Assuming that no denominator equals zero, which is equivalent to? r^2-r-6/(r-2)(r-3)
Answers
The given expression is [tex]\dfrac{ r^2-r-6}{(r-2)(r-3)}[/tex]. the option C [tex]\dfrac{ (r+2)}{(r-2)}[/tex]is correct.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
The given expression is
[tex]\dfrac{ r^2-r-6}{(r-2)(r-3)}[/tex]
By solving the numerator
[tex]r^2-r-6\\\\r^2 - (3-2)r- 6\\\\(r-3)(r+2)[/tex]
Put the solution in the above equation
[tex]\dfrac{ (r+2)(r-3)}{(r-2)(r-3)}[/tex]
[tex]\dfrac{ (r+2)}{(r-2)}[/tex]
Therefore, the option C is correct.
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Related Questions
pls answer ASAP
Lesson: Probability
Ty in advance
Answers
The probability can be calculated as given because there are a total of 52 cards.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Total number of card = 52
Number of king of heart = 1
P(getting a king of hearts) = 1/52
P(getting a spade) = 13/52 = 1/4
P (getting a 5 or a club) = (16/52) = 4/13
P(getting a 5 or a 7) = 4/52 + 4/52 = 8/52 = 2/13
P(getting a card which is not a spade) = 1 - 1/4 = 3/4
P(getting 11 of clubs) = 1/52
Thus, the probability can be calculated as given because there are a total of 52 cards.
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Answer:
1. 1
2. 51
3. 7
4. 9
Step-by-step explanation:
hope i helped
if x= 1 y=3 satisfy the linear equation 3x - 4y +9=0
Answers
Answer:
Step-by-step explanation:
3(1) + 4(3) + 9 = 0
3 + 12 + 9 = 0
24 ≈ 0
What is the remainder when f(x) = x³- 13x² + 40x + 18 is divided by x-7? Show your work.
Answers
Answer:
remainder = 4
Step-by-step explanation:
using the remainder theorem
when f(x) is divided by (x - a) then the remainder is f(a)
so when f(x) is divided by (x - 7) the remainder is f(7) , that is
f(7) = 7³ - 13(7)² + 40(7) + 18
= 343 - 13(49) + 280 + 18
= 343 - 637 + 298
= 4
Hence, the remainder is [tex]4[/tex].
What is the remainder value?
The remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient.
Applying the remainder theorem
In general when [tex]f(x)[/tex] is divided by [tex](x - a)[/tex] then the remainder is [tex]f(a)[/tex].
So, here when [tex]f(x)[/tex] is divided by [tex](x - 7)[/tex] the remainder is [tex]f(7)[/tex], that is
[tex]f(7)=7^3-13(7)^3+40(7)+18\\=343-13(49)+280+18\\=343-637+298\\=4[/tex]
Hence, the remainder is [tex]4[/tex].
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A car travelled a distance of 50km in an hour.what distance did it travel in 30min at the same speed?
Answers
1 hour = 60 minutes
Distance travelled in 60 minutes = 50 km
Distance travelled in 1 minute = 50/60
Distance travelled in 30 minutes = 50/60×30
50/60×30 = 25 km
OR
A car travelled 50 km in 60 minutes. For 30 minutes, half the distance that is 25 km.
Which is the standard form of the equation of a parabola with a focus of (8, 0) and directrix x = –8?
Answers
Answer:
Hi,
Step-by-step explanation:
directrix: x=-8
focus=(8,0)
[tex]x=\dfrac{(y-0)^2}{2*(8+8)}+\dfrac{8-8}{2}\\\\\boxed{x=\dfrac{y^2}{32}}[/tex]
What is the discriminant of the quadratic equation 0 = -x² + 4x − 2?
