Answer: A, (y-1)^2/49-x^2/81=1
The given equations are both hyperbola equations with the center shifted to (0,1). They represent different graphs due to differences in their denominators. Hyperbola equations result in a graph of two separate curves, each one a mirror image of the other.
Explanation:The equations (y-1)^2/49-x^2/81=1 and (y-1)^2/7-x^2/9=1 are both in the form of the hyperbola equation. This type of equation represents a graph that consists of two separate curves, each one a mirror image of the other, positioned about a central point called the center of the hyperbola. In these particular equations, the center of the hyperbola is shifted from the origin to the point (0,1).
Hyperbola equations are generally in the form (x-h)^2/a^2 - (y-k)^2/b^2 = 1 or (y-k)^2/a^2 - (x-h)^2/b^2 = 1
However, even though these equations are in the form of hyperbolas, they do not represent identical graphs. In the first equation, the y term is divided by 49 and the x term by 81, whereas in the second, these denominators are 7 and 9. These denominator values affect the shape and orientation of the hyperbolae, leading to different graphical representations for each equation.
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A circle has the equation x2+y2+16y−30x=0.
What is the equation of the circle in standard form, the coordinates of its center, and the length of its radius?
The equation of the circle is (x+15)2+(y−8)2=289; the center is at (−15,8), and the radius is 17 units.
The equation of the circle is (x−15)2+(y+8)2=289; the center is at (−15,8), and the radius is 289 units.
The equation of the circle is (x−15)2+(y+8)2=289; the center is at (15,−8), and the radius is 17 units.
The equation of the circle is (x−15)2+(y+8)2=289; the center is at (15,−8), and the radius is 289 units.
Answer:
Step-by-step explanation:
hello :
x2+y2+16y−30x=0 means : (x²-30x)+(y²+16y) =0
(x²-30x+15²)-15²+(y²+16y+8²) -8²=0
(x-15)²-225+(y+8)²-64=0
(x-15)²+(y+8)²=289=17²......standard form when the center is (15,- 8)
and radius 17
Final answer:
To transform x^2+y^2+16y-30x=0 into the standard form of a circle equation, we must complete the square to obtain (x-15)^2+(y+8)^2=289. The circle's center is at (15, -8) and has a radius of 17 units.
Explanation:
To rewrite the given equation of the circle x^2+y^2+16y−30x=0 into standard form, we must complete the square for both x and y terms. First, rearrange the equation to group x and y terms together: x^2−30x + y^2+16y = 0. To complete the square, take half of the coefficient of x, which is −15, square it to get 225, and add it to both sides. Similarly, take half of the coefficient of y, which is 8, square it to get 64, and add it to both sides as well.
After adding these values, the equation becomes x^2−30x+225 + y^2+16y+64 = 225+64. Now it can be written as (x−15)^2 + (y+8)^2 = 289.
The standard form of a circle's equation is (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center of the circle and r is the radius. Thus, from our equation (x−15)^2 + (y+8)^2 = 289, the center is at (15, −8) and the radius is √289 which is 17 units.
Therefore, the correct statement is: 'The equation of the circle is (x−15)^2+ (y+8)^2=289; the center is at (15, −8), and the radius is 17 units.'
find the measurement of the angle
Answer:
∠ 1 = 120°
Step-by-step explanation:
Note that ∠ Q and ∠ R are congruent, that is both 30°, thus
∠ 1 = 180° - (30 + 30)° = 180° - 60° = 120°
A circle has the equation (x−13)2+(y−1)2=4.
A: What is the center of the circle?
B: What is the radius of the circle?
Select two answers: one for question A, and one for question B.
A: (13,1)
B: 4
A: (−13,−1)
A: (−13,1)
A: (13,−1)
B: 2
B: 2–√
Final answer:
The center of the given circle is at (13, 1), and the radius of the circle is 2.
Explanation:
The equation of a circle is generally given in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. Looking at the given equation (x - 13)^2 + (y - 1)^2 = 4, we can see that it is already in this standard form.
To answer the questions:
The center of the circle is (13, 1), which comes from the terms within the parentheses being subtracted from x and y.
The radius of the circle is not simply 4, as one might surmise by a quick glance. Instead, the equation gives us the radius squared, r^2 = 4. Taking the square root of both sides, we find that the radius, r, is 2.
What percent is equivalent to the fraction 4/5?
