The solution to the equation is x = 21/4
What is Linear Equation in 1 variable?
The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution
Given data ,
The equation is x + 7/2 = 5x/3
Subtracting 7/2 on both sides , we get
x = 5x/3 - 7/2
x = ( 10x - 21 ) / 6
Multiplying 6 on both sides , we get
6x = 10x - 21
Adding 21 on both sides , we get
6x + 21 = 10x
Subtracting 6x on both sides , we get
4x = 21
Divide by 4 on both sides , we get
x = 21/4
Hence , the solution for x + 7/2 = 5x/3 is x = 21/4
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What is the following quotient?
Answer: Choice B) [tex]\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\[/tex]
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Work Shown:
[tex]\frac{5}{\sqrt{11}-\sqrt{3}}\\\\\\\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{(\sqrt{11})^2-(\sqrt{3})^2}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{11-3}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\\\[/tex]
This shows why choice B is the answer.
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Explanation:
In the second step, I multiplied top and bottom by [tex](\sqrt{11}+\sqrt{3})[/tex]This is so we can apply the difference of squares rule in step 3. The difference of squares rule is (x-y)(x+y) = x^2-y^2.In step 4, the square roots cancel out with the squaring operation. The two operations are inverses of one another, which is why they cancel.So in general, if the denominator is [tex]\sqrt{a}-\sqrt{b}[/tex] and you want to rationalize the denominator, then you should multiply top and bottom by [tex]\sqrt{a}+\sqrt{b}[/tex]. The same applies in reverse as well.
This leads to the denominator becoming [tex](\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b}) = (\sqrt{a})^2-(\sqrt{b})^2 = a-b[/tex]
Keep in mind that [tex]a \ge 0[/tex] and [tex]b \ge 0[/tex]
i’m not asking for much :(
Answer:
c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
mcfluffythebigrubberducky
Line t has slope 3/4 and passes through (0.0). Follow these steps: Step 1:
Start at (0,0), Step 2: Move right 8 units. *
Answer:
6
Step-by-step explanation:
completing step 2 will land you at (8,0). you would just need to count up from there until you reach the line.
mr johnson is grading english essays hes determined that he must grade 124 essays and that he can grade 8 per day how many days will it take mr johnson to grade all of the english essays
Answer:
16
Step-by-step explanation:
It shows the mulitplication bettween eachother.
Please help me asap
Answer:
She walked 1.5 miles, then 0.75 miles. Hence 1.5 + 0.75= 2.25 or 2 and 1/4 a mileThe blue dot is at what level on the number line
Answer:
The dot is at positive 4.
which statement best describes the solution to the system of equations?
Answer:
option a is correct
Step-by-step explanation:
I think
Answer:
D - It has a single solution: x = -3, y = 26.
Step-by-step explanation:
The number N(t) of people in a community who are exposed to a particular advertisement is governed by the logistic equation. Initially, N(0) = 200,and it is observed that N(1) = 400. Solve for N(t) if it is predicted that the limiting number of people in the community who will see the advertisement is 20,000. (Round all coefficients to four decimal places.)n(t) = ?
9514 1404 393
Answer:
n(t) = 20,000/(1 +99e^(-0.7033t))
Step-by-step explanation:
One way to write the logistic function is ...
n(t) = L/(1 +a·e^(-kt))
where L is the maximum value and parameters 'a' and k depend on boundary conditions.
Here, we have n(∞) = L = 20,000 and n(0) = L/(1+a) = 200. We also have n(1) = L/(1+a·e^-k) = 400.
Solving for 'a', we get ...
n(0) = 20000/(1+a) = 200
20000/200 -1 = a = 99
Solving for k, we get ...
n(1) = 20000/(1 +99e^-k) = 400
20000/400 -1 = 99e^-k = 49
e^-k = 49/99
k = -ln(49/99) ≈ 0.7033
So, the desired function is ...
n(t) = 20000/(1 +99e^(-0.7033t))
PLEASE HELPPPP!!!????!!?
Answer:
I might be wrong but I think it is c
Step-by-step explanation:
a) are the triangle similar
b) solve for x
Answer:
Yes, the triangles are similar because they have the same 2 angles congruent, and X=12.44
Step-by-step explanation:
the perimeter of a rectangle is 40m. one of the lengths or the sides is 5m. find the lengths of the other 3 sides.
The perimeter of a rectangle is 40m and one side of it is 5m. What is the length of the other side using an equation?
Perimeter of the rectangle =2(l+ b)=40m
If one of its side b=5, then l = (40/2)-5
= 20–5
= 15 m Therefore
Length= 15 cm
Breadth =5 cm
Answer:
perimeter means the total distance of all sides of a shape. Rectangle has 2pairs of 2 sides with the same length. If one is 5 the other pair would be 5. So 40-5-5 would be the total of the second pair , 30. 30/2=15. So there's 2 sides with 5m each, and another 2 sides with 15m each
which describes the combined variation in the formula h=V/pie r2
Answer:
The correct option is (c).
Step-by-step explanation:
The combined formula is given by :
[tex]h=\dfrac{V}{\pi r^2}[/tex] ...(1)
h is height
V is volume
r is radius
It is clear from formula (1) that h varies directly with V and inverse;y with the square of r.
Hence, the correct option is (c).
Answer:
h varies directly with V and inversely with the square of r.
Step-by-step explanation:
(Since pie is a constant, it's not said in the "sentence")
I also just got it right on the quiz.
