Answers
Answer:
The answer is:
[tex]\frac{6r-5q}{r^2-q^2}[/tex]
which agrees with the last answer option (D) in the list.
Step-by-step explanation:
In order to add rational expressions, we need to express them with the same denominator. Therefore we examine what factors there are in the first denominator, which happens to be a difference of squares which is readily factored out as:
[tex]r^2-q^2=(r+q)\,(r-q)[/tex]
the second denominator consists of only one of these factors: [tex](r+q)[/tex], then in order to express both rational expressions with the same common denominator, we multiply numerator and denominator of the second fraction by the factor: [tex](r-q)[/tex]
Then we get two expressions that can be easily added as shown below:
[tex]\frac{r}{(r+q)\,(r-q)} +\frac{5\,(r-q)}{(r+q)\,(r-q)} =\frac{r+5(r-q)}{(r+q)(r-q)} =\frac{r+5r-5q}{(r+q)\,(r-q)} =\frac{6r-5q}{r^2-q^2}[/tex]
Related Questions
Question
of 27
Which of the following shows an element of the sample space for first
tossing a coin and then rolling a number cube?
Α.Τ, Η
B. T, 2
C. 6,1
D. 4, H
Answers
The sample space for first tossing a coin and then rolling a number cube is (T, 2).
What are Outcomes of Probability?An outcome is a possible result of an experiment or trial in probability theory. Each experiment's possible outcomes are distinct, and alternative outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment).
As, the outcomes for tossing a coin is Head (H) and Tail (T).
and, the outcome for rolling a die
{1, 2, 3, 4, 5, 6}.
So, the sample space for first tossing a coin and then rolling a number cube
= ( T, 2)
Learn more about Outcome of Probability here:
https://brainly.com/question/30661698
#SPJ5
2. Kevin drives to the pizza place for lunch.
He walks 5 km east, then 5 km south, then 5
km east again.
Distance:
Displacement:
Answers
Answer: Distance = 15km ; Displacement ≅ 11'2km
Step-by-step explanation:
In Physics when we speak of distance we refer to the space traveled that is always measured on the trajectory, while displacement refers to the space from an initial position to a final position regardless of the path. When the path is a straight line, the space traveled is equal to the module of the displacement.
Distance: 5km + 5km + 5km = 15km (Red lines)
Displacement² : (10km)² + (5km)² = 100km² + 25km² = 125km²
Displacement : √125km² ≅ 11'2km (Blue line)
(See attached image)SpymoreSolve for x
X + 2w = m
Answers
Answer:
X = m - 2w
Step-by-step explanation:
just isolate the variable.
Answer:
x=m-2w
Step-by-step explanation:
Just take the +2w to the other side where it becomes negative.
A product costs $70 today, how much will the product cost in t days if the price is reduced by $5 a day
Answers
Answer:
P ($)=70-5(t)
Where p = price at t days
t = number of days
Step-by-step explanation:
The product price initially = $70
Now, every day , it reduces $5
The rate=$5 per day reduction
The price in the days will be determined by the formula below
P ($)=70-5(t)
Where p = price at t days
t = number of days
So let's assume it's on the second day
The price after the second day
P($) = 70-5(2)
P($) = 70-10
P($)= $60
The price after two days will be reduced to $60
McCoy Brothers manufactures and sells two products, A and Z in the ratio of 5:2. Product A sells for $86; Z sells for $124. Variable costs for product A are $45; for Z $49. Fixed costs are $429,500. Compute the contribution margin per composite unit.
Answers
Answer:
the contribution margin per composite unit is $365
Step-by-step explanation:
The computation of the contribution margin per composite unit is shown below:
= Contribution margin per unit for product A × ratio of A + Contribution margin per unit for product B × ratio of B
= ($86 - $45) × 5 + ($124 - $49) × 2
= $205 + $160
= $365
Hence the contribution margin per composite unit is $365
P(t) = 520/1+5e^-0.2t
Find the initial population size
Answers
To do this you would plug in 0 for t then solve the equation.
520/1+5e^-0.2(0)=
520/1+5(1)=
520/1+5=
520/6= 86.67
*
True or False? Natural Numbers are closed under division.
Answers
Answer: False
Natural numbers are not closed under division
Some natural numbers divide to get another natural number. For example, divide 10 over 2 to get 10/2 = 5.
However, there are infinitely many natural numbers that divide to get something that isn't a natural number. Example: 10/7 = 1.43 approximately. All we need is one counterexample to contradict the original statement.
A set is considered closed under division if dividing any two values in that set leads to another value in the set. More formally, if a & b are in some set then a/b must also be in the same set for that set to be closed under division.
If we changed "natural numbers" to "rational numbers", then that set is closed under division. If p, q are rational numbers then p/q is also rational. Basically, dividing any two fraction leads to some other fraction. The value of q cannot be zero.
Somebody please help!!!
(Dont judge me I forgot)
Answers
Answer:
16. 200+3
17. 30+4+0.1+0.02+0.007
18. 200+70+6+0.1+0.03
19. 30000000+4000000+100000+20000+3000+6
Step-by-step explanation:
what is the slope and the g intercept ? ( i added the picture )
Answers
Step-by-step explanation:
A straight line graph is of the form:
y = mx+b
So we get our equation in this form:
9=2x+3y
or, 9-2x=3y
or, -2x+9 = 3y
or, y= (-2x+9)/3
or, y = -2/3x + 3
So,
Slope(m)=−2/3
y-intercept (b) = 3
Therefore, slope(m) is -2/3x and y-intercept(b) is 3.
41 2/3 divined by 4 1/4
Answers
Answer:
Exact form: [tex]9 \frac{41}{51}[/tex]
Decimal form: [tex]9.80392156[/tex]
Step-by-step explanation:
[tex]41\frac{2}{3}[/tex] ÷ [tex]4\frac{1}{4}[/tex]
Let's put everything into a fraction.
[tex]\frac{41\frac{2}{3} }{4\frac{1}{4} }[/tex]
Now we have an answer.
Exact form: [tex]9\frac{41}{51}[/tex]
Decimal form: [tex]9.80392156[/tex]
Hope this helps!
Hiii, helpp thxxxxxx
Answers
Answer:
because angles on a straight line add up to 180 degrees substract (180-110), step 2; you will get 70 degrees afterwards the angle y is perpendicular it's 90 degrees.step 3;add (90+70) you get 160 .step 4;then substract (180-160) you get your answer as 20 degrees
Answer:
x = 20º
Step-by-step explanation:
Since it is a triangle, the sum of the internal angles is 180º.
We know that y = 90º, because 110º + 70º = 180º, and the line intercepts it, splitting the larger triangle into 2.
Since, y = 90º, and the other angle is 70º, we add those together to 160º.
Then, we take 180º - 160º = 20º.
x = 20º
Hope this helps.
:)
On a road map, the locations A, B and C are collinear. Location C divides the road from location A to B, such that AC:CB = 1:2. If location A is at (5,16) and location C is at (3,10). Find the coordinates of location B. A. (1,4) B. (4,13) C. (-1,-2)
Answers
Answer:
C. (-1,-2)
Step-by-step explanation:
Since C internally divides AB in the ratio AC/CB = 1/2 = m/n where m = 1 and n = 2, we use the formula for internal division.
Let A = (x₁, y₁) = (5, 16), B = (x₂, y₂) and C = (x, y) = (3, 10)
So x = (mx₂ + nx₁)/(m + n)
y = (my₂ + ny₁)/(m + n)
Substituting the values of the coordinates, we have
x = (mx₂ + nx₁)/(m + n)
3 = (1 × x₂ + 2 × 5)/(2 + 1)
3 = (x₂ + 10)/3
multiplying through by 3, we have
9 = x₂ + 10
x₂ = 9 - 10
x₂ = -1
y = (my₂ + ny₁)/(m + n)
10 = (1 × y₂ + 2 × 16)/(2 + 1)
10 = (x₂ + 32)/3
multiplying through by 3, we have
30 = y₂ + 32
y₂ = 30 - 32
y₂ = -2
So, the coordinates of B are (-1, -2)
I will give the brainiest
Venetta buys 2 pounds of pistachios and 3 pounds of almonds. The pistachios cost $4 more
per pound than the almonds. She pays a total of $48. Select all the correct statements about
this situation.
A.One pound of pistachios plus 1 pound of almonds cost $20.
B.Reducing the number of pounds of almonds by one results in a total cost of $40.
C.The pistachios cost twice as much per pound as the almonds.
D.The costa, in dollars of 1 pound of almonds is modeled as 2(a - 4) + 3a = 48.
E.
The cost p, in dollars, of 1 pound of pistachios is modeled as 2p + 3(p - 4) = 48.
Answers
Answer:
A;C;E
Step-by-step explanation:
Let cost of almond per pound be X
Cost of 3 pounds of almonds=3X
cost of pistachios per pound = X+4
Cost of 2 pounds of pistachios=2X+8
Total cost=5X+8=48
5X+8=48
5X=40
X=8
cost of one pound almond is $8
cost of one pound pistachios is $12
Please mark it brainly
In the figure points A B C D and E are collinear. If AE = 38 and BD = 15
Answers
Answer:
D. 30.5
Step-by-step explanation:
Given that A, B, C, D, and E are collinear,
AE = 38,
BD = 15, since segment BC = CD = DE, therefore
BD = ⅔ of BE
15 = ⅔*BE (substitution)
Solve for BE
Multiply each side by 3
15*3 = ⅔*BE*3
45 = 2*BE
Divide both sides by 2
45/2 = BE
22.5 = BE
BE = 22.5
Find AB:
AB + BE = AE (segment addition postulate)
AB + 22.5 = 38 (Substitution)
AB = 38 - 22.5 (Subtracting 22.5 from each side)
AB = 15.5
Find length of segment AD:
AB + BD = AD (segment addition postulate)
15.5 + 15 = AD (Substitution)
30.5 = AD
AD = 30.5
Rachael gets 94 marks in her exams.these are 47% of the total marks.find the maximum number of mark
Answers
Answer:
200 is the maximum amount
Step-by-step explanation:
94x100=9400
9400/47=200
can i have brainliest?
I need help! Please. Justify answer using Intermediate value theorem (IVT)
Answers
Step-by-step explanation:
N(t) is continuous at t = 6, so f(6) = 25(6) + 150 = 300.
f(0) = 80.
f(t) is continuous, so by Intermediate Value Theorem, f(t) must equal 250 at some point between t=0 and t=6.
An artist makes a scale drawing of a parallelogram-shaped sculpture. The scale is 10 cm on the drawing for every 8 meters on the sculpture. What is the area of the scale drawing? Show your work.
Answers
Answer:
Area of drawing= 0.315 m²
Step-by-step explanation:
Base = 6m
Height = 4.2 m
Area = height* base
Area= 4.2*6
Area= 25.2 m²
The scale is 10 cm on the drawing for every 8 meters on the sculpture.
Which is 10 cm to 800 cm
Or
0.1m to 8m
Arra of sculpture= 25.2 m²
area of drawing= (25.2*0.1)/8
Area of drawing= 0.315 m²
solve the equation
[tex] 5 = \frac{z}{4} - 3[/tex]
Answers
Answer:
z=32Step-by-step explanation:
[tex]5=\frac{z}{4}-3[/tex]
[tex]\frac{z}{4}-3=5[/tex]
[tex]\frac{z}{4}=5+3[/tex]
[tex]\frac{z}{4}=8[/tex]
[tex]z=8\cdot \:4[/tex]
[tex]z=32[/tex]
Dimensional analysis. How many seconds are in a year?
Answers
Answer:
31536000
Step-by-step explanation:
365 days x 24 hours x 60 minutes x 60 seconds = 31536000
Find the equation of the sphere centered at (-9,9, -9) with radius 5. Normalize your equations so that the coefficient of x2 is 1. -0.
Give an equation which describes the intersection of this sphere with the plane z = 0.
Answers
(a) x² + y² + z² + 18(x - y + z) + 218 = 0
(b) (x + 9)² + (y - 9)² + 56 = 0
Step-by-step explanation:
The general equation of a sphere of radius r and centered at C = (x₀, y₀, z₀) is given by;
(x - x₀)² + (y - y₀)² + (z - z₀)² = r² ------------------(i)
From the question:
The sphere is centered at C = (x₀, y₀, z₀) = (-9, 9, -9) and has a radius r = 5.
