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
What's 12/15 closest to 0,1/2 or 1
Answers
Answer:
1
Step-by-step explanation:
12/15 can be simplified as 4/5, 4/5 can be rewritten as 8/10, or 80%. 0 is of course 0%, 1/2 is 50%, and 1 is 100%. 80% is closest to 100%, so 12/15 is closest to 1.
If x2 - 6x - 16, what are the x-intercepts?
Answers
Then factorise to (x+2)(x-8)
So x intercepts are -2 and 8
Answer:
(-2, 0) and (8, 0)
Step-by-step explanation:
x2 - 6x - 16 = 0
(x - 8)(x + 2) = 0
x = -2, 8.
at a local gym you can either pay $90 for a monthly pass then pay for dollars each time you go to the gym or you can pay $13 each time you go with no monthly pass fee if you're going to the gym 17 times in a month which option is better
Answers
Answer:1st option
Step-by-step explanation:
how would you write this number in numeric form eight hundred fifty-three hundredths?
Answers
solve question >> ( - 3x)^2
Answers
Answer:
(-3x)^2 = (-3)^2(x^2)
=9x^2
Let me know if this helps!
Find mZWZY.
W
x
(8x - 1)º
(5x + 11)°
Z
Answers
Answer:
08.262=)))55668(4738dfrj
Fiona is typing an essay on her computer. She types 5/8 of a page in 1/2 hour. At this rate, how many pages can Fiona type in 1 hour? Enter the answer as an improper fraction (fraction greater than one).
Answers
Answer:
5/4 page
Step-by-step explanation:
5/8 * 2 = 10/8 = 5/4
what does 2x+2=10 equal to?
Answers
Answer:
5x =10
Step-by-step explanation:
Carol opened a savings account and deposited 2,650. The account earned 4% interest compounded annually how much money will carol have in her account after 3 years
Answers
Answer:
$2968
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 4%/100 = 0.04 per year,
then, solving our equation
I = 2650 × 0.04 × 3 = 318
I = $ 318.00
The simple interest accumulated
on a principal of $ 2,650.00
at a rate of 4% per year
for 3 years is $ 318.00.
5.
A zucchini plant in Darnell’s garden was 12 centimeters tall when it was first planted. Since then, it has grown approximately 0.5 centimeter per day.
a. Write a rule to describe the function.
b. After how many days will the zucchini plant be 0.195 meter tall?
A. h(d) = 12d + 0.5; 1.3 days
B. h(d) = 0.5d +12; 15 days
C. h(d) = 0.5d; 39 days
D. h(d) = d/0.5 = 12; 4 days
Answers
Answer:
B. h(d) = 0.5d +12; 15 days
Step-by-step explanation:
here they want to write an equation to describe the growth of the plant. set y = height of the plant (in cm). set x = days (since planting). the plant was planted on day 0 (x=0). We know that the plant was 12 cm tall when it was first planted, so we know that y(0) = 12 cm. y(0) just means the value of the equation y when x = 0, or y(x=0), or just y(0). Every day the plant grows .5 cm so we know the value of y will increase at .5cm for every x days, or .5x. Add the initial value of y (where x=0) and you have the equation y = 12 + .5x (in cm). usually we write equations in meters and not cm, so you can change it to y = .12 +.005x (in meters).
now just set your equation equal to .185 meters and solve for x
.185 = .12 + .005x
.065 = .005x
x = 13 days
Answer
(a) Find out the a rule to describe the function.
To prove
Let us assume that the days be represted by d .
Let us assume that the height of plant be represted by y.
As given
A zucchini plant in Darnell’s garden was 12 centimeters tall when it was first planted.
it has grown approximately 0.5 centimeter per day.
Than the function becomes
y = 12 + 0.5 × d
y = 12 + 0.5d
(b) Find out after how many days will the zucchini plant be 0.195 meter tall .
To prove
Let us assume that the days be represted by d .
As given
A zucchini plant in Darnell’s garden was 12 centimeters tall when it was first planted.
it has grown approximately 0.5 centimeter per day.
As
1meter = 100cm
0.195 meter convert into centimeter.
= 19.5cm
Than the equation becomes
12 + 0.5d = 19.5
0.5d = -12 + 19.5
0.5d = 7.5
d = 15 days
Therefore 15 days will the zucchini plant be 0.195 meter tall .
a) 12 + 0.5d d=day
b) 0.195/0.5=0.39d
Answer:
15 days will the zucchini plant be 0.195 meter tall .
Step-by-step explanation:
(a) Find out the a rule to describe the function.
To prove
Let us assume that the days be represted by d .
