If ray BD bisects angle CBE, ray BC is transparent to ray BA, angle CBD = (3x + 25) degrees, and angle DBE = (7x - 19) degrees, find angle ABD
Answers
Answer: The required measure of angle ABD is 148°.
Step-by-step explanation: Given that ray BD bisects angle CBE, ray BC is transparent to ray BA.
Also,
[tex]m\angle CBD=(3x+25)^\circ,~~m\angle DBE=(7x-19)^\circ,~~m\angle ABC=90^\circ.[/tex]
We are to find the measure of angle ABD.
Since ray BD bisects angle CBE, so we have
[tex]m\angle CBD=m\angle DBE\\\\\Rightarrow (3x+25)^\circ=(7x-19)^\circ\\\\\Rightarrow 3x+25=7x-19\\\\\Rightarrow 7x-3x=25+19\\\\\Rightarrow 4x=44\\\\\Rightarrow x=\dfrac{44}{4}\\\\\Rightarrow x=11.[/tex]
So, we get
[tex]m\angle CBD=(3\times11+25)^\circ=58^\circ.[/tex]
Therefore,
[tex]m\angle ABD=m\angle ABC+m\angle CBD=90^\circ+58^\circ=148^\circ.[/tex]
Thus, the required measure of angle ABD is 148°.
Related Questions
Natalia is making gift bags for her son's birthday party. Each bag costs $3.24 to make and she needs to make 15 bags. How much will the 15 bags cost?
A.) $48.60
B.) $47.40
C.) $486.00
D.) $4.74
Answers
15 x 3.24 =48.60
Answer:
48.60
Step-by-step explanation:
The answer is $48.60 you just have to multiply the amount of bags times the cost of each bag to get your amount so
15 x 3.24 =48.60
how would you translate this into an equation
"one less than the product of number and 3 is 5 more than the number itself "
Answers
Hope this helps!
Justify the last two steps of the proof.
Given MN is congruent to segment PO and MO is congruent to PN
Prove MNO is congruent to PON
Proof:
1. MN is congruent to segment PO _______ 1. Given
2.MO is congruent to PN_______ 2. Given
3. NO is congruent to ON ________ 3. ?
4.MNO is congruent to PON___ 4. ?
*Symmetric Property of congruent to; SAS
*Reflexive Property of congruent to; SAS
*Symmetric Property of congruent to; SSS
*Reflexive Property of congruent to; SSS
Answers
NO and ON are the same line. They are congruent by the reflexive property (a line segment is a reflection of itself).
Statement 4:
Shape MNO and shape PON are congruent by side-side-side since:
side PN = side MO
side MN = side PO
side NO = side ON
Answer: Fourth option
Based on the information, the correct option is 4. Reflexive Property of congruent to; SSS
What is congruence?The reflexive property of congruence states that any geometric figure is congruent to itself. In other words, any shape or object is congruent to itself.
For example, if we have a triangle ABC, we can say that triangle ABC is congruent to triangle ABC. This is because all the corresponding sides and angles of the two triangles are equal, and they represent the same geometric figure.
NO and ON are the same line. They are congruent by the reflexive property (a line segment is a reflection of itself). Shape MNO and shape PON are congruent by side-side-side since:
side PN = side MO
side MN = side PO
side NO = side ON
Learn more about congruence
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About 36,100,000 households in the U.S. have cats and about 43,300,000 households have dogs. About how may more households dogs and cats
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Find a linear function that gives the cost in dollars of buying
Pop tarts on sale two boxes cost four dollars four boxes cost six dollars
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The linear function that gives the cost in dollars of buying Pop tarts can be obtained using the equation of a straight line with passing through points (2, 4) and (4, 6) as follows:
[tex] \frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1} \\ \\ \Rightarrow\frac{y-4}{x-2} = \frac{6-4}{4-2} = \frac{2}{2} =1 \\ \\ \Rightarrow y-4=x-2 \\ \\ \Rightarrow y=x-2+4=x+2[/tex]
Therefore, the linear function that gives the cost in dollars of buying Pop tarts is y = x + 2.
