According to the given information, the equation of the ellipse is [tex](x+8)^2/256 + (y+1)^2/784 = 1.[/tex]
What is co-ordinate geometry ?Coordinate geometry, also known as analytic geometry, is a branch of mathematics that deals with the study of geometric shapes using algebraic principles. It involves the use of coordinates to represent points, lines, curves, and other geometric figures on a plane or in space.
According to the given information:we need to know the coordinates of its foci, co-vertices, and the center. We can start by finding the center of the ellipse, which is the midpoint of the line segment joining the foci:
Center = ( (-8 + (-8))/2 , (14 + (-16))/2 ) = (-8,-1)
Next, we can find the distance between the foci, which is given by:
[tex]distance between foci = 2c = sqrt[(14 - (-16))^2 + (-8 - (-8))^2] = 30[/tex]
where c is the distance from the center to either focus.
We also know that the distance between the co-vertices is given by:
distance between co-vertices = 2a = |-16 - 0| = 16
where a is the distance from the center to either co-vertex.
Finally, we can use the standard form equation for an ellipse centered at the origin:
[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]
where b is the distance from the center to either vertex.
To find b, we can use the Pythagorean theorem:
[tex]b^2 = c^2 - a^2 \\b^2 = 30^2 - 16^2\\b^2 = 784\\b = 28[/tex]
Now we have all the information we need to write the equation of the ellipse:
[tex](x+8)^2/16^2 + (y+1)^2/28^2 = 1[/tex]
Therefore, according to the given information, the equation of the ellipse is [tex](x+8)^2/256 + (y+1)^2/784 = 1.[/tex]
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2.2 × 1.6 as a fraction multiplication expression PLEase hELP I'm gonna GET GROUNDED IF I DONT DO THIS QUESTION HELP FAST!
Answer:
88/25
Step-by-step explanation:
if you do 2.2 times 1.6 equals 3.52 and then a fraction.
Answer:
2.2 × 1.6 can be expressed as a fraction multiplication expression as follows:
(22/10) × (16/10)
Simplifying the expression by canceling out the common factor of 10, we get:
22 × 16 / 10 × 10
Multiplying the numerator and denominator, we get:
352 / 100
Simplifying the fraction by dividing both the numerator and denominator by 4, we get:
88 / 25
Therefore, 2.2 × 1.6 as a fraction multiplication expression is 88/25.
What is tangent and how do you calculate it from the unit circle?
Answer:
The unit circle has many different angles that each have a corresponding point on the circle. The coordinates of each point give us a way to find the tangent of each angle. The tangent of an angle is equal to the y-coordinate divided by the x-coordinate.
You roll one six-sided die. A friend looks at the number and tells you that it is an odd number. What is the probability that you rolled a 3?
Answer: 1/3 chance or 33.33333%
Step-by-step explanation: There are only 3 odd numbers on the die, 1,3,5 so there is a 1/3 chance it is 3
Let $a \equiv 1 \pmod{4}$. Find the value of $6a + 5 \pmod{4}$Express your answer as a residue between 0 and the modulus.
The value of [tex]$6a + 5 \pmod{4}$[/tex] is given by 3 or -1 (mod4) using the proper expression.
In mathematics, modular arithmetic is a method of integer arithmetic in which numbers "wrap around" after they reach a predetermined value known as the modulus. Carl Friedrich Gauss created the contemporary method to modular arithmetic in his 1801 work Disquisitiones Arithmeticae.
We have [tex]$a \equiv 1 \pmod{4}$[/tex]
to find the value of [tex]$6a + 5 \pmod{4}$[/tex]
putting the value of a≡1
6a + 5 (mod 4)
=(6*1 + 5) (mod 4)
=11 (mod4)
11/4=2R3 or 3R-1
= 3 or -1 (mod4)
A congruence relation is an equivalence relation that is consistent with addition, subtraction, and multiplication. Congruence modulo n is one such connection.
[tex]{\displaystyle a\equiv b{\pmod {n}}.}[/tex]
Display Style: A Equivalent B Modified N.
Because of the parenthesis, the full equation—rather than just the right-hand side—is covered by the (mod n) formula (here, b). This notation should not be confused with the modulo operation's notation, b mod n (without parenthesis).
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Question 7
On June 22, 1947, in Holt, Missouri, 12 inches of rain fell in just 42 minutes. What was the average
rainfall per minute rounded to the nearest hundredth of an inch?
A
1 p
Question 8
1 pts
The average rainfall per minute is 0.29 inches.
