Answer:
Step-by-step explanation:To find the limit of p(x) as x approaches -3, we can first simplify the expression by factoring the numerator:
p(x) = (x^4 - x^3 - 1) / x^2(x + 1)
= [(x - 1)(x^3 + x^2 - x - 1)] / [x^2(x + 1)]
Now, when x approaches -3, the denominator of the fraction becomes zero, which means we have an indeterminate form of the type 0/0. To evaluate the limit, we can use L'Hopital's rule, which states that if we have an indeterminate form of the type 0/0 or infinity/infinity, we can take the derivative of the numerator and denominator separately and then evaluate the limit again.
Taking the derivative of the numerator and denominator, we get:
p'(x) = [(3x^2 - 2x - 1)(x^2 + 2x) - 2(x - 1)(2x + 1)] / [x^3(x + 1)^2]
Now, plugging in x = -3 into the derivative, we get:
p'(-3) = [(3(-3)^2 - 2(-3) - 1)((-3)^2 + 2(-3)) - 2((-3) - 1)(2(-3) + 1)] / [(-3)^3((-3) + 1)^2]
= [28 - 44] / [(-3)^3(-2)^2]
= -16 / 108
= -4 / 27
Since the derivative is defined and nonzero at x = -3, we can conclude that the original limit exists and is equal to the limit of the derivative, which is:
lim x->-3 p(x) = lim x->-3 [(x - 1)(x^3 + x^2 - x - 1)] / [x^2(x + 1)]
= p'(-3)
= -4 / 27
Therefore, the limit of p(x) as x approaches -3 is equal to -4/27.
Answer:
[tex]\lim_{x \to -3}p(x) =-\dfrac{107}{18}[/tex]
Step-by-step explanation:
Given the function [tex]p(x)=\dfrac{x^4-x^3-1}{x^2(x+1)}[/tex]
Let's give the expressions in the numerator and denominator their own function names so they are easy to refer to:
n, for numerator: [tex]n(x)=x^4-x^3-1[/tex]
d, for denominator: [tex]d(x)=x^2(x+1)[/tex]
So [tex]p(x)=\dfrac{n(x)}{d(x)}[/tex]
Now, we want the limit of p(x) as x goes to -3.
[tex]\lim_{x \to -3}p(x) =\lim_{x \to -3}\dfrac{n(x)}{d(x)}[/tex]
For limits of quotients, it is important to analyze the numerator and the denominator.
Take a moment to observe that inputting -3 into the denominator is defined and does not equal zero: [tex]d(-3)=(-3)^2((-3)+1)=-18\ne0[/tex]
Also, observe that inputting -3 into the numerator is defined: [tex]n(-3)=(-3)^4-(-3)^3-1=81+27-1=107[/tex]
Importantly, both functions n & d are polynomials, which are functions that are continuous over [tex]\mathbb{R}[/tex].
Since both functions n & d are continuous, both n & d are defined at [tex]x=-3[/tex], and [tex]d(-3)\ne0[/tex], then the limit of the quotient is the quotient of the limits:
[tex]\lim_{x \to -3}\dfrac{n(x)}{d(x)}=\dfrac{ \lim_{x \to -3}n(x)}{ \lim_{x \to -3}d(x)}[/tex]
From here, again, since n & d are continuous over [tex]\mathbb{R}[/tex] and defined at the limit, [tex]\lim_{x \to -3}n(x)}=n(-3)[/tex] and [tex]\lim_{x \to -3}d(x)}=d(-3)[/tex].
Therefore,
[tex]\lim_{x \to -3}p(x) =\lim_{x \to -3}\dfrac{n(x)}{d(x)}=\dfrac{ \lim_{x \to -3}n(x)}{ \lim_{x \to -3}d(x)}=\dfrac{n(-3)}{d(-3)}=\dfrac{107}{-18}=-\dfrac{107}{18}[/tex]
A local supermarket offers a pack of 12 sodas for $3.48 on sale, and the local discount warehouse offers the soda in a 36-can case for $11.52. Which is the better value?
If local supermarket offers a pack of 12 sodas for $3.48 on sale, and the local discount warehouse offers the soda in a 36-can case for $11.52, In terms of price per soda, the supermarket pack is the better value.
To determine which is the better value between the supermarket pack of 12 sodas for $3.48 and the discount warehouse 36-can case for $11.52, we need to calculate the price per soda for each option.