The store keeper sold 9 1/4 yards from a piece of material containing 53 yards. How much was left in the original piece?
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What is the distributive property of 60 - 50?
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Simple.
what is( ×+4 /6)=(18/12)
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x = 18/12 - 4/6. Simplify each fraction and 18/12 simplified by 6 will be 3/2 and 4/6 simplified by 2 would 2/3. The equation would now be x = 3/2 - 2/3. The least common denominator would be 6 so when converted the equation would now be 9/6 - 4/6 = 5/6 so x = 5/6. You can check your answer by substituting x in the original equation with 5/6 so it would be (5/6 + 4/6) = (18/12) and 5/6 + 4/6 = 9/6 and when expressed as a mixed number and simplified it would equal 1 1/2 and 18/12 simplified as a mixed number and simplified would equal 1 1/2.
1 1/2 = 1 1/2.
???????????????????????????
Answers
×+×+8=10
×=1
y=9
(X.Y)(1.9)
How to put 33 into 4:7
Answers
so
33 / 11 = 3
4 x 3 = 12
7 x 3 = 21
so answer
4:7 = 12:21
The Hamptons family has a fish tank holding 10,450 ml of water. The water is leaking at a rate of 270 ml per minute. Define the input and output in the given scenario
Answers
The input is any variable which goes into the system. In this case there is no input.
While the output is any variable going out of the system. In this case the output is the amount of water which leaked out.
Answer:
The number of minutes represents input and remaining water represents output.
Step-by-step explanation:
Given,
The original quantity of the water in the tank = 10,450 ml,
Also, the quantity of the water leaked per minute = 270 ml,
Thus, the quantity water leaked in x minutes = 270x
∵ Remaining water in the tank ( say y ) = Original water - leaked water
⇒ y = 10450 - 270x,
Which is the equation that shows the given scenario.
In this equation, x represents the input value and y represents the output value,
Hence, the number of minutes represents input and remaining water represents output.
A crane cable can support a maximum load of 20,000 kg. If a bucket has a mass of 4,000 kg and gravel has a mass of 1,500 kg for every cubic meter, how many cubic meters of gravel (g) can be safely lifted by the crane?
Answers
Answer:
10.67 kg of gravel can be safely lifted by the crane
Step-by-step explanation:
Maximum load that a crane can support = 20000 kg.
Bucket has a mass = 4000 kg
Gravel has a mass = 1500 kg for every cubic meter.
Let the volume of gravel is = g cubic meter
Therefore, mass of the gravel = 1500g kg
Now we form an equation to show the weight that the crane cable can support
Mass of Bucket + mass of Gravel = Total mass that a lift can support
4000 + 1500g = 20000
1500g = 20000 - 4000
1500g = 16000
[tex]g=\frac{16000}{1500}[/tex]
g = 10.67 kg
Therefore, 10.67 kg of gravel can be safely lifted by the crane.
what is 3(7x-6)<-81?
Answers
3(7x - 6) < -81
First, we need to apply the Distributive Property to the left side of the inequality.
This mathematical term means to multiply the number or variable outside of the parenthesis to all numbers and/or variables on the inside of the parenthesis.
Here's an example;
3(2 + 1)
Multiply the outside number by all inside numbers.
3(2) + 3(1)
Multiply.
6 + 3
Simplify the expression.
9.
Now that we've explained our concept for distributing, let's apply what we now know to our current problem.
3(7x - 6) < -81
Apply the Distributive Property to the left side of the inequality.
3(7x) + 3(-6)
Multiply.
21x - 18
We now have:
21x - 18 < -81
Now we need to isolate the variable. To do this, we need to make sure that 'x' is by itself. Since x is being subtracted by 18, we need to apply the opposite order of operations to both sides of the inequality.
Add 18 to both sides to isolate the variable.
21x < -63
We now need to solve for x. To solve for x, we need to divide both sides by 21, as iur variable is being multiplied by 21.
We are now left with:
x < -3
This is your final solution to your inequality.
I hope this answer helps you, and feel free to ask me any questions you have in the comments below this answer! Have a great day, and thank you for asking your question here at Brainly!
