Factor the expression below.
x2 - 81
O A. (X-9)(x - 9)
O B. (x + 27)(x-3)
O C. (x-27)(x - 3)
O D. (x + 9)(x-9)

The requried value of the proportional value of p when q = 2 is given as 245.

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,
p ∝ 1 / q²

So,
p₁/p₂ = q₂² / q₁²
Substitute value in the above equation,
20/p = 2²/7²
20 ×49 / 4 = p
p = 245

Thus, the requried value of p when q = 2 is given as 245.

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The given statement "number 3 to exponent 4" in exponential form is be written as 3⁴ , and the value of this expression is 81 .

The Exponential expression represented as "xⁿ" is read as the number x multiplied by itself "n" number of times .

we have to write "3 to exponent of 4" in exponential form ,

So , the exponential form is 3⁴ , it means that the number 3 is multiplied itself four times ;

the value of this expression is calculated as :

⇒ [tex]3^{4} = 3\times 3\times 3\times 3[/tex]

⇒ [tex]9\times 9[/tex]

⇒ 81 .

Therefore , the exponential form of "3 to the exponent of 4 " is 3⁴ .

The given question is incomplete , the complete question is

What is the exponential form of 3 to the exponent 4 ?

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Prime numbers are called prime as they come multiplicative first and other numbers are multiples of prime numbers.

As given in the question,

Prime numbers are called prime:

Therefore, prime numbers are called prime as they are multiplicative first numbers other numbers are multiples of prime number other than one.

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The line of the best fit for the data points plotted in the scatter plot is y = 0.67x + 4.05

From the question, we have the following parameters that can be used in our computation:

The graph

Using the line of the best fit, we have"

(x, y) = (0, 4) and (7, 9)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 4

Using the points, we have

9 = 7m + 4

This gives

m = 0.71

So, we have

y = 0.71x + 4

The closest to this is

y = 0.67x + 4.05

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If P(terriers) = 15%, the interpretation of the likelihood of randomly selecting a terrier from the shelter is; Unlikely

Probability of selection is one that defines the probability that a population unit is included in a sample generated by probability sampling.

For any population, the probability of any element within that population to be selected into a sample is calculated as the sample size divided by the population size.

In this case, we are told that the dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. There are three types of dogs.

We are given;

P(terriers) = 15%

This means the probability of randomly selection the other 2 dogs is way higher than that to select terriers.

Thus, we conclude that the probability of selecting terriers is unlikely due to its' low probability.

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Answer: B: Unlikely

Step-by-step explanation:

The degree of 2x² 5x² 7 is 4.

The degree of a polynomial is the highest power of the variable in a given polynomial. In this case, the highest power of the variable is 4, making the degree of the polynomial 4.

We can calculate the degree by using the formula Degree = Max (exponent of x).

In this case, the exponent of x is 2 and 5 respectively, making the degree of the polynomial 4.

Therefore, the degree of the polynomial 2x² 5x² 7 is 4.

To calculate this, we can use the following formula:

Degree = Max (exponent of x)

For the given polynomial 2x² 5x² 7, we can calculate the degree as follows:

Max (2, 5) = 5

Therefore, the degree of the polynomial 2x² 5x² 7 is 5.

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Therefore , the solution of the given problem of inequality comes out to be (x,y) = (1,4).

An inequality in mathematics is a relationship between two concepts or variables that isn't comparable. Therefore, inequality follows imbalance. When two integers are not equal, there is an inequality in mathematics. Egality and inequality are different. When two values aren't genuinely equal, the not equal basic is usually used to indicate this (). The values, whether tiny or huge, are contrasted using a variety of inequalities. By alternating the two characteristics until the constants integers become the only thing left, it is possible to solve many straightforward inequalities. However, a few things promote inequality: Negative values are halved or added to either side.

Here,

Given :

y≤ 3x+1

x-y>1

To find the value of x and y :

y≤ 3x+1

put the value of y

=> x - 3x -1 > 1

=> -2x -1>1

=>-2x > 2

=> -x>1

=>x >-1

x =1

Thus,

y≤ 3(1)+1

=> y ≤  4

Therefore , the solution of the given problem of inequality comes out to be (x,y) = (1,4).

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The table for the farmer buying dubbles is given below.

What is a graph?

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

Let the time be represented by the variable = x.

Let the number of dubbles be represented by the variable = y.

At x = 11, the number of dubbles y = 88.

Every hour, the farmer bought 6 more of them.

So, at x = 12 the number of dubbles y = 88 + 6

So, the table will be of the formula (x,y+6).

Therefore, the table for the graph is obtained.