Meredith buys a bag containing eight apples for $3.50. When she gets home, she realizes one of the apples is rotten, so she throws it away. What is the actual cost for each non-rotten apple, in cents?
Answer:
50 cents
Step-by-step explanation:
Driving 65 mph, it takes Alicia 2 hours to reach the airport to go on vacation. It then takers her 2 hours to get to her destination with a jet traveling at a speed of 350 mph. How many miles does Alicia travel to get to her destination? *
10 points
765 miles
830 miles
480 miles
415 miles
I’m giving 30 points
Answer:
830 miles
Step-by-step explanation:
By car, she travels 65 mph for 2 hours. 2 multiplied by 65 equals 130. She then travels 350 mph for 2 more hours by plane. 2 multiplied by 350 equals 700. Add the two distances together and you get 130 + 700 = 830
For an ellipse whose minor axis is vertical, how does the value of b compare to the distance from the vertices on the vertical axis to the center?
a. same c. no comparison b. different d. none of the above
Answer:
A
Step-by-step explanation:
i just took the lab assessment
i am new so i have no clue what i am doing but i have a question. what are the points for and what do you do with them?
Un radar de l'armée américaine réussit à détecter tout ce qui se trouve à un rayon représenté
par cette inéquation :
5r + 9 > 10r - 126
Trouve l'ensemble-solution de cette inéquation.
Donne ta réponse en compréhension.
aider moi svp
Répondre:
r <27
Explication étape par étape:
Compte tenu de l'inégalité 5r + 9> 10r - 126
Nous devons trouver l'ensemble de solutions
5r + 9> 10r - 126
Ajouter 126 des deux côtés
5r + 9 + 126> 10r - 126 + 126
5r + 135> 10r
5r-10r> -135
-5r> -135
Divisez les deux côtés par -5 (notez que le signe changera)
-5r / -6 <-135 / -5
r <27
Par conséquent, les ensembles de solutions sont des valeurs inférieures à 27
A quantity with an initial value of 7800 decays exponentially at a rate of 2% every 3
years. What is the value of the quantity after 4.7 decades, to the nearest hundredth?
Answer:
5683.77
Step-by-step explanation:
the next model of a sport car will cost 14.9% more than the current model. The current costs $43,000. how much will the price increase in dollars ? what will be the price of the next model
Answer:
The price of the new model will be $49,407.
Step-by-step explanation:
Percentages
The current model of a sports car costs $43,000. The new model is expected to cost 14.9% more than the current model.
The increase is:
14.9% of $43,000
=14.9/100 * $43,000
=$6,407
The cost of the new model is:
$43,000 + $6,407 = $49,407
The price of the new model will be $49,407.
Write the expression in exponential form.
3
4/16^
A)
1/4
13^
B)
3/16
4^
C)
16/3
4^
D)
3/4
16^
Answer:
B
Step-by-step explanation:
5 - 2 (a + 3b) / 2 = ? / ?
Answer:
(5-2a+6b)/2
Step-by-step explanation:
According to PEMDAS, we would multiply 2 by (a+3b) first. This would equal 2a+6b. Since this is being subtracted from 5, the numerator would equal 5-2a+6b. This would bring the simplified answer to (5-2a+6b)/2
I need help, I will give the brainiest
Also, KJL is 54
Answer:
Step-by-step explanation:
Traingle 72 LN
Simplify. 310−−√ please help me
Answer:
17.606
Step-by-step explanation:
root of 310 = 17.606
Answer:
√30/10
Step-by-step explanation:
calculator
2x2−3x−4=0 Solve using the quadratic formula.
Answer:
Step-by-step explanation:
2x2−3x−4=0
For this equation: a=2, b=-3, c=-4
2x2+−3x+−4=0
Step 1: Use quadratic formula with a=2, b=-3, c=-4.
x=
−b±√b2−4ac
2a
x=
−(−3)±√(−3)2−4(2)(−4)
2(2)
x=
3±√41
4
18 red buttons: 12 blue buttons as a fraction in simplest form
Answer:
3/2
Step-by-step explanation:
18 red buttons: 12 blue buttons
18/12
Divide the top and bottom by 6
18/6 = 3
12/6 = 2
3/2
Answer:
3/2
Step-by-step explanation:
18/12 can be broke down and easily simplified given the numbers are even.
18 divided by 2 = 9
12 divided by 2 = 6
9/6
18 divided by 3 = 6
12 divided by 3 = 4
6/4
Simplest form;
18 divided by 6 = 3
12 divided by 6 = 2
3/2
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Hope this helps!
Solve for p.
8 = = 4(p – 17)
p =
Answer:
p=19
Step-by-step explanation:
Distribute:8=4p-68
76=4p
p=19
(can I get brainliest)
work out the subtraction equation of 5 1/4 divided by 2 5/7 equals
Answer:
calculater or hackmath
Step-by-step explanation:
8/12 = 2/9
What is the answer hurry please due today
Answer:
1/3
Step-by-step explanation:
In a flower basket, the ratio of red roses to white roses is 2 to 3. There are a total of 20 roses in the basket. How many red roses are in the basket?
Analyze each step to identify if Andy made an error. Yes, he made an error in Step 1. He switched the x and y values. Yes, he made an error in Step 2. He did not distribute StartFraction 3 Over 4 EndFraction properly. Yes, he made an error in Step 3. He should have subtracted 2 from both sides. No, his work is correct.
Answer:
Step 3, because the values for x for which y^1 < y^2 also include values between 3 and 5.
Step-by-step explanation:
Just took the test.
Answer:
c
Step-by-step explanation:
it just is