by using inductive reasoning, we get the next 2 terms as 7 / 12 and 4 / 7.
We are given a sequence:
3 / 4, 2 / 3, 5 / 8, 3 / 5
We need to find the next two terms by using the inductive reasoning.
Now, we can also write this sequence as:
3 / 4, 4 / 6, 5 / 8, 6 / 10
Now, we can see that, in each term, the numerator is increasing by 1 and the denominator is increasing by 2 units.
So, the 5th term will be:
Numerator = 6+ 1 = 7
Denominator = 10 + 2 = 12
5th term = 7 / 12
And the 6th term will be:
Numerator = 7 + 1 = 8
Denominator = 12 + 2 = 14
6th term = 8 / 14 = 4 / 7
Therefore, by using inductive reasoning, we get the next 2 terms as 7 / 12 and 4 / 7.
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You know the sum of -5 and another integer is a positive integer. What can you conclude about the sign of the other integer? What can you conclude about the value of the other integer. Explain.
The sign of the other integer is positive. Value of other integer is greater than 5.
When we add two numbers of the same sign, final number has the same sign of the initial numbers
For example, we add 3 and 8,
3+8= 11
Both the numbers 3 and 8 are positive so our result is also positive.
On the other hand when we add -3 and -8, then the result will be
-3 +(-8)= -11
Both the numbers are negative, so our result also negative.
When two numbers of different sign are being added then the sign of the larger number decide the sign of the final number
For example, we add -3 and 8.
-3+8= 5
8 is larger than 3, and has positive sign, so the result will also be positive.
Suppose other number is x.
-5+x>0 (As the sum is positive)
Add 5 on both the sides
-5+x+5>0+5
x>5
As we can see the number is greater than 5 and has a positive value.
Final answer: The sign of the other integer is positive. Value of other integer is greater than 5.
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2.) A rectangular garden is 6 ft longer than it is wide. Its area is 352 ft2. What are its dimensions?
Answer:
Length = 22, Width = 16
Step-by-step explanation:
Let L be the length of the garden and W the width
The area, A = L x W = 352 ft²
It is given that L = W + 6
Substituting for L in the area equation we get
L x W
==> (W + 6) x W = 352
Expanding the brackets
==> W.W + 6.W = 352
==> W² + 6W = 352
Subtract 352 from both sides:
W² + 6W - 352 = 0
This is a quadratic equation which can be solved using the quadratic formula.
- 352 = - 16 x 22 and -16 + 22 = 6
So we can factor the quadratic equation as
(W - 16) (W + 22) = 0
==> W = 16 or W = -22
Since we can disregard negative values in this context,
W = 16 and L = W + 6 = 16 + 6 = 22
Dimensions are Length = 22, Width = 16
la la la, la la la, la la la la la~
sorry beinggreat I didnt know what to name it ;-;
[tex]31\% = \frac{31}{100} = 0.31 > 0.275 \\ 32.6\% = \frac{32.6}{100} = 0.326 > 0.310 \\ 0.325 = \frac{32.5}{100} = 32.5\% > 27.5\% \\ 0.310 = \frac{31}{100} = 31\% < 32.5\%[/tex]
only Option B is correctAnswer:
Letter B is the answer
Step-by-step explanation:
A. 31% < 0.275
31% < 27.5%
B. 32.6% > 0.310
32.6% > 31%
C. 0.325 < 27.5%
32.5% < 27.5%
D. 0.310 > 32.5%
31% > 32.5%
4. A lawn sprinkler shoots out a circle of water that goes
12 feet in all directions. What is the area of the part of the
lawn that the sprinkler waters?
What is the five number summary for the data set, 2,2,4,4,5,5,6,7,9
Answer:
4.88
Step-by-step explanation:
2+2+4+4+5+5+6+7+9=44
44÷9=4.88
Answer=4.88
A party rental company has chairs and tables for rent. The total cost to rent 9 chairs and 7 tables is $86. The total cost to rent 3 chairs and 5 tables is $52. What is the cost to rent each chair and each table
Answer: ok here is ur answer The cost for 1 chair is $2.75 and the cost for 1 table is $8.75
Use the elimination method of linear equations to find your answer.
