$D$ is on side $\overline {AB}$ of $\triangle ABC.$ We know $\triangle ABC \sim \triangle ACD$ and $\angle A =48^\circ.$ If $BC=BD,$ what is $\angle B$ in degrees?
Answers
According to the exterior angle theorem, the exterior angle of a triangle is equal to the sum of the two opposite interior angles
The measure of ∠B is 44°
Reason:
The known parameters are;
The point D is on side [tex]\overline{AB}[/tex] of triangle ΔABC
ΔABC ~ ΔACD,
∠A = 48°
BC = CD
Required:
The measure of angle ∠B
Solution:
ΔBDC is an isosceles triangle
Let x, represent ∠B
Therefore, ∠BDC = x, by base angles of an isosceles triangle
Given that ΔABC ~ ΔACD, and ΔBDC is an isosceles triangle, we have;
∠ADC = 2·x by exterior angle of a triangle theorem
Given ΔABC ~ ΔACD, ∠A = ∠A, and ∠ADC = 2·x, therefore, ∠ACD = x
Which gives;
48° + x + 2·x = 180° sum of angles in a triangle theorem
[tex]x = \dfrac{180^{\circ} - 48^{\circ}}{3} = 44^{\circ}[/tex]
∠B = x = 44°
The measure of ∠B = 44°
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Related Questions
Dana bought 144 pencils for $8.64.which equation could be used to determine the cost of each pencil,x?
A.144/8.64=x
B.x/144=8.64
C.8.64-x=144
D.144x=8.64
Answers
Answer:
144x=8.64
This way you can divide by 144 to find how much each individual pencil costs
PLEASE HELP ME !!
acellus : chords and arcs find the value of x
Answers
Answer:
8Step-by-step explanation:
since all the sides are equal then that means that x is going to equal 8.
A card is drawn at random from a standard deck. That card is not put back in the deck, and a second card is drawn at random from the remaining cards in the deck. Neither of the cards drawn so far are put back in the deck, and a third card is drawn at random from the remaining cards in the deck. What is the probability that the first card drawn is a spade, the second card drawn is a heart, and the third card drawn is a heart? Do not round your intermediate computations. Round your final answer to four decimal places.
Answers
Answer:
The probability of the given scenario occuring is about 0.0153.
Step-by-step explanation:
A standard deck contains 52 cards.
We want the first card to be a spade. In a standard deck, 13 out of the total 52 cards are spades.
So, the probability that the first card is a spade is 13/52 or simply 1/4.
Now, we will draw a second card without replacing the first card. Since we did not replace the first card, the total amount of cards in the deck is now 51.
This time, we want a heart. 13 cards of the remaining 51 will be hearts. So, the probability that the second card is a heart is 13/51.
Now that we've drawn two cards without replacing them, the total number of cards left is 50.
And since we've drawn (or would like to have drawn) a heart as our second card, the total number of cards that are hearts is now 12.
Then the probability of the third card being hearts will be 12/50 or 6/25.
Then the probability that our first card is a spades, second card is a heart, and the third and final card is also a heart without any replacements will be:
[tex]\displaystyle P(\text{spade, heart, heart})=\frac{1}{4}\cdot \frac{13}{51}\cdot \frac{6}{25}=\frac{13}{850}\approx0.0153[/tex]
The probability of the given scenario occuring is about 0.0153.
4
Select the correct answer
Erin is taking part in a play at the community theater. The cast and crew ordered T-shirts for all the volunteers. The cost of a T-shirt is $8, and the
total delivery charge is $45 per order. If the center has no more than $325 to buy T-shirts, how many T-shirts can they buy?
Answers
Answer:
The answer is B
Step-by-step explanation:
When you buy something with a credit card, which one of the following will usually save you money over the long run? A. Paying the entire amount owed each month B. Paying a small portion of the amount owed over a longer period of time C. Paying a small portion of the amount owed each month D. Paying the entire amount owed, but only every other month
Answers
Answer:
A. Paying the entire amount owed each month
Step-by-step explanation:
When we buy something with a credit card option C usually save you money over the long run.
What is credit card?A credit card represents a payment mechanism which facilitates both consumer and commercial business transactions, including purchases and cash advances. A credit card generally operates as a substitute for cash or a check and most often provides an unsecured revolving line of credit.
A. Paying the entire amount owed each month
This option is better when you don't have money and you have to manage it.
B. Paying a small portion of the amount owed over a longer period of time.
this option is not applicable
C. Paying a small portion of the amount owed each month.
This option gives more money savings if there is no interest.
D. Paying the entire amount owed, but only every other month.
This is also a money saving if there is no interest.
Thus when we buy something with a credit card option C usually save you money over the long run.
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Plastic parts manufactured using an injection molding process may exhibit one or more defects, including sinks, scratches, black spots, and son on. Let x represent the number of defects on a single part, and suppose the distribution of x is as follows: x: 0 1 2 3 4 p(x): 0.79 0.09 0.05 0.04 0.03 What is the expected value, E(X), for the number of defects on a randomly selected plastic part
Answers
Answer:
The expected value for the number of defects on a randomly selected plastic part is 0.43.
