Which ordered pair is the solution to the system of equations? {2x−y=−5x+3y=22{2x−y=−5x+3y=22 (7, 19)(7, 19) (8, 21)(8, 21) (4, 9)(4, 9) (1, 7)

Final answer:

The area of the circle, given its circumference of 65π, is calculated as 1056.25π, using the formulas for circumference and area of the circle in terms of the radius.

Explanation:

The circumference of a circle is given by the formula 2πr where r is the radius of the circle. Given that the circumference is 65π, we can find the radius by rearranging the formula: r = circumference / (2π) = 65π / (2π) = 32.5. Next, we use the formula for the area of a circle, which is A = πr², substituting the value we found for r:

A = π(32.5)² = π(1056.25) = 1056.25π.

Therefore, in terms of π, the area of the circle is 1056.25π, which corresponds to choice D of the provided options.

The approximate number of pounds of oxygen produced in the Amazon rainforest each day is [tex]\(2.8 \times 10^{10}\)[/tex] pounds.

To find out how many pounds of oxygen are produced in the Amazon rainforest each day, we first need to calculate the total amount of oxygen produced by all the trees in the rainforest annually.

The Amazon rainforest has about [tex]\(3.9 \times 10^{11}\)[/tex] trees, and each tree produces [tex]\(2.6 \times 10^2\)[/tex] pounds of oxygen per year.

So, the total amount of oxygen produced annually in the rainforest is:

[tex]\[ 3.9 \times 10^{11} \, \text{trees} \times 2.6 \times 10^2 \, \text{lb/tree/year} \][/tex]

To multiply these numbers, we can add the exponents and multiply the coefficients:

[tex]\[ (3.9 \times 2.6) \times (10^{11} \times 10^2) \, \text{lb/year} \][/tex]

[tex]\[ = 10.14 \times 10^{13} \, \text{lb/year} \][/tex]

Now, to find out how many pounds of oxygen are produced each day, we need to divide the annual total by the number of days in a year.

There are 365 days in a year, so:

[tex]\[ \text{Pounds of oxygen produced per day} = \frac{10.14 \times 10^{13} \, \text{lb/year}}{365 \, \text{days/year}} \][/tex]

[tex]\[ \text{Pounds of oxygen produced per day} = \frac{10.14 \times 10^{13}}{365} \, \text{lb/day} \][/tex]

To simplify, we divide the coefficient by 365:

[tex]\[ \text{Pounds of oxygen produced per day} = \frac{10.14}{365} \times 10^{13} \, \text{lb/day} \][/tex]

[tex]\[ \text{Pounds of oxygen produced per day} \approx 2.78 \times 10^{10} \, \text{lb/day} \][/tex]

Therefore, the approximate number of pounds of oxygen produced in the Amazon rainforest each day is [tex]\(2.8 \times 10^{10}\)[/tex] pounds.

Complete question:

A single tree produces about 2.6 × 10^2 lb of oxygen each year. The Amazon rainforest has about 3.9 × 10^11 trees. About how many pounds of oxygen are produced in the rainforest each day ?

The solution to system of equation  y = 4x - 3 and y = - x - 13 is (- 2, - 11).

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Given, A system of equations y = 4x - 3 and y = - x - 13.

If we subtract these two equations,

  y = 4x  - 3

- (y = -x - 13)

__________

0 = 5x + 10.

5x = - 10.

x = -2 and hence y = - 11.

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To calculate how long a bag of food will last for a cat eating 2/3 cup of food each day, divide the total cups in the bag by the daily consumption amount, resulting in 24 days.

A bag of 16 cups of food will last for 24 days if a cat eats 2/3 cup of food each day. To find the number of days the food will last, you need to divide the total number of cups in the bag by the amount consumed per day: 16 cups ÷ (2/3 cup/day) = 24 days.

Answer:

32 hours

Step-by-step explanation:

Let after x hours the charges of A and B are same,

Given,

For painter A,

Fixed charges = $ 376,

Additional charges per hour = $ 12,

So, the total charges for x hours = ( 376 + 12x ) dollars

For painter B,

Fixed charges = $ 280,

Additional charges pet hour = $ 15,

So, the total charges for x hours = ( 280 + 15x ) dollars

Thus,

376 + 12x = 280 + 15x

12x - 15x = 280 - 376

-3x = -96

x = 32

Hence, for 32 hours their cost will be same.

To solve the apple picking problem, we assigned variables and formulated an equation based on the relationships between the amounts each person picked. Solving the equation revealed that Andrew picks 252 pounds of apples.

Let Maria's apple pick be x pounds. According to the question, Andrew picks three times as many apples as Maria, which makes Andrew's pick 3x pounds. Jane, on the other hand, picks two times as many apples as Andrew, resulting in Jane's pick being 2(3x) or 6x pounds. Now, we know that the total weight of the apples picked by all three is 840 pounds.

We can express this as an equation:

x + 3x + 6x = 840

This simplifies to 10x = 840.

To find x, we divide both sides by 10:

x = 840 / 10

x = 84 pounds

Since Andrew picks 3x pounds, we multiply 84 by 3 to find Andrew's pick:

Andrew's pick = 3 × 84 = 252 pounds of apples.

Thus, the rates form a proportion as the rates of both are equal.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
The unit rate of sits-up = 90 / 2 = 45 sits-up per minute
Friend unit rate of sits-up = 135 / 5 = 45 sits-up per minute

From the above expressions, it is clear that rates form a proportion as rates of both are equal.

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Answer:

Equivalent Expression of given Expression is 84x - 16y - 10.6.

Step-by-step explanation:

Given Expression is :

[tex]2(14x-3y+28x+12.2-5y-17.5)[/tex]

We have to find: Equivalent Expression

To find Equivalent expression we simplify the given expression.

Consider,

[tex]2(14x-3y+28x+12.2-5y-17.5)[/tex]

Group like terms,

[tex]\implies2(14x+28x-3y-5y+12.2-17.5)[/tex]

Now solve like terms,

[tex]\implies2(42x-8y-5.3)[/tex]

Now, using Distributive Property

[tex]\implies2\times42x-2\times8y-2\times5.3[/tex]

[tex]\implies84x-16y-10.6[/tex]

Therefore, Equivalent Expression of given Expression is 84x - 16y - 10.6.

Answer:

a

Step-by-step explanation:

If 400 reduced by 2 times your age is 244, you will be 78 years old. This conclusion was reached by solving the equation 400 - 2x = 244, where x represents the unknown age.

To solve the problem given, you need to work with the equation provided: 400 decreased by 2 times your age is 244. In mathematical terms, this can be written as 400 - 2x = 244, where 'x' represents your age.

Next, you need to solve for 'x'. The first step is to isolate 'x' by moving terms around. Add 2x to both sides to get 400 = 244 + 2x and then subtract 244 from both sides to get 156 = 2x. You finish the process by dividing both sides by 2, which gives you x = 78. Therefore, if 400 reduced by 2 times your age is 244, you are 78 years old.

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To find out how many grams of strawberries are left, subtract the used grams from the total grams. Therefore, 430 grams of strawberries are left.

To determine how many grams of strawberries are left, we need to subtract the remaining grams from the total amount:

So, 430 grams of strawberries are left.