Isosceles triangle ABC contains angle bisectors segment BF, segment AD, and segment CE that intersect at X.
If segment BA is congruent to segment BC and m∠BCA = 48°, what is m∠CXA?
132°
96°
66°
24°
Answers
Answer:
The measure of angle CXA is 134°
Step-by-step explanation:
* Lets explain how to solve the problem
- Triangle ABC is an isosceles triangle where AB = BC
∵ AB = BC
- The base angles in the isosceles triangle are congruent
∴ m∠BAC = m∠BCA
∵ m∠ BCA = 46° ⇒ given
∴ m∠ BAC = 46°
- The sum of the measures of the interior angles in any triangle is 180°
∵ m∠BAC + m∠BCA + m∠ABC = 180°
- Substitute the values of angle BAC and BCA in the equation above
∴ 46 + 46 + m∠ABC = 180
∴ 92 + m∠ABC = 180
- Subtract 92 from both sides
∴ m∠ABC = 88°
- BF , AD , CE are bisectors segments of angles B , A , C and they are
intersected at point X
∵ CE bisects ∠BCA
∵ X ∈ CE
∴ m∠XCA = 1/2 m∠BCA
∴ m∠XCA = 1/2 (46) = 23°
∵ AD bisects ∠BAC
∵ X ∈ AD
∴ m∠XAC = 1/2 m∠BAC
∴ m∠XAC = 1/2 (46) = 23°
- In Δ AXC
∵ m∠XAC = 23° ⇒ proved
∵ m∠XCA = 23° ⇒ proved
∵ m∠CXA + m∠XAC + m∠XCA = 180° ⇒ interior angles of Δ
Substitute the values of angles XAC and XCA
∴ m∠AXC + 23 + 23 = 180
∴ m∠CXA + 46 = 180
- Subtract 46 from both sides
∴ m∠CXA = 134°
* The measure of angle CXA is 134°
Answer: I also have this question and because everybody is saying 134 I believe it is 132. So I hope this helps.
P.S If possible please mark it as the brainliest. thanks
Related Questions
the social security tax is 1.5% if joshua earns 23400 annually then how much will joshua pay in social security tax
Answers
Because you multiple by 100 always.
Then you also multiple to find the percentage.
23400*0.015 = 351
Geometry can someone help me out and explain please
Answers
a = 12, b = 3*sqrt(17)
========================================================
Work Shown:
3/a = a/48
3*48 = a^2
a^2 = 144
a = sqrt(144)
a = 12
--------------------
a^2 + 3^2 = b^2 ... pythagorean theorem
12^2 + 3^2 = b^2
144 + 9 = b^2
b^2 = 153
b = sqrt(153)
b = sqrt(9*17)
b = sqrt(9)*sqrt(17)
b = 3*sqrt(17)
What is the volume?
3 mm
10 mm
8 mm
Answers
Answer:
240
Step-by-step explanation:
V = L x W x H
L= 3
W= 10
H= 8
V = 3 x 10 x 8
= 240 cubic meters
Answer:
240
Step-by-step explanation:
All you have to do is multiply all of these numbers to get the answer.
The volume of a number cube is 27 cm^3. What is the length of each side of a cube?
Answers
Answer:
Side = 3 cm
Step-by-step explanation:
Given:
[tex]\text{Volume of cube} = 27 \ \text{cm}^{3}[/tex]
The formula to calculate the volume is (Side)³.
Thus, we obtained the following equation:
[tex](\text{Side})^{3} = 27 \text{cm}^{3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Side}^{3} = \text{Volume of cube}][/tex]
Cube root both sides to obtain the side length of the cube:
[tex]\implies \sqrt[3]{\text{(Side)}^{3}} = \sqrt[3]{27 \ \text{cm}^{3} }[/tex]
Evaluate the side of the cube:
[tex]\implies \sqrt[3]{\text{(Side)}^{3}} = \sqrt[3]{27 \ \text{cm}^{3} }[/tex]
[tex]\implies \sqrt[3]{\text{(Side)}\text{(Side)(Side})} = \sqrt[3]{3 \times 3 \times 3 \times \text{(cm)(cm)(cm)}}[/tex]
[tex]\implies \text{Side = 3 cm}[/tex]
Answer:
3 cm
Step-by-step explanation:
Formula
Volume of a cube = [tex]a^3[/tex] (where a is the side length)
Given that the volume of the cube is 27 cm³, to find the side length, substitute the given volume into the equation and solve for [tex]a[/tex]:
[tex]\implies 27\: \sf cm^3=a^3[/tex]
Cube root both sides:
[tex]\implies \sqrt[3]{27\: \sf cm^3} =\sqrt[3]{a^3}[/tex]
[tex]\implies \sqrt[3]{27}\sqrt[3]{\sf cm^3} =\sqrt[3]{a^3}[/tex]
[tex]\implies 3\: \sf cm=a[/tex]
[tex]\implies a=3\: \sf cm[/tex]
Therefore, the length of each side of the cube is 3 cm.
To convert 27 kg to mg, you would move the decimal point _____ places to the _____.
Answers
Answer:
To convert 27 kg to mg, you would move the decimal point 6 places to the right.
hope that's helpful to you!
The dogs at a shelter are housed in 4 different rooms. If there are 10 dogs in each room, how many dogs are housed at the shelter?
Answers
Answer:
There would be 40 dogs in the shelter.
Explanation:
4 rooms times 10 dogs in each room = 40 dogs total
Answer:
40!
Step-by-step explanation:
is this logical question?
Hello"! Need Help!
Question 1) Given 15 cot A = B. Find sin A and sec A .
Notes:-
• Kindly Don't spam
• Need Genuine Answer
• Don't copy from other website.
• Answer will be step-by-step explanation otherwise answer will be report...
Answers
↪Given 15 cot A = 8. Find sin A and sec A
Hope this helps...☆
S implify the given polynomial expressions as much as possible.
7xy(2xy - 3x + 8y + 9)
Answers
Answer:
14x^2y^2 - 21x^2y + 56xy^2 + 63xy
Step-by-step explanation:
Remark
This is a disguised form of the distributive property. Nothing can be simplified inside the brackets. So the plan is to remove them.
7xy*2xy - 3x*7xy + 8y*7xy + 9*7xy Combine the terms
14x^2y^2 - 21x^2y + 56xy^2 + 63xy
You cannot symplify anything further. If nothing could be combined before, it cannot be simplified now.
The ratio of the volumes of two similar spheres is 27:216. What is the ratio of their dimensions (Linear Scale Factor)?
Answers
Answer:
3:6
Step-by-step explanation:
27=3*3*3
216=6*6*6
Therefore the answer is 3:6
then to the lowest term = 1:2
A car driving at 20m/s accelerates at 3m/s2 for 3s. What is its final velocity? How far will it travel during this time?
Answers
Answers:
Final velocity = 29 m/s
Distance traveled = 73.5 meters
========================================================
Work Shown:
The given data is
[tex]v_i = 20 \text{ m}/\text{s} = \text{initial velocity}\\\\a = 3 \text{ m}/\text{s}^2 = \text{acceleration}\\\\t = 3 \text{ s} = \text{time duration}\\\\[/tex]
This leads to
[tex]v_f = v_i + a*t\\\\v_f = 20 + 3*3\\\\v_f = 20 + 9\\\\v_f = 29\\\\[/tex]
The final velocity is 29 m/s.
----------
We can use that final velocity to find the distance traveled.
[tex]x = 0.5*(v_i+v_f)*t\\\\x = 0.5*(20+29)*3\\\\x = 0.5*(49)*3\\\\x = 24.5*3\\\\x = 73.5\\\\[/tex]
The distance traveled is 73.5 meters.
----------
An alternative way to calculate the distance is to do this
[tex]x = \frac{(v_f)^2 - (v_i)^2}{2a}\\\\x = \frac{(29)^2 - (20)^2}{2*3}\\\\x = \frac{841 - 400}{6}\\\\x = \frac{441}{6}\\\\x = 73.5\\\\[/tex]
Or you could do this
[tex]x = v_i*t + 0.5*a*t^2\\\\x = 20*3 + 0.5*3*3^2\\\\x = 20*3 + 0.5*3*9\\\\x = 60 + 13.5\\\\x = 73.5\\\\[/tex]
For more information, check out the Kinematics equations.
A large rectangular card measures 80 centimetres by 90 centimetres.
Maria uses all this card to make small rectangular cards measuring 40 millimetres
by 15 millimetres.
Calculate the number of small cards.
Answers
1200 cards
All measurements should be taken in centimeters
Calculate the area of large rectangular card:
Length * Width 80 * 907200 cm²Calculate the area of each small cards:
Length * Width4 * 1.56 cm²Divide the area of large card by area of small card
7200 cm² ÷ 6 cm²1200Number of small cards: 1200 cards
For bigger rectangle:-
L=90cmB=80cmArea:-
LB90(80)7200cm²720000mm²For smaller rectangle
L=40mmB=15mmArea:-
LB40(15)600mm²Total cards:-
720000/6001200cardsWhich shows one way to determine the factors of 4x3 x2 – 8x – 2 by grouping? x2(4x 1) – 2(4x 1) x2(4x – 1) 2(4x – 1) 4x2(x 2) – 1(x 2) 4x2(x – 2) – 1(x – 2)
Answers
An expression has numbers, variables, and mathematical operations. The factors of the expression 4x³+x²-8x-2 by grouping are x²(4x+1)-2(4x+1).
What is an Expression?
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The factors of the expression by grouping can be done as,
[tex]4x^3+x^2-8x-2[/tex]
Take x² as the common factor from the first two terms while -2 from the last two terms,
[tex]4x^3+x^2-8x-2\\\\=x^2(4x+1)-2(4x+1)[/tex]
Thus, the factors of the expression 4x³+x²-8x-2 by grouping are x²(4x+1)-2(4x+1).
Learn more about Expression:
https://brainly.com/question/13947055
I need help with this?
Answers
Answer:
139 ft³
Step-by-step explanation:
Diameter of the cylinder is 3 ft. Therefore, the radius is 1.5 ft
Volume of the cylinder = πr²h
= 3 × 1.5 × 1.5 × 4
= 27 ft³
Volume of the cuboid (rectangular prism) = lbh
= 7×4×4
= 112 ft³
Volume of the figure = 112 + 27 = 139 ft³
5 7/12 as an improper fraction
Answers
it's a mixed fraction
hope it helps..,!!!
At 7 P.M., the temperature was 0.6°C. Over the next 3 hours, the temperature decreased by 1.9º. What was the temperature at 10 P.M.?
Answers
Answer:
2.5
Step-by-step explanation:
3 hours after 7 is 10 so add 1.9 to 0.6
10. A farmer wants to.fence in the garden shown below. Write a
simplified rational expression for the ratio of the garden's
perimeter to its area.
3x
3x
Answers
The rational expression for the ratio between the perimeter and the area is:
R = 4/3x
How to find the ratio?
We want to find the ratio, as a rational expression, between the perimeter and the area.
Remember that for a square of sidelength S, the perimeter is:
P = 4*S
And the area is:
A = S^2
Then the ratio between these two is:
R = P/A = (4*S)/(S^2) = 4/S
In this case, the sidelength is 3x, then S = 3x, replacing that we get:
R = 4/3x
If you want to learn more about rational expressions, you can read:
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transtle (-2,-2) up 1 unit then reflect the result over the x axis what are the coordinates of the final point
Answers
Answer:
(-2,1)
Step-by-step explanation:
1 unit up will change the y-value as it is moving vertically. Will make it (-2,-1)
Then, reflecting over x-axis means x-value stays the same and the sign of y-value switches.
so,
(-2,1)
Which inequality is represented by the graph?
Which point is a solution to the inequality?
Answers
Answer:
there is no picture attached here I really wish I could help
Marcus is buying a car. He borrows $10,000 from the bank at a 9% rate for 5 years. At the end of the 5 years, how much interest does Marcus pay?