Step-by-step explanation:
We have the following probability distribution:
P(X = 0) = 0.79
P(X = 1) = 0.09
P(X = 2) = 0.05
P(X = 3) = 0.04
P(X = 4) = 0.03
What is the expected value, E(X), for the number of defects on a randomly selected plastic part?
Each value multiplied by its probability. So
[tex]E(X) = 0.79*0 + 0.09*1 + 0.05*2 + 0.04*3 + 0.03*4 = 0.43[/tex]
The expected value for the number of defects on a randomly selected plastic part is 0.43.
Tell whether each kind of angle is Right, Acute or Obtuse angle. Write your answer inside the box.
Answers
Answer:
1. Right Angle
2. Acute Angle
3. Acute Angle
4. Obtuse Angle
5. Right Angle
Step-by-step explanation:
Please mark as brainliest
90 degrees = right angle
Less than 90 is acute
More than 90 is obtuse
Robin can clean 727272 rooms in 666 days.
How many rooms can Robin clean in 999 days?
rooms
Answers
Answer:
1090908 rooms
Step-by-step explanation:
calculator
Answer:
Robin can clean 9828 rooms in 9 days
Step-by-step explanation:
Since Robin can clean 727272 rooms in 666 days, we can find how many rooms she can clean in 1 day by dividing 727272 by 666
number of rooms cleaned by Robin in 1 day = 727272 rooms/666 days = 1092 rooms/day
We can then find how many rooms she can clean in 9 days by multiplying 1092 by 9
1092 rooms/day * 9 days = 9829 rooms
Maria had 4 full cement blocks and one that was 5/9 the normal size if each full block weighed 3 8/9 pounds what is the weight of the blocks maria has
Answers
Answer:
17 and 58 over 81 pounds
Step-by-step explanation:
if virginia's sales tax rate is 4.3%, what is the total cost of a $34 virgina tech t-shirt?
Answers
Answer:
35.46
Step-by-step explanation:
34 x 1.043=35.46
Building A is 464 feet tall and Building B is 321 feet tall. Dale is standing between the buildings. The angle of elevation from the point on the ground where Dale is standing is 75 degrees to the top of Building A and 48 degrees to the top of Building B, how far apart are the buildings?
Answers
Answer:
The distance between the buildings is:
D = 413.3 ft
Step-by-step explanation:
Ok, here we have two triangle rectangles, such that these triangle rectangles share a common vertex which is Dale.
One of the triangles, let's call it triangle A, has the catheti:
Distance between Dale and Building A = d1
Height of Building A = 464 ft
The other triangle (triangle B) has the catheti:
Distance between Dale and Building B = d2
Height of building B = 321ft
We want to find the distance between the buildings, which is equal to d1 + d2.
Then we want to find d1 and d2.
For triangle A:
We know that the angle at the vertex where Dale is standing, is 75°
Then the adjacent cathetus is d1, and the opposite cathetus is the height of building A.
Remember that:
Tan(θ) = (opposite cathetus)/(adjacent cathetus)
Then:
Tan(75°) = (464 ft)/(d1)
d1 = (464 ft)/(Tan(75°)) = 124.3 ft
Now for triangle B, the angle at the vertex where Dale is standing is 48°.
from this vertex, we have d2 as the adjacent cathetus and the height of build B as the opposite cathetus.
Then:
Tan(48°) = 321ft/d2
d2 = (321ft)/(Tan(48°)) = 289ft
Then the distance between the buildings is:
D = d1 + d2 = 124.3 ft + 289ft = 413.3 ft
Please find the area of the compound figures. PLEASE AND THANKS :D
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Answer:
1200
Step-by-step explanation:
if answer is correct brainliest
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5(x+8)
Help please!!!!!!!!!!!!!!!!!!
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Answer:
5x+40
Step-by-step explanation:
You would distribute 5 to x+8 and that would add up to 5x+40.
Answer:
Step-by-step explanation:
5x+40
13 points Please help 8th grade math
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Answer:
4.2
Step-by-step explanation:
Answer:
Volume of the sphere is 2065.24
I have no idea how to calculate the slope of that.
Step-by-step explanation:
3·π·7.93≈2065.23693
Find an ordered pair (x,y) that is a solution to the equation.
5x+y=6
Answers
Answer:
(0,6) and (1.2 , 0)
Step-by-step explanation:
5x + y = 6
if we take x=0
5(0) + y = 6
y = 6 ; so, one of the solution is (0,6)
if we take y=0
5x + (0) = 6
5x = 6
x = 6/5 = 1.2 ; so, the other solution is (1.2 , 0)
But basically, you can find other solutions of the equation if you do this:
5x + y = 6
5x = (6 - y)
x = (6 - y) / 5 ; so if you use whatever number of y, you will find the rigth solution for x.
and you can do the opposite too:
5x + y = 6
y = 6 -5x ; with this, you can use whatever number of x, and find the right y.
