The equivalent rates for each of the given options are;
A) 1 goal in 2 games
10 goals in 20 games
B) 1 km jogged in 6 min
5 km jogged in 12 min
C) 1 pizza eaten in 5 minutes
2 pizzas eaten in 10 minutes
D) 2 penalties in 5 games
20 penalties in 50 games.
What are the equivalent rates?We want to write two equivalent rates for the given rates.
It should be noted that different rates that have the same value are equivalent rates. You can find an equivalent rate the same way you find equivalent ratios which is to divide or multiply the numerator and the denominator by the same number.
A) 5 goals in 10 games can also be written as;
5/10 = 1/2 = 10/20
These equivalent rates are;
1 goal in 2 games
10 goals in 20 games
B) 10 km jogged in 60 min;
10/60 = 1/6 = 5/12
These equivalent rates are;
1 km jogged in 6 min
5 km jogged in 12 min
C) 6 pizzas eaten in 30 min;
6/30 = 1/5 = 2/10
These equivalent rates are;
1 pizza eaten in 5 minutes
2 pizzas eaten in 10 minutes
D) 10 penalties in 25 games;
10/25 = 2/5 = 20/50
These equivalent rates are;
2 penalties in 5 games
20 penalties in 50 games.
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Counterexamples
Instructions: Show that the conjecture is false by finding a counterexample. Change the value of n below in order to make it a counterexample.
"For every integer n, n3 is positive."
n=1
n=−3
n=2
n=5
n= Answer
Counterexample
A counterexample is an example that meets the mathematical statement's condition but does not lead to the statement's conclusion. It is used to check the validity of an argument.
We have been given the conjecture:-
"For every integer n, [tex]n^3[/tex] is positive."
We have to show that the conjecture is false by finding a counterexample.
Let us take an integer n = - 5
Finding its cube we, get
[tex]n^3[/tex] = -125
We know that,
-125 is not positive, it is negative.
Hence, the conjecture "For every integer n, [tex]n^3[/tex] is positive." is proven wrong by finding a counterexample which states otherwise.
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Find the surface area of the rectangular prism
Answer:
48
Step-by-step explanation:
kumon level C pages please i dont want to waste my time
Answer:
Image result for kumon level C
This award is presented to a student who has completed Level C10 or higher during or before their 1st-grade year. Math Level C covers multiplication and division.
Step-by-step explanation:
find the derivative of the function
f(x) = √2^3 + ln(x^3) - 2x^3 - log_3(729) - 2/x^4
Applying the rules for the constant, logarithm and exponents, the derivative of the given function is of:
f'(x) = 3/x - 6x² - 8/(x^5).
What is the derivative of the function?The function is given by:
f(x) = √2^3 + ln(x^3) - 2x^3 - log_3(729) - 2/x^4
The derivative of a sum is the sum of the derivatives, hence:
f'(x) = (√2^3)' + (ln(x^3))' - (2x^3)' - (log_3(729))' - (2/x^4)'
The derivative of a constant is of zero, hence:
(√2^3)' = 0.(log_3(729))' = 0.Hence:
f'(x) = (ln(x^3))' - (2x^3)' - (2/x^4)'.
The derivative of the logarithm is given by:
ln(h(x))' = (1/h(x)) x h'(x).
Hence:
(ln(x^3))' = 3x²/x³ = 3/x.
The derivative of the power of x is given by:
[x^n]' = nx^(n-1).
Hence:
(2x³)' = 6x². (2/x^4)' = (2x^(-4))' = -8x^(-5) = -8/(x^5).Hence the derivative of the function is given by:
f'(x) = 3/x - 6x² - 8/(x^5).
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Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 4;
zeros: -4-5i; - 5
multiplicity 2
Let a represent the leading coefficient. The polynomial is f(x) = a(________)
(Type an expression using x as the variable. Use integers or fractions for any
numbers in the expression. Simplify your answer.)
Answer: [tex]x^4 +2x^3 -14x^2 +210x+1025[/tex]
Step-by-step explanation:
By the conjugate root theorem, -4+5i is also a root.
[tex]f(x)=a(x+4-5i)(x+4+5i)(x+5)^2\\\\=a(x^2 -8x+41)(x+5)^2\\\\ =a(x^2 -8x+41)(x^2 +10x+25)\\\\=a(x^4 +2x^3 -14x^2 +210x+1025)[/tex]
Which graph represents the solution set of the system of inequalities?
