Multiplication of given polynomials = x³ + 3x² - 22x - 2
What is polynomial?A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer.
Given,
(x + 6) ( x ^2 - 3x - 4)
Using distributive property
x( x ^2 - 3x - 4) + 6( x ^2 - 3x - 4)
Again using distributive property
x³ - 3x² - 4x + 6x² - 18x - 24
Adding like terms
x³ + 3x² - 22x - 2
Hence, x³ + 3x² - 22x - 24 is multiplication of given polynomials.
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Pls hurry I really need to answer tysm
The proportion is 2 : 3 and the scale model is represented by the Black tabletop color
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the scale of the color tabletop be represented as a : b
Now , the proportion will be
The scale model of the tabletop is given by A : B = 4 inches by 6 inches
So , the proportion is 4/6 = 2 : 3
And , the black tabletop has an original size of 32 inches by 48 inches
Substituting the values in the equation , we get
4 inches by 6 inches is proportional to 32 inches by 48 inches
On simplifying the equation , we get
4/6 = 32/48
2/3 = 16/24
2/3 = 8/12
2/3 = 2/3
Hence , the proportion is 2 : 3
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What is the Area and Perimeter? WILL MARK AS BRAINLIEST.
Answer:
24
Step-by-step explanation:
4x6=24
What is 12:4 ratio in simplest form?
Answer:
12:4 ratio simplified is 3:1
Step-by-step explanation:
An image of a parallelogram is shown.
What is the area of the parallelogram?
The area of the parallelogram is 416.25 cm²
What Is the Area of Parallelogram?The area of a parallelogram refers to the total number of unit squares that can fit into it and it is measured in square units (like cm², m², in², etc). It is the region enclosed or encompassed by a parallelogram in two-dimensional space.
Given here: The height = 18.25 ft and base=22.5 ft.
Thus the area of the parallelogram is
A=18.25×22.5
A=416.25 cm²
Thus the area of the parallelogram is 416.25 cm²
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One equation of a pair of dependent linear equations is 2x + 5y = 3. The second
equation will be
The ordered pair (a,b) satisfies the inequality y < x+5
(-5, 0 ) and (0, 5) are the ordered pair satisfies the inequality y < x+5
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is y < x+5
First, we have to find the x-intercept which occurs at y = 0
0 < x + 5
x<-5
For y-intercept,
y < 0+ 5
y <5
As a result, the obtained ordered pair is (-5, 0 ) and (0, 5).
Hence, (-5, 0 ) and (0, 5) are the ordered pair satisfies the inequality y < x+5
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4) what number of floors n would make the probability of that specific sequence of customer floors as large as possible?
It depends on the specific sequence of customer floors you're looking for. Without knowing that sequence, it's not possible to determine the number of floors that would make the probability of that sequence as large as possible.
In general, the probability of a specific sequence of customer floors will depend on several factors, such as the number of floors in the building, the number of customers, and the order in which they press the buttons.
To determine the number of floors that would maximize the probability of a specific sequence, you would need to know the details of the scenario and perform a more in-depth analysis.
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Gloria recently bought a new Pixel phone. One day, she got an alert regarding her screen time for the past week. She decided she was spending too much time on her phone, so she started to keep an eye on her minutes of screen time.
One week after starting to keep an eye on her screen time, Gloria's weekly screen time was down by 15% to 884 minutes.
What was the growth factor from her initial screen time to her screen time one week later?
The growth factor is 0.85.
How did we get the value?Let's call her initial screen time "x". After one week, her screen time was 884 minutes, which is 100% - 15% = 85% of her initial screen time.
So, 884 minutes = 0.85x
Dividing both sides by 0.85, we get:
x = 1040 minutes
So her initial screen time was 1040 minutes.
The growth factor from her initial screen time to her screen time one week later is:
884 minutes / 1040 minutes = 0.85
So, the growth factor is 0.85.
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Employee Performance
Adequate
Good
Outstanding
5%
8%
10%
The employee makes 10.60 per hour.
What is the raise amount if the performance is Adequate?