Answer:
80/100 or 80%
Step-by-step explanation:
I will give the first answer brainiest :)
Answer:
A=2
Step-by-step explanation:
in the figure, parabola cuts the graph at point (2,1)
point (2,1) is one of the solution of the given quadratic equation
Hence, we can find the value of a by putting the value of x and y, we get
1=a(2-3)^2-1
= 2=a
Which is why A is 2
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Step-by-step explanation:
a=[tex]\frac{y}{(x-3^)^{2} } + \frac{1}{(x-3)^{2} }[/tex]
If sin = O =5/6, what are the values of cos O and tan O? (2 points)
Answer:
[tex]cos(\alpha )=\frac{\sqrt{11} }{6}[/tex] and [tex]tan(\alpha )=\frac{5\sqrt{11} }{11}[/tex]
Step-by-step explanation:
First we would need to solve for the missing leg in order to figure out the remaining answers.
To do this we can use the Pythagorean Theorem a² + b² = c²
Our missing leg in this case is a, so solving for a gives us [tex]a=\sqrt{c^{2} -b^{2} }[/tex]
Here our b is 5 and our c is 6. So plugging in these values we get [tex]a=\sqrt{(6)^{2}-(5)^{2} } =\sqrt{36-25} =\sqrt{11}[/tex]
With this missing leg being solved, we can use trig identities to solve for cos and tan
I used the trig identity [tex]sin(\alpha )=\frac{opposite}{hypotenuse}[/tex] to set up the triangle in the attached image. We can use the trig identity [tex]cos(\alpha)=\frac{adjacent}{hypotenuse}[/tex] which would give us [tex]cos(\alpha )=\frac{\sqrt{11} }{6}[/tex] and we can use the trig identity [tex]tan(\alpha ) = \frac{opposite}{adjacent}[/tex] which would give us [tex]tan(\alpha )=\frac{5}{\sqrt{11} } =\frac{5\sqrt{11} }{11}[/tex]
Answer:
As trigonometry property:
(sinO)^2 + (cosO)^2 = 1
tanO = sinO/cosO
Then, if sinO = 5/6 = 0.83
=> (5/6)^2 + (cosO)^2 = 1
=> cosO = +/- sqrt(1 - (5/6)^2) = +/- 0.55
=>tanO = +/- 0.83/0.55 = +/- 1.51
Hope this helps!
:)
If x = 4 and y = 6 , evaluate the following expression:
20+2(3y-4x)
By applying the PEMDAS rule, the solution to the given expression is equal to 24.
How to evaluate and solve the given expression?In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right.
Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
Based on the information provided, we have the following mathematical expression:
20 + 2(3y - 4x)
20 + 2(3(6) - 4(4))
20 + 2(18 - 16)
20 + 2(2)
20 + 4 = 24
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for each number below, is it even or odd?
Answer:
2,4,6,8,10 is even, 1,3,5,7,9 is odd. 983 is odd, 347 is odd, 36 is even, 44 is even
Step-by-step explanation:
Convert this decimal into a percentage: 1.125
Answer:
112.5 percent
Step-by-step explanation:
Answer:
112.5%
Step-by-step explanation:
Look at answer
here is some info about the goals scored in a hockey game. (math problem)
a. The mode for away goals is the 2nd quarter.
b. The mean number of goals per game is 4.8.
c. There were 4 more home goals scored than away goals in total across 10 games, with a total of 26 home goals and 22 away goals.
a. To find the mode for away goals, we need to determine which quarter had the most frequent number of away goals. Let's count the away goals for each quarter:
1st quarter: 2 away goals
2nd quarter: 9 away goals
3rd quarter: 7 away goals
4th quarter: 4 away goals
The 2nd quarter has the highest number of away goals, so the mode for away goals is the 2nd quarter.
b. To find the mean number of goals per game, we'll sum the total number of goals and then divide by the number of games:
Total number of goals = (5 + 4 + 8 + 9) + (2 + 9 + 7 + 4) = 48 goals
Number of games = 10
Mean number of goals per game = Total number of goals / Number of games = 48 goals / 10 games = 4.8 goals per game.
c. To find how many more home goals were scored than away goals in total, we'll calculate the difference in the total number of home goals and away goals:
Total home goals = 5 + 4 + 8 + 9 = 26 goals
Total away goals = 2 + 9 + 7 + 4 = 22 goals
Difference = Total home goals - Total away goals = 26 goals - 22 goals = 4 goals
In total, 4 more home goals were scored than away goals.
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I need help with this ' ASAP!
Answer:
H. 120
Step-by-step explanation:
100 students in the gym 25 are wearing a hat, 25 are wearing a T- shirt, 25 are wearing a hoodie and 25 are wearing a yankee T-shirt. If one student is randomly selected what is the probability that student is wearing a hat.
