A stationery shop orders a batch of pens from a factory.
The factory could make the batch of pens in
20 days using 12 machines.
Due to a fault, only 3 machines were used for the first 8 days.
All 12 machines were used from day 9 onwards.
Work out the total number of days taken to make the batch of pens.

Answer:

y = ± √ 7/2

Step-by-step explanation:

2*y^2-8-(6-2*y^2)=0

(2 • (y2)) - 8) - (6 - 2y2) = 0

(2y2 - 8) - (6 - 2y2) = 0

Pull out like factors :

4y2 - 14 = 2 • (2y2 - 7)

4.2 Factoring: 2y2 - 7

difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

2 • (2y2 - 7) = 0

5.1 Solve : 2 = 0

5.2 Solve : 2y2-7 = 0

Add 7 to both sides of the equation :

2y2 = 7

Divide both sides of the equation by 2:

y2 = 7/2 = 3.500

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

y = ± √ 7/2

Answer:

n + 3.9 ≤ 16

An inequality is a mathematical expression represented by less than, greater than, or equal to symbols to compare values or to measure and solve complex equations.

Answer:

units 6.0 I think good luck brother

Answer:

18.84 inches

Step-by-step explanation:

Use the formula.

2πr

Use 3.14 for π.

Use 3 for r.

2(3.14)(3)

Multiply.

2(3.14)(3)=18.84

Hope this helps!

Please mark as brainliest if correct!

Answer:

i say it would be "None of these"

Step-by-step explanation:

because say x=sisters age so, x=12     if lisa if 4 years youger, than x-4=8    (x-4)-x=(-2)      x-(x-4)=4      (x+4)-x=4    so therefore it would be none.

Answer:

none of these

Step-by-step explanation:

because we don't know her sisters age we'll use "x" and Lisa is 4 years younger so you deduct 4 from x and the equation will be '4-x'

Answer:

2 yards by 3 yards by 5 yards

Step-by-step explanation:

6 times 11 times 11 = 726

3(2*3*5) = 6*9*15 = 810

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The formula A = 1/2bh in terms of A and h is b = 2A/h and the measure of the base length is 34 feet.

In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

It is given that:

The formula A = 1/2bh

It is required to solve for b:

2A = bh

b = 2A/h

Plug A = 952 square feet

h = 56 feet

b = 2(952)/56

b = 34 feet

Thus, the formula A = 1/2bh in terms of A and h is b = 2A/h and the measure of the base length is 34 feet.

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The required statement describes the total amount a rewards customer pays for 10 ounces and 12 ounces of yogurt is earns 2 free ounces.

A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.

Given:

The horizontal axis shows ounces of yogurt purchased, numbered 2 to 22, and the vertical axis shows Total Spent (dollars) numbered 1 to 11.\

A line begins at 0, extends to 5 dollars spent at 10 to 12 ounces, and ends at 9 dollars spent at 20 ounces.

According to given question we have

In the analysis of the given options, the most likely answer to this question is A rewards customer earns 2 free ounces of yogurt because total amount paid for 10 ounces and 12 ounces is the same.

Also 9 dollars spent at 20 ounces.

Therefore, the required statement describes the total amount a rewards customer pays for 10 ounces and 12 ounces of yogurt is earns 2 free ounces.

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Answer:

A

Step-by-step explanation:

A rewards customer earns 2 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same.

Using proportions, it is found that:

1. a) 1/5 of the marbles are red.

b) 40% of the marbles are yellow.

c) 60% of the marbles are not yellow.

d) 11/20 of the marbles are green or yellow.

2) Event A, B and C are the most likely, each with equal probabilities.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For the first problem, we have that there are 3 + 4 + 5 + 8 = 20 marbles, hence:

a) 4/20 = 1/5 of the marbles are red.

b) 8/20 x 100% = 0.4 x 100% = 40% of the marbles are yellow.

c) 12/20 x 100% = 0.6 x 100% = 60% of the marbles are not yellow.

d) 3 are green and 8 are yellow, hence 11/20 of the marbles are green or yellow.

