Find the local and absolute maximum and minimum points in (x, y) format for the
function f(x) = 3/5x^5 - 9x^3 + 2 on the closed interval [-4,5]. Answer the following
questions.
a) Find all critical numbers (x- coordinates only)
b) Find the intervals on which the graph is increasing Mark critical numbers
c) Find the intervals on which the graph is decreasing.
d) Find all local maximum points.
e) Find all local minimum points.
f) Find all absolute maximum points.
g) Find all absolute minimum points.
To find the local and absolute maximum and minimum points of the function f(x) = (3/5)x^5 - 9x^3 + 2 on the closed interval [-4,5], we need to follow these steps:
a) Find all critical numbers (x-coordinates only):
To find the critical numbers, we need to identify where the derivative of the function is zero or undefined. Let's find the derivative of f(x) first:
f'(x) = 3x^4 - 27x^2
Now, set the derivative equal to zero and solve for x:
3x^4 - 27x^2 = 0
Factoring out a common factor of 3x^2, we get:
3x^2(x^2 - 9) = 0
This equation is satisfied when either 3x^2 = 0 or x^2 - 9 = 0.
For 3x^2 = 0, we have x = 0.
For x^2 - 9 = 0, we have x = -3 and x = 3.
Therefore, the critical numbers (x-coordinates) are 0, -3, and 3.
b) Find the intervals on which the graph is increasing (mark critical numbers):
To determine the intervals of increasing, we need to analyze the sign of the derivative on each side of the critical numbers. We create a sign chart for f'(x):
Interval (-∞, -3): Choose a test point x < -3, e.g., x = -4
f'(-4) = 3(-4)^4 - 27(-4)^2 = 768 > 0
The derivative is positive, indicating the graph is increasing.
Interval (-3, 0): Choose a test point x between -3 and 0, e.g., x = -1
f'(-1) = 3(-1)^4 - 27(-1)^2 = -24 < 0
The derivative is negative, indicating the graph is decreasing.
Interval (0, 3): Choose a test point x between 0 and 3, e.g., x = 1
f'(1) = 3(1)^4 - 27(1)^2 = -24 < 0
The derivative is negative, indicating the graph is decreasing.
Interval (3, ∞): Choose a test point x > 3, e.g., x = 4
f'(4) = 3(4)^4 - 27(4)^2 = 768 > 0
The derivative is positive, indicating the graph is increasing.
Therefore, the graph is increasing on the intervals (-∞, -3) and (3, ∞).
c) Find the intervals on which the graph is decreasing (mark critical numbers):
From the analysis above, we can see that the graph is decreasing on the intervals (-3, 0) and (0, 3).
d) Find all local maximum points:
To find the local maximum points, we need to examine the points where the graph changes from increasing to decreasing. By observing the sign changes in the derivative, we can identify potential local maximum points.
From our analysis in part b, we can see that the graph changes from increasing to decreasing at x = -3 and x = 0. Therefore, these are the local maximum points.
e) Find all local minimum points:
To find the local minimum points, we need to examine the points where the graph changes from decreasing to increasing. By observing the sign changes in the derivative, we can identify potential local minimum points.
From our analysis in part c, we can see that the graph changes.
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Tyrone places a carton of milk and a box of cookies together. The carton of milk has a length of 6 inches, a width of 4 inches, and a height of 8 inches. The box of cookies has a length of 5 inches, a width of 4 inches, and a height of 2 inches. What is the combined volume of the boxes?
Therefore, the combined volume of the carton of milk and the box of cookies is 232 cubic inches.
To find the combined volume of the carton of milk and the box of cookies, we need to calculate the volume of each object and then add them together.
The volume of an object can be found by multiplying its length, width, and height. Let's calculate the volume for each item:
Carton of milk:
Volume = Length × Width × Height
= 6 inches × 4 inches × 8 inches
= 192 cubic inches
Box of cookies:
Volume = Length × Width × Height
= 5 inches × 4 inches × 2 inches
= 40 cubic inches
Now, we can find the combined volume by adding the volumes of the carton of milk and the box of cookies:
Combined Volume = Volume of Carton of milk + Volume of Box of cookies
= 192 cubic inches + 40 cubic inches
= 232 cubic inches
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A 52-card deck contains 13 cards from each of the four suits: clubs ♣, diamonds ♦, hearts ♥, and spades ♠. You deal four cards without replacement from a well-shuffled deck so that you are equally likely to deal any four cards.
What is the probability that all four cards are clubs?
13/52 ⋅ 12/51 ⋅ 11/50 ⋅ 10/49 ≈0.0026
13/52 ⋅ 12/52 ⋅ 11/52 ⋅ 10/52 ≈0.0023
1/4 because 1/4 of the cards are clubs
The probability that all four cards are clubs is approximately 0.0026. Option A.
To understand why, let's break down the calculation. In a well-shuffled deck, there are 13 clubs out of 52 cards.
When dealing the first card, there are 13 clubs out of the total 52 cards, so the probability of getting a club on the first draw is 13/52.
For the second card, after the first club has been removed from the deck, there are now 12 clubs left out of the remaining 51 cards. Therefore, the probability of getting a club on the second draw is 12/51.
Similarly, for the third card, after two clubs have been removed, there are 11 clubs left out of the remaining 50 cards. The probability of drawing a club on the third draw is 11/50.
Finally, for the fourth card, after three clubs have been removed, there are 10 clubs left out of the remaining 49 cards. The probability of drawing a club on the fourth draw is 10/49.
To find the probability of all four cards being clubs, we multiply the probabilities of each individual draw:
(13/52) * (12/51) * (11/50) * (10/49) ≈ 0.0026.
This calculation takes into account the fact that the deck is being dealt without replacement, meaning that the number of available clubs decreases with each draw.
The third option, 1/4, is incorrect because it assumes that each card dealt is independent and has an equal probability of being a club. However, as cards are drawn without replacement, the probability changes with each draw. So Option A is correct.
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Note the complete question is
A 52-card deck contains 13 cards from each of the four suits: clubs ♣, diamonds ♦, hearts ♥, and spades ♠. You deal four cards without replacement from a well-shuffled deck so that you are equally likely to deal any four cards.
What is the probability that all four cards are clubs?
A.) 13/52 ⋅ 12/51 ⋅ 11/50 ⋅ 10/49 ≈0.0026
B.) 13/52 ⋅ 12/52 ⋅ 11/52 ⋅ 10/52 ≈0.0023
C.) 1/4 because 1/4 of the cards are clubs
The statement of cash flows for Baldwin shows what happens in the cash account during the year. It can be seen as a summary of the sources and uses of cash. Pleas answer which of the following is true if Baldwin issues bonds
measure abc bac=40degree abc=20degree ab=7cm
The length of side BC is approximately 3.725 cm.
In triangle ABC, we are given that angle BAC is 40 degrees, angle ABC is 20 degrees, and side AB measures 7 cm. We need to find the length of side BC.
To solve this problem, we can use the law of sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides.
Applying the law of sines, we have:
sin(ABC) / BC = sin(BAC) / AB
Since sin(ABC) = sin(20 degrees) and sin(BAC) = sin(40 degrees), we can substitute these values into the equation:
sin(20 degrees) / BC = sin(40 degrees) / 7 cm
Now, we can rearrange the equation to solve for BC:
BC = (7 cm * sin(20 degrees)) / sin(40 degrees)
Using a calculator to evaluate the trigonometric functions, we find that sin(20 degrees) ≈ 0.3420 and sin(40 degrees) ≈ 0.6428. Substituting these values into the equation:
BC ≈ (7 cm * 0.3420) / 0.6428
BC ≈ 3.725 cm
Therefore, the length of side BC is approximately 3.725 cm.
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Please answer ASAP I will brainlist
Answer:
Step-by-step explanation:
The given augmented matrix is already in reduced row echelon form. We can interpret it as a system of equations as follows:
1x + 0y + 0z + (4/5)w = 0
0x + 1y + 0z + 5w = 0
0x + 0y + 1z - 4w = 0
0x + 0y + 0z + w = -4
From the last row, we can see that w = -4. Substituting this value back into the previous rows, we get:
1x + 0y + 0z + (4/5)(-4) = 0
0x + 1y + 0z + 5(-4) = 0
0x + 0y + 1z - 4(-4) = 0
Simplifying these equations, we have:
x - (16/5) = 0
y - 20 = 0
z + 16 = 0
From the second equation, y = 20. From the third equation, z = -16. Substituting these values into the first equation, we get x - (16/5) = 0, which implies x = 16/5.