Answers
Answer:
$4500 in interest.
Step-by-step explanation:
9% of 10,000 is 900, 900 x 5 is 4500
Please Help Due Today!!!
What is the common difference,d, of the sequence?
-92, -74, -56, -38, -20
d=?
Answers
Reason:
Subtract any pair of adjacent terms
d = term2 - term1 = -74 - (-92) = -74+92 = 18d = term3 - term2 = -56- (-74) = -56+74= 18d = term4 - term3 = -38- (-56) = -38+56= 18d = term5 - term4 = -20- (-38) = -20+38= 18Each time we get the same value to confirm that we have an arithmetic sequence of common difference 18.
What is the fraction of the repeating decimal?
Answers
it's 46/99
whenever you get a question like this, you need to think: what would those fractions even be?
well it sure is not a bc 3/6 is already 0.5 and you need a lower number
it's not b either bc 4/16= 1/4 and that is 0.25
and well it can't be d either bc 13/16 is that not far away from 1
====================================================
Explanation:
Let x = 0.464646...
Multiplying both sides by 100 gets to 100x = 46.464646... which moves the decimal point over two spots to the right.
Then subtract the two equations
100x - x = 46.464646... - 0.464646...
99x = 46
x = 46/99
Notice how the decimal portions cancel out when we subtract. This is because they line up perfectly.
To confirm the answer, your calculator should show that
46/99 = 0.46464646
The "46"s going on forever.
At some point, your calculator may round the last '4' to a 5 to have it read something like 0.464646465 but this is of course rounding error.
On some calculators I tried, I noticed it displayed 0.46464646464647 which is even more strange considering the next digit (4) isn't five or larger. So that 6 shouldn't have bumped up to the 7.
find the area of given trapezium which save height is 3 cm and p1 is 12 cm and p2 is 24 cm
Answers
Answer:
Hope the picture will help you.......
A university has 34,350 students. In a random sample of 255 students, 17 speak three or more languages. Predict the number of students at the university who speak three or more languages.
Answers
Because (34350/255)*17 equals 230
Use a calculator to evaluate 9^√3 to the nearest ten thousandth.
Answers
Curtis has two bags of marbles the first bag contains 7 blue 2 yellow 6 red and 5 green marbles the second bag contains 4 blue 2 yellow 2 red and 2 green marbles soda hd have a greater probability of choosing a blue marble from the first or second bag
Answers
Answer:
Step-by-step explanation:
First Container.
Total = 7 + 2 + 6 = 15
Probility blue = 7 / 15 = 0.467
Second Container
Total = 4 + 2 +2 = 8
Probability Blue = 4/8 = 1/2 = 0.5
Answer: You are much better off drawing from the Second Container.
help me please i need to turn this in fast
Answers
$4.76 per card
hope it helps...!!!
The area of the square is 144 square inches. What is the area of the circle, to the nearest square inch? Use 3. 14 for
A 75 in
В.
19 in
C452 in
D. 113 in
Answers
What is the first step in solving the system shown below using substitution? 2x=y-1 y=3x
Answers
Answer:
you have to solve the first equation for y
Step-by-step explanation:
Step-by-step explanation:
At first put the value of y that is 3x in equation 2x=y-1.
Then put the value of x in equation y=3x that comes from the first solving part.
Pt2 check first one for the question
Answers
Answer:
what how
Step-by-step explanation:
Calculate the following unit rates.
The cookie recipe calls for 2/3 cup of brown
sugar for 1/2 batch of cookies.
Answers
Using proportions, it is found that the unit rate is of 1.33 cups of brown sugar for a batch of cookies.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
2/3 cups of brown sugar are used for half a batch of cookies. The unit rate is the amount used for one batch. Hence, the rule of three is given by:
2/3 cups - 1/2 batch
x cups - 1 batch.
Applying cross multiplication:
[tex]\frac{1}{2}x = \frac{2}{3}[/tex]
[tex]x = \frac{4}{3}[/tex]
The unit rate is of 1.33 cups of brown sugar for a batch of cookies.
More can be learned about proportions at https://brainly.com/question/24372153