What is Average?
The average of a set, also called the mean, is a measure of central tendency that represents the typical value of the set. It is found by adding up all the values in the set and then dividing by the total number of values in the set.
To find the average rainfall per minute, we need to divide the total rainfall by the number of minutes:
Average rainfall per minute = Total rainfall / Number of minutes
In this case, the total rainfall is 12 inches and the number of minutes is 42, so:
Average rainfall per minute = 12 / 42
Using a calculator or performing the division manually, we get:
Average rainfall per minute = 0.2857142857
Rounding this to the nearest hundredth of an inch, we get:
Average rainfall per minute ≈ 0.29 inches
Therefore, the average rainfall per minute during that 42-minute period was approximately 0.29 inches.
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In Biology class, Marissa is viewing cells with a microscope. Cell W
-7
measures 1.8 x 10 microns in diameter and Cell S measures
-5
7.2 x 10 microns in diameter. How many times larger is the bigger
cell than the smaller cell?
The number of times larger Cell S is compared to Cell W is 4 x 10²,
How many times larger is the bigger cell?
Scientific notation is used to compress large numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
When the power of the scientific notation is negative, it means that the number is less than 1. 0.01 would be written as 1 x [tex]10^{-2}[/tex]. Cell S is larger than Cell W.
(7.2 x [tex]10^{-5}[/tex]) ÷ (1.8 x [tex]10^{-7}[/tex])
(7.2 / 1.8) x [tex]10^{-5--7}[/tex]
4 x 10²
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A quadrilateral has two angles that measure 235° and 40°. The other two angles are in a ratio of 5:12. What are the measures of those two angles?
Answer: Let's denote the two unknown angles as x and y.
We know that the sum of the angles in any quadrilateral is 360°, so we can set up an equation using this fact:
235° + 40° + x + y = 360°
Simplifying this equation, we get:
x + y = 85° (equation 1)
We also know that the other two angles are in a ratio of 5:12. This means that:
x/y = 5/12
Multiplying both sides by y, we get:
x = (5/12)y (equation 2)
Now we can substitute equation 2 into equation 1 and solve for y:
(5/12)y + y = 85°
(17/12)y = 85°
y = (12/17) * 85°
y = 60°
Substituting y = 60° into equation 2, we can solve for x:
x = (5/12) * 60°
x = 25°
Therefore, the two angles that are in a ratio of 5:12 measure 25° and 60°, respectively.
Step-by-step explanation:
Joann had a vegetable stand where she sold tomatoes. She sold 15 tomatoes the first day. The second day she sold half of what was left. On the third day she sold 12 and sold half of what was left on the fourth day. On the fifth day there were 4 tomatoes left to be sold. How many tomatoes did she have to begin with?
On the fifth day there were 4 tοmatοes left tο be sοld. Jοann had 71 tοmatοes tο begin with.
What is prοbability?Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is a number between 0 and 1, where 0 indicates that the event is impοssible, and 1 indicates that the event is certain tο οccur.
Let's wοrk backwards frοm the last day and figure οut hοw many tοmatοes Jοann had οn the fοurth day.
On the fifth day, there were 4 tοmatοes left tο be sοld, which means she sοld half οf what was left οn the fοurth day. Sο she must have started with 8 tοmatοes οn the fοurth day (since half οf 8 is 4).
On the fοurth day, she sοld half οf what was left, which means she had 16 tοmatοes befοre she sοld any.
On the third day, she sοld 12 tοmatοes, which means she had 28 tοmatοes befοre she sοld any.
On the secοnd day, she sοld half οf what was left, which means she had 56 tοmatοes befοre she sοld any.
Finally, οn the first day, she sοld 15 tοmatοes.
Therefοre, Jοann had 71 tοmatοes tο begin with.
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Intercept form 4x + 5y = 20
By answering the question the answer is So the slope intercept expression 4x + 5y = 20 in intercept form is: x/5 + y/4 = 1
what is slope intercept?The slope-intercept form of a linear equation in mathematics is an equation of the form y = mx + b. where m is the slope of the line and b is the y-intercept, the point where the line crosses the y-axis. The slope-intercept format is a convenient way to plot equations for straight lines because it allows you to quickly see the line and determine the slope and y-intercept. The slope indicates how steep the line is, and the y-intercept indicates where the line crosses the y-axis.
The intercept form of a linear equation in two variables (x and y) is given by
x/a + y/b = 1
where a and b are the intercepts of x and y respectively.
To convert the given expression 4x + 5y = 20 to intercept form, we need to solve for the intercepts for x and y.
For x = 0, 4x + 5y = 20 becomes
0 + 5 years old = 20
y = 4
So the y-intercept is 4.
For y = 0, 4x + 5y = 20 becomes
4x + 0 = 20
x = 5
So the x-intercept is 5.
So the expression 4x + 5y = 20 in intercept form is:
x/5 + y/4 = 1
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Show that,the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞.
The sum of the arithmetic progressive sequence will be +∞, for common difference as positive that is d >0.
Explain about the arithmetic progression?The difference between every two successive terms in a sequence is the same; this is known as an arithmetic progression (AP).
A good example of an arithmetic progression (AP) is the series 2, 6, 10, 14,..., which follows a pattern in which each number is created by increasing 4 to the previous term. This annual income of a worker whose pay rises by a predetermined amount of $5000 each year serves as a real-world illustration of an AP.
The expression for an arithmetic progression:
a is the first term
l is last term
d is common difference
n is total number of terms
Sn = the sum of term
A.P = a,a+d,a+2d,a+3d,…, a+(n-1)d
l = a+(n-1)d
Sum formula:
Sn=n/2 [a+(n-1)d]
Or, Sn=n/2 [a+l]
Thus, the sum of the arithmetic progressive sequence will be +∞, for common difference as positive that is d >0.
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in one of his experiments conducted with animals, thorndike found that cats learned to escape from a puzzle box:
In one of his experiments conducted with animals, Thorndike found that cats learned to escape from a puzzle box is increased gradually
To quantify the learning process, Thorndike used a mathematical formula known as the Law of Effect equation. The equation is:
B = f(log S1/S2)
where B represents the strength of the behavior, S1 represents the satisfaction of the positive consequence, and S2 represents the degree of frustration or negative consequence.
In the context of Thorndike's puzzle box experiment, the Law of Effect equation can be used to describe how the cat's behavior changed over time as it learned to escape the puzzle box more quickly and efficiently. Initially, the cat's behavior was weak because it did not know which actions would lead to a positive outcome.
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Mrs. Cabana has 8 pets total. Three of the pets are chameleons and the rest are fish. Select all the answers that are a ratio relationship for Mrs. Cabana's pets.
Question 1 options:
Multi choice
3/5
3 to 11
3:8
5 to 8
8:1
Answer: numbers 1,3 and 4
Step-by-step explanation:
A company reported the following:
$275,270
Preferred dividends
$20,390
Shares of common stock outstanding
36,000
Market price per share of common stock
$118.87
Calculate the company's price-earnings ratio. Round your answer to two decimal places.
Net income
The company's price-earnings ratio for a company that reported net income of $275,270 with $20,390 for preferred dividends and 36,000 shares of common stock, is 16.79.
What is the price-earnings ratio?The price-earnings ratio represents the per-dollar amount that an investor can expect to invest in a company in order to receive $1 of that company's net earnings.
The price-earnings (P/E) ratio is also referred to as the price multiple.
The price-earnings (P/E) ratio compares the market price with the earnings per share.
Net income = $275,270
Preferred Dividends = $20,390
Net income available to Common Stockholders = $254,880 ($275,270 - $20,390)
Number of common stock outstanding = 36,000 shares
Market price per share of common stock = $118.87
Earnings per share (Common Stock) = $7.08 ($254,880/36,000)
Price-earnings ratio = Market price per share/Earnings per share
= 16.79 ($118.87/$7.08).
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Help please! Appreciate the help
For the given statements for domain and range, option 3 and option 4 are correct answers.
What is domain and range?The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation. With functions, we enter various numbers, and the output is a new set of numbers. The two essential characteristics of functions are domain and range. A function's domain and range are its constituent parts.
The domain of the function are all the input values while the range are the output values of the function for the given input.
In the given options, option 3 and 4 are correct as the functions have the same input but not the same output.
That is, they have the same domain, all real numbers, but not the same range.
Hence, for the given statements for domain and range, option 3 and option 4 are correct answers.
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Kingsley knows that 1inch is about 2.45 centimeters. He wants to write an equation he can use to convert any given length in inches (i) to centimeters (c)
How should Kingsley write his equation?
A.) c/i = 2.54
B.) c = 2.54i
C.) i = c/2.54
Since Kingsley wanted an equation to convert from inches to centimeters, the correct answer is B) c = 2.54i.
What is equation ?