Therefore, the solution of the system is (16/5, 20, -16, -4).
So, the correct choice is:
A. The system has exactly one solution. The solution is
(16/5, 20, -16, -4)
Question 5(Multiple Choice Worth 1 points)
(01.07 MC)
Lines BC and ED are parallel. They are intersected by transversal AE, in which point B lies between points and E. They are also intersected by transversal EC. Angle ABC measures 70 degrees. Angle CED measures 30 degrees.
Given: line BC is parallel to line ED
m∠ABC = 70°
m∠CED = 30°
Prove:m∠BEC = 40°
Statement Justification
line BC is parallel to line ED Given
m∠ABC = 70° Given
m∠CED = 30° Given
m∠ABC = m∠BED Corresponding Angles Theorem
m∠BEC + 30° = 70° Substitution Property of Equality
m∠BEC = 40° Subtraction Property of Equality
Which of the following accurately completes the missing statement and justification of the two-column proof?
m∠BEC + m∠CED = m∠BED; Definition of a Linear Pair
m∠ABC + m∠BEC = m∠BED; Angle Addition Postulate
m∠ABC + m∠BEC = m∠BED; Definition of a Linear Pair
m∠BEC + m∠CED = m∠BED; Angle Addition Postulate
Answer:
m∠BEC + m∠CED = m∠BED; Angle Addition Postulate
Step-by-step explanation:
You need to show that <BED is made up of angles BEC and CED by the Angle Addition Postulate.
m∠BEC + m∠CED = m∠BED; Angle Addition Postulate
NO LINKS!! URGENT HELP PLEASE!!
Please help with 35
Answer:
x = 4
Step-by-step explanation:
By property, if two tangents are drawn from an external point , then they are equal
⇒ 2x + 3 = 11
⇒ 2x = 11 - 3
⇒ 2x = 8
⇒ x = 8/2
⇒ x = 4
Answer:
x = 4
Step-by-step explanation:
To find the value of x, we can use the Two-Tangent Theorem.
The Two-Tangent Theorem states that if two tangent segments are drawn to a circle from the same external point, the lengths of the two tangent segments are equal.
Therefore:
[tex]\begin{aligned}AD &= AB\\\\2x+3&=11\\\\2x+3-3&=11-3\\\\2x&=8\\\\\dfrac{2x}{2}&=\dfrac{8}{2}\\\\x&=4\end{aligned}[/tex]
Therefore, the value of x is 4.
F(x)=square root of 9-kx^2/k show your work
Sure! Here’s the solution:
F(x)=k9−kx2
First, let’s square both sides to get rid of the square root:
F(x)2=k9−kx2
Now, let’s multiply both sides by k to isolate the term with x^2:
kF(x)2=9−kx2
Next, let’s move all terms to one side of the equation:
kF(x)2+kx2=9
Finally, let’s factor out x^2:
x2(k+kF(x)2)=9
And solve for x^2:
x2=k+kF(x)29
Answer:
√((9 - kx^2) / k)Step-by-step explanation:
To show the work for evaluating the function f(x) = √(9 - kx^2) / k, we can follow these steps:
Step 1: Simplify the expression under the square root:9 - kx^2
Step 2: Divide the expression by k:(9 - kx^2) / k
Step 3: Take the square root of the expression:√((9 - kx^2) / k)
Note: It is important to consider any domain restrictions or assumptions about the values of k and x that would make the expression valid. For example, if k is negative, the expression would have an imaginary result.Determine the surface area and volume
The surface area of the cone is: 213.66 cm²
The volume of a cone is: 7.33 cm³
How to find the surface area and volume?The formula for the surface area of a cone is:
T.S.A = πrl + πr²
where:
r is radius
l is slant length
From the diagram and using Pythagoras theorem,we have:
l = √(7² + 5²)
l = √74
Thus:
TSA = (π * 5 * √74) + (π * 5²)
TSA = 213.66 cm²
Formula for the volume of a cone is:
V = ¹/₃πr²
V = ¹/₃π * 7
V = 7.33 cm³
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Use the formulas to answer this question.
