We have to solve the equation
\(\sqrt[]{x+3}=x+1\)To do this we are going to take the second power in both sides of the equation. Then
\(\begin{gathered} \sqrt[]{x+3}=x+1 \\ (\sqrt[]{x+3})^2=(x+1)^2 \\ x+3=x^2+2x+1 \\ x^2+2x+1-x-3=0 \\ x^2+x-2=0 \end{gathered}\)Now we use the general formula for quadratic functions
\(\begin{gathered} x=\frac{-1\pm\sqrt[]{1^2-4(1)(-2)}}{2(1)} \\ =\frac{-1\pm\sqrt[]{1+8}}{2} \\ =\frac{-1\pm\sqrt[]{9}}{2} \\ =\frac{-1\pm3}{2} \end{gathered}\)Then
\(\begin{gathered} x=\frac{-1+3}{2}=\frac{2}{2}=1 \\ or \\ x=\frac{-1-3}{2}=-\frac{4}{2}=-2 \end{gathered}\)Now, in a rational equation we have to be careful; since we have to take the power to solve it, it appears that the equation has two solutions but, as we are about to see, this is not the case. What we have to do know is to plug the values we obtained in the original equation to see which one is in fact a solution.
Let's see if x=1 is a solution, pluggin the value in the equation we have
\(\begin{gathered} \sqrt[]{1+3}=1+1 \\ \sqrt[]{4}=2 \\ 2=2 \end{gathered}\)hence, x=1 is a solution of the equation.
Let's see if x=-2 is a solution:
\(\begin{gathered} \sqrt[]{-2+3}=-2+1 \\ \sqrt[]{1}=-1 \\ 1=-1 \end{gathered}\)but this is a contradiction, then x=-2 is not a solution.
Therefore the solution to the equation is x=1.
Select the number that round to 387.4 when rounded to the nearest tenth.
A. 387.461
B. 387.344
C. 387.309
D. 387.352
E. 387.779
Answer:
D
Step-by-step explanation:
When rounding, the number 5 is rounded up. So the number 387.352 will be rounded up 387.4. Other options are not suitable. Correct answer is "D"
If you think my answer is the best, please mark it as the Brainliest.
Thank you! :))
1. If the demand (price) function is P(Q) = 100 − 4Q, find expressions for revenue function, R(Q) and marginal revenue function, MR(Q). Hence estimate the MR for 10 units of sales.
for each parallel lines. you are given the measure of one angle
Answer:
The question is not complete
a lorry travels at a speed of 54km/he how far does it go in 1minutes?
Answer:
PLEASE MARK AS BRAINLIEST
Step-by-step explanation:
Speed per hour = 54 km
We have to find Speed per minute
For that...
60 minutes ---- 54 km(cuz, 1 hr = 60 minutes
1 minute -----?
=54/60 km/minute
=9/10 km/minute
= 0.9 km/minute
SO THE LORRY WILL TRAVEL 0.9 KM IN A MINUTE
A six sided dice is rolled. The set of equally likely outcome is (1,2,3,4,5,6). Find the probability of rolling a number less than 12.
The probability of rolling a number less than 12, given that all sides in the dice have an equally likely outcome, is 1 .
How to find the probability ?The probability of an event happening is defined as the number of ways the event can happen divided by the total number of possible outcomes.
Since there is only one way for the event "rolling a number less than 12" to happen (i.e., any of the six possible outcomes), and there are six possible outcomes in total, the probability of rolling a number less than 12 :
= 1 / 6 + 1 / 6 + 1 / 6 + 1 / 6 + 1 / 6 + 1/ 6
= 1
This is because all the numbers are lower than 12.
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Assume that the halting language \(H_T_M\) is reducible to
some language B (\(H_T_M\) \($\leq$\) \(_m\) B). Is it possible that is decidable? Answer true/false and explain. Please help me this answer?