For f(x)=-3x+6, find f(-4)
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At the half ime show, a marching band marched in formation. the lead drummer started at a point with coordinates (–2, –5) and moved 3 steps up and 1 step right.
a. write a rule to describe the translation.
b. what were the coordinates of the drummer's final position?
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b) (-1, -2)
1. The radius, r, of a circle is one-half of the length of its diameter, d.
r = d
2r = d
+ r = d
r=d
r=
Answers
Answer:
2r=d stands as correct
Step-by-step explanation:
Is it possible for two different numbers, when squared, to give the same result? What does this result tell you about solving an equation when the variable is squared? How many solutions will an equation like this have? Will there always be the same number of solutions for any equation with a squared variable? Explain.
Answers
go to purplemath it helps me and it might help you
Let's assume x and y the 2 numbers.
x²=y²
x²-y²=0
(x-y)(x+y)=0
x=y or x=-y
When the variable is squared we introduce extra solutions :
we must verify if each solution is exact.
If then 2 numbers are differents, x=-y
Example: 5 and -5 ==> 5²=25 , (-5)²=25
The square root of 2.25 is
A.15
B.1.5
C.0.15
D.irrational
Answers
what is the measure of an angle that turns through 1/12 of a circle
Answers
Work: 1/12 x 360˚ = 30˚
Answer: 30˚
The measure of an angle that turns through 1/12 of a circle is 30 degree.
What is Angle?A pair of rays (half-lines) with a shared terminal are combined to form an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.
We know the complete is 360 degree.
Then, to turn 1/12 of circle
= 360 x 1/2
= 360 / 12
= 30 degree
Thus, the measure of angle is 30 degree.
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Thirty-five states in a country have four-star hotels. Assume the country has 50 states. (a) What fraction of the states can claim at least one four-star hotel? (b) How many states do not have a four-star hotel? (c) Write the fraction of states without a four-star hotel.
a. The fraction of states with a four-star hotel ........ (Simplify your answer.)
Answers
the portion of states that have a four star hotel compared to how many states there are uses the fraction 35/50. You must simplify this, and to do this you find the greatest value with can divide the numerator and the denominator. This is 5. 35/5=7, and 50/5= 10, therefore, 7/10
(b) 15
simply subtract the number of states which have a four star hotel from the total number of states
(c) 3/10
this is the same logic as (a). use the answer you got from part b, and simplify the fractions
The fraction of states with at least one four-star hotel is 7/10, 15 states do not have a four-star hotel, and the fraction of states without a four-star hotel is 3/10.
Answer to Student's Question
(a) To find the fraction of states with at least one four-star hotel, we divide the number of states with a four-star hotel by the total number of states. Therefore, the fraction is 35/50, which simplifies to 7/10.
(b) To determine how many states do not have a four-star hotel, we subtract the number of states with a four-star hotel from the total number of states: 50 - 35 = 15. So, there are 15 states without a four-star hotel.
(c) Finally, the fraction of states without a four-star hotel is the number of states without such hotels divided by the total number of states. This is 15/50, which can be simplified to 3/10.
An arithmetic sequence with a thrid term of 8 and constant difference of 5
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Let point C be between V and W on VW. Given that VW = 61, VC = z + 13, and CW = z + 8, solve for z. A. 18 B. 19 C. 20 D. 21
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Therefore:
VC + CW = VW
z+13+z+8 = 61
2z+21=61
2z=61-21
2z=40
z=40/2
z=20
Find the inverse of f(x)= -x + 3
Answers
The most important property of g and f being inverses of each other, is that
g(f(x))=x, also f(g(x))=x
so, what one function 'does' to x, the other 'undoes' it.
Thus, we have:
f(g(x))=x and alos f(g(x))= -g(x)+3, from the rule
thus :
-g(x)+3=x
-g(x)=x-3
g(x)=-x+3
check: f(g(x))=f(-x+3)=-(-x+3)+3=x-3+3=x
Answer: the inverse of f is g, such that g(x)=-x+3
x + y = 12
x - y = 10
What is the value of the x-determinant for the system shown?
