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2 years ago

A basket of the fruit contains 12 apples, 8 bananas, and 6 oranges. What is the ratio of bananas to apples? (Please simplify)

Mathematics

1 answer:

mrs_skeptik [129]2 years ago

6 0

Answer:

2 : 3

Step-by-step explanation:

bananas to apples = 8 : 12

simplify by dividing both values by highest common factor of 4:

8 ÷ 4 : 12 ÷ 4 = 2 : 3

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Commercial agents earn 5% of the cost of each product they sell. If an agent earns

kicyunya [14]

Based on the information the cost of the product is $40,000.

Given:

Percentage earn=5% or 0.05

Amount earned=$2,000

Let x represent the cost of the product

Hence:

Formulate

.05x = $2000

Divide both sides by .05

x=$2,000/.05

x=$40,000

Inconclusion the cost of the product is $40,000.

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Classify each conic section and write its equations in standard form. Show work.

svp [43]

Answer:

The conic is ellipse of equation (x - 1)²/22 + (y + 4)²/44 = 1

Step-by-step explanation:

* Lets revise how to identify the type of the conic

- Rewrite the equation in the general form,

Ax² + Bxy + Cy² + Dx + Ey + F = 0

- Identify the values of A and C from the general form.

- If A and C are nonzero, have the same sign, and are not equal

to each other, then the graph is an ellipse.

- If A and C are equal and nonzero and have the same sign, then

the graph is a circle

- If A and C are nonzero and have opposite signs, and are not equal

then the graph is a hyperbola.

- If either A or C is zero, then the graph is a parabola

* Now lets solve the problem

The equation is 4x² + 2y² - 8x + 16y - 52 = 0

∴ A = 4 and C = 2 ⇒ same sign and different values

∴ The equation is ellipse

* The standard form of the ellipse is

(x - h)²/a² + (y - k)²/b² = 1

- Lets try to make this form from the general form

- Group terms that contain the same variable, and move the

constant to the opposite side of the equation

∴ (4x² - 8x) + (2y² + 16y) = 52

- Factorize the coefficients of the squared terms

∴ 4(x² - 2x) + 2(y² + 8y) = 52

- Complete the square for x and y

# To make completing square

- Divide the coefficient of x (or y) by 2 and then square the answer

- Add and subtract this square number and form the bracket of

the completing the square

# 2 ÷ 2 = 1 ⇒ (1)² = 1 ⇒ add and subtract 1

∴ 4[(x² - 2x + 1) - 1] = 4(x² - 2x + 1) - 4

- Rewrite as perfect squares ⇒ 4(x -1)² - 4

# 8 ÷ 2 = 4 ⇒ (4)² = 16 ⇒ add and subtract 16

∴ 2[(y² + 8y + 16) - 16] = 2(y² + 8y + 16)² - 32

- Rewrite as perfect squares ⇒ 2(y + 4)² - 32

∴ 4(x - 1)² - 4 + 2(y + 4)² - 32 = 52

∴ 4(x - 1)² - 4 + 2(y + 4)² = 32 + 4 + 52

∴ 4(x - 1)² + 2(y + 4)² = 88 ⇒ divide all terms by 88

∴ (x - 1)²/22 + (y + 4)²/44 = 1

8 0

3 years ago

2m3 of soil containing 28% silt was mixed into 1 m3 of soil containing 13% of silt. What is the silt content mixture?

Leto [7]

Alright
so
28% of 2 m³=0.28 times 2=0.56 m³ of silt in the first mixture

13% of the 1 m³=0.13 times 1=0.13 m³ of silt in 2nd

total is 0.56 m³+0.13 m³=0.69 m³ of silt
and the total is 2m³+1m³=3m³

so
0.69/3=0.23=23%

answer is D

6 0

3 years ago

10)

Kipish [7]

Answer:

-600

Step-by-step explanation:

The rate of change of a function f(x) in a certain interval $(x_1,x_2)$ is the ratio between the change of the function and the change in the value of x:

$r=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

The rate of change of a function tells how much the value of the function is changing per change in unit of x: therefore, for a linear function it corresponds to the slope of the line.

In this problem, the function f(x) is equal to the value of the business machine in dollars, while the variable x represents the number of years.

Here we are told that the machine was purchased for

$q=\$4500$

while its value decreases by $600 each year, so

$m=-600\$$

This means that the linear function that represents the value of the machine after x years is:

$y=4500-600x$

Therefore, the rate of change of the function is -600.

3 0

3 years ago