{y>−2x−2y≤x+4
The graph represents the solution set of y > -2x - 2 and y ≤ x + 4 is graph (a)
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to solve the system of inequalities graphically?The system of inequalities is given as
y > -2x - 2
y ≤ x + 4
Next, we plot the system of inequalities on a graph (see attachment)
From the attached graph, we have both lines of the graph intersect at (-2, 2)
Also, we can see that the graph has two lines (one shaded and one closed line)
By comparing the attached graph and the graphs in the list of options, we can see that the graph represents the solution set of the system of inequalities is graph (a)
Hence, the graph represents the solution set of the system of inequalities is graph (a)
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HELP PLS LAST ONE
Simplify (4y³ – 2y +9) − (2y³ − 3y² + 4y + 7).
can you help me solve me this math problems?
1. 200 - 7/21
2. 50 - 4/7
3. 24 1/4 - 20 3/5
4. 10 5/8 - 6 4/9
5. 6 1/2 - 5 3/4
Step-by-step explanation:
1.
200 - 7/21 = (200×21 - 7)/21 = (4200 - 7)/21 =
= 4193/21 = 599/3 = (199×3 + 2)/3 =
= 199 2/3
we could have seen that 7/21 = 1/3.
so, then this problem was
200 - 1/3 = (200×3 - 1)/3 = 599/3 = 199 2/3
(see above)
2.
50 - 4/7 = (50×7 - 4)/7 = (350 - 4)/7 =
= 346/7 = (49×7 + 3)/7 = 49 3/7
3.
24 1/4 - 20 3/5 = (24×4 + 1)/4 - (20×5 + 3)/5 =
= 97/4 - 103/5
to calculate this we need to bring both fractions to the save denominator. the LCM (lowest common multiple) of 4 and 5 is 20.
so,
97/4 - 103/5 = (97×5)/(4×5) - (103×4)/(5×4) =
= 485/20 - 412/20 = 73/20 =
= (3×20 + 13)/20 = 3 13/20
4.
10 5/8 - 6 4/9 = (10×8 + 5)/8 - (6×9 + 4)/9 =
= 85/8 - 58/9
the LCM of 8 and 9 is 72.
85/8 - 58/9 = (85×9)/(8×9) - (58×8)/(9×8) =
= 765/72 - 464/72 = 301/72 =
= (4×72 + 13)/72 = 4 13/72
5.
6 1/2 - 5 3/4 = (6×2 + 1)/2 - (5×4 + 3)/4 =
= 13/2 - 23/4
the LCM of 2 and 4 is 4.
13/2 - 23/4 = (13×2)/(2×2) - 23/4 =
= 26/4 - 23/4 = 3/4
The distance remaining to a destination after t minutes is given by d(t) = 340-0. 85t, measured in miles. The graph of d(t) is shown below.
After how many minutes is the destination reached?
In 400 minutes, it will reach the destination.
What is distance?
Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in everyday language (e.g. "two counties over"). The term is also frequently used metaphorically to refer to a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between strings of text) or a degree of separation, as spatial thinking is a rich source of conceptual metaphors in human thought (as exemplified by distance between people in a social network). The concept of a metric space is used in mathematics to formalise the majority of these notions of distance, both literal and figurative.
Distance is equal to speed × time. Time is equal Distance/Speed.
we have given, d(t)=340-0.85t
where, t is the time and d(t) is the distance.
when t = 0 we get,
d(t)=340
If we set d(t)=0 we get, 0= 340- 0.85t
add with 0.85t on both side
0.85t=340
t= 340/0.85
t= 400 minutes
Hence, the time taken to reach the destination is 400 minutes.
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HELP ME PLEASE !!!!!!
5. The value of x = 15
6. The converse that must be used is: C. Same-side exterior ∠s converse.
7. The proof is completed in the explanation part.
8. Slope of AB = 7/4; Slope of CD = -4/7, they are perpendicular.
What is the Same-Side Exterior Angles Theorem?The same-side exterior angles theorem states that same-side exterior angles that are on the same side of a transversal are supplementary to each other. Its converse states that if same-side interior angles are supplementary, then the lines they lie on are parallel to each other.
5. 10x - 22 + 3x + 7 = 180 [same-side exterior angles theorem]
13x - 15 = 180
13x = 180 + 15
13x = 195
x = 15
6. The converse that must be used to show that lines y and x are parallel to each other is: C. Same-side exterior angles converse.
7.
Statements Reasons
1. ∠6 ≅ ∠8 1. Given
2. y║z 2. Corresponding ∠s converse
3. ∠2 and ∠3 are supplementary 3. Same Side Interior ∠s
8. Given:
A(-3, 8)
B(1, 15)
C(10, -9)
D(3, -5)
Slope = change in y / change in x
Slope of AB = (8 - 15)/(-3 - 1) = -7/-4 = 7/4
Slope of CD = (-9 -(-5))/(10 - 3) = -4/7
-4/7 is the negative reciprocal of 7/4. Perpendicular lines have slope that are negative reciprocals of each other.
