Answer: C
Step-by-step explanation: Got it right
Final answer:
The matrix form representing the given situation with Janelle and Louisa's ages is a system of linear equations derived from the word problem, and can be represented as: [1 -1 | -5] and [0.5 -0.5 | -1.5].
Explanation:
The question involves setting up equations based on the given word problem and representing them in matrix form. The situation describes a relationship between the ages of Janelle and Louisa, with Janelle being five years younger than Louisa. In three years, Janelle will be half of Louisa's age. This can be represented with two equations:
j = l - 5
j + 3 = 0.5 * (l + 3)
These equations can then be represented in matrix form. Matrices are used in mathematics to represent systems of linear equations, and the equations stages can be translated into a matrix where each row represents an equation:
Matrix for the system of equations:
[1 -1 | -5]
[0.5 -0.5 | -1.5]
The first row of the matrix represents the first equation, showing the coefficients of j and l, and the constant term on the right side of the equation. The second row represents the second equation with the respective coefficients and constant term.
You eat at several Mexican restaurants and decide that Mexican food is hot. What type of reasoning is this?
Answer:
This is an example of inductive reasoning.
Step-by-step explanation:
You eat at several Mexican restaurants and decide that Mexican food is hot. This is an example of inductive reasoning.
Inductive reasoning is defined as the type of reasoning, where multiple premises are considered and all are believed to be true. These are combined to obtain a specific conclusion.
Find the quotient of the quantity negative 6 times x to the 2nd power times y to the 8th power plus 12 times x times y to the 3rd power minus 36 times x times y to the 2nd power all over 6 times x times y to the 2nd power.
Answer:
The quotient is:
[tex]xy^6+2y-6[/tex]
Step-by-step explanation:
We are asked to find the quotient of the mathematical expression which is given in terms of variable x and y is represented as:
[tex]=\dfrac{6x^2y^8+12xy^3-36xy^2}{6xy^2}[/tex]
Here the numerator is:
[tex]6x^2y^8+12xy^3-36xy^2[/tex]
and the denominator is:
[tex]6xy^2[/tex]
We can also represent our numerator term by the method of factoring it as:
[tex]6x^2y^8+12xy^3-36xy^2=6xy^2(xy^6+2y-6)[/tex]
Hence, our expression gets converted by replacing the numerator term to:
[tex]\dfrac{6x^2y^8+12xy^3-36xy^2}{6xy^2}=\dfrac{6xy^2(xy^6+2y-6)}{6xy^2}\\\\\dfrac{6x^2y^8+12xy^3-36xy^2}{6xy^2}=xy^6+2y-6[/tex]
Hence, the quotient is:
[tex]xy^6+2y-6[/tex]
Cassidy wrote the linear equation y=5x+4 Then, she wrote the equation of the line that is parallel to y=5x+4 and that passes through (8,–2). If her new equation is in the form y=5x+b what is the value of b? please helpppp
The angles of a triangle measure 4 degrees 86 degrees and 90 degrees classify the triangle
What is the mid point of (-4,-6), (3,-6)
U=-2a-3/ka, write an equation to solve for a (do not actually answer)
Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. C = 71°, a = 27, c = 26
We have
SinC/ c = Sin A / a
Sin 71/ 26 = Sin A / 27
Sin A = 27 Sin 71 / 26 = about .982
So°
Sin-1(.982) = A = 79. 08°
Then angle B = 180 - 71 - 79.08 = 29.92°
And b is given by
b/sin29.92 = 26/sin 71
b = 26sin29.92/sin71 = about 13.72
But A could also be an obtuse angle = 180 - 79.08 = 100.92°
So we have
B = 180 - 71 - 100.92 = 8.08°
And we have
b / sin 8.08 = 26/sin71
b = 26sin8.08/sin 71 = 3.865
Which is true about the completely simplified difference of the polynomials 6x6 − x3y4 − 5xy5 and 4x5y + 2x3y4 + 5xy5?
6.25=r to the second power. what is r?
Find the slope and give the slant of the line passing through the given pairs of points (4,-1)(-2,3)
y=f(x) is odd (f(-x)=-f(x)) and f(x>0) = x^2-5x-12, x is not = to 0. What points does the line f(x)=12 go through.
