If BE−→ B E → bisects ∠ABD and m∠ABE = 62°, find m∠ABD
Answers
Line segment BE bisects ∠ABD as shown in the figure.
Therefore
m∠ABE = m∠DBE
and
m∠ABD = m∠ABE + m∠DBE
Because m∠ABE = 62°, therefore m∠DBE = 62°, so that
m∠ABD = 62° + 62° = 124°
Answer: m∠ABD = 124°
Based on the definition of an angle bisector, m∠ABD = 124°.
What is Angle Bisector?An angle bisector is a line segment that divides an angle into two smaller angles that are congruent.
BE is an angle bisector, therefore:
m∠ABD = 2(m∠ABE)
m∠ABD = 2(62)
m∠ABD = 124°
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Related Questions
Suppose you buy a CD for $500 that earns 2.5% APR and is compounded quarterly. The CD matures in 3 years. How much will the CD be worth at maturity?
Answers
A=p (1+r/k)^kt
A future value?
P present value 500
R interest rate 0.025
K compounded quarterly 4
T time 3years
A=500×(1+0.025÷4)^(4×3)
A=538.82
8x-2y over 10xy if x=4 and y=-7
Answers
The value of the expression 8x-2y over 10xy when x=4 and y=-7 is -0.1643 (rounded to four decimal places).
Explanation:To evaluate the expression 8x-2y over 10xy when x=4 and y=-7, we substitute these values into the expression:
8(4)-2(-7) over 10(4)(-7)
Simplifying further,
32+14 over -280
46 over -280
Therefore, the value of the expression 8x-2y over 10xy when x=4 and y=-7 is -0.1643 (rounded to four decimal places).
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8% of x is equal to 48
Answers
answer
8% of 600 is equal to 48
divide 48 by 8%
48/0.08 = 600
check
600*0.08 = 48
x=600
In a batch of 280 water purifiers, 12 were found to be defective. What is the probability that a water purifier chosen at random will be defective? Write the probability as a percent. Round to the nearest tenth of a percent if necessary
Answers
If 12 were found to be defective out of 280 the experimental probability of a purifier being defective is:
12/280 which is:
4.3% (to nearest tenth of a percent)
Answer:
[tex]\text{Probability}=4.3\%[/tex]
Step-by-step explanation:
Given : In a batch of 280 water purifiers, 12 were found to be defective.
To find : What is the probability that a water purifier chosen at random will be defective? Write the probability as a percent.
Solution :
Total number of batch of purifiers = 280
Number of defective purifiers = 12
The probability that a water purifier chosen at random will be defective is given by,
[tex]\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total outcome}}[/tex]
[tex]\text{Probability}=\frac{12}{280}[/tex]
[tex]\text{Probability}=\frac{3}{70}[/tex]
Converting into percentage,
[tex]\text{Probability}=\frac{3}{70}\times 100[/tex]
[tex]\text{Probability}=4.28\%[/tex]
Round to nearest tenths,
[tex]\text{Probability}=4.3\%[/tex]
Explain how the GCF helps with the distributive property. Why is it so important to use the GCF when factoring a sum of two numbers?
Answers
GCF is the greatest common factor, that divides two number and the distributive property is that when a number multiplied with each number in the bracket and then perform addition or subtraction etc.
GCF help with distributive property and it is important to use when factoring a sum of two numbers. For example we have to add fractions 2/3 and 4/9, now the GCF is 9
2/3 + 4/9
= 2(3) + 4 (1) / 9
Now 2 is the common factor, so it allow us to use the distributive property.
= 2 (3 + 2) / 9
= 2(5) /9
=10 / 9 is the answer.
The domain of the function is given. Find the range.
f(x) = 2x - 1
Domain: {-2, 0, 2, 4}
Answers
So for x = -2, f(x) = 2(-2) - 1 = -5
The range will consist of -5 and the other 3 values of f(x) found for x = 0, x=2 and x=4.
25 decreased by 1/5 of a number is 18
Answers
The equation for the student's question is 25 - (1/5)x = 18. Solving for x involves simple algebraic manipulation, resulting in x being equal to 35.
Explanation:The student's question '25 decreased by 1/5 of a number is 18' is a basic algebra problem. We could represent the unknown number as x. So the equation would be 25 - (1/5)x = 18.
To solve the equation 25 decreased by 1/5 of a number is equal to 18, we can set up the equation as 25 - (1/5)x = 18, where x is the unknown number.
To isolate x, we first subtract 25 from both sides of the equation:
- (1/5)x = -7.
Next, we can multiply both sides of the equation by -5 to eliminate the fraction:
x = (-7) * (-5) = 35.
To solve for x, first, add (1/5)x to both sides to get 25 = 18 + (1/5)x.