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The Volume of the Bluetooth speaker is 0.36cm³

The capacity of the Bluetooth speaker = Volume of both the hemispherical parts + Volume of the cylindrical part

Given that,

The volume of a hemisphere of radius 'r' = 2/3πr³

The volume of a cylindrical = πr²h where r is

the radius of the base of the cylinder and h is the height.

The hemisphere and the cylinder will have the same radius r =0.25cm

Since the total length of the toy is 2 cm, the length of the conical part

will be 2−0.25−0.25=1.5cm

Hence, the Volume of the bluetooth speaker =2×( 2/3*22/7 *0.25³) + (22/7 *0.25²*1.5) = 0.36cm³

Correct question: A BlueTooth speaker is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of the entire capsule is 2 cm The capacity of the Bluetooth speaker is?

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We cannot construct a triangle with side lengths 2.5 cm, 3.0 cm and 6.5 cm as they don't follow the Triangle Inequality Theorem.

It is not possible to construct a triangle using the given side lengths of 2.5 cm, 3.0 cm, and 6.5 cm. This is because of the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, if we take 2.5 cm and 3.0 cm as two sides, the sum of their lengths is 5.5 cm. But the length of the third side (6.5 cm) is greater than 5.5 cm, so these three side lengths cannot form a triangle.

It is important to note that this theorem applies to any triangle, whether it is acute, right or obtuse-angled triangle. It is also important to note that this theorem is necessary for the formation of a triangle, and without it, it would not be possible to form a triangle.

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The equation does not represent the graph

The equation is given as

f(x) =3x² + 6x - 24

Calculate f(0) and f(1)

f(0) =3(0)² + 6(0) - 24 = -24

f(1) =3(1)² + 6(1) - 24 = -15

On the graph, we have

f(0) = -16

This means that the equation is not the graph

This is when x = 0

So, we hav

f(0) = -16

From the question, we have the following parameters that can be used in our computation:

The graph

The vertex of a graph is the minimum or the maximum of a graph

In this case, it is a minimum and the minimum is located at (-1, -18)

Hence , the vertex is (-1, -18)

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Answer:

Step-by-step explanation:

In Similar polygons, the corresponding angles are congruent, but the corresponding sides are proportional. So, similar polygons have the same shape, whereas their sizes are different. There would be certain uniform ratios in similar polygons.

Answer:

It's D, because the point intercepts at (0, 3), which is 3 up from the y position. What the difference is from this graph and the others is that this graph has a y-intercept of positive 3, and starts at an x point of -3. The x and y values should be inverted in order for this to be correct, so that is why option D is correct.

Hope this helps!

The simplified exponential notation of the given expression is 9[tex]a^{2}b[/tex].The following polynomials, then put the resolution in the right spot.

A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x. This statement is written as x/2 + 6 in a mathematical expression.

given

the expression as:

=[tex](\frac{18}{2})( \frac{a^{3} }{a})(\frac{b^{2} }{b})[/tex]

know  [tex]\frac{a^{m} }{a^{n} } = a^{m - n}[/tex]

So,   =[tex](\frac{18}{2})( \frac{a^{3} }{a})(\frac{b^{2} }{b})[/tex] =  9[tex]a^{2}b[/tex].

The simplified exponential notation of the given expression is 9[tex]a^{2}b[/tex].The following polynomials, then put the resolution in the right spot.

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Actually forget this answer

Answer:

8/5, -5/8

Step-by-step explanation:

[tex]5x+8y=-8 \\ \\ 8y=-5x-8 \\ \\ y=-\frac{5}{8}x-1[/tex]

So, the slope of the given line is -5/8.

Answer:

Summary: The polygons are similar but not necessarily drawn to scale, the value of x is 13 units.

Step-by-step explanation:

pls follow 4 more :) tysm

The numeric value of the expression A = LW, when L = 50 and W = 15, is given as follows:

A = 750.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The expression for this problem is defined as follows:

A = LW.

The input values of L and W are given as follows:

L = 50, W = 15.

Then the numeric value of the expression is found replacing the lone instance of L by 50 and the lone instance of W by 15, as follows:

A = 50 x 15

A = 750.

As there is only a single multiplication operation, precedence is not relevant for this problem.

The problem asks for the numeric value of the expression A = LW when L = 50 and W = 15.

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A two-step equation is an algebraic issue that can be resolved in two steps.

Two-step equations typically take the form ax b = c, where a, b, and c are real numbers.

For instance, 2 - 3x = 7 is an illustration of a two-step equation.

Use the following steps to solve 2-step equations:

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Answer:

Two step equations are algebraic equations and are the equations that can be solved in exactly two steps and gives the final value of the variable in two steps.

