To divide the given polynomial by x + 2, use polynomial long division, which involves dividing the leading term, multiplying the divisor, subtracting, and repeating the process until all dividend terms are addressed.
To divide the polynomial -2x^3 - 5x^2 + 4x + 2 by x + 2, we can use the process of polynomial long division. This method is similar to long division with numbers, where we divide, multiply, subtract, bring down the next term, and repeat the process until we have gone through all terms of the dividend.
The process would look like this:
Divide the first term of the dividend (in this case, -2x^3) by the first term of the divisor (x), yielding -2x^2.Multiply the entire divisor (x + 2) by this quotient (-2x^2) and subtract the result from the dividend.Bring down the next term of the dividend and repeat the process until there are no terms left to bring down.The final result would be the quotient of the division, which may or may not have a remainder.
when an aircraft takes off, it accelerates until it reaches its takeoff speed V. in doing so it uses up a distance R of the runway, where R is proportional to the square of the of the takeoff speed. if V is measured in miles per hour and R is measured in feet, then 0.1639 is the constant of proportionality. if an aircraft has a takeoff speed of about 215 miles per hour, how much runway does it need?
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Janice makes 4 pizzas for dinner. There are 5 people to eat dinner. How much will each person get to eat?
find the surface area of the toolbox
What is the GCF of 14x^2 and 4xy? A. 10x B. 28x^2y C. 2x2 D. 2x
Grace has 2 cups of strawberries and plans to divide this amount into equal parts to make 3 strawberry pies. What fraction of a cup of strawberries will be used for each pie?
Number of cups of Strawberries are there for 3 pies =2
Now we apply unitary method here to find how many strawberries are need for 1 pie.
Number of cups of Strawberries required for 1 pie = 2/3
Answer: So Grace would require 2/3 cups of Strawberries for making one pie.
Andy and alex both decided to order prints of their photos. Andy ordered 40 small 4x6 inch prints and 10 large 8x10 inch prints. He paid a total of $32.50 for his photos. Alex paid 20$ for 20 small 4x6 inch prints and 8 large 8x10 inch prints. How much do the small and large sized prints cost
Final answer:
To find the cost of small and large prints, we create two equations based on Andy's and Alex's orders and solve for the two variables. The small 4x6 inch prints cost $0.50 each, and the large 8x10 inch prints cost $1.25 each.
Explanation:
To solve how much small and large sized prints cost, we can set up a system of linear equations based on the information given:
Andy's order: 40 small prints and 10 large prints for $32.50Alex's order: 20 small prints and 8 large prints for $20.00Let s represent the cost of a small 4x6 inch print, and let l represent the cost of a large 8x10 inch print. We can then form the equations:
40s + 10l = 32.5020s + 8l = 20.00By dividing the first equation by 2, we get:
20s + 5l = 16.25Subtracting the second equation from this result gives:
(20s + 5l) - (20s + 8l) = (16.25 - 20)-3l = -3.75l = 1.25With the cost of a large print found, we can plug this back into the second equation to find the cost of a small print:
20s + 8(1.25) = 2020s + 10 = 2020s = 10s = 0.50Therefore, the cost of a small 4x6 inch print is $0.50 and a large 8x10 inch print is $1.25.
After 5 months, the number of subscribers to a newspaper was 5,730. After 7 months, the number of subscribers to the newspaper was 6,022. Which equation models the number of newspaper subscribers y after x months? y = –146x – 5,000 y = 146x + 5,000 y = 146x – 5,000 y = –146x + 5,000
The low temperature in Leroy’s town one day was -4. The difference between the high temperature and the low temperature that day was 6. The equation h-(-4)=6 can be used to find h, the high temperature in the town that day in degrees Fahrenheit. What was the high temperature in the town that day, in degrees Fahrenheit?
Michael will be travelling out of town for business. During his travel, he is scheduled to have 4 dinners, 5 lunches, and 3 breakfasts. His employer will pay him for these meals at the following rate: $ 22.65 for dinner, $ 10.95 for lunch, and $ 6.53 for breakfast.
Lisa and Frank shared 1/3 pound of cherries equally what fractional part of a pound did each person receive?
