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2. Write the formula for the circumference of a circle.



a. Calculate the circumference of circle B if the diameter is 8 inches.


b. Calculate the radius of circle B if the circumference is 94.2 square centimeters.

Answer: [tex](-\infty, -1) \cup (1, \infty)[/tex]

Step-by-step explanation:

The function is always positive when it has a positive leading coefficient (since that means the graph will open up), and when the discriminant is negative (meaning the graph will never cross the x-axis).

Condition I. Leading coefficient is positive

[tex]m^2 -1 > 0 \implies m < -1 \text{ or } m > 1[/tex]

Condition II. Discriminant is negative

[tex](2(m-1))^2 -4(m^2 -1)(2) < 0\\\\4(m^2 -2m+1)-8(m^2 -1) < 0\\\\4m^2 -8m+4-8m^2 +8 < 0\\\\-4m^2 -8m+12 < 0\\\\m^2 +2m-3 > 0\\\\(m+3)(m-1) > 0\\\\m < -3 \text{ or } m > 1[/tex]

Taking the intersection of these intervals, we get [tex]m < -1[/tex] or [tex]m > 1[/tex].

At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree

see the attached figure to better understand the problem

Applying the Pythagorean Theorem

(3h+1)^2=h^2+35^2

9h^2+6h+1=h^2+1,225

solve for h

9h^2-h^2+6h+1-1,225=0

8h^2+6h-1,224=0

Solve the quadratic equation

Using a graphing tool

the solution is

If an M amount is borrowed for a time t at a discount rate of r per year, then the discount D is calculated as

Substitute the following values to get the bank's discount.

Therefore, the bank's discount is Php 288.75.

To calculate for proceeds, subtract the amount borrowed by the bank's discount.

The proceeds given to Ali is Php 21,711.25.

Priya uses 24 drops of red dye,

She also uses 16 drops of blue dye,

We are told to find the ratio of drops of red dye to the total drops dye.

Hence, the ratio of drops of red die to the total drops of die to the simplest rato is

3 : 5.

Solve x:

We're going to use the following formula:

If we replace our values:

Therefore, the length is pi.

We have that the volume of sphere is

and the volume of a cube is

so if s=r=3. The volume of the sphere is greater.

If they have the same volume, we get that

when s=r=2 we have that

so the volume of the sphere is greater

Step 1

The domain and range of a function is the set of all possible inputs and outputs of a function respectively. The domain is found along the x-axis, the range on the other hand is found along the y-axis.

Find the domain of the graph of the function of women using interval notation.

Step 2

Find the range of the graph of the function of women using interval notation.

Therefore, the domain and range in interval notation for the women respectively are;

Given:

After coming from school to home,

He played video games for 45 minutes.

Then he took 30 minutes to finish his homework.

When John finished his homework, it was 4:25 PM.

To find:

The time at which John got home from school

Explanation:

According to the problem,

Total time to play video games and do homework is,

So, the time he got home from school will be,

Final answer:

The time he got home from school is 3:10 P.M.

The equation of a straight line is

y = mx + c

4x + 20y = -180

make 20y the subject of the formula

20y = -180 - 4x

20y = -4x - 180

divide all through by 20

20y/20 = -4x/20 - 180/20

y = -1/5x - 9

The answer is y = -1/5x - 9 where your slope is -1/5 and intercept is -9

The volume of a triangle right prism is given by the formula

We have the expression:

We must evaluate the expression for:

• m = 7,

• n = 9.

Replacing the values of m and n in the expression above, we get:

Answer

44

The expression that represents the area of the rectangle is 6x²+29x+35.

Given that, a rectangle has sides measuring (2x + 5) units and (3x + 7) units.

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Part A:

Now, area = (2x+5)(3x+7)

= 2x(3x+7)+5(3x+7)

= 6x²+14x+15x+35

= 6x²+29x+35

So, the area of a rectangle is 6x²+29x+35

Part B:

A polynomial's degree is the highest or the greatest power of a variable in a polynomial equation.

Here, the degree of the expression 6x²+29x+35 is 2.

Part C:

Closure property of multiplication states that if any two real numbers a and b are multiplied, the product will be a real number as well.

Here, we obtained product of two binomials is trinomial

Therefore, the expression that represents the area of the rectangle is 6x²+29x+35.

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The slope in the equations represent the change in temperature by the change in lattitude. This means that for each unit change in the latitude the temperature will decrease by an amount given by the slope.

In probability , there are two events independent events and dependent events.

Independent Events :

Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur.

Example

. Choosing a marble from a jar AND landing on heads after tossing a coin.

Dependent Events :

If whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.

Example

Buying ten lottery tickets and winning the lottery.

This is the formula for combinations

In this case, n = 10 and k = 5

C = 10!/(10-5)!(5)! = 3628800/(120)(120) = 3628800/14400 = 252

Answer:

252 different line u

Let's find the derivative of y:

Evaluate the derivative for x = 2:

Now, we have the slope, let's use the point-slope formula to find the equation:

Answer:

y = 8x - 21

Answer

You must play 24 rounds to recover the cost of the club

Step-by-step explanation:

The amount golf charged for using their set clubs = $54

They charged $42 for using personal course

let x be the number of rounds played

let y be the total cost of the clubs

Since you will be buying a set of clubs worth $280

Then, the first equation is

a. y = 280 + 42x

b. y = 54x

c . Calculate the number of rounds that must be played to recover the cost of the clubs

To calculate this, we need to equate equations a and b together

280 + 42x = 54x

Collect the like terms

280 = 54x - 42x

280 = 12x

Isolate x by dividing through by 12

280/12 = 12x/12

x = 23.3333

Hence, you must play 24 rounds to recover the cost of the club

Therefore the right answer is option D = 1. The values of the variables will be obtained when the system of linear equations is solved; this is referred to as the solution of a linear equation.