The raise amount if the performance of the employee is adequate, would be $ 0. 53
How to find the raise amount ?To find the raise amount when the performance by an employee for the period is adequate, the formula is:
= Current pay per hour x Raise percentage for adequate work
Current pay per hour = $ 10. 60 per hour
Raise percentage for adequate work = 5 %
The raise amount is therefore :
= 10. 60 x 5 %
= 10. 60 x 0. 05
= $ 0. 53
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write each equation in slope-intercept form. Identify the slope and y-intercept. Then graph the line described by the equation.
-4x+2y=10
Answer:
y = 2x + 5
The slope: 2
Y-intercept: 5
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = the slope
b = y-intercept
Our equation
-4x+2y=10
2y = 4x + 10
y = 2x + 5
The slope: 2
Y-intercept: 5
Anya fed her dog 3/4 cup of dog food in the morning and another 5/6 cup in the evening. How much did her dog eat over the course of the day?
Answer: 1 7/24
Step-by-step explanation:
(in survey done in a group of 500 children, 250 children liked doughnut only and 30% liked bread but not doughnut. If every children likes at least one of them.): (i)Find the number of children who liked both doughnut and bread. (ii)Find the number of children who like bread
Step-by-step explanation:
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A cylinder shaped pipe is 24 inches long and has a diameter of 6 inches. Witch measurements is closest to the lateral surface area of the pipe in square inches?
The lateral surface area of the cylinder for the given measurements is equal to 452.16 square inches.
Pipe is in form of cylinder
Diameter of the cylinder = 6 inches
Height of the cylinder 'h' = 24 inches
Radius of the cylinder 'r' = diameter / 2
= 6/ 2
= 3inches
lateral surface area of the cylinder = 2πrh
value of π = 3.14
Substitute the value we get,
⇒lateral surface area of the cylinder = 2 × π × 3 × 24
⇒lateral surface area of the cylinder = 144π square inches
⇒lateral surface area of the cylinder = 144 × 31.4
⇒ lateral surface area of the cylinder = 452.16 square inches
Therefore, the lateral surface area of the cylindrical pipe is equal to 452.16 square inches.
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The exam results for the students in a class are shown in the frequency tree below
Given that the student did not pass the exam, the probability that they revised is 24%.
What is the probability?Probability refers to the likelihood, odds or chance of an expected outcome given many possible outcomes.
Probability is the quotient of expected outcomes over total outcomes.
The total number of students in the class = 33
The total number of students who revised = 19
The total number of students who revised and failed the exam = 8
The probability that the student revised but failed the exam = 8/33 = 24%
or (8/19 x 19/33)
Thus, the probability that a student chosen at random from the class revised but failed the exam is 24%.
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1. A function that has a V-shaped graph that opens up or
down is a(n)
2. The lowest or highest point on the graph of an absolute value
function is the
3. The line that divides the graph of an absolute value function
into two sections that are reflections of each other is the
1. A function that has a V-shaped graph that opens up or down is the absolute value function.
2. The lowest or highest point on the graph of an absolute value function is the vertex.
3. The line that divides the graph of an absolute value function into two sections that are reflections of each other is the line of symmetry.
What is the absolute value function?
The absolute value function of vertex (h,k) is given by the equation presented as follows:
y = |x - h| + k.
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Find the value of x in the supplement
The value of 'x' in the linear pair of angles is 126°.
What is a transversal?We know when a transversal intersects two parallel lines at two distinct points,
Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.
We know the sum of linear pair of angles is 180°.
Therefore, From the given information
(x - 6)° + 60° = 180°.
x + 54° = 180°.
x = 180° - 54°.
x = 126°.
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Given right triangle A B C ABC with altitude B D ‾ BD drawn to hypotenuse A C ‾ AC . If A D = 11 AD=11 and A C = 21 , AC=21, what is the length of A B ‾ AB in simplest radical form?
The length of AB is [tex]2\sqrt{105}[/tex].
What is an altitude?An altitude is a line which passes through the vertex of the triangle and meets the opposite side at the right angle. A triangle has three altitudes.
Consider the triangle ABC, with right angle at B,
Let AB = x, BC = y, BD = z.
By pythagoras theorem,
[tex]AC^{2} =AB^{2} +BC^{2}[/tex]⇒[tex]x^{2} +y^{2} = 21^{2}[/tex]----------(1)
From triangle ADB,
[tex]z^{2} +11^{2} =x^{2}[/tex]-------(2)
[tex]z^{2} +10^{2} =y^{2}[/tex]--------(3)
(2)-(3), we get, [tex]x^{2} -y^{2} =21[/tex]-----(4)
subtract (1) and (4) we get,
[tex]x^{2} =420[/tex]
⇒[tex]x=2\sqrt{105}[/tex]
Hence, the length of AB is [tex]2\sqrt{105}[/tex] in simplest radical forms.
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find the product 5^56 × 5^22 × 5^-96
Answer:
5^-18
Step-by-step explanation:
here is the answer please mark me as the brainliest
p to view steps... 9 p 2 − 1 p q − 2 q ÷ 1 − 3 p 3 p − 6 9 p 2 - 1 p q - 2 q ÷ 1 - 3 p 3 p - 6
By applying Algebraic fractions simplifying concept, it can conclude that the simplified expression is - (9p + 3) / q.
Algebraic fractions simplifying can be done by factoring the quantifier and denominator, then dividing by the common factors of the quantifier and denominator.
We have the following algebraic fraction:
((9p² - 1) / (pq - 2q)) / (1 - 3p) / (3p - 6)
To simplify this expression, we will do the following steps:
First, we apply the division rule: (a/b) / (c/d) = ad / bc:
((9p² - 1) / (pq - 2q)) / (1 - 3p) / (3p - 6)
⇔ ((9p² - 1) (3p - 6)) / ((pq - 2q) (1 - 3p))
Then we find the factors of (9p² - 1), that are (3p - 1) (3p + 1):
⇔ ((3p - 1) (3p + 1) (3p - 6)) / ((pq - 2q) (1 - 3p))
Factor other expressions that are not already factored in:
⇔ ((3p - 1) (3p + 1) 3 (p - 2)) / (q (p - 2) (1 - 3p))
Now we cancel the common factor (p - 2), so we have:
⇔ (3 (3p - 1) (3p + 1)) / (-q (3p - 1))
Then we cancel the common factor (3p -1), so we have:
⇔ (3 (3p + 1)) / -q
Finally, we expand the expression:
⇔ - (9p + 3) / q
Thus the simplified expression is - (9p + 3) / q.
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lamar is customizing his next pair of basketball shoes. the following table shows the design components and how many options he has for each. * how many different shoe combinations can lamar create?
By applying Fundamental counting principle, it can be concluded that there are 2560 different shoe combinations that can be created.
Fundamental counting principle states that if the first event can be done in k₁ different ways, the second event can be done in k₂ different ways, and so on until the [tex]n^{th}[/tex] event, then the number of different ways of all these events is K, where:
K = k₁ x k₂x . . . x kₙ
The following table shows the design components and how many options Lamar has for each:
Design component Number of options
Primary color 8
Secondary color 8
Sole color 8
Lace color 5
Then we can calculate the number of different combinations that can be created as follows:
Number of combinations = number of option₁ x number of option₂ x
number of option₃ x number of option₄
= 8 x 8 x 8 x 5
= 2560
Thus there are 2560 different shoe combinations that can be created.
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Nolan had 20 dollars to spend on 3 gifts. He spent 9 34 dollars on gift A and 3 12
dollars on gift B. How much money did he have left for gift C?
Therefore, Nolan has 8 dollars left to spend on gift C.
Nolan spent 9 dollars and 34 cents on gift A,
and 3 dollars and 12 cents on gift B,
for a total of
9 + 3 = 12 dollars and
34 + 12 = 46 cents spent so far.
Nolan started with 20 dollars, so he has 20 - 12 = 8 dollars remaining for gift C.
By using wildcards (such as "x" and "y") that are replaced with random values when the quiz is taken, simple calculated questions provide a technique to build individual numerical questions whose response is the result of a numerical formula that contains changeable numerical values.
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Is the midpoint rule an overestimate or underestimate?
The midpoint rule is an overestimate.
This is because the midpoint rule is a form of numerical integration which approximates the area under a curve by summing the areas of rectangles that are divided into equal intervals. These rectangles are centered on the midpoints of the intervals.
Because the rectangles are centered on the midpoints instead of the endpoints of each interval, the midpoint rule overestimates the area under the curve as the rectangles are wider than the intervals.
