Which statement describes the solutions of this equation? 2/x+2 + 1/10 = 3/x + 3
Answers
The statement that describes the solution of the equation is:
Option A: The equation has two valid solutions and no extraneous solution
How to find the solution of the equation?The equation we want to solve is given as:
\(\frac{2}{x + 2} + \frac{1}{10} = \frac{3}{x + 3}\)
Multiply through by 10(x + 2)(x + 3) to get:
20(x + 3) + (x + 2)(x + 3) = 30(x + 2)
Expanding gives:
20x + 60 + x² + 5x + 6 = 30x + 60
x² - 5x + 6 = 0
Using quadratic equation calculator gives:
x = 2 or x = 3
Thus, the equation has two valid solutions and no extraneous solution
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Related Questions
please help me????????
Answers
Solve for x: 3(x - 5) = -9
PLEASE HELP MEEEE
Answers
Answer:
X=2
Step-by-step explanation:
first you need to equivalent the expression that have equal bases then make the exponents equal that turned into x-5=2 and move all terms not containing x to the right side that’s makes x=7
Which of these equations is produced as a step when the Euclidean algorithm is used to find the gcd of given integers? (121,120) (Check all that apply.) Check All That Apply 121=1⋅120+1 120=120⋅1+0 121=121⋅1+0 120=120⋅0+120 120=1⋅0+120 NOTE. This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Which of these equations is produced as a step when the Euclidean algorithm is used to find the ged of given integers? (123,277) (Check all that apply.) Check All That Apply 277=2⋅123+31 123=3⋅31+30 30=30⋅1+0 31=31⋅1+0 30=30−0+30 31=1⋅30+1
Answers
The equations that apply for the first set are 121=1⋅120+1 and 120=120⋅1+0, and the equations that apply for the second set are 277=2⋅123+31, 123=3⋅31+30, 31=31⋅1+0, and 30=30⋅1+0.
For the first set of integers (121,120), the equations that are produced as steps when using the Euclidean algorithm to find the gcd are:
121=1⋅120+1
120=120⋅1+0
For the second set of integers (123,277), the equations that are produced as steps when using the Euclidean algorithm to find the gcd are:
277=2⋅123+31
123=3⋅31+30
31=31⋅1+0
30=30⋅1+0
So the equations that apply for the first set are 121=1⋅120+1 and 120=120⋅1+0, and the equations that apply for the second set are 277=2⋅123+31, 123=3⋅31+30, 31=31⋅1+0, and 30=30⋅1+0.
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If you do this question for me you'll get 100 points!
A room worker was dropped from the roof of a building in free fall. find the following:
1- The velocity of the stone after a time of 5 s.
2- The displacement of the stone within (s 5).
Take the acceleration of free fall g = 9.8 m/s2
Answers
#1
Initial velocity=u=0m/sTime=t=5sAcceleration=a=9.8m/s^2Final velocity=v
\(\\ \sf\longmapsto v=u+at\)
\(\\ \sf\longmapsto v=0+5(9.8)\)
\(\\ \sf\longmapsto v=49m/s\)
#2
Displacement=s\(\\ \sf\longmapsto s=ut+\dfrac{1}{2}at^2\)
\(\\ \sf\longmapsto s=0(5)+\dfrac{1}{2}(9.8)(5)^2\)
\(\\ \sf\longmapsto s=4.9(25)\)
\(\\ \sf\longmapsto s=122.5m\)
Answer:
tysm
Step-by-step explanation:
5
5
m/s2
lol
seven less than the product of 6 and a number equals 8. Use the variable w for the unknown number. Write it as an equation
Answers
Answer: 6w - 7 = 8
Step-by-step explanation:
We will write an equation using w for the unknown number using the mathematical vocabulary used in the sentence.
seven less than ➜ - 7
product of 6 and a number ➜ 6w
equals 8 ➜ = 8
6w - 7 = 8
At the end of Week 3 of my baseball team's season, our record is 5 wins and 7 losses. Each week after that, we win 3 games and lose 1 game. At the end of which week will my team have first won at least twice as many games total this season as it has lost?
Answers
Answer:
Week 6
Step-by-step explanation:
Week 3 you are 7-5
Week 4 you are 10-6
Week 5 you are 13-7
Week 6 you are 16-8
16/8 = 2 so week 6 is your answer
what is the answer ? 16h +5 - 6h
Answers
Answer:
10h + 5
Step-by-step explanation:
16h + 5 - 6h
combine like terms
16h - 6h + 5
10h + 5
if I misunderstood the question please let me know!
