a. the equation for the hyperbola is x^2 / 4 - y^2 / 12 = 1. b. the equation for the hyperbola is [(x - 4)^2 / 9] - [(y - 3)^2 / 7] = 1.
A) To find the equation for the hyperbola with vertices (±2, 0) and foci (±4, 0), we can use the standard form equation for a hyperbola:
[(x - h)^2 / a^2] - [(y - k)^2 / b^2] = 1,
where (h, k) represents the center of the hyperbola, a is the distance from the center to the vertices, and c is the distance from the center to the foci.
In this case, the center is at (0, 0) since the vertices are symmetric with respect to the y-axis. The distance from the center to the vertices is a = 2, and the distance from the center to the foci is c = 4.
Using the formula c^2 = a^2 + b^2, we can solve for b^2:
b^2 = c^2 - a^2 = 4^2 - 2^2 = 16 - 4 = 12.
Now we have all the necessary values to write the equation:
[(x - 0)^2 / 2^2] - [(y - 0)^2 / √12^2] = 1.
Simplifying further, we get:
x^2 / 4 - y^2 / 12 = 1.
Therefore, the equation for the hyperbola is:
x^2 / 4 - y^2 / 12 = 1.
B) To find the equation for the hyperbola with foci (4, 0) and (4, 6) and asymptotes y = 1 + (1/2)x and y = 5 - (1/2)x, we can use the standard form equation for a hyperbola:
[(x - h)^2 / a^2] - [(y - k)^2 / b^2] = 1,
where (h, k) represents the center of the hyperbola, a is the distance from the center to the vertices, and b is the distance from the center to the foci.
From the given information, we can determine that the center of the hyperbola is (4, 3), which is the midpoint between the two foci.
The distance between the center and each focus is c, and in this case, it is c = 4 since both foci have the same x-coordinate.
The distance from the center to the vertices is a, which can be calculated using the distance formula:
a = (1/2) * sqrt((4-4)^2 + (6-0)^2) = (1/2) * sqrt(0 + 36) = 3.
Now we have all the necessary values to write the equation:
[(x - 4)^2 / 3^2] - [(y - 3)^2 / b^2] = 1.
To find b^2, we can use the relationship between a, b, and c:
c^2 = a^2 + b^2.
Since c = 4 and a = 3, we can solve for b^2:
4^2 = 3^2 + b^2,
16 = 9 + b^2,
b^2 = 16 - 9 = 7.
Plugging in the values, the equation for the hyperbola is:
[(x - 4)^2 / 9] - [(y - 3)^2 / 7] = 1.
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Bernard works for a business that sells and repairs tires. He can repair tires in an hour work day. What is Bernard's unit rate for the number of tires repaired in one hour?
Answer:
3 tires per hour
Step-by-step explanation:
Bernard works for a business that sells and repairs tires. He can repair 24 tires in an 8 hour work day. What is Bernard's unit rate for the number of tires repaired in one hour?
Number of tires repaired per day = 24 tires
Number of time used to repair tire per day = 8 hours
What is Bernard's unit rate for the number of tires repaired in one hour?
Number of tires repaired in one hour = Number of tires repaired per day / Number of time used to repair tire per day
= 24 tires / 8 hours
= 3 tires per hour
The unit rate for the number of tires repaired in one hour is 3 tires per hour
Can someone please help me with this question
Answer
180 - x
Step-by-step explanation:
opposite angles of a quadrilateral inscribed in a circle are supplementary
Answer:
180-x !!!
Step-by-step explanation:
i had some time to think about it
If Ann travels 50 meters North, 200 meters East and 150 meters South, what is her total distance travelled ? A. 150 meters B.400 meters C. 250 meters D. 0 meter
Answer:
400 meters
Step-by-step explanation:
50 + 200 + 150 = 400
Mark leaves his house at 12:53
He gets to the shop at 14:23
His average speed was 20km/h
How far away is the shop from Mark's house?
Answer: His house is 43.33334 kilometers
Luke now takes 20 cards numbered 1 to 20. Show how the cards can
be paired to give an LCM of 60.
Answer:
Step-by-step explanation:
The pair members cannot be multiplied. Look at the last numbers that are prime starting with eleven
What are you going to pair these primes with
11 13 17 19
So they must be added (or maybe subtracted).
1 19
2 18
3 17
4 16
5 15
6 14
7 13
8 12
9 11
and 20 which no matter how you do this, there will be 1 card left over.
Each of them adds to 20 so the LCM is 20
Alyssa walked 1.34 fewer miles than Emily. Alyssa walked 7.45 miles. How many miles did Emily walk?
If the family plans to move to their retirement home in 10 years, which pool would be more cost effective to install? How do
you know?