Let us assume that the height of plant be represted by y.
As given
A zucchini plant in Darnell’s garden was 12 centimeters tall when it was first planted.
it has grown approximately 0.5 centimeter per day.
Than the function becomes
y = 12 + 0.5 × d
y = 12 + 0.5d
(b) Find out after how many days will the zucchini plant be 0.195 meter tall .
To prove
Let us assume that the days be represted by d .
As given
A zucchini plant in Darnell’s garden was 12 centimeters tall when it was first planted.
it has grown approximately 0.5 centimeter per day.
As
1meter = 100cm
0.195 meter convert into centimeter.
= 19.5cm
Than the equation becomes
12 + 0.5d = 19.5
0.5d = -12 + 19.5
0.5d = 7.5
d = \frac{7.5}{0.5}
d = 15 days
Therefore 15 days will the zucchini plant be 0.195 meter tall .
Solve the real-world situation by using the substitution method.
The number of DVDs sold at a store in a month was 923 and the number of DVDs sold decreased by 12
per month. The number of Blu-ray Discs sold in the same store in the same month was 505 and the
number of Blu-ray discs sold increased by 26 per month. Let d represent the number of discs sold and t
represent the time in months.
The system of equations
{d=923-12t
{d=505+26t
can be used to represent this situation.
If this trend continues, how many months will the number of DVDs sold equal the number of Blu-ray discs
sold? How many of each is sold in that month?
There will be ____ DVDs and Blu-Ray discs sold per month in ____ months.
Answers
Answer:
In 11 months, the number of DVDs sold and Blue-Ray discs sold will be same, 791 of each.
Step-by-step explanation:
In the equation d = 923-12t, substitute 505+26t (from the second equation) for 'd'. We get
505 + 26t = 923 - 12t
-505 + 12t -505 + 12t
38t = 418
t=11
d = 923-12(11) = 791
d = 505+26(11) = 791
After 11 months, selling 791 of each.
Hope this helps.
Answer:
791
Step-by-step explanation:
PLEASE ACTUALLY ANSWER!!
Answers
Answer:
a) C
b) 4.5[tex]cm^{2}[/tex]
Step-by-step explanation:
Use the formula:
Lh([tex]\frac{1}{2}[/tex])Apply this to triangle A
2(3)÷2Solve.
3=area of Triangle AApply this to triangle B
2(3)÷2Solve.
3=area of Triangle BApply this to Triangle C
3(3)÷2Solve
4.5= area of Triangle CAs you can see, Triangle C has the greatest area.
50-8-30+28¿como lo puedo resolver?
Answers
Answer:
40
~
Puedes resolverlo simplificando la ecuación.
~
You can solve it by simplifying the equation.
~
Answer:
50 - 8 - 30 + 28 =
(50 + 28) - (8 + 30) =
78 - 38 =
40
Its much easier to solve 78 - 38 than 50 - 8 - 30 + 28, which is why you simplify the question before calkylating it.
sorry i dont know Spanish...
but hope i could help :D
Use the Distributive Property to write each expression as an equivalent expression. Then evaluate the expression. **SHOW THE PROPERTY** 1. 2/5(s + 20) and
2. –6(12 – 8)
Answers
Answer:
1. 2/5s + 8
2. -24
Step-by-step explanation:
1.
2/5(s + 20)
(2/5)(s) + (2/5)(20)
2/5s + 8
2.
-6(12 - 8)
(-6)(12) - (-6)(-8)
-72 + 48
-24
Map Proportionality: You have a map where Indy and Fort Wayne are 19 centimeter apart. Kokomo and Indy are 9.5 cm apart on the map. If you know that Indy and Fort Wayne are actually 120 miles apart, how far apart would Indy and Kokomo be in real life? Express your answer rounded to the nearest tenth of
Answers
Answer: 60 miles
Step-by-step explanation:
On a map, Indy and Fort Wayne are 19 centimeter apart while Kokomo and Indy are 9.5 cm apart on the map.
In real life, Indy and Fort Wayne are actually 120 miles apart, the distance between Indy and Kokomo in real life would then be:
= 9.5 × 120/19
= 120/2
= 60 miles
Indy and Kokomo are 60 miles apart in real life.
The price of gas increases from $2.20 per gallon on Monday to $2.31 per gallon on Tuesday. What is the percent of increase?
Answers
Answer:
5% increaseeee
Find the rate of change of the function by using two points from the table.
x y
1 15
2 11
3 7
4 3
Answers
The rate of change of the function is -4.
What is the slope of a line?The slope of a line indicates the direction and the steepness of the line. The formula for the slope of a line passing through the points (x₁,y₁) and (x₂, y₂) is m = (y₂-y₁)/(x₂-x₁).
