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3 years ago

Find the orthocenter of ABC

Mathematics

1 answer:

Tresset [83]3 years ago

5 0

(6,4)
This website helps
https://www.mathportal.org/calculators/analytic-geometry/triangle-calculator.php

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A container in the shape of a rectangular prism holds 651.168 cubic inches when completely filled with water. The container has

serg [7]

Answer : 3.4

Explanation: 12.6 x 15.2= 191.52
651.168 / 191.52 = 3.4

3 0

3 years ago

A circle is inscribed in a square with a side length of 144. If a point in the square is chosen at random, what is the probabili

____ [38]

Given :

A circle is inscribed in a square with a side length of 144.

So, radius of circle, r = 144/2 = 72 units.

To Find :

The probability that the point is inside the circle.

Solution :

Area of circle,

$A_c = \pi r^2\\\\A_c = 3.14 \times 72^2\ units^2\\\\A_c = 16277.76 \ units^2$

Area of square,

$A_s = (2r)^2\\\\A_s = ( 2 \times 72)^2\ units^2\\\\A_s = 20736\ units^2$

Now, probability is given by :

$P = \dfrac{A_c}{A_s}\\\\P = \dfrac{16277.76}{20736}\\\\P = 0.785$

Therefore, the probability that the point is inside the circle is 0.785 .

4 0

3 years ago

Convert the following decimals into rational numbers: 1.4325

matrenka [14]

Answer

$\frac{573}{400}$

step-by-step explanation:

$\frac{1.4325}{1}$ × $\frac{10000}{10000}$ = $\frac{14325}{10000}$

Simplify

$\frac{14325}{10000}$ ÷ $\frac{25}{25}$ = $\frac{573}{400}$

5 0

3 years ago

Write the first 4 multiples of 3/8

sesenic [268]

Multiples of 3

: 3, 6, 9, 12, 15, 18, 21, 24, ...

Multiples of 4

: 4, 8, 12, 16, 20, 24, ...

Multiples of 8

: 8, 16, 24, ..

Find the smallest number that is shared by all rows above. This is the LCM.

LCM = 2424

Method 2: By Prime Factors

List the prime factors of each number.

Prime Factors of 3

: 3

Prime Factors of 4

: 2, 2

Prime Factors of 8

: 2, 2, 2

Find the union of these primes.

2,2,2,32,2,2,3

Multiply these numbers: 2\times 2\times 2\times 3=242×2×2×3=24. This is the LCM.

LCM = 2424

3 0

3 years ago

2. In a school of 320 students, 85 students are in the band, 200 students are on sports teams, and 60 students

Alja [10]

Answer:

60 students are involved in either band or sports.

95 students are not involved in either sports or band.

Step-by-step explanation:

Given:

In a school of 320 students, 85 students are in the band, 200 students are on sports teams, and 60 students participate in both activities.

Now, to find the students are involved in either sports or band. And students who are not involved in either sports or band.

Total number of students = 320.

Number of students in the band = 85.

Number of students in the sports team = 200.

Number of students participate in both activities = 60.

Thus, 60 students are involved in either band or sports.

So, the number of students in the band adding number of students in the sports team we get:

200 + 85 = 285.

Then, to subtract the number of students participate in both activities we get:

285 - 60 = 225.

Thus, the remaining students are = 225.

Now, to get the students who are not involved in either sports or band we subtract the total number of students from the remaining students:

$320-225$

$=95.$

Therefore, 60 students are not involved in either band or sports. 95 students are not involved in either sports or band.

8 0

3 years ago