H_TM is reduced to HALT_TM and as such, HALT_TM is undecidable.
How to Interpret Machine Language?A language is referred to as Decidable or Recursive if there is a Turing machine that accepts and halts on every input string w. This tells us that every decidable language is Turing-Acceptable.
Now, we are told that the halting language is reducible to some language B. This means that it is an undecidability via reduction.
Now, Using the idea that “ If A is undecidable and reducible to B, then B is undecidable.” Suppose R decides HALT_TM, we will construct S to decide ATM .
S = “On input (M, B)
This means that H_TM is reduced to HALT_TM and as such, HALT_TM is undecidable.
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Which function has the same range as \(f(x)= - 2\sqrt{x} =-3 + 8\\\)
Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].
To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).
The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.
In other words, the range of f(x) is (-∞, 5].
So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.
Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.
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The price of a train ticket consists of an initial fee of
$
5
$5dollar sign, 5 plus a fee of
$
2.75
$2.75dollar sign, 2, point, 75 per stop. Julia has
$
21
$21dollar sign, 21 and would like to travel
50
5050 kilometers. She wants to know the largest number of stops she can afford to buy on a ticket
Step-by-step explanation:
this is very difficult to read.
if I understand correctly, then a train ticket costs first an initial fee of $5, and then $2.75 per stop.
Julia has $21.
to find the max. number of stops she can buy, we need first to deduct the $5 initial fee. she would need to pay that no matter how many stops she wants to have.
so, she has 21-5 = $16 available for stops.
as 1 so costs $2.75, we need to find out how often 2.75 fits into 16.
that is what division is for.
by calculating 16/2.75 we find out exactly how often 2.75 fits into 16.
now, with a calculator this is easy.
but let's say, we need to do this by hand.
then we should consider 2.75 as a fraction.
it is, in fact, 2 3/4 or 8/4 + 3/4 = 11/4.
remember, dividing by a fraction is the same as multiplying by the upside-down fraction.
so, 16/ 11/4 = 16 × 4/11.
to understand it even better we can write 16 as fraction too : 16/1.
that means we have
16/1 × 4/11 = (16×4) / (11×1) = 64/11 = 5 9/11 = 5.818181...
so, she can buy max. 5 stops. for the 6th stop she does not have the full money anymore.
Angle FGH= Angle FEI. complete the proof tvaf angle GHI= angle EIH!
Answer:
As follows,
Step-by-step explanation:
Statement Reason
GH=EI CPCTC
△GHI≅△EIH By SSS axiom.
Mila bought a computer with a price tag of $1,200.
After tax the total was $1,284. What was the rate of the
tax?
Answer: 7%
Step-by-step explanation:
It costs $350 to spend 4 nights at the Econo Motel. It costs $475 to spend 6 nights at the Bluebird Inn. Which of these statements is true?
Answer: A
Step-by-step explanation: The bluebird Inn is more expensive per night because 475 is greater than 350.
PLEASE HELP I WILL MARK YOU BRAINLEIST
\(\tt Step-by-step~explanation:\)
We could see that the size of both images does not change, so it is not a dilation. The image is not mirrored either, so it is not a reflection. Finally, the image does not seem to change place that much from the preimage, so it should not be a translation, either. That means our answer is a rotation, because the image rotated about 180º.
\(\large\boxed{\tt Our~final~answer:~Rotation}\)
What is the y-intercept of the line representing Beatrice's monthly music subscription bill as a function of the number of songs she downloaded?
$$
The y-intercept of the line representing Beatrice's monthly music is 20
How to determine the y-intercept of the lineFrom the question, we have the following parameters that can be used in our computation:
y = -.95x + 20
To calculate the y-intercept of the line, we set x = 0
So, we have
y = -.95 * 0 + 20
Evaluate
y = 20
Hence, the y-intercept of the line representing Beatrice's monthly music is 20
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Question
What is the y-intercept of the line representing Beatrice's monthly music subscription bill as a function of the number of songs she downloaded?