A die has 6 possible outcomes, numbered 1 to 6, hence the probabilities(number of desired outcomes divided by number of total outcomes) are given as follows:

Event A, B and C are the most likely, each with equal probabilities.

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According to the question, the given rational expression can be simplified which is as shown below:

Rational expression = [tex]\frac{12-4x}{x^{2} -9}=\frac{4(3-x)}{(x-3)(x+3)}[/tex]

For the simplification of the given expression, calculate the factors of the numerator as well as denominator terms and divide them from each other. In this change the sign of the expression before dividing with each other.

Rational expression = [tex]\frac{-4}{(x+3)}[/tex]

The rational expression are also known as polynomial expression. The highest degree of these expression is two. And these expression uses concept of factor rule.

Therefore, the final expression is [tex]\frac{-4}{(x+3)}[/tex]

What is polynomial expression?

Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.

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The relation (x, y) = {(-4, -1), (-2, 4), (0, -1), (2, 1), (4, 4)} is a function

The relation is given as

(x, y) = {(-4, -1), (-2, 4), (0, -1), (2, 1), (4, 4)}

As a general rule:

A relation that is considered to be a function is any relation whereby the elements of the domain has exactly one element of the range.

This means that an x value must have exactly one y value

Using the above as a guide, we can conclude that the relation (x, y) = {(-4, -1), (-2, 4), (0, -1), (2, 1), (4, 4)} is a function

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Possible question

Determine whether the relation is a function. Explain.

(x, y) = {(-4, -1), (-2, 4), (0, -1), (2, 1), (4, 4)}

The answer to this question is: og(x³y⁵) = 3log(x) + 5log(y)

In mathematics, the logarithm is that the function to exponentiation. which means the logarithm of a given number x is that the exponent to which another fixed number, the base b, must be raised, to supply that number x. within the simplest case, the logarithm counts the amount of occurrences of the identical consider repeated multiplication

To solve this question, we need only 2 identities, i.e.,

log(a*b) = log(a) + log(b)   ...(1)

log(aⁿ) = nlog(a)                ...(2)

Using 1, we can expand log x³ y⁵ as: log x³ y⁵ = log(x³) + log(y⁵)       ...(3)

Using 2, we can expand both the terms as: log(x³) = 3log(x)log(y⁵) = 5log(y)

Putting them in equation 3, we get:3log(x) +5log(y)

Therefore, log(x³y⁵) = 3log(x) + 5log(y)

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Based on the number of birdhouses that Felipe has to build in the holiday season, the meters of wood that Felipe needs would be 23 ⁵/₈ meters

First, find out the number of birdhouses Felipe needs to make:

= Normal number of birdhouses x Increase in holiday season

= 12 x 4¹/₂

= 54 birdhouses

The meters of wood he needs are:

= Number of birdhouses to be made / Number of bird houses he usually makes x Meters of wood needed for birdhouses Felipe usually makes

= 54 / 12 x 5¹/₄

= 23 ⁵/₈ meters

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The expression is simplified to  -5. 05u - 6

An algebraic expression can be defined as a mathematical expression made up variables, coefficients, terms, factors and constants.

These algebraic expressions are also made up of arithmetic operations, such as;

From the information given, we have the expression;

(3.65u − 11) − (−5 + 8.7u)

Now, expand the bracket, we get;

3. 65u - 11 + 5 - 8. 7u

collect like terms

3. 65u - 8. 7u - 11 + 5

Add/substract the values

-5. 05u - 6

Hence, the expression is -5. 05u - 6

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The inverse of the function y = log₂(2x) is f ⁻¹(x) = 2ˣ⁻¹.

Given the function is :y = log₂ 2x

we are asked to find the inverse of the function.

steps to find inverse function are:

Change f(x) to y to get y = ax + b for the provided function f(x) = ax + b.

To get x = ay + b from the equation y = ax + b, replace x with y and y with x.

Here, find y and solve for x = ay + b.

Then we get y = (x - b/a).

Finally, we can substitute y = f-1(x) with f-1(x) = (x - b)/a.

now interchange the positions of x and y in the function.

x = log₂ 2y

the next step is to isolate the dependent variables.

f ⁻¹(x) = 2ˣ ⁻ 1

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Answer:

50 degrees

Step-by-step explanation:

let's take the triangle to be right angled at b

so b=90                           1                

and c=40 (assumption)   2

so a+b+c=180(angle sum property)

from 1 and 2

a+90+40=180

a=180-130

therefore a=50

Answer:

50

Step-by-step explanation:

90= right side

40= acute side

180 - (90+ 40)= 50.

Answer:

#2 Alternate interior angles: 4 & 5 and 3 and 6

#4 :

m∠6 = 55°

m∠3 = 55°

m∠1 = 125°

Reasons: See below

Step-by-step explanation:

Angles 6 and 8 are supplementary angles since they are on the same straight line intersected by another straight line.

So m∠6 + m∠8 = 180
m∠6 + 125 = 180
m∠6 = 180-125= 55°

Angles 3 and 6 are alternate interior angles and equal to each other
m∠3 = m∠6 = 55°

Angles 1 and 3 are supplementary angles whose sum of measures should add up to 180°
m∠1 + m∠3 = 180
m∠1 + 55 = 180
m∠1 = 180-55 = 125°

Answer: = 7.27 × 108                          

(scientific notation)

with calculate significant figures         = 7.3 × 108

                                                           (scientific notation)

Step-by-step explanation: hope this helps

Answer:

212.

Step-by-step explanation:

Given: 3m^2 + 2p^2 - 15

When m = 3 and p = 10

Substituting the values

= 3(3)^2 + 2(10)^2 - 15

By further calculation

= 3(9) + 2(100) - 15

So we get

= 27 + 200 - 15

= 212

Therefore, the value of the expression is 212.

Answer:

Associative property of addition!

Step-by-step explanation:

You have to add the numbers a lot!!

Commutative property is the answer Bec of addition says that the change in order of numbers in addition will not change the result.

Therefore, for variable x and y the commutative property of addition is x+y=y+x.

When two quantities, say X and Y, are related in such a way that an increase or decrease in the value of X results in an increase in the value of Y, direct variation occurs, whereas indirect or inverse variation occurs when an increase in the value of X results in a decrease in the value of Y and vice versa.

Therefore, direct variation occurs when two quantities, say X and Y, are related in such a way that an increase or decrease in the value of X results in an increase in the value of Y whereas indirect or inverse variation occurs when two quantities, say X and Y, are related in such a way that an increase in the value of X results in a decrease in the value of Y and vice versa.

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Answer:4/ 1/5=20 or 4/.20=20

Step-by-step explanation: brainliest?

Go ahead and ask the question!! <3

Answer:

y=-2x-1

Step-by-step explanation:

y=mx+b

-7=-2(3)+b

-7=-6+b

-1=b

y=-2x-1

Step-by-Step:

___________

1. We are given the following:

[tex]4 < -9.9-(-10x+1)[/tex]

This being said, the first thing we need to do is switch sides, writing it as follows:

[tex]-9.9-(-10x+1) > 4[/tex]

___________

2. Next, we need to add 9.9 to both sides of the equation.

[tex]-9.9-(-10x+1)+9.9 > 4+9.9[/tex]

___________

3. Then, we simplify.

[tex]-(-10x+1) > 13.9[/tex]

____________

4. Now, we add 1 to both sides of the equation.

[tex]10x-1+1 > 13.9+1[/tex]

____________

5. We simplify again.

[tex]10x > 14.9[/tex]

____________

6. Next, we divide both sides by 10.

[tex]\frac{10x}{10} > \frac{14.9}{10}[/tex]

____________

7. Finally, simplify one more time.

[tex]x > 1.49[/tex]

Hence, out solution is [tex]x > 1.49[/tex]

Hope this helps!

Answer:

No solution

Step-by-step explanation:

-8l2x -5l =16  When I divide both sides by -8

l2x - 5l = -2

The absolute value cannot equal a negative number.