The sum of the number x and 13 is 62

Answer:  The required expression is [tex]x^2-5x+4.[/tex]

Step-by-step explanation:  We are given that

[tex]p(x)=x^2-1,\\\\q(x)=5(x-1).[/tex]

We are to find the expression that is equivalent to (p-q)(x).

We know that for any two functions f(x) and g(x), we have

[tex](f-g)(x)=f(x)-g(x).[/tex]

Therefore we get

[tex](p-q)(x)\\\\=p(x)-q(x)\\\\=(x^2-1)-(5(x-1))\\\\=x^2-1-5x+5\\\\=x^2-5x+4.[/tex]

Thus, the required expression is [tex]x^2-5x+4.[/tex]

subtract the cost of the shirt from the amount she gave the cashier

20.00 - 14.98 = 5.02

 using subtraction she would get $5.02 back in change

The object is a meter stick that models a line.

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature.

Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things.

In daily language, a line segment with two points designating its endpoints is also referred to as a "line."

From the given choices:

A meter stick models a line.

Therefore, the object is a meter stick.

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Answer:

[tex]N=\frac{33,000H}{62.4s}[/tex]

Step-by-step explanation:

We have been given an equation [tex]H=\frac{62.4Ns}{33,000}[/tex]. We are asked to solve our given equation for N.

Multiply both sides by 33,000:

[tex]H*33,000=\frac{62.4Ns}{33,000}*33,000[/tex]

[tex]33,000H=62.4Ns[/tex]

Switch sides:

[tex]62.4Ns=33,000H[/tex]

Divide both sides by [tex]62.4s[/tex]:

[tex]\frac{62.4Ns}{62.4s}=\frac{33,000H}{62.4s}[/tex]

[tex]N=\frac{33,000H}{62.4s}[/tex]

Therefore, the value of N is [tex]\frac{33,000H}{62.4s}[/tex].

Answer:

Neither is the answer.

Step-by-step explanation:

If a line y = m₁x + c₁ and y = m₂x + c₂ are perpendicular to each other then m₁ × m₂ = -1

If both the lines are parallel to each other then m₁ = m₂

Now two lines have been given as

y = 4x - 1 ----------(1)

12x = 3y + 7

3y = -12x + 7

y = -4x + [tex]\frac{7}{3}[/tex]------(2)

Now from equation (1) and equation (2),

m₁ = 4 and m₂ = -4

Since m₁ ≠ m₂

Therefore, these lines are not parallel

m₁ × m₂ = 4 × (-4) = -16

Therefore, both the lines are neither parallel nor perpendicular.

Answer:

Sample Response: Identify the unit rate as 0.75 miles per 1 minute. Since there are 60 minutes in an hour, multiply 0.75 time 60 to find how far the car travels in one hour.

Step-by-step explanation:

Answer: above the dash line!

The number of miles that Mercury travels in 4 minutes will be 7,200 miles.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.

As Mercury revolves around the sun, it travels at a rate of approximately 30 miles per second.

Convert the rate into miles per minute. Then we have

Rate = 30 x 60

Rate = 1,800 miles per minute

At this rate, the number of miles that Mercury travels in 4 minutes will be given as,

D = 1,800 x 4

D = 7,200 miles

The number of miles that Mercury travels in 4 minutes will be 7,200 miles.

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When two objects are moving in opposite directions, their relative speed is the sum of their speeds. In this scenario, the trucks will be 728 miles apart after 6.5 hours of travel.

The problem here is essentially an application of the concept of relative speed. The two trucks are traveling in opposite directions, so you add their speeds together to get the relative speed at which they are moving apart. That results in a combined speed of 48 mph (north) + 64 mph (south) = 112 mph. Now, to find out when they will be 728 miles apart, you divide the total distance by the combined speed:

728 miles ÷ 112 mph = 6.5 hours.

So, both trucks will be 728 miles apart after 6.5 hours.

