Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 8
and AD = 2, what is the length of AC?
Answers
Answer:
x = 32
Step-by-step explanation:
∠BCA = ∠DBA (90 - ∠DBC)
∠A = ∠A
ΔABD similar to ΔACB
AC/AB = AB/AD
x / 8 = 8 / 2
x = 32
The length of AC if The right triangle ABC with altitude BD drawn to hypotenuse AC, AB = 8 and AD = 2, is 32.
What is the triangle?Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.
Given:
The right triangle ABC with altitude BD drawn to hypotenuse AC,
AB = 8 and AD = 2,
Check if the triangle Δ ABD similar to Δ ACB
∠ BCA = ∠ DBA (90 - ∠ DBC)
∠ A = ∠ A
Thus, Δ ABD is similar to Δ ACB by AAS similarity,
Calculate the length of AC by using the similarity property,
AC/AB = AB/AD
x / 8 = 8 / 2
x = 32
Thus, the value of AC is 32.
To know more about Triangles:
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Related Questions
Describe how you could use algebraic operations to solve the equation 1 = -3x + 4
Answers
Answer:
x=1
Step-by-step explanation:
3x=4-1
3x=3
x=1
Find the slope given the two points below:
(-8, — 11), (-1, 17)
Answers
Answer:
Slope: 4
Step-by-step explanation:
Answer: The slope is 4
Step-by-step explanation:
Slope formula:
[tex]m = \frac{y_{2}-y_{1} }{x_{2}- x_{1} }[/tex]
[tex]m = \frac{17 - (-11) }{-1 -(-8) }[/tex]
[tex]m = \frac{17 +11 }{-1 +8}[/tex]
[tex]m = \frac{28 }{7}=m = \frac{4}{1}=m =4[/tex]
m = 4
The slope is 4
Help me Pls U WILL GET BRAINLISTED
Answers
Answer:
(1/3)(9x+27) > x + 33
multiply out the 1/3
3x + 9 > x + 33
subtract x and 9 from both sides
2x > 24
x > 12
D) because you dont include the 12
Step-by-step explanation:
Find the range of the given data set.
-4, -3, -1, -1, 0, 1
-3
3
5
-5
Answers
Answer:
10
Step-by-step explanation:
Range of data = Highest value - Lowest value
Here,
Highest value = 5
Lowest value = -5
Range = 5 - (-5)
= 5 + 5
= 10
Help please!
Acellus
Find the value of x.
B
6
X+1
D
А Е
4
Х
С
A
x = [?]
Enter
Answers
Answer:
x = 2
Step-by-step explanation:
In the given figure
∵ ABC is a triangle
∵ D is a point on side AB
∵ E is a point on side BC
∵ DE // AC
∵ AC is the third side of the triangle
→ That means DE divides the sides AB, BC into parts that have the same ratio
∴ [tex]\frac{BD}{DA}[/tex] = [tex]\frac{BE}{EC}[/tex]
∵ BD = 6 and DA = 4
∵ BE = x + 1 and EC = x
→ Substitute them in the ratio above
∴ [tex]\frac{6}{4}[/tex] = [tex]\frac{x+1}{x}[/tex]
→ By using the cross multiplication
∵ 6 × x = 4 × (x + 1)
∴ 6x = 4(x + 1)
∴ 6x = 4(x) + 4(1)
∴ 6x = 4x + 4
→ Subtract 4x from both sides
∵ 6x - 4x = 4x - 4x + 4
∴ 2x = 4
→ Divide both sides by 2 to find x
∴ x = 2
-1/4n - n= -5/6
What does n equal, Please I need this done very quickly!!
Answers
Answer:
n = 2/3
Step-by-step explanation:
Tania has roll of cloth that is 52.5 feet long . She uses the cloth to make scarves that are each 3.75 feet long How many scarves can Tania make
Answers
Answer:
14 scarves
Step-by-step explanation:
Change the divisor 3.75 to a whole number by moving the decimal point 2 places to the right. Then move the decimal point in the dividend the same, 2 places to the right.
We then have the equations:
5250 ÷ 375 = 14
and therefore:
52.5 ÷ 3.75 = 14
Both calculated to 0 decimal places.
The radio station usually plays 116,800 songs in a year. Last year there was a 16% decrease in the number of songs played. What was the amount of songs played on the radio station last year?
Answers
Answer:
Number of songs played last year = 98,112 songs
Step-by-step explanation:
Given:
Number of songs played = 116,800
Decrees songs = 16% = 0.16
Find:
Number of songs played last year
Computation:
Number of songs played last year = Number of songs played[1-Decrees songs]
Number of songs played last year = 116,800[1-0.16]
Number of songs played last year = 98,112 songs
solve
thanks and give how you done it too
Answers
Answer:
x = 4
Step-by-step explanation:
7x + 16/11 = 4
11 x 7x + 16/11 = 4 x 11
7x + 16 = 44
7x + 16 - 16 = 44 - 16
7x = 28
7x/7 = 28/7
x = 4
Check:
7x + 16/11 = 4
7(4) + 16/11 = 4
28 + 16/11 = 4
44/11 = 4
4 = 4 (note that this number is not the answer, just to check if each side is balanced, the actual answer is 4)
Bam !
