Answer:
Center is at (0,0)
Step-by-step explanation:
An equation of ellipse in standard form is:
[tex]\displaystyle{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2} = 1[/tex]
Where center is at point (h,k)
From the equation of [tex]\displaystyle{x^2+5y^2-45=0}[/tex]. First, we add 45 both sides:
[tex]\displaystyle{x^2+5y^2-45+45=0+45}\\\\\displaystyle{x^2+5y^2=45}[/tex]
Convert into the standard form with RHS (Right-Hand Side) equal to 1 by dividing both sides by 45:
[tex]\displaystyle{\dfrac{x^2}{45}+\dfrac{5y^2}{45}=\dfrac{45}{45}}\\\\\displaystyle{\dfrac{x^2}{45}+\dfrac{y^2}{9}=1}[/tex]
Therefore, the center of ellipse is at (0,0) since there are no values of h and k.
the vertex of this parabola is at (-5,-2) when the x value is -4 the y value is 2 . what is the coefficient of the squared expression in the parabola's equation
The vertex coefficient of the parabola with vertex (- 5, - 2) and the point (- 4, 2) is equal to 1.
What is the vertex coefficient of the equation of the parabola?
In this question we must find the vertex coefficient of the equation of the parabola, which is the vertex form of the quadratic equation:
y - k = C · (x - h)²
If we know that (h, k) = (- 5, - 2) and (x, y) = (- 4, 2), then the vertex coefficient is:
2 - (- 2) = C · [- 4 - (- 2)]²
4 = C · (- 2)²
C = 1
The vertex coefficient of the parabola with vertex (- 5, - 2) and the point (- 4, 2) is equal to 1.
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What are the domain and range of the function?
domain:
range:
domain:
range:
domain:
range:
domain:
range:
The domain of f(x) = √(x - 7) +9 is x ≥ 7 and the range of f(x) = √(x - 7) +9 is y ≥ 9
How to determine the domain and the range?The function is given as:
f(x) = √(x - 7) +9
Set the radicand greater than or equal to 0
x - 7 ≥ 0
Add 7 to both sides
x ≥ 7
The above represents the domain
Set the radicand to 0
f(x) = 0 +9
So, we have
f(x) = 9
This represents the minimum value of the range.
So, the range is y ≥ 9
Hence, the domain of f(x) = √(x - 7) +9 is x ≥ 7 and the range of f(x) = √(x - 7) +9 is y ≥ 9
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Answer:
Step-by-step explanation:
Its A
Perfect pizza has 16 toppings listed on their menu. how many ways could a customer choose a pizza that contains 5 different toppings?
Answer:
4368 ways
Step-by-step explanation:
Use nCk for this. 16C5. This is [tex]\frac{n!}{(n-k)!(k!)}[/tex]. This becomes[tex]\frac{16!}{(11!)(5!)}[/tex]. This is [tex]\frac{16*15*14*13*12}{5*4*3*2*1}[/tex] due to 16! and 5! canceling out. This becomes 4368.
You purchase one microsoft july $72 put contract for a premium of $1. 32. what is your maximum possible profit?
The maximum possible profit = $7068
For given question,
One Microsoft July $72 put contract for a premium of $1.32
The payoff arise from put option is max (K - S, 0) - P
Now it would be maximum at S = 0
And, the maximum payoff is
K - 0 - P
= K - P
= 72 - 1.32
= $70.68
We assume that for each and every contract the number of shares is 100
So, the maximum profit gained from this strategy is
= $70.68 × 100 shares
= $7068
The maximum profit that will be gained from this strategy is $7068
Therefore, the maximum possible profit = $7068
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The SEC requires registrants to have their quarterly financial statements reviewed by an independent accounting firm but does not mandate that a review report be included in a Form 10-Q. Under what circumstances must a review report accompany quarterly financial statements in a 10-Q? Why doesn't the SEC routinely require public companies to include their review reports in their 10-Q filings?
The SEC routinely require public companies to include their review reports in their 10-Q filings because it is said to be made up of fewer details and the financial statements inclusive that are known to be unaudited.
Note that Form 10-Q is asked for because it is often used to make comparison of a company’s previous financial quarter to that of its current financial quarter.What is Form 10-Q?Form 10-Q is known to be a type of a report that is often needed by the Securities and Exchange Commission (SEC) and it is one that all public company need to file on quarterly basis.
Note also that The SEC is known to have made and need the form in accord to the pursuant of the Securities Exchange Act of 1934 and this form helps them to keep investors well informed about the state of their financial health and all that is taking place at the companies they have invest in or will choose to invest in.
Hence, Form 10-Q is asked for because it is often used to make comparison of a company’s previous financial quarter to that of its current financial quarter.
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In the circle below, if AD is a diameter, and the length of chord BC = 36, find the length of the segment BP.
Answer:
b. 18
Step-by-step explanation:
The perpendicular bisector of a chord is a diameter of the circle. Conversely, if the diameter is perpendicular to a chord, it also bisects it.
Segment lengthsBC = BP +PC
BC = 2×BP . . . . . . . BP = PC
BP = BC/2 = 36/2 = 18 . . . . . . . divide by 2; substitute given values
The length of segment BP is 18 units.
A store has a 40 percent off sale on headphones. With this discount, the price of one pair of headphones is $36. What is the original price of the pair of headphones
Answer:
Discount =40\%
Selling price of headphone =\$36
Solution --
we know that,
MP=SP * 100/(100-D\%)
putting values now we get,
MP = 36 * 100 / 60=60$
so, initial price of Headphone was =$60
Students in Ms. Valendra’s science class planted 13 in different places around the school yard. After one month, they measured the heights of the conifers. They rounded each measurement to the nearest 1/4
Considering the dot plot, it is found that the tallest conifer is 3.25 inches taller than the shortest conifer.
What does a dot plot shows?It shows, with dots, the number of times that each of the measures appears in a data-set.
Researching this problem on the internet, and finding the dot plot, we have that:
The shortest conifer measures 6 and 1/4 = 6.25 inches.The tallest conifer measures 9.5 inches.The difference is:
9.5 - 6.25 = 3.25 inches.
Hence the tallest conifer is 3.25 inches taller than the shortest conifer.
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(Sequences and Summations) How would you solve this? Please give an explanation rather than just answering the question.
Step-by-step explanation:
To find the Tth term of an arithmetic progression, you should use the formula: Tn: a + (n-1)d, whereby 'a' is the first term, you have to find 'n' and 'd' is the difference between the first 2 numbers to find out by how much the arithmetic progression is increasing or decreasing. Hence, 29/30 minus 4/5 equals to 1/6. 'a' is 4/5 and 'd' is 1/6.
Use the above formula by replace a and d then you'll get the answer. Hope this helps.
What type of number is -560{,}114−560,114minus, 560, comma, 114? Choose all answers that apply: Choose all answers that apply:
The type of numbers which -560 and 114 are include the following:
B. Integer.
C. Rational.
What is a numerical data?A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.
The types of numbers.In Mathematics, there are six (6) common types of numbers and these include the following:
Natural (counting) numbers: these are 1, 2, 3, 4, 5, 6, .....114, ....560.Whole numbers: these comprises all natural numbers and 0.Integers: these are whole numbers that may either be positive, negative, or zero such as ....-560, ...... -114, ..... -4, -3, -2, -1, 0, 1, 2, 3, 4, .....114, ....560.Rational numbers: these comprises fractions, integers, and terminating (repeating) decimals such as ....-560, ...... -114, ..... -4, -3, -2, -1, -1/2, 0, 1, 1/2, 2, 3, 4, .....114, ....560.Irrational numbers: these comprises non-terminating or non-repeating decimals.Real numbers: these comprises both rational numbers and irrational numbers.In this context, we can infer and logically deduce that -560 and 114 are both an integer and a rational number.
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Complete Question:
What type of number is -560, 114? Choose all answers that apply:
A. Whole number
B. Integer
C. Rational
D. Irrational
Can someone help pls
Answer:
x = 0, x = 5
Step-by-step explanation:
x² - 5x = 0 ← factor out x from each term
x(x - 5) = 0
equate each factor to zero and solve for x
x = 0
x - 5 = 0 ⇒ x = 5
subtract the squre of m from the ratio of p andq
The expression that represent the given statement is p/q - m²
Writing an expressionFrom the question, we are to write an expression for the word problem
We are to write an expression for the statement
"Subtract the square of m from the ratio of p and q"
Square of m = m²
Ratio of p and q = p/q
Thus,
subtract the square of m from the ratio of p and q, becomes
p/q - m²
Hence, the expression that represent the given statement is p/q - m²
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Identify each expression and value that represents the area under the curve y = x2 4 on the interval [-3, 2].
The area under the curve y = x² + 4 on the interval [-3, 2] exists [tex]$\frac{95}{3}[/tex].
What is the area under the curve y = x² + 4 on the interval [-3, 2]?The area under a curve between two points exists seen by accomplishing a definite integral between the two points. To estimate the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. This area can be estimated by utilizing integration with given limits.
