The equivalent expression of (q² − r²s) (q⁴ + q²r²s + r⁴s²) is q⁶ - r⁶s³
How to factor the expression?The expression is given as:
(q² − r²s) (q⁴ + q²r²s + r⁴s²)
Expand the expression
(q² − r²s) (q⁴ + q²r²s + r⁴s²) = q²(q⁴ + q²r²s + r⁴s²) − r²s(q⁴ + q²r²s + r⁴s²)
Open the brackets
(q² − r²s) (q⁴ + q²r²s + r⁴s²) = q⁶ + q⁴r²s + q²r⁴s² -q⁴r²s - q²r⁴s² - r⁶s³
Evaluate the like terms
(q² − r²s) (q⁴ + q²r²s + r⁴s²) = q⁶ - r⁶s³
Hence, the equivalent expression of (q² − r²s) (q⁴ + q²r²s + r⁴s²) is q⁶ - r⁶s³
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Complete questionFactor the expression. (q² − r²s) (q⁴ + q²r²s + r⁴s²)
What second degree polynomial function has a leading coefficient of -2 and root 4 with a multiplicity of 2
The second degree polynomial with leading coefficient of -2 and root 4 with multiplicity of 2 is:
[tex]p(x) = -2*(x - 4)*(x - 4) = -2*(x - 4)^2[/tex]
How to write the polynomial?
A polynomial of degree N, with the N roots {x₁, ..., xₙ} and a leading coefficient a is written as:
[tex]p(x) = a*(x - x_1)*(x - x_2)*...*(x - x_n)[/tex]
Here we know that the degree is 2, the only root is 4 (with a multiplicity of 2, this is equivalent to say that we have two roots at x = 4) and a leading coefficient equal to -2.
Then this polynomial is equal to:
[tex]p(x) = -2*(x - 4)*(x - 4) = -2*(x - 4)^2[/tex]
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Ryan Massey wants to deposit the following into his savings account: 28 ten-dollar bills, 9 five-dollar bills,
20 quarters, 85 dimes, 32 pennies, and three checks for $654.24, $100.00, and $458.92. He wants to
receive $50.00 in cash.
After he withdraws $50.00 in cash the bank reconciliation shows that Ryan would have: $1 501.98 in bank balance.
What is the solution to the above?Add all the deposits
Total = $338.82
Add the checks
654.24 + 100.00 + 458.92
= $1,213.16
Total amount deposited is: Cash + Check
1,213.16 + 338.82
Total Deposit = $1,551.98
Less withdrawal of $50
$1,551.98 - $50
Balance left = 1 501.98
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Full Question:
Ryan Massey wants to deposit the following into his savings account: 28 ten-dollar bills, 9 five-dollar bills, 20 quarters, 85 dimes, 32 pennies, and three checks for $654.24, $100.00, and $458.92. He wants to receive $50.00 in cash.
How much cash would he lave left after he withdraws $50.00 in cash?
What is the diameter of this circle if the circumference is 30 inches?
Answer:
d≈9.55
Step-by-step explanation:
the answer is 9.55 inches
Answer:
diameter = 9.55 in
Step-by-step explanation:
Circumference = pi x diameter so re-arrange
circumference / pi = diameter
30 / pi = diameter
9.55 in = diameter
What is the radius of the circle with equation (x + 1/5) ^ 2 + (y - 2/5) ^ 2 = 1/25
Answer:
1/5
Step-by-step explanation:
In the circle equation shown, the 1/25 all by itself on the right side of the equation is r^2.
r^2 = 1/25
Squareroot both sides.
r = 1/5
(y^3-2)(y^2+11) what is the answer
Answer:
[tex]y^{5}[/tex] + 11y³ - 2y² - 22
Step-by-step explanation:
(y³ - 2)(y² + 11)
each term in the second factor is multiplied by each term in the first factor.
y³(y² + 11) - 2(y² + 11) ← distribute both parenthesis
= [tex]y^{5}[/tex] + 11y³ - 2y² - 22
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Given circle A with radius 15, find the length of arc FD. Give your answer rounded to the nearest hundredth.