One leg of a right triangle has length 11 and all sides are whole numbers. Find the lengths of the other two sides.
The other leg = and the hypotenuse =
The lengths of the other two sides of the right triangle are 36 and 85, respectively.
To find the lengths of the other two sides of a right triangle when one leg has a length of 11, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's denote the lengths of the other leg and the hypotenuse as x and y, respectively.
According to the Pythagorean theorem, we have:
x² + 11² = y²
To find the values of x and y, we need to find a pair of whole numbers that satisfy this equation.
We can start by checking for perfect squares that differ by 121 (11^2). One such pair is 36 and 85.
If we substitute x = 36 and y = 85 into the equation, we have:
36² + 11² = 85²
1296 + 121 = 7225
This equation is true, so the lengths of the other two sides are:
The other leg = 36
The hypotenuse = 85
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In December 2016 the average price of unleaded
If the left-hand limit of is equal to the right-hand limit of as x approaches 10, the limit of as x approaches 10 is and the value of k is .
The limit of f(x) as x approaches 10 is 315 and The value of k is 250.
The function f(x) is a piecewise function, so we need to evaluate it separately for x < 10 and x >= 10.
[tex]f(x)= { \frac{(0.1x(2)+20x+15,x < 10)}{(0.25x(3)+k,x > 10)}[/tex]
For x < 10, the function is equal to 0.1x^2 + 20x + 15. So the left-hand limit of f(x) as x approaches 10 is equal to 0.1(10)^2 + 20(10) + 15 = 315.
For x >= 10, the function is equal to 0.25x^3 + k. So the right-hand limit of f(x) as x approaches 10 is equal to 0.25(10)^3 + k = 250 + k.
Since the left-hand limit and the right-hand limit are equal, the limit of f(x) as x approaches 10 is also equal to 315, and the value of k is equal to 250.
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what is the period of y=cos x?
The cosine function repeats its pattern every 2π radians (or 360 degrees), we can say that the period of y = cos(x) is 2π.
The period of the function y = cos(x) is 2π.
To understand the period of the cosine function, we need to examine its graph. The cosine function is a periodic function that oscillates between -1 and 1 as x varies. It repeats its pattern over regular intervals.
The cosine function completes one full cycle from 0 to 2π radians (or 0 to 360 degrees). This means that within this interval, the cosine function goes through one complete oscillation, starting from its maximum value of 1, then going through its minimum value of -1, and returning back to 1.
Since the cosine function repeats its pattern every 2π radians (or 360 degrees), we can say that the period of y = cos(x) is 2π.
This means that for any value of x, the value of cos(x) will repeat after an interval of 2π.
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(Comparing Data LC)
The histograms display the frequency of temperatures in two different locations in a 30-day period.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
A IQR, because Sunny Town is symmetric
B IQR, because Beach Town is skewed
C Range, because Sunny Town is skewed
D Range, because Beach Town is symmetric
IQR, because Sunny Town is symmetric should be used for both sets of data to determine the location with the most consistent temperature?(option a).
1. The question asks for the measure of variability that should be used to determine the location with the most consistent temperature when comparing the data from two different locations.
2. The first option, A, suggests using the Interquartile Range (IQR) because Sunny Town is symmetric. This means that the data in Sunny Town is evenly distributed around the median, indicating consistency in temperatures.
3. The second option, B, proposes using the IQR because Beach Town is skewed. Skewness implies an asymmetrical distribution, which may indicate less consistency in temperatures.
4. The third option, C, suggests using the Range because Sunny Town is skewed. Skewed data in Sunny Town might imply a larger spread and less consistency in temperatures.
5. The fourth option, D, recommends using the Range because Beach Town is symmetric. However, symmetric data indicates consistency, making the Range less suitable as a measure of variability.
6. Considering the explanations for each option, the best choice is A, IQR, because Sunny Town is symmetric. The symmetric distribution suggests that the temperatures in Sunny Town are consistent and evenly distributed around the median.
7. Therefore, the measure of variability that should be used for both sets of data to determine the location with the most consistent temperature is the IQR, as indicated by option A.
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Roger can run one mile in 9 minutes. Jeff can run one mile in 6 minutes. If Jeff gives Roger a 1 minute head start, how
long will it take before Jeff catches up to Roger? How far will each have run?