Answer:
10h + 5
Step-by-step explanation:
16h + 5 - 6h
10h + 5
why that's the answer? because the variable can't move or change so that's the final answer of the equation
Halp me plass halp me
Answers
Answer:
(x - 5, y - 7)
Step-by-step explanation:
A translation is a type of transformation that moves a figure up, down, left or right but does not change its appearance in any other way.
The pre-image is the original figure prior to transformation, so in this case the pre-image is the green arrow PQRSTUV.
The image is the result of a transformation, so in this case the image is the red arrow P'Q'R'S'T'U'V'.
To determine the series of translations that takes the pre-image to the image, choose one point on the pre-image and compare with its corresponding point on the image:
pre-image P = (2, 2)image P' = (-3, -5)Subtract the x and y values of the pre-image from the x and y values of the image:
translation of x-value: -3 - 2 = -5translation of y-value: -5 - 2 = -7Therefore, the translation that moves the pre-image to the image is:
(x - 5, y - 7)⇒ 5 units to the left, 7 units down.
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7 cost? 5 cost $7.50
Answers
Answer:
10.5
Step-by-step explanation:
7.5/5=1.5
1.5x7=10.5
Answer:10.5
Step-by-step explanation
7.50 divided by 5 = 1.5
1.5 times 7 = 10.5
A regular pentagon is such that is vertices Lie
circumference of a circle of radius
on
the
4.5cm. find the length of aside of the
pentagon to the nearest mm.
Answers
Answer: The length of a side of a regular pentagon can be found using the formula, side = 2r * sin(π/5), where r is the radius of the circle that the pentagon is inscribed in. Using this formula, the length of a side of the pentagon is approximately 4.08 cm or 40.8 mm (rounded to the nearest mm).
e Structure What is the length of a pool with a perimeter
6 feet? Explain how you found the answer. Then describe
You can use a feature of the pattern to find the length.
Answers
Answer:
To begin to answer this question, you will want to determine the equation for the volume of a rectangular prism. In this case, the equation is length times width times height or:
V = l * w * h
In the question, you are given several pieces of information that you can then plug into the equation. For example, you know the volume is 21,904 ft3 because they tell you that directly. You also know that the pool is 8 feet deep. I consider the depth to be the same as the height. With that information, you now have the equation:
21,904 ft3 = l * w * (8ft)
You are also told that the length is 2 times the width. Written as an equation, you would say that
l = 2w
Now, you can substitute that 2w for l to get the equation:
21,904 ft3 = (2w) * w * 8ft
We know that when you multiply a variable times itself, you get a squared variable, so 2w * w = 2w2 and that
21,904 ft3 = 2w2 * 8ft
Now, you can solve the equation to find w. At this point, it is easiest to drop the units of feet on the numbers to do the math. As long as all your numbers are in the same units (i.e. feet), you are good to go. Start by dividing each side by 8 to get
2738 = 2w2
Then divide both sides by 2 to get
1369 = w2
Finally, for this portion, take the square root of 1369 to get
w = 37 feet.
But you're not done yet. You know the width, and you know that l = 2w. Plug the value for w (37) into this equation to get the length, which is 74 feet.
The final answer is that the width of the pool is 37 feet and the length is 74 feet.
You can check your answer by plugging the length, width, and height (depth) into the equation for volume to see if you get 21,904ft3.
If you take 8 ft x 37 ft x 74 ft, you get 21,904 ft3 and you know that you answer is correct.
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLIEST
Use characteristics of quadratic functions to graph = − 1 2 x 2 − 2 + 1
a) Identify the axis of symmetry. ___________________
b) Find the coordinates of the vertex. ___________________
c) Graph the function using the table below. Plot at least five points.
d) Identify the domain of the function. ___________________
e) Identify the range of the function. ___________________
Answers
Answer:
A =25
b =35
c = 120
e = 310
simplify :
12⁷*28⁶
_______
21⁷*16⁶
Answers
Answer:
Step-by-step explanation:
Prime factorize 12 , 28 , 21 and 16
12 = 2 * 2 * 3 = 2² * 3
28 = 2 * 2 * 7 = 2² *7
21 = 3 * 7
16 = 2 * 2 * 2 * 2 = 2⁴
\(\dfrac{12^{7}*28^{6}}{21^{7}*16^{6}}=\dfrac{(2^{2}*3)^{7}*(2^{2}*7)^{6}}{(3*7)^{7}*(2^{4})^{6}}\\\\\\\\=\dfrac{2^{2*7}*3^{7}*2^{2*6}*7^{6}}{3^{7}*7^{7}*2^{4*6}}\\\\\\=\dfrac{2^{14}*3^{7}*2^{12}*7^{6}}{3^{7}*7^{7}*2^{24}}\\\\\\=\dfrac{2^{14+12-24}*3^{7-7}}{7^{7-6}}\\\\\\=\dfrac{2^{2}*3^{0}}{7^{1}}\\\\\\=\dfrac{2^{2}}{7}\)
Hint:
\(a^{m}*a^{n}=a^{m+n}\\\\\\(a^{m})^{n}=a^{m*n}\\\\\dfrac{a^{m}}{a^{n}}=a^{m-n} \ if \ m >n\\\\\\\dfrac{a^{m}}{a^{n}}=\dfrac{1}{a^{n-m}} \ if \ n>m\)
Simplify the expression:
(6 + 8) + x = 14
Answers
Answer:
x=0 is your answer
Step-by-step explanation:
(6 + 8) + x = 14
14+x=14
x=14-14
x=0
Answer:
The answer is x = 0
Step-by-step explanation:
1) Remove parentheses.
\(6 + 8 + x = 14\)
2) Simplify 6 + 8 + x to x + 14.
\(x + 14 = 14\)
3) Cancle 14 on both sides.
\(x = 0\)
Therefor, the answer is x = 0.
The arc length x = True O False 4(3 + y)² on the interval [1, 4] is approximately 131 units.
Answers
The statement is false. The arc length of the curve defined by x = 4(3 + y)² on the interval [1, 4] is not approximately 131 units.
To find the arc length of a curve, we use the formula ∫ √(1 + (dx/dy)²) dy, where the integral is taken over the given interval.
In this case, the equation x = 4(3 + y)² represents a parabolic curve. By differentiating x with respect to y and substituting it into the arc length formula, we can calculate the exact arc length over the interval [1, 4].
However, it is clear that the arc length of the curve defined by x = 4(3 + y)² cannot be approximately 131 units, as this would require a specific calculation using the precise integral formula mentioned above.
Therefore, the statement is false, and without further calculations, we cannot determine the exact arc length of the given curve on the interval [1, 4].
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If point B is reflected across the y axis, what are the coordinates of the new point?
(-3,2)
(-2,-3)
(-2,3)
(3,-2)
Answers
Answer: (3,-2)
Step-by-step explanation: We're reflecting to the y-axis, thus, we're going to reflect to the right.
(-x,-y) ⇒ (x,-y)
Our current coordinate is (-3,-2)...let's convert it now...
(3,-2)
I hope this helps!
Answer:
(3, -2).
Step-by-step explanation:
When you reflect across the y axis the y coordinate stays the same and the x axis changes sign : (x, y) --> (-x, y).
So B (-3, -2) --> (3, -2).
4) Victoria bought 50 beads. She paid $6 for
the beads. How much did each bead cost?
Define a variable and write an equation.
Solve the equation.
Answers
Answer: $0.12
Step-by-step explanation:
50x = 6
Use x as your variable
Fill in the following blanks with the appropriate matching words from the "word bank”. Some words may be used more than once.Intersection Union DisjunctionConjunctionWord bank: maybe, mostly, or, for, and, but
Answers
Intersection AND
Union AND, MOSTLY
Disjunction OR
Conjunction AND
For these words, we have:
Intersection, when we and the common results between two sets
So, Intersection A ∩ B A and B
A ={1,2,3} B= {3,4,5} A ∩ B ={3}
Disjunction, OR
When some conditions apply either to one set or to another.
A V B = OR
He is American OR He is British
A OR B
Union, AND, Mostly
When we want all the elements that belong to both Sets
So A ∪ B means A and all the elements from A and all the elements from B, no need no repeat the same element.
A = {1,2,3} B= {3,4,5} A ∪ B ={ 1,2,3,4,5}
Conjunction
A ^ B = AND,
In Logic and Set Theory and we have conjunction, we can use the word
He is a New Yorker AND He is American.