Hence,

The correct Option is D = 1

Given

[tex]x^2+x-1\\[/tex] = 0

[tex]\frac{1-x}{2x^2} +\frac{ x^2}{2x-2}[/tex] = ?

From  [tex]x^2+x-1\\[/tex] = 0

[tex]x^2 = 1-x[/tex]

Therefore,

[tex]\frac{1-x}{2x^2} +\frac{ x^2}{2x-2}[/tex]  =  [tex]\frac{x^2}{2x^2} + \frac{x^2}{2(x-1)}[/tex]

[tex]\frac{1}{2} + \frac{x^2}{2(x-1)}[/tex]

[tex]\frac{1}{2} + \frac{1}{2}[/tex]

= 1

Therefore the right answer is option D = 1

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We have the next formula to find the length is

where

r=10

theta=45°

the arc length is 5/2 pi cm

We will have the following:

Now, we will solve for the following:

This value in degrees is:

So, the solution is located in the interval:

Answer

Option D is correct.

The dog looked at the cat with caution.

is the same as

The dog looked at the cat warily.

Explanation

The word warily means 'using caution' or 'cautiously'.

Hope this Helps!!!

We are given the expression B=3Mn/2 and told to express M in terms of B and n. This means that we should apply mathematical operations on both sides of the equation so we "isolate " M on one side of the equality sign. We begin with the given equation

First, we multiply both sides by 2, so we get

Next, we divide by 3 on both sides, so we get

Finally, we divide both sides by n, so we get

In this case, we have succesfully expressed M in terms of B and n

To be a matrix to be invertible the determinant of the matrix must be non zero thus for k ≠ 2 the matrix will be invertible.

matrix, a collection of numbers lined up in rows and columns to produce a rectangular array.

In computer graphics, where they have been used to describe picture transformations and other alterations.

The elements of the matrix, also known as the entry, are the numerals.

A matrix will be invertible only and only if the determinant is non-zero.

Given the matrix A.

The determinant of A is that |A| will be,

|A| = -3(8 - 8) - 0(-k + 2) - 3(-4k + 8) ≠ 0

0 + 0 + -3(-4k + 8) |A| ≠ 0

-4k + 8 ≠ 0

-4k ≠ -8

k ≠ 2

Hence "To be a matrix to be invertible the determinant of the matrix must be non zero thus for k ≠ 2 the matrix will be invertible".

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If you start at (9,2) and then move left 9 units, you'll end up at (0, 2)

The total number of people that were there altogether at the radio show is 175 people.

From the information, there were 5 people wearing boots at the rodeo for every 2 people who were not wearing boots.

It was also illustrated that there were 125 people wearing boots at the rodeo last night, those that aren't wearing boots will be illustrated by x.

2/5 = x/125

Collect like terms

5x = 125 × 2

5x = 250

Divide

x = 250/5

x = 50

Those not wearing boots = 50

Total number of people will be:

= Those wearing boots + Those not wearing

= 125 + 50

= 175

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Answer:

175

Step-by-step explanation:

Step-by-step explanation:

a probability is always

desired cases / totally possible cases

the first case I assume means that we need the probability to pick 2 odd-numbered balls in a row, if we do not put the first drawn ball back into the box.

starting condition :

15 basks in total.

1, 3, 5, 7, 9, 11, 13, 15 = 8 odd numbered balls

2, 4, 6, 8, 10, 12, 14 = 7 even numbered balls

the probability for the first ball to be odd numbered :

8/15

now we have

14 remaining balls in total.

7 remaining odd numbered balls.

the probability of the second ball being odd numbered is

7/14 = 1/2

so, the probability of both as one combined event is

8/15 × 1/2 = 4/15 = 0.266666666...

now back to the starting condition.

the probability to pick an even numbered ball is

7/15

we put the ball back in and pull a second time.

the probability to an even numbered ball is

7/15

so, the probability of both as one combined event is

7/15 × 7/15 = 49/225 = 0.217777777...

We have that the sample consist in n=13 students. The percentile formula is given by

where x denotes the percentaje. In the first case, p=38, then, we have

then, we get

that is, P_38 corresponds to 41 miles driven.

In the second case, by substituting x=60 in our formula, we get

which gives

that is, P_60 corresponds to 56 miles driven.

Then, the answers are:

This means that approximately 38% of the data lie below 41, when the data are ranked.

This means that approximately 60% of the data lie below 56, when the data are ranked.

The rate at which the length of a side is decreasing when the area of the triangle is 100 cm² is equal to -0.227 centimeters per minute.

Rate of change is a type of function that describes the average rate at which a quantity either decreases or increases with respect to another quantity.

Mathematically, the area of an equilateral triangle can be calculated by using this formula;

A = (√3/4)s²

Where:

Next, we would determine the side length of a square by making s the subject of formula as follows:

s = (√4A)/√3

s = (√4 × 100)/√3

Side length, s = 15.20

Note: The rate of change (dA/dt) is negative because it is decreasing.

By applying chain rule of differentiation, the rate of change (dA/dt) in area of this equilateral triangle with respect to time is given by:

dA/dt = (√3/4)(2s)ds/dt

dA/dt = (√3/4) × (2 × 15.20) × -3

dA/dt = -0.227 centimeters per minute.

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step 1

Find out the volume of the rectangular container

Substitute given values

step 2

Find out the weight of the container

Multiply the volume by the density of 0.99 pounds per cubic foot

0.99*470.25=465.5475 pounds

step 3

Multiply the weight by the factor of $4.37 per pound

so

4.37*465.5475=$2,034.44

therefore