Find m∠ABD and m∠CBD given m∠ABC = 111∘
The Equations are (-10x+58)∘ and (6x+41∘)
Write and Solve an equation

Find MABD And MCBD Given MABC = 111The Equations Are (-10x+58) And (6x+41)Write And Solve An Equation

Answers

Answer 1

Answer:

x=-3

<ABD=88

<CBD=23

Step-by-step explanation:

We know that <ABC is made up of 2 angles: <ABD and <CBD.

We also know that the m<ABC is 111.

Therefore, <ABD and <CBD added together must equal 111.

<ABD+ <CBD =111

We know that <ABD is -10x+58 and <CBD is 6x+41, so we can substitute these in.

-10x+58+6x+41=111

Combine like terms

(-10x+6x)+(58+41)=111

-4x+99=111

Now we need to solve for x. First, move all the constants to the same side. Subtract 99 from both sides, since 99 is being added to -4x.

-4x+99-99=111-99

-4x=12

Next, divide both sides by -4, since -4 and x are being multiplied.

-4x/-4=12/-4

x=-3

Now we know x, and can substitute it in to find the angle measures.

<ABD

-10x+58

-10(-3)+58

30+58

88

<CBD

6x+41

6(-3)+41

-18+41

23

Answer 2

[tex]m \angle ABD = 88^{\circ}\\m \angle CBD = 23^{\circ}[/tex]

Given:

m∠ABC = 111∘

m∠ABD = (-10x+58)∘

m∠CBD = (6x+41)∘

First, find the value of x by creating an equation

Thus:

[tex]m\angle ABD + m \angle CBD = m \angle ABC[/tex] (angle addition postulate)

Substitute

[tex](-10x+58) + (6x+41) = 111[/tex]

Solve for x

[tex]-10x+58 + 6x+41 = 111[/tex]]

Add like terms

[tex]-10x+58 + 6x+41 = 111\\-4x + 99 = 111\\-4x = 111 - 99\\-4x = 12\\[/tex]

Divide both sides by -4

[tex]x = -3[/tex]

Find m∠ABD and m∠CBD by plugging in the value of x

[tex]m\angle ABD = -10x + 58 \\m\angle ABD = -10(-3) + 58 \\m\angle ABD = 88^{\circ}[/tex]

[tex]m \angle CBD = 6x + 41\\m \angle CBD = 6(-3) + 41\\m \angle CBD = 23^{\circ}\\[/tex]

Therefore:

[tex]m \angle ABD = 88^{\circ}\\m \angle CBD = 23^{\circ}[/tex]

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Related Questions

A circle has a radius of 5/3 units and is centered at (9.2 -7.4)

Write the equation of the Circle.

Answers

Answer:

(x - 9.2)^2 + (y + 7.4)^2 = (5/3)^2

Step-by-step explanation:

We start with (x - h)^2 + (y - k)^2 = r^2.  The center is (h, k) and the radius is r.

Then we have:

(x - 9.2)^2 + (y + 7.4)^2 = (5/3)^2

Please Help Now Running out of time! In Sal’s sock drawer, there are 2 red, 2 blue, 2 yellow, 2 black, and 2 green socks. If he randomly picks one sock from the drawer, and then another, which fractions should Sal multiply to find the probability of choosing a pair of green socks?

Answers

Answer:

Step-by-step explanation:

C

Answer:

C

Step-by-step explanation:

2/10 1/9

A bag contains 12 red, 30 blue, 20 green, 10 yellow, and 8 black marbles. Nancy chooses 1 marble from the bag. What is the probability that the marble is red, blue, or black?

A.18
B.38
C.58
D.78

Answers

Step-by-step explanation:

Total marbles = 12 + 30 + 20 + 10 + 8 = 80

Probability = 12 + 30 + 8 = 50

= 50 / 80 = 5 / 8

please help!!! i really need the answer to this question, ill mark you as brainleist​

Answers

Hey there! I'm happy to help you! :)

We see that there are 160 songs in total. Let's split them up into groups of rock, country, and pop.