The equation that represents the curve exists
y = x² + 4
To estimate the area under the curve in the interval of [-3, 2] will be
[tex]$&\text { area }=\int_{-3}^{2} x^{2}+4 d x \\[/tex]
[tex]$&=\left[\frac{x^{3}}{3}+4 x\right]_{-3}^{2} \\[/tex]
[tex]$&=\frac{1}{3}\left[x^{3}\right]_{-3}^{2}+4[x]_{-}^{2} _{3} \\[/tex]
simplifying the above equation, we get
[tex]$&=\frac{1}{3}\left[(2)^{3}(-3)^{3}\right]+4[(2)-(-3)] \\[/tex]
[tex]$&=\frac{1}{3}[8+27]+4[2+3] \\[/tex]
[tex]$&=\frac{1}{3}(35)+20 \\[/tex]
[tex]$&=\left(\frac{95}{3}\right)[/tex]
Therefore, the area under the curve y = x² + 4 on the interval [-3, 2] exists [tex]$\frac{95}{3}[/tex].
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trị tuyệt đối(x+1) = 3*x
u need first to understand the thing
find the size of each of the angles marked with letter
Answer: ||||||| n=41° |||||| m=59° IIIII p=260° IIII
Step-by-step explanation:
Alternate angle:
<m=<59°
m=59°
<n=<41°
n=41°
______________
p+41°+59°= 360°
p+100°=360°
p=360°-100°
p=260°
Answer:
n = 49
m= 31
p= 280
Step-by-step explanation:
41 + n = 90
n= 90 -41 = 49
59 + m = 90
m = 90 - 59 = 31
Hope this helps!
p + n + m = 360
p = 360 - 49 - 31 = 280
Rewrite 2X = 128 as a logarithmic equation.
Olog,128=2
log2x = 128
log2128 = x
log128x = 2
The equation 2^x = 128 as a logarithmic equation is log₂(128) = x
How to rewrite the equation as a logarithmic equation?The equation is given as:
2^x = 128
Take the logarithm of both sides
log(2^x) = log(128)
Rewrite as:
x * log(2) = log(128)
Divide both sides of the equation by log(2)
x = log(128)/log(2)
Apply the change of base rule
x = log₂(128)
Hence, the equation 2^x = 128 as a logarithmic equation is log₂(128) = x
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Please help!!!!!!!!!!!!!!!!!!!!!!!!1
Answer:
6
Step-by-step explanation:
Given an isosceles triangle the two sides opposite of congruent angles are equal to eachother, so you can create an equation setting the two sides equal to eachother and solve for x.
[tex]x+4=3x-8\\x=3x-12\\-2x=-12\\x=6[/tex]
The length of AC is simply x, therefore 6
A road sign says:
Beaston: 10 mi (17 km)
Assuming that each of these numbers is rounded to the nearest unit, what is the actual range of possible miles to Beaston? Give your answer in interval notation, rounded to 2 decimal places.
(1 mile is exactly 1.609344 kilometers.)
Based on the fact that the road sign's distance to Beaston is rounded to the nearest unit, the actual range of possible miles to Beaston is 9.50 ≤ x ≤ 10.49.
How far is it to Beaston?Based on the fact that the miles to Beaston are rounded to the nearest mile, the first thing to do is to find the lowest and highest numbers that can be rounded to 10 miles.
The lowest number that you can round to 10 miles is:
= 9.5 miles
Because of the 0.5 attached to the 9 miles, you will round up to 10 instead of down to 9.
The highest number that you can round to 10 miles at two decimal places is 10.49 miles.
The reason this is the highest is that the 0.4 is the tenths number just before 0.5. This means that you round the whole number down to 10.
Assuming the distance to Beaston is x, the interval would then be:
9.50 ≤ x ≤ 10.49.
In conclusion, the range of miles of Beaston is 9.50 ≤ x ≤ 10.49.
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Describe how the figure at the right
shows that 36 +27= 9 X (4 + 3).
See below for the description of the figure
How to describe the figure?The equation is given as:
36 + 27 = 9 * (4 + 3)
Open the bracket
36 + 27 = 9 * 4 + 9 * 3
The above when represented on a figure is represented by the given figure.
From the figure, we have the following highlights:
There are two partitions on the figureOne represents 9 * 4, while the other represents 9 * 3This means that the figure has 7 columns and 9 rows where the partitions on the figure are the product of the rows and column in each partition
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8. Solve for x.
