What are the foci of the ellipse given by the equation 100x2 + 64y2 = 6,400?
Answers
[tex]\frac{ x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1[/tex]
Being:
a: Semi-major axis
b: Semi-minor axis
Our equation is:
[tex]100 x^{2} + 64y^{2} = 6400[/tex]
Multiplying this equation by:
[tex] \frac{1}{(100)(64)} [/tex]
Then:
[tex]\frac{ x^{2}}{64} + \frac{y^{2}}{100} = 1[/tex]
We can see that:
[tex]a = \sqrt{100} = 10[/tex]
[tex]b = \sqrt{64} = 8[/tex]
Then the semi-major axis is on the y-axis, and the focus are located there, so:
[tex]F_{1} = (0,c)[/tex]
[tex]F_{2} = (0,-c)[/tex]
We also know that the relation between a, b and c is:
[tex]c^{2} = a^{2} - b^{2}[/tex]
[tex]c^{2} = 100 - 64 = 36[/tex]
[tex]c = \sqrt{36} = 6[/tex]
Then, the focus are:
[tex]F_{1}(0,6)[/tex]
[tex]F_{1}(0,-6)[/tex]
Quadratic relations and comic sections unit test part 1
11. a. (0, +/- 6)
Related Questions
What is the sum of the measures of the exterior angles of any convex polygon? A. 720 B. 180 C. 90 D. 360
Answers
The world's biggest rubber band ball has a surface area of 27648. Using 3 as pi for both surface area and volume, estimate the volume of the ball.
Question 5 options:
358966
788428
442368
257854
Answers
surface area of sphere=4*pi*r²
r=√[surface area/(4*pi)]
for surface area=27648
r=√[27648/(4*3)]-------> r=√2304-----> r=48 units
volume of a sphere=(4/3)*pi*r³-----> (4/3)*3*48³---> 442638 units³
the answer is
442368
Radical Expressions and Data Analysis Unit Portfolio
ALGEBRA 1 B
Directions: Complete each of the tasks outlined below. Task 1
For 7 days keep track of the number of pieces of mail you receive at your home.
a. Put your data into a frequency table having intervals of 0–4, 5–9, 10–14, and 15–19.
b. Use the frequency table to create a histogram of the data.
c. Doyounoticeanypatternsinthehistogram?
Task 2
a. Pick 9 different dog breeds and find their average weights. List each breed and weight. Find the mean, median, and mode of the data. Which measure of central tendency best describes the data? Explain your answer.
b. How much would a 10th dog have to weight for the average weight in part (a) to be 250 pounds? Explain how you determined your answer.
Task 3
Pick a city in Maryland and determine the average high temperatures for each month. Record this in a table.
a. Create a box-and-whisker plot for the data.
b. What is the median temperature?
c. 75%ofthetemperaturesarebelowwhatvalue?Howdoyouknow? d. 75% of the temperatures are above what value? How do you know? e. What conclusions can you draw about the temperature in Maryland?
Answers
a) Data and frequency table are attached in picture #1.
b) The histogram is attached in picture #2
c) As the intervals increase the number of pieces of mail received, the frequency decreases, therefore we can say that are received few pieces of mail are received more often.
TASK 2
a) The list of breeds and weights are reported in picture #3.
In order to find the mean, sum up all the weights and divide by 9:
m = (8 + 10 + 15 + 29 + 32 + 75 + 77 + 80 + 85) / 9 = 45.67 lbs
In order to find the median, you need to select the central value of your distribution: since you have 9 values, the central one will be in the fifth position:
M = 32 lbs
In order to find the mode, you need to select the value which shows more frequently: in this case, every value shows only once, therefore the mode cannot be determined.
The data are best described by the mean because they are almost symmetrically distributed between the least and the biggest values, while the median is more towards the small-weight side of the distribution.
b) In order to have an average of 250 lbs, the tenth dog should weight 2089 lbs.
Indeed, if the average is 250 lbs for 10 dogs, it means that the total sum of their weights is 250 × 10 = 2500 lbs. We know that the sum of the first 9 dogs is 411 lbs, therefore, the tenth dog should weight 2500 - 411 = 2089 lbs.
