1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
natima [27]
2 years ago
11

Work out the area of triangle ABC.

Mathematics
1 answer:
AleksAgata [21]2 years ago
8 0

Answer:

A = 4 cm²

Step-by-step explanation:

The area of a triangle is calculated as

A = \frac{1}{2} bh ( b is the base and h the perpendicular height )

b = AC = 3\sqrt{2} + \sqrt{2} = 4\sqrt{2}

h = BD

Calculate BD using Pythagoras' identity in Δ ABD

BD² = AB² - AD²

      = (2\sqrt{5} )² - (3\sqrt{2} )²

     = 20 - 18 = 2 ( take square root of both sides )

BD = \sqrt{2}

Then

A = \frac{1}{2} × 4\sqrt{2} × \sqrt{2} = 2 × \sqrt{2} × \sqrt{2} = 4 cm²

You might be interested in
13 plus 5 times a number is no more than 30
omeli [17]
From what I'm reading from this question, there's one answer.

13 + 5 * 1 = 18 

Unless maybe I'm missing something?
5 0
3 years ago
The ordered pair R(-2,7) is translated 5 units to the right and down 2 units. which of the following descirbes the translation u
grigory [225]
Choice D is the correct answer.
For translations, moving to the right 5 units means you add 5 to x, and moving down 2 units means you subtract 2 from y. D is the only choice that accurately represents this.

Hope this helps
3 0
2 years ago
Statistics Question. Use the Desmos graphing calculator to find the least-squares regression line for the dataset in the table:
Soloha48 [4]

Given:

The table of values.

To find:

The least-squares regression line for the data set in the table by using the desmos graphing calculator.

Solution:

The general form of least-squares regression line is:

\hat{y}=mx+b           ...(i)

Where, m is the slope and b is the y-intercept.

By using the desmos graphing calculator, we get

m\approx 2.55,b\approx -6.435

Substitute these values in (i).

\hat{y}=(2.55)x+(-6.435)

\hat{y}=2.55x-6.435

Therefore, the correct option is A.

8 0
2 years ago
370 College freshmen were interviewed. 200 were registered for an Advanced Math class. 270 were registered for an English class
frozen [14]

Answer:

Step-by-step explanation:

To aid in understanding, draw three circles...

100 were registered for both Math and English.

50 were registered for both Sport and English but not Math.

70 were registered for Math, Sport, and English.

From here we will be able to calculate for those that signed up for only English class: Total number of students that signed up for english class

a. none signed up only for Maths (refer to attached document)

b. How many signed up for neither Math nor English meaning they signed up for only sports which is 70 from the venn diagram in the attachment.

c. How many signed up for an English class and at least one other class?

From the venn diagram:

we could have an English class and maths class - 100

we could also have an a English class and sports - 50

Thus total is 150.

d. What is the total fee for all the students enrolled in classes

From the diagram, 120 (english only and sport only) enrolled for only one class = 120 x $100 = $12,000

From the diagram, 180 (english and sport, maths and sport and english and maths) enrolled for two classes = 180 x $150 = $27,000

From the diagram, only 70 enrolled for the three classes = 70 x $200 = $14,000

Total fees = $12,000 + $27,000 + $14,000 = $53,000

5 0
3 years ago
At an ocean-side nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water t
grandymaker [24]

Answer:

(a1) The probability that temperature increase will be less than 20°C is 0.667.

(a2) The probability that temperature increase will be between 20°C and 22°C is 0.133.

(b) The probability that at any point of time the temperature increase is potentially dangerous is 0.467.

(c) The expected value of the temperature increase is 17.5°C.

Step-by-step explanation:

Let <em>X</em> = temperature increase.

The random variable <em>X</em> follows a continuous Uniform distribution, distributed over the range [10°C, 25°C].

The probability density function of <em>X</em> is:

f(X)=\left \{ {{\frac{1}{25-10}=\frac{1}{15};\ x\in [10, 25]} \atop {0;\ otherwise}} \right.

(a1)

Compute the probability that temperature increase will be less than 20°C as follows:

P(X

Thus, the probability that temperature increase will be less than 20°C is 0.667.

(a2)

Compute the probability that temperature increase will be between 20°C and 22°C as follows:

P(20

Thus, the probability that temperature increase will be between 20°C and 22°C is 0.133.

(b)

Compute the probability that at any point of time the temperature increase is potentially dangerous as follows:

P(X>18)=\int\limits^{25}_{18}{\frac{1}{15}}\, dx\\=\frac{1}{15}\int\limits^{25}_{18}{dx}\,\\=\frac{1}{15}[x]^{25}_{18}=\frac{1}{15}[25-18]=\frac{7}{15}\\=0.467

Thus, the probability that at any point of time the temperature increase is potentially dangerous is 0.467.

(c)

Compute the expected value of the uniform random variable <em>X</em> as follows:

E(X)=\frac{1}{2}[10+25]=\frac{35}{2}=17.5

Thus, the expected value of the temperature increase is 17.5°C.

7 0
3 years ago
Other questions:
  • A cylinder is a type of prism.<br> true<br> false
    8·1 answer
  • How to subtract fractions
    10·1 answer
  • If x plus one upon X equal to 11 find the value of x square + 1 upon x square
    11·1 answer
  • The height, h, in feet, of an object thrown upward from a height of 144 feet is a function of time, t, in seconds. The height ca
    13·1 answer
  • What is the probability of rolling a five on the first die and a six on the second die?
    15·1 answer
  • A8 x 3B= C730<br> How to calculate values of a b and c
    11·2 answers
  • Here are six number cards -4,-2,-1,5,6,8 <br> arrange the cards into three pairs with the same total
    7·2 answers
  • Help me plz I don’t really understand geometry
    10·1 answer
  • 50 POINTS Ayliah is 7 years more than 1/2 of Deb's age<br> use x for the variable
    7·1 answer
  • Compute (5 2/3)^2-(4 1/3)^2
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!