An equation is a statement that asserts the equality of two expressions, usually separated by an equals sign (=). The expressions on either side of the equals sign may contain one or more variables, which are unknown values that can be determined by solving the equation.
Kingsley wants to convert a given length in inches to centimeters. He knows that 1 inch is about 2.45 centimeters.
Let's call the length in inches "i" and the length in centimeters "c".
We want to find an equation that relates i and c. We know that 1 inch is about 2.45 centimeters, so we can write:
1 inch = 2.45 centimeters
To convert from inches to centimeters, we can multiply the length in inches by 2.45. So:
c = 2.45i
This is the equation Kingsley can use to convert any given length in inches to centimeters.
Alternatively, we can rearrange this equation to solve for i:
c = 2.45i
Divide both sides by 2.45:
c/2.45 = i
So the equation for converting from centimeters to inches is:
i = c/2.45
Therefore, since Kingsley wanted an equation to convert from inches to centimeters, the correct answer is B) c = 2.54i.
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Will tracks the high and low tempters in his town for five days during a cold spell in January his results are shown in the table below
Days when change in temperature more than 10° F are Option B)Tuesday and E) Friday.
Define change in temperaturecalculating the difference by deducting the end temperature from the initial temperature. The temperature difference is therefore 75 degrees Celsius - 50 degrees Celsius = 25 if something begins at 50 degrees Celsius and ends at 75 degrees Celsius.
Change in temperature on Monday from High to low
=15-10=5°F
Change in temperature on Tuesday from High to low
=8-(-4)=12°F
Change in temperature on Wednesday from High to low
=-2-(-5)=3°F
Change in temperature on Thursday from High to low
=-3-(-7)=4°F
Change in temperature on Friday from High to low
=-1-(-12)=11° F
Days when change in temperature more than 10° F are Tuesday and Friday.
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The Complete question is attached below:
What is the slope from (-8, 9) to (-4,6)
Answer:
m = -3/4
Step-by-step explanation:
Calculation of the Slope of a line
The information provided about the line is that the line passes through the points (-8, 9) to (-4,6)
Therefore, the first step consists in computing the slope. The formula for the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Now, by plugging the corresponding numbers is , we get that the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-9}{-4-(-8)} =\frac{6-9}{-4+8} =-\frac{3}{4}[/tex]
So then, we find that the slope is [tex]m=-\frac{3}{4}[/tex] and that the line passes through the point [tex](-8,9)[/tex].
Consider two agents, Alice and Bob, who have utility functions 0.3x3 + 0.72A if xa > XB (0.314 +0.72B if XB > XA UA(2A, 2B) = UB(XA, XB) 4X A – 32B if XB > IA -0.32A + 1.3xB if x A > XB If Alice is the dictator in the dictator game with a $10 endowment, then she will offer Bob (A) $0; (B) $5; (C) $2; (D) $10.
The utility that maximizes the possible utility of both the agents Alice and Bob is equal to option D. $10.
Compare Alice's utility from each option and choose the one that maximizes her utility.
Let us consider each option,
If Alice offers Bob $0, her utility will be,
If XA > XB then
UA (XA , XB )= 0.3x3 + 0.72A
UA(10,0)
= 0.3(10)³ + 0.72(10)
= 307.2
If Alice offers Bob $5, Bob's utility will be,
UB(10,5)
= 0.314 + 0.72(5)
= 0.314 + 3.6
= 3.914
And Alice's utility will be,
UA(5,10)
= -0.32(5) + 1.3(10)
= 11.4
Total utility for both Alice and Bob will be,
UA(5,10) + UB(10,5)
= 11.4 + 3.914
= 15.314
If Alice offers Bob $2, Bob's utility will be,
UB(10,2)
= 0.314 + 0.72(2)
= 1.754
And Alice's utility will be,
UA(2,10)
= -0.32(2) + 1.3(10)
= 12.4
So the total utility for both Alice and Bob will be,
UA(2,10) + UB(10,2)
= 12.4 + 1.754
= 14.154
If Alice offers Bob $10, Bob's utility will be,
UB(10,10)
= 0.314 + 0.72(10)
= 7.514
And Alice's utility will be,
UA(10,10)
= 0.3(10)³ + 0.72(10)
= 307.2
So the total utility for both Alice and Bob will be,
UA(10,10) + UB(10,10)
= 307.2 + 7.514
= 314.714
Therefore, utility which maximizes the total utility for both Alice and Bob is given by option (D) $10.
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Which of the following numbers is the reciprocal of 0.4?
F.