For the supermarket pack, the price per soda can be found by dividing the total cost by the number of sodas in the pack:
Price per soda = $3.48 / 12 = $0.29
For the discount warehouse case, the price per soda can be found by dividing the total cost by the number of sodas in the case:
Price per soda = $11.52 / 36 = $0.32
From these calculations, we can see that the price per soda is lower for the supermarket pack at $0.29 compared to $0.32 for the discount warehouse case. Therefore, in terms of price per soda, the supermarket pack is the better value.
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Beth has three as much money as Dennis. Dennis has $20 more than Will. If all of them had a total of $1260, how much money does Beth have?
Answer:
Beth has $752
Step-by-step explanation:
First we lay out what we know:
Beth: 3x+20
Will: x
Dennis: x+20
Next we write the equation:
3x+20+20+x+x=1260
Then we add any numbers that can be added to each other:
5x+40=1260
Then we solve,
We first minus 40 from both sides of the equation,
5x+40=1260
-40 -40
---------------------
5x=. 1220
Last we divide 1220 by 5,
5x=1220
÷5. ÷ 5
----------------
x=244
Now that we know that x is 244 we fill in the blanks,
Beth: 732+20
Will: 244
Dennis: 244+20
Then we just solve the equations,
Beth: 732+20=752
Will: 244
Dennis: 244+20=264
That's it,
if you want to check your work you can add them all up and if they equal 1260 it's correct.
752+244+264=1260
Your welcome, have a good day/night.
-5-4-3-2
y
5
3
+ do
Mark this and return
23
Which equation represents a circle with the same
radius as the circle shown but with a center at (-1, 1)?
(x-1)2 + (y + 1)² = 16
(x-1)² + (y + 1)² = 4
(x + 1)² + (y-1)² = 4
O(x + 1)² + (y-1)² = 16
Save and Exit
Next
Submis
The equation that represents the circle is (x + 1)² + (y - 1)² = 16
Writing the equation that represents a circleThe equation of a circle with center (h,k) and radius r is:
(x - h)² + (y - k)² = r²
To find the equation of the circle with center (-1,1) and radius 4, we need to shift the center of the circle to (-1,1).
We can do this by replacing x with (x - (-1)) = (x + 1) and y with (y - 1) in the equation of the original circle. This gives:
(x + 1)² + (y - 1)² = 16
This equation represents a circle with center (-1,1) and radius 4.
Therefore, the correct option is (O) (x + 1)² + (y - 1)² = 16.
The other options do not have the correct center or radius to describe the circle.
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bao mom is picking him up from the ice rink she is at home which is located at the origin (0,0) how many total units is the ice rink away from the origin explain
The total units of length for the ice rink away from the origin is 14.42 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
Note: Ice rink is located at point (12, 8).
By substituting the given end points into the distance formula, we have the following;
Distance = √[(12 - 0)² + (8 - 0)²]
Distance = √[(12)² + (8)²]
Distance = √[144 + 64]
Distance = √208
Distance = 14.42 units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Solve For X
Solve For Y
Using the properties of a parallelogram, the values of x and y are:
x = 9; y = 22.
How to Find x and y in the Parallelogram?Since the opposite sides are parallel and equal to each other in the parallelogram above, therefore, Opposite angles are equal (or congruent) while the consecutive angles are supplementary to each other.
Therefore, we have:
6y = 180 - 48
6y = 132
Divide both sides by 6:
6y/6 = 132/6
y = 22
(5x + 3) + 6y = 180
5x + 3 + 6(22) = 180
5x + 135 = 180
5x = 180 - 135
5x = 45
x = 9
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S=4lw +2wh s=92 l=9 w=2
Answer:
h=5
Step-by-step explanation:
Substituting in 92 for s,
92=4lw+2wh
Substituting in 9 for l,
92=4(9)(w)+2wh
Substituting 2 for w,
92=4(9)(2)+2(2)(h)
Simplifying by multiplying terms
92=72+4h
Subtract 72 on both sides
20=4h
Divide by 4 on both sides
5=h
Simplify. (x-6)^3Write your answer without using negative exponents.
Answer:
x^3-18x^2+108x-216
There is a formula for this simplification, and you can write the answer directly if you remember the formula.
PLS HELP ME OUT! A sporting event has a promotion in which the first 1,000 fans to enter the arena receive either a blue cap or a red cap. A random number generator is used to simulate the color of a cap given to a person where indicates a blue cap and indicates a red cap. Ten simulations, each consisting of ten random numbers, are conducted, and the results
are shown in the following table:
Based on the simulations, what is the probability that ten hats given to ten people will consist of more blue caps than red caps? a. 0.20
b. 0.40 c. 0.60 d. 0.80
The probability that ten hats given to ten people will consist of more blue caps than red caps is given as follows:
a. 0.2.
Here, we have to calculate a probability:
A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The outcomes in which there are more blue than red caps are those in which the number of zeros is greater than the number of ones, hence the number of desired outcomes is of:
2. (simulation number 7 and simulation number 10).
Hence the probability is of:
p = 2/10
p = 0.2.
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Solve. Show the system of equations used and your work in solving the system.
A phone store sells Android phones for $400 and iOS phones for $650 each. This
week they sold a total of 110 phones and earned $54,000. How many Android and
how many iOS phones did they sell?
Let's assume that the number of Android phones sold is x and the number of iOS phones sold is y. Then we can write two equations based on the given information:
x + y = 110 (equation 1)
400x + 650y = 54000 (equation 2)
To solve for x and y, we can use any method of solving systems of equations. Here, we will use the substitution method:
From equation 1, we can solve for x in terms of y: x = 110 - y
Substitute x = 110 - y into equation 2 and solve for y:
400(110 - y) + 650y = 54000
44000 - 400y + 650y = 54000
250y = 10000
y = 40
Substitute y = 40 into equation 1 and solve for x:
x + 40 = 110
x = 70
Therefore, the phone store sold 70 Android phones and 40 iOS phones.
Suppose that the functions f and g are defined as follows.
Find f.g and f+ g. Then, give their domains using interval notation.
Using interval notation, the domain of f.g and f+g is [1/4, ∞).
Given, f(x)= 1/ (5x² + 3) and [tex]g(x) = \sqrt{4x-1}[/tex]
To find f.g, we substitute g(x) into f(x) and simplify:
f.g(x) = f(g(x))
[tex]=f(\sqrt{4x-1})[/tex]
[tex]=\frac{1}{5(\sqrt{4x-1})^2 +3}[/tex]
= 1/(5(4x-1)+3)
= 1 / (20x - 2)
To find f+g, we add the functions f(x) and g(x):
f+g(x) = f(x) + g(x)
= [tex]\frac{1}{5x^2+3}+\sqrt{4x-1}[/tex]
The domain of f.g and f+g is the intersection of the domains of f(x) and g(x).
The domain of f(x) is all real numbers except for the values of x that make the denominator zero, i.e., 5x² + 3 = 0. This equation has no real solutions, so the domain of f(x) is all real numbers.
The domain of g(x) is the set of all real numbers that make the argument of the square root non-negative, i.e., 4x - 1 ≥ 0. Solving this inequality, we get x ≥ 1/4.
Therefore, the domain of f.g and f+g is x ≥ 1/4.
Using interval notation, the domain of f.g and f+g is [1/4, ∞).
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Who can help me with this?
The original price of this car is equal to $6,600.
What is a percentage?In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
Assuming the original price is represented by the variable x, we have the following:
12.5/100 × x = x - 5,775
0.125x = x - 5,775
5,775 = (x - 0.125x)
5,775 = 0.875x
x = 5,775/0.875
x = $6,600.
In conclusion, we can logically deduce that the percentage Pat Bain paid is 87.5%.
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Suppose the function f(t) = e^t describes the growth of a colony of bacteria, where t is hours. find the number of bacteria present at 5 hours
a) 59.598
b) 148.413
c) 8.155
d) 79. 432
The number of bacteria present at 5 hours is (b) 148.413
How can the number of bacteria present be described?From the question, we were given,
f(t) = eᵗ
Then f(t) = number of bacterials present at a particular time t.
f(5) = number of bacterial present at 5 hours
So, we have
f(5) = e⁵
f(5) = 148.413
Then this can be written in the whole number as 148 which implies that the second option is correct because using f(t) = eᵗ to describes the growth of a colony of bacteria will provide us with the answer
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Bandar Industries manufactures sporting equipment. One of the company’s products is a football helmet that requires special plastic. During the quarter ending June 30, the company manufactured 3,500 helmets, using 2,485 kilograms of plastic. The plastic cost the company $16,401.
According to the standard cost card, each helmet should require 0.66 kilograms of plastic, at a cost of $7.00 per kilogram.
