A polygon has vertices at (4, 1), (4, 7), (10, 7) and (10, 1). How does the perimeter of the polygon change if each coordinate is multiplied by 3?
the weight of an object on the moon is about .167 of its weight on Earth. How much does a 180 lb astronaut weigh on the moon?
How many dozens are there in 22 gross of nails
In 22 gross of nails, there are 264 dozens as one gross is equal to 12 dozen.
To find out how many dozens are there in 22 gross of nails, we need to determine the number of dozens in one gross and then multiply it by 22.
One gross is equal to 12 dozen.
So, to find the number of dozens in 22 gross of nails.
we can multiply 12 (number of dozens in one gross) by 22:
12 x 22
= 264
Therefore, there are 264 dozens in 22 gross of nails.
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Lilly has a bag of 140 colored marbles. The bag has an equal number of green and blue marbles and an equal number of red and yellow marbles. If Lilly arranged all of the green marbles in groups of 8 and all of the blue marbles in groups of 7, how many red marbles are in the bag?
F(x, y) = x2 + y2 + 4x − 4y, x2 + y2 ≤ 81 find the extreme values of f on the region described by the inequality.
The extreme values of a function are the minimum and the maximum values of the function.
The extreme values are: -8 and 131.91
The given parameters are:
[tex]\mathbf{F(x,y) = x^2 + y^2 + 4x - 4y}[/tex]
[tex]\mathbf{x^2 + y^2 \le 81}[/tex]
Find the gradient of F(x,y)
[tex]\mathbf{f_x(x) = 2x + 4}[/tex]
[tex]\mathbf{f_y(y) = 2y - 4}[/tex]
Set to 0, to solve for x and y
[tex]\mathbf{2x + 4 = 0}[/tex]
[tex]\mathbf{2x = -4}[/tex]
[tex]\mathbf{x = -2}[/tex]
[tex]\mathbf{2y - 4 = 0}[/tex]
[tex]\mathbf{2y = 4}[/tex]
[tex]\mathbf{y = 2}[/tex]
So, the critical point is:
[tex]\mathbf{(x,y) = (-2,2)}[/tex]
Also, we have: [tex]\mathbf{x^2 + y^2 \le 81}[/tex]
Calculate the gradients
[tex]\mathbf{g_x = 2x}[/tex]
[tex]\mathbf{g_y = 2y}[/tex]
Equate the gradients as follows:
[tex]\mathbf{f_x = \lambda \cdot g_x}[/tex]
[tex]\mathbf{f_y = \lambda \cdot g_y}[/tex]
So, we have:
[tex]\mathbf{2x + 4 = \lambda \cdot 2x}[/tex]
[tex]\mathbf{2y - 4 = \lambda \cdot 2y}[/tex]
Make [tex]\mathbf{\lambda}[/tex] the subject, in the above equations
[tex]\mathbf{\lambda = \frac{x + 2}{x}}[/tex]
[tex]\mathbf{\lambda = \frac{y - 2}{y}}[/tex]
Equate the above equations, so we have:
[tex]\mathbf{\frac{x + 2}{x} = \frac{y - 2}{y} }[/tex]
Cross multiply
[tex]\mathbf{xy + 2y = xy - 2x}[/tex]
Subtract xy from both sides
[tex]\mathbf{2y =- 2x}[/tex]
Divide both sides by 2
[tex]\mathbf{y =- x}[/tex]
Substitute [tex]\mathbf{y =- x}[/tex] in [tex]\mathbf{x^2 + y^2 = 81}[/tex]
[tex]\mathbf{x^2 + (-x)^2 = 81}[/tex]
[tex]\mathbf{x^2 + x^2 = 81}[/tex]
[tex]\mathbf{2x^2 = 81}[/tex]
Divide both sides by 2
[tex]\mathbf{x^2 = \frac{81}{2}}[/tex]
Take square roots
[tex]\mathbf{x = \±\frac{9}{\sqrt2}}[/tex]
Rationalize
[tex]\mathbf{x = \±\frac{9\sqrt2}{2}}[/tex]
Recall that: [tex]\mathbf{y =- x}[/tex]
So, we have:
[tex]\mathbf{y = \±\frac{9\sqrt2}{2}}[/tex]
The ordered pairs are:
[tex]\mathbf{(x,y) = \{(\frac{9\sqrt2}{2},-\frac{9\sqrt2}{2}),(-\frac{9\sqrt2}{2},\frac{9\sqrt2}{2})\}}[/tex]
Hence, the points are:
[tex]\mathbf{(x,y) = \{(-2,2),(\frac{9\sqrt2}{2},-\frac{9\sqrt2}{2}),(-\frac{9\sqrt2}{2},\frac{9\sqrt2}{2})\}}[/tex]
Substitute these values in [tex]\mathbf{F(x,y) = x^2 + y^2 + 4x - 4y}[/tex]
[tex]\mathbf{F(2,2) = (-2)^2 + 2^2 + 4(-2) - 4(2) =-8}[/tex]
