help please, will give brainliest!
A. the equation has two true solutions
B. the equation had one true solution
C. the equation has one extraneous solution
D. the equation has one true solution and one extraneous solution
Answers
Answer:
C. the equation has one extraneous solutionStep-by-step explanation:
Given equation:
x/(x - 1) + 2/(x + 2) = -6/(x² + x - 2)Common denominator is x² + x - 2, consider x ≠ 1 and x≠ -2
Multiply both sides by x² + x - 2:
x(x + 2) + 2(x - 1) = -6x² + 2x + 2x - 2 + 6 = 0x² + 4x + 4 = 0(x + 2)² = 0x + 2 = 0x = -2There is one solution but it is not true one.
Option C is correct
Answer:
[tex] \frac{x}{x - 1} + \frac{2}{x + 2} = \frac{ - 6}{ {x}^{2} + x - 2 } \\ \frac{x(x + 2) + 2(x - 1)}{(x - 1)(x + 2)} = \frac{ - 6}{ {x}^{2} + x - 2} \\ \frac{ {x}^{2} + 2x + 2x - 2 }{ {x}^{2} + 2x - x - 2} = \frac{ - 6}{ {x}^{2} + x - 2} \\ \frac{ {x}^{2} + 4x - 2 }{ {x}^{2} + x - 2} = \frac{ - 6}{ {x}^{2} + x - 2 } \\ {x}^{2} + 4x - 2 = - 6 \\ {x}^{2} + 4x + 4 = 0 \\ {x}^{2} + 2 \times 2 \times x + {2}^{2} = 0 \\ {(x + 2)}^{2} = 0 \\ x + 2 = 0 \\ \boxed{x = - 2 }[/tex]
x =-2 is the right answer.C. the equation has one extraneous solution.
Related Questions
what is 1/4 of 3 1/2
Answers
Answer:
7/8
Step-by-step explanation:
.25x3.5=.875
Answer: 7/8 I hope this helps
Step-by-step explanation:
3 1/2
1 3/4
7/8
Write the product in its simplest form:
бу - бу?
Answers
Answer:
6y(1-ysquare)
Step-by-step explanation:
You have to bring out the common multiple
Answer:
36y^4
Step-by-step explanation:
6 x 6 = 36
If the variable has no exponent then it is 1.
1 + 3 = 4
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
What are roots of the equation -90=x (x-18)
Answers
Answer:
-90=[tex]x[/tex]([tex]x[/tex]-18)
-90=[tex]x^{2}[/tex]-18[tex]x[/tex]
[tex]0=x^{2}-18x+90[/tex]
[tex]x=9+3i or 9-3i[/tex]
Step-by-step explanation:
you need to use quadratic formula and you will find square root a negative ( -9 ), which is an imaginary no.
square root (-9) = 3i
If the length of a cube is 2cm then find the surface area of the cube?
Answers
Given:
Length of a cube is 2 cm
To Find:
Surface area of the cube
Solution:
A cube consists of 6 faces.
The area of each face = side x side
So, the total surface area of a cube = 6 x
side x side
Let a be the length of the given cube
: Surface area of a cube = 6a square
a = 2 cm (Given)
Surface area of cube = 6 x 22 =(6 x 4) = 24 cm square.
Hence, the surface area of the given
cube is 24cm square.
Hope it helps!
Cinco amigos van al cine. La entrada cuesta 4,50$ dos no tienen dinero y los otros tres deciden invitarles ¿Cuanto dinero tiene que poner de mas cada uno?