Hope this helps ^w^
Answer:
x = 4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of EqualityStep-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{7x + 16}{11} = 4[/tex]
Step 2: Solve for x
Multiply 11 on both sides: [tex]\displaystyle 7x + 16 = 44[/tex]Subtract 16 on both sides: [tex]\displaystyle 7x = 28[/tex]Divide 7 on both sides: [tex]\displaystyle x = 4[/tex]Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: [tex]\displaystyle \frac{7(4) + 16}{11} = 4[/tex][Frac] Multiply: [tex]\displaystyle \frac{28 + 16}{11} = 4[/tex][Frac] Add: [tex]\displaystyle \frac{44}{11} = 4[/tex][Frac] Divide: [tex]\displaystyle 4 = 4[/tex]Here we see that 4 does indeed equal 4.
∴ x = 4 is the solution to the equation.
100th term for 5, 2, -1
Answers
Answer:
100th term = -1485
Step-by-step explanation:
Arithmetic Progressionthe nth term, Tn:[tex]t_{n} = a + (n - 1)d[/tex]
n = number of terms
= 100
a = first term
= 5
d = difference
= second term - first term
= 2 - 5
= -3
substitute the values into the formula
[tex]t_{100} = 5(100 - 1)( - 3)[/tex]
[tex]t_{100} = 5(99)( - 3)[/tex]
[tex]t_{100} = 495( - 3)[/tex]
[tex]t_{100} = - 1485[/tex]
What is m<3? Thank you
Answers
===================================================
Explanation:
Let
x = the measure of angle 2y = the measure of angle 3The goal is to find y
For now, focus on the interior angles of triangle DEF. We have these three angles:
D = 90 (due to the square angle marker)E = angle 1 = 53F = angle 2 = xThose interior three angles add to 180. This is true for any triangle.
D+E+F = 180
90+53+x = 180
143+x = 180
x = 180-143
x = 37
angle 2 = 37 degrees
Now we can find y.
Focus on angles 2 and 3, which are x and y respectively. These two angles add to 180 because they form a straight line. Note: the triangle's angles summing to 180 is closely related to this idea where angle 2 and angle 3 are a linear pair.
So this means,
(angle2)+(angle3) = 180
x+y = 180
37+y = 180
y = 180-37
y = 143
angle 3 = 143 degrees
It's not a coincidence that we ended up with a previously calculated value of 143. It turns out that adding the remote interior angles D and E leads to the exterior angle EFG.
D+E = 90+53 = 143 = angle EFG
I'm using the remote interior angle theorem. Some textbooks may call this the exterior angle theorem. In my opinion, the phrasing "remote interior angle theorem" is more descriptive.
helpp i’m confused !!!!
Answers
Answer:
2
Step-by-step explanation:
Answer: To find x you to figure out if the two longest sides of the triangle are equal. to do that find all angles to help.
Step-by-step explanation:
At a lemonade stand, pink lemonade costs $2.50 and sweet tea lemonade costs $4. In one morning, the stand sells 21 drinks for $67.50. How many pink lemonades were sold?
Answers
Answer:
lemonade = 11
Step-by-step explanation:
let p = pink lemonade
let t = sweet tea
create a system of equations -- one with quantity, one with associate costs
p + t = 21
2.5p + 4t = 67.5
substitution method: let t = 21 - p
2.5p + 4(21 - p) = 67.5
2.5p + 84 - 4p = 67.5
-1.5 p = -16.5
p = 11
t = 21 - 11
t = 10
This photo is the problem I have to solve for x help please
Answers
Answer:
1
Step-by-step explanation:
What are the slope and the y-intercept of the linear function that is represented by the graph?
Answers
help please meeeee....
Answers
The value of sales at the shop decreases from 145,000 a year to 129,000 find the percentage decrease in the value of sales
Answers
Answer:
11.0344828%
Step-by-step explanation:
145000 - 129000 = 16000.
16000/145000 = 16/145 = 0.110344828
Therefore there was a 11.0344828% decrease
Answer:
11.03% that is the percentage decrease
2. For which equation is y = 7 a solution
2 &. 3
Which is a equation
Answers
Answer:
equation b ............
The perimeter of a rectangle is 24 inches. If the length of
the rectangle is less than the width of the
rectangle, which of the following best illustrates the
domain for the length of this rectangle?
20 points
Answers
Answer:
C
Step-by-step explanation:
its more than likely to be C
1000cm in the ratio of 4:5:6
Answers
Step-by-step explanation:
4+5+6=1000
1000/15
4 . 5. 6= 266.4 . 333. 399
9514 1404 393
Answer:
266 2/3 : 333 1/3 : 400
Step-by-step explanation:
The total of ratio units is 4+5+6 = 15, so the fraction of 1000 that each portion represents is ...
