**Which of the following represents the sum of all possible solutions to the equation below?(18 - 3w)/(w+6)=w^2/(w+6)(A) -9(B) -3(C) 3(D) 9
Answers
We need to solve the given equation and then find the sum of all possible solutions.
The equation is:
\(\frac{18-3w}{w+6}=\frac{w^2}{w+6}\)Notice that the denominator on both sides is w+6. Since the denominator can't be zero, we have:
\(\begin{gathered} w+6\ne0 \\ \\ w\ne-6 \end{gathered}\)Thus, -6 can't be a solution.
Now, we can solve the equation by rewriting it as
\(\begin{gathered} \frac{18-3w}{w+6}\cdot(w+6)=\frac{w^2}{w+6}\cdot(w+6) \\ \\ 18-3w=w^{2} \\ \\ w^{2}+3w-18=0 \end{gathered}\)Now, we can use the quadratic formula to solve it:
\(\begin{gathered} w=\frac{-3\pm\sqrt[]{3^{2}-4(1)(-18)}}{2(1)} \\ \\ w=\frac{-3\pm\sqrt[]{9+72}}{2} \\ \\ w=\frac{-3\pm\sqrt[]{81}}{2} \\ \\ w=\frac{-3\pm9}{2} \\ \\ w_1=\frac{-3-9}{2}=-6\text{ (this solution is not possible)} \\ \\ w_2=\frac{-3+9}{2}=3 \end{gathered}\)Therefore, the only possible solution is 3. And the sum of all possible solutions is 3.
Related Questions
Write 15 + 45 as a product of two factors using the GCF
and the distributive property
Answers
Answer:
15(1 + 3)
Step-by-step explanation:
15 written in its prime factors is 3 × 5 (15 × 1)
45 written in its prime factors 3 × 3 × 5 (15 × 3)
The greatest common factor is 15: 15 × 1 = 15 and 15 × 3 is 45
∴ 15 + 45 = 15(1 + 3)
Hope this helps!
(15 + 45) can be written as 15 + 45 = 15(1 + 3)
What is distributive property?when a factor is multiplied by the sum/addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation.
Given:
15 + 45
Now, 15 can be factorised as prime factors
= 3 × 5 (15 × 1)
45 an be factorised prime factors
= 3 × 3 × 5 (15 × 3)
Thus, greatest common factor is 15:
=15 × 1 = 15 and 15 × 3 is 45
Hence, (15 + 45) can be written as 15 + 45 = 15(1 + 3)
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Write 3 numbers that are divisible by 2,
5, and 10.
Answers
Answer:A number is divisible by 2 if it ends in 2, 4, 6, 8 or 0. A number is divisible by 5 if it ends in 5 or 0. A number is divisible by 10 if it ends in a 0.Apr 8, 2018
My friend iis bumped and so am I. Question : graph the function described by the equation y = 2x − 2.
Answers
the graph of the equation y = 2 x - 2 is being obtained.
We are given the equation:
y = 2 x - 2
We need to make the graph of the equation.
We will first find some points on this equation:
x y
0 -2
1 0
2 2
3 4
4 6
5 8
Now, we will plot these points on the graph and join them with a dark line to obtain the graph of the equation y = 2 x - 2.
Therefore, the graph of the equation y = 2 x - 2 is being obtained.
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What’s the x intercept?
Answers
Answer:
The x-intercept would be (1,0)
Step-by-step explanation:
The point (1,0) is where the line intercepts (or crosses) the x-axis, therefore making it the x-intercept.
Avani is trying to find the height of a radio
antenna on the roof of a local building. She
stands at a horizontal distance of 21 meters
from the building. The angle of elevation
from her eyes to the roof (point A) is 42°,
and the angle of elevation from her eyes to
the top of the antenna (point B) is 51°. If
her eyes are 1.5 meters from the ground,
find the height of the antenna (the distance
from point A to point B). Round your
answer to the nearest meter if necessary.
Answers
Answer:
The height of the antenna is 7.0 m
Step-by-step explanation:
Let the height of the antenna be represented by x, and the distance from Avani's eyes to the top of the building A by y. And let z = x + y, so that:
Tan 42 = \(\frac{y}{21}\)
y = Tan 42 x 21
= 0.9004 x 21
= 18.9084
y = 18.91 m
Also,
Tan 51 = \(\frac{z}{21}\)
z = Tan 51 x 21
= 1.2349 x 21
= 25.9329
z = 25.93 m
Therefore,
x = z - y
= 25.93 - 18.91
= 7.02
x = 7.02 m
The height of the antenna is 7.0 m
A line crosses the y-axis at (0,55). What is the y-intercept of this line?