28°
X
Answer:
if X is the angle degree like I think it is, then X = 56 degrees
Step-by-step explanation:
isosceles triangles will have 2 equal base angles.
90 degree angle - 28 = 62°
62 is now each base angle.
62 times 2 angles equals 124
the final angle, x, is 180 - 124 = 56°
PLEASE HELP IM STUCK
Answer:
If I'm not mistaken that is the answer
Use the elimination method to solve each linear system.
1) 2x-9y=-55 and x+2y=18
2) 3x+2y=7 and 6x-6y=-6
3) 6x+10y=2 and 7x+4y=-13
4) 3x+2y=5 and x-2y=-1
Abby mixes cinnamon and nutmeg to make 25g of a spice mix. Cinnamon costs 9 cents per gram, and nutmeg costs 12.5 cent per gram. The spice mix costs 9.7 cents per gram. How much of each spice does Abby need to use?
Answer:
1) x=4, y=7
2) x=1, y=2
3) x=-3, y=2
4) x=1, y=1
word problem) 5g of nutmeg and 20g of cinnamon
Step-by-step explanation:
1)
2x-9y=-55
2(x+2y) = 2x+4y = 36
(2x+4y)-(2x-9y)=36-(-55)
13y = 91
y = 7 so x = 4
2)
2(3x+2y) = 6x+4y = 14
6x-6y=-6
(6x+4y)-(6x-6y) = 14-(-6)
10y = 20
y = 2 so x = 1
3)
2(6x+10y) = 12x+20y = 4
5(7x+4y) = 35x+20y = -65
(35x+20y) - (12x+20y) = -65-4
23x = -69
x = -3 so y = 2
4)
just add them
(3x+2y)+(x-2y) = 5+(-1)
4x = 4
x = 1 so y= 1
last)
c+n = 25
9c + 12.5n = 25*9.7 = 242.5
9(c+n) = 9*25
9c+9n=225
9c+12.5n - 9c-9n = 242.5-225
3.5n = 17.5
n = 5 so c = 20
5g of nutmeg and 20g of cinnamon
In a game, a player earns 100 points for each question answered correctly and earns -30 points for each question answered incorrectly. A player answered 14 questions correctly and 6 questions incorrectly.
Part A) Write a numeric expression to represent the total number of points the player earned.
Part B) Determine the total number of points.
The general expression is 130 x - 600 and total points scored by the player is 1220
A) Let the number of correctly answered questions be x.
∴ Number of incorrectly answered questions will be 20 - x.
+ 100 points is awarded for each question answered correctly while -30 points is awarded for each question answered incorrectly.
Thus, the general equation becomes
= 100x - (20 - x)(-30)
= 100x +30x - 600
= 130x - 600
Thus the general expression becomes 130 x - 600
B) The player answers 14 questions correctly, thus x = 14
Substituting the value of x =14 in the general equation we get,
= 130(14) - 600
= 1820 - 600
= 1220.
Thus the total points scored by the player will be 1220
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Two spheres have volumes of 87 cm³ and 647 cm³. If the surface area of the smaller sphere is 167 cm², what is the
surface area of the larger sphere?
64 cm²
96 cm²
128 cm²
256 cm²
The surface area of the larger sphere is equal to 636.365 square centimeters.
How to determine the surface area of the sphere by the use of direct variation formulas
In this question we must estimate the surface area of the smaller sphere. By geometry we know that the volume of a sphere is directly proportional to the cube of its radius and the surface area is directly proportional to the square of radius, then the volume to surface area ratio is equal to:
V/A = k · r (1)
Where:
r - Radiusk - Proportionality constantThen, we can derive the following relationship between the two spheres by eliminating the proportionality constant:
V/(A · r) = V'/(A' · R) (2)
Where:
r - Radius of the smaller sphere.R - Radius of the larger sphere.First, we need to determine the radii of the spheres:
Larger radius
R = ∛(3 · V' / 4π)
R = ∛(3 · 647 / 4π)
R ≈ 5.365 cm
Smaller sphere
r = ∛(3 · V / 4π)
r = ∛(3 · 87 / 4π)
r ≈ 2.749 cm
Lastly, we find the surface area of the larger sphere:
A · r · V' = A' · R · V
A' = (A · r · V') / (R · V)
A' = (167 · 2.749 · 647) / (5.365 · 87)
A' = 636.365 cm²
The surface area of the larger sphere is equal to 636.365 square centimeters.
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If there are 3 line, the 1st and 2nd line are parallel to each other, the third line are parallel to the 2nd line, does that mean all 3 line are parallel to each other?