The equation is y = -.95x + 20
slove for x9x-3-8x=7-×
The given expression : 9x - 3 -8x = 7 -x
Simplify for x
\(\begin{gathered} 9x-3-8x=7-x \\ 9x-3-8x-7+x=0 \\ 9x-8x+x-3-7=0 \\ 2x-10=0 \\ 2x=10 \\ x=5 \end{gathered}\)x = 5
Answer : x = 5
Need help with these two problems
how would you factorise 3y + 12
Answer:
lol it so easy man 3(y+4) is the answer
Find the area of shaded region.
Answer: A is 36 cm^2
Step-by-step explanation:
"What is the rest wavelength of an emission line observed at 2148 nanometers in a galaxy 100
Megaparsecs away from the Milky Way? Your answer should be significant to four digits."
The rest wavelength of the emission line observed at 2148 nanometers in the galaxy 100 million light-years away is approximately 2103 nanometers.
The rest wavelength of an emission line can be determined by applying the concept of redshift, which is a phenomenon observed in astrophysics where light from distant objects is shifted towards longer wavelengths due to the expansion of the universe.
In this case, the emission line is observed at 2148 nanometers (or 2.148 micrometers) in a galaxy located 100 million light-years away. To calculate the rest wavelength, we need to consider the redshift factor. Redshift, denoted by z, is defined as the observed wavelength divided by the rest wavelength minus 1.
Given that the observed wavelength is 2.148 micrometers and the galaxy is located 100 million light-years away, we need to convert the distance into a redshift factor using the cosmological relationship between redshift and distance. Assuming a standard cosmological model, we can use the Hubble constant to estimate the redshift.
The Hubble constant represents the rate at which the universe is expanding. Taking a typical value of the Hubble constant as 70 kilometers per second per megaparsec, we find that the redshift factor, z, is approximately 0.021.
To determine the rest wavelength, we rearrange the redshift equation as \((observed wavelength) = (1 + z) \times (rest wavelength)\). Substituting the values, we get \((2.148 micrometers) = (1 + 0.021) \times (rest wavelength).\)
Simplifying the equation, we find the rest wavelength to be approximately 2.103 micrometers or 2103 nanometers.
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4 2/3 ÷ 7 = ?
help pleaseee
Answer:
0.66666666666
Step-by-step explanation:
this is a real answer
Find the area of the shaded portion in the equilateral triangle with sides 6. Show all work for full credit.
(Hint: Assume that the central point of each arc is its corresponding vertex.)
The area of the shaded portion in the equilateral triangle with sides 6 is 9√3 - 36π.
To find the area of the shaded portion in the equilateral triangle, we need to determine the area of the three arcs and subtract it from the area of the equilateral triangle.
First, let's find the area of one arc. Each arc has a radius equal to the length of the side of the equilateral triangle, which is 6. The formula for the area of a sector is A = (θ/360)πr², where θ is the central angle in degrees.
In an equilateral triangle, each interior angle measures 60 degrees, so the central angle of the arc is 120 degrees (360 degrees divided by 3). Plugging these values into the formula, we get A_arc = (120/360)π(6)² = (1/3)π(6)² = 12π.
Since there are three identical arcs, the total area of the arcs is 3 times the area of one arc, which is 3(12π) = 36π.
Now, let's find the area of the equilateral triangle. The formula for the area of an equilateral triangle is A_triangle = (√3/4)s², where s is the length of a side.
Plugging in the value of the side length, we have A_triangle = (√3/4)(6)² = (√3/4)(36) = 9√3.
Finally, we subtract the area of the arcs from the area of the equilateral triangle to find the shaded portion's area: A_shaded = A_triangle - A_arc = 9√3 - 36π.
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Ken owns 500 shares of LaceNBrace, which makes hockey equipment. He receives a notice stating the company will be paying $0.15 dividend per share. What is the total dividend payment he receives for that quarter? O $750 O $8.50 O $7.55 O $75
Ken will receive a total dividend payment of $75 for that quarter.
We have to given that,
Ken owns 500 shares of LaceNBrace, which makes hockey equipment.
And, He receives a notice stating the company will be paying $0.15 dividend per share.
Now, For the total dividend payment Ken receives for that quarter, we can multiply the dividend per share by the total number of shares he owns:
= $0.15 per share x 500 shares
= $75
Therefore, Ken will receive a total dividend payment of $75 for that quarter.
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FIND THE TOTAL SURFACE AREA
30 Length
12 base
9 Hieght
The surface area of the rectangular prism is 1476 square units
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
30 mm by 12 mm by 9 mm
The surface area of the rectangular prism is calculated as
Surface area = 2 * (Length * Width + Length * Height + Width * Height)
Substitute the known values in the above equation, so, we have the following representation
Area = 2 * (30 * 12 + 30 * 9 + 12 * 9)
Evaluate
Area = 1476
Hence, the area is 1476 square units
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find x
a.204
b.90
c.78
d.102
Answer:
Hope you can understand my handwriting though
1. If F(x) = 2x-10 then what is f(-3)
2 .If F(x) = x^2 + 7 then what is f (2)
Answer:
1. f(-3) = -16
2. f(2) = 11
Step-by-step explanation:
just replace x with the number
1. f(-3)= 2(-3)-10
f(-3)= -6-10
f(-3)= -16
2. f(2)= 2^2+7
f(2)= 4+7
f(2)=11
Evaluate the function
f(x) = 3x^2 + 4x + 19
Find f(-7)
Answer:
Step-by-step explanation:
3
x
2
+
4
x
+
19
−
f
(
x
)
=
0
A virus jumps from monkeys to humans. The number of people P(t) who have been infected with the virus t weeks after the jump grows logistically. Suppose that initially 10 people are infected with the virus and that the continuous growth rate is 1.78. It is estimated that in the long run approximately 5000 people will have been infected with the virus. The virus is spreading the fastest approximately:________
a. 3.5 weeks after the jump.
b. 4.0 weeks after the jump.
c. 4.5 weeks after the jump.
d. 5.0 weeks after the jump.
e. None of the above is correct.
Answer:
e. None of the above is correct.
Step-by-step explanation:
The general formula for exponential growth is;
P= a(1 + r)^t
Where;
P = total number infected after a given time interval
a = initial number of infected people
r = growth rate of infection
x= time taken in weeks
Hence;
5000= 10(1 + 1.78)^t
5000/10 = (1 + 1.78)^t
500 = (1 + 1.78)^t
log 500 = tlog(1 + 1.78)
t = log 500/log(1 + 1.78)
t = 2.699/0.444
t = 6 weeks
The virus is spreading the fastest approximately 5.0 weeks after the jump.
What is exponential?An exponential equation is an algebraic expression that has an equality and at least one unknown in one of its exponents. To be considered an equation, an expression must have at least one unknown, which is an unknown number represented by a letter, and an equality relationship.
The general formula for exponential growth is;
P= a(1 + r)^t
Where;
P = total number infected after a given time interval = 5000a = initial number of infected people = 10r = growth rate of infection = 1.78x= time taken in weeksHence;
\(5000= 10(1 + 1.78)^t\\5000/10 = (1 + 1.78)^t\\500 = (1 + 1.78)^t\\log 500 = tlog(1 + 1.78)\\t = log 500/log(1 + 1.78)\\t = 2.699/0.444\\t = 6 weeks\)
\(t=6-1=5 weeks\)
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What is the area of this polygon?
A = 220 cm2
A = 242 cm2
A= 248 cm2
A = 270 cm2
Answer:
A = 220 cm²
Step-by-step explanation:
The area of the rectangle is :
11cm x 18cm198 cm²The area of the triangle is:
1/2(15cm - 11cm)(18cm - 7cm)1/2(4cm)(11cm)1/2(44cm²)22 cm²The total area is:
198 cm² + 22cm²220 cm²-Chetan K
The area of this polygon is equal to 220 cm².
Area of Compound ShapesThis exercise requires your knowledge about the area of compound shapes. For solving this, you should:
Identify the basic shapes; Calculate your individual areas; Sum each area found.For finding the area, the steps are presented below.
STEP 1 - Identify the basic shapes.
The polygon is composed of one triangle and one rectangle. Therefore, you should sum the area of these geometric figures.
STEP 2 - Find the area of the triangle.
Area of the triangle - \(A_{triangle}=\frac{bh}{2}\) . The figure shows:
b= length of the base= 18-7=11 cm
h=height=15-11=4cm
Then, \(A_{triangle}=\frac{bh}{2}=\frac{11*4}{2}=\frac{44}{2} =22 cm^2\).
STEP 3 - Find the area of the rectangle.
Area of the rectangle- \(A_{rectangle}=bh\) . The figure shows:
b= length of the base= 18 cm
h=height= 11 cm
Then, \(A_{rectangle}=bh=18*11=198cm^2\) .
STEP 4 - Find the area of the polygon .
\(A_{polygon}=A_{triangle}+A_{rectangle}\\ \\ A_{polygon}=22+198\\ \\ A_{polygon}=220cm^2\)
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An ecological group suspects lobsters are consuming dangerous levels of mercury in a region of the world. Dangerous levels of mercury are classified when they reach beyond 6.5 parts per million. A random sample of 25 lobsters in the region were tested and the data is shown in the stemplot.
Stemplot for Mercury Levels.
2|2 4;
2|;
3|1 4;
3|5 8;
4|0 2;
4|5 6;
5|0 1 3 3 4;
5|6 8 9;
6|3 4;
6|6 7 8;
7|1 2;
7|
Key: 2|2 = 2.2 parts per million
Part A: What proportion of the lobsters in the sample have dangerous levels of mercury in their systems? (4 points)
Part B: Construct and interpret a 95% confidence interval for the mean mercury levels of the lobsters if the sample of 25 lobsters has a mean mercury level of 5.05 parts per million and standard deviation of 1.45 parts per million. (6 points)
Part A: 5 out 25 lobsters have dangerous levels of mercury
Part B: the 95% confidence interval is given by (4.45, 5.65)
since everything is given all I had to do is find the critical value which can be found from the resource packet = 2.064
Using the formula we find 5.05+-2.064*1.45/5 = ( 4.45,5.65)
For this case, we have 95% of confidence that the true mean for the average number of lobsters with dangerous levels of mercury is between 4.45,5.65
Select the correct answer.
Which statement correctly compares the graph of function g with the graph of function ??
FE) = e²-
g(x) = ² - 4
O A.
OB.
O C.
O D.
The graph of function g is a horizontal shift of the graph of function to the right.
The graph of function g is a vertical stretch of the graph of function f.
The graph of function g is a vertical compression of the graph of function f.
The graph of function g is a horizontal shift of the graph of function f to the left.
Reset
Next
A statement that correctly compares the graph of function g with the graph of function f include the following: C. The graph of function g is a vertical compression of the graph of function f.
What is a dilation?In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.
Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.
When the parent function \(f(x) = e^x -4\) is vertically compressed by a scale factor of 1/2, the transformed function g(x) is given by the following equation;
g(x) = kf(x)
g(x) = 1/2f(x)
\(g(x) = \frac{1}{2} e^x -4\)
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Determine the surface area and volume. Note: The base is a square.
Answer:
volume=60cm3, surface area=96cm2
Step-by-step explanation:
volume=1/3×(6×6)×5
=60cm3
surface area= 4(1/2×6×5)+(6×6)
=96cm2