Therefore, to get the equation of the sphere, substitute these values into equation (i) as follows;
(x - (-9))² + (y - 9)² + (z - (-9))² = 5²
(x + 9)² + (y - 9)² + (z + 9)² = 25 ------------------(ii)
Open the brackets and have the following:
(x + 9)² + (y - 9)² + (z + 9)² = 25
(x² + 18x + 81) + (y² - 18y + 81) + (z² + 18z + 81) = 25
x² + 18x + 81 + y² - 18y + 81 + z² + 18z + 81 = 25
x² + y² + z² + 18(x - y + z) + 243 = 25
x² + y² + z² + 18(x - y + z) + 218 = 0 [equation has already been normalized since the coefficient of x² is 1]
Therefore, the equation of the sphere centered at (-9,9, -9) with radius 5 is:
x² + y² + z² + 18(x - y + z) + 218 = 0
(2) To get the equation when the sphere intersects a plane z = 0, we substitute z = 0 in equation (ii) as follows;
(x + 9)² + (y - 9)² + (0 + 9)² = 25
(x + 9)² + (y - 9)² + (9)² = 25
(x + 9)² + (y - 9)² + 81 = 25 [subtract 25 from both sides]
(x + 9)² + (y - 9)² + 81 - 25 = 25 - 25
(x + 9)² + (y - 9)² + 56 = 0
The equation is therefore, (x + 9)² + (y - 9)² + 56 = 0
I need help with this please
Answers
Answer:
C
Step-by-step explanation:
Simplify 200xyz3 .
Answers
Simplify the Integer part of the SQRT
Step-by-step explanation:
Factor 200 into its prime factors
200 = 23 • 52
for what value of c is the relation a function?
Answers
Answer:the answer is 1, b option i just take the tes
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
the answer is one
A machine was able to make 32 bags of Hot Cheetos in 8 seconds. What is
the rate made per second? *
Answers
Answer: 32÷8=4
Please brainliest
What is the solution to the equation 1 + 3x = -13 + 5x? Convert your answer to a decimal, if necessary.
Answers
Answer:
x=7
Step-by-step explanation:
[tex]1 + 3x = - 13 + 5x[/tex]
Collect like terms and simplify
[tex]3x - 5x = - 13 - 1 \\ - 2x = - 14[/tex]
Divide both sides of the equation by -2
[tex] \frac{ - 2x}{ - 2} = \frac{ - 14}{ - 2} [/tex]
Simplify
[tex]x = 7[/tex]
Answer:
Step-by-step explanation:
1 + 3x = 5x - 13
-2x + 1 = -13
-2x = -14
x = 7
Select the correct answer.
Angela uses 3 cup of strawberries to make 6 of a liter of smoothie. What is the unit rate in cups of strawberries per liter of smoothie?
OA. cups per liter
B. cups per liter
OC. cups per liter
OD. cups per liter
Answers
If there are 3 cups of strawberries per 6 liters of smoothie, that means that there is [tex]\frac{1}{2}[/tex] cups of strawberries per liter of smoothie.
[tex]\frac{3}{6}=\frac{1}{2}[/tex]
Hope this helps.
頑張って!
this is easy but im hella lazy and dont feel like doing this pls help me, i mark brainliest! ty ❤️
Answers
Answer:
D. It is a decimal that terminates after 3 decimal places
I hope this helps!
Find the area of each
Answers
Answer:
The area should be 56.4
Step-by-step explanation:
When you try to find the area of a triangle you have to multiply the base and height, which was 12km and 9.4 km,and you divide it by 2.
is 5(a + b) and (a + b)5 equal?
Answers
Answer:
yes totally
Step-by-step explanation:
5a+5b=5a+5b
simplify
4( 2u - 2) - 3(u + 5)
Answers
Answer:
5u - 23
Step-by-step explanation:
Answer:
4( 2u - 2) - 3(u + 5)
(4*2u + 4*-2)-(3*u + 3*5)
8u-8-3u+15
8u-3u-8+15
5u+7
Step-by-step explanation:
I hope this helped you.
Please mark Brainliest.
Have a great day!!!!!!!!!