Perform the indicated operation. 1 2/3 + 5 3/8
A. 7 1/24
B. 6 5/24
C. 6 124
Answer: The correct option is (A) [tex]7\dfrac{1}{24}.[/tex]
Step-by-step explanation: We are given to perform the following indicated operation :
[tex]E=1\dfrac{2}{3}+5\dfrac{3}{8}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following rule :
[tex]a\dfrac{b}{c}=\dfrac{ac+b}{c}.[/tex]
From (i), we get
[tex]E\\\\=1\dfrac{2}{3}+5\dfrac{3}{8}\\\\\\=\dfrac{5}{3}+\dfrac{43}{8}\\\\\\=\dfrac{40+129}{24}\\\\\\=\dfrac{169}{24}\\\\\\=7\dfrac{1}{24}.[/tex]
Thus, the required answer is [tex]7\dfrac{1}{24}.[/tex]
Option (A) is CORRECT.
Use a table to compute the product below. (x2 + x + 9)(x - 6) A. x3 - 5x2 + 3x - 54 B. x3 - 5x2 - 3x - 54 C. x3 - 6x2 + 3x - 54 D. x3 - 7x2 + 3x - 54
x - 32 = 73 what dose x equal
x - 32 = 73
to get x add 32 to 73
32 +73 = 105
x = 105
What is the concentration of a new solution obtained by mixing 25ml of water with 125ml of a 20% salt solution in water?
We want to find the concentration (percentage of salt in volume) in a mix of 25 mL of water an 125 mL of a 20% salt solution.
We will find that the concentration is: 16.7%
Let's see how to get that.
The concentration will be given by the quotient between the amount of salt and the total volume.
The amount of salt will be given by:
s = 125mL*0.2
This is because a 20% of these 125 mL are salt.
And the total volume is just the sum between the volume of water (25 mL) and the volume of salt solution (125 mL)
v = 25 mL + 125 mL = 150 mL
Then the concentration will be:
s/v = 0.2*(125 mL)/(150 mL) = 0.167
Now we multiply this by 100% to get:
0.167*100% = 16.7%
The concentration of the mixture will be 16.7%, so when we mixed the solution with water the concentration decreased, as expected.
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An airplane has a total of 414 packets of crackers, pretzels, and peanuts available for passengers.
There are n packets of crackers.
There number of packets of pretzels is 9 more than twice the number of packets of crackers.
The number of packets of peanut is 3 times the number of packets of pretzels.
Part B
The airplane has seats for 144 passengers. The seats are arranged in 48 rows, with 3 seats in each row.
There are 132 passengers on a certain flight.
There are exactly 2 passengers in x rows.
There are exactly 3 passengers in y rows.
Write a system of linear equations that can be used to model the situation. Use your system to determine the number of rows with exactly 2 passengers and the number of rows with exactly 3 passengers. Show your work.
A system of linear equations can be used to model the given situation. The number of rows with exactly 2 passengers can be found by solving the equation 2x = 12, and the number of rows with exactly 3 passengers can be found by solving the equation 3y = 12.
Explanation:To write a system of linear equations, we need to translate the given information into algebraic expressions.
Let n be the number of packets of crackers.
According to the problem:
The number of packets of pretzels is 9 more than twice the number of packets of crackers: p = 2n + 9The number of packets of peanuts is 3 times the number of packets of pretzels: pn = 3(2n + 9)To determine the number of rows with exactly 2 passengers and 3 passengers:
Let x be the number of rows with exactly 2 passengersLet y be the number of rows with exactly 3 passengersThere are 48 rows and 3 seats in each row, so the total number of seats is 48 * 3 = 144132 passengers are on the flight, so there are 144 - 132 = 12 unoccupied seatsEach row with exactly 2 passengers contributes 2 unoccupied seats, so 2x = 12Each row with exactly 3 passengers contributes 3 unoccupied seats, so 3y = 12The system of linear equations is:
p = 2n + 9
pn = 3(2n + 9)
2x = 12
3y = 12
We can solve this system of equations to find the values of x and y.
Sharon spent 3.45 on sunflower seeds the price of sunflower seeds is 0.89 per pound how many pounds of sunflower seeds did sharon buy
(a^2^n - a^n - 6) / (a^n + 8) That's a power of 2n the 2n is an exponent
"what is the value of the digit in the ten thousands place for this number"
Write the equation of a line perpendicular to the line 3x +7y =21 with a y-intercept of (0, 2). Write your answer in standard form. Please explain how I can solve this, please!
A student solution to the equation 3X +2 equals 15 the show. Describe and correct the error that the student made.
Which of the following expression simplifies to 4/15?
A. -2/3-2/5
B. -2/5+2/3
C. -2/3 +2/5
D. 2/5+2/3
Answer quick plz
You are making gift baskets. each basket will contain three different types of candles: tapers, pillars ad jar candles. tapers cost $1 each, pillars cost $4 each, and jar candles cost $6 each. you put 8 candles costing a total of $24 in each basket, and you include as many tapers as pillars and jar candles combined. how many of each type of candle will be in a basket?