Not including the head start, it will take
-
■
--
minutes for Jeff to catch up to Roger.
Each person runs 1/3 of a mile when Jeff catches up to Roger.
================================================
Explanation
x = number of minutes that Jeff runs
x+1 = number of minutes Roger runs
Roger has the head start of 1 minute, so he has been running for 1 minute longer compared to Jeff.
Roger runs 1 mile in 9 minutes. His unit rate is 1/9 of a mile per minute.
Jeff's unit rate is 1/6 of a mile per minute.
Let's set up a table with what we have so far
[tex]\begin{array}{|c|c|c|c|} \cline{1-4} & \text{Distance} & \text{rate} & \text{time}\\\cline{1-4}\text{Jeff} & d & 1/6 & \text{x}\\\cline{1-4}\text{Roger} & d & 1/9 & \text{x}+1\\\cline{1-4}\end{array}[/tex]
The distance equation for Jeff is d = (1/6)x
The distance equation for Roger is d = (1/9)(x+1)
note: distance = rate*time
Both runners travel the same distance when Jeff catches up to Roger, so both "d"s are the same value at this specific moment. Set the right hand sides equal to each other and solve for x.
(1/6)x = (1/9)(x+1)
18*(1/6)x = 18*(1/9)(x+1)
3x = 2(x+1)
3x = 2x+2
3x-2x = 2
x = 2
Jeff runs for 2 minutes when he catches up to Roger.
----------
Check:
Jeff runs for 2 minutes, at 1/6 of a mile per minute, so he runs 2*(1/6) = 2/6 = 1/3 of a mile.
Roger runs for 2+1 = 3 minutes (remember he gets the head start) at 1/9 of a mile per minute, so he has run 3*(1/9) = 3/9 = 1/3 of a mile as well.
Both men have run the same distance which confirms Jeff catches up to Roger at this point. The answer is confirmed.
A shop gives an offer saying '20% discount on all products and if your bill amount (after the discount) is more than Rs 1000,
then you will get further discount of 20% on the bill amount).
Aditi buys goods worth Rs 2400 by marking price. What is the amount she needs to pay?
Answer:
Step-by-step explanation:
To calculate the amount Aditi needs to pay, we need to apply the discounts step by step based on the given offer.
Step 1: 20% discount on all products
The marked price of the goods is Rs 2400. Applying a 20% discount means she will get a reduction of 20% of the marked price.
20% of Rs 2400 = (20/100) * Rs 2400 = Rs 480
After the first discount, the new bill amount is Rs 2400 - Rs 480 = Rs 1920.
Step 2: Additional 20% discount on the bill amount if it exceeds Rs 1000
The new bill amount after the first discount is Rs 1920. If this amount exceeds Rs 1000, Aditi will get a further discount of 20% on this bill amount.
Since Rs 1920 is greater than Rs 1000, we can apply a 20% discount to it.
20% of Rs 1920 = (20/100) * Rs 1920 = Rs 384
The final amount Aditi needs to pay after both discounts is Rs 1920 - Rs 384 = Rs 1536.
Therefore, Aditi needs to pay Rs 1536.
Please answer ASAP I will brainlist
(a) The average cost in 2011 is $2247.64.
(b) A graph of the function g for the period 2006 to 2015 is: C. graph C.
(c) Assuming that the graph remains accurate, its shape suggest that: A. the average cost increases at a slower rate as time goes on.
How to estimate the average cost in 2011?Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:
g(x) = -1736.7 + 1661.6Inx
where:
x = 6 corresponds to the year 2006.
For the year 2011, the average cost (in dollars) is given by;
x = (2011 - 2006) + 6
x = 5 + 6
x = 11 years.
Next, we would substitute 11 for x in the function:
g(11) = -1736.7 + 1661.6In(11)
g(11) = $2247.64
Part b.
In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.
Part c.
Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.
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determine the value of x
Answer:
[tex]x = 5\sqrt3[/tex]
Step-by-step explanation:
We can solve for the side length x in this 30-60-90 triangle by using the ratio of side lengths for that specific type of right triangle:
1 : [tex]\sqrt3[/tex] : 2In this triangle, we can identify the smallest side (corresponding to 1 in the ratio) as 5. This means we can solve for x by multiplying 5 by [tex]\sqrt3[/tex]. Thus:
[tex]\boxed{x = 5\sqrt3}[/tex]
joan’s finishing time for the bolder boulder 10k race was 1.81 standard deviations faster than the women’s average for her age group. there were 410 women who ran in her age group. assuming a normal distribution, how many women ran faster than joan? (round down your answer to the nearest whole number.)