[tex]\mathbf{F(\frac{9\sqrt2}{2},-\frac{9\sqrt2}{2}) = (\frac{9\sqrt2}{2})^2 + (-\frac{9\sqrt2}{2})^2 + 4(\frac{9\sqrt2}{2}) - 4(-\frac{9\sqrt2}{2}) =131.91}[/tex]
[tex]\mathbf{F(-\frac{9\sqrt2}{2},\frac{9\sqrt2}{2}) = (-\frac{9\sqrt2}{2})^2 + (\frac{9\sqrt2}{2})^2 + 4(-\frac{9\sqrt2}{2}) - 4(\frac{9\sqrt2}{2}) =30.09}[/tex]
Hence, the extreme values of the function are: -8 and 131.91
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Is the symbol (x¯¯) used for the population mean or sample mean?
choices are.....
population mean
sample mean
The symbol x is the sample mean, and the Greek symbol μ is the population mean.
Explanation:The symbol x is the sample mean, and the Greek symbol μ is the population mean. Calculating the Standard Deviation: If x is a number, then the difference x - mean is called its deviation. In a data set, there are as many deviations as there are items in the data set. The deviations are used to calculate the standard deviation. If the numbers belong to a population, in symbols, a deviation is x - μ. For sample data, in symbols, a deviation is x - x.
a construction crew Must build 4 miles of road in one week on Monday they build 1/2 mile of road in one week on Tuesday they build 1/3 mile of road how many more miles of road are left to build
A pizzeria baked 12 pizza pies in 3 hours. At this rate, how many pizza pies can they bake in 7 hours?
What is the meaning of the term theorem
Convert 5.4 ⋅ 103 to standard form. 0.0054 0.00054 5,400 54,000
Answer:
5400
Step-by-step explanation:
Convert 5.4 ⋅ 103 to standard form.
[tex]5.4 \ times \ 10^3[/tex]
for 10^3 we add 3 zeros
10^3= 10 times 10 times 10=1000
[tex]5.4 \ times \ 10^3[/tex]
Replace 10^3 by 1000. then multiply with the decimal number
[tex]5.4 \ times \ 1000[/tex]
When we multiply by 1000 we move the decimal point 3 places to the right
5400
help me solve this, Pre-Calculus Question
I only need the last part
what is the least common denominator for 5/6 and 3/8
4 1/6 divided by 1 2/3 =
If a radio station call letters must begin with either K or W and must include either two or three additional letters, how many different possibilities are there?
There are a total of 26 letters that can be made to follow. There are 4 independent events here, namely:
First: Starts with K and followed by two additional letters = 1 * 26 * 26 = 676
Second: Starts with K and followed by three additional letters = 1 * 26 * 26 * 26 = 17,576
Third: Starts with W and followed by two additional letters = 1 * 26 * 26 = 676
Fourth: Starts with W and followed by three additional letters = 1 * 26 * 26 * 26 = 17,576
The total possibilities that can be made from here is:
Total possibilities = 676 + 17,576 + 676 + 17,576
Total possibilities = 36,504
five friends went to a local restaurant and all had the buffet at $6.75 each. the following is the restaurant bill. does it seem reasonable 5($6.75) =&67.50
Triangle ABC has two known angles. Angle A measures 55 degrees. Angle b measures 30 degrees.What is the measure of angle C?
How much do parents pay per day? If a childcare center charges $150 per week during the school year. In the summer, parents can pay a prorated amount based on the number of days of attendance.
There are 365,493 blue pens and 549,384 black pens how many more black pens are there then blue pens
By subtracting the number of blue pens from the number of black pens, we find that there are 183,891 more black pens than blue pens.
To find out how many more black pens there are than blue pens, we need to subtract the number of blue pens from the number of black pens. The student provided the numbers as 365,493 blue pens and 549,384 black pens.
Here is the calculation:
Number of black pens: 549,384Number of blue pens: 365,493Difference (black pens - blue pens): 549,384 - 365,493 = 183,891There are 183,891 more black pens than blue pens.
Picture above, please make sure to show work:)
A car manufacturer claims that, when driven at a speed of 50 miles per hour on a highway, the mileage of a certain model follows a normal distribution with mean μ = 30 miles per gallon and standard deviation σ= 4 miles per gallon.
Please need help as quick as you can . What is the slope of the line that passes through the points (16, –1) and (–4, 10)? A. -20/11 B. -11/20 C. 11/20 D. 20/11
For the x-values 1, 2, 3, and so on, the y-values of a function form a geometric sequence that increases in value. What type of function is it? A. Exponential growth B. Decreasing linear C. Increasing linear D. Exponential decay
Answer:
Option A: Exponential growth
Step-by-step explanation:
If for values of x values of y increases and forms a geometric sequence then it would be an exponential growth function because geometric sequence is an exponential function and since, it is increasing hence, an exponential growth.
Option B is incorrect because because y is not decreasing
Option C and D are incorrect because geometric sequence can never be linear since, it gives common ratio.
Final answer:
The function described, where y-values form an increasing geometric sequence as x-values increase, is characterized as Exponential growth. This is consistent with an exponential curve where the rate of growth is proportional to the current value, which aligns with the behavior of a geometric sequence.
Explanation:
For the given scenario where the y-values of a function form a geometric sequence that increases for the x-values 1, 2, 3, and so on, the type of function is described as Exponential growth. This is because in a geometric sequence each term after the first is found by multiplying the previous term by a constant called the common ratio, which is analogous to the exponential function where the growth rate of the value is proportional to its current value. The more the x-value increases, the higher and faster the y-value grows, following the pattern of an exponential growth curve.
Answer A. Exponential growth fits the description as it involves an increasing geometric sequence. Answer B. Decreasing linear refers to a linear function that decreases with each increment in x, which does not describe the function in question. Similarly, Answer C. Increasing linear describes a function that increases at a constant rate, not geometrically. Answer D. Exponential decay would imply the y-values decrease as x increases, which is also not the case described.
After doing this I got 1/4. Can someone plz show and explain what I did wrong? 7- 3r = r - 4(2 + r)
A child can explain that 3x2 represents three sets of two
A child can correctly explain that 3 x 2 represents three sets of two. This child is most likely in Piaget's Concrete Operational stage option (C) is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
As we know,
A young toddler may properly identify three sets of two as being represented by 3 x 2.
This child is most likely in Piaget's Concrete Operational stage.
Thus, a child can correctly explain that 3 x 2 represents three sets of two. This child is most likely in Piaget's Concrete Operational stage option (C) is correct.
The complete question is:
A child can correctly explain that 3 x 2 represents three sets of two. This child is most likely in Piaget's _____________ stage.
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Determine all possible angles θ for equilibrium, 0∘<θ<90∘.
Eric has 4 bags of 10 marbles and 6 single marbles . how many marbles does eric have
Lin was waiting to check out at a store. She estimated her total bill to be $20. The actual total was $24.16. What is the difference between Lin’s estimate and the actual total?
Answer:
4.16
Step-by-step explanation:
Sence Lin estimated $20 and her actucal bill was $24.16. To find the difference, we subtract 20 from 24.16.
[tex]24.16-20=4.16[/tex]
At a sports camp, there is one counselor for every 12 campers. If there are 156 campers attending the camp, which equivalent ratios could be used to find the number of counselors?
The equivalent ratios could be used to get the number of counselors who will be 13.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
At a sports camp, there is one counselor for every 12 campers.
If there are 156 campers attending the camp.
The equivalent ratios could be used to get the number of counselors who will be
⇒ 156 / 12
⇒ 13
The equivalent ratios could be used to get the number of counselors who will be 13.
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Find the area of the specified region shared by the circles r = 4 and r = 8sin
Write the equation of a line, in general form , that has an slope of zero and a y-intercept of (0, -6).