TASK 3
The city picked is Baltimore, the year 2017.
The table is attached in picture #4.
a) The box-and-whisker plot is attached in picture #5.
b) The median is the central value of the distribution, which is:
42.4, 45.3, 46.8 | 54.7, 57.6, 66.0 | 69.1, 76.5, 80.6 | 85.8, 87.8, 90.0
where we marked with a tally the quartiles.
Since we have 12 values, the median will be the average between the two central values:
M = (66.0 + 69.1) / 2 = 67.1 °F
c) 75% of the temperatures are below 83.2 °F.
Indeed, this value represents the third quartile. The position of the third quartile can be found by the formula:
3/4 · (n + 1) = 3/4 · (12 + 1) = 3/4 · 13 = 9.75
Therefore, since we did not get in integer position, the third quartile will be the average between the numbers in position 9 and 10:
q₀.₇₅ = (80.6 + 85.8) / 2 = 83.2 °F
d) 75% of the temperatures are above 50.8 °F.
Indeed, this value represents the first quartile. Similarly to point c), the position can be found by the formula:
1/4 · (n + 1) = 1/4 · 13 = 3.25
And therefore:
q₀.₂₅ = (46.8 + 54.7) / 2 = 50.8 °F.
e) Baltimore in 2017 had a median high temperature of 67.1 °F.
25% of the year the high temperatures were warmer than 83.2 °F, with no outlier above 90.0 °F which was the hottest temperature.
25% of the high temperatures were colder than 50.8 °F, with no outlier below 42.4 °F, which was the coldest high temperature.
Si un ángulo de un rombo mide 39 grados , ¿ cuánto miden los demás ?
Answers
If an angle of a rhombus measures 39 degrees, how much do others measure?
we know that
A rhombus is an equilateral (all sides are the same length) quadrilateral.
The consecutive angles of a rhombus are supplementary (add up to 180 degrees).
Opposite sides are parallel, and opposite angles are equal
see the picture to better understand the problem
in this problem
let
A=39°
A+B=180--------> B=180°-39°-----> B=141°
the answer is
the angles of the rhombus are
39° 141° 39° 141°
the answer in spanish
sabemos que
Un rombo es un polígono con cuatro lados (cuadrilátero) siendo los cuatro iguales. Tiene cuatro ángulos interiores iguales dos a dos.
Los ángulos consecutivos de un rombo son suplementarios (suman 180 grados).
en este problema
hagamos
A=39°
A+B=180--------> B=180°-39°-----> B=141°
la respuesta es
los angulos del rombo son
39° 141° 39° 141°
Please help with easy math problem.
What is the value of d to the nearest tenth?
A. 11.2
B. 13.8
C. 16.7
D. 17.5
Answers
Answer:
Option B is correct
d = 13.8
Step-by-step explanation:
Definition:
If two secant segments are drawn to a circle from the same external point(P),
the product of the length of one secant segment and its external part is equal to product of the length of the other secant segment and its external part.
As per the statement:
Labelled the diagram:
then;
PA = 14 units , AB = 20 units, PC = 16 units and CD = d units
Find PB and PD:
PB = 14+20 = 34 units
PD = 16+d units
then by above definition we have;
[tex]PA \cdot PB = PC \cdot PD[/tex]
⇒[tex]14 \cdot 34 = 16 \cdot (16+d)[/tex]
⇒[tex]476=16 \cdot (16+d)[/tex]
Divide both sides by 16 we have;
[tex]29.75 = 16+d[/tex]
Subtract 16 from both sides we have;
13.75 = d
or
d = 13.75 units
Therefore, the value of d to the nearest tenth is, 13.8
given that A=43 degrees , B=82 degrees and c=28, solve triangle ABC. Round to the nearest hundredth. A) C= 93 degrees , b= 33.8 , a= 23.3 B) C= 55 degrees , b= 33.8 , a= 23.3 C) C= 55 degrees , b= 23.3 , a= 33.8 D) C= 93 degrees , b= 23.3 , a= 33.8
Answers
a^2 = b^2 + c^2 - 2bccosA
substituting;
(43^2)=(82^2)+(28^2)-2(82)(28)cosA
A=23.3 degrees
and the other angles can be determined using sine law
sin A/ a = sin B/ b = sin C/ c
Thus,
B= 33.8 degrees
and
C= 55 degrees
A rectangular piece of sheet metal has a length that is 6 in. less than twice the width. a square piece 3 in. on a side is cut from each corner. the sides are then turned up to form an uncovered box of volume 1536 in. cubed find the length and width of the original piece of metal.
Answers
width=x in
length=2x-6
when 3 inches square is cut from the corner, the new dimensions will be:
width=(x-6) in
length=(2x-6-6)=(2x-12) in
height=3 in
thus the volume will be:
(x-6)(2x-12)3=1536
solving the above we get:
x=-10 or x=22
thus the original:
width=22 in
length=22*2-6=38 in
The price of an iteam has been reduced by 75%. The original price was $45. What is the price of the item now?
Answers
The new price of the item after 75% reduction is $11.25.
To find the price of the item after a 75% reduction:
Calculate the amount of the reduction: 75% of $45 is $33.75.
Subtract the reduction from the original price: $45 - $33.75 = $11.25.
Which mesurments are greater than 130 fluid ounces 5 quarts, 16 cups, , 9 pints, 2 gallons, or 1 gallon i am not good with math ty?
Answers
Hope this helped!
-Jello-
Answer:
5 quarts , 9 pints, 2 gallons
Step-by-step explanation:
Can you please solve this equation?
Answers
x = -52 4/17
the full answer in attachments
Look at the question on the first image then answer on the second image
Answers
32^2 +x^2 = 60^2
1024 + x^2 = 3600
x^2 = 3600 - 1024
x^2 = 2576
x = sqrt(2576)
x = 50.75
length = 51 inches
Which statement provides a counterexample to the following faulty definition? A square is a figure with four congruent sides. Question 8 options: A six-sided figure can have four sides congruent. A rectangle has four sides. Some triangles have all sides congruent. A square has four congruent angles.
Answers
Answer:
1. The six-sided figure can have 4 sides congruent but is not a square.
Step-by-step explanation:
We are given the statement,
'A square is a figure with four congruent sides'.
It is required to find the statement which is the counter-example for the above statement.
For the counter-example, the statement should hold:
1. The figure has 4 congruent sides
2. The figure is not a square.
According to the options, we see that,
The six-sided figure can have 4 sides congruent but is not a square.
Thus, option 1 is true.
A counterexample to the faulty definition will be that A six-sided figure can have four sides congruent.
It should be noted that a rectangle has four sides while there are some triangles that have all their sides congruent and a square has four congruent angles as well.The statement that a six-sided figure can have four sides congruent is the correct option.In conclusion, the correct option is A.
Read related link on:
https://brainly.com/question/3452116
A and B have coordinates –2 and 10 on a number line. If it is marked off into 10 congruent segments, which one of the following coordinates is NOT one of the marked points? a. –0.8 c. 1.6 b. –0.6 d. 2.8
Answers
Answer:
b. - 0.6
Step-by-step explanation:
Since, the total coordinates from -2 to 10 = 10 - (-2) = 10 + 2 = 12,
Also, if it is divided into 10 congruent segments,
Then, the length of each segment = [tex]\frac{12}{10}[/tex] = 1.2,
That is, the difference between the marked point is 1.2,
So, the marked points from -2 to 10 are,
-2, -0.8, 0.4, 1.6, 2.8, 4.0, 5.2, 6.4, 7.6, 8.8, 10,
Hence, except -0.6 all points are the marked points,
Option b is correct.
Find an explicit rule for the nth term of the sequence.
2, -8, 32, -128, ...
Answers
a2=-8
a3=32
a4=-128
a2/a1=(-8)/2→a2/a1=-4
a3/a2=32/(-8)→a3/a2=-4
a4/a3=(-128)/32→a4/a3=-4
a2/a1=a3/a2=a4/a3=r=-4
an=a1*r^(n-1)
an=2*(-4)^(n-1)
The explicit rule for the nth term of the given sequence is an=2*(-4)^(n-1)
A triangle has an angel of 25 degrees. The other two angles are in a ratio of 15:16. What are the measures of those two angles?