Answer:
Step-by-step explanation:
but is their any answer choices
PLSSSSSSSSSSSSSS HELPPP FOR REAL SOMEBODDYY REWARD BRAINLIEST!!!!!!!!!!!!!!!!!
Answer:
1. x = 3
2. (1, 0)
3. x = 3, -2
4. 144
5. -3 + 4√3
Step-by-step explanation:
Plz help I’ll give brainliest
1. y= -5
2. m=0
3. I dont know
1. 3x+4y=-20
x=0
3×0+4y=-20
0+4y=-20
y=-5
2. m=y/x
m=0/1
m= 0
3. Sorry
What is the volume of the following rectangular prism? height : 1 3/4
base : 1/2
Answer:
I need length, width, and height to find the volume, the equation is LxWxH
So it would be L x W x 1 3/4
Step-by-step explanation:
If you comment what the length and width is ill do it!
Is j+j+j+j and j with the power of four equivalent?
Answer:
No, they are not equivalent.
Step-by-step explanation:
j + j + j + j = 4j
j^4
Let's say j = 2
4j = 8
j^4 = 16
Answer:
NO
Step-by-step explanation:
j+j+j+j
remember multiplication is repeated addition!
j+j+j+j = 4j
THIS IS DIFFERENT! powers are repeated MULTIPLICATION.
j^4 = j to the power of 4 = j * j * j * j, NOT j+j+j+j !!!!!
у
80
The graph of quadratic function
is shown on the grid.
What is a solution to r(x) = 0?
60
40
A -50
20
B 4
х
-4
4
8
12
- 16 -12 -8
16
C 14
-20
D-60
vo
-60
-80
Answer:
C 14
Step-by-step explanation:
$17.99 with an 11.25% tax
Answer:
it's 2.0
hope that helps
helpppp please
On a map, 2 inches represent an actual distance of 28 miles. If the actual distance
between two cities is 322 miles, how many inches apart will the two cities be on the
map?
644 inches
23 inches
2 inches
28 inches
Please help asap. This is khan acadamy
Answer:
xr 30 degrees
Step-by-step explanation:
the angles always add up to 180 sooo
53+97=150
180-150=30
there's how u solve these kinds of problems
hope this helps
help please 100 point
Answer:
Solution given:
we have
<A+<B=exterior <C[sum of two opposite interior angle of a triangle is equal to the exterior angle in a triangle]
So
3x-13+ 2x+4=116°
5x-9=116°
5x=116°+9°
x=125/5
x=25
Now
<A=3×25-13=62°
<B=2×25+4=54°
Answer:
[tex]3x - 13 + 2x + 4 = 166 \\ 5x - 9 = 116 \\ 5x = 166 + 9 \\ 5x = 125 \\ x = \frac{125}{5} \\ x = 25 \\ \\ a = 3 \times 25 - 13 = 62 \\ b = 2 \times 25 + 4 = 54[/tex]
What is the point-slope form of a line with slope
(-3, 6)?
nun
that contains the point
A. y- 3 = (x+3)
B. y+6 = {(x+3)
O C. y- 6 = - 3(x+ 3)
O D. y-6 = {(x+3)
4. A Tesla dealership is having a sale on their cars. This week you can save 15% off
the total price. If the retail price of the Tesla is $30,190, what is the discount?
Answer:
25,661.5
Step-by-step explanation:
30160x15%=4528.50
30160-4528.50=25,661.50
Please help me will mark brainliet
Answer:
The degree of the term is 5
Don't forget to mark me as brainliest
Triangle ABC was reflected across an axis.
A. State what axis it was reflected across
B. Give the ordered pairs of the reflected triangle
Determine the equation of the circle graphed below
The equation of the circle graphed below is (x - 2)² + (y + 3)² = 25.
To determine the equation of a circle, we need the center and the radius of the circle. In the graph below, the center appears to be at (2, -3) and the radius appears to be 5.
Therefore, we can use the standard equation of a circle,
which is (x - h)² + (y - k)² = r²,
where (h, k) is the center of the circle and r is the radius.
Substituting the values of the center and radius, we obtain the equation of the circle as follows:(x - 2)² + (y + 3)² = 25
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A cylinder has a radius of 4 units and a height of 7 units. What is the volume in cubic units
Answer:
The answer is 352 cubic units
Mr. Smith's class took a test! The scores of one group are listed below.
70, 60, 80, 85, 90
What is the mean absolute deviation of the data set?
Answer:
B
Step-by-step explanation:
Answer:
77
Step-by-step explanation:
add them all together and then divide by 5
Graph a line that has a slope of 5/2 and includes the point (-2, -7)
Ethel had 4 feet of ribbion she used 1 1/2 feet for a craft project how many feet of ribbon does she have left
In the figure below, 7 ||
m. Find x.