(A.) -22
(B.) -12
(C.) -2
Answers
Final answer:
The value of the x-determinant for the system of equations is (C) -2, which is found by evaluating the determinant of the system's coefficient matrix.
Explanation:
To find the x-determinant for the system of equations given below:
x - y = 10
We can set up the coefficient matrix for these equations:
Matrix [A] =
| 1 1 |
| 1 -1 |
The determinant of this matrix is calculated by multiplying the diagonal elements and then subtracting the product of the off-diagonal elements. Hence, the determinant (det A) = (1)(-1) - (1)(1) = -1 - 1 = -2.
Therefore, the value of the x-determinant is (C) -2.
I thought of a number, multiplied it by 2 1/2 , divided the result by 1 1 /5 , subtracted 7/18 from it, and got 1 5/6 . What was my number?
Answers
The student's original number was 1 3/45. This was obtained by reversing the processes described in the problem and applying them to the final number.
Explanation:
To solve this problem, we basically need to reverse the operations given in the problem and perform them on the final answer 1 5/6. Let's start:
Add 7/18 to 1 5/6. The sum is 2. Multiply 2 by 1 1/5. The product is 2 2/5. Finally, divide 2 2/5 by 2 1/2. The quotient, which is the number the student originally thought of, is 48/45 or 1 3/45.
So the student's original number was 1 3/45.
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Mark draws one card from a standard deck of 52. he receives $ 0.35 for a heart, $ 0.55 for a jack and $ 0.85 for the jack of hearts. how much should he pay for one draw
Answers
To find out how much Mark should pay for one draw, calculate the expected value by multiplying the payouts for a heart, a jack, and the jack of hearts by their respective probabilities. Sum these values to find the amount Mark should pay per draw to make the game fair, which is $0.135.
To determine how much Mark should pay for one draw from the deck of 52 cards, we need to calculate the expected value (EV) of one draw. The EV is calculated by multiplying each outcome by its probability and summing these products.
The deck has 13 hearts, so the probability of drawing a heart (excluding the jack of hearts) is 12/52 or 3/13. Drawing any jack other than the jack of hearts has 3 possible outcomes in the remaining 51 cards; the probability is 3/52. The jack of hearts is a single card with a probability of 1/52. The remaining 36 cards are neither hearts nor jacks and yield no payout.
The EV is calculated as follows:
(12/52 × $0.35) for a heart
(3/52 × $0.55) for a jack
(1/52 × $0.85) for the jack of hearts
Adding these up we get: (3/13 × $0.35) + (3/52 × $0.55) + (1/52 × $0.85) = $0.13538. To ensure the game is fair and the host neither loses nor gains money in the long term, Mark should pay $0.135 per draw.
The Kendal Company manufactures automobile engine parts. Running the manufacturing operations requires 12 watts (units of electricity per hour). The amount of electricity required to run the manufacturing operations and lighting the facility is given by y = 12x + 24, where x is the number of hours of manufacturing and y is the amount of electricity expended. How much electricity is used on a day when no parts are manufactured? (x 0, y 0)
Answers
Answer:
The answer is 24 watts.
Step-by-step explanation:
Running the manufacturing operations requires 12 watts (units of electricity per hour).
The amount of electricity required to run the manufacturing operations and lighting the facility is given by [tex]y=12x+24[/tex]
Here x is the number of hours of manufacturing and y is the amount of electricity expended.
When there are no parts manufactured, then x = 0
[tex]y=12(0)+24[/tex] = 24.
Only individuals over the age of 60 need to create an estate plan? True or False
Answers
Answer: False
Step-by-step explanation: People of any age over 21 need to complete an estate plan or a will. If you don't complete an estate plan or a will, anything you have could be left to the government. Regardless of your age or income, you always want to have a plan to distribute your money should you die unexpectedly.
Find an equation of the sphere with points p such that the distance from p to a(−3, 6, 4) is twice the distance from p to b(5, 3, −2).
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How many ways are there to separate these 10 people into two groups, if no group can have less than 2 people?