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Related Questions
Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F - G) (6) =
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The ordered pair (6, 9) in the definition of G tells you G(6) = 9.
(F-G)(6) = F(6) - G(6) = 8 - 9 = -1
Thanks for the explanation mate that was helpful^^
What substitution should be used to rewrite 4x12 – 5x6 – 14 = 0 as a quadratic equation? u = x2 u = x3 u = x6 u = x12
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Answer: [tex]u=x^6[/tex]
Explanation:
A quadratic equation is an equation written in the form
[tex]au^2 + bu + c=0[/tex] (1)
where a,b,c are coefficients and where u is the variable.
Our original equation is:
[tex]4x^{12} - 5x^6 -14=0[/tex]
If we make the substitution [tex]u=x^6[/tex], we obtain
[tex]4u^2 -5u-14 =0[/tex]
Which corresponds to eq.(1), with coefficients a=4, b=-5, c=-14.
In 1934 there was an extreme drought in the great plains. In the number 1934, is the value of the 9 in the hundreds place ten times the value of the 3 in the tens place?
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1,000 + 900 +30 +4
so the value of the 3 is 30, of the 9 is 900 and of the 1 is 1000.
900 is indeed 10 times 30, so
"the value of the 9 in the hundreds place ten times the value of the 3 in the tens place"
Answer: true
How do you subtract
-6 - (-7)?
Can you explain it step by step too? Thanks!
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what is the average group numbers for 85,92,84,85,96,95
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(85 + 92 + 84 + 85 + 96 + 95)/6 = 537/6 = 89.5
you're answer is 89.5 as average
hope this helps
find the center and radius for the circles with the following equation x^2+y^2-4x+6y+11=0
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Is the gcf of any two even numbers always even?
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the gcf can be found by factoring the 2 numbers and finding the factors common to both
any even number can be represented as 2n where n is an integer
so 2 even numbers are 2n and 2m
their factored form will be 2*n and 2*m, currently, their greatest common factor is 2*c where c is the gcf of n and m
and the gcf has to be an integer so c is an integer and therfor the gcf of 2n and 2m is even because it is 2c
yes, it is always even
C= m over 3 π d to the second power , for m
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C = 1/3 d^2 m π is equivalent to 1/3 d^2 m π = C:1/3 π d^2 m = C
Divide both sides by (π d^2)/3:Answer: m = (3 C)/(π d^2)
Joe's annual income has been increasing each year by the same dollar amount. The first year his income was $20,400 and the 11th year his income was $31,400. In which year was his income $40,200?
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Joe's income was $40,200 in the 18th year.
Explanation:To find the year in which Joe's income was $40,200, we need to determine the rate at which his income increases each year.
Given that his income increased by the same dollar amount each year, we can calculate the increase by subtracting his income in the first year from his income in the 11th year: $31,400 - $20,400 = $11,000.
Next, we can divide the increase in income by the number of years to find the increase per year: $11,000 ÷ 10 = $1,100.
Finally, to find the number of years it takes for his income to reach $40,200, we can divide the difference between $40,200 and $20,400 by the increase per year: ($40,200 - $20,400) ÷ $1,100 = 18.
Therefore, Joe's income was $40,200 in the 18th year.
15 greater than blank divided by 400
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15 more than A (blank) / 400
The ordered pair (3, –1) is a solution of which system?
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y < = x + 1.....(3,-1)...x = 3 and y = -1
-1 < = 3 + 1
-1 < = 4 (correct)
y > = -2.....(3,-1)....y = -1
-1 > = -2 (true)
so ur answer is the first one
To determine the system of equations to which the ordered pair (3, –1) is a solution, we must find equations where substituting 'x' with 3 and 'y' with –1 produces true statements for both equations in the system.
Explanation:The question pertains to finding the system of equations for which the ordered pair (3, –1) is a solution. To determine the correct system, we would need to identify equations that have both 'x' and 'y' variables. An ordered pair is composed of an 'x' coordinate and a 'y' coordinate, following the form (x, y). In this case, the 'x' value is 3, and the 'y' value is –1. If the ordered pair (3, –1) is a solution to a system of linear equations, it must satisfy both equations in the system. This means that when we substitute 'x' with 3 and 'y' with –1 into each equation, the equations should hold true.
For example, if we have a system of equations:
y = 2x - 7y = -x + 2Substituting 'x' with 3 and 'y' with –1 into both equations, we get:
–1 = 2(3) - 7, which simplifies to –1 = 6 - 7 and further to –1 = –1–1 = -3 + 2, which simplifies to –1 = –1Since the ordered pair (3, –1) satisfies both equations, then (3, –1) is a solution to this system. To identify the system of equations the ordered pair belongs to, you would similarly test the pair in the given systems to see which one(s) it satisfies.
You wave goodbye to a friend after physics class, and she rides off on her bike. after 3.0 s, she is 15 m away. how far away will she be after 30 s ?
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Final answer:
After 30 seconds, she will be 150 meters away.
Explanation:
To calculate how far the friend will be after 30 seconds on her bike, we must assume a constant velocity since no acceleration is mentioned. Given that she is 15 meters away after 3 seconds, we can calculate her velocity using the formula v = d/t, where v is velocity, d is distance, and t is time.
First, we find her velocity:
v = 15 m / 3 s = 5 m/s
Now that we have her velocity, we can calculate how far she will be after 30 seconds:
Distance = Velocity × Time = 5 m/s × 30 s = 150 m
Therefore, after 30 seconds, she will be 150 meters away.
A printer prints 28 photos in 8 minutes, how many minutes does it take to print 21 more photos?
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Which equals 3.5 photos per minutes.
Then you have to divide 21 by the photos per minute.
Which gives you your answer; It takes 6 minutes to print 21 more photos
Can someone please help me with this?
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Ax=B
where
A=[[6,-1],[-2,2]]
B=[2,16]
To solve for x, premultiply by the inverse of A
x=A^(-1)B
The inverse of A can be found as
A^(-1) = [[2,1],[2,6]]/(6*2-(-1)(-2)) [2,16]
=[[2,1],[2,6]]/10 [2,16]
=[[0.2,0.1],[0.2,0.6]] [2,16]
Verify the solution by matrix multiplication:
x=0.2*2+0.1*16=2
y=0.2*2+0.6*16=10
substitute into original equation,
6x-y=12-10=2 ok
-2x+2y=-4+20=16 ok.
It will be your duty as a student to find the right option from the answer.
18/x = 6/10 please put the work this question is hard
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(18)(10)= 6x
180=6x
Divide both sides by 6
30=x
Final answer: x=30
The sum of three consecutive integers is 153. Find the integers.
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x+x+1+x+2= 153
3x+3=153
3x=150
x=50
Final answer: 50, 51, 52
What is the base 8 representation of 112
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Answer:
160^8
Step-by-step explanation:
The base 8 representation of 112 is 160.
Explanation:The base 8 representation of 112 is 160.
To convert a number to base 8, you can divide the number by 8 repeatedly and write down the remainders in reverse order.
Here's the step-by-step process:
Divide 112 by 8: 112 ÷ 8 = 14 with a remainder of 0.Divide 14 by 8: 14 ÷ 8 = 1 with a remainder of 6.Divide 1 by 8: 1 ÷ 8 = 0 with a remainder of 1.Write down the remainders in reverse order: 160.
A recipe calls for 3 2/3 cups os flour. Earl used 7 1/3 cups. How did he increase the recipe?
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7 1/3 = 22/3
3 2/3 = 11/3
22/3 - 11/3 = 11/3 = 3 2/3
Use matlab to calculate the probability to get 3 times of '5' in 8 throws of a fair die
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q = 1 - p = 5/6, the probability of not getting a '5'.
Number of trials = 8
Expected number of successes = 3
The probability is
₈C₃ (1/6)³ (5/6)⁵ = 56*0.00463*0.40188 = 0.1042
Answer: 0.1042
evaluate the numerical expression 8×{[(7+4)×2]-(11-7)×4]}
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8x(22 - 4 x 4)
8x(22 - 16)
8x6 = 48
A rectangle has a width that is 3 more than twice the length. Its perimeter is 96 inches. What is width of the rectangle, in inches?
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-3 -3
2x=93
÷2 ÷2
x=46.5
the width of the rectangle is 46.5 inches
The width of the given rectangle is 33 inches.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Let's say the width of the rectangle is W while the length is L.
Given that,
A rectangle has a width that is 3 more than twice the length.
So,
W = 2L + 3
And,
Perimeter = 2(L + W) = 96
L + W = 48
By substitution,
L + 2L + 3 = 48
3L = 45
L = 15
So,
W = 2(15) + 3 = 33
Hence "The width of the given rectangle is 33 inches".
For more about rectangles,
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Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system
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[tex] \left[\begin{array}{ccc}1&h&4\\3&6&8\end{array}\right][/tex]
We perform the following matrix operations
[tex] \left[\begin{array}{ccc}1&h&4\\3&6&8\end{array}\right] -3R_1+R_2\rightarrow R_2 \\ \\ \left[\begin{array}{ccc}1&h&4\\0&6-3h&-4\end{array}\right] \frac{1}{6-3h}R_2\rightarrow R_2 \\ \\ \left[\begin{array}{ccc}1&h&4\\0&1&\frac{-4}{6-3h}\end{array}\right] -hR_2+R_1\rightarrow R_1 \\ \\ \left[\begin{array}{ccc}1&0& \frac{24-8h}{6-3h} \\0&1&\frac{-4}{6-3h}\end{array}\right][/tex]
Thus, the matrix is consistent for
[tex]h\neq6-3h \\ \\ h+3h\neq6 \\ \\ 4h\neq6 \\ \\ h\neq \frac{6}{4} \\ \\ h\neq \frac{3}{2} [/tex]
To determine the value(s) of h for a consistent linear system, the augmented matrix must not have any row that implies a contradiction, like 0x + 0y = c where c is non-zero. The exact values of h depend on the matrix itself and usually involve row reduction to identify non-contradictory solutions. The provided examples do not appear to relate directly to a linear system matrix.
