The domain for the function f(x) = 2x² + 5√(x + 2) is all real numbers greater than or equal to -2.
In interval notation, we can express this as:
Domain: x ∈ [-2, ∞)
Given is a function f(x) = 2x² + 5√2, we need to determine the domain of the function,
To complete the statement, we need to determine the domain for the function f(x) = 2x² + 5√(x + 2).
The domain of a function represents all the possible values of x for which the function is defined.
In this case, we need to consider two factors that can restrict the domain:
For a real number to be a valid input for the square root (√), the expression inside the square root (x + 2) must be greater than or equal to 0.
Otherwise, we would encounter the issue of taking the square root of a negative number, which is not defined in the real number system.
There are no other restrictions in the function that would cause it to be undefined for certain values of x.
Since x² is defined for all real numbers, there are no issues there.
Let's solve the inequality for the square root expression:
x + 2 ≥ 0
Subtract 2 from both sides:
x ≥ -2
So, the domain for the function f(x) = 2x² + 5√(x + 2) is all real numbers greater than or equal to -2.
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The area of a rectangle is 0.8 square units. The length is 3.2 units and the width is x units.What is the value of x?
What is 8q+3(10q^2+2)+8
if f(x) = (x+1)^-1 and g(x) = x-2, what is the domain of f(x) divided by g(x)
You invest $3,756.00 and buy 100 shares of a company's stock. Their value increases by 12%. How much is each share worth?
Answer:
Each share worth is $42.0672 .
Step-by-step explanation:
As given
You invest $3,756.00 and buy 100 shares of a company's stock.
Their value increases by 12%.
12% is written in the decimal form
[tex]= \frac{12}{100}[/tex]
= 0.12
Share value increase = 0.12 × Investment cost
= 0.12 × 3756
= $450.72
Total value of shares becomes after increases of 12% = Share value increase + Investment cost .
Total value of shares becomes after increases of 12% = $3756+ $450.72
= $4206.72
[tex]Each\ shares\ worth = \frac{Total\ value\ of\ shares\ after\ increase\ of\ 12\%}{Number\ of\ shares}[/tex]
[tex]Each\ shares\ worth = \frac{4206.72}{100}[/tex]
Each shares worth = $42.0672
Therefore the each share worth is $42.0672 .
A cylinder is a type of prism.
true
false
Find the probability that 4 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places.
The probability that 4 randomly selected people all have the same birthday, ignoring leap years, is 0.00000002 when rounded to eight decimal places.
Explanation:The problem is asking about the probability that 4 people, selected at random, all have the same birthday. Since we're ignoring leap years, each person can have a birthday on any of 365 days of the year. The probability that the first person has a birthday on any day of the year is 1, because there's no restriction on when their birthday can be. However, the probability that the second, third, and fourth people share this same birthday becomes much less.
Given that we've selected a specific day for the first person, the second person has a 1 in 365 chance (or approximately a 0.00274 chance) of having that same birthday. The same applies for the third and fourth person. Since each of these events is independent (meaning the outcome of the first event doesn't change the probability of the next event), we can find the total probability by multiplying the individual probabilities together: 1 (for the first person) * 0.00274 (for the second person) * 0.00274 (for the third person) * 0.00274 (for the fourth person) = 0.000000020500. To the eight decimal place, this becomes 0.00000002.
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The table below represents an exponential function.
table represents an exponential function.
What is the interval between neighboring
x-values shown in the table?
What is the ratio between neighboring y-values?
In given table of exponential function,
The interval between neighboring x-values is of 1 unit.
The ratio is 4 between neighboring y-values
Observing given table.
To find interval between neighboring x-values . We have to take difference between consecutive x - values.
[tex]1-0=2-1=3-2=4-3=5-4=1[/tex]
Since, in every consecutive x- values , difference of 1 is present.
So, The interval between neighboring x-values is of 1 unit.
To find ratio between neighboring y-values , we have to take ratio of consecutive y - values.
[tex]\frac{4}{1}=\frac{16}{4}=\frac{64}{16}=\frac{256}{64}=4[/tex]
Thus, The ratio is 4 between neighboring y-values
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which of the following could be the equation of the graph shown below
Answer:
-4x+2y+-6 and y=3x-2
Explain why two similar right triangles will have the same cosine ratios.
The triangle JKL shown on the coordinate grid below is reflected once to map onto triangle J'K'L': Triangle JKL is drawn on a 4 quadrant coordinate grid with vertices J is at 8, 1. K is at 5, 7. L is at 3, 4. If vertex L' is at (−3, 4), what are the coordinates of vertex J'?
Answer:
The vertex J' is at (-8,1).
Step-by-step explanation:
If is given that the triangle JKL reflected once to map onto triangle J'K'L'.
The vertices of the triangle JKL are J(8,1), K(5,7) and L(3,4). The vertex L'(-3,4).
[tex]L(3,4)\rightarrow L'(-3,4)[/tex]
It is in the form of
[tex](x,y)\rightarrow (-x,y)[/tex]
Since the y-coordinate remains same and the sign of x coordinate is changed. It shows the reflection across the y axis.
The vertices of image are,
[tex]K(5,7)\rightarrow K'(-5,7)[/tex]
[tex]J(8,1)\rightarrow J'(-8,1)[/tex]
Therefore the vertex J' is at (-8,1).
Find the sum of the first 15 terms of the series 4+16+64+256+...
a rectangle has sides 2x + 3 and x - 4. what is the perimeter of the rectangle
Find the area of a regular hexagon with a 48-inch perimeter.
48√3 in2
96√3 in2
192√3 in2
in2 means inches squared
SOMEONE PLEASE HELP!!!!
Which area formula or formulas show(s) a joint variation?