Answers
Answer:
\(\huge\boxed{\sf{b=55\:(b=y-intercept\:;)}}\)
Step-by-step explanation:
Hello.
The y-intercept of a line is a point where the graph touches the y-axis.
Y-intercepts always have an x-coordinate of 0.
Now, what is the y-intercept?
If we have a point (0, b) then b is the y-intercept.
This is just a formula, so don't think that the y-intercept is b, okay?
The y-intercept is b, but only in formulae. :)
Using the formula, we can deduce that
the y-intercept is 55.
I hope it helps.
Have a great day.
\(\boxed{imperturbability}\)
Rectangle MNPQ is graphed on a coordinate grid with vertices at MCU,), N(4,14), P(8,6),
and QC-8,-2). Rectangle MNPQ is dilated by a scale factor of 3 with the origin as the center
of dilation to create rectangle M'N'P'Q'.
Which ordered pair represents the coordinates of vertex M'?
A
B (3u, 3v)
C (u + 3,v + 3)
33
D
Answers
The radius of a circle is 3m. Find it’s area in terms of pi.
Answers
Answer:
\(\sf A = 9\pi \, m^2\)
Step-by-step explanation:
We can solve for the area of this circle by plugging the given radius value (3m) into the formula:
\(\sf A = \pi r^2\)
\(\sf A = \pi (3m)^2\)
\(\boxed{\sf A = 9\pi \, m^2}\)
The area in terms of \(\pi\) is \(\sf 9\pi\).
What is Area?Area of a two dimensional shape is the total region which is bounded by the object's shape.
Given that,
Radius of the circle = 3 m
Area of a circle \(\sf = \pi r^2\), where r is the radius
\(\sf = \pi (3)^2\)
\(\sf = 9\pi\)
Hence the area in terms of \(\pi\) is \(\sf 9\pi\).
Learn more about Area:
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on a map, 1 inch equals 8.7 miles. If two cities are 2.5 inches apart on the map, how far are they actually apart?
The distance between the cities is ? miles
Answers
Answer:
the distance between the cities is 21.75 miles.
Step-by-step explanation:
1 inch = 8.7 miles.
2.5 inches x 8.7 miles/inch = 21.75 miles
Can someone help me with number 2 please?
Answers
Answer:
I notice that the size of the watermelons has grown at a steady positive rate over the seven days.
In a right triangle, the hypotenuse is 12 cm and one leg is 7 cm. What is the length of the other leg? A. 11.7 cm B. C. 12.7 cm B. 9.7 cm D. 7.9 cm
Answers
Answer:
B. 9.7
Step-by-step explanation:
√12²-7²=√144-49=√95=9.7
HELP NEEDED ASAP
2. Consider the following transformed function
y = −2 Sin [2( − 45°)] + 1
a) Graph the five key points of Parent function on the provided grid. [1mark]
b) State the following for the transformed function [2marks]
Amplitude=
period=
Horizontal Phase shift =
Equation of axis=
c) Graph at least two cycles of the transformed function by transforming the key points of the parent function. (Don’t forget to label the x-axis and y -axis)
Answers
The five key points of the parent function are:
Domain: Set of all real numbersRange: Set of all real numbers from -1 to 1 (inclusive)No vertical asymptoteNo horizontal asymptoteMaximum: (π/2 + 2πn, 1)The five key points of the parent functionThe function is given as:
y = -2 sin[2(x - 45)] + 1
The above function is a sine function, and the parent function of a sine function is
y = sin(x)
The properties of the above function are:
Domain: Set of all real numbersRange: Set of all real numbers from -1 to 1 (inclusive)No vertical asymptoteNo horizontal asymptoteMaximum: (π/2 + 2πn, 1)The transformed functionThe transformed function is given as:
y = -2 sin[2(x - 45)] + 1
A sine function is represented as:
y = A sin[Bx + C] + D
Where:
A represents the amplitudePeriod = 2π/BC represents horizontal phase shiftUsing the above representations, we have:
Amplitude = -2Period = 2π/2 = πHorizontal phase shift, C = 2 * -45 = -90Equation of the axis, y = 1The graph of the functionSee attachment for the graph of the sine function y = -2 sin[2(x - 45)] + 1
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![HELP NEEDED ASAP 2. Consider the following transformed functiony = 2 Sin [2( 45)] + 1a) Graph the five](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/eCTld3JxtKBvdEeycvKbaqjBy3BK4B7r.jpeg)
The probability of a coin landing on heads when it is flipped is
0.5.
What is this probability written as a percent?
Answers
Answer:
50%
Step-by-step explanation:Since there is a 0.5 chance of the coin landing on heads add a zero and take off the .0 and you get 50%.
Answer:
50%
Step-by-step explanation:
The theoretical probability to get either heads or tails is 0.5 (or 50 percent). The probabilities of all possible outcomes should add up to 1 (or 100 percent), which it does.