Explanation:To determine the value(s) of h that result in the matrix representing a consistent linear system, we must ensure that there are no contradictions within the augmented matrix. If the matrix represents a system of linear equations, consistency is achieved when the system has at least one solution. A contradiction would occur if a row in the augmented matrix had all zeros in the coefficient part and a non-zero value in the last column, corresponding to an equation like 0x + 0y = c (where c is non-zero), which has no solution.
The exact values of h would be determined by the context of the specific matrix and its elements, usually involving row reduction to echelon form to identify possible contradictions. In some cases, specific values of h can lead to a row of all zeros, which does not affect consistency, but a particular non-zero value in the rightmost column would create inconsistency. Without the explicit matrix, we cannot provide the exact values of h.
In the examples provided, it seems there is a mix of mathematical equations and expressions that are not directly related to a specific matrix or linear system. As such, the value of h in those expressions may refer to concepts like the uncertainty principle in quantum mechanics or gravitational force in physics, and thus do not pertain to solving a system of linear equations.
You have diving lessons every fifth day and swimming lessons every third day. Today have both lessons in how many days will you have both lessons on the same day again.
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We know the LCM of 3 and 5 is 15.
So, 15 days.
Hope this helps!
The diving and swimming lessons will occur on the same day after 15 days because 15 is the smallest common multiple of 3 and 5.
Explanation:The question pertains to finding a common multiple of the numbers 3 and 5. These numbers represent the intervals at which you have swimming and diving lessons respectively. The first common multiple of 3 and 5, other than 1, is 15. Therefore, you will have both lessons on the same day again after 15 days.
This comes from the idea that a number's multiples are the set of numbers formed by multiplying that number by any of the whole numbers. So, the multiples of 3 are 3, 6, 9, 12, 15, 18, etc., while the multiples of 5 are 5, 10, 15, 20, etc. The number 15 is a multiple of both 3 and 5, therefore, it is a common multiple of 3 and 5.
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4y-4=16 what is the answer
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4y -4 (+4) = 16 + 4
4y = 20
4y/4 = 20/4
y = 5
hope this helps
+4 +4
4y=20
y=5
Hanna shops for socks that cost $2.99 for each pair and blouses that cost $12.99 each. Let x represent the number of pairs of socks purchased, and let y represent the number of blouses purchased. Which equation models the purchases she made with $43.92?
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Then $2.99x+$12.99y=$43.92.
Answer:
2.99x + 12.99y = 43.92
Step-by-step explanation:
Here, x represents the number of pairs of socks purchased, and let y represents the number of blouses purchased.
Since, the cost of each pair of socks is $ 2.99 and the cost of a blouse is $ 12.99,
Thus, the total cost of x pairs of socks and y blouses = ( 2.99x + 12.99y ) dollars,
According to the question,
Total cost is $43.92,
⇒ 2.99x + 12.99y = 43.92
Which is the required equation.
For any integer x, x squared -x will always produce an even value
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The square of an even number will generate an even number and
The square of an odd number will generate an odd number
Answer:
[tex](x^2 - x)[/tex] will always have an even value.
Step-by-step explanation:
We are given an integer x.
Let x be even, then it can be written in the form x = 2n, where n is an integer.
If we evaluate,
[tex](x^2 - x) = (2n)^2 - 2n = 4n^2 - 2n = 2(2n^2 - n)[/tex]
Thus, it have an even value.
If we take x to be an odd integer, then,it can be written in the form x = 2n+1, where n is an integer.
[tex](x^2 - x) = (2n+1)^2 - 2n = 4n^2 + 2n = 2(2n^2 + n)[/tex]
Thus, it have an even value.
Thus,
[tex](x^2 - x)[/tex] will always have an even value.
F = 3.5 x is a linear relationship. what data would you plot along the y-axis, the x-axis?
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What is the unit rate per bottle if a pack of 28 bottles of juice sells for $7? $0.25 per bottle $0.75 per bottle
$2.50 per bottle
$4.00 per bottle
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divide cost by number of bottles
7/28 = 0.25 per bottle
check 28 * 0.25 = 7.00
When is estimation an effective way to determine an answer
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A bag of fertilizer covers 2500 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 410 feet by 65 feet.
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Rectangular lawn is 410 x 65. Area= lw=(410)(65)=26650
26650/2500=10.66 so since we cannot purchase .66 of a bag, we will need 11 bags.
Answer:
11 bags
Step-by-step explanation:
Let x bags of fertilizer should be purchased.
The dimension of rectangular lawn is 410 feet by 65 feet.
The area of rectangle is given by
Area = length × width
Thus, the area of rectangular lawn is
Area = 410 × 65
Area = 26650
Now, one bag of fertilizer covers 2500 square feet of lawn.
Thus, we have
[tex]\frac{1}{2500}=\frac{x}{26650}\\\\2500x=26650\\\\\x=\frac{26650}{2500}\\\\x=10.66[/tex]
Hence, the required number of bags = 11.