Which graph represents f(x)= -1/2x^3
Answer:
Last graph represents the given function.Step-by-step explanation:
First, we need to consider a few rules about transformation of functions, specifically about the negative sign and the division of the function by a number.
The negative sign indicates that the function has to be reflected regarding the vertical axis. The normal function is like the third option, and the reflect one is like the last graph.
On the other hand, the fraction presents a contraction of the function size, but this characteristics is not enough to select the right graph, because third and fourth options have the same size.
Therefore, according to the negative sign in the given function, the correct answer is the last graph.
We want to see which one of the given graphs is the graph of the function:
f(x) = (-1/2)*x^3
The correct graph is the last one, positive at the left, when x is negative, and negative at the right, when x is positive.
Let's analyze our function, first we know that the parent cubic function:
g(x) = x^3
Is negative for negative values of x and positive for positive values of x, then the graph is below the horizontal axis at the left, and above the horizontal axis at the right.
But our function multiplies this by a negative number, -1/2.
Then that is inverted, we should see that at the left, the graph is above the horizontal axis, and at the right the graph is below the horizontal axis.
Then the correct option is the last graph.
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Complete the relationship. 3.5 milliliters = __________ centiliters.
Using radicals what is an equivalent expression of y 1/5
Which of the following points are more than 5 units from the point P(−2, −2)? Select all that apply. A A (2, 1) B B (4, −1) C C (2, −3) D D (−6, −6) E E (−5, 1)
The distance between any 2 points P(a,b) and
Q(c,d) in the coordinate plane, is given by the formula:
[tex]|PQ|= \sqrt{ (a-c)^{2} + (b-d)^{2}}[/tex]
Using this formula we calculate the distances |PA|, |PB|, |PC|, |PD| and |PE| and compare to 5.
[tex]|PA|= \sqrt{ (-2-2)^{2} + (-2-1)^{2}}= \sqrt{16+9}= \sqrt{25}=5 [/tex]
[tex]|PB|= \sqrt{ (-2-4)^{2} + (-2+1)^{2}}= \sqrt{36+1}= \sqrt{37} \approx 6 [/tex]
[tex]|PC|= \sqrt{ (-2-2)^{2} + (-2+3)^{2}}= \sqrt{16+1}= \sqrt{17}\approx4 [/tex]
[tex]|PD|= \sqrt{ (-2+6)^{2} + (-2+6)^{2}}= \sqrt{16+16}= \sqrt{32}\ \textgreater \ \sqrt{25}=5 [/tex]
[tex]|PE|= \sqrt{ (-2+5)^{2} + (-2-1)^{2}}= \sqrt{9+9}= \sqrt{16}=4 [/tex]
Answer: B and D
Analyze the statements below and complete the instructions that follow. If Mike gets paid today, then Mike will go to the bank. Mike did not get paid today. If possible, draw a conclusion from the given statements. A. Mike will go to the bank. B. Mike will not go to the bank. C. Mike will get paid today. D. No conclusion is possible.
Given the statements, we cannot conclude whether Mike will or will not go to the bank; therefore, no conclusion is possible.
Explanation:The statement 'If Mike gets paid today, then Mike will go to the bank' sets up a conditional relationship where Mike going to the bank is dependent on whether he gets paid or not. The second statement 'Mike did not get paid today' is a fact that allows us to draw a conclusion about the first conditional statement.
Since the condition for Mike going to the bank (getting paid) is not met, we cannot conclude that Mike will go to the bank based on the information given. However, this also does not mean that Mike will not go to the bank for some other reason. Therefore, the only valid conclusion we can draw here is option D: 'No conclusion is possible' about Mike's action related to going to the bank.
What is the product of −2 1/4 and −4 1/ 2 ?
Enter your answer as a mixed number, in simplified form, in the box.
Answer: 81/8 simplified form = 10 1/8 mixed form
Step-by-step explanation:
Hi, to answer this question we have to solve the expression:
First, we have to convert the mixed fractions into improper fractions:
-2 1/4 = -(2 x 4 +1) /4 = -9/4
-4 1/2 = -( 4 x 2 + 1 ) / 2 = -9/2
Next, we have to simply multiply both numbers:
-9/4 x -9/2 = 81/8 simplified form = 10 1/8 mixed form
Feel free to ask for more if needed or if you did not understand something.
I thought of a number, added 4 5/7 to it, and got the number 12 times as big as my original what was my number
Answer:
3/7
Step-by-step explanation: