1) In triangle ABC, we know that AB = 5, BC = 9, and CA = 7. D is a point on BC such that AD bisects ∠BAC. What is DC?
2)] O is the circumcenter of 4ABC. If OB = OC = BC, what is ∠BAC
Answers
9514 1404 393
Answer:
1) 5.25
2) 95.74°
Step-by-step explanation:
1) The angle bisector divides the triangle into proportional segments.
DC/BD = CA/BA
We know that BD+DC = 9, so we can fill in the above equation with known values to get ...
DC/(9-DC) = 7/5
5·DC = 7(9 -DC) . . . . cross multiply
12·DC = 63 . . . . . add 7·DC
DC = 63/12 = 5.25
__
2) Angle BAC can be found using the Law of Cosines.
a² = b² +c² -2bc·cos(A)
cos(A) = (b² +c² -a²)/(2bc) = (7² +5² -9²)/(2·7·5) = -7/(70) = -1/10
A = arccos(-1/10) ≈ 95.739°
The measure of ∠BAC is about 95.74°.
_____
Additional comment
The circumcircle is irrelevant to the questions asked here.
Related Questions
Just need this one and I’ll be good
Answers
Answer:
8
Step-by-step explanation:
Sarah is a computer engineer and manager and works for a software company. She receives a fixed annual increase in the number of projects she handles each year. She worked on 129 projects in the fourth year of her employment and 207 projects in her tenth year
Answers
Answer: See explanation
Step-by-step explanation:
You didn't say what you'll like to calculate but let me help out.
Fourth year = 129 project.
Tenth year = 207 projects
We can form this into an arithmetic progression
Tn = a + (n-1)d
4th year = a + 3d = 129 ........ i
10th year = a + 9d = 207 ....... ii
Subtract equation i from equation ii
6d = 78
d = 78/6 = 13
This means that 13 new projects are added every year
For the first year, the number of projects done was:.
a + 3d = 129
a + 3(13) = 129
a + 39 = 129
a = 129 - 39 = 90
She worked on 90 projects in the first year.
Question is in the image
Answers
Answer:
5y=5(4/5x+2)
Simplify
5(4/5x+2)
Solve -4h-3>4
Please answer as fast as you can.
Answers
Answer:
h< −7/4
Step-by-step explanation:
Answer:
h<−7/4
Step-by-step explanation:
−4h−3>4
Step 1: Add 3 to both sides.
−4h−3+3>4+3
−4h>7
Step 2: Divide both sides by -4.
−4h / −4 > 7 / −4
h< −7 /4
what's £1200 plus 20% tax
Answers
Answer:
1,439.75 pounds
Step-by-step explanation:
i cant give perfect explination because i deal with $ not pounds but that should be right
the senior class has 225 members. there are 55 more boys in the class than girls. how many boys and girls are there
Answers
Answer:
85 girls and 140 boys
Step-by-step explanation:
are the angels vertical or adjacent
Answers
Answer:
Adjacent
Step-by-step explanation:
Adjacent angles are when two angles have a common side and a common vertex (corner point) and don't overlap.
Vertical angles are each of the pairs of opposite angles made by two intersecting lines.
In this diagram, the angles are adjacent.
Hope this helps and answers your question! :)
Help me! I’ll mark you brainly!
Answers
Answer:
Step-by-step explanation:
15) 1
16) 4
17) 21.95
The value of a mountain bike y (in dollars) can be approximated by the model y=200(0.75)t, where t is the number of years since the bike was new.
Would this table show growth or a decline (decay)? How do you know?
Identify the annual percent increase or decrease in the value of the bike.
Estimate when the value of the bike will be $50.
Answers
Leslie can buy her dog's food at Petco for $25 and receive 9 packs with four cans in each. Leslie can buy the same food at Petsmart for the same price with 7 packs of six cans in each. Which store should Leslie buy her dog food from?
Answers
Answer:
Leslie should buy her dog food from Petsmart because the price per can is cheaper
Step-by-step explanation:
Step one;
given data
At Petco, we are told that she receives 9 packs with four cans each for $25
Hence Petco gives a total of 9*4= 36cans
the cost of each can will be 25/36
=$0.69 per can
Step two:
At Petsmart, we are told that she receives 7 packs with six cans each for $25
Hence Petsmart gives a total of 7*6= 42cans
the cost of each can will be 25/42
=$0.59 per can
Leslie should buy her dog food from Petsmart because the price per can is cheaper
On Monday, I bought 1 dog and 2 cats for a total cost of $6.75. On Tuesday, /
bought 1 dog and 3 cats for a total cost of $9.25. Can you find the price of each
item
Answers
Write an equation in slope-intercept form of the line that passes through the points.
Answers
Answer: y = x + 4
Step-by-step explanation: use the slope intercept form y = mx+b
2) Read and answer the following
12 points
Kenisha goes to the market with $30 in
her wallet. She is going to buy candy and
water bottles. Each candy at the market
costs $2 and each water bottle costs $1.
Which of the following equations can
represent the amount of candy and water
Kenisha can buy at the market?
$30 = c + $2w
O $30 = $2c + W
$30 + w = $20
$30 -2C = -W
Answers
A museum gift shop manager wants to put 1,644 polished rocks into small bags to sell as souvenirs. If the shop manager wants to put 13 rocks in each bag, how many complete bags can be filled? How many rocks will be left over?
Answers
On a 40-question test, Peggy answers 34 questions correctly. What percent of the questions does she answer correctly?
A. 85%
B. 0.75
C. 1.17%
D. 8.5%
Answers
Answer:
A.) 85%
Step-by-step explanation:
find the value 1/2+1/3+1/4=
plz answer step by step
i will give you 5 star
Answers
Answer:
[tex]\frac{13}{12}[/tex]
Step-by-step explanation:
Find the LCM of 2, 3, 4: 12Alter the numerators to fit the denominators (steps not shown): [tex]\frac{6}{12} + \frac{4}{12} + \frac{3}{12}[/tex] [tex]\frac{6}{12} + \frac{4}{12} + \frac{3}{12} = \frac{13}{12}[/tex]I hope this helps!
A fish tank has 42 gallons of water and is being drained at a rate of 2 gallons per minute. Another tank is empty and is being filled at a rate of 4 gallons per minute. After how many minutes will both tanks have the same amount of water?
Answers
Answer:
6 mins and 30 secs
Step-by-step explanation:
After 7 minutes, both tanks have the same amount of water.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.
Given is that a fish tank has 42 gallons of water and is being drained at a rate of 2 gallons per minute. Another tank is empty and is being filled at a rate of 4 gallons per minute.
We can write the drain function as -
D(x) = 42 - 2x
The function that gives the amount of water in second tank will be -
F(x) = 4x
Equating both, we get -
D(x) = F(x)
42 - 2x = 4x
42 = 6x
x = 42/6
x = 7
Therefore, after 7 minutes, both tanks have the same amount of water.
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Even numbers greater than -37 but less than -25
Answers
Answer:
-36, -34, -32, -30, -28, -26
Step-by-step explanation:
Troy needs to buy a rod, reel, lures, line, and a license to go fishing. The sporting goods store has a rod for $67, a reel for $42, a lure for $8 and a line for $11. The license will cost $38. Round each cost to the nearest 10 and then choose the best estimate of the total cost of paying for these five items.
A. $130
B. $150
C. $170
D. $190
Answers
The best estimate of the total cost of paying for these five items will be $170. Then the correct option is C.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Troy needs to buy a rod, reel, lures, line, and a license to go fishing.
The sporting goods store has a rod for $67, a reel for $42, a lure for $8 and a line for $11.
The license will cost $38.
Then the best estimate of the total cost of paying for these five items will be
⇒ 67 + 42 + 8 + 11 + 38
⇒ $166
Round each cost to the nearest 10. Then we have
⇒ $ 170
Then the correct option is C.
More about the Algebra link is given below.
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rearranging formula Solve 4(x + 3) = 6
Answers
Answer:
x = - [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Given
4(x + 3) = 6 ← distribute left side
4x + 12 = 6 ( subtract 12 from both sides )
4x = - 6 ( divide both sides by 4 )
x = [tex]\frac{-6}{4}[/tex] = - [tex]\frac{3}{2}[/tex]
Explain why 2 times 2 is 4
Answers
Answer:
2 times 2 is 4
Step-by-step explanation:
okay so i have 2 cookies right, my big brother gave me 2 more. how many do i have ? i should have 4 because 1 plus 1 plus 1 plus 1 is 4.