Answers
Answer: 8
Step-by-step explanation:
The discriminant is [tex]b^2-4ac[/tex]
in the equation:
[tex]-x^2+4x-2[/tex]
A = -1, B = 4, C = -2
plug into equation
[tex]4^2-4(-1)(-2)[/tex]
[tex]16-8[/tex]
⇒ [tex]8[/tex]
helppppp fast Write The (9m)^4 without exponents
Answers
Hi Student!
Looking at the problem, we are given a variable with a coefficient that is to the power of 4. We are asked to write the same expression but without exponents which means that we need to factor out the exponents to each of the items inside of the parenthesis.
Expand the expression
[tex](9m)^4[/tex][tex](9)^4*(m)^4[/tex]Simplify the expression
[tex]6561*m^4[/tex][tex]6561m^4[/tex]Therefore, the final answer for writing the expression [tex](9m)^4[/tex] without exponents would be [tex]6561m^4[/tex] after expanding the expression.
What is the area, in square centimeters, of the shaded part of the rectangle below?
Answers
Answer:
probably it
Step-by-step explanation:
First, get the area of the rectangle then subtract the triangle, the result will be the shaded area:
area rec = 18 * 11
area rec = 198 cm²
small side of tri = 11 - 5
small side of tri = 6 cm
area tri = (height * width) / 2
area tri = (6 * 18) / 2
area tri = 108 / 2
area tri = 54 cm²
area shaded = 198 - 54
area shaded = 144 cm²
How much
was it check out the photo and please awnser i really need it for my exam And thank you
Answers
Answer:
She would need at least 11 buses leaving 17 spare seats.
Step-by-step explanation:
171+22+13= 206
206/20= 10.3
10.3 = 11
A truck driver is driving from Nome, Alaska to Death Valley, California. Because he is traveling between locations with extreme temperatures, he needs to check the weather continuously to make sure the gas in his truck remains in liquid form. The gas he uses freezes at −40° F and evaporates at 140° F. Part A: Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form. (2 points) Part B: Describe the graph of the inequality completely from Part A. Use terms such as open/closed circles and shading directions. Explain what the solutions to the inequality represent. (4 points) Part C: In January 1989, the temperature in Nome, Alaska dropped to −49° F. Would the gas in the driver's truck have remained in liquid form so he could have driven on this day? Why or why not? (4 points)
I need part b
Also I need it asap please and thanks
Answers
The answers to the options are:
The inequality that represent the temperatures is -40°F < x <140°FOpen interval −49° F is not in the interval of -40°F ad -140°F and as such, he cannot drive.What is the inequality of the temperature?This inequality is known tp imply that the normal body temperature is taken (subtracted) from the minimum and maximum body temperature.
Note that in case A, the The inequality that represent the temperatures is less than sign.
In case b, it is an open interval because it means that in -40°F to -140°F , it is not equal to as that is the reason that the gas cannot stay liquid.
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A rectangle is divided into 4 equal rows with 4 squares in each row. mark says 1 square is 1/4 of the whole rectangle. kareem says 1 row of the whole rectangle.
Answers
Kareem is correct
4 rows = each row is 1/4 of the rectangle
What’s the answer for this?
Answers
Answer:2x
Step-by-step explanation:
Use the following net to find the volume of the solid figure it represents.
Answers
Answer:
(d) 48 yd³
Step-by-step explanation:
The net shown is of a rectangular prism. To find its volume, we need to know its dimensions. The volume will be the product of those dimensions.
__
edge lengthsThe area of a rectangle is given by the formula ...
A = LW
So, if we know one of the dimensions, we can find the other from ...
W = A/L . . . . . divide by L
For the right-most rectangle, the area is 24 yd², and its length is given as 6 yd. Then the other dimension of that rectangle is ...
W = 24 yd²/(6 yd) = 4 yd
__
For the left-most rectangle, the area is 12 yd², so its width is ...
W = 12 yd²/(6 yd) = 2 yd
__
volumeNow we know the dimensions of the cuboid are 6 yd by 4 yd by 2 yd. Its volume is ...
V = LWH = (6 yd)(4 yd)(2 yd) = 48 yd³
The volume of the solid figure is 48 yd³.
The volume of the solid figure is 48 cubic yd if the length, width, and height of the solid figure are 6, 4, and 2 yd respectively option fourth is correct.
What is a rectangular prism?It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape. It is also called a cuboid.
We have a net of the solid figure shown in the picture.
From the figure, the face has 24 square yards area and one side length is given, we can calculate the width of this face:
24 = 6×w
w = 4 yd
From the face that has 8 square yards area, we can calculate the height of the solid net:
8 = 4h
h = 2 yd
Volume of the solid net = 6×4×2 = 48 cubic yd
Thus, the volume of the solid figure is 48 cubic yd if the length, width, and height of the solid figure are 6, 4, and 2 yd respectively.
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A line passes through the point(1,6) and is parallel to y=4x+6. what is the value of b?
Answers
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y= \stackrel{\stackrel{m}{\downarrow }}{4}x+6\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is 4 and passes through (1 , 6)
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{4}(x-\stackrel{x_1}{1})[/tex]
[tex]y-6=4x-4\implies y=4x\underset{\stackrel{\uparrow }{b}}{+2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
What is the volume, in cubic inches, of a cube with an edge length of 12 inch? Explain or show your reasoning.
Answers
Answer:
1,728
Step-by-step explanation:
v = a³
v = 12³
v = 1,728 in³
Circumference if a circle with a diameter of seven
Answers
Answer:
Circumference = 2 x pi x r
Radius, r = 7/2
Circumference = 2 x 22/7 x 7/2
= 22 cm
Answer:
21.99
Step-by-step explanation:
2 times pi times radius
What is the solution to this system of equations? negative 5.9 x minus 3.7 y = negative 2.1. 5.9 x 3.7 y = 2.1. (0, negative 2.1) (0, 2.1) infinitely many solutions no solution
Answers
The solution to this system of equations is infinitely many solutions
How to determine the solution?The system of equations is given as:
-5.9x -3.7y = -2.1.
5.9x + 3.7y = 2.1.
Add both equations to eliminate a variable
-5.9x + 5.9x - 3.7y + 3.7y = -2.1 + 2.1
Evaluate
0 +0 = 0
Evaluate the sum of zeros
0 = 0
Both sides of the equations are the same
Hence, the solution to this system of equations is infinitely many solutions
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Answer:
Option C is correct. The system of linear equation -5.9x - 3.7y = -2.1 and 5.9x +3.7y = 2.1 have infinitely many solutions.
What is system of linear equation?
The system of linear equations is "a set of two or more linear equations or variables is called system of linear equation".
What is infinitely many solutions?
An equation has infinitely many solutions only if "the two lines are coincident and having the same y-intercept".
According to the question,
The system of linear equation,
-5.9 x - 3.7y = -2.1 → (1)
5.9 x + 3.7y = 2.1 → (2)
The equation (1) is same as the equation (2) only the difference equation (1) is multiplied by (-1). Both equation give the same line. To check if above equations have same y-intercept, the equation can be written in slope intercept form y = m x +c where 'm' is the slope of the line, 'c' is the 'y-intercept'.
y = - (5.9/3.7) x + 2.1 [From equation (1)]
y = -(5.9/3.7) x + 2.1 [From equation (2)]
The both equation have same y-intercept. Therefore, the system of linear equations have infinitely many solution.
Hence, the system of linear equation -5.9x - 3.7y = -2.1 and 5.9x +3.7y = 2.1 have infinitely many solutions.
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Step-by-step explanation:
The annual water usage in rockport increases at a rate of 10% every year as the town gets bigger. this year, the town used 6,740 megaliters of water. in 7 years, how much water will be used annually?
if necessary, round your answer to the nearest hundredth.
Answers
4618 mega liters of water, in 7 years, will be used annually.
What is interest?Interest is the outlay you pay to borrow money. Interest is often deliberated as an annual percentage of a loan amount.
here, we have,
I=PRT/100
=6740×10/100×7
=674×1×7
=4618
the nearest hundredth is a 4618 this is the answer.
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Answer:
13,134.35 megaliters
Step-by-step explanation:
Plug in 6,740 megaliters for the initial amount, 0.1 for the rate of increase, and 7 years for the time elapsed.
y
= a(1+r)t
y
= 6,740(1+0.1)7 Plug in values
y
= 6,740(1.1)7 Add
y
= 6,740(1.94871…) Simplify
y
= 13,134.35325… Multiply
Round to the nearest hundredth.
13,134.35325… → 13,134.35
To the nearest hundredth, Rockport will use 13,134.35 megaliters of water annually.
In 2009, a principal of $3600 was invested at 3.75% interest, compounded annually. let t be the number of years since 2008. let y be the value of investment, in dollars. Write an exponential function showing the relationship between y and t.
Answers
Answer:
3,600 x (1.0375) ^ 1
Step-by-step explanation:
Compund interest formula.
IA * (r + 1) ^t
IA = Initial amount; r = rate (as decimal); t = time (in years)
IA = 3600
r = .0375
t = 1 (2008-2009)
3,600 x (1.0375)^1
-- Gage Millar, Algebra 1/2 Tutor, (Pending Pre-Calc Tutor)
Today, Isaac needs to walk his dog, water the garden, and feed his fish. DDD is the number of minutes it takes to walk his dog, GGG is the number of minutes it takes to water the garden, and FFF is the number of minutes it takes to feed his fish.
The expression G+(D+F)G+(D+F)G, plus, left parenthesis, D, plus, F, right parenthesis describes the total number of minutes it takes Isaac to do all three tasks. We can also use the expression (G+D)+F(G+D)+Fleft parenthesis, G, plus, D, right parenthesis, plus, F to represent the same quantity.
Match each amount in the situation with the expression that represents it.
For reference:
The dog is an animal, and he needs to go outside to walk.
The garden is a bunch of plants (not an animal), and it is outside.
The fish is an animal, and she lives in a water tank inside.
Answers
The correct matching of each amount in the situation with the expression that represents it is:
The total Minutes of the tasks involving animals.-D+F (Dog and fish)The total Minutes of the tasks not involving animals.-G (Garden)The total Minutes of the Inside tasks.-F (Fish)The total Minutes of the Outside tasks.-G+D (Garden and Dog)Explanations of the expressionsGiven that:
D = number of minutes it takes to walk his dogG = number of minutes it takes to water the garden; andF = number of minutes it takes to feed his fishWe have the situations and expressions that need to be matched such that:
D+FG+DGFTherefore, considering the situation,
The total Minutes of the Inside tasks.The total Minutes of the Outside tasks.The total Minutes of the tasks involving animals.The total Minutes of the tasks not involving animals.The correct matching is given as:
The total Minutes of the tasks involving animals.-D+F (Dog and fish)The total Minutes of the tasks not involving animals.-G (Garden)The total Minutes of the Inside tasks.-F (Fish)The total Minutes of the Outside tasks.-G+D (Garden and Dog)Read more about mathematical expressions here:
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pls help me pls it's my homework
Answers
Answer:
i think its just water bro
How do I solve this?
Answers
Answer:
-7/8
Step-by-step explanation:
Quadratic formula is ax^2 + bx + c
In this case, x = -b/2a, which is -7/(2(4)) = -7/8
Answer:
x = - [tex]\frac{7}{8}[/tex]
Step-by-step explanation:
given a quadratic in standard form
f(x) = ax² + bx + c (a ≠ 0 )
then the equation of the axis of symmetry is
x = - [tex]\frac{b}{2a}[/tex]
f(x) = 4x² + 7x + 6 ← is in standard form
with a = 4 and b = 7
then equation of axis of symmetry is
x = - [tex]\frac{7}{2(4)}[/tex] = - [tex]\frac{7}{8}[/tex]
Please Help I Don't Understand.