Answer:
1/4 or 25%
Step-by-step explanation:
So there are 1/4 of the students wearing each of the items. 1/4=25% if you are asked for it. I hope this helps.
im not verry good at these can you help me please
Answer:
It is A
Step-by-step explanation:
A because, you multiply -2 on both sides on the side with the x it cancels out on the one with the 5 it turns into -10 so the answer would be A
Please help will give brainliest!!! I need help ASAP
Answer:
Area = 54.1 ft²
Perimeter = 25.5 ft
Step-by-step explanation:
Area:
The formula for the area of a circle is (A = πr²). The radius is r, and r is half of the diameter, or d. So, it would be:
A = (3)(4.25)²
A = (3)18.0625
A = 54.1
Perimeter:
The perimeter, of circumference, formula for a circle is (C = πd), where C is the circumference and d is the diameter.
C = (3)(8.5)
C = 25.5
Hope this helps! Sorry it is a bit late! Have a great day! :)
The bar of the square pyramid shown has and area of 576 units. If the slant height of the pyramid is 29 units, what is the height of the pyramid?
Answer:
[tex]\sqrt{697}[/tex]
Step-by-step explanation:
If the base of the square pyramid has an area of 576 units, then the side length must have a length of [tex]\sqrt{576}=24[/tex]. 24/2=12, and using the pythagorean theorem you can find that the height of the pyramid is [tex]\sqrt{29^2-12^2}=\sqrt{697}[/tex]. Hope this helps!
The total cost C (in dollars) to rent a 14-foot by 20-foot canopy for d days is given
by the function C(d) = 15d + 30, where the setup fee is $30 and the charge per
day is $15. The setup fee increases by $20. The new total cost T is given by the
function T(d) = C(d) + 20. Describe the transformation from the graph of C to
the graph of T.
hi i think its 2 because 15 times 2 is 30
The graph of a linear function C(d) will shift 20 units left side if the total cost C (in dollars) to rent a 14-foot by 20-foot canopy for d days is function C(d) = 15d + 30.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The total cost C (in dollars) to rent a 14-foot by 20-foot canopy for d days is given by the function:
C(d) = 15d + 30
The charge per day is $15. The setup fee increases by $20.
The new total cost T is given by the function
T(d) = C(d) + 20
Plug C(d) = 15d + 30 in the above function:
T(d) = 15d + 30 + 20
T(d) = 15d + 50
The graph of a linear function C(d) will shift 20 units left side.
Thus, the graph of a linear function C(d) will shift 20 units left side if the total cost C (in dollars) to rent a 14-foot by 20-foot canopy for d days is function C(d) = 15d + 30.
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Find the value of x.
x =
Answer:
4
Step-by-step explanation:
The bottom half needs to be equal due to it's symmetrical sides.
Answer:
3
Step-by-step explanation:
^^
Amanda's employer deducts $350 from her paycheck each month for her family's health insurance plan. Jer gross monthly salary is $4,500. What percent of her gross pay goes towards health insurance?
Answer: about 7 %
Step-by-step explanation: you take 350 and divide it by 4500
Answer:
hope it helps
Step-by-step explanation:
Brooklyn is starting a running plan to train for a race . In the first week of her running plan , Brooklyn will run 8 miles . The plan calls for Brooklyn to increase her weekly mileage by 1.5 miles every week . If Brooklyn sticks to the plan , how many miles would she be expected to run during her 19th week of training plan ?
Answer:
36.5 miles
Step-by-step explanation:
Answer:
write out the first three terms (ex. the first term was 8 miles for the first week)
find out the arithmetic sequence or d. (d= 1.5)
plug into explicit formula.
answer: 35
find the valu of x.
Answer:
Easy! X is going to be 58° degree's as well, because of the Vertical Angles Theorem!
Answer:
58 degrees
Step-by-step explanation:
It is symmetrical to the other side, which is 58 degrees.
John has an account balance of -$30.00 and Steve has an account balance of
-$50.00. Who has more debt?
A. Steve
B. John
Answer:
A. Steve
Step-by-step explanation:
Steve has to pay $50. So he has more debt than John
a snail travel 1/5 of inch in an hr how long will it take to travel 5 inches
Answer:
25 hours
Step-by-step explanation:
5/.2=25
Answer:
25 hours
Step-by-step explanation:
If it travels 1/5 of an inch in an hour, then it travels 1 inch every 5 hours. We want 5 inches, so 5 hours x 5 is 25 hours. :)
What is the volume of the triangular prism?
