Given right triangle ABCABC with altitude \overline{BD} BD drawn to hypotenuse ACAC. If BC=10BC=10 and DC=5,DC=5, what is the length of \overline{AC}? AC ?
Answers
Answer: [tex]\overline{AC}=[/tex] 12.5
Step-by-step explanation: The triangle ABC and its altitude [tex]\overline{BD}[/tex] is represented in the figure below.
Altitude is a segment of line that link a vertex and the opposite side, forming a right angle.
So, because of [tex]\overline{BD}[/tex], now we have two similar triangles, which means that ratios of corresponding sides are equal:
[tex]\frac{\overline{BD}}{\overline{BC}} =\frac{\overline{AD}}{\overline{BD}}[/tex]
[tex]\overline{BD}^{2}=\overline{BC}.\overline{AD}[/tex] (1)
This is always true for a right triangle and a altitude drawn to the hypotenuse.
Triangle BDC is also right triangle. So, we can use Pythagorean theorem to determine the missing side.
[tex]\overline{BC}^{2}=\overline{CD}^{2}+\overline{BD}^{2}[/tex]
[tex]\overline{BD}^{2}=\overline{BC}^{2}-\overline{CD}^{2}[/tex] (2)
Substituting (2) into (1):
[tex]\overline{BC}^{2}-\overline{CD}^{2}=\overline{BC}.\overline{AD}[/tex]
We want to find f, so:
[tex]\overline{AD}=\frac{\overline{BC}^{2}-\overline{CD}^{2}}{\overline{BC}}[/tex]
[tex]f=\frac{10^{2}-5^{2}}{10}[/tex]
f = 7.5
The length of [tex]\overline{AC}[/tex] is
[tex]\overline{AC}=f+5[/tex]
[tex]\overline{AC}=7.5+5[/tex]
[tex]\overline{AC}=12.5[/tex]
The length of the hypotenuse of triangle ABC is 12.5 units.
Answer:
x = 20
Step-by-step explanation:
Related Questions
algebraic expression the sum of 12 and k
Answers
The perimeter of a quadrilateral garden is 4x2+3x-4. The first side is represented by x2+2x+15. The second and third sides are each represented by x2-x-10. What expression represents the fourth side? Write a justification of your result.
Answers
Answer:
[tex]y = x^{2} + 3x + 1[/tex]
Step-by-step explanation:
Perimeter equals the sum of the lengths of the sides.
Let y = the length of the fourth side
[tex]4x^{2} + 3x - 4 = x^{2} + 2x + 15 + x^{2} -x - 10 + x^{2} - x - 10 + y[/tex]
[tex]4x^{2} + 3x - 4 = 3x^{2} - 5 + y[/tex]
[tex]x^{2} + 3x + 1 = y[/tex]
A car travels 825 miles in 15 hourso How many
miles does the can
travel in
I hour. Helps
ASAP
Answers
Given RS = 6, ST = 3, and SL = 4, find the required measure. (Part of the answer is provided for you.)
KT =
Answers
Answer:
https://brainly.com/question/1593288
Step-by-step explanation:
This was answered previously on here
Answer:
Square root of 61
Step-by-step explanation:
It was correct on my assignment
What is the value of the expression 22 + 62 ÷ 22? (1 point)
Answers
Answer: 22+62÷22
22+2.8181
24.8181
So 22+62÷22 is about 24.8181
hope this helps have a nice day❤️❤️❤️
Step-by-step explanation:
Answer:
22.73
Step-by-step explanation:
22+62=84
84/22=22.7380952381
You use 2 1/3 feet of string to make one bracelet. How many can you make with 10 1/2 feet of string?
Answers
Plz Help Its Math and very confusing! (Btw this is her lil sister alexis!) Don't tell her i don't have this link so i use her brainly???
Answers
Answer:
Step-by-step explanation:
Round the ratio 4:8
to 5 then divide (/), =51
HELP PLEASE!
Could someone give me the answer ASAP since it is due very soon please! Thank you :)
Answers
Answer:
27/8
Step-by-step explanation:
3 3/8
you multiply the denominator by the whole number and then add into numerator. so
8 x 3 = 24
24+ 3 =27
Answer= 27/8
HELP ! On #1 ASAP for math
Answers
Answer: 1=2x 2=(0, 1/4)
Step-by-step explanation:
14. Write the equation in slope-intercept form that passes through the two points.
(1, 2) and (3,-8)
Answers
Answer: y=5x+7
Step-by-step explanation:
If you draw a graph or use a graphing calculator the points and then connect them you will see that the y-intercept is 7 and the slope is 5/1. Slope intercpt form is y=mx+b. So the equation is y=5x+7.
Answer:
let (x1,y1)=(1, 2)
and(x2,y2)=(3,-8)
Step-by-step explanation:
we have
y-y1=(y2-y1)(x-x1)/(x2-x1)
y-2=(-8-2)(x-1)/(3-1)
y-2=-10(x-1)/2
y-2=-5(x-1)
y-2=-5x--5
y+5x=5+2
5x+y=7 is the required equation.note :-×-=+
Circle all of the equations
that are nonlinear.
A. y = 5 + x
B. xy = 4
C. y = 7x4
D. 2x - y = 8
Answers
Answer:
B and C
Step-by-step explanation:
Just not linear lol
Annie has 4 1/2 feet of rope what is the greatest number of 3/4 foot pieces that annie can cut from the rope
Answers
Answer:
6
Step-by-step explanation:
4 1/2 divided by 3/4 is 6. so 6 pieces
The greatest number of 3/4 foot pieces that Annie can cut from the rope
is 6.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Annie has 4 1/2 feet of rope.