Answers
A) 25 + x + y = 180 which equals
A) x + y = 155
B) 15x = 16y
B) x = 16y / 15
Then substituting this into A)
A) (16y / 15) + y = 155
Multiplying both sides by 15
A) 16y + 15y = 2,325
A) 31y = 2,325
y = 75
Putting this into equation A)
A) 25 + x + y = 180
A) 25 + x + 75 = 180
A) 100 + x = 180
A) x = 80
What is the factorization of the polynomial below?
–x2 – 15x – 54
A. (x – 9)(x + 6)
B. (x + 9)(x + 6)
C. –1(x + 9)(x + 6)
D. (x + 9)(x – 6)
Answers
Answer:
Option C, -(x + 9)(x + 6) or,
-1(x + 9)(x + 6)
Explanation:
We can begin the factorization process by factoring out the negative -1 from each term in the polynomial. This changes the expression to:
-1(x² + 15x + 54)
This factored-out negative will follow all the way to the answer so any answer not containing a -1 factored out can eliminated. Options A, B, and D do not have this negative. Therefore, they are ruled out. But let's continue to confirm Option C.
With the polynomial within the parentheses in quadratic expression ax² + bx + c form, we start by finding which factor pair for the product and coefficient a and constant c has a sum equating to coefficient b. This may sound complicated but this is not the case in practice.
Coefficient a = 1
Constant c = 54
Coefficient b = 15
The product of a and b = 1(54) = 54
Now, we list factors of 54. I like to list them as factor pairs:
1, 54; 2, 27; 3, 18; 6, 9
Next, find which factor pair has a sum of 15. That would be 6 and 9. We now substitute these values as the coefficients b, separate the terms into pairs as binomials, and factor out their greatest common factors (GCF).
-(x² + 6x + 9x + 54)
-[(x² + 6x) + (9x + 54)]
The GCF between x² and 6x is x. The GCF between 9x and 54 is 9. So:
-[x(x + 6) + 9(x + 6)]
If the binomial within each set of parentheses matches, you have found the factors for your polynomial. They are the polynomial within the binomial within the parentheses and the GCFs that were factored out of each:
-x² - 15x - 54 = -(x² + 15x + 54) = -(x + 9)(x + 6)
Final answer:
The factorization of the polynomials [tex]-x^2 - 15x - 54[/tex] is obtained by finding two numbers that multiply to -54 and add up to -15, which are -9 and -6. The factored form is -1(x + 9)(x + 6).
Explanation:
The factorization of the polynomial [tex]-x^2 - 15x - 54[/tex] can be approached by looking for two numbers that multiply to give the product of the coefficient of x2 (which is -1) and the constant term (which is -54), and at the same time, add up to give the coefficient of x (which is -15). After finding such numbers, we can then express the polynomial in its factored form.
In this case, the numbers that satisfy these conditions are -9 and -6. Multiplying these gives 54 (which is the negative of the constant -54 when considering the leading negative sign of the polynomial), and adding them gives -15.
Therefore, the polynomial can be factored as -1(x + 9)(x + 6), which corresponds to answer option C.
Jessica had m beads. She used 18 of them to make a necklace for her mom. Then she used the rest to make k bracelets for her friends, with the same number of beads in each bracelet. How many beads did she use to make each bracelet?
Answers
x/k = t
t is the number in each bracelet
please give brainliest if this helped!! :D
The height reached by amal's rocket was 1/4 of the height reached by min's rocket. Amal's rocket REAched a height of 15 meters. Which equation could be used to find the height reached by min's rocket
Answers
1- You have that
- The height reached by amal's rocket was 1/4 of the height reached by min's rocket.
- Amal's rocket REAched a height of 15 meters.
2. Therefore, let's call "x" to the height reached by min's rocket. Then, you have:
(1/4)x=15
x/4=15
Which equation could be used to find the height reached by min's rocket?
The answer is: x/4=15
The height reached by Min's rocket could be found by using the equation (1/4)*h = 15, where 'h' denotes the height of Min's rocket. Amal's rocket height is 1/4 of the height of Min's rocket.