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The sum of the interior angles of the polygon is 1440° and the number of sides of the polygon is 10 sides

The sum of the interior angles of a polygon is given by the formula

Sum of Interior angles of a polygon with n sides is

nθ = 180 ( n - 2 )

where n is the number of sides

θ = angle in degrees

Given data ,

Let the sum of the interior angles of the polygon be S

Now , the number of sides = n

The sum of the exterior angles of a polygon = 360°

And , each interior angle measure is four times the measure of each exterior angle

Substituting the values in the equation , we get

180 ( n - 2 ) = 4 ( 360 )

On simplifying the equation , we get

180n - 360 = 1440

Adding 360 on both sides of the equation , we get

180n = 1800

Divide by 180 on both sides of the equation , we get

n = 10 sides

Hence , the number of sides of the polygon is 10 and it is a decagon

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The correct answer is d. [tex](x + 1)(x - 1)(x^2 - 1)[/tex].

To find the least common multiple (LCM) of the two polynomials[tex]\(x^3 - x^2 + x - 1\) and \(x^2 - 1\)[/tex], we need to factor each polynomial and then find the LCM of the factors.

First, let's factor [tex]\(x^3 - x^2 + x - 1\)[/tex]:

[tex]\(x^3 - x^2 + x - 1 = x^2(x - 1) + (x - 1) = (x^2 + 1)(x - 1)\)[/tex].

Now, let's factor [tex]\(x^2 - 1\)[/tex]:

[tex]\(x^2 - 1 = (x + 1)(x - 1)\)[/tex].

The LCM of two polynomials is the product of the highest powers of all the factors that appear in either polynomial. Here, we have the factors [tex]\(x - 1\), \(x + 1\), and \(x^2 + 1\)[/tex] from the first polynomial, and the factors [tex]\(x - 1\) and \(x + 1\)[/tex] from the second polynomial.

Since [tex]\(x^2 + 1\)[/tex] is already the highest power of [tex]\(x^2 + 1\) , \(x - 1\) and \(x + 1\)[/tex] are the highest powers of [tex]\(x - 1\) and \(x + 1\)[/tex] respectively, the LCM is simply the product of all these factors:

[tex]\((x + 1)(x - 1)(x^2 + 1)\)[/tex].

However, we notice that [tex]\(x^2 - 1\)[/tex] is actually equal to [tex]\((x + 1)(x - 1)\)[/tex], and since [tex]\(x^2 + 1\)[/tex] is not a factor of [tex]\(x^2 - 1\)[/tex], we do not include it in the LCM. Therefore, the LCM is just [tex]\((x + 1)(x - 1)\)[/tex].

But we must also consider the polynomial [tex]\(x^3 - x^2 + x - 1\)[/tex], which can be rewritten as [tex]\((x^2 + 1)(x - 1)\)[/tex]. Since [tex]\(x^2 + 1\)[/tex] is not a factor of [tex]\(x^2 - 1\)[/tex], it must be included in the LCM to account for the additional factor in the first polynomial.

Thus, the LCM of [tex]\(x^3 - x^2 + x - 1\) and \(x^2 - 1\)[/tex] is [tex]\((x + 1)(x - 1)(x^2 - 1)\)[/tex], which corresponds to option d. This is because we take the highest powers of the common factors [tex]\((x + 1)\) and \((x - 1)\)[/tex], and include the additional factor from the first polynomial, which is [tex]\(x^2 - 1\)[/tex] since [tex]\(x^2 + 1\)[/tex] is not a factor of[tex](x^2 - 1\))[/tex].

Therefore, the final answer is [tex]\(\boxed{(x + 1)(x - 1)(x^2 - 1)}\)[/tex].

~~~~~~~~~~The answer is 366 m/min~~~~~~~~~~~~~~~~~~ First, convert the turtles speed to meters per minute. 27 km/h * 1000 m/km = 27000 m/h / 60 min/h = 450 m/min Now convert the girls speed to meters per minute. 14 dm/s / 10 dm/m * 60 s/min = 84 m/min Now subtract the girl's speed from the turtle's speed. 450 m/min = 84 m/min = 366 m/min

Answer:

yes, it will always be a polynomial but depending on how many terms it has, the answer may change

Step-by-step explanat