Answers
BE and CD are parallel, so the triangles ABE and ACD are similar. Then the following relation holds:
AE/AD = AB/AC
10/(10 + 8) = x/(x + 6)
Solve for x :
10 (x + 6) = x (10 + 8)
10x + 60 = 18x
8x = 60
x = 60/8 = 7/5
Which explains whether or not the graph represents a direct variation?
On a coordinate plane, a line goes through points (0, 0) and (1, 3).
The graph has a constant of variation of 3, so it represents a direct variation.
The graph has a slope of 3, so it represents a direct variation.
The graph has a positive slope, so it does not represent a direct variation.
The graph does not begin at the origin, so it does not represent a direct variation.
Answers
The line passes through the origin and if it has a constant of variation of 3, so it represents a direct variation , Option A is the correct answer.
What is Direct Variation ?When a quantity increases and the other quantity also increases , then those two quantities are said to be in direct variation.
It is asked in the question that which option depicts whether On a coordinate plane, a line goes through points (0, 0) and (1, 3) , represents a direct variation
As it is mentioned in the question that the line passes through the origin and if it has a constant of variation of 3, so it represents a direct variation.
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Answer:
a
Step-by-step explanation:
What is the distance between these two points: (2, 3) and (- 5, 4)
Answers
Let's apply the distance formula:⇒d=√(x2−x1)²+(y2−y1)²⇒d=√(5−2+(−4−(−3))² ⇒d=√3²+(−7)²⇒d=√9+49 ⇒d=√58 Therefore, the distance between the two points (2,−3) and (5,−4) is √58 units.
PLEASE ANSWER
What is the degree of the polynomial -2x²y² – ½ z?
- 1
- 2
- 4
- 6
Answers
Detailed Answer:
The degree of a polynomial is the highest power in the polynomial. Here the highest power is 2 hence the degree is 2. Polynomials with the degree 2 are also called quadratic polynomials.
43.7826087 rounded to the nearest tenth
Answers
Answer:
43.8
When you round look at the number after the one your rounding up to. If its greater than 5 round up. If its lower than 5 keep it the same number
Need help with Trigonometry
Answers
Answer:
29
Step-by-step explanation:
using Pythagorean theory.
equate it to the hypotenus.
thus- hyp sq=adjacent sq +opposite sq
Pls solve question 4b. Verrry urgent . Ok tyy
Answers
Answer:
[tex]y = 3\left(x-\dfrac{3}{2}\right)^2+\dfrac{41}{4}[/tex]
Step-by-step explanation:
Given equation:
[tex]y = 3x^2 - 9x + 17[/tex]
Factor out 3 from the first 2 terms:
[tex]y = 3(x^2 - 3x) + 17[/tex]
Divide the coefficient of x by 2 and square it: (-3 ÷ 2)² = 9/4
Add this inside the parentheses and subtract the distributed value of it outside the parentheses:
[tex]y = 3\left(x^2 - 3x+\dfrac{9}{4}\right) + 17-\dfrac{27}{4}[/tex]
Factor the parentheses and combine the constants:
[tex]y = 3\left(x-\dfrac{3}{2}\right)^2+\dfrac{41}{4}[/tex]
plumber a charges an initial fee of $45 plus a rate of $60 per hour. Plumber B charges $225 flat. Explain how you would determine the number of hours it will take for both plumbers to charge the same amount? HELP IM TAKING A TEST!
Answers
Answer:
3 Hours
Step-by-step explanation:
Plumber A.
Initial fee: $45
Per Hour: $60
Plumber B.
Full rate: $225
To determine the number of hours it will take for both plumbers to charge the same amount you have to start with $45.
Then add 60$ every hour.
$45 + $60 = $105
$105 + $60 = $165
$165 + $60 = $225
Therefore, it takes 3 hours for them to charge the same rate.