This means that the midpoint rule produces a larger area than the exact area under the curve. This is why the midpoint rule is an overestimate.
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The midpoint rule is an overestimate of the definite integral. The midpoint rule is a numerical integration method used to approximate the definite integral of a function.
It works by dividing the interval of integration into smaller subintervals and approximating the integral by summing the areas of rectangles whose heights are determined by the function evaluated at the midpoint of each subinterval.
Since the rectangles in the midpoint rule are taller at the midpoint and shorter at the endpoints, this method generally overestimates the true area under the curve. However, if the function is well-behaved and the subintervals are small enough, the error between the midpoint rule approximation and the true definite integral can be made arbitrarily small.
In conclusion, the midpoint rule is an overestimate of the definite integral, but the error can be made small by using smaller subintervals.
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9.
Hanif makes green paint by mixing blue paint and
yellow paint in the ratio
blue: yellow = 7:3
He buys blue paint in 50 litre containers, each costing £225
He buys yellow paint in 20 litre containers, each costing £80
He wants to sell the green paint in 5 litre tins.
Make 40% profit on each tin.
How much should he sell each tin for?
Answer:
your profit is 400
Step-by-step explanation:
50×225
What is the slope of a line containing the points 5,5 and -9,0
The slope of a line containing the points 5,5 and -9,0 is 5/14.
What is the slope of a line which passes through points ( p,q) and (x,y)?If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
Given;
The two points 5,5 and -9,0
m= 0-5/-9-5
m=-5/-14
m=5/14
Therefore, the slope will be 5/14.
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(8^x/4+4)=(8^-19x/4)
Answer:x = 1/60
Step-by-step explanation:
(8^x/4+4)=(8^-19x/4)
Apply fraction cross multiply: a/b = c/d then a*d = c*b
8^x * 4 = (4+4) * 8^-19x
simplify
8^x * 4 = 8 * 8^-19x
Apply exponet rules
xln(8) + ln(4) = (-19x +1) ln(8)
then just solve
x= 1/60
while y = -1/8
Rewrite 1/4 book as a unit rate
A.1/12. 1/3hour
B.3/4
C.12
D. 1 1/3
The required unit rate is [tex]\frac{3}{4}[/tex] book/ hour
What is Unit rate:When two different types of quantities with various units are being compared, the ratio of rate is applied. On the other hand, the unit rate shows how many units of one quantity are equivalent to one unit of another. A unit rate is a ratio between two separate units with 1 as the denominator.
Here we have
1/4 book/ 1/3 hour
We can convert the given fraction into a unit rate as given below
=> 1/4 book/ 1/3 hour
=> [tex]\frac{1}{4} \times (\frac{3}{1})[/tex] book/ hour
=> [tex]\frac{3}{4}[/tex] book/ hour
Therefore,
The required unit rate is [tex]\frac{3}{4}[/tex] book/ hour
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Line M goes through the points (-2,-8) and (1,1). Which pair of points
lies on a straight line that intersects Line M?
(-3,-2), (2,6)
(-2,-1), (3,14)
(0,2), (1,5)
(2,1), (-5,-20)
The equation of line m passing through the points (-2,-8) and (1,1) is y = 3x - 2
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept.
Line M goes through the points (-2,-8) and (1,1). Hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-(-8)=\frac{1-(-8)}{1-(-2)} (x-(-2))\\\\y=3x-2[/tex]
The equation of line m is y = 3x - 2
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Given the two concentric circles with center N below, LN = 13.5. Find the area of
the shaded region. Round your answer to the nearest tenth if necessary.
Answer:
371.54 sqr units
Step-by-step explanation:
area of a circle=πr²
area of inner circle=3.142×8×8=201.088 square units.
area of outer circle = 3.142×13.5×13.5=572.6295 square units
572.6295-201.088=371.5415 square units
=371.54 sqr units
What are the Multiples of 8 ?
Answer: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80…
Step-by-step explanation:
The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80… and so on. It is a sequence where the difference between each next number and the preceding number, i.e. two consecutive results, is 8.
(-2/3) (4/5) + (-2/3) (-2/5)
Answer: -0.26666666666
Step-by-step explanation: