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4 years ago

A = {1, 3, 5, 7, 9}

Mathematics

1 answer:

lions [1.4K]4 years ago

5 0

Answer:

Option B is correct.

Step-by-step explanation:

A = { 1, 3, 5, 7, 9 }

B = { 2, 4, 6, 8, 10 }

C = { 1, 5, 6, 7, 9 }

(B∩C) = {6} [Common element in set B and set C]

Now A∪(B∩C) = { 1, 3, 5, 6, 7, 9 }

Option B is the answer.

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A triangle has a height that is 2 inches more than three times the base and an area of 60 in. Find the base and the height of th

const2013 [10]

Answer:

Height = 20, Base = 6

Step-by-step explanation:

The area of a triangle is $\frac{bh}{2}$

where b is the base and h is the height

$H = 3B + 2\\\frac{B(3B + 2)}{2}=60\\\\3B^2 + 2B = 120\\3B^2+2B - 120=0\\$

We can factor by grouping

$3B^2 - 18B + 20B - 120 = 0\\3B(B - 6) + 20(B-6) = 0\\GCF the (B-6)\\(B-6)(3B+20)=0\\B = 6, B = \frac{-20}{3}$

Length can only be positive, so we know that the base is 6 in

The height must be 2 + 3(6) = 20

Height = 20, Base = 6

8 0

3 years ago

Two consecutive even integers have the following property. When the smaller integer is added to three times the larger integer,

Valentin [98]

Answer:

See below.

Step-by-step explanation:

Let the smaller integer be n.

Then the larger integer is n + 2.

"When the smaller integer is added to three times the larger integer, the result is two less than five times the smaller integer."

The correct equation is:

n + 3(n + 2) = 5n - 2

His mistake is not using parentheses on the left side. Since he left out the parentheses, the left side is not "the smaller integer added to three times the larger integer", but rather it is "the smaller integer added to 2 plus 3 times the smaller integer."

n + 3(n + 2) = 5n - 2

n + 3n + 6 = 5n - 2

4n + 6 = 5n - 2

8 = n

n = 8

n + 2 = 10

The integers are 8 and 10.

6 0

2 years ago

Juan brought 4 Tshirts and leather jacket. The T shirts were all the same price, and the price of the leather jacket was 6 times

Alex

Let us say that:

x = the number of T shirts bought = 4

y = the number of leather jackets bought = 1

a = the price of the T shirts

b = the price of the leather jackets

With the given variables, we can say that the total cost is:

total cost = a x + b y

Since, b = 6 a, therefore:

total cost = a x + 6 a y

total cost = a (x + 6 y)

Since total cost is 209, therefore we can calculate for a since x and y are also given:

209 = a (4 + 6 * 1)

209 = a (10)

a = $20.9

<span>Therefore each T shirt cost $20.9</span>

7 0

3 years ago

Th sum of three numbers is 64. The second number is 3 more than the first. The third number is

ladessa [460]

<span>Three numbers can be defined as x, y, and z.
x + y + z = 64
y = x+3
z = 2x - 11
.
substitute for y and z
x + (x+3) + (2x-11) = 64
4x -8 = 64
4x = 72

x = 18
.
y = x+3 = 21
z = 2x -11 = 2(18) -11 = 36-11 = 25
.
x + y + z = 18 + 21 + 25 = 64
Correct.
.
Answer: The three numbers are 18, 21, and 25.</span>

8 0

3 years ago

Complete the sentences to describe the different levels of organization in living things.

alexandr1967 [171]

Answer:

A system is a group of organs that work together to perform a common function.

An organ is a group of tissues that work together to perform a common function.

An organism is a group of organ systems that work together to perform a common function.

A cell is a basic unit of structure and function of all living things.

A tissue is a group of cells that work together to perform a common function.

Step-by-step explanation:

The different levels of organization in living things are defined below from smallest to largest:

Cell is the smallest unit of life. It is the basic structural, functional, and biological unit for all living things.

Tissue is a group of cells working together to accomplish a special function. Examples of tissue are connective tissue, muscle tissue.

Organ is a group of tissues working together to perform a specific function. Examples of organs are heart, liver etc.

System is a group of organs working together to perform a particular task and provide stability to the body. Example is muscular system, nervous system etc.

Organism consists of a group of system working together to perform a specific function. An organism is a living thing with an organized structure

7 0

3 years ago

Read 2 more answers