Then, subtract 18 from both sides to obtain 7 = (1/5)x. Finally, multiply both sides by 5 to find the value of x. Thus, x equals 35.
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Suppose a study estimated that 85% of the residents of a town (with an error range of ±12 percentage points at 95% confidence) favor building a new community center. Which of the following percentages of the town's residents may favor building a new community center?
A. 69%
B. 79%
C. 59%
D. 99%
Answers
The confidence interval for a given sample value can be calculated using the following formula:
Confidence interval = Average value ± Margin of error
Which in this case the values are:
Average value = 85%
Margin of error = 12%
Therefore substituting the given values into the equation will give us:
Confidence interval = 85 ± 12
Confidence interval = 73, 97
Therefore the percentage of the residents of the town who are favour of building a new community center ranges from 73% to 97%.
Based from the given choices, only letter B 79% is within this range:
Answer:
B. 79%
Answer:
B. 79%
Step-by-step explanation:
yes
which one is it? need help please
Answers
y + 2x = 4
--------------------subtract
-2 1/3x = -14
-7/3x = -14
x = -14 (-3/7)
x = 6
2x + y = 4
2(6) + y = 4
y = 4 - 12
y = -8
(6, -8)
answer
C. (6, -8) (third choice)
(04.01 LC)
Which of the sets of ordered pairs represents a function?
A = {(2, −2), (5, −5), (−2, 2), (−5, 5)}
B = {(4, 2), (4, −2), (9, 3), (9, −3)}
Only A
Only B
Both A and B
Neither A nor B
Answers
Answer:
Only A
Step-by-step explanation:
Let's remember the definition of a function:
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
In A, each input has exactly one output so it's a function.
But in B, the inputs 4 and 9 have two different outputs, it can't represent a function.
The answer is only A.
1,226 days late to answer this question but that will not stop me!
The answer is... drumroll please ... Only A :]
Why do we state restrictions for rational expression and when do we state the restrictions?
Answers
We state restrictions for rational expressions to ensure that the denominator does not equal zero, as division by zero is undefined in mathematics. The restrictions are the values of the variable that make the denominator equal to zero. We state the restrictions whenever we are simplifying, performing operations with, or solving rational expressions.
A rational expression is an expression that can be written in the form of a fraction, where the numerator and the denominator are polynomials. The denominator of a rational expression cannot be zero because division by zero is not defined in mathematics. Therefore, when working with rational expressions, it is crucial to identify the values of the variable that would make the denominator equal to zero. These values are the restrictions, or domain restrictions, for the rational expression.
For example, consider the rational expression [tex]\(\frac{1}{x-3}\)[/tex]. The denominator is[tex]\(x-3\)[/tex]. To find the restriction, we set the denominator equal to zero and solve for [tex]\(x\)[/tex]:
[tex]\[x - 3 = 0\][/tex]
[tex]\[x = 3\][/tex]
Therefore, the restriction for this rational expression is [tex]\(x \neq 3\)[/tex], meaning that [tex]\(x\)[/tex] can be any real number except 3.
We must state these restrictions whenever we perform operations such as simplifying, adding, subtracting, multiplying, or dividing rational expressions, as well as when we are solving rational equations. This ensures that the operations are valid and that the solutions to the equations do not include any undefined expressions.
In summary, stating restrictions for rational expressions is a critical step in avoiding mathematical errors and ensuring that the expressions and equations we work with are well-defined.
A phone company offers two monthly plans. Plan A costs $30 plus an additional $0.15 for each minute of calls. Plan B costs $16 plus an additional $0.20 for each minute of calls.
For what amount of calling do the two plans cost the same?
What is the cost when the two plans cost the same?
Answers
Plan A = 30 +0.15x
Plan B = 16 +0.20x
30+0.15x = 16+0.20x
subtract 16 from each side
14 +0.15x = 0.20x
subtract 0.15x from each side
14=0.05x
x = 14/0.05 = 280 minutes
280*0.15 = 42 +30 = $72
280 * 0.20 = 56 +16 = 72
280 minutes and cost $72 each
Plan A : 30 + 0.15 m
Plan B: 16 + 0.20 m
For what amount of calling do the two plans cost the same?
30 + 0.15m = 16 + 0.20m
0.05m = 14
m = 280
280 minutes of calling, the two plans cost the same
What is the cost when the two plans cost the same?
Plan A: 30 + 0.15 m = 30 + 0.15 (280) = 72
Plan B: 16 + 0.20 m = 16 + 0.20 (280) = 72
answer
It's cost $72 when the two plans cost the same
Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than or equal to y. Also, the sum of y and two-third of x is less than 4. Which graph represents the possible solutions?
Answers
(2/3)x - 3 ≥ y
or
y ≤ (2/3)x - 3 (1)
The second inequality is
y + (2/3)x < 4
or
y < 4 - (2/3)x (2)
A graph of the two inequalities indicates the solution as a shaded region in the figure below.