I A=s^2
II A=pir^2
III A=l*w
Select one:
a. III only
b. II and III
c. II only
d. I, II, and III
Answer:
Step-by-step explanation:
Factor the polynomial below.
30x^2 + 15x^2 +10x
What are the solutions of the equation z2-12z+36=0
A movie theater sold 422 tickets on Friday. On Saturday, they sold 518 tickets. What was the approximate percentage that ticket sales increased on Saturday?
A phone banking password consists of 2 letters followed by 4 digits. The letters B, I, S, and O are not used, and the last digit cannot be 0. How many different passwords are possible?
5,148,000
4,840,000
4,356,000
3,175,524
There are 4,356,000 different passwords are possible.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A phone banking password consists of 2 letters followed by 4 digits.
And, The letters B, I, S, and O are not used, and the last digit cannot be 0.
Hence, We can formulate;
Number of different passwords are possible are,
⇒ 22 × 22 × 10× 10 × 10 × 9.
⇒ 4,356,000
Thus, There are 4,356,000 different passwords are possible.
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The circle shown below has ab and bc as its tangents: ab and bc are two tangents to a circle which intersect outside the circle at a point
b. if the measure of arc ac is 160°, what is the measure of angle abc? 80° 40° 60° 20°
Answer:
Answer: 20°
Step-by-step explanation:
help factoring trinomial
need 2 numbers when added = 5 and when multiplied = -24
answer is D
-3+8 = 5
-3*8 = -24
What is the correct way to write 6.3 × 10^8 in standard notation? (25 Points)
In the case of a triangle with angle measures of 30°, 60°, and 90° and a hypotenuse length equal to x, what is the perimeter of the triangle in terms of x?
For a 30-60-90 triangle with a hypotenuse of length x, the perimeter would be defined by the formula x(3 + √3)/2.
Explanation:In terms of mathematics, the question discusses a right triangle, specifically a 30-60-90 triangle. When it comes to a 30-60-90 triangle, certain ratios of sides exist. In this triangle, the ratio of the lengths of the sides opposite the 30°, 60° and 90° angles are 1:√3:2. Given that the length of the hypotenuse is x, the sides opposite the 30° and 60° angles would be x/2 and x√3/2, respectively. So, the perimeter of the triangle could be determined by adding up the lengths of all three sides i.e., x + x/2 + x√3/2. The simplified form of this equation indicates that the
perimeter
of the triangle = x(1 + 1/2 + √3/2), which can also be written as x(3 + √3)/2.
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A delivery truck uses $375 in gasoline during a 3 week period. if the truck is driven 5 days per week, how much is spent on gas each day?
Final answer:
Approximately $17.86 is spent on gas each day.
Explanation:
To find out how much is spent on gas each day, we need to divide the total amount spent on gas by the number of days in the 3-week period.
First, let's calculate the number of days in 3 weeks. Since there are 7 days in a week, there are 3 × 7 = 21 days in 3 weeks.
Next, we divide the total amount spent on gas, $375, by the number of days: $375 ÷ 21 = $17.86
Therefore, approximately $17.86 is spent on gas each day.
which angles are corresponding angles? check all that aply
The diagram below shows equilateral triangle ABC sharing a side with square ACDE. The square has side lengths of 4. What is BE? Justify your answer.
BE is [tex]7.73[/tex]
What is Square?
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.
What is equilateral triangle?
In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.
According to question, The diagram below shows equilateral triangle ABC sharing a side with square ACDE.
We have to find BE.
Now, AB [tex]= 4[/tex] and AE [tex]= 4.[/tex]
The angle EAB is [tex]90+60 = 150[/tex]°
Using the law of the cosines, we get
[tex]BE^2 = AE^2 + AB^2 - 2(AB)(AE)cos(150)[/tex]
[tex]=4^2 + 4^2 -[/tex][tex]2(4)(4)[/tex]×[tex]\frac{\sqrt{3} }{2}[/tex]
⇒[tex]BE=7.73[/tex]
Hence, we can conclude that BE is [tex]7.73[/tex]
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A point lies in quadrant 2. If it is rotated 180 degrees counterclockwise, which quadrant will the point come to rest?
When a point in quadrant 2 is rotated 180 degrees counterclockwise, it will land in quadrant 4.
A point lies in quadrant 2. If it is rotated 180 degrees counterclockwise, which quadrant will the point come to rest?
Begin in quadrant 2 (Q2).Rotating 180 degrees counterclockwise leads to the point's final position in quadrant 4 (Q4).I need help with this problem and a few others
Women athletes at the university of colorado, boulder, have a long-term graduation rate of 67% (source: the chronicle of higher education). over the past several years, a random sample of 38 women athletes at the school showed that 21 eventually graduated. does this indicate that the population proportion of women athletes who graduate from the university of colorado, boulder, is not less than 67%? use a 5% level of significance. find the p-value of the test statistic (round to the nearest ten thousandths).
The solution would be like this for this specific problem:
H0: p = p0, or
H0: p ≥ p0, or
H0: p ≤ p0
find the test statistic z = (pHat - p0) / sqrt(p0 * (1-p0) / n)
where pHat = X / n
The p-value of the test is
the area under the normal curve that is in agreement with the alternate
hypothesis.
H1: p ≠ p0; p-value is the area in the tails greater than |z|
H1: p < p0; p-value is the area to the left of z
H1: p > p0; p-value is the area to the right of z
Hypothesis equation:
H0: p ≥ 0.67 vs. H1: p < 0.67
The test statistic is:
z = ( 0.5526316 - 0.67 ) / ( √ ( 0.67 * (1 - 0.67 ) / 38 )
z = -1.538681
The p-value = P( Z < z
)
= P( Z < -1.538681 )
= 0.0619
Relations and functions need help please.
NEED HELP ASAP PLEASE!!!