For this test remember all questions have two answers. Please put the smaller answer in the first blank. Solve. x2=12
Answers
2.1 Solve : x2-12 = 0
Add 12 to both sides of the equation :
x2 = 12
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 12
Can √ 12 be simplified ?
Yes! The prime factorization of 12 is
2•2•3
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 12 = √ 2•2•3 =
± 2 • √ 3
The equation has two real solutions
These solutions are x = 2 • ± √3 = ± 3.4641 /This is the answer
8.4.4. Define sets. How many kinds of sets Also list the operation of sets. Give the short activites for teaching Learning Union of sets. 2+2+2+4=10)
Answers
In mathematics, a set is a well-defined collection of distinct objects, called elements or members of the set. These objects can be anything: numbers, letters, people, or even other sets.
he concept of sets is fundamental in various branches of mathematics, including set theory, algebra, and statistics.There are different kinds of sets based on their properties:
Finite set: A set with a specific number of elements, which can be counted.Infinite set: A set with an endless number of elements.Empty set: A set with no elements. It is denoted by the symbol Ø or {}.
Singleton set: A set with only one element.Subset: A set whose elements are all contained within another set.Universal set: A set that includes all the possible elements of interest in a particular context.Operations on sets involve various ways of combining or manipulating sets:
Union: The union of two sets A and B is the set that contains all the elements from both sets. It is denoted by A ∪ B.Intersection: The intersection of two sets A and B is the set of elements that are common to both sets. It is denoted by A ∩ B.
Complement: The complement of a set A, denoted by A', is the set of all elements that are not in A but are in the universal set.Difference: The difference between two sets A and B is the set of elements that are in A but not in B. It is denoted by A - B.
Cartesian Product: The Cartesian product of two sets A and B is the set of all possible ordered pairs, where the first element is from set A and the second element is from set B. It is denoted by A × B.
For teaching the concept of the union of sets, you can use the following activity:
Activity: Venn Diagrams
Draw two overlapping circles on the board or use physical cut-out circles.Label one circle as Set A and the other as Set B.
Ask the students to suggest elements for each set and write them inside the circles.Discuss the elements that are common to both sets and write them in the overlapping region.Explain that the union of sets A and B represents all the elements in both sets.
Combine the elements from sets A and B, including the elements in the overlapping region, and write them in a new circle labeled as A ∪ B.Emphasize that the union includes all the distinct elements from both sets without repetition.
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Three students that share a townhouse find that their electric bill for October is $2.23 less than the September bill. The
total of both bills is $292.43, and each bill is split evenly among the roommates. How much did each owe in September?
Answers
Answer:
$47.48
Step-by-step explanation:
Let x = the amount owed Sept.
x + x - 2.23 = 292.43 Combine like terms
2x -2.23 = 292.43 Add 2.23 to both sides
2x - 2.23 + 2.23 = 292.43 + 2.23
2x = 294.66 Divide both sides by 2
\(\frac{2x}{2}\) = \(\frac{294.66}{2}\)
x = 147.33 this is the bill for September
Oct. 147.33 -2.23 = 145.10 This is the Bill for Oct.
Total:
147.33 + 145.10 = 292.43
292.43 ÷ 3 = 97.48 This is what each will owe rounded to the nearest penny.
The heights in inches of players on Tracy basketball team are shown. Find the mean of the data:
Player Height. (In.)
58,60,61,59,63
Answers:
56.8in
58.5in
60in
60.2in
Answers
Answer:
To find the mean of the data, we add up all the heights and then divide by the number of players:
Mean = (58 + 60 + 61 + 59 + 63) / 5
Mean = 301 / 5
Mean = 60.2 inches
Therefore, the mean height of the players on the Tracy basketball team is 60.2 inches.
The answer is 60.2in.
Step-by-step explanation:
can someone help me please
Answers
Step-by-step explanation:
11.
\( \frac{x - 4}{ \frac{x}{4} - \frac{4}{x} } \)
\( \frac{x - 4}{ \frac{ {x}^{2} }{4x} - \frac{16}{4x} } \)
\( \frac{x - 4}{ \frac{ {x}^{2} - 16 }{4x} } \)
\( \frac{x - 4}{ \frac{(x + 4)(x - 4)}{4x} } \)
\( \frac{4x}{x + 4} \)
12.
\( \frac{ \frac{ {x}^{2} - 1 }{x} }{ \frac{(x - 1) {}^{2} }{x} } \)
\( \frac{ {x}^{3} - x}{ {x}^{3} - 2 {x}^{2} + x } \)
\( \frac{x( {x} - 1)(x + 1) }{x( {x} - 1) {}(x - 1) } \)
\( \frac{x + 1}{x - 1} \)
13.
\( \frac{ \frac{ {t}^{2} }{ \sqrt{ {t}^{2} + 1} } - \sqrt{ {t}^{2} + 1} }{ {t}^{2} } \)
\( \frac{ \frac{ {t}^{2} }{ \sqrt{ {t}^{2} + 1 } } - \frac{ {t}^{2} + 1}{ \sqrt{ {t}^{2} + 1 } } }{ {t}^{2} } \)
\( \frac{ \frac{1}{ \sqrt{ {t}^{2} + 1 } } }{ {t}^{2} } \)
\( \frac{ - \frac{ \sqrt{ {t}^{2} + 1 } }{ {t}^{2} + 1 } }{ {t}^{2} } \)
\( - \frac{ \sqrt{ {t}^{2} + 1} }{ {t}^{2}( {t}^{2} + 1) } \)
14.
\( \frac{3x { }^{ \frac{1}{3} } - x {}^{ \frac{ - 2}{3} } }{3x {}^{ - \frac{2}{3} } } \)
\( \frac{3x - 1}{3} \)
Select the negation of the following statement.
If it is night time, then the sky looks blue.
0 It is not night time, and the sky does not look blue.
It is night time, and the sky does not look blue.
0 If it is not night time, then the sky does not look blue.
0 If the sky does not look blue, then it is not night time.
Answers
Which fraction is equivalent to 1?
1/2
8/16
11/12
9/9
Answers
Answer:
9/9
Step-by-step explanation:
Answer:
9/9
Step-by-step explanation:
nine divided by nine equals 1
Question 2(Multiple Choice Worth 1 points) (07.03 MC) Lacey has $36 to spend. She buys a pair of sunglasses for $14.89 and a hat for $9.33. Lacey buys a scarf with the remaining money. How much does Lacey spend buying a scarf? $4.66 $7.44 $11.78 $24.22
Answers
Answer:
11.78
Step-by-step explanation:
What’s the slope intercept form.slope -3/4 and passes through (8,-3)
Answers
Answer:
Step-by-step explanation:
y + 3 = -3/4(x - 8)
y + 3 = -3/4x + 6
y = -3/4x + 3
help me please I will give you so much point and mark you as bril\
PLZ
PLZ
PLZ
ANYBODY?
Answers
giving brainliest !! *easy*
Answers
Answer:
To convert an angle measure to radians, multiply it by pi/180.
Step-by-step explanation:
310 * pi/180 = 31pi/18 = 5.41 rad
(GIVING BRAINLIEST!!)
Ingrid dug a trench eighteen twentieths of a meter long. The next day she dug nine twentieths of a meter more of the trench. What is a reasonable estimate of the total length of the trench?
A) one half meter
B) 1 meter
C) one and one half meters
Answers
Answer:
Solution :-
On first day, Ingrid dug eighteen twentieth of a meter = (18/20) of 1 meter = (18/20) * 1 = (9/10) meters .
Now,
→ Next day, Ingrid dug nine twentieth of a mater = (9/20) of 1 meter = (9/20) * 1 = (9/20) meters .
So,
→ Total length of the trench = Ingrid dug in first day + Ingrid dug next day = (9/10) + (9/20) = (9*2 + 9)/20 = (18 + 9)/20 = (27/20) = 1.35 meters.
Therefore,
→ Total length of the trench = 1.35m ≈ 1.00 meter .
Hence, a reasonable estimate of the total length of the trench is 1.00 meter.
so, b
Step-by-step explanation:
Answer:
2 meters
Step-by-step explanation:
9 + 10 = ? (im not dumb i wanna give u points its just )
Answers
Answer:21 obviously it’s actually (19) don’t tell anyone
Step-by-step explanation:
How many sixths are there in 2/3
Answers
Answer:
4 Sixths
Step-by-step explanation:
Consider again the tossing of a pair of dice. Find the probability the
sum is greater than 6. (Round to the hundredths)
Answers
Answer:
7/12 or 58.333%
Step-by-step explanation:
There are the 36 possible outcomes.
6+5+4+3+2+1 = 21 are greater than 6
Probability is 21/36 = 7/12 or 58.333%
Giving brainliest to CORRECT answer.
Answers
Answer:
B) (-3,4)
Step-by-step explanation:
I graphed the function on the graph below to show you that vertex of the function.
If this answer is correct, please make me Brainliest!
The answer is B because it appears on my graphing calculator as this.
q/8 = 4/5 I need a step by step explanation please
Answers
Answer:
q = 6 2/5
Step-by-step explanation:
q/8 = 4/5
Using cross products
q*5 = 8*4
5q = 32
Divide each side by 5
5q/5 = 32/5
q = 6 2/5