Use basic identities to simplify the expression. sin2θ + tan2θ + cos2θ
Answers
sin^2 (θ) + tan^2 (θ) + cos^2 (θ)
To be able to simplify this, we need to have knowledge on the different trigonometric identities. These identities are expressions which would relate the different trigonometric functions. For this case, we use two known basic identities. These are
sin^2 (θ) + cos^2 (θ) = 1
1 + tan^2 (θ) = sec^2 (θ)
We simplify as follows:
sin^2 (θ) + tan^2 (θ) + cos^2 (θ) = sin^2(θ) + tan^2 (θ) + cos^2 (θ)
= 1 + tan^2 (θ)
= sec^2
Therefore, the expression sin^2 (θ) + tan^2 (θ) + cos^2 (θ) is equal to sec^2 (θ). Other form that would also be equivalent to the same expression would be sin^2 (θ) + sin^2 (θ) / cos^2 (θ) + cos^2 (θ).
just need to check these answers
Answers
Good luck in your next tests.
The length of the shadow of a flagpole was found to be 72 feet. the shadow of a 3 foot picket fence in line with the flagpole was 4 feet. what is the height of the flagpole?
Answers
We can solve this problem by simply using ratio and proportion. Let us call the height of the flagpole to be X. Therefore the ratio and proportion would be:
3 ft is to 4 ft and X ft is to 72 ft
3 / 4 = X / 72
X = (3 / 4) * 72
X = 54 ft
The height of the flagpole is 54 ft.
What are the exact solutions of x2 − 3x − 1 = 0?
Select one:
a. x = the quantity of 3 plus or minus the square root of 5 all over 2 Incorrect
b. x = the quantity of negative 3 plus or minus the square root of 5 all over 2
c. x = the quantity of 3 plus or minus the square root of 13 all over 2
d. x = the quantity of negative 3 plus or minus the square root of 13 all over 2
Answers
Values: a = 1; b = - 3; c = -1
Solving:
[tex]X ^{2}-3X-1=0[/tex]
[tex]X= \dfrac{-(-3) \pm \sqrt{(-3) ^{2}-4(1)(-1) } }{2(1)}[/tex]
[tex]X= \dfrac{3 \pm \sqrt{9+4} }{2}[/tex]
[tex]X= \dfrac{3 \pm \sqrt{13} }{2}\ ===\ \textgreater \ \ Answer:\ \boxed{ \textbf{Option\ {C.}}}[/tex]
GOOD LUCK...!!!
Stanfing in your tree house 50ft off the ground you look down at a 60 degree angle how many feet from the base of the tree is the frisbee
Answers
multiply 50 x tan(60) = 86.6 feet.
round your answer as needed
2 Questions~
Evaluate the expression.
38+16⋅12÷2−(30⋅2)
Simplify this expression.
5 + 10 ÷ 5
3
7
10
15
Answers
Your answer would be a.
Answer: 3
hope this helps! :)
~Izzie
Which of the following is true when probability answer is written in the form of a fraction
Answers
In probability, a fraction does not need to be simplified but converting to a percentage or decimal can aid in interpretation, with percentages being fractions with a denominator of 100. (First option)
When a probability answer is written in the form of a fraction, it is important to know how to handle the result. Simplifying the fraction is not generally required, especially in Probability Topics, where the focus is on understanding the probability itself rather than the arithmetic of fractions.
However, converting the probability to a percentage is a common practice that can help with interpretation. This is done by writing the value of the percent as a fraction with a denominator of 100 and then simplifying it if possible.
Converting a fraction to a decimal is another common step, which involves dividing the numerator by the denominator. It's also important to note that for rounding answers to probability problems, the convention is to round to four decimal places.
What is the 5th term of an arithmetic sequence if t3 = 10 and t7 = 26?
18
20
22
24
Answers
A doorway is 8 feet high and 4 feet wide. A square piece of plywood needs to be moved through the doorway. The plywood is 10 feet long and 10 feet wide. The door is a rectangle with a height of 8 feet, and a width of 4 feet. A dotted line shows the diagonal.
Will the piece of plywood fit through the door if it is tilted diagonally?
A. No, because the length of the diagonal is close to 9 feet.
B. No, because the height of the door is less than 10 feet.
C. Yes, because the length of the diagonal is close to 11 feet.
D. Yes, because the sum of the height and width of the door is greater than 10 feet.
Answers
d^2=x^2+y^2
d^2=8^2+4^2
d^2=64+16
d^2=80
d=√80
d=4√5 ft
d≈8.944
So
A. No because the diagonal is close to 9 feet.
After calculating the diagonal of the doorway to be approximately 8.944 feet using the Pythagorean theorem, it's clear that the 10-foot square piece of plywood will not fit diagonally through the door. Thus, the correct answer is option (A).