Which value of x makes the equation 0.1x - 2.5 = 1.0 true
A 10
B 15
C 20
D 35
Answers
Answer:
D 35
Step-by-step explanation:
When figuring this out you can just plug in your answers if you want to take it the easier way by just putting in the 35 in places of x and multiplying 0.1 times 35 gets you 3.5 so 3.5 minus 2.5 is 1
Answer:
xDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Step-by-step explanation:
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD.........................................................D :D
An object of mass m is in free fall. which set of equations describe the x and y positions of the particle as a function of time? take +y to be up.
x = xo + vot, y = yo + vot - 1/2gt^2
x = xo + voxt - 1/2gt^2, y = yo + voyt - 1/2gt^2
No answer text provided
x = xo + voxt, y = yo + voyt - 1/2gt^2
x = xo + voxt, y = yo + voyt
Answers
The answer is "x = xo + voxt, y = yo + voyt - 1/2gt^2."
The set of equations that describe the x and y positions of a particle as a function of time is:x = xo + voxt, y = yo + voyt - 1/2gt^2.An object of mass m is in free fall. It is necessary to describe the x and y positions of the particle as a function of time. These positions are dependent on the time taken to reach each position during the free fall.Therefore, we can write the positions in terms of the initial position, velocity, acceleration due to gravity, and time. The set of equations that describes the x and y positions of the particle is:x = xo + voxt, y = yo + voyt - 1/2gt^2Where,x = x-coordinate of the particle at time t.xo = initial position of the particle in the x direction.vo = velocity of the particle in the x direction.t = time elapsed since the initial time.y = y-coordinate of the particle at time t.yo = initial position of the particle in the y direction.voy = velocity of the particle in the y direction.g = acceleration due to gravity. (taken as -9.8 m/s²)Therefore, the answer is "x = xo + voxt, y = yo + voyt - 1/2gt^2."
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Suppose the volume of timber in a forest at a certain time ( t ) is given by the function: V(t)=10t−0.2t
2
. Determine the number of years that would be associated with the maximum volume of timber. Answer: Suppose the volume of timber in a forest was given by the function: V(t)=20t. Determine the profit-maximizing number of years ( t ) that a forester would wait before harvesting the timber when the interest rate was 20%. Answer:
Answers
The profit-maximizing number of years (t) that a forester would wait before harvesting the timber is approximately 9.9 years.
Given the volume of timber in a forest at a certain time (t) as: V(t) = 10t - 0.2t^2
Let's differentiate the given volume function w.r.t 't' to find the maximum value of timber as follows:
dV(t)/dt = 10 - 0.4t
Now, equate dV(t)/dt = 0 to find the value of 't' for which V(t) is maximum.0
= 10 - 0.4t0.4t = 10t
= 10/0.4t = 25years
Therefore, the number of years that would be associated with the maximum volume of timber is 25 years.
Let's suppose the volume of timber in a forest is given by the function: V(t) = 20t
We need to find the profit-maximizing number of years (t) that a forester would wait before harvesting the timber when the interest rate is 20%.
It is given that, the interest rate (i) = 20%
=0.2
The cost of harvesting the timber is given by the formula:
C = K +r*W where K is the fixed cost,
r is the interest rate,
and W is the amount of timber harvested.
Let's suppose the fixed cost (K) = $50 and the price of timber (p)
= $10 per unit.
Therefore, the profit function can be written as:
P(t) = p*V(t) - C
= $10*20t - (50 + 0.2*10t)
= $200t - 50 - 2t= 198t - 50
Now, differentiate P(t) w.r.t t to find the value of t for which P(t) is maximum.
dP(t)/dt = 198Equating dP(t)/dt
= 0, we get,0
= 198t
= 198/20t
= 9.9
Therefore, the profit-maximizing number of years (t) that a forester would wait before harvesting the timber is approximately 9.9 years.
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Circle O has a circumference of approximately 250π ft. Circle O with diameter d is shown. What is the approximate length of the diameter, d? 40 ft 80 ft 125 ft 250 ft
Answers
Answer:
250 ft
Step-by-step explanation:
circumference of circle 'C' is defined as
C = 2πr
250π = 2πr
r = 250π/2π
r= 125
d = 2r = 2×125 = 250 .
diameter of the given circle is 250 ft
The diameter of the circle is 250ft
Data;
Circumference = 250πdiameter = dCircumference of a CircleThe formula of circumference of a circle is given as
\(c = 2\pi r\)
Let's substitute the values in here and solve
\(c = 2 \pi r\\250\pi = 2 \pi r\\r = 125ft\)
The length of the radius is 125ft
But the length of diameter of a circle is twice the length of the radius
\(d = 2r\\d = 2 * 125\\d = 250ft\)
The diameter of the circle is 250ft
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The expression -370+13m represents a submarine that began at a depth of 370 feet below sea level and ascended at a rate of 13 feet per minute. What was the depth of the submarine after 9 minutes?
Answers
Answer:
Depth after 9 minutes is -253 feet
Step-by-step explanation:
Since we can find the submarine's depth as a function of time, m (in minutes), lets use the function to calculate the answer.
We are given the equation for depth: Depth(m) = -370+13m
Depth(x) means that the equation will tell us the submarine's depth after m minutes. The equation is missing the units, but we know from the statement that the initial depth is -370 feet and the rate of ascention is +13 feet/min. So we can enhance the equation by rewriting it with the units.
Depth(m) = -370ft+13(feet/minute)*m [m is minutes]
The sub's depth after 9 minutes is:
Depth(9) = -370ft+13(feet/minute)*(9 minutes)
Depth(9) = -370ft + 13*(9)
Depth(9) = -370+117
Depth(9) = -253 feet
First four terms of each sequence.
1) Tn=25-5n
2) [a1=5
an=an-1+7, where n>=2
3) The first five terms of a sequence are 15, 8, 1, -6, and -13.
a. write the next three terms of the sequence, show the rule.
Answers
The next three terms of the sequence would be:
-20, - 27 , -34
How to solve for the arithmetic progression in order to determine the terms of s seequenceThe rule is to subtract 7 from the every term that is on the question in other to get the next term
Lets assume the rule =
T = a - 7
we have
15 - 7 = 8
8 - 7 = 1
1 - 7 = -6
- 6 - 7 = - 13
- 13 - 7 = - 20
-20 - 7 = -27
- 27 - 7 = - 34
- 34 - 7 = -41
-41 - 7 = -48
The next three terms of the sequence would be:
-20, - 27 , -34
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Kate's mother is 32 years older than she is. In 4 years' time, her mother will be triple Kate's age. How old is Kate now?
Answers
Kate is currently 12 years old.
What are linear equations?
A linear equation is an algebraic equation that represents a straight line on a graph. It is an equation of the form:
y = mx + b
Let's start by defining some variables to help us solve the problem.
Let's say that Kate's current age is K.
We know that her mother is 32 years older, so her mother's current age is K + 32.
In 4 year's time, Kate's age will be K + 4 and her mother's age will be (K + 32) + 4 = K + 36.
We also know that in 4 years' time, Kate's mother will be triple Kate's age. So we can write the following equation:
K + 36 = 3(K + 4)
Expanding the brackets, we get:
K + 36 = 3K + 12
Subtracting K and 12 from both sides, we get:
24 = 2K
Dividing both sides by 2, we get:
K = 12
Hence, Kate is currently 12 years old.
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Find the value of ( 3 raise to 0 + 4 raise to-1) × 2 raise to 2
Answers
Answer:
The answer is 5
Step-by-step explanation:
(3^0 + 4^-1) 2²
Zero power rule and Negative power rule:
(1 + 1/4) 4
Add then multiply:
(1.25) 4
=5
If m LAOD = (10x - 7)° and m L BOC = (7x + 11)°, what is m L BOC?
Answers
Let p: A number is greater than 25.
Let q: A.number is less than 35.
If p ^ q is true, then what could the number be? Select two options.
Answers
Answer:
Here we do not have the options, so I will answer in a general way.
We have two statements:
p = A number is greater than 25
q = A number is less than 35
We want to have:
p ^ q is true
This means:
p and q are true.
So, we need to find a number such that both conditions are meet, so we need to find a number N such that
The number N is greater than 25 (from p)
The number N is less than 35 (from q)
So N can be any number between 25 and 35
So, some of the possible values of N are:
N = 26
N = 27
N = 28.6
N = 33
N = 34
Concluding, any number N ∈ (25, 35) can be a solution.
(Note that N = 25 and N = 35 are not solutions)
if the gas station has 80 customers on Tuesday, how many customers can be predicted to get a Dr.pepper?
Answers
Answer:
12
Step-by-step explanation:
how do i dertermine if x-1 is a factor of 3x^2-2x+5
Answers
The given polynomial is
\(3x^2-2x+5\)To know if the factor x-1 is a zero of the polynomial, we just have to replace x = 1 in the expression. If we get zero, then z-1 is a solution.
\(3(1)^2-2(1)+5=3\cdot1-2+5=3-2+5=1+5=6\)Since x = 1 didn't result in zero, we can deduct that x-1 is not a solution to the given expression.