All categories

1 year ago

In the diagram below, if AB = 25, AC = 15, and BD = 5, then find the length of DC.

Mathematics

1 answer:

ivann1987 [24]1 year ago

3 0

The length of DC based on the information given about the triangle is 19.37.

<h3>How to calculate the length?</h3>

Based on the given information, it should be noted that:

AB² = AD² + BD²

25² = AD² + 5²

625 = AD² + 25

AD² = 625 - 25

AD² = 600

AD = √600

AD = 24.5

DC² = AD² + - AB² (Pythagoras theorem)

DC² = 24.5² + 15²

DC² = 375.25

DC = 19.37

Learn more about triangle on:

brainly.com/question/1058720

#SPJ1

You might be interested in

Point B ∈ AC. Find the length of segments AB and BC if AC = 20 cm and: AB:BC = 3:7

madam [21]

Answer:

Length of AB = 6 cm

Length of the segment BC = 14 cm

Step-by-step explanation:

Here, B is a point on a segment AC.

AB : BC = 3:7

Length of the segment AC = 20 cm

Now, let the common ratio between the segment is x.

So, the length of AB = 3 x , and Length of BC = 7 x

Now, AB + BC = AC

⇒ 3x + 7x = 20

or, 10 x = 20

or, x = 2

Hence, the length of AB = 3 x = 3 x 2 = 6 cm

and the length of the segment BC = 7x = 7 x 2 = 14 cm

7 0

3 years ago

Read 2 more answers

If f(x) = x + 4 and g(x)=x^2-1, what is m(g o f)(x)?

Andreas93 [3]

Until now, given a function f(x), you would plug a number or another variable in for x. You could even get fancy and plug in an entire expression for x. For example, given f(x) = 2x + 3, you could find f(y2 – 1) by plugging y2 – 1 in for x to get f(y2 – 1) = 2(y2 – 1) + 3 = 2y2 – 2 + 3 = 2y2 + 1.

In function composition, you're plugging entire functions in for the x. In other words, you're always getting "fancy". But let's start simple. Instead of dealing with functions as formulas, let's deal with functions as sets of (x, y) points:

Let f = {(–2, 3), (–1, 1), (0, 0), (1, –1), (2, –3)} and

let g = {(–3, 1), (–1, –2), (0, 2), (2, 2), (3, 1)}.

Find (i) f (1), (ii) g(–1), and (iii) (g o f )(1).

(i) This type of exercise is meant to emphasize that the (x, y) points are really (x, f (x)) points. To find f (1), I need to find the (x, y) point in the set of (x, f (x)) points that has a first coordinate of x = 1. Then f (1) is the y-value of that point. In this case, the point with x = 1 is (1, –1), so:

8 0

2 years ago

Read 2 more answers

Let f (x) = -1/2(x + 2)+ 5

bogdanovich [222]

Answer:

Rate of change = -1

Step-by-step explanation:

Given:

f(x) = -½(x + 2)² + 5

Required:

Average rate of change from x = -3 to x = 1

Solution:

Rate of change = $\frac{f(b) - f(a)}{b - a}$

Where,

a = -3,

f(a) = f(-3) = -½(-3 + 2)² + 5 = -½(-1)² + 5 = 4.5

b = 1,

f(b) = f(1) = -½(1 + 2)² + 5 = -½(9) + 5 = 0.5

Plug in the values into the formula:

Rate of change = $\frac{0.5 - 4.5}{1 - (-3)}$

Rate of change = $\frac{-4}{4}$

Rate of change = -1

8 0

2 years ago

Miranda has 19 pieces of candy. She wants to give an equal number of pieces to her 6 friends. How many pieces of candy will each

yan [13]

Answer:

3 1/6

Step-by-step explanation:

19/6= 3.1666666666666 also known as 3 1/6

check your work by multiplying 3 1/6 by 6 and get 19

3 0

3 years ago

What is the probability that the mean duration of the 24 rowers with idna exceeds 63 minutes?

statuscvo [17]

Answer:

Step-by-step explanation:

Given that: Training-session duration of female rowers with normal iron status is Normally distributed, with mean 69 minutes and standard deviation 18minutes.

Solution:

z score shows the relationship between sample means. The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by the formula:

$z=\frac{x-\mu}{\sigma}\\\\for\ sample(n):\\\\z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\where\ \mu=mean,\sigma=standard\ deviation,x=raw\ score$

Given that μ = 69 minutes, σ = 18 minutes, n = 24

For x > 63 minutes:

$z=\frac{x-\mu}{\sigma / \sqrt{n} } =\frac{63-69}{18/\sqrt{24} }=-1.63$

From the distribution table, P(x > 63) = P(z > -1.63) = 1 - P(z < 1.63) = 1 - 0.0516 = 0.9484

7 0

2 years ago