The question is whether a 10-foot square piece of plywood can fit through an 8-foot by 4-foot doorway when tilted diagonally. To determine if the plywood can fit, we need to calculate the diagonal of the doorway using the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as c² = a² + b² where c is the hypotenuse, and a and b are the other two sides.
Let's apply the theorem to our doorway:
Height (a) = 8 feet
Width (b) = 4 feet
Diagonal (c) = ?
We calculate the diagonal:
c² = a² + b²
c² = 8² + 4²
c² = 64 + 16
c² = 80
c = sqrt(80)
c = 8.944 feet (approx)
The diagonal of the doorway is approximately 8.944 feet, which is less than the 10 feet length of the plywood. Therefore, the correct answer is:
No, because the length of the diagonal is close to 9 feet.
The option (A) is correct.
Find the area of a regular hexagon whose side length is 16 in. and the apothem is 8 square root of 3 in
Answers
polygon area = 6 * 16 * 13.8564064606 / 2
polygon area = 665.1075101088 square inches
Answers for 1.2.1 how can I describe a graph
Answers
Hope this helps!
What is the length of CF? look at image attached
Answers
СF * DF = BF * EF
СF * 14 = 7 * 17
14СF = 119
СF = 119/14
СF = 8.5
Can anyone please help ASAP, will give thanks and all that fun stuff
Answers
(every time i use a in this, i mean a1)
Answer:
The answer is B!!!!
Mary, who is sixteen years old, is four times as old as her brother. how old will mary be when she is twice as old as her brother? explained
Answers
16 ÷ 4 = 4
Now that you have two ages, you can just make a list to find the answer.
16 and 4
18 and 6
20 and 8
22 and 10
24 and 12
12.38 in expanded form
Answers
10 + 2 + .3 + .08 = 12.38
To write a number in expanded form just means to write the number in a layout and when you add it up it will become the number you needed to write in expanded form.
So, 12.38 written in expanded form is:- 10 + 2 + .3 + 0.8
Hope this helps. Please make me brainliest
JL is a common tangent to circles M and K at point J. If angle MLK measures 61ᵒ, what is the length of radius MJ? Round to the nearest hundredth. (Hint: Show that triangles LMJ and LKJ are right triangles, and then use right triangle trigonometry to solving for missing sides of the right triangles.)
Answers
To find the length of radius MJ, we can use right triangle trigonometry. Firstly, we can show that triangles LMJ and LKJ are right triangles. Then, we can use the given angle MLK of 61ᵒ to find the length of radius MJ, using the sine function. The equation to find MJ is MJ = rM * sin(29ᵒ).
Explanation:To find the length of radius MJ, we can use right triangle trigonometry. Firstly, we can show that triangles LMJ and LKJ are right triangles. Since JL is a common tangent, it is perpendicular to the radii of the circles at points J. Therefore, angle LMJ and angle LKJ are right angles. Now, we can use the given angle MLK of 61ᵒ to find the length of radius MJ.
Let's call the radius of circle M rM and the radius of circle K rK. In triangle LMJ, we have the following relationships:
angle LMJ = 90ᵒ (since it is a right triangle)angle MLJ = angle MLK - angle JLK = 61ᵒ - 90ᵒ = -29ᵒ (since angle JLK is a right angle)angle MJL = angle JML = 90ᵒ - angle MLJ = 90ᵒ - (61ᵒ - 90ᵒ) = 119ᵒUsing the sine function, we can find the length of side MJ:
sin(angle MLJ) = length of side MJ / length of side LJ
sin(-29ᵒ) = MJ / rM
Since sin(angle MLJ) = -sin(angle MJL), we can rewrite the equation as:
sin(29ᵒ) = MJ / rM
Now, we can rearrange the equation to solve for MJ:
MJ = rM * sin(29ᵒ)
Since we are not given the values of rM or rK, we cannot find the specific value of MJ. However, we can use this equation to find the length of radius MJ if we are given the values of the radii of the circles and the given angle MLK.
Remember to round the answer to the nearest hundredth as specified in the question.
The point (–3, –5) is on the graph of a function. Which equation must be true regarding the function?
f(–3) = –5
f(–3, –5) = –8
f(–5) = –3
f(–5, –3) = –2
Answers
Answer:
Option 1st is correct
[tex]f(-3) = -5[/tex]
Step-by-step explanation:
If any point [tex](x, y)[/tex] is on the graph then we can write the function as:
[tex]y= f(x)[/tex]
where
x is the independent variable and
y is the dependent variable.
As per the statement:
The point (–3, –5) is on the graph of a function.
⇒x = -3 and y = -5
By above definition we have;
[tex]f(-3) = -5[/tex]
Therefore, the equation must be true regarding the function is, [tex]f(-3) = -5[/tex]