All categories

3 years ago

Please help ;-; what is the answer?

Mathematics

1 answer:

VashaNatasha [74]3 years ago

7 0

Answer:

5.7

Step-by-step explanation:

The altitude divides right triangle ABC into similar right triangles ADB and BDC. The ratios of short leg to long leg will be proportional in these similar triangles, so you have ...

AD/BD = BD/CD

Cross multiplying gives ...

AD·CD = BD²

(x+3)(2x+3) = 5²

2x² +9x = 16 . . . . . perform the multiplication, subtract 9

2(x² +4.5x) = 16

2(x² +4.5x +2.25²) = 16 +2(2.25²) . . . . . add 2(2.25²) to complete the square

2(x +2.25)² = 26.125 . . . . . write as a square

x +2.25 = √13.0625 . . . . . .divide by 2, take the positive square root

x = -2.25 +√13.0625 . . . . subtract 2.25 to find x

We want the value of CD, so ...

CD = 2x +3 = 2(-2.25 +√13.0625) +3

CD = -1.5 +2√13.0625 ≈ 5.7284

The length of CD is about 5.7 units.

You might be interested in

I need help with this problem I didn't really pay that much attention to this part of the subject.

Flauer [41]

To check if a piecewise defined function is continuous, you need to check how the pieces "glue" together when you step from one domain to the other.

So, the question is: what happens at x=3? If you reach x=3 from values slightly smaller than 3, you obey the rule f(x)=log(3x). So, as you approach 3, you get values closer and closer to

$\log(3\cdot 3)=\log(9)$

Similarly, if you reach x=3 from values slightly greater than 3, you obey the rule f(x)=(4-x)log(9). So, as you approach 3, you get values closer and closer to

$(4-3)\log(9)=\log(9)$

So, the function is continuous at x=3, because both pieces approach log(9) as x approaches 3.

4 0

3 years ago

1.) Which movie had the Lower Q3 as shown in the box plot?

KonstantinChe [14]

<h3>Answer: Movie A</h3>

Q3, or third quartile, is visually located at the right edge of the box. Movie A shows to have a smaller Q3 value as it is to the left of Q3 for movie B.

6 0

3 years ago

An architect planned to construct two similar stone pyramid structures in a park. The

kondaur [170]

Answer:

1) Change the length of side AB to 2 feet

Step-by-step explanation:

Given that both structures are similar, it follows that the ratio of their corresponding lengths are equal.

To find out what should be the correct length of AB that she should change to, set up the proportion showing the ratio of 2 corresponding lengths of both structures. Thus:

$\frac{PR}{AC} = \frac{PQ}{AB}$

We will assume AB is unknown.

PR = 7.5 ft

AC = 2.5 ft

PQ = 6 ft

Plug in the values into the equation

$\frac{7.5}{2.5} = \frac{6}{AB}$

Cross multiply

$AB*7.5 = 6*2.5$

$AB*7.5 = 15$

Divide both sides by 7.5

$AB = 2$

The architect should change the length of AB to 2 ft

7 0

2 years ago

Read 2 more answers

What is the square cube law?

viktelen [127]

Answer:

The square–cube law (or cube – square law) is a mathematical theory, implemented in a number of scientific contexts, which defines the relationship between the volume and the surface area as a shape 's size increases or decreases.

Hope this helps!

3 0

2 years ago

Read 2 more answers

Sandy works at a clothing store. She makes $7 per hour plus earns 10% commission on her sales. She worked 78 hours over the last

olga2289 [7]

Answer:

rounded, she will earn around $2,757.43 for the two weeks.

3 0

3 years ago