Answer:
20°
156°
46°
my
E
D
B
The length of arc FD with a radius of 15 and angle of 120° is 10π units.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The length of an arc is given by:
arc length = (Ф/360) * 2π*radius
Let us assume that the angle is 120°
arc FD = (135/360) * 2π(15) = 10π
The length of arc FD with a radius of 15 and angle of 120° is 10π units.
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Which choices are equivalent to the expression below? Check all that apply.
√8√8
A. √8
B. 8
C. √√8.8
D. 64
E. √16
F. 64
I hope this photo will help you.
If AABD
ACBD,
LA = 32° and ZC = 5x - 13
A
C
x =
B
D
[?]
Answer: 9
Step-by-step explanation:
By CPCTC,
[tex]32=5x-13\\\\45=5x\\ \\ x=9[/tex]
A grandfather is 51, while his grandson is 11. in how many years will the grandfather's age be twice the age of his grandson?
Answer:
29 years
Step-by-step explanation:
In 29 years the grandson will be 40 and the grandfather will be 80. 80 is twice as much as 40.
Answer: 29 years
Step-by-step explanation: if the grandfather is 51 when the grandson is 11 then the grandfather was 40 when his grandson was born. This mean the grandfather will be 80 when the grandson is 40. 40-11=29
I really need help on this question
Answer:
24Step-by-step explanation:
Since 20 is 4/3 * 15, the answer must be 4/3 * 18
4/3 * 18 = 24, so the answer is 24
Triangle not drawn to scale
Given: m&A=40°,m&B=88°,a=15cm. Then b
= _?__cm to the nearest hundredth
Answer:
b = 23.3
Step-by-step explanation:
First, we need to determine whether this is a right or non-right triangle.
We know that the sum of all the angles in a triangle must add up to 180, so we can add angles A and B and subtract the sum from 180:
[tex]180-(40+88)=180-128=52[/tex]
The 52 indicates that it is a non-right triangle, so we must rely on either the law of sines or law of cosines to find the measure of b.
Given that we have angle A and its resulting side, a, along with angle B, we can use the law of sines:
[tex]\frac{sin A}{a}=\frac{sin B}{b}[/tex]
[tex]\frac{sin 40}{15}=\frac{sin 88}{b}\\ \\ 15*sin 88=b * sin 40\\\\b=\frac{b*sin 40}{sin 88}\\ \\b=23.3216=23.3[/tex]
A bucket is in the shape of a frustum with top diameter 20cm and bottom diameter 12cm. If the height of the bucket is 8cm, calculate the volume of the bucket
Answer: V≈1642 cm³.
Step-by-step explanation:
D=20 cm d=12 cm h=8 cm V=?
[tex]R=\frac{D}{2}=\frac{20}{2} =10 \ (cm).\\ r=\frac{d}{2}=\frac{12}{2}=6 \ (cm).\\ \boxed {V=\frac{1}{3} *\pi *h*(R^2+R*r+r^2)} \ \ \ \ \ \Rightarrow\\V=\frac{1}{3}*\pi *8*(10^2+10*6+6^2)\\V=\frac{1}{3}*\pi *8*(100+60+36)\\ V=\frac{8}{3} *\pi *196\\V=\frac{8*196*\pi }{3} \\V\approx1642\ cm^3.[/tex]
Which of the following is a valid probability distribution? Probability distribution A is shown. The probabilities of 1, 2, 3, 4, 5 and 6 are all 0.2. Probability distribution B is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.3; 5 is 0.2; 6 is 0.1. Probability distribution C is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.4; 5 is 0.1; 6 is 0.1. Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.
Considering the given probability distributions, distribution D is valid.
When a probability distribution is valid?A probability distribution is valid if:
There are no negative probabilities.The sum of all probabilities is of 1.In this problem, only distribution D has a sum of 1, hence it is the only valid distribution.
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Answer:
Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.
Step-by-step explanation:
The answer above is correct.
Easy! 40 PTS!!! Log Functions
Answer:
C
Step-by-step explanation:
When x is negative 1/2 ^x becomes 1 / ( 1/2 ^x) meaning it is quite large as x becomes more negative
when x = 0 the value is 1
as x increases from 0 to + inf the value becomes smaller...but never negative
the only graph that fits is C
A triangle has one side length of 2x
2 + 5x + 3. The other two sides of the triangle have lengths x
2 + 2x and
3x − 2. Determine the simplified expression that represents the total perimeter of the triangle.
The simplified expression that represents the total perimeter of the triangle is 2x^2 + 10x + 3
How to determine the perimeter?The side lengths are given as:
2x^2 + 5x + 3, 2 + 2x and 3x - 2
Add these lengths to determine the perimeter (P)
P = 2x^2 + 5x + 3 + 2 + 2x + 3x - 2
Collect like terms
P = 2x^2 + 5x + 2x + 3x + 3 + 2 - 2
Evaluate the like terms
P = 2x^2 + 10x + 3
Hence, the simplified expression that represents the total perimeter of the triangle is 2x^2 + 10x + 3
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The Ramos family drove to their family reunion. Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours. After lunch, they drove at a constant rate of 45 miles per hour for 2 hours. How many total miles did the Ramos family drive?
ASAP
Anyone is here
Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours -> They drove a total of 55 x 3 = 165 miles.
After lunch, they drove at a constant rate of 45 miles per hour for 2 hours -> They drove a total of 45 x 2 = 90 miles.
So, the total amount of miles the Ramos family drove is 165 + 90 = 255 miles.
Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours.
[tex]\longrightarrow \tt{55*3=165}[/tex]
After lunch, they drove at a constant rate of 45 miles per hour for 2 hours.
[tex] \longrightarrow \tt{45*2=90}[/tex]
Total miles the Ramos family drive
[tex] \longrightarrow \tt{165+90=255}[/tex]
[tex]answer : \pink{255} \: \tt{miles}[/tex]
what postulate is this?
A. SSS (side side side)
B. SAS (side angle side)
C. ASA (angle side angle)
D. AAS (angle angle side)
Answer:
the answer is c ASA
Step-by-step explanation:
i think I. not sure
Maira has a total of Rs.1040 as currency notes in the denomination of Rs.10, Rs.20 and Rs.50. The ratio of the number of Rs.10 notes and Rs.20 notes is 2:5. If she has a total of 30 notes, how many notes of each denomination she has.
Answer:
Given that,
Maira has a total of Rs.1040 as currency notes in the denomination of Rs.10, Rs.20 and Rs.50.
The ratio of the number of Rs.10 notes and Rs.20 notes is 2:5.
She has a total of 30 notes with her.
Let assume that
Number of Rs 10 notes be 2x
Number of Rs 20 notes be 5x
Number of Rs 50 notes be 30 - (2x + 5x) = 30 - 7x
So,
[tex]\begin{gathered}\qquad \:\boxed{\begin{aligned}& \qquad\sf \:Denomination \: of \: Rs \: 10=2x\qquad \: \\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 20=5x\\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 50=30 - 7x\end{aligned}} \qquad \\ \\ \end{gathered}[/tex]
Now,
Amount in form of Rs 10 = 10 × 2x = Rs 20x
Amount in form of Rs 20 = 20 × 5x = Rs 100x
Amounts in form of Rs 50 = 50 × (30 - 7x) = Rs 1500 - 350x
Now, According to statement
[tex]\begin{gathered}\sf \: 20x + 100x + 1500 - 350x = 1040 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \: 120x + 1500 - 350x = 1040 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \: 1500 - 230x = 1040 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \:- 230x = - 460 \\ \\ \end{gathered}[/tex]
[tex]\sf \: \implies x = 2 [/tex]
Hence,
[tex]\begin{gathered}\qquad \:\boxed{\begin{aligned}& \qquad \:\sf \:Denomination \: of \: Rs \: 10=4\qquad \: \\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 20=10\\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 50=16\end{aligned}} \qquad \\ \\ \end{gathered}[/tex]
━━━━━━━━━━━━━━━━━━━━━If the set u = {all positive integers} and set a = {x|x ∈ u and x is an odd positive integer}, which describes the complement of set a, ac?
A = {x|x ∈ U and is an even positive integer}
The universal set(U) consists of only positive integers.
Given, A = {x|x ∈ U and x is an odd positive integer}.
That means the set A contains all those elements which belongs to the universal set and should be a positive odd number.
refers to the complement of A. It means that it will contain all those elements that belong to U but does not belong to A.
All the positive odd integer is made up of two types of number ,i.e, positive and negative number.
So,this set will contain all the element belonging to U and should be an even positive integer.
Therefore,Ac = {x|x ∈ U and is an even positive integer}.
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Answer:D:Ac = {x|x ∈ U and is an even positive integer}
Step-by-step explanation:
edge 2022
A book seller gains 30% on the cost price by selling a book for $130.Calculate the cost price of the book.
Answer:
Let the cost price be x
Selling price, S.P. = 130Gain % = 30%[tex]\rm{C.P. = \dfrac{S.P. \times 100}{100+ gain \% }}[/tex]
[tex]\rm{C.P. = \dfrac{130 \times 100}{100+30}}[/tex]
[tex]\rm{ C.P. = \dfrac{130}{30} }[/tex]
[tex]\large{\boxed{\rm{ C.P. = \dfrac{13}{3}}}}[/tex]
Use synthetic division to find the expression for the area of the base of a rectangular prism with height x 4 and volume x3 2x2 – 17x – 36. 2x2 – 9x x2 6x – 24 x2 – 2x – 9 –4x2 8x 36
The expression for the area of the base of Prism is x2 – 2x – 9
The volume of a rectangular prism is this
Volume = Area x Height
Substituting the given expressions
x3 + 2x2 - 17x - 36 = Area x (x + 4)
Area = (x3 + 2x2 - 17x - 36) / (x + 4)
Now, let's use synthetic division
-4 | 1 2 -17 -36
---- __-4___8___36
1 -2 -9 0
The expression for the area is
Area = x2 - 2x - 9
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A coordinate grid showing Number of Classes on the horizontal x-axis and Total Cost in dollars on the vertical y-axis with 2 lines. The first line passes through (0, 10) and a point at (4, 32). The second line passes through (0, 0) and a point at (2, 15).
Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Up charges a monthly fee, plus an additional fee per class. What is the system of equations representing these costs?
y = 5.5x and y = 7.5x + 10
y = 7.5x and y = 5.5x
y = 7.5x and y = 5.5x + 10
y = 7.5x + 10 and y = 5.5x + 10
The system of equations representing these costs are; y = 7.5x and y = 5.5x + 10
How to find the equation of a line?The slope of the first line is;
m = (y2 - y1)/(x2 - x1)
m = (32 - 10)/(4 - 0)
m = 5.5
Now, the first coordinate has a y-intercept of 10. Thus, the equation here for the cost is; y = mx + c = 5.5x + 10
The slope of the second line is;
m = (y2 - y1)/(x2 - x1)
m = (15 - 0)/(2 - 0)
m = 7.5
Now, the first coordinate has a y-intercept of 0. Thus, the equation here for the cost is; y = mx + c = 7.5x + 0 = 7.5x
Thus, the system of equations representing these costs are;
y = 7.5x and y = 5.5x + 10
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Answer:
y = 7.5x and y = 5.5x + 10
Step-by-step explanation:
[tex] \bf \huge x {}^{2} + 5 = 6[/tex]
solve for x :
[tex] \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]
[tex] \tiny \textsf{Song recommendations \:? }~ [/tex]
Given :
x² + 5 = 6Subtract 5 from each side :
x² + 5 - 5 = 6 - 5x² = 1Take the root on each side :
√x² = √1x = ±1Hence, the values of x are :
[tex]\fbox {x = 1}[/tex][tex]\fbox {x = -1}[/tex][tex]x^2+5=6\\x^2=1\\x=1 \vee x=-1[/tex]
Identify the axis of symmetry the function graphed below.
Answer: A. X = -1
Step-by-step explanation:
An axis of symmetry is the line that divides the object into two equal halves, creating a mirror-like reflection. Only at x = -1 will that occur.
HELP PLSSSSS! 10 points for whoever and good ratings
Answer:
Hello! The answer is 19.25 m²
Step-by-step explanation:
A = 1/2(4 + 7)3.5
A = 1/2(11)3.5
A = (5.5)3.5
A = 19.25 m²
Answer:
19.25 m²
Step-by-step explanation:
A = (1/2)(b1 + b2)h
A = (1/2)(7 m + 4 m)(3.5 m)
A = 19.25 m²
Given the following graph of a point on the polar plane, name another set of coordinates that could also represent this point using a
positive "value and a negative "O" value, where -360 ≤ 0 ≤ 0. State your answer in the form: (r,0) with "O" in degrees without the
degree symbol.
Answer:
(r,0)
Step-by-step explanation:
what’s the sun of -6 4/5 and 6 4/5
Answer:
the answer is 0.
Step-by-step explanation:
When you are adding two of the same numbers together, and one of them is positive while the other is negative, they cancel each other out.
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathsf{-6 \dfrac{4}{5} + 6 \dfrac{4}{5}}[/tex]
[tex]\mathsf{= \dfrac{-6 \times 5 + 4}{5}+ \dfrac{6 \times 5 + 4}{5}}[/tex]
[tex]\mathsf{= \dfrac{-30 + 4}{5}+ \dfrac{30 + 4}{5}}[/tex]
[tex]\mathsf{= \dfrac{-34}{5} + \dfrac{34}{5}}[/tex]
[tex]\mathsf{= 0}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{0}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A random sample of 16 ATM transactions at the Last National Bank of Flat Rock revealed a mean transaction time of 2.8 minutes with a standard deviation of 1.2 minutes. The width (in minutes) of the 95 percent confidence interval for the true mean transaction time is
The width (in minutes) of the 95 percent confidence interval for the true mean transaction time is 1.2786 minutes.
Sample size (n) = 16.
Sample mean = 2.8 minutes.
Sample standard deviation (σ) = 1.2 minutes.
Confidence interval given = 95%.
The degree of freedom (df) can be calculated as n - 1.
df = n - 1 = 16 - 1 = 15.
Since, the level of confidence is 95%, the level of significance α = 1 - 0.95 = 0.05.
From the T-Distribution table, we take the value at critical value α/2 with the degree of freedom 15.
[tex]t_{\frac{\alpha }{2} ,15}[/tex] = 2.131.
Now, the margin of error can be shown as follows:
[tex]E = t_{\frac{\alpha }{2} ,15} * \frac{\sigma}{\sqrt{n} } \\\Rightarrow E = 2.131 * \frac{1.2}{\sqrt{16} }\\ \Rightarrow E = 0.6393[/tex]
The width at the confidence interval of 95%, is twice the margin of error, that is:
Width = 2*E = 2*0.6393 = 1.2786.
Thus, the width (in minutes) of the 95 percent confidence interval for the true mean transaction time is 1.2786 minutes.
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Please help me Ill mark you brainlest
Answer:
Step-by-step explanation:
What is the slope of each of these three graphs?
[5] No slope (or a slope of 0)
There is no incline or decline to the line, so there is no slope.
[6] 1
We can use "rise over run" since we have clear points on the graph. See attached.
[7] Undefined slope
This slope of this line is undefined. The formula for slope is [tex]\frac{\text{change in y}}{\text{change in x}}[/tex] which becomes [tex]\frac{0}{0}[/tex] in a case like this. You cannot divide by 0, giving a slope of undefined.