Step-by-step explanation:

Example 1: Solve the two step equation (x/6) - 7 = 11

Solution: To solve the given two step equation, we will follow the steps discussed above in the article.

Step 1: Add 7 to both sides of the given two step equation

(x/6) - 7 + 7 = 11 + 7

= (x/6) = 18

Step 2: Multiply both sides of the equation by 6.

6 × x/6 = 6 × 18

= x = 108

Answer: Hence the solution to the given two step equation (x/6) - 7 = 11 is x = 108.

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The normal approximation to the binomial distribution is possible in the following case: C. n = 40; p= 0.3

The binomial distribution is defined as the probability of x successes on n trials, with (p) probability of a success on each trial. It can be approximated to the normal distribution with the formula;

Mean; μ = np

Standard deviation; σ = √(np(1 - p)

The conditions are;

np ≥ 10

√(np(1 - p) ≥ 10

Looking at the given options, the only one that fits this conditions is Option C because;

np = 40 x 0.3 = 12.

n(1 - p) = 40 x 0.9 = 36

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d = 0.4 p, where the sales price of the bookshelf is $51, is the function that depicts the percentage off of a regular price.

When an item's price is lowered, it is said to be on sale. Multiplying the cost of an item by the % discount will give you the discount's value.

Discount = Original Price × Percentage Discount

$85 × 40%

$85 × 0.4 = $34.

Original cost less any discounts equals sales price.

$85 - $34 = $51.

The discount is the amount that separates an item's selling price from its marked (or list) price. Discount is therefore calculated as follows: Discount=List price – Selling price. Take advantage of deals like the buy one, get one free promotion or 15% off shirts, for instance. On an item with a price per hundred displayed, you have a percentage discount. An item that was previously priced at Rs. 1,000 is now being offered for Rs. 900 thanks to a 10% percentage discount.

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Answer: 10 made the honor roll

Step-by-step explanation:

It is not possible to construct a triangle whose sides are 3 cm 4 cm and 7 cm because the sum of two sides(3 cm and 4 cm) are equal to the third sides(7 cm). The equal sides can not form a triangle.

In the given question, we have to check that it is possible to construct a triangle whose sides are 3 cm 4 cm and 7 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.

To check this we firstly add the 3 and 4

3 + 4 = 7

7 = 7

Now we add 3 and 7

3 + 7 > 4

10 > 4

Now we add 4 and 7

7 + 4 > 3

11 > 3

It is not possible to construct a triangle whose sides are 3 cm 4 cm and 7 cm because the sum of two sides(3 cm and 4 cm) are equal to the third sides(7 cm). The equal sides can not form a triangle.

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The complete question is:

Can you form a triangle using lengths 3cm 4 cm and 7 cm?

The total number of baseball cards that Peter owns is 154.

Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another.

Two amounts are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent."

Given that,

Peter owns a total of one hundred and forty-four prized baseball cards.

He adds seven more American League players and three more national league players.

Total baseball cards he owns = 144+ 7+3 = 154

The ratio of American to national = 9:5 = 9/5 = 1.8

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Answer: 2x+2y+10

Step-by-step explanation:

Yo, whats good.

You basically want to simplify the same terms. For example, you can simplify 6x and -4x. You want to reorder everything so you can simplify it.

6x-4x+2y+3+7

= 2x+2y+10

lol have fun

3×3/4 is the expression which gives the 2.25 miles  mala walks her dog each day.

An expression is combination of variables, numbers and operators.

Given that mala walk her dog 3 times a day

Each walk is 3/4 mile.

We have to find the expression tell how many mile mala walks her dog each day.

The miles walk by Mala and her dog=3×3/4

=9/4

=2.25 miles.

Hence, 3×3/4 is the expression which gives the 2.25 miles  mala walks her dog each day.

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There is a linear relationship between exercise intensity and cardiac output. Therefore, when one rises, the other rises as well.

Cardiac output quantifies the volume of blood that your heart can pump in a minute. The phrase "exercise intensity" refers to how hard your body is working throughout a workout. These two are directly related to one another in some way.

The increase in cardiac output is linearly associated with exercise intensity up until the point of exhaustion. This happens as a direct result of the interaction between the heart rate and stroke volume reactions to the intensity of activity. Therefore, cardiac output will increase as exercise intensity does.

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Answer:

see below

Step-by-step explanation:

a. 1+3x = 3x + 1 --> infinite, it's the same thing

b. 4x + 1 = 3x + 2 --> x=1 one solution

c. 5x + 1 = 5x - 2 --> no solution. it's not possible

d. -3(x+1)=-3x+3 --> x=-1, one solution