Answer:
20
Step-by-step explanation:
Given f of x is equal to 1 over the quantity x minus 3 end quantity and g of x is equal to the square root of the quantity x plus 3 end quantity comma what is the domain of f (g(x))?
[–3, ∞)
[–3, 6) ∪ (6, ∞)
(–∞, 3) ∪ (3, ∞)
ℝ
The domain of the composite function is given as follows:
[–3, 6) ∪ (6, ∞)
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given as follows:
[tex](f \circ g)(x) = f(g(x))[/tex]
In this problem, the functions are:
[tex]f(x) = \frac{1}{x - 3}[/tex].[tex]g(x) = \sqrt{x + 3}[/tex]The composite function is of the given functions f(x) and g(x) is:
[tex]f(g(x)) = f(\sqrt{x + 3}) = \frac{1}{\sqrt{x + 3} - 3}[/tex]
The square root has to be non-negative, hence the restriction relative to the square root is found as follows:
[tex]x + 3 \geq 0[/tex]
[tex]x \geq -3[/tex]
The denominator cannot be zero, hence the restriction relative to the denominator is found as follows:
[tex]\sqrt{x + 3} - 3 \neq 0[/tex]
[tex]\sqrt{x + 3} \neq 3[/tex]
[tex](\sqrt{x + 3})^2 \neq 3^2[/tex]
[tex]x + 3 \neq 9[/tex]
[tex]x \neq 6[/tex]
Hence, from the restrictions above, of functions f(x), g(x) and the composite function, the domain is:
[–3, 6) ∪ (6, ∞)
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A rectangle has a length of x-8 and a width of x-9. Which equation below describes the perimeter, P, of the rectangle in terms of x?
a. P=x² - 17x+72
b. P=x-17
c. P = 2x-17
d. P = 4x - 34
*show your work*
Answer:
d.
Step-by-step explanation:
Given a length [tex]l[/tex] and a width [tex]w[/tex], we can express the perimeter of a rectangle as [tex]2(l+w)[/tex].
Therefore the perimeter [tex]P[/tex] can be expressed as
[tex]2\times[(x-8)+(x-9)]\\=2\times(2x-17)\\=4x-34[/tex]
what is the absolute value of -45/6. I need serious help
Answer:
[tex]\frac{15}{2}[/tex]
Step-by-step explanation:
The absolute value of a number is just its distance from zero. In other words, if it's negative, the absolute value would make the number positive. This makes the absolute value [tex]\frac{45}{6}[/tex]. Now, reduce to get[tex]\frac{15}{2}[/tex].
Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$
When [tex]n=0[/tex], we have
[tex]5^{3^0} + 1 = 5^1 + 1 = 6[/tex]
[tex]3^{0 + 1} = 3^1 = 3[/tex]
and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)
Suppose this is true for [tex]n=k[/tex], that
[tex]3^{k + 1} \mid 5^{3^k} + 1[/tex]
Now for [tex]n=k+1[/tex], we have
[tex]5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)[/tex]
so we know the left side is at least divisible by [tex]3^{k+1}[/tex] by our assumption.
It remains to show that
[tex]3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1[/tex]
which is easily done with Fermat's little theorem. It says
[tex]a^p \equiv a \pmod p[/tex]
where [tex]p[/tex] is prime and [tex]a[/tex] is any integer. Then for any positive integer [tex]x[/tex],
[tex]5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3[/tex]
Furthermore,
[tex]5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3[/tex]
which goes all the way down to
[tex]5^{3^k} \equiv 5 \pmod 3[/tex]
So, we find that
[tex]\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3[/tex]
QED
Please help!!! 24 points!!!
Answer:
-24
Step-by-step explanation:
-6 × f(3) - 6 × g(-1) = ?
to answer this we need to find the functional values of the functions at the specified points.
f(3) = -2
we find this easily : we go to x = 3 on the x-axis, and then see there at what y value a vertical line is intersecting the functional graph. the intersection is below the x-axis, so the y value is negative.
g(-1) = 6
we go to x=-1, and we find that a vertical line there will intersect the g curve at y = 6.
and that's really it.
now we need to calculate it all in the main expression :
-6 × -2 - 6 × 6 = 12 - 36 = -24
you remember, that multiplications and divisions have to happen before any addition of subtraction ?
What is the domain and range of the quadratic function given by the equation /(x) = 2(x-4)] - 2
The domain of the function is the set of all real numbers and the range of the function is the set of all values greater than -2
How to determine the domain and the range?The function is given as:
f(x) = 2(x -4)^2 - 2
A quadratic function can take any real number as its input.
So, the domain of the function is the set of all real numbers
The vertex of the above function is:
Vertex = (4, -2)
And the leading coefficient is:
a = 2
The y value of the vertex is;
y = -2
Because the value of a is positive, then the vertex is a minimum.
This means that the range of the function is the set of all values greater than -2
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Sharon is planting tulip
bulbs in her garden. In the
catalog she sees a disclaimer that there is a 1/15 probability that a bulb will not flower. If Sharon plants 90 bulbs, how many tulips can she expect to see in her garden?
Answer:
84 flowers.
Step-by-step explanation:
We must multiply 90 by 1/15 to get 6 bulbs that will not flower. 90-6 is 84.
The coconut milk is in a can but he doesn’t know how much the can holds.
The can is 12 cm high and the diameter is 8 cm.
Using the formula V = π r2 h, work out how much coconut milk is in the can.
Use 3 as a value for π.
Give your answer using the correct units.
Simplify:
x² + 3x + 2 /x² - 4x - 5
x² + 7x + 12 / x²-3x - 28
[tex]\\ \rm\Rrightarrow \dfrac{x^2+3x+2}{x^2-4x-5}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x^2+2x+x+2}{x^2-5x+x-5}[/tex]
[tex]\\ \rm\Rrightarrow {(x+2)(x+1)}{(x-5)(x+1)}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x+2}{x-5}[/tex]
And
[tex]\\ \rm\Rrightarrow \dfrac{x^2+7x+12}{x^2-3x-28}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x^2+4x+3x+12}{x^2-7x+4x-28}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{(x+4)(x+3)}{(x-7)(x+4)}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x+3}{x-7}[/tex]
Please help with this geometry question!
Answer:[tex]\sqrt{303.51}[/tex]
Step-by-step explanation:
The difference in the radii of the two circles is [tex]4.3-1.8=2.5[/tex] inches.
Since the tangent has a length of 2.5 inches, by the Pythagorean theorem, the required distance is
2. Grade points are assigned as follows: A = 4, B = 3, C = 2, D = 1, and F = 0. Grades are weighted according to credit hours. If a student receives one A in three-credit class, one D in three-credit class, three B in three-credit class and two C in one-credit class, what is the student’s grade point average?
Based on the student's grades, and the credit hours, their grade point average is 2.60.
What does the student get as their GPA?First, find the grade points earned:
= (4 x 3) + (1 x 3) + (3 x 3) + (2 x 1)
= 12 + 3 + 9 + 2
= 26
The GPA is:
=Grade points earned / total number of credits
= 26 / (3 + 3 + 3 + 1)
= 26 / 10
= 2.6
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WHAT TWO EQAUL NUMBERS ADD TO THE EVEN NUMER 40
Answer:
20
Step-by-step explanation:
20+20=40
What is the discount and sale price of a $300 item that has been discounted at 10%?
Answer:
Discount: $30 off
New Sale Price: $270
Step-by-step explanation:
$300*10% =
30
$300-30=
$270
or
$300*.1=
30
$300-30=
$270
The difference of the square of a number and 9 is equal to 8 times that number. Find the positive solution.
[tex]x {}^{2} - 9 = 8x \\ x {}^{2} - 8x - 9 = 0 \\ x = \frac{ - ( - 8) + \sqrt[]{( - 8) {}^{2} - 4(1)( - 9)} }{2( {1}^{}) } [/tex]
[tex]x = \frac{8 + \sqrt{64 + 36} }{2} = \frac{8 + \sqrt{100} }{2} = \frac{8 + 10}{2} = 9[/tex]
Answer: x = 9
Step-by-step explanation:
The difference of the square of a number and 9 is equal to 8 times that number. Find the positive solution.
let x = a number
[tex]x^2-9=8x\\x^2-8x-9\\(x-9)(x+1)\\x-9 = 0\\x=9\\x+1=0\\x=-1[/tex]
taking only the positive solution, we get x = 9
A = {1, 2, 6}
B = {x|x is an odd whole number less than 8}.
Find An B.
Answer:
A∩B = { 1 }
Step-by-step explanation:
Consider the sets :
A = {1, 2, 6}
B = {x ;where x is an odd whole number less than 8}
Suppose the numbers of B are natural numbers (not integers).
Then
B = {1 , 3 , 5 , 7}
We obtain :
A = {1, 2, 6} and B = {1 , 3 , 5 , 7}
The intersection of A and B or the set A∩B :
is the set of the common numbers of A and B.
Then
A∩B = { 1 }
The set A intersection B(or, A∩B) for the given set A and set B exists {1}.
What is A intersection B, (A∩B)?"The set A intersection B(or, A∩B) exists described as the set composed of all elements that belong to both A and B".
The intersection of a set A with a B exists the set of elements that exist in both sets A and B. The intersection exists represented as A∩B.
The intersection of two mathematical objects exists where they overlap. For geometric objects, the intersection exists as a point or group of points where the objects cross.
For numerical or non-numerical sets, the intersection exists every number or object the two sets contain in common.
Given: A = {1, 2, 6}
B = {x | x is an odd whole number less than 8}.
From the above information, we get
⇒ B = {1, 3, 5, 7}
If A = {1, 2, 6} and B = {1, 3, 5, 7}
then A∩B = {1, 2, 6} ∩ {1, 3, 5, 7}
A∩B = {1}
Therefore, the correct answer A∩B exists {1}.
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PLEASE IF ANYONE CAN HELP I HAVE 35 MINUTES LEFT 1-8 ANSWERS ONLY WILL DO THANK YOU
Answer:
1. x=2 2.
y=1
Step-by-step explanation:
Im sorry I TRIED :(
Is this Network a HAMILTONIAN Circuit? If so write the path.
The path of the given Hamiltonian diagram is A, E, B, C, D, F. See explanation below.
What is a Hamiltonian Path?A Hamiltonian path, also known as a traceable path, is one that visits each vertex of the graph precisely once.
A traceable graph is one that contains a Hamiltonian path.
Hence, the path is given as;
A, E, B, C, D, F
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As seen in the diagram below, Shandra is building a walkway with a width of feet
to go around a swimming pool that measures 8 feet by 6 feet. If the total area of the
pool and the walkway will be 168 square feet, how wide should the walkway be?
The walkway should be about 2.57feet.
What is the total surface area?
The total surface area of the building is the sum of the total faces of an object contains.
The formula is expressed as:
TSA = 2(lw + wh + lh)
where,
l is the length ,w is the width , h is the height
Calculation
Given the following parameters
TSA = 168 square feet
length = 8 feet and Height = 6 feet
Required
Width of the walkway, Substitute the given values in the formula
168 = 2(lw + wh + lh)
84 = (8(6) + 6w + 8w)
84 = 48 + 14w
4w = 84 - 48
14w = 36
w = 2.57feet
The walkway should be about 2.57feet.
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Super confused need help
If two points on a line are A(10, −3) and B(12, 9), the rise is __________, and the run is __________, so the slope of the line is __________.
The rise is the difference in y-coordinates:
y₂ - y₁ = 9 - (-3) = 12The run is the difference in x-coordinates:
x₂ - x₁ = 12 - 10 = 2The slope is the quotient of rise over run:
m = 12/2 = 6========================
If two points on a line are A(10, −3) and B(12, 9), the rise is 12, and the run is 2, so the slope of the line is 6.
Select the correct answer.
Which of the nets below will make a closed cube?
Mariatu Yakubu
The net that represents a cube is (b) net b
How to determine the net?A cube has 6 faces
This means that the net must have 6 faces
For a net to represent a cube, there must be four adjacent faces
And 2 two adjacent faces
Where
One of the two adjacent faces is at the end of the fourth faceThe other is at the 3rd positionBoth 2 faces do not face the same directionThe net that represents the above scenario is net (b)
Hence, the net that represents a cube is (b) net b
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The Apollo space program lasted from 1967 until 1972 and included 13 missions.The missions lasted from as little as Z hours to as long as 30ours.The duration of each flight is listed below. 9 195 241 295 142% 142% 147 a.Expain why the flight times b.Find Mean and the Median of flight times c.Find range and the standard deviation of flight times
The mean and the median based on the information given will be 166.08 and 195.
How to calculate the value?It should be noted that the mean is also the average. It's gotten by adding all the numbers and dividing by 13. This will be 166.08.
The median is simply the middle number. This will be 195.
The range will be:
= 301 - 7
= 294
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The following contingency table gives the results of a sample survey of Sowetan male and female respondents regarding their preferred mobile phone service provider.
What is the probability of selecting a respondent who does not prefer Cell C?
a.
0.2250
b.
0.50
c.
0.3750
d.
0.65
e.
0.7750
The probability of selecting a respondent who does not prefer Cell C is 0.775
How to determine the probability?The complete question is in the attached image
From the attachment, we have
Prefer cell C = 90
Total = 400
So, the number of respondents that do not prefer cell C is
Do not = 400 - 90
Do not = 310
The probability is then calculated as:
P = 310/400
Evaluate
P = 0.775
Hence, the probability of selecting a respondent who does not prefer Cell C is 0.775
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Ross Martin arrived at the following tax information gross salary 56,145 interest earnings 205 dividend income 65 standard deduction 12,000 itemized deductions 11,250 adjustments to income 1200 what amount with Ross report as taxable income income
The amount that Ross report as taxable income will be $31965.
What is a taxable income?Taxable income refers to the base upon which an income tax system imposes the tax.
In other words, the taxable income is the income over which the government imposed tax. It includes some or all items of income and is reduced by expenses and other deductions.
From the information:
Gross salary = $56,145
Interest earnings = $205
Dividend income = $65
Standard deduction = $12,000
Itemized deductions = $11,250
Adjustments to income = $1,200
The taxable income is given by:
= Gross salary + Interest earnings + Dividend income - Standard deduction - Itemized deductions - Adjustment to income
= 56145 + 205 + 65 - 12000 - 11250 - 1200
= $31965
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PLEASE HELP EDGE2022 Which inequality is represented by the graph?
y ≥ –2(x + 1)2 + 5
y ≤ –2(x + 1)2 + 5
x ≥ –2(y + 1)2 + 5
x ≤ –2(y + 1)2 + 5
The inequality graphed is the one in the first option.
Which inequality is represented by the graph?
On the graph we can see a solid parabola, the parabola opens downwards, and we can see that the vertex of the parabola is on the point (-1, 5).
And the shaded region is above the parabola.
Then the inequality is of the form:
y ≥ parabola.
By knowing where is the vertex, we know that:
parabola = -a*(x + 1)^2 + 5
Then the correct option is the first one.
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Please help me answer this question, 20 POINTS!
Buns,cost 40p each. Cakes cost 55p each. I spend exactly £4.35 on buns and cakes.
How many of each did I buy?
It's 4 buns & 5 cakes
Hope my explanation to the other one helps, if not, you can draw them; while following the steps & you may get it better.
E.g draw a box for the bun & a circle for the cake, then, adding them up to get the 95p. Also, you keep taking away from 435p
The graph of the function f(x) = (x - 3)(x + 1) is shown.
Ty
-10-8-6
10
8
6
-6
8
-10-
6
10
X
Which describes all of the values for which the graph is
positive and decreasing?
O all real values of x where x < -1
O all real values of x where x < 1
O all real values of x where 1
O all real values of x where x > 3
Answer:
all real values of x where x < -1
Step-by-step explanation:
See attached graph.
Imogen buys some sandwiches costing £3.50.
She has a 20% off coupon.
How much discount will Imogen receive?
K
4
Teacher increases spatial awareness for children as they use position words and provide experience through mapping and manipulating shapes.
a. True
b. False
It is true teachers can increase spatial awareness as they use position words or implement mapping and shape manipulation.
Whatis spatial awareness?This refers to the ability to understand the position of one's body in relation to space and other objects as well as understanding how location and movement work.
How can spatial awareness be increased in children?In children spatial awareness can be increased through:
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Dana believes that she needs to study for at least 14 hours to be prepared for her monthly accounting test. If she can study for 4 hours per day, what is the minimum number of days that she should allow to study for the test?