Answers
Answer:
Costo unitario= $3
Step-by-step explanation:
Dada la siguiente información:
Entrada= $4.5
Cantidad de entradas de más= 2
Cantidad de amigos que pagan= 3
Primero debemos calcular el total a pagas de más:
Total a pagar de más= 2*4.5= $9
Ahora, cuánto debe pagar cada uno:
Costo unitario= costo total / cantidad de personas
Costo unitario= 9/3
Costo unitario= $3
2. Rachel makes cranberry almond cookies. The number of cups of cranberries and the number of cups of almonds are shown in the table below. What is the ratio of cups of cranberries to cups of almonds? 1 point
Answers
Answer:
no table
Step-by-step explanation:
add on number line10 +(-3)
Answers
helpppppppppppppppppp
Answers
Answer:
2 solutions
Step-by-step explanation:
Given the expression
2m/2m+3 - 2m/2m-3 = 1
Find the LCM of the expression at the left hand side:
2m(2m-3)-2m(2m+3)/(2m+3)(2m-3) = 1
open the bracket
4m²-6m-4m²-6m/(4m²-9) = 1
Cross multiply
4m²-6m-4m²-6m = 4m² - 9
-12m = 4m² - 9
4m² - 9+12m = 0
4m² +12m-9 = 0
Since the resulting equation is a quadratic equation, it will have 2 solutions since the degree of the equation is 2
The sales tax in a certain county is 7%. If an item marked at $19.94 is sold within the county, estimate the final cost of the item once tax is included.
Answers
Given:
Rate of sales tax = 7%
Marked price of an item = $19.94
To find:
The final cost of the item once tax is included.
Solution:
We have,
Rate of sales tax = 7%
Marked price of an item = $19.94
[tex]\text{Sales tax}=\dfrac{7}{100}\times 19.94[/tex]
[tex]\text{Sales tax}=1.3958[/tex]
Now, final cost of the item once tax is included is
[tex]\text{Final cost}=\text{Marked price}+\text{Sales tax}[/tex]
[tex]\text{Final cost}=19.94+1.3958[/tex]
[tex]\text{Final cost}=21.3358[/tex]
Therefore, the final cost of the item once tax is included is $21.3358.
!! please, anybody help me. It doesnt have to be perfect. Just something!!
A boat’s velocity, measured in meters per second, is described by vector = 〈 -3, 4 〉. In two or more complete sentences explain how to find the speed of the boat and the direction it is traveling in standard position. In your final answer, include all of your calculations.
Answers
Velocity is a vector, so it has a magnitude and direction.
Speed is its magnitude, which is obtained from
|〈-3, 4〉 m/s| = √((-3 m/s)² + (4 m/s)²) = √(25 m²/s²) = 5 m/s
Its direction is an angle θ made with the positive horizontal axis, satisfying
tan(θ) = (4 m/s) / (-3 m/s) = -4/3 → θ = arctan(-4/3) + 180°n
where n is any integer. Now you have to consider that the x coordinate is negative and the y coordinate is positive, so 〈-3, 4〉 points into the second quadrant, and we get an angle there for n = 1 of about
θ ≈ 126.87°
Alternatively, you can use the vector 〈1, 0〉 in place of the axis, then compute the angle by relating it to the dot product, so θ is such that
〈-3, 4〉 • 〈1, 0〉 = |〈-3, 4〉| |〈1, 0〉| cos(θ)
(-3)•1 + 4•0 = √((-3)² + 4²) • √(1² + 0²) cos(θ)
-3/5 = cos(θ) → θ = arccos(-3/5) + 360°n
where again, n is any integer, and we get the same solution θ ≈ 126.87° in the second quadrant when n = 0.
The temperature of a freezer started at 18ºC. After cooling for a few hours, the freezer had a temperature of –12ºC. What is the difference between the new, colder temperature and the original temperature?
Negative 12 minus 18
Negative 12 minus (negative 18)
18 minus 12
18 + (negative 12)
Answers
Answer:
Its a
Step-by-step explanation:
took the test egde 2021
The difference between the new, colder temperature and the original temperature is 30 ° C.
What is temperature ?"Temperature, measure of hotness or coldness expressed in terms of any of several arbitrary scales and indicating the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature). Temperature is not the equivalent of the energy of a thermodynamic system; e.g., a burning match is at a much higher temperature than an iceberg, but the total heat energy contained in an iceberg is much greater than the energy contained in a match. Temperature, similar to pressure or density, is called an intensive property—one that is independent of the quantity of matter being considered—as distinguished from extensive properties, such as mass or volume."
Given,
The old temperature is = 18°C
The new temperature is = -12°C
The difference in temperature is [tex](-12\°C - 18\°C) = 30\°C[/tex]
Hence, A is the correct option.
To know more about temperature here
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What is being supported in the protest depicted?
A)Women wanted President Wilson to champion their right to vote.
B)Women demanded President Wilson recognize their right to free speech.
C)Women criticized President Wilson for sending troops to fight in the war.
D)Women expected President Wilson to provide equal pay for their work in the factories.
Answers
Answer:
the person above me is right it is A or one
Step-by-step explanation:
Need the answer please and with work. I had put B but that is incorrect.
Answers
Answer:
Step-by-step explanation:
You answer goes to minus infinity. There is no answer and you are correct.
someone please help me asap! i will give branniest!
Answers
In the cookie jar there are 20 cookies. 1/4
of the
cookies are peanut butter and the rest are
chocolate chip. How many cookies are
chocolate chip?
Answers
Answer:
15 chocolate chip
Step-by-step explanation:
1/4 of 20 is 5
this means there are 5 peanut butter cookies.
so 20-5= 15
this means there are 15 chocolate chip cookies
hope this helps!
Jada wants to know how fast the water comes out of her faucet. What information would she need to know to be able to determine that? AND HELP, WILL MARK BRAINLIEST!!!
Answers
Answer:
The distance the water is traveling and the time it took.
Step-by-step explanation:
The speed formula is s= d/t so I would guess that is what the question means.
(Sorry if I didn't take a lot of time to answer, it had caps so I would guess that you needed the answer fast. )
Solve for x.
Enter your answer in the box.
X=
Answers
Answer:
x = 3 ; y = 30
Step-by-step explanation:
Δ is equilateral or equiangular ⇒ m∠A = m∠B = m∠C = 60°
(2y)° = 60° ⇒ y = 30
(25x - 15)° = 60° ⇒ x = 3
Given that y varies inversely with x, and y = 60 when x = 2, find x if y = 24
Answers
Step-by-step explanation:
xy = k, where k is a real constant.
When x = 2, y = 60.
=> (2)(60) = k, k = 120.
Hence when y = 24, x(24) = (120), x = 5.
The Power of a Product rule says that when we multiply expressions with
variables we...
Answers
Answer:
simplify a power of a power by multiplying the exponents and keeping the same base.
Step-by-step explanation:
Solve and state the correct answer for the trigonometric equation below
tan y = 6 - 4 cot y where
[tex] 0 \leqslant y \leqslant 360[/tex]
Answers
Answer:
y = {37.4°, 79.2°, 217.4°, 259.2°}Step-by-step explanation:
Given
tan y = 6 - 4 cot yWe now that
cot y = 1/tan ySubstitute tan y with x:
x = 6 - 4/xx² = 6x - 4x² - 6x + 4 = 0x² - 6x + 9 = 5(x - 3)² = 5x - 3 = ± √5x = 3 + √5x = 3 - √5Replace x with tan y:
tan y = 3 + √5 ⇒ y = arctan (3 + √5) ≈ 79.2° + 180°ktan y = 3 - √5 ⇒ y = arctan (3 - √5) ≈ 37.4° + 180°kAnswer is:
y = {37.4°, 79.2°, 217.4°, 259.2°}Which of the following has no solution?
(x + 1 < -1) ∩ (x + 1 < 1)
(x + 1 ≤ 1) ∩ (x + 1 ≥ 1)
(x + 1 < 1) ∩ (x + 1 > 1)
Answers
Answer:
(x + 1 ≤ 1) ∩ (x + 1 ≥ 1) (the second option)
Step-by-step explanation:
there are no elements that are contained in all of the intervals thus making the second expression have no solution
Each large roll of ribbon has 20yards. Each package takes 3 feet of ribbon. How many packages can be wrapped
Answers
Answer:
20
Step-by-step explanation:
20*3/3 = 20
The number of yards in 1 foot is 3 thus 20 packages can be wrapped.
What is unit conversion?To convert any unit into another is called a unit conversion.
In order to convert units, we need to care about their dimensions their dimension should not be changed.
As per the given,
Length of ribbon = 20 yards
Each package required = 3 feet
Since 1 yard = 3 feet so,
Each package required = 1 yard
The number of packages that can be wrapped = 20/1 = 20
Hence" The number of yards in 1 foot is 3 thus 20 packages can be wrapped".
To learn more about unit conversion,
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Car rideshare services are a popular option for people needing to move about in large cities. The scatterplot shows the distances of trips and fares, in dollars, for an adult living in a city over a period of a month. The value of r for the scatterplot is 0.950.
How would the value of the correlation coefficient change if the fares were plotted on the x-axis and distances on the y-axis?
The value of the correlation coefficient would be –0.950.
The value of the correlation coefficient would not change.
The value of the correlation coefficient would be closer to 0.
The value of the correlation coefficient would be closer to 1.
Answers
Answer:
The value of the correlation coefficient would not change.
Step-by-step explanation:
If the relationship between distance of trips and fares in dollars gives a correlation coefficient value of 0.950. This can be interpreted to mean that the relationship between both variables is strong and positive such that an increase in distance leads to corresponding increase in fares of the trip and vice versa. Thus, interchanging the axis upon which the variables are plotted would still tied the same correlation Coefficient value as the correlation coefficient does not depend on the axis upon which the variables are plotted.
Step-by-step explanation:
If its change it will not be right
Solve for x using the
distributive property.
-5(x - 2) = -20
Answers
Answer:
x=6
Step-by-step explanation:
-5(x - 2) = -20
first multiple 5 by x and -2
-5x 10 = -20
subtract 10 from 10 and -20
-5x=-30
then divide 5
x=6
Hellppp please!!! Find the area of the shaded region
Answers
Answer:
1600-400pi
Step-by-step explanation:
There are 2 semicircles making it a full circle. We are doing (40*40)-the area of the circle. We do 20*20 since that it is the radius and get 400. We then multiply it by pi. We get 400pi. Now we find the area of the square. This is 40*40 which gives us 1600. 1600-400pi is our answer
sam drove 220 miles on 8 gallons of gas. find the unit rate.
Answers
Answer:
27.5
Step-by-step explanation:
Answer: I got 27.5
Step-by-step explanation:
This is a fraction equal to
220 miles ÷ 8 hours
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 8
220 miles ÷ 8
8 hours ÷ 8
=
27.5 miles
1 hour
=
27.5 miles
hour
= 27.5 miles per hour
Roger has the graph of F(x)=-4x^2 but needs to sketch the graph of G(x)=(x+3)^2 + 2/3. Describe how Roger can use the graph of F(x) to sketch the graph of G(x).
Answers
Answer:
See below
Step-by-step explanation:
Given
Parent function f(x)= -4x^2Transformed function g(x) = (x+3)^2 + 2/3We need to describe the transformations from f to g
The transformation steps are:
f(x) = -4x^2 → 4x^2 → x^2 → (x+3)^2 → (x+3)^2 + 2/3 = g(x)So there are four transformations:
Reflect over x-axisStretch horizontally by a factor of 4Translate left by 3 unitsTranslate up by 2/3 unitsPLEASE HELP I NEED THIS ASAP PLEASE PLEASE
Answers
4 pi
Explanation: for one whole cycle it’s 4 pi
6. John is signed up for a running race. He wants to
choose the shortest race. His choices are 2.5 kilometers
or 5.0 kilometers. Which is the shorter race?
Answers
Answer:
yo mama (first one ) .bsnisjehdvxbnxjx
Please help ASAP it’s due in 10 minutes pleaseeee I’m begging u