ROCK

Our problem says that 3/8 of the songs are rock songs. We know that we have 160 songs. We just need to multiply 3/8 by 160 and we will have the number of rock songs.

3/8*160=60

Therefore, we have 60 rock songs.

COUNTRY

We see that 25% of our songs are country songs. 25% is the same thing as 1/4, or 0.25. We can multiply this by our total number of songs to see how many are country.

0.25(160)= 40

We have 40 country songs.

POP

All we have in the problem is that the remaining songs are pop. The nice thing is is that we already know how many rock and country songs we have, so we can simply subtract those from 160 and we will then be able to tell how many pop songs there are.

160-60-40= 60

Therefore, there are 60 pop songs.

I hope that this helps you! Have a wonderful day!

Which of the following inequalities is correct?

Answers

Answer:

a < b < c

Step-by-step explanation:

a is -4, which is less than b, at 1, and c at 7.

If this answer is correct, please make me Brainliest!

Answer:

the answer is a it cant not be b,c

Someone please help me. I’m not good at mah but I would be thankful for ur help.

Answers

the perimeter is 44 inches!!

Answer:

1. 44 inches

hope this helps :)

Please please please please please please please pppppppllllllllllleeeeeeeaaaaasssseeehelp

Answers

Answer:

70

Step-by-step explanation:

its in the tens value

Answer:

70

Step-by-step explanation:

The number is in the tenths place.

Kathy found the volume of the figure using the expression (4 * 3 * 8) + (10 * 3 * 4). Sandy found the volume of the figure using the expression (3 * 10 x 4) + (4 * 3 * 4). Use the drop-down menus to explain who is correct. 10 cm Click the arrows to choose an answer from each menu, The expression for the volume of the figure was correctly determined by Choose... because the figure was divided into two rectangular → prisms that Choose...

Answers

Answer:

The correct options are;

1) Sandy is correct

2) The figure was divided into two rectangular prisms that are calculated separately

Step-by-step explanation:

Here we have to divide the figure into two rectangular prisms so as not to calculate for a dimension twice

Therefore, the figure can be split into a horizontal prism at the top with dimensions and volume = 10 × 4 × 3 and the vertical prism below will now have a dimension and hence, volume of 4 × 4 × 3

Therefore the volume of the figure is the sum of the volumes of the two prisms found as follows;

Volume of the figure =  10 × 4 × 3 + 4 × 4 × 3  = 168

We can try the othe way to confirm as follows

Volume of the prism below = 4 × 3 × 8 = 96

Volume of the horizontal prism above is now = 4 × 3 × 6 = 72

Volumre of the figure = 96 + 72 = 168

Therefore, since the volume = (10 × 4 × 3) + (4 × 4 × 3), Sandy is correct

Because the figure was divided into two rectangular prisms that are calculated separately.

Answer:

1(sandy is correct)

2(do not overlap

Step-by-step explanation:

The value of x 3y, for x = -2 and y = 3, is -24. True False

Answers

Answer:

true

Step-by-step explanation:

x^3 y when x = -2 and y = 3

(-2)^3  * 3

-8 *3

-24

This is true

Which has a value closest to 9?
✓99
V83
VIO
V63

Answers

Answer:

[tex]\sqrt{83\\}[/tex] has the closet value to 9 bc its 9.11

V83 because it makes the most sense

of the following numbers, which has the most factors of 3?
a) 81
b) 270
c) 999
d) 3333

Answers

Answer:

81 has the most factors of 3

Step-by-step explanation:

To conclude which of the following options has the most factors of 3, take each of the number's prime factorization, which will help us solve the problem.

( 1 ) 81 is a composite number and is 9 squared. Knowing that 3 squared = 9, we can say that the prime factorization of 81 = 3 [tex]*[/tex] 3 [tex]*[/tex] 3 [tex]*[/tex] 3, which can also be denoted as 3⁴.

( 2 ) 270 is a composite number. The exponents in the prime factorization are 1, 3, and 1, and therefore it's prime factorization is - 3 [tex]*[/tex] 5 [tex]*[/tex] 3 [tex]*[/tex] 2 [tex]*[/tex] 3, composed of 3 3s.