Required:
1. What is the standard quantity of kilograms of plastic (SQ) that is allowed to make 3,500 helmets?
2. What is the standard materials cost allowed (SQ × SP) to make 3,500 helmets?
3. What is the materials spending variance?
4. What is the materials price variance and the materials quantity variance
1. The standard quantity of plastic allowed to make 3,500 helmets is 2,310 kilograms.
2. The standard materials cost allowed to make 3,500 helmets is $16,170.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
1. The standard quantity of kilograms of plastic (SQ) allowed to make 3,500 helmets can be calculated as:
SQ = Standard quantity per unit × Actual output
= 0.66 kg/helmet × 3,500 helmets
= 2,310 kg
Therefore, the standard quantity of plastic allowed to make 3,500 helmets is 2,310 kilograms.
2. The standard materials cost allowed (SQ × SP) to make 3,500 helmets can be calculated as:
Standard materials cost allowed = Standard price × Standard quantity allowed
= $7.00/kg × 2,310 kg
= $16,170
Therefore, the standard materials cost allowed to make 3,500 helmets is $16,170.
3. The materials spending variance can be calculated as the difference between the actual cost incurred and the standard cost allowed:
Materials spending variance = Actual materials cost - Standard materials cost allowed
= $16,401 - $16,170
= $231 (Favorable)
Therefore, the materials spending variance is $231 (Favorable).
4. The materials price variance and the materials quantity variance can be calculated as follows:
Materials price variance = (Actual price - Standard price) × Actual quantity
= ($16,401/2,485 kg - $7.00/kg) × 2,485 kg
= $9,141.77 (Unfavorable)
Materials quantity variance = (Actual quantity - Standard quantity allowed) × Standard price
= (2,485 kg - 2,310 kg) × $7.00/kg
= $1,225 (Unfavorable)
Therefore, the materials price variance is $9,141.77 (Unfavorable) and the materials quantity variance is $1,225 (Unfavorable).
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find the margin of error given the values of C, stigma, and n.
c= 0.95, stigma=3.4, n=100
E=?
The margin of error is E = 0.67.
To find the margin of error
We can use the formula:
E = z* (σ / sqrt(n))
Where
E is the margin of errorz* is the z-score corresponding to the desired level of confidence Cσ is the population standard deviation (also known as the population parameter) n is the sample sizeIn this case, we are given that C = 0.95, σ = 3.4, and n = 100. We can use a standard normal distribution table to find the z-score that corresponds to a 95% confidence level, which is approximately 1.96.
Substituting the values:
E = 1.96 * (3.4 / sqrt(100))
E = 1.96 * 0.34
E = 0.6664
Rounding to two decimal places, the margin of error is approximately 0.67.
Therefore, the margin of error is E = 0.67.
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Which expression is equivalent to 6^2/7 ?
Answer: A
Step-by-step explanation:
well i did alll of them and got A
area of traingle is what if square root 6 in height iand base is square root 24
The area of the triangle that has height of √6 and a base of √24 is calculated as: 6 square units.
How to Find the Area of a Triangle?The area of a triangle = 1/2 * b * h, where:
h is the height of the triangle, and
b is the base length of the triangle.
Given the following:
Height of triangle = √6
Base length of the triangle = √24
Plug in the values:
Area of triangle = 1/2 * √24 * √6
= (√24 * √6) / 2
= √144 / 2
= 12/2
Area of triangle = 6 square units.
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Solve for x. −−9x+5<17 AND13x+25<−1
Answer: x<4/3
Step-by-step explanation: 17-5=12/9
If the third and fourth term of an arithmetic sequence are -1 and -4, what are the first and second terms?
Answer: 5 and 2
Step-by-step explanation:
In an arithmetic sequence, the difference between consecutive terms is constant. Since the third and fourth terms are -1 and -4, the common difference is -4 - (-1) = -3. Therefore, the second term is -1 - (-3) = 2 and the first term is 2 - (-3) = 5. So the first and second terms of the sequence are 5 and 2 respectively.
PLEASE HELP ME WITH THIS IM SO CONFUSED
The probability of hitting the shaded region is 0.755 or 75.5%.
What is the probability of hitting the shaded region?To find the probability of hitting the shaded region, we need to find the area of the shaded region and divide it by the area of the entire square.
Let's label the side length of the small square as x.