Our equations for this problem are:
3c+5t=52 and 9c+7t=86
1. Multiply the entire first equation by -3.
-3(3c+5t=52)
2. Simplify the equation from above:
-9c-15t=-156
3. Stack the two equations on top of each other and add/subtract:
-9c-15t=-156
9c+7t=86
4. You should be left with -8t=-70. Simplify this to find the value of t:
t=8.75
5. Plug the value of t into any of the original equations and solve for c.
3c+5(8.75)=52
6. Simplify the equation above:
3c+43.75=52
7. Subtract 43.75 from both sides of the equation:
3c=8.25
8. Divide both sides by 3 to get your c value:
c=2.75
Step-by-step explanation: i really hope this helps pls lmk if i am wrong (:
20₁
R
Which two triangles are similar? The triangles are not
drawn to scale.
S
6
4.8
3.6
5.5
B
W
6.9
4.1
Y
A ATUVAWXY
AQRS-AWXY
AQRSATUV
T
1.8
2.4
U
The two similar triangles in this problem are given by:
C. QRS and TUV
What are similar triangles?
Similar triangles share these two features:
Hence, the similar triangles are QRS and TUV, as the side lengths proportions are given as follows:
3/6 = 2.4/4.8 = 1.8/3.6.
Hence option C is correct.
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A supermarket wants to send codes for $0.25 off a bag of chips to its rewards program members. Each coupon code will have one digit followed by four letters. The letters D and E and the digits 0, 5, and 8 will not be used. So, there are 24 letters and 7 digits that will be used. Assume that the letters can be repeated. How many such coupon codes can be generated?
Using the Fundamental Counting Theorem, it is found that 2,322,432 codes can be generated.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Considering that the ode will have one digit followed by four letters, the parameters are given as follows:
[tex]n_1 = 7, n_2 = n_3 = n_4 = n_5 = 24[/tex]
Hence the number of codes that can be generated is:
N = 7 x 24 x 24 x 24 x 24 = 2,322,432.
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Function yes or no what is the domain and range
Step-by-step explanation:
I assume the grid units are single units (1, 2, 3, ...).
to be a function every value of x must have exactly one value of y.
but that is violated at x = 2. at that point y can be either +3 or -3 (indicated by the 2 points at x=2).
so, no, it is not a function.
the domain is the interval or set of all valid x (input) values.
since we have no continuous curve but single points, it is a set :
x € {-4, -3, -2, 1, 2, 3, 6}
the range is the interval or set of all valid y (function result) values. again, it is a set for the same reasons :
y € {-3, -2, 0, 1, 3, 4}
Alfonso and Cordell each bought one raffle ticket at the state fair. If 50 tickets were randomly sold, what is the probability that Alfonso got ticket 14 and Cordell got ticket 23? Express your answer as a fraction in simplest form.
The probability that Alphonso gets ticket 14 and Cordell gets ticket 23 is = 1/2450
Alphonso can pick a ticket from 50 tickets in 50 ways;
When Alphonso pick a ticket, then Cordell can pick a ticket in 49 ways;
Total number of ways = 50 × 49 = 2450;
Alphonso can get ticket 14 and Cordell can get ticket 23 in only one way;
So, the probability that Alphonso gets ticket 14 and Cordell gets ticket 23 is = 1/2450;
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find the area of the circle
The area of the circle based on the information illustrated is C. 28.26ft².
What will the area be?It should be noted that the area of a circle is given as:
= πr²
In this case, the radius is 3ft.
Therefore, the area will be:
= πr²
= 3.14 × 3²
= 3.14 × 9
= 28.26 ft²
In conclusion, the area of the circle is 28.26ft².
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Triangle XZ is translated 4 units up and 3 units left to yield urz. What is the distance between any two corresponding points on 2 and
DRYZ?
OA 7 units
OB √nts
OD. 25 units
The value of x is 5
Question is based on the Pythagorean theorem :
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple
Consider the triangle given above:
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse.
According to the definition, the Pythagoras Theorem formula is given as:
X is the side opposite to the right angle, hence it is a hypotenuse.
Now, by the theorem we know;
Hypotenuse2 = Base2 + Perpendicular2
x2 =[tex]4^{2} +3^{2}[/tex]
x2 = 16+9
x = [tex]\sqrt{25}[/tex]
Therefore, the value of x is 5
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Luis and Jasmine are making scale drawings of the front of their school for an art contest. Luis uses the scale 3 in. to 10 ft. Jasmine uses the scale 5 in. to 20 ft. The tree in front of the school in Luis's drawing is 7.5 inches tall. How tall is the tree in Jasmine's drawing?
The height of the tree in Jasmines drawing is; 6.25 inches tall
How to interpret Scale Drawing?The scale factor used by Louis is; 3in : 10 ft
The scale factor used by Jasmine is; 5in : 20ft
We are told that the tree in front of the school in Luis's drawing is 7.5 inches tall. Thus;
True height of tree in Louis drawing is; (7.5 * 10)/3 = 25 ft
Thus, height of tree in Jasmines drawing = (25 * 5)/20 = 6.25 inches tall
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Evaluate fog and go f and use the results to determine if g is the inverse function of f.
If [tex]f,g[/tex] are inverses of one another, then
[tex]f\circ g(x) = g\circ f(x) = x[/tex]
Given [tex]f(x)=x^2-1[/tex] and [tex]g(x)=\sqrt{x-8}[/tex], then
[tex]f\circ g (x) = f(g(x)) = f(\sqrt{x-8}) = \left(\sqrt{x-8}\right)^2 - 1 = \boxed{x - 9} \neq x[/tex]
so right away we know [tex]f[/tex] and [tex]g[/tex] are not inverses.
In the other direction, we come to the same conclusion.
[tex]g\circ f(x) = g(f(x)) = g(x^2 - 1) = \sqrt{(x^2-1)-9} = \boxed{\sqrt{x^2 - 9}} \neq x[/tex]
4. Convert 3,500,000,000 to a single digitscientific
Answer:
3.5 × 10 to the 8th power
Step-by-step explanation:
Solve for x.
x³ = 1000
Enter your answer in the box.
X =
Answer:
10
Step-by-step explanation:
10*10*10=1000
10^3=1000
e At its highest
is 5,762 feet
At its lowest point, the elevati
15. Make Sense and Persevere At its bio
point, the elevation of a county is 5,762
above sea level. At its lowest point. th
of the county is 9 feet below sea level.
ow sea level.
a. What is the difference between the highest and lowest points of the country?
The difference between the highest and the lowest points of the country is 5771 feet.
What is subtraction?The operation of subtraction is used to calculate the difference between two numbers. If you have an object group and remove a couple of them, the object group gets smaller.
The process of subtracting one number from another is called subtraction. The way to calculate the difference between two numbers is by using the basic arithmetic operation of subtraction, which is represented by the symbol (-).
Let the sea level be x.
The highest point of the country is 5,762 feet above the sea. So, we can write it as
x+5,762
Since the lowest point is 9 feet below sea level, we can write this expression:
x-9
The difference is the result of subtraction. Therefore, we can find the expression that represents the difference between the elevations by subtracting x+5,762 and x-9:
(x+5,762)-(x-9)
= x+5762-x+9
= 5762+9
=5771 feet
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Translate the image by (3x - 1, y + 5) D(1,2)→ D'_ E(-3,-5)→E'. F(4,-1)→→ F
The image of D (1, 2) is D' ( 2, 7).
The image of E (-3 -5) is E' ( -10, 0).
The image of F (4, -1) is F' ( 11, 4).
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given points are;
D (1, 2), E(-3, -5) and F(4, -1)
Now, The rule is to find the image of points is;
(x, y) → (3x - 1, y + 5)
Hence,
The image of D (1, 2) = (3 * 1 - 1, 2 + 5)
= (3-1, 7)
= (2, 7)
The image of E (-3 -5) = (3*-3 - 1, -5 + 5)
= (-9-1, 0)
= (-10, 0)
The image of F (4, -1) = (3*4 - 1, -1 + 5)
= (12-1, 4)
= ( 11, 4 )
Therefore, The image of D (1, 2) is D' ( 2, 7).
The image of E (-3 -5) is E' ( -10, 0).
The image of F (4, -1) is F' ( 11, 4).
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What is the area of the figure shown below?
Round your answer to the nearest tenth, but do not include "ft2" with your response.
Answer:
37.5
Step-by-step explanation:
5x5 = 25. That's your square. For the triangle, 5x5 = 25. 25/2 = 12.5 25+12.5 = 37.5.
If ∠HJK is 35° and ∠FJI is 95°, what is the measure of ∠KJG?
Answer:
180-(35+95)=50
Step-by-step explanation:
Any triangle in the world sum of its angle equal 180
help please and explain why
The units of the trail map at the right are in kilometers. Suppose the trails are straight. Find the distance you would travel along each trail to the nearest tenth of a kilometer.
(see picture)
The distance of each of the paths are as follows;
25) Distance of Low Trail is; d = 17.1 km
26) Distance of willow walk is; d = 20.6 km
27) Distance of Pond Walk is; d = 8.5 km
28) Distance of Meadow Trail is; d = 22.8 km
How to find the Distance between Coordinates?
The formula for distance between two coordinates is;
d = √[(x1 - x2)² + (y1 - y2)²]
25) Distance of Low Trail is;
d = √[(14 - 12)² + (-2 - 15)²]
d = 17.1 km
26) Distance of willow walk is;
d = √[(10 + 4)² + (12 - 1)²]
d = 20.6 km
27) Distance of Pond Walk is;
d = √[(-4 + 12)² + (12 - 15)²]
d = 8.5 km
28) Distance of Meadow Trail is;
d = √[(14 + 4)² + (12 + 2)²]
d = 22.8 km
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How do I solve this??
Answer:
Step-by-step explanation:
Answer: 144
Step-by-step explanation:
A number y satisfies y²⁴ - 256 = 0. What equation does the number x = y⁴ satisfy?
Answer:
> y²⁴- 256 = 0
> (y⁴)
x-256 = 0
or
x= 256
Step-by-step explanation: i have no idea if i am right but pls lmk if i am wrong have a good day/night (: <3
I need help on this please and thank you!
By inductive reasoning we can say that the conclusion is based on observing the four numbers in the sequence.
How to use Inductive Reasoning?
We are given the arithmetic series as;
5, 10, 15, 20, .......
From the formula of the nth term of an arithmetic series, we know that;
a_n = a + (n - 1)d
where;
a is first term
n is position of term
d is common difference
Thus, for this series, it is clear that the common difference is 5. Thus the fifth term is;
a_5 = 5 + (5 - 1)5
a_5 = 5 + 20
a_5 = 25
Thus, by inductive reasoning we can say that the conclusion is based on observing the four numbers in the sequence.
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please help will give Brainly!
Answer:
Range is 21
I believe
Step-by-step explanation:
What is the value of f(2) when f(x)= 3x-7?
Earl Bean sells shoes for Target. Target pays Earl $10 per hour plus 4% commission on all sales. Assume Earl works 39 hours for the week and has $6,000 is sales. What is Earl's gross pay?
B
What is the intersection of the two planes?
The intersection of the two planes is a Line.
According to the statement
We have to find that the Intersection of the planes.
So, For this purpose, we know that the
An intersection is a single point where two lines meet or cross each other.
From the given information:
A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors.
And then the intersection of the plane becomes:
Then
The intersection of two planes is a line. If the planes do not intersect, they are parallel.
They cannot intersect at only one point because planes are infinite.it means parallel planes have no intersection point.
So, The intersection of the two planes is a Line.
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The sum of 8 and three times a number is 41
Answer:
The number is 11
Step-by-step explanation:
First turn this into a mathematical equation
8+3x=41
subtract 8 from both sides
3x=33
divide both sides by 3
x=11