Please Help!!!
(x-3)^2/64 + (y+5)^2/100 = 1
a. Identify the coordinates of the center of the ellipse.
b. Find the length of the major and minor axes.
c. Find the coordinates of the foci.
d. Graph the ellipse. Label the center and foci.,
Answers
[tex]\frac{(x - xc)^{2} }{ a^{2} } + \frac{(y - yc)^{2} }{ b^{2} } = 1[/tex]
Indeed, you have:
[tex]\frac{(x-3)^{2} }{64} + \frac{(y+5)^{2} }{100} = 1[/tex]
Therefore you can easily find:
a) the coordinates of the center:
in your case xc = 3 and yc = -5
hence C(3 , -5)
b) lenght of the major and minor axis:
in your case a² < b²:
a² = 64 ⇒ a = 8 (ATTENTION! This is the semi-minor axis)
b² = 100 ⇒ b = 10 (again, this is the semi-major axis)
Therefore,
minor axis 2a = 16 and major axis 2b = 20
c) coordinates of the foci:
Since you have a² < b², foci have the generic coordinates F₁₂ (xc , yc+/-c)
where c = √(b² - a²)
Let's compute c = √(100 - 64) = √36 = 6
yf₁ = -5 - 6 = -11
yf₂ = -5 + 6 = -1
Therefore:
F₁ (3, -11) and F₂(3, +1)
d) the graph is in the picture attached
Related Questions
What is a quartic function with only the two real zeroes given?
x=5 and x=1
Answers
The answer is
Y=x^4-6x^3 +6x^2 -6x+5
The quartic function with only two real zeroes given as; x=5 and x=1 is; x⁴ -12x³ +46x²-60x +25
With two zeroes given for a quartic equation;
The zeroes must appear twice each such that the factors of the function are;
(x-5), (x-5) , (x -1) and (x- 1)The quartic function is therefore:
(x² -10x +25) (x² -2x +1)(x² -10x +25) (x² -2x +1)x⁴ -2x³ +x² -10x³ +20x² -10x + 25x² -50x +25(x² -10x +25) (x² -2x +1)x⁴ -2x³ +x² -10x³ +20x² -10x + 25x² -50x +25= x⁴ -12x³ +46x²-60x +25
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The diagram represents the enlargement of a rectangle by using a scale factor of 6
Answers
5*1 is the dimension of the original rectangle.
What is Scale?The scale is the proportion that is used to show how the dimensions of a model or scaled figure compare to the equivalent dimensions of the real figure or item. In contrast, a scale factor is a number that is multiplied by each component of an item to create an expanded or reduced figure.
Given With a scale factor of 6, the diagram depicts the expansion of a rectangle.
and the new rectangle is 30*6 in size.
The scaling factor is 6
thus,
the length of the original rectangle = 30/6
the length of the original rectangle = 5
the width of the original rectangle = 6/6
the width of the original rectangle = 1
therefore, the dimension of the original rectangle is 5*1.
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Complete question:
What measurements did the initial rectangle have?
Which diagram represents rx ◦ RO,180°?
Answers
Answer:
the correct answer is B
If 12 is added to the square of a positive integer, the result is 133. Find the positive integer
Answers
2. So, if 12 is added to the square of a positive integer, you can write the following the expression:
12+x²=133
3. You can obtain the value of the positive integer "x", by clearing it. Then, you have:
12+x²=133
x²=133-12
x=√(133-12)
x=√121
x=11
Therefore, the positive integer is: 11
11___________________________
Thaddeus wants to attend a sports camp this spring that costs $170.00 for the week. He rakes leaves during the fall and earns $58.35. He shovels snow during the winter and earns $85.80. How much more money does Thaddeus need to earn to pay for the sports camp? Write your answer as a decimal. Thaddeus needs to earn
Answers
He need $25.85 more to pay.
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Charge for week = $170
earnings from leaves raking = 58.35
Earnings from snow shoving = 85.80
Total earnings = 85.80 + 58.35 = $144.15
So, he need more
=170 - 144.15
=$25.85
Hence, He need $25.85 more to pay.
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Jim makes and sells denim knapsacks for $10.50 apiece. The knapsacks cost $7 apiece to produce.
Jim makes ____% profit on each knapsacks.
Show your work.
A. 33
B. 50
C. 75
D. 125
Answers
In this problem, to solve for the gross profit, you have to deduct the cost of each knapsack to its selling price.
The gross profit of Jim is $3.50 ($10.50 - $7).