Then, we know that the diagonal of the small square is 7, so we can use the Pythagorean theorem to solve for x:
x^2 + x^2 = 7^2
2x^2 = 49
x^2 = 24.5
So the area of each white square is x^2 = 24.5 square units.
Let's label the side length of the large square as y.
Then, we know that the diagonal of the large square is 20, so we can use the Pythagorean theorem to solve for y:
y^2 + y^2 = 20^2
2y^2 = 400
y^2 = 200
So the area of the large square is y^2 = 200 square units.
Now, we can find the area of the shaded region by subtracting the area of the two white squares from the area of the large square:
Area of shaded region = Area of large square - 2 * Area of white square
= 200 - 2(24.5)
= 151
Therefore, the probability of hitting the shaded region is:
Probability = Area of shaded region / Area of entire square
Probability = 151 / 200
Probability = 0.755 or 75.5% (rounded to one decimal place)
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Find the approximate area of the shaded region below, consisting of a right triangle with a circle cut out of it. Use 3.14 as an
approximation for pi.
O 1.254 square meters
O 312 square meters
O2, 822 square meters
O 314 square meters
Answer:
(a) 1.254 square metersStep-by-step explanation:
We are given a figure, consisting of a right triangle with a circle cut out of it.
To Calculate : area of the shaded region below,
First Let's find the Area of the right triangle:
Area(triangle) = 1/2 × Base × Height
= 1/2 × 56 × 56
= 1/2 × 3136
= 3136/2
= 1568 m².
Now, We are diameter of the circle = 20 m
Radius of the circle = 20/2 = 10 m
Area of circle = πr²Acc. to question we have to use 3.14 as an
approximation for pi.
Area (circle) = 3.14 × 10 × 10
Area (circle) = 3.14 × 100
Area (circle) = 314 m²
Area of shaded region = Area of triangle - Area of circle =
= 1568 m² - 314 m²
= 1.254 square meters
Therefore, The approximate area of the shaded region is 1.254 square meters.
Option (a) is the required answer
Find the terms: a=_1=8, r=0.7
The formula of the nth term of the sequence is f(n) = 8 *0.7r^(n - 1)
Finding the terms of the sequence:From the question, we have the following parameters that can be used in our computation:
a=_1=8, r=0.7
Express properly
So, we have
First term, a = 8
Common ratio, r = 0.7
The above definition is of a geometric sequence that has a first term of 8 and a common ratio of 0.7
Using the above as a guide, we have the following:
f(n) = a * r^(n - 1)
substitute the known values in the above equation, so, we have the following representation
f(n) = 8 *0.7r^(n - 1)
Hence, the nth term of the sequence is f(n) = 8 *0.7r^(n - 1)
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ACTIVITY 2: Solve the following problems completely.
1) The amount is php 340,060
2) The rate is 13%
3) The amount is php 137,622
What is the compound interest?Compound interest is commonly used in many types of financial products, such as savings accounts, CDs, and loans.
1)
[tex]A = P(1 + r/n)^nt\\A = 80000( 1 + 0.16)^9.75\\A = php 340,060[/tex]
2)
[tex]12300 = 9750(1 + r)^2\\12300/9750 = (1 + r)^21.26 = (1 + r)^2\\ln 1.26 = 2 ln1 + r\\ln 1.26/2 = ln1 + r\\0.12 = ln1 + r\\e^{0.12} = 1 + r\\r = e^{0.12} - 1\\r = 0.13\\r = 13%[/tex]
3)
[tex]A = 50000(1 + 0.15/2)^2 * 7\\A = php 137,622[/tex]
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Someone help i really need help with this
Answer:
35 pages per minute
Step-by-step explanation:
175/5= 35
Check
35 x 5 = 175
175/35= 5
If the median of a data set is 13 and the mean is 13, which of the following is most likely?
Select the correct answer below:
a. The data are skewed to the left.
b. The data are skewed to the right.
c. The data are symmetrical.
Answer:
C
Step-by-step explanation:
if the mean and median are the same, the graph will be symmetrical
which has the greatest rate? y = -x , y = 3/4x +1, y = 1/2x +2, y = x
The function that has the greatest rate of change is y = x
Which function has the greatest rate of change?From the question, we have the following parameters that can be used in our computation:
y = -x ,
y = 3/4x +1,
y = 1/2x +2,
y = x
A linear function is represented as
y = mx + c
Where
rate of change = m
So, we have
y = -x , rate = -1
y = 3/4x +1, rate = 3/4
y = 1/2x +2, rate = 1/2
y = x, rate = 1
This means that the function with the highest rate is y = x
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write two different equations with variables and draw a diagram to solve the situation. For cleaning the attic Kristin was given $18. now she has $50. how much money did she have before
Once again, we get the same answer: Kristin had $32 before receiving the $18 for cleaning the attic. we solve this by forming equation and solving it
what is equation ?