I hope this helps you!!!
Which equation best represents the relationship
between x and y in the graph?
PLEASE FOR BRAINLSIT!!!!
Answers
PLEASE HELP I NEED TO FINISH THIS NOW!!!
Gethyn drinks 48 fluid ounces of water in one day. He needs to drink 8 cups in total. How many more cups does he need to drink? (4 points) Group of answer choices 2 cups 6 cups 384 cups 768 cups
Answers
Answer:
The answer is 6
Step-by-step explanation:
Since you have to divvied 40 to 8 witch gives you 6
The number of bacteria in a petri dish triples every month, if the dish started with 25 bacteria, how many will there be an 8 months?
Answers
Answer:
600
Step-by-step explanation:
25x3 (per month) therefore it would be 75 times 8
Answer:
164025
Step-by-step explanation:
Will give brainliest!!
Two lines, A and B, are represented by the following equations:
Line A: 4x + 4y = 16
Line B: x + y = 4
Which statement is true about the solution to the set of equations? (4 points)
Group of answer choices
A) It is (1, 2).
B) It is (1, 5).
C) There are infinitely many solutions.
D) There is no solution.
Answers
Answer:
Infitite solutions (C)
Step-by-step explanation:
They are the same line.
Which represents the polynomial written in standard form
Answers
Answer:
The answer is the third option
Step-by-step explanation:
A rectangular prism has a length of 9 in., a width of 4 in., and a height of 112 in.
The prism is filled with cubes that have edge lengths of 12 in.
How many cubes are needed to fill the rectangular prism?
Answers
Answer:
432
Step-by-step explanation:
Answer: 4032
Step-by-step explanation: 9x4x112 is 4032
i took the test and pls give brainiest
Someone help plzzzzz
Jack bought an automatic water bottle feeder for his cat. A
diagram of the bottle is shown below. What is the maximum
amount of water that the bottle can hold?
Hon
8.5 in
12.5
I
Answers
The maximum amount of water that the bottle can hold is 2251.77 cubic inches.
What is volume?
A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
To find the maximum amount of water that the bottle can hold, we need to find the volume of the bottle.
The bottle is in the shape of a cylinder with a height of 12.5 inches and a radius of 8.5/2 = 4.25 inches.
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.
Substituting the values, we get:
V = π(4.25)²(12.5)
V = 2251.77 cubic inches
Therefore, the maximum amount of water that the bottle can hold is 2251.77 cubic inches.
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A skyscraper is 807 feet tall. Each floor is about 12 feet tall. About how many floors de building have? Select the correct answer below and fill in the answer box to complete your choice. OA. You need an estimate: 800-10 = floors OB. You need an exact answer, 807 - 12 = floors C. You need an estimate: 1000-20 = floors OD. You need an estimate: 500- 25 = floors.
Answers
Answer:
D
Step-by-step explanation:
807 divided by 12 = 67.25
A bike store sells scooters at a 54% markup. If the store bought each scooter for $29.25, what is the resale price to the nearest dollar? Show your work
Answers
9514 1404 393
Answer:
$45
Step-by-step explanation:
The relation is ...
resale price = cost + markup
= cost + 0.54×cost
= 1.54×cost
Then the resale price is ...
resale price = 1.54×29.25 = 45.045 ≈ 45.00
The resale price is $45.00.
-0.5
0
1
-2
1.5
Where is Point D on the number line?
?
Answers
Answer:
Its -1.9 for where point D is
3(5)+2(w-1)=
Cual es el valor de la expresión algebraica?
Answers
Answer:
distribute
2(w-1)
a(b-c)=ab-ac
(3)(5)+(2)(w)+(2)(−1)
=15+2w+−2
combine like terms
15+2w+−2
=(2w)+(15+−2)
=
2w+13Step-by-step explanation:
https://qcv.gg/rXpglU
a/5=b/7 if b#0 what is the value of a/b
Answers
Answer:
A = 20
b = 28
Step-by-step explanation:
a = 20/5 = 4
b = 28/7 = 4
ohn needs to serve some beer to a customer. At first he ordered 1 pint then he added 4 ounces more, then he decided to add 1/4 tablespoons more. John only has measuring cups which got him a bit confused. How many cups he needs to serve the customer to make it up to his order?
Answers
Answer:
the answer to this question 2 cups
Step-by-step explanation:
2 cups is equal to a pint
Find the circumference and area of a circle A with a diameter of 26 inches.
Please I need the answer ASAP. Thank you very much.
Answers
Answer:
Circumference: 81.681 in; Area: 530.929 in
Step-by-step explanation:
To find circumference we use the formula pi x diameter. Which in this case is pi x 26 in, or approximately 81.681 in.
For the area, we use pi x r^2. r = 1/2 d, so r = 13in. Therefore, the area is equal to 169 x pi in, which is about 530.929 in.