[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[
Answer:
[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[
Step-by-step explanation:
[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[
Answer:
[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[
Step-by-step explanation:
what this is?
TIME REMAINING
01:48:30
On a coordinate plane, 2 lines are shown. Line H J has points (negative 4, negative 2) and (0, 4). Line F G has points (negative 4, 1) and (0, negative 2).
Which statement best explains the relationship between lines FG and HJ?
They are perpendicular because their slopes are equal.
They are perpendicular because their slopes are negative reciprocals.
They are not perpendicular because their slopes are equal.
They are not perpendicular because their slopes are not negative reciprocals.
Answer:
Its b i bealive
Step-by-step explanation:
Five angels of a hexagon are 123,124,118,130’110. Calculate the six angle
Answer:
The sixth angle is 115°.
Step-by-step explanation:
Number of sides in a hexagon = n =6
Sum of interior angles = (n−2)180°
= (6−2)180 ∘
= 720
∴ Let the six angle of hexagon be x.
⇒ x + 123 + 124 + 118 + 130 + 110 = 720°
⇒ x + 605 = 720°
⇒ x = 720 - 605
⇒ x = 115
On her breakfast tray, Aunt Lily had a little vase of flowers - a mixture of primroses and celandines. She counted up the petals and found there were 39. "Oh, how lovely!" she said, "exactly my age; and the total number of flowers is exactly your age, Rose!" How old is Rose?
(NB: Primroses have five petals on each flower and Celandines have eight petals on each flower). Please show working
Rose's age should be a whole number, we can round 7.8 to the nearest whole number, which is 8.
Let's assume the number of primroses in the vase is p, and the number of celandines is c.
Each primrose has 5 petals, so the total number of primrose petals is 5p.
Each celandine has 8 petals, so the total number of celandine petals is 8c.
According to the given information, the total number of petals is 39. Therefore, we can set up the equation:
5p + 8c = 39 (Equation 1)
Aunt Lily mentions that the total number of flowers is exactly Rose's age. Since Rose's age is not provided, we'll represent it with the variable r.
The total number of flowers is p + c, which is also equal to Rose's age (r). Therefore, we have another equation:
p + c = r (Equation 2)
We need to find the value of r (Rose's age). To do that, we'll solve the system of equations by eliminating one variable.
Multiplying Equation 2 by 5, we get:
5p + 5c = 5r (Equation 3)
Now we can subtract Equation 1 from Equation 3 to eliminate the p term:
(5p + 5c) - (5p + 8c) = 5r - 39
This simplifies to:
-3c = 5r - 39
Now, let's rearrange Equation 2 to solve for p:
p = r - c (Equation 4)
Substituting Equation 4 into the simplified form of Equation 3, we have:
-3c = 5r - 39
Substituting r - c for p, we get:
-3c = 5(r - c) - 39
Expanding, we have:
-3c = 5r - 5c - 39
Rearranging the terms, we get:
2c = 5r - 39
Now we have a system of two equations:
-3c = 5r - 39 (Equation 5)
2c = 5r - 39 (Equation 6)
To solve this system, we can eliminate one variable by multiplying Equation 5 by 2 and Equation 6 by 3:
-6c = 10r - 78 (Equation 7)
6c = 15r - 117 (Equation 8)
Now, let's add Equation 7 and Equation 8 to eliminate c:
-6c + 6c = 10r + 15r - 78 - 117
This simplifies to:
25r = 195
Dividing both sides by 25, we get:
r = 7.8
Since Rose's age should be a whole number, we can round 7.8 to the nearest whole number, which is 8.
Therefore, Rose is 8 years old.
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Which of the following is equal to the fraction below? (7/4)11
Answer:
It's A
Step-by-step explanation:
Use the following models to show the equivalence of the fractions 35 and 610 a) Set model
Use the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set model
Which property is illustrated by the following statement? If A ABC = A DEF,
and ADEF=AXYZ, then AABC=AXYZ.
B.
A
с
E
D
O A. Reflexive
O B. Symmetric
O C. Transitive
O D. Commutative
F
Z
The property that is illustrated by the statements is Transitive. Option C
How to determine the propertyUsing the principle of transitivity, if two objects are equal to a third, they are also equal to one another.
From the information given, we have that;
< ABC = <DEF
< DEF = < XYZ
This simply proves that < ABC and < XYZ are both equivalent to < DEF in this situation.
By using the transitive property, we can determine that A ABC and A XYZ are also equal. This attribute enables us to construct relationships between many elements based on their equality to a shared third element and to connect logically equalities.
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NO LINKS!! URGENT HELP PLEASE!!
The perimeter of a shape is 15 cm and the area is 25 cm^2
Find the area of the larger shape if it is being enlarged by a scale factor of 6
Answer:
900 cm²--------------------------
Area is the product of two dimensions hence the ratio of areas of similar figures is the square of the scale factor.
Let the area of the enlarged shape be A, and the scale factor be k = 6.
Then we have the area of the larger shape:
A = 25*k²A = 25*6²A = 900 cm²answer ASAP I will brainlist and i will answer two questions on your page
Using row operations to write the augmented matrix, the value of x, y and z are 2, -12 and 11
What is the solution to the system of equations?To solve the system using row operations, we'll write the augmented matrix and perform row operations to transform it into row-echelon form. Here are the steps:
1. Write the augmented matrix for the system of equations:
[1 1 -1 | 1]
[4 -1 1 | 9]
[1 -3 2 | -14]
2. Perform row operations to transform the matrix into row-echelon form:
R2 = R2 - 4R1
R3 = R3 - R1
[1 1 -1 | 1]
[0 -5 5 | 5]
[0 -4 3 | -15]
3. Perform row operations to further transform the matrix into row-echelon form:
R2 = -R2/5
R3 = -4R2 + R3
[1 1 -1 | 1]
[0 1 -1 | -1]
[0 0 -1 | -11]
4. Perform row operations to obtain a diagonal of 1s from left to right:
R1 = R1 + R3
R2 = R2 + R3
[1 1 0 | -10]
[0 1 0 | -12]
[0 0 -1 | -11]
5. Perform row operations to transform the matrix into reduced row-echelon form:
R3 = -R3
[1 1 0 | -10]
[0 1 0 | -12]
[0 0 1 | 11]
The resulting matrix corresponds to the system of equations:
x + y = -10
y = -12
z = 11
Therefore, the solution to the given system of equations is x = -10 - y, y = -12, and z = 11.
So, the solution is x = -10 - (-12) = 2, y = -12, and z = 11.
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Please answer ASAP I will brainlist
Answer:
There is one solution. The solution is 2, 18, 19.
Step-by-step explanation:
If you want me to show working tell me in the comments and I'll edit the answer
Answer:
A. (2, 18, -19)
Step-by-step explanation:
To solve:
Z is the most suitable variable to remove first
Add the first equation to the second equation: (this conveniently removes both y and z)
(x+y-z) + (4x-y+z) = 1+9
Simplify
5x = 10
Solve
x = 2
Multiply the second equation by 2 and minus it to the third equation: (Solve for y)
2(4x-y+z) - (x-3y+2z) = 2(9) - (-14)
Simplify
8x-2y+2z-x+3y-2z=18+14
7x+y=32
Substitute using x=2
7(2) + y = 32
y = 32 - 14
y = 18
Now substitute x and y for their respective values into Equation 1
2 + (-18) - z = 1
Simplify
-z = 19
z = -19
So :
x = 2, y = 18 , z = -19
Evaluate |x - y| + 4 if x = -1, y = 3, and z = -4.
Answer:
8
Step-by-step explanation:
Substitute the values in the expression, we have:
[tex]\displaystyle{|-1-3|+4}[/tex]
Evaluate:
[tex]\displaystyle{|-4|+4}[/tex]
Any real numbers in the absolute sign will always be evaluated as positive values. Thus:
[tex]\displaystyle{|-4|+4 = 4+4}\\\\\displaystyle{=8}[/tex]
Hence, the answer is 8. A quick note that z-value is not used due to lack of z-term in the expression.