To compute the gross profit rate, you have to divide the gross profit ($3.50) to the cost of each knapsack ($7).
$3.50 / $7 = 0.5 or 50%
Therefore, Jim makes 50% profit on each knapsack.
Easy Money CLick here
Answers
PLEASE HELP ME! I keep getting the wrong answer.
Given the parent functions f(x) = 5x − 1 and g(x) = 3x − 9, what is g(x) − f(x)?
g(x) − f(x) = 3x − 8 − 5x
g(x) − f(x) = 3x − 10 − 5x
g(x) − f(x) = −2x − 8 − 3x
g(x) − f(x) = −2x − 10 − 3x,
Answers
FAN AND MEDAL!!
The formula for the circumference of a circle is C = 2πr, where r is the radius. Rearrange the formula to solve for r and select the correct option below.
r = C over 2 pi
r = 2πC
r = C − 2π
r = 2 pi over C,
Answers
The reference angle for an angle whose measure is 260 degrees is
Answers
the difference of a number t and 7 is greater than 10 and less than 20....show me how to write this as an inequality.,
Answers
Scott and Harry went cycling every day. They increased the number of minutes of cycling every week as described below: Scott: Cycled for 10 minutes every day in the first week, 15 minutes in the second week, 20 minutes in the third week, and 25 minutes in the fourth week. Harry: Cycled for 10 minutes every day in the first week, 20 minutes in the second week, 40 minutes in the third week, and 80 minutes in the fourth week. Which statement best describes the methods used by Scott and Harry to increase the time they spent cycling? Scott's method is linear because the number of minutes increased by an equal number every week. Harry's method is linear because the number of minutes increased by an equal factor every week. Both Harry's and Scott's method is exponential because the number of minutes increased by an equal factor every week. Both Harry's and Scott's method is exponential because the number of minutes increased by an equal number every week.
Answers
Answer:
Scott's method is linear because the number of minutes increased by an equal number each week.
Arithmetic progressions use the linear method.
The graph proves it, by obtaining a straight line.
Step-by-step explanation:
Scott used an arithmetic progression, with a ratio of 5, that is adding 5 to the value of each previous week.
Let us call the time in minutes of each week, so the arithmetic progression is of the following linear form:
S1 = k0 = 10
S2 = k1 + 5 = 10 + 5 = 15
S3 = k2 + 5 = 15 + 5 = 20
S4 = k3 + 5 = 20 + 5 = 25
See attached chart.
Harry used a geometric progression, with a ratio of 2, that is multiplying by 2 the value of each week.
Let us call time in minutes of each week, so the geometric progression is of the following exponential form:
S1 = k0 = 10
S2 = k1 x 2 = 10 x 2 = 20
S3 = k2 x 2 = 20 x 2 = 40
S4 = k3 x 2 = 40 x 2 = 80
See attached chart.
Let's analyze the four options given:
Scott's method is linear because the number of minutes increased by an equal number each week.
True: The graph proves it, by obtaining a straight line.
Also, Arithmetic progressions use the linear method.
Harry's method is linear because the number of minutes increased by an equal factor each week.
False: The graph shows that it is not linear, a straight line is not obtained.
Both Harry and Scott's method are exponential because the number of minutes increases by an equal factor each week.
False: Scott's method is linear.
Both Harry and Scott's method are exponential because the number of minutes increases by an equal number each week.
False: Scott's method is linear.
Identify the trinomial that is a perfect square. HELP ASAP
A.64x^2 − 90x + 25
B.64x^2 − 70x + 25
C. 81x^2 − 70x + 16
D. 81x^2 − 72x + 16
Answers
You can find this by taking the square roots of the outside numbers and multiplying them by each other and 2 to see if they equal the middle number.
can anyone help me solve these two questions
1 you have 75% of your pay direct/-deposit how much is given to you as a check per week ?
2. of the amount direct-deposited problem 1 you have 50% placed into a savings account how much is deposited in the savings account each month?,
Answers
Final answer:
The student takes home a check of $25.94 each week after deductions and direct deposit. Of the amount direct-deposited, $38.92 is placed into a savings account weekly, resulting in $155.68 being deposited into the savings account monthly.
Explanation:
To solve the first problem, we must start by calculating the gross income for one week of work:
Gross income = Hourly rate × Hours worked per week = 13.76 × 10 = $137.60Next, we calculate each of the deductions from the gross income:
FICA = Gross income × FICA rate = $137.60 × 7.65% = $10.52Federal tax withholding = Gross income × Federal tax rate = $137.60 × 9.8% = $13.48State tax withholding = Gross income × State tax rate = $137.60 × 7.13% = $9.82Now we calculate the total deductions:
Total deductions = FICA + Federal tax + State tax = $10.52 + $13.48 + $9.82 = $33.82The net income after deductions is:
Net income = Gross income - Total deductions = $137.60 - $33.82 = $103.78We then determine the amount directly deposited:
Direct deposit amount = Net income × Direct deposit percentage = $103.78 × 75% = $77.84The remaining paycheck given as a check each week is:
Check amount = Net income - Direct deposit amount = $103.78 - $77.84 = $25.94For the second question, we already know from the scenario that $77.84 is directly deposited. We just need to calculate the amount that goes into the savings account:
Savings deposit per week = Direct deposit amount × Savings account percentage = $77.84 × 50% = $38.92 per weekTo find the monthly savings deposit, we assume there are 4 weeks in a month:
Savings deposit per month = Savings deposit per week × 4 = $38.92 × 4 = $155.68 per monthWrite and simplify the equation you would use to solve the problem below. Scott has a jar of quarters and dimes. If there is $4.15 in the jar, and there are 4 dimes, how many quarters are in the jar?
A. x(25 + 10) = 415
B. 25x + 40 = 415
C. 25x + 10 = 415
D. 4 * 10x + 25x = 415
Answers
The explanation is shown below:
1. You have that:
- There is $4.15 in the jar.
-There are 4 dimes in the jar.
2. Therefore:
1 quarter=25 cents
4 dimes=40 cents
$4.15=415 cents
3. Then, you have that the equation you would use to solve the problem and to calculate how many quarters are in the jar, is:
25x+40=415
Use the identity below to complete the tasks: a3 + b3 = (a + b)(a2 - ab + b2) Use the identity for the sum of two cubes to factor 8q6r3 + 27s6t3. What is a? What is b? Factor the expression. es003-1.jpg es003-2.jpg es004-1.jpg es005-1.jpg es006-1.jpg
Answers
a is 2q^2r
b is 3s^2t
the expression factored is...
(2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)
The given expression is a sum of two cubes. The factorization of the given expression is [tex](2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)[/tex].
Given:
The given identity is, [tex]a^3 + b^3 = (a + b)(a^2 - ab + b^2)[/tex].
It is required to factorize [tex]8q^6r^3 + 27s^6t^3[/tex] using the given identity.
The given expression can be written in the form of sum of two cubes as,
[tex]8q^6r^3 + 27s^6t^3=2^3q^6r^3 + 3^3s^6t^3\\=(2q^2r)^3+(3s^2t)^3[/tex]
Here, a and b are [tex]2q^2r[/tex] and [tex]3s^2t[/tex] respectively.
Now, the factorization of the given expression can be one as,
[tex]a^3 + b^3 = (a + b)(a^2 - ab + b^2)\\(2q^2r)^3+(3s^2t)^3=(2q^2r+3s^2t)((2q^2r)^2-(2q^2r)(3s^2t)+(3s^2t)^2)\\=(2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)[/tex]
Therefore, the factorization of the given expression is [tex](2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)[/tex].
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If your credit reports shows different scores, what should you do?
A) Nothing, the credit bureaus will recognize the mistake and fix it for you.
B) Get in touch with credit bureaus to see if they have different or inaccurate information on your credit history.
C) Research online to see how you can get into the system and fix it yourself.
D) Visit your local bank and have them fix it for you.
Answers
Answer:
(B) is correct
Step-by-step explanation:
As the credit reports shows different scores so it will be resolved by credit bureaus and the report only shows different scores in case they have incorrect or different info about our credit history so we should contact the credit bureaus and ask them to correct the information of our credit history.
So, the right answer is (B).
PLEASE HELP ME QUICK
PLEASE EXPLAIN AND IF 2 PPL ANSWER I WILL GIVE BRAINLIEST..
THX
Answers
The one on the page with the question.
Question 4 Unsaved
What is the value of θ for the acute angle in a right triangle?
sin(θ) = cos(58°)
Question 4 options:
32°
58°
122°
29°
Answers
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The angle sum property of a triangle states that:
Sum of three angles of a triangle is 180 degrees.
Now we are given a right angled triangle here.
The question can be described as shows in figure.
Here ABC is a triangle right angles at B.
The other angle is 58 degrees.
