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 1

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.

Given Right Triangle ABCABC With Altitude \overline{BD} BD Drawn To Hypotenuse ACAC. If BC=10BC=10 And
Answer 2

Answer:

x = 20

Step-by-step explanation:


Related Questions

Use the interactive graph below to sketch a graph of y = -2 • 3^x + 5.

Answers

Answer:d = rand(20);

figure(1)

imagesc(d)

text(5, 22, sprintf('\\uparrow\nLTO'), 'HorizontalAlignment','center', 'FontWeight','bold')

Step-by-step explanation:

i know

The graph of the function is attached.

What is an exponential graph?

A curve that depicts an exponential function is known as an exponential graph. A curve with a horizontal asymptote and either an increasing slope or a decreasing slope called an exponential graph. i.e., it begins as a horizontal line, increases or drops gradually, and then the growth or decay accelerates.

Given the graph of function,

The graph of any exponential function is parallel to an  axis and drop and increase show the decay or growth,

since the  equation,

y = -2(3ˣ) + 5

has a negative sign the graph will go down,

y-intercept for the graph is 3,

when x = 0, y = 3

and the graph will be in the fourth quadrant.

Hence the graph will be in the fourth quadrant.

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whats is 17 1/4 plus 7/8​

Answers

Answer:

I love Math anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

i looked it up n got 18.125.

Lynn is making a snack. The recipes call for 3/8 cup of water for oats and 1/4 cup of water for dried fruit. She only has 1 cup of water. Does she have enough to make her snack? Explain

Answers

Answer: She has enough.

Step-by-step explanation:

You need to add up the quantities of water needed first. That will then tell if she has enough water.

Convert the fractions to decimals then add them up:

3/8 = 0.375

1/4 = 0.25

= 0.25 + 0.375

= 0.625 cups of water is required.

This is less than the 1 cup she has so she has enough water to make the snack.

What is the difference between vertical and horizontal lines?

Answers

Answer:

A vertical line is any line parallel to the vertical direction. A horizontal line is any line normal to a vertical line. Horizontal lines do not cross each other.

hi! horizontal goes down _____, vertical goes up |

hope this helps!

Ok last question its very "hard" mods don't delete

what is 3x+12= 42

Answers

Answer:

x is 10.

Step-by-step explanation:

3x + 12 = 42

Subtract 12 from both sides

3x = 42 - 12

Subtract 12 from 42 to get 30

3x = 30

Divide both sides by 3

x = 30/3

Divide 30 by 3 to get 10

x = 10

One year, the population of a city was 252,000. Several years later it was 201,600. Find the percent decrease.

Answers

Answer:

0010110010100100001010010010101010010101010010010

001010010010100010010101000001010000101001010010

Respuesta en número binarios

170 in ratio of 9:8 sorry I’m not to good at math

Answers

Answer:

if 170 is subbed for 9, then the answer is 151.111111111(continued) and if its in the 8, then the answer is 191.25

Step-by-step explanation:

hope this helps

5/8 + 3/4 divide by -2/3 - 5/6

Answers

Answer: -4/3

Step-by-step explanation: hope this helps :)

What is this answer this is a little tricky for me

Answers

Answer:

the answer is a

Step-by-step explanation:

B is your answer it’s quadrilateral <3

plz help this is what might get m to a 100 so plz help me

Answers

Answer:

I'd say it's the first dot in from the left (close to 2.4)

Step-by-step explanation:

the square root of 6 is 2.4494, and that's very close to 2.4

An rectangle has 18 cm As the base and 17 cm as the height what is the area

Answers

Answer:

306

Step-by-step explanation:

I think you just multiply 18 x 17=306

List the ordered pairs shown in the mapping diagram

Answers

Answer:

(0,4)

(1,6)

(2,8)

(3,1)

(4,0)

The required ordered pair mentioned in the mapping diagram is (0,4), (1,6), (2,8), (3,1), and (4,0).

What is coordinate?

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

What is a mapping diagram?

A mapping diagram is used to illustrate the relationship between sets of domains and ranges.

here,
From the mapping diagram,
Each arrow represents the ordered pairs,
So,
The ordered pair is given as,
(0,4), (1,6), (2,8), (3,1), and (4,0)


Thus, the required ordered pair mentioned in the mapping diagram are (0,4), (1,6), (2,8), (3,1), and (4,0).

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please answer these questions

Answers

What’s the question

Which of the following is a polynomial?

Answers

Answer:

A. 3x^2+6x is a polynomial

Hi! Could you help me me out and solve these two problems? "eight less than the product of seven and xxx", and "the sum of six and the product of three and d". Thank you!

Answers

Given:

The given statement are:

a. Eight less than the product of seven and x.

b. The sum of six and the product of three and d.

To find:

The expression for the given statements.

Solution:

a.

Product of 7 and x is 7×x = 7x.

Eight less than the product of seven and x is 7x - 8.

Therefore, the required expression for the statement "Eight less than the product of seven and x" is 7x-8.

b.

Product of 3 and d is 3×d = 3d.

The sum of six and the product of three and d is 6+3d.

Therefore, the required expression for the statement "The sum of six and the product of three and d" is 6+3d.

I dont understand how to do this, looking for someone who can help

Answers

the answer should be a segment. have a great day :)))

Given the set of ordered pairs: {(1,3), (2,7), (x,5), (6,4)}.
What is a value for x that would NOT make the set a function? Explain why.

Answers

Answer:

2

Step-by-step explanation:

2 is a value of x that would not make the set a function because a function can't have multiple coordinates wit hthe same domain (x-coordinate). 2 is a domain that has already been used in the point (2,7). If this is used in (x,5), the point would become (2,5) and repeat a domain.

Note:

The x-coordinate could also be 1 or 6 because they have been used as domains as well.

Hope it helps!

Help me please:( I need it

Answers

Answer:

y = 18

Step-by-step explanation:

30² = 24²  + y²

900 = 576 + y²

y = [tex]\sqrt{324}[/tex]

y = 18

Evaluate P(5, 3).
1. 15
2. 20
3. 60

Answers

The answer is option 3 - 60

In your own words what is the definition of reflection (in geometry)

Answers

Answer:

a reflection is an isometry, which means the original and image are congruent, which can be reffered to as a flip

Step-by-step explanation:

Find the area of the triangles put together.

Answers

Answer:

i might be compltely wrong but i am geting 24

Step-by-step explanation:i probply am wrong

10) using opposite operations solve for x

30 = - 6 x + 12

Answers

X=-3 that’s the answer your welcome

Triangle similarity-
Solve for x!!!
Please help!

Answers

Answer: im thinking it is 5 but i could be totally wrong. im not the smartest lol

Step-by-step explanation:

SOMEONE PLEASE HELP ME WITH THIS QUESTION!

Answers

Answer:

i dont know but i have a pic for u

Step-by-step explanation:

At most 3 because 21% of 10 people is 2.1 people so the most would be 3 according to that statistic.

which value of x makes the equation 1.25(4 x-10)=7.5 true?
A. 3.5
B. -1
C. -0.5
D. 4​

Answers

Answer:

4

Step-by-step explanation:

1.25(4x-10)=7.5

First step is to divide the 1.25 on both sides

4x-10 = 6

next step is to get x by itself by adding 10 to both sides

4x = 16

continue getting x by itself by dividing both sides by 4

x = 4.

Find the composition (f ∘ g)(–2) for the functions f(x) = 2x + 1 and g(x) = x2 – 3.

Answers

Answer:

Step-by-step explanation:

(f∘g)(x) = f(g(x))

 = f(x²-3)

 = 2(x²-3) + 1

 = 2x² - 5

(f∘g)(-2) = 2(-2)² - 5

  = 2·4 - 5

  = 8 - 5

  = 3

The composition (f ∘ g)(–2) for the functions f(x) = 2x + 1 and g(x) = x2 –  3 will be 3

What is composition of a function ?

The composition of a function is an operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)). It means here function g is applied to the function of x. So, basically, a function is applied to the result of another function.

The notation used for composition is: (f o g)(x) = f(g(x))

(fog)(x) = f(g(x))

this implies , (fog)(-2) = f(g(2))

given :

f(x) = 2x + 1

g(x) = x2 – 3

(fog)(x) = f(g(x)) = f(x^2 - 3)

                        =  2 (x^2 -3) +1

                        = 2x^2 - 5                                    equation 1

fog(-2) =  f(g(2))

substituting the value of x = 2 in equation 2

           = 2 * (2)^2 -5

           = 3

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Write the equation in standard form using integers.
y = - 2/3x -5
The equation in standard form is

Answers

The Answer is: 2x+3y=-15

Which relationship describe angles 1 and 2

Vertical angles
Adjacent angles
Supplementary angles
Complementary angles

Answers

They are supplementary angles. They are located on a straight line, and when added together they will add up to 180 degrees.

What is the correct factorisation of?
X^2+6x+8​

Answers

Answer:

Step-by-step explanation:

Given that: x  

2

+6x+8

                 =x  

2

+4x+2x+8,        (split middle term)

                 =(x  

2

+4x)+(2x+8),    (group pair of terms)  

                 =x(x+4)+2(x+4),         (factor each binomials)

                 =(x+4)(x+2),              (factor out common factor (x+4)

Hence factors of x  

2

+6x+8 are (x+4)(x+2)

x² + 6x + 8

= x² + 4x + 2x + 8

= x(x+4) + 2(x+4)

= (x+4)(x+2)

What is the value of A when we rewrite
(1/7)^x-2 - (1/7) ^x as A x (1/7)^x

Answers

Answer:

48

Step-by-step explanation:

Khan Academy

The value of [A] will be 48.

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is that we have rewritten -

(1/7)ˣ ⁻ ² - (1/7)ˣ  as  [A] x (1/7)ˣ

We have (1/7)ˣ ⁻ ² - (1/7)ˣ  rewritten as [A] x (1/7)ˣ. So, we can write -

(1/7)ˣ ⁻ ² - (1/7)ˣ = [A] x (1/7)ˣ.

Now, we can write [(1/7)ˣ ⁻ ² - (1/7)ˣ] as :

[(1/7)ˣ / (1/7)²] - (1/7)ˣ

(1/7)ˣ [1/(1/7)² - 1]

We have -

(1/7)ˣ ⁻ ² - (1/7)ˣ = [A] x (1/7)ˣ.

So, we can write -

(1/7)ˣ × [1/(1/7)² - 1] =  [A] × (1/7)ˣ.

On comparing, we  get -

[A] = [1/(1/7)² - 1]

[A] = 48

Therefore, the value of [A] will be 48.

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