An equation is a mathematical statement that shows that two expressions are equal. It usually consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems in various fields, including mathematics, physics, engineering
In the given question,
Let's use "x" to represent the amount of money Kristin had before receiving the $18 for cleaning the attic. We can set up the following equation:
x + 18 = 50
This equation represents the total amount of money Kristin has now, which is $50, after receiving the $18 for cleaning the attic. To solve for "x", we can subtract 18 from both sides of the equation:
x + 18 - 18 = 50 - 18
x = 32
Therefore, Kristin had $32 before receiving the $18 for cleaning the attic.
Alternatively, we can also use a diagram to represent the situation. We can draw a rectangle to represent the total amount of money Kristin has now, which is $50. We can then divide the rectangle into two parts: one part representing the $18 she received for cleaning the attic, and the other part representing the amount of money she had before. We can label this unknown amount as "x", and set up the following equation:
x + 18 = 50
This equation is the same as the one we set up earlier. To solve for "x", we can again subtract 18 from both sides of the equation:
x + 18 - 18 = 50 - 18
x = 32
Once again, we get the same answer: Kristin had $32 before receiving the $18 for cleaning the attic.
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Solve for x. Round to the nearest tenth, if necessary.
Answer:
Step-by-step explanation:
You are looking for the tangent ratio, which is opposite side over adjacent side. Using the tangent ratio of an angle of 37°.
tan37° = x/89
.75355405 = x/89
.75355405 · 89 = x/89 · 89/1
67.06 = x
rounded to 67.1
Answer:
67.1? that's what I got lol
Solution to augmented matrix? Never seen a problem like this one. How do I solve it?
The row of zeros at the bottom immediately lets us conclude "infinitely many solutions". This system is consistent and dependent. This is because we have 0x+0y+0z = 0 aka 0 = 0 which is always true for any choice of x, y, and z.
The second row of values lead to the equation 0x+0y+1z = 6, aka z = 6
The first row says: 1x+6y+0z = 1 which is the same as x+6y = 1
Let's say we isolate x
x+6y = 1
x+6y-6y = 1-6y
x = 1-6y
Then we have these three values or expressions
x = 1-6yy = any real numberz = 6All of the infinitely many solutions are of the form (x,y,z) = (1-6y, y, 6)
A lot of textbooks will use a parameter such as t, so we could write it as (1-6t, t, 6).
The choice of the letter for the parameter does not matter. I think t is most popular because it represents time. Each (x,y,z) point could represent a particle's location at any given time.
If t = 0, then we have (1, 0, 6)If t = 1, then we have (-5, 1, 6)If t = 2, then we have (-11, 2, 6)If t = 3, then we have (-17, 3, 6)and so on.
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Conclusion:
There are infinitely many solutions of the form (x,y,z) = (1-6t, t, 6) where t is any real number.
This system is consistent and dependent.
Malaika has a number of candies. She can give out 12 to each of her friends and have 3 left over. or she can give 9 out to each of her friends and have 12 left over. How many friends can receive candy?
If she can give out 12 to each of her friends and have 3 left over. or she can give 9 out to each of her friends and have 12 left over, Malaika has 3 friends who can receive candies.
Let's suppose Malaika has "c" candies, and "f" is the number of friends she has.
According to the problem statement, we have two equations:
c = 12f + 3
c = 9f + 12
To solve for "f", we can set the two equations equal to each other:
12f + 3 = 9f + 12
Simplifying the equation, we get:
3f = 9
Dividing both sides by 3, we get:
f = 3
We can verify our solution by plugging "f=3" back into one of the original equations:
c = 12f + 3
c = 12(3) + 3
c = 39
So, Malaika has 39 candies in total. We can also check the other equation to make sure it is true:
c = 9f + 12
c = 9(3) + 12
c = 39
Both equations are true, so our solution of "f=3" is correct.
To learn more about equation click on,
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the price of a shirt was $25, but it is now on sale for $20. what is the percent decrease in price?