Using angle sum property:
∠A + ∠B +∠C =180
let ∠A = 58° and ∠B =90°
So we have ,
58° + 90° +∠C =180
148°+∠C=180°
∠C = 32°
Answer : Angle C is 32 degrees.
Option A is correct choice
order the following numbers from least to greatest. sqrt 11, -0.4, (-4/3), 0.8, sqrt 2
Answers
3 < sqrt 11 < 4
order least to greatest
(-4/3), -0.4, 0.8, sqrt 2, sqrt 11
The numbers arranged from least to greatest will be -0.4, -1.33, 0.8, 1.41, and 3.32.
What is ascending order?It is the order of the numbers in which a smaller number comes first and then followed by the next number and then the last number will be the biggest one.
The decimal number is the sum of a whole number and part of the fraction number. The fraction number is greater than zero but less than one.
The numbers are given below.
√11, -0.4, (-4/3), 0.8, √2
Convert all the numbers into decimal form, then we have
√11, -0.4, (-4/3), 0.8, √2
3.32, -0.4, -1.33, 0.8, 1.41
Then the numbers arranged from least to greatest will be -0.4, -1.33, 0.8, 1.41, and 3.32.
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A chemist weighed out 101. g of potassium. Calculate the number of moles of potassium she weighed out.
Round your answer to 3 significant digits.
Answers
The solution to this is,
to find moles, convert grams to mole by the equation
grams(mole/gram)=moles
101. g of potassium(1 mole potassium/39.10 g potassium)=2.58 moles potassium
Answer:
101 g of Potassium is equivalent to 2.583 moles of Potassium.
Step-by-step explanation:
As per definition of moles, molecular weight of a substance = 1 mole
So molecular weight of Potassium = 39.0983 g
∵ 39.0983 g weight of Potassium = 1 mole
∴ 1 g weight of Potassium = [tex]\frac{1}{39.0983}[/tex] g
∴ 101 g of Potassium = [tex]\frac{101}{39.0983}[/tex] g
= 2.583 moles
Therefore, 101 g of Potassium is equivalent to 2.583 moles of Potassium.
50 POINTS!!!!! HELP Soybean meal is 16% protein; cornmeal is 8% protein.How many pounds of each should be mixed together in order to get 320-lb mixture that is 9% protein?
How many pounds of cornmeal should be in the mixture? How many pounds of soybean should be in the mixture?
Answers
We have then:
x: Amount of soybean meal
320 - x: quantity of cornmeal
We now write the equation that models the problem:
[tex]0.16x + 0.08 (320-x) = 0.09 (320) [/tex]
Rewriting we have:
[tex]0.16x + 25.6 - 0.08x = 28.8 [/tex]
From here, we clear x:
[tex]0.16x - 0.08x = 28.8 - 25.6 0.08x = 3.2 x = 3.2 / 0.08 x = 40[/tex]
Then, the amount of Soybean meal is:
[tex]x = 40 lb [/tex]
The amount of cornmeal is:
[tex]320 - x = 320 - 40 = 280 lb [/tex]
Answer:
cornmeal: 280 lb
Soybean: 40 lb.
a triangle has verices at (4,-2), (-3,0) and (1,3). what is the approximate perimeter of the triangle?
1. 17 units
2.18 units
3.19 units
4.20 units
Answers
You have three points and need to find the distances between each pair of them. You can do this with the Pythagoras theorem applied to each: For the first pair (1, 3), (2, -3)(2 - 1) is the change in distance between the x-coordinates and(3 - -3) is the change in distance between the y (2 - 1)2 + (3 + 3)2 = c21 + 36 = c2c = √37 Repeat for (2, -3), (-1, -1) and(-1, -1), (1, 3) Add your c's together and you will have your perimeter
Have a nice day
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Answers
1) Trigonometric properties.
2) trigonometric equations
3) Division of fractions.
Answer:
cotx = root (15) / 7
See attached image.
cot θ = √15 / 7
Explanation:
csc θ = 1 / sin θ
In a right angled triangle, sin θ = opposite / hypotenuse
This means that:
csc θ = hypotenuse / opposite = 8 / 7
So, we have:
opposite = 7 units and hypotenuse = 8 units
We will use the Pythagorean theorem to get the adjacent side as follows:
(hypotenuse)^2 = (opposite)^2 + (adjacent)^2
(8)^2 = (7)^2 + (adjacent)^2
(adjacent)^2 = 15
adjacent = √15 units
Now, we want to get the value of cot θ.
