Compare the slopes of the lines for y = f(x) andy = g(x) to determine if each pair of lines is parallel.
SEE EXAMPLE 1
18
f(x) g(x)
0 20 22
g
х
1
35
37
s
2
50
52
3
65
67
Answers
Answer:
Step-by-step explanation:
Slope of a line passing through two points and
will be given by,
Slope 'm' =
Function 'f' passes through two points (0, 20) and (1, 35).
Slope of the line =
= 15
Similarly function 'g' is passing through (0, 22) and (1, 37).
Slope of the line = 15
Therefore,
Since, slopes of both the lines are equal, lines will be parallel.
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let x be radius
let 4x be height
V=(pi)(r)^2h
108(pi)=(pi)x^2(4x)
divide both sides by pi
108=x^2(4x)
108=4x^3
divide both sides by 4
27=x^3
cube root both sides
x=3
therefore the radius is 3 and the height is 12
b) How many different choices of books could the class make?
a) The number of different ways the course could unfold is
Answers
Answer:
a) 840 different ways
b) 35 different choices of books
Step-by-step explanation:
We know that our literature class will read a total of 4 novels this year.
All novels chosen by class vote from a list of 7 possible books offered by the teacher.
Wherever we have an experiment which is formed by sub - experiments that can occurred in
ways, the total number of ways in which the whole experiment
can be developed is :
x
x ... x
Then, for a) if it matters what order we read the books in, the total number of different ways could the course unfold is :
(I)
Because for the first book there are 7 different choices. Now, given that we choose the first book, we only have 6 different choices for the second one.
Continuing with the idea, we deduce the equation (I).
For item b) :
Wherever we have different objects and we want to find the ways that we can choose
objects from that group, we need to use the combinatorial number.
We define the combinatorial number as :
Then, if we apply this to the problem, the total different choices of books if we want 4 novels voting from a total of 7 possible books is :
a) 840 different ways
b) 35 different choices of books
Final answer:
The number of different ways the course could unfold is 210, and the number of different choices of books the class could make is 35.
Explanation:
The number of different ways the course could unfold is equal to the number of permutations of the 4 books chosen from the list of 7. This can be calculated using the formula for permutations: P(n, r) = n! / (n - r)!. In this case, n = 7 (the number of books) and r = 4 (the number of books chosen). Using the formula, we get P(7, 4) = 7! / (7 - 4)! = 7! / 3! = 7 imes 6 imes 5 = 210.
The number of different choices of books the class could make is equal to the number of combinations of the 4 books chosen from the list of 7. This can be calculated using the formula for combinations: C(n, r) = n! / (r! (n - r)!). In this case, n = 7 (the number of books) and r = 4 (the number of books chosen). Using the formula, we get C(7, 4) = 7! / (4! (7 - 4)!) = 7! / (4! imes 3!) = (7 imes 6 imes 5) / (4 imes 3 imes 2) = 35.
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Answers
Number 12 have factors 12 = ( 1,2,3,4,6,12)
Number 18 have factors 18= ( 1,2,3,6,9,18 )
According to this we can conlude that numbers 12 and 18 have in common (1,2,3 and 6).
Good luck!!!
2 and 6 can go into it evenly
Answers
The volume of the jewelrybox is 60 1/2 cubic inches.
The area of a square with a side length of 5 1/2 inches can be found by multiplying the length of one side by itself, giving:
Area = (5 1/2) × (5 1/2) = 30 1/4 square inches
The height of the box is 2 inches.
Therefore, the volume of the jewelry box can be found by multiplying the area of the base by the height of the box, giving:
Volume = Area x Height = (30 1/4) × 2 = 60 1/2 cubic inches
Thus, the volume of the jewelrybox is 60 1/2 cubic inches.
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Answers
The two consecutive integers that the sum is 149 are 74 and 75.
What is an expression?
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the number is 149. The two consecutive integers can be calculated as below,
Suppose the two consecutive integers are x and ( x + 1 ).
x + ( x + 1 ) = 149
2x + 1 = 149
2x = 148
x = 148 / 2
x = 74
The second integer would be,
x + 1 = 74 + 1 = 75
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PLS PLS PLS HELP IM FAILING GEOMETRY RNNNNN
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By the Definition of congruent property, we have proved that:
VW ≅ VX
Congruent Property:
The three properties of congruence are the reflexive property of congruence, the symmetric property of congruence and the transitive property of congruence. These properties can be applied to line segments, angles, triangles, or any other shape.
Given: VZ ≅ VY and WY ≅ XZ
Prove: VW ≅ VX
Proof:
(Given): VZ ≅ VY and WY ≅ XZ
By the Definition of Congruent Substitute:
VZ = VY and WY = XZ
⇒ VZ = VX + XZ , and,
VY = VW + WY
By Substituting
VX + XZ = VW + WY
Again,
VX + WY = VW + WY
Now,
By Subtraction property of Equality
VX = VW
VW = VX (Definition of congruent property.)
Complete Question:
IF VZ congruent of VY and WY congruent of XZ. Prove that VW is Congruent of VX.
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