It is given that p varies inversely as q. If p = 12 and q = 45 find p, if q is 135.

Answers

Answer 1

Answer:

[tex]p =4[/tex]

Step-by-step explanation:

Given

Variation: Inversely

[tex]p = 12[/tex] when [tex]q = 45[/tex]

Required

Determine p when [tex]q = 135[/tex]

First, we need to determine the relationship between p and q

Since, it is an inverse variation.

The relationship is:

[tex]p\ \alpha\ \frac{1}{q}[/tex]

Convert to an equation

[tex]p= k *\frac{1}{q}[/tex]

[tex]p= \frac{k}{q}[/tex]

Where k = constant of variation

Make k the subject

[tex]k = p * q[/tex]

When [tex]p = 12[/tex] and [tex]q = 45[/tex]

[tex]k = 12 * 45[/tex]

[tex]k = 540[/tex]

To solve for p when q = 135

Substitute 135 for q and 540 for k in [tex]p= \frac{k}{q}[/tex]

[tex]p = \frac{540}{135}[/tex]

[tex]p =4[/tex]


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Dividing fractions is the same as multiplying the reciprocal.

As an easy way to remember this, you can use the Keep it, Switch it, Flip it method.

Keep: [tex]\frac{4}{9}[/tex]

Switch: the division sign to multiplication.

Flip Flip the numbers of [tex]\frac{2}{1}[/tex], or find it's reciprocal. [tex]\frac{1}{2}[/tex] turns into [tex]\frac{2}{1}[/tex].

Now, your problem looks like this:

[tex]\frac{4}{9}[/tex] * [tex]\frac{2}{1}[/tex] (which should be the answer to your first blank)

Multiply across.

4 x 2 = 8 and 9 x 1 = 9, so: [tex]\frac{8}{9}[/tex] should be the second blank.

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Step-by-step explanation:


Find the slope of the line that passes through (3, 8) and( 2,10)

Answers

Answer:

slope is -2

Step-by-step explanation:

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Adams High School is going to select a committee. The committee will have a faculty member, a male student, a female student, a parent, and a school board member. Here are the positions and the people interested in each. Position People interested Faculty member Mr. Jackson, Mrs. Washington Male student Tom, Omar, Keith, Justin Female student Donna, Charmaine, Rita, Keiko Parent Dr. Ward, Ms. Allen, Mrs. Flores, Mrs. Smith School board member Dr. Davis, Ms. Young, Mrs. King, Mr. Adams Based on this list, how many ways are there to fill the five committee positions?

Answers

Answer:

512 ways

Step-by-step explanation:

Given

Selection

Faculty Member = 1

Male Student = 1

Female Student = 1

Parent = 1

School Board Member = 1

Select from:

Faculty Member = 2

Male Student = 4

Female Student = 4

Parent = 4

School Board Member = 4

Required

Determine how many ways they can be selected

There are 2 faculty members of which 1 will be selected from.

Any of these two members may be selected.

So, Selection = 2

There are 4 male students of which 1 will be selected from.

Any of these four students may be selected.

So, Selection = 4

There are 4 female students of which 1 will be selected from.

Any of these four students may be selected.

So, Selection = 4

There are 4 parents of which 1 will be selected from.

Any of these four parents may be selected.

So, Selection = 4

There are 4 school board members of which 1 will be selected from.

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[tex]Selection = 2 * 4 * 4 * 4 * 4[/tex]

[tex]Selection = 512[/tex]

Hence, there are 512 ways

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Answers

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Answers

Answer:

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Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define

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Step 2: Solve for y

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Answer:

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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Upgrade to Premium

Step-by-step explanation:

Fractions consisting of integers are only undefined if the denominator is zero. All other combinations will give you a rational number.

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Given that:

Sides of a triangle are in the ratio 2:3:4

Let :

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Answers

Complete question :

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Answer:

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Time taken by Ella = 37.6 minutes

Time taken by Miranda = 9 1/10 minutes sooner than Ella

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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This article is about the math term. For other uses, see Slope (disambiguation).

For the grade (incline or gradient or pitch or slope) of any physical feature, see Grade (slope).

Slope: {\displaystyle m=\left({\frac {\Delta y}{\Delta x}}\right)=\tan(\theta )}{\displaystyle m=\left({\frac {\Delta y}{\Delta x}}\right)=\tan(\theta )}

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A line is decreasing if it goes down from left to right. The slope is negative, i.e. {\displaystyle m<0}m<0.

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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