Answer: 0.3333
Part A.
Molly wrote the following quotation to solve the problem: 2 . 1/3 = n.
Do you agree with Molly's equation? Support your answer with information from the problem.
Answer with explanation:
1)
If we divide 1/3 pounds equally among two people then each of them will get a share of:
[tex]\dfrac{1}{2}\times \dfrac{1}{3}\\\\=\dfrac{1}{6}\\\\=0.1666\ pounds[/tex]
Hence,the given answer that each will get 0.3333 pounds is incorrect.
2)
Molly wrote the following quotation to solve the problem: 2 . 1/3 = n.
This is an incorrect equation since this equation does not represent the half share of 1/3 pounds.
It represents the double amount of 1/3 pounds.
How many outcomes are there in the sample space for rolling 1 die?
Answer:
6
Step-by-step explanation:
A rectangular garden is 6 feet long and 4 feet wide. A second rectangular garden has dimensions that are double the dimensions of the first garden. What is the percent of change in perimeter from the first garden to the second garden? The perimeter increases % from the first garden to the second garden.
Answer:
100%
Step-by-step explanation:
When the dimensions double, the perimeter doubles.
The percent change can be found from ...
percent change = ((new value)/(old value) -1) × 100%
Filling in your values, you have ...
percent change = ((2×(old perimeter))/(old perimeter) -1) × 100%
= (2 - 1) × 100%
= 100%
The perimeter increases by 100% from the first garden to the second.
Consider the quadratic equation x2=4x-5. How many solutions does the equation have
10 points!!!
Todd Gunderson went into a partnership with two of his friends. Manny and Jose, to share a route delivering newspapers. Manny owns 1/4 of the partnership, while Jose has a 1/5 interest. If the partnership's monthly revenue amounts to $765, how much of that is Todd's? Round to the nearest cent.
The gandhara region is the home of many portrayals of ____.
Determine the rigid transformations that will map ΔABC to ΔXYZ.
a. Translate vertex B to vertex Z; reflect ΔABC across side AB.
b. Translate vertex X to vertex C; rotate ΔXYZ to align the sides and angles.
c. Reflect ΔABC across side AB; translate vertex C to vertex X.
d. Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.
Solution: The correct option is d, i.e., Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.
Explanation:
we know that the sum of angles of a triangle is always [tex]180^{\circ}[/tex]. In ΔXYZ,
[tex]\angle X +\angle Y +\angle Z=180^{\circ}[/tex]
[tex]35^{\circ} +\angle Y +47^{\circ}=180^{\circ}[/tex]
[tex]\angle Y +82^{\circ}=180^{\circ}[/tex]
[tex]\angle Y =98^{\circ}[/tex]
In both triangles it is noticed that the sides AC and XZ are equal. In given triangles [tex]\angle A =\angle X=35^{\circ}[/tex] and [tex]\angle B =\angle Y=98^{\circ}[/tex].
By AAS rule of congruence ΔABC and ΔXYZ are congruent triangles, therefore we can transform ΔABC to ΔXYZ. For the transformation of ΔABC to ΔXYZ translate the vertex having same angle and rotate the triangle to align the sides and angles.
Since vertex X and vertex A have same angle, therefore we translate vertex X to vertex A and rotate ΔXYZ to align the sides and angles.
Hence the correct option is d.
Answer: d
Step-by-step explanation:
Use the following figure to answer the question. 1 and 4 are _____ angles. corresponding vertical supplementary adjacent
Answer:
vertical angles
Step-by-step explanation:
We need to identify ∠1 and ∠4 are which type of pair of angles .
Since we are given the options :
1, correspoding angles: Corresponding Angles
When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles.
2. vertical angles : The angles opposite each other when two lines cross. They are always equal.Vertical" refers to the vertex (where they cross), NOT up/down
3. supplementary angles : Two Angles are Supplementary when they add up to 180 degrees
4. adjacent angles:Two angles are Adjacent when they have a common side and a common vertex (corner point) and don't overlap.
Thus according to definitions ∠1 and ∠4 are vertical angles
The length of a rectangle is 3 times the width. The difference between the length and the width is 8 feet. Determine the rectangle's length
The length of the rectangle will be 12 units.
What is a rectangle?
The rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of ractangle = 2( length + width).
Let say,
Length = l and width = w
Given,
length of a rectangle is 3 times the width
l = 3w
The difference between the length and the width is 8 feet
l - w = 8
By equation 1 and 2
3w - w = 8
2w = 8
w = 4
Substitute into equation 1
l = 3(4)
l = 12 units.
So the length of the rectangle will be 12 units.
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what is 0.080 as a fraction
Answer:
To write 0.080 as a fraction you have to write 0.080 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
0.080 = 0.080/1 = 0.8/10 = 8/100
So your final answer is: 0.080 as a fraction equals 8/100
Step-by-step explanation:
The decimal number 0.080 as a fraction is A = 2/25
Given data:
The decimal number is represented as 0.080
Step 1: Count the number of decimal places in the given decimal. So, there are three decimal places.
Step 2: Write the decimal as the numerator of the fraction. The decimal 0.080 becomes the numerator 80.
Step 3: Determine the denominator of the fraction. Since there are three decimal places, the denominator should be 10 raised to the power of the number of decimal places. So, the denominator is 10³ = 1000.
Putting it all together, 0.080 as a fraction is 80/1000.
Dividing both the numerator and denominator by 40:
80 ÷ 40 / 1000 ÷ 40 = 2/25
Hence, 0.080 as a simplified fraction is 2/25.
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if the parent function is square root of x, describe the translation of this function square root x+7
The function [tex] y=\sqrt{x} [/tex] sits with its starting point at the origin. The function [tex] y=\sqrt{(x-h)}+k [/tex] is translated h units to the left or right and k units up or down. Since our radicand, the value under the square root sign, is x+7, putting that into our standard form it would be x-(-7) because minus a negative is a positive. So we move the parent graph to the left (-7 moves to the left) 7 units. There is no number k so our function is not moving up or down. Only to the left 7.
Christian got a haircut yesterday afternoon if the hair stylist charged $18 and christian gave 20% tip how much dod he pay for the haircut
Answer:
He paid $ 21.6 for the haircut.
Step-by-step explanation:
Given,
The amount charged by hair stylist = $ 18,
The percentage of tip = 20 %,
So, the amount of the tip = 20 % of 18
= 0.2 × 18
= $ 3.6,
Hence, the total amount paid by him for haircut = The amount charged by hair stylist + Tip
= $ 18 + $ 3.6
= $ 21.6
Zakai cuts a piece of birthday cake as shown below.
What is the volume of the piece of cake?
The given family of functions is the general solution of the differential equation on the indicated interval. find a member of the family that is a solution of the initial-value problem. y = c1e4x + c2e−x, (−∞, ∞); y'' − 3y' − 4y = 0, y(0) = 1, y'(0) = 2
Solution:
The given differential equation is,
[tex]y=C_{1}e^{4 x}+C_{2}e^{-x}[/tex]------(A)
Differentiating once,with respect to x,
[tex]y'=4C_{1}e^{4 x}-C_{2}e^{-x}[/tex]-------(1)
Differentiating again with respect to x,
[tex]y"=16C_{1}e^{4 x}+C_{2}e^{-x}[/tex]-------(2)
Equation (1) + Equation (2)
y' +y" [tex]=20 C_{1}e^{4 x}[/tex]
[tex]C_{1}=\frac{y'+y"}{20e^{4 x}}[/tex]
4 ×Equation (1) - Equation (2)
4 y'- y"[tex]=-5 C_{2}e^{-x}[/tex]
[tex]C_{2}=\frac{4y'-y"}{-5e^{-x}}[/tex]
Substituting the value of [tex]C_{1},C_{2}[/tex] in A,we get
[tex]y=\frac{y'+y"}{20}+\frac{4 y'-y"}{-5}\\\\ 20 y=y'+y"-16 y'+4 y"\\\\ 20 y=-15 y'+5y"\\\\ 4 y+3 y'-y"=0[/tex]
As, y(0)=1 , and y'(0)=2, gives
[tex]C_{1}+C_{2}=1\\\\ 4C_{1}-C_{2}=2[/tex]
gives , [tex]5C_{1}=3\\\\ C_{1}=\frac{3}{5}\\\\ 5 C_{2}=2\\\\ C_{2}=\frac{2}{5}[/tex]
So, member of the family that is a solution of the initial-value problem, [tex]y=C_{1}e^{4 x}+C_{2}e^{-x}[/tex] is
[tex]5 y=3 e^{4 x}+2 e^{-x}[/tex]
By what percent will a fraction decrease if its numerator is decreased by 50% and its denominator is decreased by 25%?
Answer:
33.33% will work
Step-by-step explanation:
RSM BOI
Which undefined term is needed to define an angle????
POINT WASNT AN OPTION ON MY TEST. THE ANSWER WAS PLANE. THE ANSWER CAN BE POINT, LINE, OR PLANE.
Answer:
Line
Step-by-step explanation:
A line is a undefined term used to define a angle. An angle is the corner that is created where two non-parallel lines meet/ intersect
ASAP Select the statement that correctly describes the expression below.
(2x+5)^2
a) the sum of the square of 2 times x and 5
b)the square of the sum of 2 times x and 5
c)the square of 2 times the addition of x and 5
d)the sum of 2 times x and the square of 5
Answer:
Option B
Step-by-step explanation:
The given expression is ( 2x + 5)²
We have to form a statement to describe the expression given.
(2x + 5)² square of sum of 2 times x and 5
Option B is the correct answer.
trapezoid: b1=3 m;b2 =4m A= 7 m2 What is the missing
dimension
Simplify 10/16 to lowest terms and find an equivalent fraction that has a denominator of 32?
Answer:
The lowest fraction for [tex]\frac{10}{16}[/tex] is [tex]\frac{5}{8}[/tex] and a equivalent fraction with denominator of 32 is [tex]\frac{20}{32}[/tex].
Step-by-step explanation:
First, to have the fraction to the lowest terms we will have to divide the numerator and denominator by 2, this is:
[tex]\frac{10/2}{16/2}=\frac{5}{8}[/tex]
As can be seen the expression couldn't be simplified more because there is no a common number that could divide the numerator and denominator.
Second, to have an equivalent fraction with 32 in the denominator we will have to multiply the denominator by 2 and of course the numerator, this is:
[tex]\frac{10*2}{16*2}=\frac{20}{32}[/tex]
The lowest fraction for [tex]\frac{10}{16}[/tex] is [tex]\frac{5}{8}[/tex] and a equivalent fraction with denominator of 32 is [tex]\frac{20}{32}[/tex].
To simplify 10/16 to lowest term, it becomes 5/8. An equivalent fraction of 5/8 with 32 as the denominator is 20/32.
Explanation:To simplify 10/16 to its lowest term, we have to find the greatest common divisor of 10 and 16, which is 2. Hence, when we divide both the numerator and the denominator by 2, we get 10/2 = 5 and 16/2 = 8. So, the fraction 10/16 simplified to its lowest term is 5/8.
Now, to find an equivalent fraction with 32 as the denominator, we need to multiply both the numerator and the denominator of 5/8 by the same number so as not to change the value of the fraction. Here, we multiply by 4 (since, 8*4 = 32) to get 5*4 = 20 on the numerator. Therefore, an equivalent fraction of 5/8 with 32 as the denominator is 20/32.
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A store charges 7% sales tax. Which expression can be used to find the total cost of an item with a price of p? 0.07p 0.93p 1.07p 7.00p
If you have an item that costs 10 dollars and a sales tax of 7% you could do it this way
10 * 7/100 = 0.70 dollars.
The total cost is 10.70 dollars. or 10 dollars and 70 cents.
The best way to do the total however is to multiply the cost by 1.07. You will get the number the customer has to pay.
10 * 1.07 = 10.70
So for any price (p) it would be 1.07*p
Answer:
1.07p
Step-by-step explanation:
The tax equals the price times the tax rate
We know the price p and the tax rate 7%
tax = p*7%
Changing this to decimal form
tax = .07p
The final price of the item is the sales tax plus the price
final price = tax + price
.07p +p
1.07p