( 3 ) If we put all of it together we have the factors 3 x 3 x 3 x 37 = 999. It can also be written in exponential form, with 3 to the power of 3 - hence having 3 factors of 3.

And finally the value 3333 has the prime factorization of 3 [tex]*[/tex] 11 [tex]*[/tex] 101, and as you can see it has 1 factor of 3. 81, having 4 factors of 3, is present with the most factors, and therefore is our solution.

Number 81 has the most number of factor 3. Option A is correct.

A number from the options to be determined that has the most number of factor 3.

What are the factors?

factors can be defined by splitting the value into multipliable values.

Here,
Factors of 81 = 3,3,3,3            Number of factor 3 = 4
Factors of 270 =2,3,3,3,5       Number of factor 3 = 3  
Factors of 999 =3,3,11             Number of factor 3 = 2
Factors of 3333 = 3,11             Number of factor 3 = 1
As per the above comparison, 81 has the most number of factor 3.

Thus, Number 81 has the most number of factors 3.

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A stick 1 meter long casts a shadow 1.5 meters long. A building casts a shadow 17 meters long. How tall is the building (to 2 decimal places)

Answers

I’m not sure keep trying

What is the area of the triangle shown below?

Answers

Answer:

48

Step-by-step explanation:

Split it into 2 right triangles flip one around and you have a rectangle who's area is equal to 10x6.

a=6

c=2

b=?

Solve for b:


Use the formula to help you answer the question below. Do not include units
in your answer.
Rate . Time = Distance
How many hours will it take to complete a 45-km bike ride if you go 12 km per
hour the whole time?

Answers

It will take about 3.75 hours to complete.

BC =
Round your answer to the nearest hundredth.

Answers

Answer:

Since its a right triangle you automatically know the C is 90 degrees. And since all triangle have to add up to 180 degrees, you know B has to equal 40 degrees.

A= 50

B= 40

C= 90

B + C

40 + 90

BC = 130 degrees

Answer:

2.3

Step-by-step explanation:

Khan

(x + m)(x + n) if m= 5 and n = -7

Answers

Answer:

[tex]x^2-2x-35[/tex]

Step-by-step explanation:

[tex](x+5)(x-7)=[/tex]

[tex]x^2+5x-7x-35=[/tex]

[tex]x^2-2x-35[/tex]

Hope this helps!

Answer:

X^2-2x-35

Step-by-step explanation:

(X)(x)+(x)(-7)+(5)(x)+(5)(-7)

X^2-7x+5x-35

X^2-2x-35

Hope that was the answer you were looking for

Determine whether each statement is true or false.

(FINALEXAM)

Answers

Answer:

1. False

2. True

Step-by-step explanation:

Number 1 False
Number 2 true

Write a formula for quadratic function if its graph has the vertex at point (0,6) and passes through the point (−1,−2).

Answers

Answer:

y = - 8x² + 6

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (0, 6), thus

y = a(x - 0)² + 6, that is

y = ax² + 6

To find a substitute (- 1, - 2) into the equation

- 2 = a(- 1)² + 6, that is

- 2 = a + 6 ( subtract 6 from both sides )

- 8 = a

y = - 8x² + 6

The formula of the quadratic function is [tex]y = -8x^2 + 6[/tex]

A quadratic function is represented as:

[tex]y = a(x - h)^2 + k[/tex]

The vertex of the quadratic function is given as:

[tex](h,k) = (0,6)[/tex]

So, we have:

[tex]y = a(x - 0)^2 + 6[/tex]

This gives:

[tex]y = ax^2 + 6[/tex]

The quadratic function passes through (-1,-2).

So, we have:

[tex]-2 = a(-1)^2 + 6[/tex]

[tex]-2 = a + 6[/tex]

Subtract 6 from both sides

[tex]a = -8[/tex]

Substitute -8 for a in [tex]y = ax^2 + 6[/tex]

[tex]y = -8x^2 + 6[/tex]

Hence, the formula of the quadratic function is [tex]y = -8x^2 + 6[/tex]

Read more about quadratic functions at:

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Stephanie and alejandro
were planning thier wedding.
Stephine saved up four times.
more money than alejandro
because he lost his job at walmart. Together $15,600 How much did each one save ?
steps ?

Answers

Answer:

Stephanie saved

Step-by-step explanation:

x+4x=15600

5x=15600

divide by 5 on both sides

you get 3120

since stephanie got 4 times more, you multiply 3120*4 and get 12480

therefore, Alejandro saved 3120

: )

How do you know when expression are equivalent

Answers

Answer:

If two things are equivalent, they are the same. Equivalent expressions are expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will each give you the same value when you simplify.

Step-by-step explanation:

Answer: Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(

Step-by-step explanation:

Solve the following system of equations using any method you want.
y + 2x = 2
2x - 5y = 14 please help

Answers

2x+y=2
2x-5y=14
Subtract the two equation
6y= -12
Y= - 2
Put y= -2 in any equation
2x-2=2
2x=4
X=2

Answer:

y = - 2, x = 2

Step-by-step explanation:

Remove x and solve for y

2x - 2x - 5y - y = 12

-6y = 12

y = - 2

Substitute y back into the equation

-2 + 2x = 2

2x = 4

x = 2

What is the area of one of the triangular faces?
4 in
3 in
7 in
7 in
5 in
4 in
5 in

Answers

Answer:6

Step-by-step explanation:

I got it corrected on the assignment

Answer:

it is 6

Step-by-step explanation:

the person above me is right :) have a nice day

(◍•ᴗ•◍)✧*。

Write a linear equation from a slope and a point

Answers

Slope=4/2 point=(1,2)
2=4/2(1)+b
b=0
y=2x

The volume of a rectangular prism is v = Lwh, where v is the volume, L is the length, w is the width, and h is the height. Rewrite this equation with w solved in terms of v, l, and h.

Answers

Answer:

w=v/lh

Step-by-step explanation:

lwh=v

To isolate w, we'd have to divide both sides by (lh)

Therefore, w = v/lh

Hope this helped and have a good rest of your day!

Find the area of a circle whose circumference is 87 m.
A. 4 m 2
B. 8 m2
C. 16 m2
D. 64 m2

Answers

Answer:

None of those are right, the answer is about 602.32 m2

Step-by-step explanation:

George still has 40 percent of his book to read. If George has read 180 pages, how many pages does he still have to read? How do you know?

Answers

Answer:  72

Step-by-step explanation:    so you do a line = line method the lines should look like they are fractions.  

you do it for the both numbers the percent is always out of 100.

it should look like this

40%            ?

--------- = -----------    

100%       180

then you cross multiply 40 and 180 and than divide it by 100.   your answer should be 72.    you later replace the ? with 72

you know this because It is smaller than 180 and its bigger than the number 40.

The number pages left to read is 12 pages.

Given that, George still has 40 percent of his book to read.

What is percentage?

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Let the total number of pages be x.

Now, x-40% of x=180

⇒ x-0.4x=180

⇒ 0.6x=180

⇒ x=180/0.6

⇒ x=300

So, remaining pages = 300-180=120

Therefore, the number pages left to read is 12 pages.

To learn more about the percentage visit:

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Ken baked a pan of brownies for a potluck. The number of squares he cuts the brownies into will depend on the number of people attending the potluck. s = the number of squares Ken cuts the brownies into. p = the number of people attending the potluck. Which of the variables is independent and which is dependent?

Answers

Answer:

P is the independent variable while S is the dependent variable

Hope this Helps :)

Which graph represents -x+ 8y > - 24

Answers

Kind of need a picture to help answer the question.

(9x2+3x-5) - (3x2+4x-10)

Answers

Answer:

39

Step-by-step explanation:

I'm assuming x is supposed to be a multiplication sign.

You need to use PEMDAS for this:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

(9x2+3x-5)-(3x2+4x-10)=

(18-15)-(6-40)=

3-(-36)=

3+36=

39

!!!!!!NEED HELP !!!!!! y=-50x + 750 which of the following does NOT match the equation shown.

Answers

Answer:

I think its B

Hope it helps :/

Answer:

y=10x-50

Step-by-step explanation:

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