A) 57.75 m3
B) 115.5 m3
C) 231.0 m3
D) 462.0 m3
Answer:
B) [tex]115.5m^3[/tex]
Step-by-step explanation:
to find the volume we need to find first the area of the triangle, and then multiply by 11 which is the length of the prism:
the measurements are:
[tex]base=7m[/tex]
[tex]height=3m[/tex]
[tex]length=11m[/tex]
the area of the triangle in one side is:
[tex]triangle=\frac{(base)(height)}{2} \\triangle=\frac{(7m)(3m)}{2}\\ triangle=\frac{21m}{2}\\ triangle=10.5m^2[/tex]
and now to find the volume of the prism we multiply the area of the triangle by the length of the prism:
[tex]volume=(triangle)(height)\\volume=(10.5m^2)(11m)\\volume=115.5m^3[/tex]
which is option B)
Answer:
115.5 [tex]m^{3}[/tex]
Step-by-step explanation:
V = 1/2a·c·h
V = 1/2(3)(7)(11) = 115.5
Mrs. Turner baked 120 cookies. She decided to give 1/6 of them to her students. How many did she take to her students?
Answer:
20
Step-by-step explanation:
120÷6=20
select all the pairs that are alternate interior angles
Answer:
- ∠3 & ∠5
- ∠2 & ∠8
----------------------------------------------------------------------
Interior Angles - Angles that appear INSIDE the transversal
Transversal - The shape you see with two parallel lines intersecting it.
Alternate - Opposite of each other, on the other side as well.
The alternate interior angles are the pair of ∠2,∠8 and ∠3,∠5.
What is alternating interior angle?Alternate interior angles are the angles which are formed when two parallel lines cut by a transversal line.
Hence, the pair ∠2,∠8 and ∠3,∠5 are alternating interior angle.
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Miguel will study for the quiz on which he is likely to do worse by guessing.
Which quiz should he study for?
A. History, because he must get more questions correct.
B. Science, because the probability of getting all questions correct is
0.016, which is lower than for history (0.031).
C. History, because the probability of getting all questions correct is
0.031, which is lower than for science (0.75).
D. Science, because the probability of getting all questions correct is
0.075, which is lower than for history (0.25).
Answer:
B: Science
Step-by-step explanation:
The reason B is correct is because 0.016 is lower than all the other possibility. A has no math to compare, but the others do, making it easier to determine the correct answer.
I hope this helps. If you have any more questions, please feel free to post them and someone will be able to help you, whether it's myself or others. Please leave a like, rating, and if possible, Brainliest. Have a great day!
Answer:c
Step-by-step explanation:
Can someone check to see if this is correct?
Answer:
yes
Step-by-step explanation:
Answer:
yes it is correct good job
Step-by-step explanation:
Which function is equivalent to f(x) = -4(x + 7)2 – 6?
A. f(x) = -4x2 – 56x - 202
B. f(x) = -4x2 + 14x + 43
C. f(x) = --4x2 - 56x - 172
D. f(x) = -4x2 + 190
Answer:
A
Step-by-step explanation:
Given
f(x) = - 4(x + 7)² - 6 ← expand factor using FOIL
= - 4(x² + 14x + 49) - 6 ← distribute parenthesis by - 4
= - 4x² - 56x - 196 - 6 ← collect like terms
= - 4x² - 56x - 202 → A
The equivalent function is [tex]f(x)=-4x^{2} -56x-202[/tex]
Option A is correct.
Equivalent function :The given function is,
[tex]f(x)=-4(x+7)^{2}-6[/tex]
We have to expand above function.
[tex]f(x)=-4(x+7)^{2}-6\\\\f(x)=-4(x^{2} +14x+49)-6\\\\f(x)=-4x^{2} -56x-196-6\\\\f(x)=-4x^{2} -56x-202[/tex]
Thus, the equivalent function is [tex]f(x)=-4x^{2} -56x-202[/tex]
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If the mean of the data set is 158 thousand dollars, find the revenue for the Granton location. 121,189,147,?
Answer:
175
Step-by-step explanation:
Since the mean is 158
(121+189+147+x)/4=158
121+189+147+x=632
x=175
Answer:
[tex]175[/tex] (thousand dollars) - written in [tex]2/22/2021[/tex]
Step-by-step explanation
In order to know the answer in the question, we should need to solve for the [tex]x[/tex] (Granton). It is other way around in solving for the mean because in here the mean is given. After using this formula, [tex]\frac{121+189+147+x}{4}=158[/tex] we derived at our answer that Granton has a revenue of [tex]175[/tex] (thousand dollars).
Dorian has two bags. Each bag has the letters A, B, and C written on little pieces of paper inside of it. He draws one letter from each bag. What is the probability that he draws out a vowel and a consonant? A. B. C. D.