Answer:
x+65°=120°[by alternate interior angle]
x=120°-65°
x=55°
Please Please help me
Answer:
1. 30
Step-by-step explanation:
First, place the numbers from least to greatest.
11,13,23,37,45,58
Then, find the middle number (or two middle numbers).
In this case, the middle numbers are 23 and 37.
Third, we find the mean of these numbers.
23+37=60
60/2=30
So your answer is 30.
Repeat this method for the other problems.
Both antibiotics were prescribed in high dosage slow release capsules. The function C(x)=5log(x+1)+10 models the concentration of levofloxacin in mol/L over a time x, in hours. The function D(x) = 10log(x+1)+5 models the concentration of metronidazole in mol/L over a time x in hours. a) Which of the two drugs has a higher initial concentration in the blood stream? Justify your answer with an explanation. (2K, A) b) Determine when C(x) = D(x) algebraically and state what this represents in this situation. (6K, A, T) c) If Mathews is instructed to take both antibiotics at once the concentration levels could be modeled by the function(C+D)(x). How would the graph of (C+D)(x) differ from the individual graphs of C(x) and D(x)? Explain. (2T)
a) The initial concentration of levofloxacin (represented by C(x)) in the bloodstream is higher than the initial concentration of metronidazole (represented by D(x))
b) There is no algebraic solution for when C(x) = D(x) in this situation.
c) The graph of (C+D)(x) would show a steeper increase and higher values compared to the individual graphs of C(x) and D(x), indicating a higher concentration of the drugs when taken together.
a) The initial concentration of a drug in the bloodstream can be determined by evaluating the functions C(x) and D(x) at x = 0. Plugging in x = 0 into both functions, we find that C(0) = 5log(0 + 1) + 10 = 5log(1) + 10 = 5(0) + 10 = 10, and D(0) = 10log(0 + 1) + 5 = 10log(1) + 5 = 10(0) + 5 = 5. Therefore, the initial concentration of levofloxacin (represented by C(x)) in the bloodstream is higher than the initial concentration of metronidazole (represented by D(x)).
b) To find when C(x) = D(x), we set the two functions equal to each other and solve for x: 5log(x + 1) + 10 = 10log(x + 1) + 5. Subtracting 10log(x + 1) from both sides, we get 5log(x + 1) - 10log(x + 1) = 5. Simplifying, we have -5log(x + 1) = 5. Dividing by -5, we find log(x + 1) = -1. This equation can be rewritten in exponential form as 10^(-1) = x + 1, which simplifies to 0.1 = x + 1. Subtracting 1 from both sides, we get x = -0.9. However, since time cannot be negative, there is no solution to the equation. Therefore, there is no algebraic solution for when C(x) = D(x) in this situation.
c) The graph of (C+D)(x) would represent the combined concentration levels of both antibiotics when taken together. It would differ from the individual graphs of C(x) and D(x) by showing a higher overall concentration. Since (C+D)(x) is the sum of the two individual functions, the resulting graph would be the sum of their concentrations at each point in time. This means that at any given time, the concentration of the combined antibiotics would be the sum of the concentrations of levofloxacin and metronidazole at that time. The graph of (C+D)(x) would show a steeper increase and higher values compared to the individual graphs of C(x) and D(x), indicating a higher concentration of the drugs when taken together.
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Use the following information to answer the next five exercises. A doctor wants to know if a blood pressure medication is effective. Six subjects have their blood pressures recorded. After twelve weeks on the medication, the same six subjects have their blood pressure recorded again. For this test, only systolic pressure is of concern. Test at the 1% significance level. Table 1: Blood pressure of six patients A-F, before and after using the medication. Patient A B C D E F AB Before 161 162 165 162 166 171 After 158 159 166 160 167 169
The P-value is less than the significance level of 0.01, we reject the null hypothesis and conclude that the medication is effective in lowering blood pressure.
How to explain the hypothesisThe null hypothesis is that the medication has no effect on blood pressure. The alternative hypothesis is that the medication lowers blood pressure.
The test statistic is the paired t-test. This is because we have two samples of data that are paired together, namely the blood pressure measurements before and after taking the medication.
In this case, the P-value is 0.034. Since the P-value is less than the significance level of 0.01, we reject the null hypothesis and conclude that the medication is effective in lowering blood pressure. The medication is effective in lowering blood pressure.
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The first day, Brian saw 31 birds and twice as many squirrels as birds. The second day, Brian saw 20 birds and 42 squirrels. Which of the following is a good estimation of how many birds and squirrels Brian saw in the two days?
Answer: A good estimation would be about 150.
Step-by-step explanation:
To estimate we can round instead of using exact numbers.
First day he saw about 30 birds and twice as many squirrels, meaning about 60 squirrels. This is about 90 total when added together.
Second day he saw 20 birds and about 40 squirrels so about 60 when added together.
Add day one and day two totals for...
90+60=150