Therefore, CD and AB are perpendicular.
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find the 6th term of the sequence 4, 6, 9,...
Answer:
30.375
Step-by-step explanation:
this is a geometric sequence, meaning it has a common growth factor
to find the growth factor, you divide a term by the previous term (example: 9/6)
so for this problem:
9/6 = 1.5
6/4 = 1.5
so 1.5 is the common growth factor
then you just multiply so:
9 • 1.5 = 13.5
13.5 • 1.5 = 20.25
20.25 • 1.5 = 30.375
4, 6, 9, 13.5, 20.25, and 30.375
so 30.375 is your 6th term
hope this helps :)
Theodora had practiced playing table tennis for hours by the end of the week. If each day the practice lasted for of an hour, how many days did she practice during the week?
Answer:
7 hours
Step-by-step explanation:
each day she practices 1 hour and there are 7 days in a week so 7 hours by the end of the week
Enola bought 14 chicken wings for $29.40. How much would it cost for 5 wings?
Answer:
x=10.50
Step-by-step explanation:
14 = 5
________
29.40 = x
cross multiply - 29.40 x 5 = 147
Then u would divide like this
14/14=1 147/14=10.5
are the angles on, inside, or outside the circle
nswer
First image
Angle ABC covers around the inside and outside of the circle.
Second image
Angle x l
hird image
Angle DBE l
ngle of arc DE l
ngle of arc AC l
ourth angle
ll the angles at U lie inside the circle.
ngle 78° l
ngle 114° l
ope this Helps!!!
Bonjour, je vous demande de l'aide pour ce gros exercice de maths niveau seconde merci d'avance.
Answer:
type in english
Step-by-step explanation:
english please
Hi please help me if you do I would be happy
A photo collage consists of seven equal-sized square photos arranged in a row to form a rectangle. If the total area of the collage is 567 square inches, what is the length of the collage?
The length of the square collage will be 63in.
In the question, It is stated that a photo collage is made by arranging 7 square shaped photos in a row. The arrangement is done in such a way that it forms a rectangle. The total area of the collage is 567 square inches. We have to find out the length of the Collage.
Given that, the photos arranged are of square shape then their length and breadth must be equal. So,
Side of square photo: x
Now, seven photos were arranged, So,
Length of collage = 7x
Breadth of collage = x
We know the Area of the Rectangle is Length*Breadth
Putting Area A = 567, l = 7x, and b = x, we get:
=> Area = l*b
=> 567 = 7x*x
=> 567 = 7x²
=> x² = 81
=> x = 9
We get x = 9, We know length = 7x so l = 63in
Hence, the Length of the Collage will be 63 inches.
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I would like to cover a box with contact paper. The box is 18in X 1'1 in x ain How much square in of Contact paper will be used.
The total amount contact paper required will depend on total surface area of the box which will be 778 square inches.
As per the question statement, we are given a box with dimensions
(18in x 1ft 1in x 5 in) and we are supposed to find the total amount contact paper required to cover it.
The total amount contact paper required to cover it will depend on the total surface area of the box.
Given length(L) = 18 inches
Given width(W) = 1 ft 1 in = 13 inches
Given height(H) = 5 inches
Total Surface Area of the box is given by the formula
Area = 2(LW + WH + HL)
Area = 2(18*13 + 13*5 + 5*18)
Area = 2*389
Area = 778 square inches
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If m = 8 and 3m + 72=4y – 56, then by the Substitution Property of Equality, 3(8) + 72 = 4y − ???
Answer:
56
Step-by-step explanation:
3m + 72 = 4y - 56
3(8) + 72 = 4y - 56
24 + 72 = 4y - 56
96 = 4y - 56
4y = 152
y = 38
3(8) + 72 = 4y - x
24 + 72 = 152 - x
96 = 152 - x
-56 = -x
x = 56
write an equation that passes through the point -9, 4 and is parallel to y=2/3x+19
The equation of the line that is parallel to y = 2/3x + 19 and passes through (-9, 4) is: y = 2/3x + 10.
How to Write the Equation of Parallel Lines?Two lines that are parallel have equal slope (m).
In the slope-intercept form of the equation of given line, y = mx + b:
m = slope of the lineb = y-intercept of the line.Given:
A point (-9, 4)
Equation, y = 2/3x + 19.
The slope (m) = 2/3.
The line that passes through (-9, 4) and is parallel to y = 2/3x + 19 would also have a slope (m) = 2/3.
Substitute (x, y) = (-9, 4) and m = 2/3 into y = mx + b to find the value of b:
4 = 2/3(-9) + b
4 = -6 + b
4 + 6 = b
b = 10
To write the equation, substitute m = 2/3 and b = 10 into y = mx + b:
y = 2/3x + 10.