Therefore, The greatest number of 3/4 foot pieces Annie can cut can be obtained by dividing the length of the total rope by the length of each piece which is,
= (4 1/2)/(3/4).
= (9/2)×(4/3).
= 36/6.
= 6.
So, 6 pieces are possible.
learn more about fractions here :
https://brainly.com/question/10354322
#SPJ2
Write an inequality to match the graph below.
Answers
lets use x as the variable in this situation
x > -2 or x is greater than negative two.
hope this helps
What is an equation of the line that passes through the points (-2, 7) and (1, -8)?
Answers
Answer:
Im not a hundred percent sure
but
y=-5x+7
expand and simplify (X+7) (x-2)
Urgent please my teacher threatened me with an axe
Answers
Answer:
x²+5x-14
Step-by-step explanation:
expand out the brackets:
x²-2x+7x-14
simplify:
x²+5x-14
A bakery uses 44 cups of flour to make 10 loaves of bread. How many cups of flour are there per loaf?
Answers
Answer: 4.4
Step-by-step explanation:
44 divided by 10
Answer:
4.4 cups of flour
Step-by-step explanation:
You would have to divide 44(cups of flour) by 10(loaves of bread) to get the amount of cups of flour for each loaf. 44/10=4.4
Do ACT score reports come in the mail?
Answers
Answer: Yes
Step-by-step explanation:
They usually come in three months after you take the test. I think I got mine in the middle of May.
Find the equation of the line whose slope is 1/3
and goes through the point (3, 1).
A. y= 1/3x
B. y= 1/3x + 1
C. y= 1/3x + 2
D. y= 1/3x + 8/3
Answers
Answer:
It means that when x = 3, y = 1, obviously when the first function expression takes 3, y = 1
Solve for x
A )180
B)55
C)115
D)82.5
Answers
Answer:
55
Step-by-step explanation:
AB // DC
∠B + ∠C = 2x + 15 + x = 180
3x = 165
x = 55
Answer: B. 55
Step-by-step explanation:
You need to know that within one parallelogram, the same-side interior angles are supplementary angles, meaning that they add up to 180°.
---------------------------------------------------------------------------------------
Given
(2x+15)+x=180
Expand parenthesis
2x+15+x=180
Combine like terms
3x+15=180
Subtract 15 on both sides
3x+15-15=180-15
3x=165
Divide 3 on both sides
3x/3=165/3
x=55
Hope this helps!! :)
Please let me know if you have any questions
A racecar driver completes a race 30 laps in 15 minutes at a constant speed. what is the driver's speed?
Answers
Answer:
200 mph/321 km/h if the track is 1 mile long and 100 mph/160 km/h if the track is 2 miles long
Step-by-step explanation:
Solve the inequality for x.
22 >x-5
Answers
Answer:
x < 27
Step-by-step explanation:
22 > x - 5
Subtract x from both sides.
-x + 22 > -5
Subtract 22 from both sides.
-x > -27
Divide both sides by -1. Remember that when you multiply or divide an inequality by a negative number, the inequality sign changes direction.
x < 27
Hi everyone,can someone please help me with this question please help me I really really need help please answer it correctly
Answers
Answer:
the fourth which passed through (0;2)
Answer:
graph 4
Step-by-step explanation:
If the slope is positive then the graph is linear increasing function.
If the slope is negative then the graph is linear decreasing function.
Graph 1) slope = 4/3
Graph 4) slope = -3/2
So, Graph 4 is linear decreasing function.
Expand and simplify (x − 3)(2x + 1)(3x - 2)
Answers
Answer:
6[tex]x^{3}[/tex]- 19[tex]x^{2}[/tex]+[tex]x[/tex]+6
Step-by-step explanation:
Answer:
6x³ - 19x² + x + 6
Step-by-step explanation:
There is a bag filled with 2 blue, 4 red and 5 green marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting 2 different colours?
Answers
Answer:
58.5% (94886869494949)
Step-by-step explanation:
EZ math. (but take note of my username)
GOOD AT MATH!! PLEASE HELPPP
Answers
Answer:
The answer is C
Step-by-step explanation:
solve this problem. -16r=272
Answers
Answer:
-17
Step-by-step explanation:
-16r=272
16r=-272
r=-17
Answer:
r=(-17)
Step-by-step explanation:
-16r=272
/-16 /-16
r=(-17)
at a local gym you can either pay $90 for a monthly pass then pay $4 each time you go to the gym or you can pay $13 each time you go with no monthly pass fee for how many visits to the gym in a month is the cost of the two options the same?
Answers
Answer:
10
Step-by-step explanation:
What's the diffrence between an Arithmatic sequence and a Geometric sequence?
Answers
Answer:
An arithmetic sequence has a constant difference between each term.
A geometric sequence has a constant ratio.
Help !! I need to do this fast !!!!!
Answers
Answer:
3 and 6
Step-by-step explanation:
can i get brainliest please? thanks!
hope this helps!
(7th grade math question)
Evan bought a pair of shoes for $120 there is a discount on the shoes for 10% off and the tax is 5%. What is the total price?
A) 105.46
B) 113.40
C) 108.00
D) 109.36
please answer soon
Answers
It's B I think. I might have done it wrong. But I pretty sure it's B
Answer:
It’s B
Step-by-step explanation: