Use synthetic division and the Remainder Theorem to find P(a)

P(x)=x^4+10x^3+8x^2+4x+10 ; a=2


2


–114


56


146

Answer:

Step-by-step explanation:

C) x1/4y1/2

Answer: 0.6

Step-by-step explanation:

The fractions have the form shown below:

[tex]\frac{a}{b}[/tex]

Where: a is the numerator and b is the denominator.

To convert a fraction to a decimal number, you must divide the numerator by the denominator.

You know that the fraction is three-fifths, which is written as following:

[tex]\frac{3}{5}[/tex]

Therefore, when you divide the numerator 3 by the denominator 5, you obtain the following decimal number which is equivalent to that fraction:

 [tex]\frac{3}{5}=0.6[/tex]

Answer:

0.6

Step-by-step explanation:

Answer: 25

Step-by-step explanation:

Pythagorean theorem

c=√a²±b²

So it was 7=A

And it was 24=b

solving that it gives us 25

This isn’t that much of help sorry but this is the basic info on how to solve it you can learn more by searching videos about the Pythagorean thermom.

Hope this helps-A

The maximum width of the slot is 25cm (Option A).

To find the maximum width of the mail slot, we need to calculate the length of the diagonal (the dotted line) in the rectangle. The diagonal of a rectangle can be found using the Pythagorean theorem.

Given:

- The length of the rectangle (one side) = 24 cm

- The height of the rectangle (other side) = 7 cm

The formula for the diagonal [tex]\( d \)[/tex] is:

[tex]\[ d = \sqrt{(length)^2 + (height)^2} \][/tex]

Substituting the given values:

[tex]\[ d = \sqrt{24^2 + 7^2} \][/tex]

[tex]\[ d = \sqrt{576 + 49} \][/tex]

[tex]\[ d = \sqrt{625} \][/tex]

[tex]\[ d = 25 \, \text{cm} \][/tex]

So, the maximum width of the mail slot is 25cm.

Full Question:

Joel is mailing a large envelope to his cousin. The envelope has pictures inside, so he doesn't want to bend it.

The mail slot has the dimensions shown. The dotted line shows the widest part of the slot.

What is the maximum width of the mail slot?

A) 25

B) 31

C) 22

D) 20

The correct answer for this completion exercise shown above is the second option (Option B), which is: B. Parent

 Therefore, you have:"In each family of function, the parent function is the most basic function in the family"

 By definition, the most basic fucntion in each family of functions is called “parent fucntion”. A family of function is a set of function that when you graph them, you can notice that they have common charateristics.

Answer:

there is no solution

Step-by-step explanation:

Rex uses 2.25 gallons of paint on the shed, which is [tex]\( \frac{3}{4} \)[/tex] of the 3 gallons of paint he uses on the garage.

To find out how much paint Rex uses on the shed, we need to calculate [tex]\( \frac{3}{4} \)[/tex] of the amount of paint he uses on the garage.

Rex uses 3 gallons of paint on the garage.

Therefore, the amount of paint he uses on the shed is:

Paint used on the shed = [tex]\frac{3}{4} \times 3[/tex]

Calculating this:

Paint used on the shed = [tex]\frac{3 \times 3}{4}[/tex]

= [tex]\frac{9}{4}[/tex]

= 2.25

So, Rex uses 2.25 gallons of paint on the shed.

Final answer:

Michelle's stamp collection consists of 60% U.S. stamps, determined by solving equations based on the given information that U.S. and Mexican stamps make up 80% of her collection and there are three times as many U.S. stamps as Mexican stamps.

Explanation:

The student asked what percent of Michelle's stamp collection is made up of U.S. stamps if 80% are U.S. and Mexican stamps and there are 3 times as many U.S. stamps as Mexican stamps. To solve this, let's call the percentage of U.S. stamps 'U' and the percentage of Mexican stamps 'M'. According to the given information, U + M = 80%, and U = 3M.

We substitute the second expression into the first to get 3M + M = 80%, which simplifies to 4M = 80%. Dividing both sides by 4 gives M = 20%. As the number of U.S. stamps is three times the number of Mexican stamps, we calculate U as 3 × 20% = 60%. So, the percentage of U.S. stamps in Michelle's collection is 60%.

the answer to your question

is the letter  C

Let's explore the equation to see why the graph of the formula that is given sounds like:

((x−5)²/(4)²) + (y²/(7)²) = 1

This equation represents the standard form of an ellipse:

((x−h)²/a²) + ((y-k)²/(b)²) = 1

Where:

*The ellipse's center is (h,k).

*The semi-major axis's length, or horizontal radius, is denoted by a.

*The semi-minor axis's length, or vertical radius, is b.

Comparing the given equation to the standard form, we see that:

*h=5 (center is at x=5)

*a=4 (semi-major axis length)

*b=7 (semi-minor axis length)

Since both a and b are positive and the denominators of both terms are squared, the graph represents an ellipse. Therefore, the correct answer is F. An ellipse.

The given equation is in the form of an ellipse:

((x−5)²/(4)²) + (y²/(7)²) = 1

It matches the standard form of an ellipse equation:

((x−h)²/a²) + ((y-k)²/(b)²) = 1

where (h,k) is the center of the ellipse, and a and b are the lengths of the semi-major and semi-minor axes, respectively.

In this equation, h=5, a=4, and b=7, indicating the ellipse is centered at (5,0) with a horizontal radius of 4 and a vertical radius of 7.

Therefore, the correct answer is F. An ellipse.

Complete Question:

What shape is the graph of the equation below?

A. A line

B. A circle

C. A parabola opening to the right

D. A hyperbola opening to the right and left

E. A hyperbola opening up and down

F. An ellipse

Final answer:

The limit of a function as x approaches negative infinity is the value that the function f(x) approaches as x becomes very large in the negative direction. For example, the limit of 1/x is 0 as x approaches negative infinity, while the limit of 1/x² approaches positive infinity. Functions that oscillate, like sin(\u03C0/x), do not have a limit at infinity.

Explanation:

When discussing the limit of a function f(x) as x approaches negative infinity, we are essentially asking what value f(x) gets closer to as x becomes very large and negative. For instance, consider the function 1/x. As x approaches negative infinity, 1/x gets closer to 0, and we say that the limit of 1/x as x approaches negative infinity is 0. Similarly, for a function like 1/x² which "blows up" or increases rapidly as x approaches 0 from either side, we notice that as x approaches negative infinity, the function approaches positive infinity since the squared term always results in a positive number.

However, not all functions have limits at infinity. For functions that oscillate, such as sin(\u03C0/x), as x approaches 0, it oscillates indefinitely between -1 and +1 and does not approach a specific value.

The formal definition of a limit at infinity states: If there is a number L such that f(x) gets arbitrarily close to L when x is sufficiently large (positively or negatively), we write lim f(x) = L as x → -∞.

To calculate the perimeter of a rectangle in scientific notation, divide the given area by the width to find the length, then use the perimeter formula (P = 2×length + 2×width), accounting for the power of 10 in your calculations to maintain proper notation.

The perimeter of a rectangle can be found using the formula P = 2×length + 2×width. Given the area of the rectangle (2.76 x 10^12 square units) and the width (4.6 x 10^5 units), we can find the length by dividing the area by the width. The length would therefore be the area divided by the width which is (2.76 x 10^12) / (4.6 x 10^5) = 6 x 10^6 units. Now that we have the length and width, we can calculate the perimeter by substituting into the formula: P = 2×(6 x 10^6) + 2×(4.6 x 10^5) = 1.2 x 10^7 + 9.2 x 10^5. Converting the width to the same power of 10, we get P = 1.2 x 10^7 + 0.092 x 10^7 = 1.292 x 10^7 units. This expresses the perimeter in scientific notation.

Answer:

Length = 4 inches, width = 5 inches

Step-by-step explanation: