Using it's concept, the domain of the function is given as follows:
{x| –2 ≤ x <= 5}
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function.
The function described is defined for x between -2 and 5, hence the domain is given by the following interval:
{x| –2 ≤ x <= 5}
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Answer:
{x| –2 ≤ x < 5}
Step-by-step explanation:
David's car was valued at $38,000 in the year 2007. If it is continuously depreciating in value by 6% every year, how much will it be worth in 2017
The car will be worth $20467 in 2017
How to determine the worth in 2017?The given parameters are:
Initial value, a = 38000
Depreciation rate, r = 6%
The value of the car after x years is represented by the following exponential equation
V(x)= a(1 - r)^x
Substitute the known values in the above equation
V(x) = 38000 * (1 - 6%)^x
2017 is 10 years from 2007
This means that x = 10
So, we have:
V(x) = 38000 * (1 - 6%)^10
Evaluate
V(x) = 20467
Hence, the car will be worth $20467 in 2017
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sixteen thousand, four hundred eighty-two. Write this number in standard
In a recent year, the population of Springfield, Illinois was one hundred
form. Show your work in the space below. Remember to check your solutic
Answer:
16482 this is the answer
find the zeros of the following
please solve step by step
1. x³+x²-4x-4=0
2. 2x³-11x²+17x-6=0
Question 1
[tex]x^3 + x^2 - 4x-4=0\\\\x^2 (x+1)-4(x+1)=0\\\\(x^2 -4)(x+1)=0\\\\(x-2)(x+2)(x+1)=0\\\\x=-2, -1, 2[/tex]
Question 2
By inspection, we know that [tex]x=2[/tex] is a root.
[tex]\frac{2x^3 - 11x^2 + 17x-6}{x-2}=2x^2 - 7x+3[/tex].
So, we can factor the equation as
[tex](x-2)(2x^2 - 7x+3)=0\\\\(x-2)(x-3)(2x-1)=0\\\\x=\frac{1}{2}, 2, 3[/tex]
Determine whether the following series converges or diverges using any test. Be sure to clearly state what test(s) you are using and check any conditions needed to apply that test.
According to the ratio criterion, the rational series presented in the picture converges as x < 1. The limit L was 4 /5.
How to determine whether a series converges by ratio criterioHerein we have a series in rational form, whose convergence can be proved by the ratio criterion, whose defintion is shown below:
x = lim (n → ∞) |aₙ/aₙ₊₁| (1)
The series converges if x < 0 and diverges when x > 1. If x = 1, the criterion cannot be used and another criterion must be used instead. Now we proceed to apply it on the expression behind the series:
|aₙ/aₙ₊₁| = [(2 · n + 1) · (2 · n + 2)] / [5 · (n + 1)²]
|aₙ/aₙ₊₁| = [4 · n² + 5 · n + 2] / [5 · n² + 10 · n + 5]
Then, by applying the limit property for rational equations we find that limit of the expression within the series is:
L = 4 / 5
According to the ratio criterion, the rational series presented in the picture converges as x < 1. The limit L was 4 /5.
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By the ratio test, the series diverges.
[tex]\displaystyle \lim_{k\to\infty} \left| \frac{5^{k+1} ((k+1)!)^2}{(2(k+1))!} \cdot \frac{(2k)!}{(5^k (k!)^2}\right| = 5 \lim_{k\to\infty} \frac{(k+1)^2}{(2k+2)(2k+1)} = \frac54 > 1[/tex]
Factor the polynomial completely
10³ -25r² - 12r + 30
can someone help me with these kind of fractions
[tex]\frac{1}{2} of \frac{2}{3}[/tex]
Answer:
[tex]\frac{2}{6}[/tex] or [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
To find a fraction of a fraction simply multiply the numerators and denominators into another fraction:
[tex]\frac{1}{2}*\frac{2}{3} = \frac{2}{6} = \frac{1}{3}[/tex]
Answer:
1/3.
Step-by-step explanation:
'of' means multiply. so
1/2 of 2/3
= 1/2 * 2/3
= 1*2 / 2*3
= 2/6
= 1/3.
PLEASE HELP BRAIBLIST ANSWER PLS
Answer:
[tex]m=-3[/tex]
Step-by-step explanation:
Given points:
[tex](5,3),(8,-6)[/tex]
1. Find the slope
The slope of a line between two points equals the change in the points' y-coordinates (rise) over the change in their x-coordinates (run).
The coordinates of point 1 are: [tex]x_1=5,y_1=3[/tex]
The coordinates of point 2 are: [tex]x_2=8,y_2=-6[/tex]
To find the slope, plug the points' x and y-coordinates into the formula and combine to simplify:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-6-3}{8-5}[/tex]
[tex]m=\frac{-9}{3}[/tex]
[tex]m=-3[/tex]
an alloy is made with 3 gram of silver 18 gram of copper 6 gram of aluminium and three Gram of zinc find what part of the total is used for each metal?
Answer:
see explanation
Step-by-step explanation:
total parts = 3 + 18 + 6 + 3 = 30
3 grams of silver = [tex]\frac{3}{30}[/tex] = [tex]\frac{1}{10}[/tex]
18 grams of copper = [tex]\frac{18}{30}[/tex] = [tex]\frac{3}{5}[/tex]
6 grams of aluminium = [tex]\frac{6}{30}[/tex] = [tex]\frac{1}{5}[/tex]
3 grams of zinc = [tex]\frac{3}{30}[/tex] = [tex]\frac{1}{10}[/tex]
PLEASE I NEED THIS FAST there are 3 denominations of bills in a wallet: $1, $5, and $10. there are 5 fewer $5-bills than $1-bills there are half as many $10-bills if there is $115 altogether, find the number of each type of bill in the wallet
The number of $1, $5 and $10 are 49, 44 and 22 respectively.
How to use equation to find the number of bills?There are 3 denominations of bills in a wallet: $1, $5, and $10.
There are 5 fewer $5-bills than $1-bills.
let
x = number of $1 bills
Hence,
number of $5 bills = x - 5
There are half as many $10-bills as $5-bills.
number of $10 bills = 1 / 2 (x - 5)
Therefore,
x + x - 5 + 1 / 2 (x - 5) = 115
2x - 5 + 1 / 2 x - 5 / 2 = 115
2x + 1 / 2 x - 5 - 5 / 2 = 115
5 / 2 x - 7.5 = 115
2.5x = 115 + 7.5
x = 122.5 / 2.5
x = 49
Number of $1 bills = 49
Number of $5 bills = 49 - 5 = 44
Number of $10 bills = 1 / 2 (49 - 5) = 22
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Canceling units is also called: a. changing the value c. multiplication b. unit analysis d. making connections
Canceling units is also called unit analysis.
This is also called dimensional analysis.
What is a unit of analysis in statistics?
The unit of analysis is the entity that you're analyzing. It's called this because it's your analysis (what you want to examine) that determines what this unit is, rather than the data itself.Because it is the analysis you do in your study that determines what the unit is. For instance, if you are comparing the children in two classrooms on achievement test scores, the unit is the individual child because you have a score for each child.For example -
1 ft = 12 in
3 ft = [tex]3 ft * \frac{12 in }{1 ft}[/tex]
3 ft = ( 3 * 12 ) in ⇒ 36 in
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Twenty-four $4$-inch wide square posts are evenly spaced with $5$ feet between adjacent posts to enclose a square field, as shown. What is the outer perimeter, in feet, of the fence? Express your answer as a mixed number.
Answer:
129 1/3 is the answer
Question 8
725
A cable measures inch outside diameter and has a wrap of cotton that is 1000
1000
65
inch thick and covering of rubber insulation that is inch thick. What is the
diameter of the copper conductor (wire)?
Based on the thickness of the rubber insulation and outside diameter, the diameter of the copper conductor is 0.376 inch.
What is the copper wire's diameter?The diameter of the copper wire can be found by the formula:
= Outer diameter - ( 2 x cotton insulation) - (2 x rubber insulation)
Solving gives:
= 500/ 1,000 - (2 x 12/ 1,000) - (2 x 50 / 1,000)
= 0.5 - (2 x 0.12) - (2 x 0.05)
= 0.376 inch
= 376 / 1,000 inch
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Find the value of x
a. 13 b. 14/5 c. 5 d. 8
Answer:
C. 5
Step-by-step explanation:
The product of chord segment lengths is the same for the two crossing chords.
ApplicationOne chord has segment lengths 4 and 10; the other has segment lengths x and 8.
(4)(10) = (x)(8)
40/8 = x = 5 . . . . . . . divide by the coefficient of x
The value of x is 5, making option C the right choice, using the chord theorem.
The chord theorem, also known as the intersecting chords theorem, is a statement in basic geometry that explains the relationship between the four line segments formed by two intersecting chords inside of a circle. According to this statement, the products of the line segment lengths on each chord are equal.
In the question, we are asked to find the value of x.
Using the chord property, we know that:
8*x = 4*10,
or, 8x = 40,
or, x = 40/8,
or, x = 5.
Thus, the value of x is 5, making option C the right choice, using the chord theorem.
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Need help with my math please. 31-41. Read the directions carefully please.
Answer:
31. (98,765 x 9) + 3 = 888,888
32. (12,345 x 9) + 6 + 111,111
33. 3367 x 15 + 50,505
34. 15,873 x 28 = 555,555
35. 33,334 x 33,334 = 1,111,155,556
36. 11,111 x 11,111 = 123,454,321
41. 3 + 9 + 27 + 81 + 243 = 3(243 -1) / 2
42. 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 = 5/6
Conjecture -> solve these problems and see if they are equal on both ends
EX: 3 + 9 + 27 + 81 + 243 -> 363
3 x 242 = 726 -> 726/2 = 363
Verified
A square pyramid has a height of 6 units and a volume of 70 units3. if a square prism has the same base area and volume as the square pyramid, what is its height?
The height is 2 units.
What is a square pyramid?In terms of geometry, a square pyramid is a pyramid with a square base and four lateral faces. A pyramid is a polyhedron with three or more triangle faces that meet above its base. A square pyramid is a pentahedron, a three-dimensional form with a total of five faces.Find the area of the base of the square pyramid:
The volume of the square pyramid is equal to [tex]V=\frac{1}{3} BH[/tex]
B is the area of the base, and H is the height of the pyramid
[tex]H= 6 units[/tex]
[tex]V=70 units^{3}[/tex]
Solve: B
[tex]70=\frac{1}{3} B(6)\\ \\ B=\frac{70}{2} \\ \\ = 35units[/tex]
To find the height of the square prism:
The volume of the square prism is equal: [tex]V=Bh[/tex]
B is the area of the base and h is the height of the prism
[tex]B=35 units^{2}[/tex]
[tex]V=70units^{3}[/tex]
Solve: h
[tex]70=\frac{35}{h}[/tex]
[tex]h=2units.[/tex]
The height is 2 units.
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The height of the square pyramid exists 2 units.
How to estimate the area of the base of the square pyramid?Volume of the square pyramid
[tex]$V = \frac{1}{3}BH[/tex]
where B exists in the area of the base H lives at the height of the pyramid
we have H = 6 [tex]$$unit^3[/tex]
V = 70 [tex]$$unit^3[/tex]
substitute in the formula and solve for B, we get
[tex]$70 = \frac{1}{3}B(6)[/tex]
B = [tex]$\frac{70}{2}[/tex]
= 35 [tex]$$unit^3[/tex]
To estimate the height of the square prism
Volume of the square prism = Bh
Where B exists the area of the base
h exists the height of the prism
we have B = 35 and V = 70
substitute in the formula and solve for h
70 = (35)h
h = 2 units.
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Each gallon of porch and deck paint covers 200 square feet. how many gallons are needed to cover 1241 square feet?
7 gallons are needed to cover 1241 square feet.
In this question,
Each gallon of porch and deck paint covers 200 square feet.
To find out how many gallons of paint needs, we have to divide the total area of deck by the amount of deck that one gallon covers.
We use the unitary method to find out how many gallons of paint needs.
Using unitary method,
1241 / 200 = 6.205
However, we cannot buy a fraction of a gallon of paint.
So, the amount of gallons of paint needed is approximately equal to 7 gallons.
Therefore, 7 gallons are needed to cover 1241 square feet.
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Instructions: Find the length of the arc. Round your answer to the nearest tenth.
Answer:
7
Step-by-step explanation:
The length of the arc can be calculated via a simple proportion:
2 pi r : 360° = x : 45°
Where r is the radius of the circumference and x the length of the arc we want to know. Isolating the x:
x = (2 pi r : 360) * 45 = (2 pi * 9 : 180) * 45 = 18 pi : 360 * 45 = 18pi : 8 = 7
A regular octagon has side lengths of 8 centimeters. what is the approximate area of the octagon?
Answer:309
Step-by-step explanation:
The selling price, s, of an item is s = c mc, where c is the cost of the item and m is the percent markup based on cost. what is the formula solved for m? m = startfraction s minus c over c endfraction m = startfraction s c over c endfraction s minus c = m s c = m
Answer:
s - c over c = m or (s-c)/c = m
Step-by-step explanation:
s = c * mc
s -c = mc
(s - c) / c = m
Answer:
A ) m=s-c/c
Step-by-step explanation:
help please. which one is right?
Answer: B
Step-by-step explanation: If it goes through a point, flip that point around and that is the point of the inverse. Do that for multiple points to get your answer, which is B
please please please please please please please please please please please please please please please please please help mey,
Answer:
See below
Step-by-step explanation:
REMEMBER sec = 1/cos ...so the left side is
[1/cos -1] / [1/cos +1 ]
get common denominator for numerator and denominator
[ (1 -cos) /cos ] / [ (1+cos) / cos ]
now flip the bottom fraction and multiply to get
[(1-cos/cos) ] * [ cos / (1+cos) ] which simplifies to ( the 'cos' term cancels)
(1-cos) / (1+cos) done !
HELPPP ASAP 25PTS! Find the area of the shape
Answer:
480
Step-by-step explanation:
cosa/2-tana +sina/1-cota=cosa+sina
Answer:
Cosa/2-tana+sina
Step-by-step explanation:
Cosatana
If ph term of A.P. is q and qth term is p, then (p+q) term is??
If the pth term of an arithmetic progression is q and qth term is p then the (p+q) th term is 0.
Given that the p th term of an A.P is q aand q th term is p.
We are required to find the (p+q) th term of that A.P.
Arithmetic progression is a sequence in which all the terms have common difference between them.
N th term of an A.P.=a+(n-1)d
p th term=a+(p-1)d
q=a+(p-1)d-------1
q th term=a+(q-1)d
p=a+(q-1)d---------2
Subtract equation 2 by 1.
q-p==a+(p-1)d-a-(q-1)d
q-p=pd-qd-d+d
q-p=d(p-q)
d=(p-q)/(q-p)
d=-(p-q)/(p-q)
d=-1
Put the value of d in 1.
q=a+(p-1)(-1)
q=a-p+1
a=q+p-1
(p+q) th term=a+(n-1)d
=q+p-1+(p+q-1)(-1)
=q+p-1-p-q+1
=0
Hence if the pth term of an A.P is q and qth term is p then the (p+q) th term is 0.
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Find the midpoint of the line segment joining (–4, –2) and (2, 8).
A regular hexagon has an apothem of 14.7 inches and a perimeter of 101.8 inches. what is the area of the hexagon? square inches
Answer:
748.23 in^2.
Step-by-step explanation:
Area = 1/2 * apothem * perimeter
= 1/2 * 14.7 * 101.8
= 748.23 in^2.
Answer:
748.23
Step-by-step explanation:
An amusement park sells adults' and
children's passes. An adult's pass is $25,
and a child's pass is $15. A group spent
$440 on 20 passes. How many children's
passes did the group purchase?
A
Answer:
6 children passes
Step-by-step explanation:
a = adult and c = children
25a + 15c = 440 and a + c = 20
c = 20 - a
25a + 15(20-a) = 440
25a + 300 - 15a = 440
25a - 15a = 440 - 300
10a = 140
a = 140/10
a = 14 and this is 14 adult tickets
Now we plug the a value into the equation to find the c value
14 + c = 20
c = 20 - 14
c = 6
Verify answer:
25(14) = 15(6) = 440
350 + 90 = 440
440 = 440
The combination for opening a safe is a four-digit number made up of different digits. How many different combinations cna you make, using only odd digits?
Answer:
120
Step-by-step explanation:
My choices are: 1, 3, 5, 7, 9. I cannot repeat any of the numbers.
The first spot, I have 5 choices. The second spot, I have 4 choices, the third spot, I have 3 choices and the final spot has only 2 choices.
5x4x3x2 = 60
Lou received requests for 150 tickets for their art show. The number of requests was 120% of the number of tickets they had. How many tickets do they have?
Answer:
180
Step-by-step explanation:
If she received requests for 150 tickets, and that is 120% of what they have, you would find 20% of 150. You would do this because 100% of 150 is 150, now you need to add the other 20%, so you have to find 20% of 150. Which is 30. You would then add that to 150 sine it is 120% of what they have. So, they have 180 tickets
Graph the image of the given polygon under a dilation with a scale factor of 1/3 and center of dilation (0, 0) .
The image of the given polygon under a dilation with a scale factor of 1/3 about the center of dilation (0, 0) is A'(0, 0), B'(1, 2) and C'(-1, 1)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation.
Let us assume that the polygon has vertex at A(0, 0), B(3, 6) and C(-3, 3)
The image of the given polygon under a dilation with a scale factor of 1/3 about the center of dilation (0, 0) is A'(0, 0), B'(1, 2) and C'(-1, 1)
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