Use a calculator to find the mean of the data. {211, 226, 186, 221, 181, 228, 207, 215, 203, 203, 204, 196, 226, 212, 212, 201, 219, 191, 191, 185, 193, 231}
The mean of the given data is 206.5.
What is a mean?A dataset's mean (also known as the arithmetic mean, as opposed to the geometric mean) is the sum of all values divided by the total number of values. It is the most widely used measure of central tendency and is frequently referred to as the "average."It is the total (sum) of all the values in a set of data, such as numbers or measurements, divided by the number of values in the list. Add up all of the values in the set to find the mean. Then divide the total by the number of possible values.To find the mean of the given data:
Sum of values = 211 + 226 + 186 + 221 + 181 + 228 + 207 + 215 + 203 + 203 + 204 + 196 + 226 + 212 + 212 + 201 + 219 + 191 + 191 + 185 + 193 + 231 = 4,542
Number of values = 22
Mean = 4,542 ÷ 22 = 206.5
Therefore, the mean of the given data is 206.5.
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Answer:
Step-by-step explanation:
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex]2 \sqrt{5} \: + \: 7 \sqrt{5} \\ \sqrt{5} \: ( \: 2 + \: 7 \: ) \\ \sqrt{5} \: ( \: 9 \: ) \\ 9 \sqrt{5} [/tex]
Option 1
The simplification of the expression 2√5 + 7√5 is: 9√5.
So, Option A. is correct.
To simplify the expression 2√5 + 7√5, we can combine the like terms.
Both terms have the same radical expression, which is √5, so we can add their coefficients together.
2√5 + 7√5 = (2 + 7)√5
Now, simplify the coefficients:
2 + 7 = 9
Therefore, the simplified expression is:
2√5 + 7√5 = 9√5
So, the final answer is 9√5.
So, Option A. is correct.
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Find the largest 4-digit number which is a perfect square.
Answer:
To find the biggest 4-digit number which is a perfect square, we have to take the square of biggest 2-digit number. ∴ The biggest 4-digit number which is a perfect square = 9801.
Step-by-step explanation:
mark as brainlest answerAnswer:
9801
Step-by-step explanation:
well we know 100 squared is the first 5 digit square number so it must be 99 squared, which is 9801
11 points please help me
From the given sample data in the table on the backpack weight, we have;
(a) The means of the samples are;
First sample = 6.375Second sample = 6.375Third sample = 6.625(b) The range is 0.25
(c) The true statements are;
A single sample mean will tend to be a worse estimate than the mean of the sample meansThe farther the range of the sample means is from zero, the less confident they can be their estimate.How can the mean of the sample means be found?(a) The sample means of each of each of the three samples are found as follows;
[tex]Mean = \frac{ \sum \: x}{n} [/tex]
Where;
x = The value of a data point
[tex] \sum \: x = Sum of the data [/tex]
n = Sample size
The mean of the first sample, S1, data is therefore;
[tex]Mean \: S1 = \frac{3 + 7 + 8 + 3 + 7 + 9 + 6 + 8}{8} [/tex]
3+7+8+3+7+9+6+8 = 51
Which gives
[tex]Mean \: S1 = \frac{51}{8} = \mathbf{6.375\[/tex]
Mean of the first sample = 6.375Similarly, we have;
[tex]Mean \: S2 = \frac{8 + 6 + 4 + 7 + 9 + 4 + 6 + 7}{8} [/tex]
8 +6+4+7+9+4+6+7 = 51
Which gives;
[tex]Mean \: S2 = \mathbf{\frac{51}{8}} = 6.375 [/tex]
Mean of the second sample = 6.375
[tex]Mean \: S3 = \frac{9 + 4 + 5 + 8 + 7 + 5 + 9 + 6}{8} [/tex]
9+4+5+8+7+5+9+6 = 53
Which gives;
[tex]Mean \: S3 = \frac{53}{8} = \mathbf{6.625} [/tex]
Mean of the third sample = 6.625(b) The range of the means of the sample means is found as follows;
Range = Largest value - Smallest value
Which gives;
Range of the sample means = 6.625 - 6.375 = 0.25(c) The population mean is given by the mean of the sample means. That is, a very good estimate of the sample mean is given by the mean of the sample means.
The true statements are therefore;
A single sample mean will tend to be a worse estimate than the mean of the sample meansThe farther the range of the sample means is from zero, the less confident they can be their estimate.Learn more about the mean of the sample means of a collection of data here:
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Which statement is most likely to be true for this distribution?
Answer:
A
Step-by-step explanation:
the means is less than the median