4/15 : 5/15 : 6/15 = 4/15 : 1/3 : 2/5
Multiplying 1000 by these fractions gives ...
1000(4/15) : 1000/3 : 1000(2/5)
= 266 2/3 : 333 1/3 : 400
my feet are asleep,,,.T.T, I'm also stressed and cold and tired
Answers
Answer:
Ok its friday be happy
Step-by-step explanation:
Good morning can y’all help me
Answers
Answer:
-1/2 anwserchoice B
Step-by-step explanation:
negitive (-) and then rise (1 up) over run (two over)
good morning to you aswell <3
At least two teachers must accompany every five elementary students on a field trip. If 45 students are going
on the trip, what is the minimum number of teachers needed?
Answers
Answer:
9
Step-by-step explanation:
divide 5 into 45 which equals 9
Answer:
The minimum number of teachers needed for this trip is 18.
Step-by-step explanation:
The slope for this is 5/2. So the equation is y = (5/2)x. We know the y is 45 students. So we do division. In the end, we get x = 18 teachers.
Triangles similar to the same triangle are ______ to each other.
A) congruent
B) similar
C) close
D) parallel
Answers
Answer:
b. similar because they are said to be similar if their corresponding angles are congruent and the corresponding sizes are in proportion.
amir rented a dvd and it was due to be returned on 28 march he actually returned it to the shop on 16 april the rental shop applies 7p for everyday the dvd is overdue. Work out the total fine paid by amir give your answer in £
Answers
Answer:
£133
Step-by-step explanation:
March had 31 days
Extra days used in March = March 31 - March 28
= 3 days
Extra days used in April = 16 days
Total extra days used = Extra days used in March + Extra days used in April
= 3 days + 16 days
= 19 days
Cost per extra days = £7
Total fine for 19 extra days = £7 × 19
= £133
Total fine paid = £133
The total fine paid by amir should be £133.
The calculation is as follows:March had 31 days
Extra days used in March should be
= March 31 - March 28
= 3 days
Now
Extra days used in April = 16 days
And,
Total extra days used = Extra days used in March + Extra days used in April
= 3 days + 16 days
= 19 days
Cost per extra days = £7
Total fine for 19 extra days = £7 × 19
= £133
Learn more: brainly.com/question/16911495
A house worth £80,000 in January 2012 is set to decrease in value by 7% per year.
A more optimistic forecast suggests that the value of the house will increase by 4% per year. According to this forecast, how much will the house be worth in January 2015?
Answers
Answer:
The house would be worth £89989.12 in January 2015.
Step-by-step explanation:
With respect to the optimistic forecast, the value of the house will increase by 4% per year.
For the first year (January 2012 to January 2013),
4% of £80000 = 0.04 x £80000
= £3200
The cost of the house = £80,000 + £3200
= £83200
For the second year (January 2013 to January 2014), we have;
4% of £83200 = 0.04 x £83200
= £3328
The cost of the house = £83200 + £3328
= £86528
For the third year (January 2014 to January 2015), we have;
4% of £86528 = 0.04 x £86528
= £3461.12
The cost of the house = £86528 + £3461.12
= £89989.12
According to the forecast, the house would be worth £89989.12 in January 2015.
Coupon A: off 30% of $63 shoes
Answers
Hope this helps!!!!
Jahnay is following this recipe to make cakes.
Jahnay uses 750 g of sugar.
How many cakes is Jahnay making?
Recipe: Makes 1 Cake
200 g flour
125 g butter
150 g sugar
2 eggs
Answers
750/150 = 5
750/150 = 5
Jahnay is making 5 cakes
Sandra has a checking account at Wells Fargo Bank. During the month of May, she made deposits totaling $2,458.52 and wrote checks totaling $789.23. He paid a maintenance fee of $25 and earned $3.24 in interest. Her balance at the end of the month was $4,492.76. What was the balance at the beginning of May.
Answers
what is the correct prime factorization of 24?
Answers
Answer:
24= 2*2*2*3= 2^3*3
Step-by-step explanation:
Answer:
prime factorization of 24 = 2 * 2 * 2 * 3 = 2^3 * 3
Step-by-step explanation:
List the first several prime numbers: 2, 3, 5, 7, 11, 13, ...
Now start with 2. Divide 24 by 2 as many times as possible. Then move on to 3, to 5, etc. until you end up with 1.
Divide only by prime numbers.
Start by dividing 24 by 2:
24/2 = 12 12 is divisible by 2, so divide 12 by 2.
12/2 = 6 6 is also divisible by 2, so divide 6 by 2.
6/2 = 3 Since 3 is not divisible by 2, move onto 3.
3/3 = 1 When you get to 1, stop. The prime factors are all the prime numbers in boldface that you divided by.
prime factorization of 24 = 2 * 2 * 2 * 3 = 2^3 * 3