MATHEMATICS HIGH SCHOOL

When the queen counted her jewels, she found that she had five pearls for each diamond, two opals and three rubies for each diamond, and two emeralds for each opal. If she has three diamonds, how many jewels does she have altogether?

Answers

Answer 1

Answer:

I believe she would have 45 gems total

3 diamonds

5 pearls per diamond = 15 pearls

2 opals and 3 rubies per diamond= 6 opals and 9 rubies

2 emeralds per opal= 12 emeralds

3+15+6+9+12= 45 gems total

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Allison has 5 times as many baseball cards as football cards. In all, she has 120 baseball and football cards. How many baseball cards does Allison have?

Answers

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A zoo keeper wants to fence a rectangular habitat for goats. The length of the habitat should be at least 80 feet, and the perimeter of the habitat should be no more than 300 feet. a. Write and graph a system of linear inequalities

b. Write two possible solutions:

Answers

In inequality system, for the zoo keeper fencing, the greater than sign used for at least word of habitat length and less then sign used for no more than word.

a) The system of inequalities for the given problem is,

$x\geq80$
$y\leq-x+150$
The graph which shows the inequalities of is attached below.
b) The dimensions for two possible solution are 90 ft by 20 ft and 110 ft by 30 ft.

What is linear inequality system?

Inequality equation is the equation in which the two expressions are compared with greater than, less than or other inequality signs. The system having linear inequality equations is called the linear inequality system.

Given information-

The length of the habitat should be at least 80 feet.

The perimeter of the habitat should be no more than 300 feet.

Suppose $x$ is the length of the rectangular habitat and $y$ is the width of the rectangular habitat.

As the length of the habitat should be at least 80 feet. Thus the value of $x$ should be more than or equal to the 80 feet. Therefore,

$x\geq80$

Perimeter of the rectangle is twice the sum of length and width. As the perimeter of the habitat should be no more than 300 feet. Thus,

$2(x+y)\leq300\n2x+2y\leq300\ny\leq-x+150$

Hence, the system of inequalities for the given problem is,

$x\geq80$

$y\leq-x+150$

The graph which shows the inequalities of is attached below.

As in the graph attached below shown the area which can be gives the solution for the given system. We take two points as, (90,20)and (110,30).

Thus the dimensions for two possible solution are 90 ft by 20 ft and 110 ft by 30 ft.

Hence,

a) The system of inequalities for the given problem is,
$x\geq80$
$y\leq-x+150$
The graph which shows the inequalities of is attached below.
b) The dimensions for two possible solution are 90 ft by 20 ft and 110 ft by 30 ft.

Learn more about the linear inequality system here;

brainly.com/question/17724536

a. Write and graph a system of linear inequalities
Here's the equation of a system of linear inequalities.
x >= 80
2x + 2y <= 300 -----> y <= -x + 150

For the graph, it is attached as image.

b. Write two possible solutions:These are the two possible solutions to the given equation of linear inequality.

90 feet by 20 feet
110 feet by 30 feet.

Pllsss I needddd helpp

Answers

I can’t see, make it clear

The sum of three numbers is 2100. The first number (x) is equal to the sum of the other two (y and z) which are equal to each other. What are the three numbers (x, y, and z)? A) (1050, 525, 525) B) (1050, 524, 525) C) (1050, 526, 523) D) (1051, 525, 524)

Answers

Answer:

Let's solve the problem step-by-step:

We are given that the sum of three numbers is 2100. Let's call the first number x and the other two numbers y and z.

From the information given, we know that x = y + z, and y = z (the other two numbers are equal to each other).

Substituting y = z into x = y + z, we have x = 2z.

We are also given that the sum of the three numbers is 2100. So, we can write the equation x + y + z = 2100.

Substituting x = 2z and y = z, we have 2z + z + z = 2100.

Simplifying the equation, we have 4z = 2100.

Dividing both sides of the equation by 4, we find z = 525.

Substituting z = 525 back into y = z, we find y = 525.

Finally, substituting z = 525 and y = 525 back into x = 2z, we find x = 1050.

Therefore, the three numbers are x = 1050, y = 525, and z = 525.

Among the options provided, the correct answer is A) (1050, 525, 525).

The area of a triangle is 12 cm squared. If the base of the triangle is 4 cm what is the height

Answers

Answer:

6 cm

Step-by-step explanation:

Simplify the expressions (x-2) (3x-4)

Answers

This expression can be simplified using the FOIL method of multiplication (first, outer, inner, last).

First: x · 3x = 3x²
Outer: x · -4 = -4x
Inner: -2 · 3x = -6x
Last: -2 · -4 = 8

Combine all these terms, and it leaves you with your final answer:
3x² - 10x + 8

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