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mcdonald's sells the big mac for $2.50 in 1998, while a competing restaurant, burger king, sold the whopper for $0.75. The management of Mcdonalds develops a business plan for future growth that projects an increase in the price of big macs of $0.25 per year, while the management of burger king develops a plan aimed at increasing the price of the whopper by 15% each year.
What would be the function of both burger king and mcdonalds
The function of both burger king and mcdonalds cost are respectively; C(n) = 0.75(1.15)ⁿ and C(n) = 2.5 + 0.25n
How to find the function sequence?The formula for the nth term of an arithmetic sequence is given as;
aₙ = a + (n - 1)d
where;
a is first term
n is position of term
d is common difference
For McDonald's, we are told that the initial price is $2.50 and the common difference is $0.25. Thus, the function will be;
C(n) = 2.5 + 0.25n
where n is number of years after 1998
We are told that the cost in burger king increases by 15% each year. Thus, using formula for geometric progression, the function is;
C(n) = 0.75(1 + 0.15)ⁿ
C(n) = 0.75(1.15)ⁿ
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HELP ASAP HAS TO BE DONE BY TONIGHT
Answer:
first drop down is, doesn't matter. Second one is, must be the negative reciprocal of the slope of the original line. Third is, must be different from the y intercept of the original line. If the y intercepts are the same, the two lines will intersect as proven by one of the questions asked by the user.
Step-by-step explanation:
Hope this helps! :)
Which ordered pair could you remove from the relation {(–1, 0), (1, 3), (2, 2), (2, 3), (3, 1)} so that it becomes a function
Answer:(3,1)
Step-by-step explanation:
Because you cant have (1,3) and (3,1).
Answer:
(2,3)
or (2,2) if the function does not need to be continuous.
Step-by-step explanation:
For a set of points to be considered a function, it must be true that for every X value, you have only a single Y value solution.
In other words, looking through your points listed, you would remove any point where an X value appears twice with different Y values.
[tex](X,Y)\\(-1,0)\\(1,3)\\(2,2) < -\\(2,3) < -\\(3,1)\\\\[/tex]
Notice the two points with arrows, both have 2 as their X value, but different Y values. Removing either one of them would make this a function. Although, by removing (2,3) the function has the potential to also be continuous, because having two of the same Y value for different X values would cause a piece-wise function which is generally non-continuous.
Answer the questions in the photo ( will mark brainliest if correct )
Angles of a polygon add to 360 degrees. To find the measure of each exterior angle of a regular n-gon. divide 360 by n.
18) 27.719) 36020) 12021) 36022) 4523) 20Which equation compares the number of computers in b to the number a?
Answer:
3 × 5 = 15
Step-by-step explanation:
5 is the common number
Simplify.
3c + 6d + 3d = ?
Answer 3c+9d
Step-by-step explanation: add 3c 9d
Five less than the quotient of eighteen and a number n in algebraic expression
The provided sentence "Five less than the quotient of eighteen" is converted into an algebraic expression as 18/x - 5.
What is defined as the algebraic expression?Algebraic expressions are mathematical statements that result from operations on variables and constants including such addition, subtraction, multiplication, and division. We simply combine like terms to explain an algebraic expression. As a result, similar variables will be combined. A same powers will now be combined from the like variables.Five less than the quotient of eighteen and a number
We must convert the provided sentence into an algebraic expression.
Let "x" represent the number.
Therefore,
Five less than that of the quotient of eighteen and "x"
The term quotient refers to the outcome of division.
Therefore,
18/x - 5
That is, Five less than the quotient of eighteen and x.
As a result, the provided sentence is converted into an algebraic expression.
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Jason's square bedroom has an area of 112 square feet. The length of one
of his room is between what two whole numbers?
Multiplying Radicals.
2. What is the value of x when y = 17 for the quadratic function
f(x) = x² + 6x + 10?
A. -7 only
B. 1 only
C. 7 only D. -7 and 7
E. -7 and 1
Value of x when y = 17 for the quadratic function f(x) = x² + 6x + 10 is -7 and 1. That is option E.
Given, y=17 :
17 = x² + 6x + 10
Move 17 to RHS (right-hand side) :
0 = x² + 6x - 7
Using the Middle Splitting method:
0 = x² + (7x - 1x) - 7
0 = x(x + 7) - 1(x+7)
0 = (x - 1) (x + 7)
Now, equate both the equations (x-1) and (x+7) separately with 0.
The first value of x is
(x - 1) = 0
x = 1
The second value of x is
(x + 7) = 0
x = -7
∴ The values of x are -7 and 1. According to the question, that is option E.
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Make x the subject of the equation. Y=2x-a
Answer:
1/2y+1/2a=x
Divide both sides by2, then but the a value on the other side.