One focus of a hyperbola is located at (−1, 7). One vertex of the hyperbola is located at (−1, 5). The center is (−1, −3). What is the equation of the hyperbola?
Answer:
C) (y+3)^2/64-(x+1)^2/36=1
Step-by-step explanation:
Just took the review in edg
To solve this problem, we just need to substitute the values into the equation and solve. the equation of hyperbola and solve. This will give
[tex]\frac{(y+ 3)^2}{64} - \frac{(x+1)^2}{36} =1[/tex]
Equation of a HyperbolaThe standard equation of a hyperbola is given as
[tex]\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1\\[/tex]
The data given are;
focus = (-1, 7)vertex = (-1, 5)center = (-1, -3)Let's substitute the values into the equation of hyperbola and solve. This will give
[tex]\frac{(y+ 3)^2}{64} - \frac{(x+1)^2}{36} =1[/tex]
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Simplify the expression. 12P5 : 11,880 95,040 7,920 1,235,520
So the correct answer is B. 95,040
Texas has 254 counties, California has 58 counties, Florida has 67 counties,how many more counties does texas have than the number of counties in California and Florida combined
Help please ...........MATH
) find the function satisfying the y′−3y=9e6t y′−3y=9e6t and y(0)=3.y(0)=3.
A circle has radius of 119.3 mm. What is the circumstance of the circle
If rectangle ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A' lie?
Answer:
A' would be return to its original position .
Step-by-step explanation:
Given : If rectangle ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°.
To find : where would point A' lie.
Solution : We have given that ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°
By the reflection rule over y axis .( x ,y) →→ ( -x ,y)
Suppose A ( x ,y) if we reflect it over y axis then
A( x ,y) →→ A'( -x ,y)
Now reflect it over x axis (-x ,y) →→( -x ,-y)
Now rotate by 180° it become ( -x, -y) →→( x ,y)
Hence , it return to its original position .
Therefore, A' would be return to its original position .
10 POINTS!!!
Premier Tire sells three categories of tires: good, better, and best. The good tires cost $106, the better tires cost $156, and the best tires cost $190. The good tires sell 3 times as fast as the best tires and the better tires sell 2.5 times as fast as the best tires. If the total amount of tire sales in January was $233,480, how many of each category of tire was sold? (Round your answer to the nearest whole number.)
If $200 is put in the bank and each year the account earns 5% simple interest, then how much interest will be earned in two years?
John ran the 100-m dash with a time of 9.96 sec. If this pace could be maintained for an entire 26-mi marathon, what would his time be?
By calculating the average speed of a 100-meter dash and then applying it to the marathon distance, it would take approximately 1.16 hours, or 1 hour, 9 minutes, and 28 seconds to complete a 26-mile marathon at that pace.
Explanation:The student is asking how long it would take for someone to run a 26-mile marathon if they maintained the same speed as a 100-meter dash completed in 9.96 seconds. To calculate this, we first need to find the runner's average speed during the 100-meter dash. The speed (v) is distance (d) divided by time (t), so:
v = d / t = 100 meters / 9.96 seconds = 10.04 meters/second
Next, we convert the marathon distance from miles to meters. There are 1,609.34 meters in a mile, so:
26 miles * 1,609.34 meters/mile = 41,842.84 meters
To find the time (t) to run the marathon, we divide the total distance by the average speed:
t = 41,842.84 meters / 10.04 meters/second = 4,167.49 seconds
Finally, we convert seconds to a more understandable unit of time, hours and minutes:
4,167.49 seconds / 60 seconds/minute = 69.46 minutes
69.46 minutes / 60 minutes/hour ≈ 1.16 hours
So, John would complete the marathon in approximately 1.16 hours, or 1 hour, 9 minutes, and 28 seconds if he could maintain his 100-meter dash pace for the entire marathon.
given than segment FE is parallel to segment DG, which of the following statements is no true
which equation is equivalent to log3(x+5)=2
What is the sum of the polynomials? (8x2-9y2-4x)+(x2-3y2-7x)
Answer:
D
Step-by-step explanation:
An artist wants to reduce the size of a drawing using a scale factor of 3:13:1 . The original drawing has an area of 720 square inches. What is area of the new drawing? Enter your answer in the box.
Answer: 80
MsEHolt is correct, the answer is 80[tex]in^2[/tex]
The hypotenuse of a right triangle measures 10 inches, and the side opposite to ∠θ, one of the non-right angles, is 5 inches long. The measure of ∠θ is
Describe two different methods to find the elapsed time from 2:30 PM to 2:58 P. M.
Explain how you can use a model to find 4X 3/8. Include a drawing and a solution
a sticker price on a new vehicle is $33985 , but the dealer cost is $27700 and you want to offer 4% over the dealer cost. what would be the offered amount?
Rewrite 17/20 and 21/25, so that they have a common denominator then use <,>or = to order 17/20 and 21/25
To the nearest tenth, find the perimeter of ∆ABC with vertices A(-1,4), B(-2,1) and C(2,1). Show your work
ANSWER
The perimeter is 11.4 units
EXPLANATION
Perimeter is the distance around the figure.
We use the distance formula,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
to determine the length of all the sides and add them.