Explanation:In the question, it is stated that the height of Amal's rocket is 1/4 of the height reached by Min's rocket. Since the height attained by Amal's rocket is given as 15 meters, we can establish an equation to find the height reached by Min's rocket. Let's denote the height of Min's rocket as h. We know that 1/4 of Min's rocket height equals Amal's rocket height. So it can be represented as:
(1/4)*h = 15
By solving this equation, we can find the height attained by Min's rocket.
Learn more about Height of Rockets here:https://brainly.com/question/29070000
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Use the x-intercept method to find all real solutions of the equation. x^3-10x^2+29x+-20=0
Answers
Answer:
C. is the answer 1,4 or 5
Step-by-step explanation:
Taylor is a 35-year-old woman who has not yet planned for retirement. She would like to retire at age 70. Answer each question using complete sentences.
Part I: In what type of investment should Taylor deposit her money? Why?
Part II: At what age, or point in your life, would you like to start saving for retirement?
Part III: In what type of investments would you like to deposit your money into when you start saving for retirement? Why?
Answers
Part II: I would state saving for my retirement immediately i start earning. Preferably at my 20s.
Part III: If I am saving for my retirement i would invest in a fixed deposit account. This way my money would be increasing with interest and still getting the dividends at the end of every year.
How many ways are there to choose a committee of 7 people from a group of 10 people?
720
120
840
5040
Answers
Have a GREAT day!
Verify the identity. Help please!!!
Answers
[tex]L.H.S \\ \\ = 1+ sec^{2} *sin^{2}x \\ \\ =1+ \frac{1}{cos^{2}x } sin^{2}x \\ \\ =1+tan^{2}x \\ \\ =sec^{2}x \\ \\ = R.H.S [/tex]
Thus, the Left hand side has been proved equal to Right Hand Side.
A new medical test provides a false positive result for hepatitis 2% of the time that is a perfectly healthy subject being tested for hepatitis will test as being infected 2% of the time. And research, the test is given to 30 healthy (not having hepatitis) subjects. Let X be the number of subjects who test positive for the disease
A. What is the probability that all 30 subjects will appropriately test as not being infected?
B. What are the mean and standard deviation of X?
C. To what extent do you think this is a viable test to use in the field of medicine?
Answers
The probability of success, i.e. the probability that a healthy subject tests positive is given as 2% = 0.02
Part A:
The probability that all 30 subjects will appropriately test as not being infected, that is the probability that none of the healthy subjects will test positive is given by:
[tex]P(X)={ ^nC_xp^x(1-p)^{n-x}} \\ \\ P(0)={ ^{30}C_0(0.02)^0(1-0.02)^{30-0}} \\ \\ =1(1)(0.98)^{30}=0.5455 [/tex]
Part B:
The mean of a binomial distribution is given by
[tex]\mu=np \\ \\ =30(0.02) \\ \\ =0.6[/tex]
The standard deviation is given by:
[tex]\sigma=\sqrt{np(1-p)} \\ \\ =\sqrt{30(0.02)(1-0.02)} \\ \\ =\sqrt{30(0.02)(0.98)}=\sqrt{0.588} \\ \\ =0.7668[/tex]
Part C:
This test will not be a trusted test in the field of medicine as it has a standard deviation higher than the mean. The testing method will not be consistent in determining the infection of hepatitis.
Find the measure of an angle between 0 and 360 that is coterminal with 370°
Answers
A 370° angle can be thought of as one 360° and one 10° angle. The 360° would take you one full turn around a circle. The 10° angle would take you 10° into another turn. So simply going 10° would get you to the same place on the circle as going 370°. Make sense?
Final answer:
To find an angle coterminal with 370° that is between 0 and 360 degrees, subtract 360° from 370°, yielding a coterminal angle of 10°.
Explanation:
To find the measure of an angle between 0 and 360 degrees that is coterminal with 370°, we simply subtract 360° from the given angle until the result falls within the desired range. Here is the calculation:
Start with the given angle: 370°.
Subtract 360° from 370° to find the coterminal angle: 370° - 360° = 10°.
The resulting angle of 10° is between 0° and 360° and is therefore the coterminal angle we are seaching for.
evaluate 3P4, I didn’t understand this question but if you know it would great if you could explain!!!
15,120
36
3,024
504
Answers
Answer:
3,024
Step-by-step explanation:
To babysit one child, Fernando charges $10 to drive to the appointment plus $4 per hour. He saves 30% of the total amount he earns. Brenna charges $6 per hour and saves 25% of the total amount she earns. Which equation can be used to determine the number of hours, h, after which Fernando and Brenna will have saved the same amount of money?
Answers
Explanation:
1) Fernando's earnings:
10 + 4h ← 10 is a fix charge, h is the number of hours and 4 is the rate per hour
2) Fernando's savings
0.30 (10 + 4h) ← 30% = 30 / 100 = 0.3
3 + 1.2h ← distributive property
3) Brenna's earnings
6h ← h is the number of hours, 6 is the rate per hour
4) Brenna's savings
0.25(6h) ← 25% = 25/100 = 0.25
1.5h ←0.25 × 6 = 1.5
5) Equal savings
3 + 1.2h = 1.5h
1.5th- 1.2h = 3 ← transpose terms
0.3h = 3 ← combine like terms
h = 3 / 0.3 = 10 ← divide by 0.3
Answer: h = 10
Answer:
(C) 0.3(10 + 4h) = 0.25(6h)
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a total of 45mg of medication is dissolved in a solution containing 300ml. if 20ml of the solution are administered to a patient, how many milligrams of medication does the patient receive
Answers
(Multiply 45mg by 20ml and then divide by 300ml I believe. )
((:
Find the arc length of a central angle of 7pi/3 in a circle whose radius is 3 inches
Answers
To calculate the arc length, multiply the angle in radians (7pi/3) by the radius (3 inches). After simplifying, the arc length for this circle is 21 inches.
To find the arc length for a central angle of 7pi/3 radians in a circle with a radius of 3 inches, we use the formula for arc length, which is the product of the central angle in radians and the radius of the circle.
The formula for the arc length (As) is given by:
As = r times theta
Where:
r is the radius of the circle.
theta is the central angle in radians.
Substituting the given values, we get:
As = 3 inches times 7pi/3 radians
The 7pi/3 terms cancel out the pi/3 from the angle and /3 from the radius, giving us:
As = 3 times 7 inches
The arc length is therefore 21 inches.
Find the number of sides when:
a. The measure of each interior angle of a regular polygon is 156 degrees.
b. The measure of each exterior angle of a polygon is 36 degrees.
Answers
(n-2)×180=156n
24n =360
n =15
360/n =36
n = 10
a)15 b)10
Final answer:
To find the number of sides of a polygon, one can use the relations between interior or exterior angles and the number of sides. For an interior angle of 156 degrees, the polygon has 15 sides. For an exterior angle of 36 degrees, the polygon has 10 sides.
Explanation:
The question is about finding the number of sides of a polygon based on the interior and exterior angles. For part (a), where the measure of each interior angle of a regular polygon is 156 degrees, and for part (b), where the measure of each exterior angle is 36 degrees, we can use specific formulas to find the number of sides.
Part A: Interior Angle 156 Degrees
For a regular polygon, the formula connecting the number of sides (n) to an interior angle (A) is A = [(n-2) * 180] / n. Solving for n when A = 156 degrees gives us:
156 = [(n-2) * 180] / n
Solving this equation yields n = 15, meaning the polygon has 15 sides.
Part B: Exterior Angle 36 Degrees
The measure of each exterior angle of a polygon (E) is related to the number of sides (n) by the formula E = 360 / n. When E = 36 degrees:
36 = 360 / n
Solving for n gives us n = 10. Therefore, the polygon has 10 sides.
a photographer's camera sits on a tripod that is 1.8 m above the ground. The base of the tripod is 44 m from the base of a tree. The photographer's spot woodpecker in a tree at a 39 degree angle of elevation. To the nearest tenth of a meter, how high above the ground is the woodpecker? A.37.4m B.36.0m C.35.6m D.34.2m