4
G. -0.4
H. 10.4
J. 2.5
K. 5.2
Answer:
J. 2.5
Step-by-step explanation:
A reciprocal is the inverse of a number. The reciprocal of a number is 1 divided by the number.
With a decimal number, it's best to convert the number into fraction form. In fraction form, you just have to switch the numerator and denominator to find the reciprocal.
0.4 = 4/10 = 2/5
Reverse the numerator and denominator to get 5/2.
Convert 5/2 to a decimal:
5/2 = 2.5
I need help with this
The angles can be named with one letter are 2.
What is angles?Angles are a type of geometric shape which are formed when two straight lines intersect at a point. They are measured in degrees, usually between 0 and 360. Angles can be classified as acute, right, obtuse, straight and reflex, and the sum of any three angles in a triangle will always equal 180 degrees. Angles can be used in various ways, from providing stability in construction work to helping to identify other shapes. They can also be used to measure the size and shape of objects and to calculate distances and areas on maps. Angles are an important part of mathematics, geometry and trigonometry, and are used in a variety of applications in science and engineering.
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A teacher has a large yellow bulletin board in her classroom. She decides to use purple paper to frame a smaller rectangle inside the original board. The paper will create a border that is x inches wide. The teacher's bulletin board plan and dimensions are shown below.
Look at the picture then choose the answer from the options below:
Select the true statement about the expression.
A.
The factor (96 − 2x) represents the length, in inches, of the uncovered portion of the bulletin board.
B.
The term 4x2 represents the area, in square inches, of the entire bulletin board.
C.
The factor (48 − 2x) represents the height, in inches, of the bulletin board including the decorative border.
D.
The term -288x represents the area, in square inches, of the decorative border.
Option A: The factor (96 − 2x) represents the length, in inches, of the uncovered portion of the bulletin board.
How to obtain the area of a rectangle?To obtain the area of a rectangle, you need to multiply the dimensions of the rectangle, which are the length and the width.
Hence the formula for the area of the rectangle is given as follows:
Area = Length x Width.
The area of the uncovered region is given by the total area subtracted by the area of the covered region.
Then the dimensions for the uncovered region are given as follows:
96 - 2x.48 - 2x.The area of the covered region is given as follows:
4x².
The area of the entire region is given as follows:
4x² - 288x + 4608.
Hence the correct statement is given by option A.
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show how you would fit a piecewise quadratic equation to the following points: (-2,1), (-1,-1), and (1,2).
The required Quadratic fitting the given observations become y = 7/6x² + 3/2x - 2/3
The given points are (-2,1), (-1,-1) and (1,2).
Let us assume the quadratic fitting the given points be:
y = ax² + bx + c
Substituting the given points in this quadratic, and solving for the values of a, b and c, we get
1 = a (-2)² + b(-2) + c = 4a - 2b + c
-1 = a (-1)² + b(-1) + c = a - b + c
2 = a (1)² + b (1) + c = a + b + c
The values of a, b and c are:
then, b = 3/2
then, a = 7/6
then, c = -2/3
therefore, so, the required Quadratic fitting the given observations become:
y = 7/6x² + 3/2x - 2/3
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A rectangle has a length 2 m less than twice its width. When 5 m are added to the width, the resulting figure is a square with an area of 144m2. Find the dimensions of the original rectangle.
find the coordinates of point p that is 3/4 of the way along the directed line segment from c(6,-5) to d(-3,4)
The coordinates of point P that is 3/4 of the way along the directed line segment from C(6, -5) to D(-3, 4) are (-0.75, 1.75).
To find the coordinates of point P that is 3/4 of the way along the directed line segment from C(6, -5) to D(-3, 4), we can use the following formula:
P = (1 - 3/4)C + (3/4)D
First, we find the vector CD = D - C:
CD = (-3, 4) - (6, -5) = (-9, 9)
Then we can plug in the values and simplify:
P = (1 - 3/4)C + (3/4)D
P = (1/4)(6, -5) + (3/4)(-3, 4)
P = (3/4)(-3, 4) + (1/4)(6, -5)
P = (-2.25, 3) + (1.5, -1.25)
P = (-0.75, 1.75)
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Use the power of a power property to simplify the numeric expression.
(91/4)^7/2
Using the power property to simplify the expression (9¹⁺⁴)⁷⁺², we have 9^7/8
Given the expression
(9¹⁺⁴)⁷⁺²
To simplify this expression using the power of a power property, we need to multiply the exponents:
(9¹⁺⁴)⁷⁺² = 9(¹⁺⁴ ˣ ⁷⁺²)
Simplifying the exponents in the parentheses:
(9¹⁺⁴)⁷⁺² = 9⁷⁺⁸ or 9^7/8
Therefore, (9¹⁺⁴)⁷⁺² simplifies to 9^(7/8).
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fill in the blank. Find the kinetic energy of the following particles that each have a de Broglie wavelength of 0.50 nm.? (a) photons ____eV = 2480eV
The kinetic energy of particle with a de Broglie wavelength of 0.50 nm is 82.6 eV.
The given de Broglie wavelength of 0.50 nm corresponds to photons. The formula for the kinetic energy of a particle with a given de Broglie wavelength λ is given by:
K = (hc/λ) - mc^2
where h is Planck's constant, c is the speed of light, and m is the rest mass of the particle.
For photons, the rest mass is zero, so the formula simplifies to:
K = hc/λ
Plugging in the given wavelength of 0.50 nm, we get:
K = (6.626 × 10^-34 J s × 3.00 × 10^8 m/s) / (0.50 × 10^-9 m)
K = 1.3252 × 10^-17 J
Converting to electronvolts (eV), we use the conversion factor 1 eV = 1.602 × 10^-19 J:
K = (1.3252 × 10^-17 J) / (1.602 × 10^-19 J/eV)
K = 82.6 eV (rounded to three significant figures)
Therefore, the kinetic energy of photons with a de Broglie wavelength of 0.50 nm is 82.6 eV (rounded to three significant figures).
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A coin is tossed and then the spinner is spun. Determine the probability that you toss Heads and spin a Red.
1/6
1/10
0
1/12
The probability of getting the toss Heads and spin a Red when A coin is tossed and then the spinner is spun is 1/6 option A.
Events classified as independent do not depend on other events for their occurrence. For instance, if we toss a coin in the air and it lands on head, we can toss it again and this time it will land on tail. Both instances include separate occurrences of the two events.
Formula for probability,
P = number of outcomes/Total outcomes
P = n/T
We have probability of getting a head is, n = 1
S = {H, T}
Total Outcome = 2
So Probability p1 = 1/2
The probability of getting the red after spun is
S = {R, R, B, B, G, G}
n = 2
Total outcome = 6
p2 = 2/6 = 1/3
Total number of probability for toss Heads and spin a Red.
P = p1 x p2
P = 1/2 x 1/3
P = 1/6
Therefore, probability is 1/6.
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a rectangular prism with a volume of 20 in^3 is dialited with a scale facotr of 2. what is the volume of the new figure?
The volume of the new rectangular prism is 160 in³ after it has been dilated with a scale factor of 2.
In this case, the scale factor is 2, which means that the dimensions of the original figure will be multiplied by 2 to get the dimensions of the new figure.
Volume of rectangular prism = length x width x height
20 = l x w x h
Next, we need to find the new dimensions of the rectangular prism after it has been dilated by a scale factor of 2. We can do this by multiplying each dimension of the original rectangular prism by 2.
New length = 2 x l
New width = 2 x w
New height = 2 x h
Now we can find the volume of the new rectangular prism by using the same formula as before, but with the new dimensions:
Volume of new rectangular prism = (2 x l) x (2 x w) x (2 x h)
Simplifying this expression, we get:
Volume of new rectangular prism = 8 x (l x w x h)
We know that l x w x h is equal to the volume of the original rectangular prism, which is 20 in³. So we can substitute this value into the expression to get:
Volume of new rectangular prism = 8 x 20 in³
Volume of new rectangular prism = 160 in³
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A parabola opening up or down has vertex (0, -3) and passes through (-8, 5). Write its
equation in vertex form.
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=0\\ k=-3\\ \end{cases}\implies y=a(~~x-0~~)^2 + (-3)\hspace{4em}\textit{we also know that} \begin{cases} x=-8\\ y=5 \end{cases} \\\\\\ 5=a(-8-0)^2-3\implies 8=64a\implies \cfrac{8}{64}=a\implies \cfrac{1}{8}=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} y=\cfrac{1}{8}x^2-3 \end{array}} ~\hfill[/tex]
Find the following answers:
Answer:
Step-by-step explanation:
[tex]\{A\cup B \}=\{1,2,3,7,10,11,12,14,16,17,18,19 \}\\\\\{A \cap B \}=\{ 1,7,10,14\}[/tex]
A∪B: Any element which is in either or both sets.
A∩B: Only elements that are in both A and B.