We know that:
cot θ = 1 / tan θ
Since tan θ = opposite / adjacent
Therefore:
cot θ = adjacent / opposite = √15 / 7
Hope this helps :)
You are buying a $24.50 item that has 6% sales tax. You give the cashier $40 to pay for the item. How much change do you get back?
Answers
Answer:
14.03
Step-by-step explanation:
I took a test
There are $14.03 get change do you get back.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
You are buying a $24.50 item that has 6% sales tax.
And, You give the cashier $40 to pay for the item.
Here, You are buying a $24.50 item that has 6% sales tax.
Hence, The amount of sales tax = 6% of $24.50
= 6/100 × $24.50
= $1.47
Thus, The amount of charge = $40 - ($24.50 + $1.47)
= $40 - $25.97
= $14.03
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our family shares all the minutes in your cell phone plan. Every 30 days you get 4,800 minutes. Four people share the minutes. How many minutes can each person use per day if the minutes are split fairly?
Answers
.. (4800 min)/(30 day)*/(4 person)
.. = 4800/(30*4) min/day
.. = 40 min/day/person
Each person can use 40 minutes per day.
Sept Apr June Nov all have 30 days.
4800/4 = 1200 (monthly allotment per month) / person
1200 / 30 = 40 minutes per day.
All the others have 31 days
4800 / 4 = 1200 minutes per month
1200/31 = 38.71 minutes per day = 38 minutes 42 seconds Don't make that last 42 seconds to your boy friend/girl friend.
Except February which has 29 days on leap years.
Each has 1200 minutes per month
1200/29 = 41.37 minutes = 41 minutes 22 seconds.
or
February has 28 day days most years.
each person has 1200 minutes per month.
1200 / 28 = 42.86 minutes = 42 minutes and 51 minutes
What type of graph is useful when depicting piece rates?
A. Bar graph
B. Scatterplot
C. Slope
D. Linear graph
Answers
Therefore, the type of graph that is useful when depicting piece rates is the "Scatter plot".
You can use a Scatter Plot to show the relationship between two sets of data or two variables, this is called "Correlation".
It is formed by two axes: one of them is horizontal and the other one is vertical.
A linear graph is most useful when depicting piece rates as it clearly shows the continuous relationship and trend between the number of items produced and the pay received, represented by a positive, negative, or zero slope.
When depicting piece rates, which relate the payment an individual receives to the number of pieces produced or tasks completed, a linear graph or line graph is often most useful. Linear graphs effectively illustrate relationships between two variables, such as the number of items produced (on the x-axis) and the amount of money earned (on the y-axis), highlighting trends and changes over a range of values. A bar graph may be best to illustrate comparisons when showing the relationship of separate and distinct categories. However, in the context of piece rates, where there is a continuous relationship between work done and pay received, the connected data points in a line graph provide a clear visual of the rate of payment as it changes with the number of pieces.
Understanding the appearance of slopes is essential in reading graphs. A positive slope indicates an increase or upward trend in the relationship between the two variables, a negative slope represents a decrease or downward trend, and a zero slope indicates a consistent, flat relationship with no change over time.
Three consecutive odd integers are such that the square of the third integer is 1515 greater than greater than the sum of the squares of the first two. one solution is 33, 55, and 77. find three other consecutive odd integers that also satisfy the given conditions.
Answers
x-----------> first odd integer
x+2--------> second consecutive odd integer
x+4-------> third consecutive odd integer
we know that
(x+4)²=15+x²+(x+2)²-------> x²+8x+16=15+x²+x²+4x+4
x²+8x+16=19+2x²+4x-------> x²-4x+3
x²-4x+3=0
using a graph tool----------> to calculate the quadratic equation
see the attached figure
the solution is
x=1
x=3
the answer is
the first odd integer x is 1
the second consecutive odd integer x+2 is 3
the third consecutive odd integer x+4 is 5
Answer:
Step-by-step explanation:
what are the similarities between reflections translations rotations and dilations?
Answers
If an experiment with a random outcome is repeated a large number of times, the empirical probability of an event is likely to be close to the true probability. this mathematical theorem is called what? choose the correct answer below. the random number table the law of binomial probability the law of simulation the law of large numbers
Answers
Imagine flipping a coin. There is a 50% likelihood that you would get tails. However, it doesn't happen all the time. If you flipped it just a few times, you could get all tails and have 100% tails.
However, if you did the experiment a lot of times (a large number), you almost certainly wouldn't get all tails. You would get close to 50%. That is the main point of the law.
The more trials you do, the more likely you will get close to the theoretical value.