Michelle has x dollars Tony has 9 dollars fewer than Michelle. Drag and drop the expression to write an expression that represents the total amount of money Michelle and Tony have together.
Answers
do you want to be friends cos i riley riley riley riley riley riley need some friends because i only have 2 friends and 1/2 of the answer is 0 and the other 1/2 of the answer is 13 so your answer is 13 because 0-13=13 please follow me and i'm not saying this in a weird way i just need some flowers and some friends...please i'm begging you please friend me and follow me!!!................
Answer:
x +(x-9)
Step-by-step explanation:
x is Michelle's money. Tony has 9 dollars less than michelle x-9. to find out how much they have in total you have to put it together.
HELP ME PLEASE ASAP?!?!
What is the area of the obtuse triangle given below?
Answers
Answer:c
Step-by-step explanation:
According to Hatfield, which kind of love is about caring and intertwining your
life?
A. Attachment
B. Intimate love
C. Passionate love
D. Companionate love
Answers
the correct answer is companionate love.
According to Hatfield, the kind of love that is about caring and intertwining your life is companionate love.
Option D is the correct answer.
What is compassionate love?Companionate love is a type of love characterized by feelings of intimacy and affection but without the intense passion or sexual attraction associated with passionate love.
We have,
Companionate love typically involves a deep level of commitment, trust, and mutual support between partners who have a strong emotional bond.
In companionate love, partners may still experience physical attraction to each other, but the primary focus is on building a strong, long-term partnership based on mutual respect, communication, and shared experiences.
This type of love is often seen in long-term relationships or marriages, where partners have developed a deep understanding and appreciation for each other over time.
Overall, companionate love is about caring for and supporting your partner through the ups and downs of life and building a life together based on shared values, goals, and interests.
Thus,
The kind of love that is about caring and intertwining your life is companionate love.
Learn more about compassionate love here:
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Write an expression that matches the sum of 2 thirteens and 3 sixes.
Answers
if it needs to be simplified further just plug that into a calculator
-5(3x-7)+11=1 What would this be?
Answers
Answer:
x = 3
Step-by-step explanation:
-5(3x -7) + 11 = 1
Distribute 5:
-15x + 35 + 11 = 1
Combine like terms:
-15x + 46 = 1
Subtract by 46 =
-15x = 1 - 46
-15x = -45
Divide by -15:
x = -45 / -15
x = 3
Answer:
x=3
Step-by-step explanation:
Use the distributive property to multiply −5 by 3x−7.
−5(3x−7)+11=1
Add 35 and 11 to get 46.
−15x+35+11=1
Subtract 46 from both sides.
−15x+46=1
Subtract 46 from 1 to get −45.
−15x=1−46
Divide both sides by −15 and you get x=3.
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HURRY WILL MARK BRAINLESS
Which expression is equivalent to ပါ။ (C) - -
Answers
First to Answer
Answer:
The correct option is the third option. -2 1/4 / -2/3 = 3 3/8
-9/4 / -2/3 = 3 3/8
which of the following must be true
Answers
Answer: it is c
Step-by-step explanation:
A 20-ounce bottle of shampoo costs $23. What is the price per ounce?
Answers
Answer:
$1.15 per ounce.
Step-by-step explanation:
$1.15 x 20 = $23.00
Answer:
$0.87
Step-by-step explanation:
Find the value of x.
28°
Answers
The value of x is 56 degrees.
What is a Right Angle Triangle ?A right angle triangle is any angle in which the value of the angle is 90°
The value of the other angle in the right angle will be 90 - 28 = 62°
Since the two triangles in the figure are isosceles triangles, the two angle at the base of an isosceles triangle will be the same.
Sum of the angle of a triangle = 180°
Then, 62 + 62 + x = 180
124 + x = 180
make x the subject of formula
x = 180 - 124
x = 56
Therefore, the value of x is 56 degrees.
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