[tex]|AB|=\sqrt{(-2--1)^2+(1-4)^2}[/tex]
[tex]|AB|=\sqrt{(-1)^2+(-3)^2}[/tex]
[tex]|AB|=\sqrt{1+9}[/tex]
[tex]|AB|=\sqrt{10} \approx 3.162[/tex]
[tex]|AC|=\sqrt{(2--1)^2+(1-4)^2}[/tex]
[tex]|AC|=\sqrt{(2+1)^2+(1-4)^2}[/tex]
[tex]|AC|=\sqrt{(3)^2+(-3)^2}[/tex]
[tex]|AC|=\sqrt{9+9}[/tex]
[tex]|AC|=\sqrt{18} \approx 4.24[/tex]
[tex]|BC|=\sqrt{(2--2)^2+(1-1)^2}[/tex]
[tex]|BC|=\sqrt{(2+2)^2+(1-1)^2}[/tex]
[tex]|BC|=\sqrt{(4)^2+(0)^2}[/tex]
[tex]|BC|=\sqrt{14}=4[/tex]
Therefore perimeter=[tex]|AB|+|BC|+|AC|[/tex]
=[tex]4.00+3.16+4.24[/tex]
=[tex]11.40[/tex] units
Evelyn is waiting in line for concert tickets. She is 2.5 blocks from the ticket booth. 16 blocks equals 1 mile. Each person takes up about 2 feet in the line. Which calculation can be used to find about how many people are ahead of Evelyn in line?
Answer:
1/2 person over feet
Step-by-step explanation:
yw!
Sal can mop a certain floor in 8 minutes by himself.If Sal and ben can mop the floor together in 6 minutes,how long does it take Ben to mop the floor alone?
A dice is rolled, then a coin is tossed. What is the probability of getting a 5 then tails?
The chance of rolling a 5 on a six-sided dice is 1/6, and the probability of getting a tails in a coin toss is 1/2. The total probability of both these independent events occurring is (1/6) * (1/2) = 1/12 or approximately 0.0833 on a decimal scale.
Explanation:The question is asking for the probability of rolling a 5 on a dice and then getting a tails on a coin toss. To get the total probability, we multiply the individual probabilities together.
First, let's consider a fair six-sided die. The chance of rolling a 5 (or any specific number between 1 and 6) is 1/6.
Next, we consider a fair coin, which has two outcomes: heads or tails. So, the probability of getting tails is 1/2.
The total probability of both these events occurring is (1/6) * (1/2) = 1/12. So, the probability of rolling a 5 and then tossing a tail is 1 in 12 or approximately 0.0833 on a decimal scale.
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Leroy's total employee compensation was $50,150 last year. His total job expenses for traveling and for professional developement for the year were $3,500. Which of the following represents his total job benefits?
a.
$53,650
b.
$50,150
c.
$46,650
d.
$47,650
Answer is :
a.
$53,650
100% correct
Answer:
Correct answer is a.$53,650
Step-by-step explanation:
Total job benefits includes both employee compensation and the expenses for traveling and for professional development for the year.
So we need to add those together to fond the total job benefits.
Total job benefits = employee compensation + expenses for traveling and for professional development
Total job benefits = $[tex]50,150+3500[/tex]
=$[tex]53,650[/tex]
Therefore correct answer is a.$53,650
Answer:
a. $53,650
Step-by-step explanation:
A spherical helium balloon has a diameter of 30 cm. How much helium is needed to fill the balloon, in cubic centimeters? Round your answer to the nearest centimeter
Compounding with different interest rates a deposit of $750 earns interest rates of 10.5 percent in the first year and 7.5 percent in the second year. what would be the second year future value? $890.91 $885.00 $829.43 $1,635.00
Order the numbers 0.64, 2/3 , 65%, and 7/10 from least to greatest.
Answer:
0.64, 65%, 2/3, 7/10
Step-by-step explanation:
The first step to solve this problem is writing all numbers on the same format:
I am going to write as percentages in the decimal format. So
0.64 = 0.64
2/3 = 0.667
65% = 65/100 = 0.65
7/10 = 0.7
So the correct answer is:
0.64, 65%, 2/3, 7/10
Is the given sequence arithmetic? If so, identify the common difference. 3.2, 3.5, 3.8, 4.1, . . .
Rewrite the standard equation in slope-intercept form: 3x-8y=24
The equation 3x - 8y = 24 can be written in slope intercept form as y = [tex]\frac{3}{8}[/tex] x - 3.
What is Slope?Slope of a line is defined as the value of the change in the values of the y coordinates with respect to the change in the values of the x coordinate.
It can also be defined as the tangent of the angle that the line makes with the X axis.
The standard equation of a line in slope intercept form is, y = mx + c, where m is the slope and c is the y intercept.
y intercept is the y coordinate when the line touches with the Y axis. The x coordinate of that point will be zero.
The given equation is,
3x - 8y = 24
Subtracting both sides of the equation with -3x,
3x - 8y - 3x = 24 - 3x
-8y = 24 - 3x
Dividing both sides by -8, we get,
y = -3 + [tex]\frac{3}{8}[/tex] x
y = [tex]\frac{3}{8}[/tex] x - 3
Hence the standard equation in slope intercept form for 3x - 8y = 24 is y = [tex]\frac{3}{8}[/tex] x - 3.
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Beethoven wrote 9 symphonies and mozart wrote 27 piano concertos. if a university radio station announcer wishes to play first a beethoven symphony and then a mozart concerto, in how many ways can this be done?
There are 243 different ways the university radio station announcer can play a Beethoven symphony followed by a Mozart concerto, calculated by multiplying the number of Beethoven symphonies (9) by the number of Mozart concertos (27).
Explanation:To determine how many different ways the university radio station announcer can play a Beethoven symphony followed by a Mozart concerto, we use the fundamental principle of counting. Since there are 9 Beethoven symphonies and 27 Mozart piano concertos, we multiply the two numbers together.
The calculation is as follows:
Beethoven symphonies: 9 optionsMozart concertos: 27 optionsTherefore, the total number of combinations for playing one Beethoven symphony followed by one Mozart concerto is:
9 symphonies × 27 concertos = 243 possible combinations
This shows there are 243 different ways the radio station announcer can choose a pairing of a Beethoven symphony and a Mozart concerto to play back-to-back.
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