Consider the two points (1,15) and (2,11).
The rate of change of the function is nothing but the slope of the line passing through the points (1,15) and (2,11) which is:
m = (11 - 15)/(2 -1)
m = -4
Hence, the rate of change of the function is -4.
To learn more about slopes, click here:
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What is 7x + 10 = 7x + 10
Answers
Answer:
Infinite solitutions
Step-by-step explanation:
The expressions are the exact same, so there are infinite solutions.
Answer:
infinite solutions
Step-by-step explanation:
Please HELP im so confused
3x-8y=7
2y+16x=15
Answers
Answer: x=1, y=-0.5
Step-by-step explanation:
I just need help on which option
Answers
The answer is option two
What is the exponent form? 6 x 6 x 6
A. 6 cubed
B. 6 to the power of 2
C. 6 squared
D. 6 x 3
Answers
Answer:
C.6 squared
Step-by-step explanation:
1,275÷588 rounded pls i need some help
Answers
1dp=2.2
2dp=2.7
3dp=2.8
Find the vertical distance between the two points !!!!! Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answers
Answer:
The answer will be 7,-3
Step-by-step explanation:
1. Write the equation of the line passing through the point (-2, 2) that is
parallel to y=-x-5 in slope-intercept form.
Answers
creo que quieres decir la suma
si es la suma eso da 2.8
A store offers a 30% discount on a clarinet that was marked up by 5% form the original retail price for $405.the sales tax is 9%. What does the clarinet cost?.
Answers
Answer:
$324.46
Step-by-step explanation:
$405 × 0.05= $20.25 is how much it is marked up if the original price is $405.
$405 +$ 20.25 = $425.25 is the new total of the clarinet
Now 30 % of $425.25... $425.25×0.30= $127.58 is what 30% is.
You have to subtract th $127.58 from $425.25 to get the discounted price.
$425.25 - $127.58 = $297.67
Next you have to calculate for the 9% and add it to the discounted price.
$297.67 × .09 = $26.79
$297.67 + $26.79= $324.46
$324.46 is the cost of the clarinet.
Find the length of BC
Answers
Answer:
It would be 123
Step-by-step explanation:
Solve x + 10 = 3x + 4 *
Answers
Answer:
x= 3 hope it helps thanks
Please tell me how to do problems like 4.6x8.3(I need an explination) WILL GIVE BRAINLIEST NO TROLLING OR BAN
Answers
Answer:
you just multiply normaly and the decimals get multiplied too
Step-by-step explanation:
4.6*8.3=38.18 4*8= 38 and 6*3= 18 so the answer is 38.18
The Hendricksons are in charge of bringing treats for 50 football players. They brought 3 coolers of popsicles and 2 coolers of ice cream sandwiches. Each player is going to randomly select a cooler from which to get their treat. Which statement best predicts how many players will get a popsicle?
Answers
There are 5 coolers in total. There are 3 coolers of popsicles, which means 3/5 of the coolers are popsicle coolers.
To find out how many football players will get a popsicle, multiply the amount of football players (50) by the chance they will pick a popsicle cooler (3/5).
50 x 3/5 = 30 football players
Answer:
There will be close to 30 football players but probably not exactly 30 football players who get a popsicle.
Step-by-step explanation:
Its correct on Khan Academy
Carter is going to invest $210 and leave it in an account for 5 years. Assuming the interest is compounded annually, what interest rate, to the nearest tenth of a percent, would be required in order for Carter to end up with $250?
Answers
Answer:360
Step-by-step explanation:g-g5
The rate of interest will be 0.35.
What is compound interest?
Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
Compound interest formula[tex]CI = P(1+\frac{r}{n}) ^{nt} -P[/tex]
and, the Amount is given by
[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]
Where,
A is amount
P is principal
r is rate of interest
n is number of times interest is compounded per year
t is time
According to the given question
Principal, P = $210
Amount, A = $250
Time, t = 5 years
n = 1
Therefore, the interest rate is given by
Amount = [tex]P(1+\frac{r}{n}) ^{nt}[/tex]
⇒[tex]250 = 210(1+\frac{r}{1}) ^{5}[/tex]
⇒[tex]\frac{250}{210} =(1+r)^{5}[/tex]
⇒[tex]1.19 = (1+r)^{5}[/tex]
⇒[tex]\sqrt[5]{1.19} = 1+r\\[/tex]
⇒ 1.035 = 1 + r
⇒ r = 1.035 - 1
⇒ r = 0.35
Hence, the interest rate is o.35.
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