior class raised $555. How much did the freshman class raise?

Answers

Answer:

y= 2x + 85

y= $555

x= $235

Step-by-step explanation:

Let y be the amount the senior class raised

Let x be the amount the freshmen class raised

Insert known values

$555 = 2x + $85

Subtract 85 from both sides

$470 = 2x

Isolate the variable (x) by dividing each side by 2

$235 = x

Hope this helps! :)

what is the slope intercept form of 7,-1 5,6

Answers

Answer:

[tex]y = - \frac{7}{2} x + \frac{47}{2}[/tex]

The distance between Point P and Point Q was 3600 m. Beng Leong started jogging
at 08 35 from Point P and reached Point Q at 08 50. At the same time, Sam started
jogging from Point P at a speed of 200 m/min. Who jogged at a faster speed?
How much faster was his speed?

Answers

Answer:

Ben ran at a speed of 240m/min and Sam ran at a speed of 200m/min So Ben is faster by a rate of 40/min

Step-by-step explanation:

Ben's miles per minutes

[tex] \frac{3600}{15} = 240[/tex]

Sam's miles per minute

Given

Which equation shows y=3x−15 in standard form?

A. 15x−5y=1

B. 15x+5y=−1

C. 5x−15y=1

D. 5x−15y=−1

Answers

Answer:

c  5x -15y =1

Step-by-step explanation:

5x-15y=1

-5x -15y= 1 -5x     change the signs on both sides of the equation

     15y = -1 +5x      divide both sides by 15

         y = -1/15 + 1/3 x    Reorder the terms

         y = 3x-15

              :)

     

     

All options are wrong here.

Given equation is  [tex]y=3x-15[/tex].

the equation given here is in form of [tex]y=mx+c[/tex] . The general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis) .

We have to write [tex]y=3x-15 \\[/tex] in standard form.

The standard form for linear equations in two variables is Ax+By=C.

Now we convert [tex]y=3x-15[/tex] in standard form.

Here [tex]y=3x-15\\[/tex]

[tex]y-3x=-15\\\\-y+3x=15[/tex]

[tex]3x-y=15[/tex]

But no options match with the above standard form of equation.

Hence all options are wrong here.

For more details on standard form for linear equations follow the link:

https://brainly.com/question/7380540

What is the first step when solving the equation 3(3x-5x)+2=-8

Answers

Answer:

Collect the like terms

Step-by-step explanation:

(3x-5x)

3x (-2x) + 2 = -8

multiply the parenthesis and then add the like terms

Use a calculator to find a value of θ between 0° and 90° that satisfies the statement. Write your answer in degrees and minutes rounded to the nearest minute.


csc(theta)= 4.1191

Answers

Answer:

[tex]\theta = 14.1\ degrees[/tex]

[tex]846\ minutes[/tex]

Step-by-step explanation:

Given

[tex]csc(\theta) = 4.1191[/tex]

Required

Solve for [tex]\theta[/tex]

[tex]csc(\theta) = 4.1191[/tex]

[tex]csc(\theta) = \frac{1}{sin(\theta)}[/tex]

So, we have:

[tex]\frac{1}{sin(\theta)} = 4.1191[/tex]

Invert both sides

[tex]sin(\theta) = \frac{1}{4.1191}[/tex]

[tex]sin(\theta) = 0.2428[/tex]

Take [tex]sin^{-1}[/tex] of both sides

[tex]sin^{-1} sin(\theta) = sin^{-1}0.2428[/tex]

[tex]\theta = sin^{-1}0.2428[/tex]

[tex]\theta = 14.0518577574[/tex]

[tex]\theta = 14.1\ degrees[/tex] --- approximated

Convert to minutes:

[tex]1\ degree = 60\ minutes[/tex]

So:

[tex]14.1\ degrees = 14.1 * 60\ minutes[/tex]

[tex]14.1\ degrees = 846\ minutes[/tex]

You measure the period of a mass oscillating on a vertical spring ten times as follows:

Period (s): 1.06, 1.31, 1.28, 0.99, 1.48, 1.37, 0.98, 1.31, 1.59, 1.55

Required:
What are the mean and (sample) standard deviation?

a. Mean: 1.228, Standard Deviation: 0.2135
b. Mean: 1.325, Standard Deviation: 0.1674
c. Mean: 1.292. Standard Deviation: 0.2211
d. Mean: 1.228, Standard Deviation: 0.2098
e. Mean: 1.292, Standard Deviation: 0.2135

Answers

Answer:

Step-by-step explanation:

Mean is the ratio of sum of the dataset to the sample size. Mathematically:

[tex]\overline x = \frac{\sum Xi}{N}[/tex]

Xi are the individual periods

N is the sample size

[tex]\sum Xi = 1.06+1.31+1.28+0.99+1.48+1.37+0.98+1.31+1.59+1.55\\\sum Xi = 12.92[/tex]

N = 10

Substitute

[tex]\overline x = \frac{12.92}{10}\\\overline x = 1.292[/tex]

hence the mean of the samples is 1.292

For the standard deviation:

[tex]\sigma = \sqrt{\frac{\sum (x-\overline x)^2}{N} } \\[/tex]

[tex]\sum (x-\overline x)^2 = (1.06-1.292)^2+ (1.31-1.292)^2+ (1.28-1.292)^2+ (10.99-1.292)^2+ (1.48-1.292)^2+ (1.37-1.292)^2+ (0.98-1.292)^2+ (1.31-1.292)^2+ (1.59-1.292)^2+ (1.55-1.292)^2\\\sum (x-\overline x)^2 = 0.43996[/tex]

Substitute into the formula:

[tex]\sigma = \sqrt{\frac{0.43996}{10} }} \\\sigma = \sqrt{{0.043996}}} \\\sigma = 0.2098[/tex]

Hence the standard deviation is 0.2098

30 point question! WILL AWARD BRAINLIEST!

A ball is thrown across a playing field from a height of h = 5 ft above the ground at an angle of 45° to the horizontal at the speed of 20 ft/s. It can be deduced from physical principles that the path of the ball is modeled by the function
y = − (32/(20^2))x2 + x + 5


Find the horizontal distance the ball has traveled when it hits the ground. (Round your answer to one decimal place.)

Answers

y = [-32/(20)^2]x^2 + x + 5
a.) For maximum height, y' = 0
y'= (-32/200)x + 1 = 0
32/200x = 1
x = 200/32 = 6.25
The maximum height attained by the ball is [-32/(20)^2](6.25)^2 + 6.25 + 5 = 8.125 feet.

b.) At the point the ball hits the ground, y = 0
y = [-32/(20)^2]x^2 + x + 5 = 0
x = 16.3 ft

Answer:

Answers are down below ;)

Step-by-step explanation:

y = − (32/(20^2))x2 + x + 5

Plug into the calculator: -32/20^2 = -.08x^2

 Find the maximum height attained by the ball:

Rewrite the equation:

y= -.08x^2 + x +5

This parabola is a negative meaning that it will be maximum

to find the maximum we use the formula -b/2a

-(1)/ 2 (-.08) = -1/ -.16= 6.25

we plug 6.25 back into the equation y= -.08(6.25)^2+ (6.25) +5 = 8.125

The maximum height attained by the ball: 8.125 feet

Find the horizontal distance the ball has traveled when it hits the ground.

This can be found with the quadratic equation, x = [-b ± √(b2-4ac)]/2a

a= -.08 , -b= -1, c= 5 (When you are plugging in the numbers, make sure to break them down).

-(-1)± √(-1)^2-4(-.08)(5)] 2(-.08) -->

[-1 ± √(1 + 1.28)]/-.16 = [-1 ± √(2.6)]/-.16 = [-1 ± 1.61]/-.16 =

The horizontal distance of the ball is x = 16.31 feet

Say thank you by commenting down below :)

SOMEONE PLEASE HELP ILL GIVE BRAINLIEST

Answers

Answer:

A.

Step-by-step explanation:

If b^2 = 25 then b= Answer it please

Answers

Answer:

b = 5

mark me as brainliest plz!! :DD

You have 8 donuts and you want to give 1/4 of them to a friend. How many donuts would your friend get?​

Answers

Answer: pretty sure the friend would get 2 donuts

Step-by-step explanation:

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