Answer:
the answer is d (x+4)^2/9 - (y-1)^2/25
Step-by-step explanation:
its correct on edge
The standard form of the given equation is [tex]\dfrac{(x+4)^2}{9}-\dfrac{(y+1)^2}{25}=1[/tex]
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Begin by grouping the x terms together and the y terms together, and getting the constant on the other side of the equals sign:
25x² +200x - 9y² +18y = -166
Now we need to complete the square on the x terms and the y terms. Do this by first factoring out the leading coefficient from each, the 25 from the x's and the 9 from the y's:
25(x² +8x) - 9 (y² +2y) = -166
Now take half the linear term in each set of parenthesis, square it, and add it to both sides, remembering the multiplier outside (the 25 and the 9). Our x linear term is 8. Half of 8 is 4, and 4 squared is 16, so we add a 16 into the parenthesis with the x's; our y linear term is 2. Half of 2 is 1 and 1 squared is 1, so we add a 1 into the parenthesis with the y's:
25(x² +8x + 16)-9(y²+2y +1) = -166+400-9
Note the 400 and -9 on the right side now. 25 times 16 is 400; we didn't just add in a 16, we have to multiply the scalar number into it before we know what we really added in. And the -9 comes from multiplying the -9 times 1.
The reason we do this is to get the perfect square binomials on the left that we created while completing the square:
25(x+4)² - 9 (y+1)²= 225
Now, finally, we will divide both sides by 225 to get this conic into the standard form:
[tex]\dfrac{(x+4)^2}{9}-\dfrac{(y+1)^2}{25}=1[/tex]
This is a hyperbola with a horizontal transverse axis and a center of (-4, -1). The reason we know it's not an ellipse is because an ellipse will always have a + sign separating the x-squared from the y-squared whereas a hyperbola always has a - sign separating them. And we also know it's not a circle because the values of the leading coefficients weren't the same.
Therefore the standard form of the given equation is[tex]\dfrac{(x+4)^2}{9}-\dfrac{(y+1)^2}{25}=1[/tex]
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is it true or false that all whole numbers are natural numbers
Answer:it can very
Step-by-step explanation:
It depends on which definition of 'whole numbers' you use.
Some definitions say the whole numbers are the set of positive integers including zero; or the set of all non-negative integers. In this case, the answer would be 'false', since the set of integers includes negatives.
However, if you are using a definition of whole numbers which includes positive integers, including zero, and their negatives, the answer would be 'true'. Figure out how the term 'whole numbers' is being defined, then you can get your answer.
Answer:
every natural number is a whole number, but, every whole number is not a natural number.
Step-by-step explanation:
what is the greatest common factor of 10, 30 and 45
Answer:
5
Step-by-step explanation:
3. Given f(x)=-2(5)
Find f (4)
Answer:
f
(
x
)
=
2
, means, whatever be the value of
x
, f(x)=2#.
∴
f
(
−
4
)
=
2
.
Write the equation in standard form for the circle x^2 + y^2 + 16x + 28 = 0.
Answer:
( x + 8 ) ^2+ y^2= 36
Step-by-step explanation:
A circular garden has a diameter of 8 yards. What is the area of the garden?
Use 3.14 for TT.
O A. 12,56 yd
O B. 200.96 yd2
O c. 25.12 yd?
O D. 50.24 yd?
A locker door is 13 inches wide by 27 inches tall. A company will use a scale factor of 2.5 to change the dimensions
of the door. What will be the new height of the locker door?
Answer:67.5
Step-by-step explanation:The question asked the HEIGHT. So multiply the scale factor (2.5) and the inches tall (27).
Given that y = } 1/2(x1 + x2)c, what is y when X 1 = 3, X2 = 5, and c = 6?
Answer:
24
Step-by-step explanation:
1/2(x1+x2)c x1=3 , x2=5 , c=6
:- 1/2(3+5)6 ( BODMAS)
:- 1/2(8)6 divide 8 by 1/2
:- (4)6 multiply both of them and the result = 24
what is the distributive property for 15x+25?
Answer:
5(3x+5)
Step-by-step explanation:
Answer:
5(3x + 5)
Step-by-step explanation:
Factor out 5 of 15x + 25 then you'll get your answer.
Hope this helps:)
CAN SOMEONE PLEASE HELP ME WITH THIS ITS DUE TODAY I WILL BRAINLIEST WHO EVER TELLS ME THE ANSWER
Answer:
There is a error that is
Not : 4 × 6
Correct: 4 × 4
Step-by-step explanation:
Given ,
Base of the parallelogram = 4 in.
Height of the parallelogram = 4 in.
Therefore,
Area of the parallelogram = base × height
= 4 in. × 4 in.
[tex] = 16 {in.}^{2} (ans)[/tex]
4. The teacher recommends that students read for 20
minutes each night. How many pages will the
student complete?
proportional relationships
A gardener can increase the number of dahlia plants in an annual garden by either buying new bulbs each year or dividing the existing to create new plants. The table below shows the expected number of bulbs for each method.
Answer:
May I please have the question or the table?
Step-by-step explanation:
Answer:here’s the table I don’t have the answer tho.
Step-by-step explanation:
choose the correct answer 1 1/12 - 7/10 greater than half or less than half
Answer:
less than half
Step-by-step explanation:
13/12 - 7/10 = 23/60
In figure 5, what are the values of x and y?
(4x - 12)
(7y+12)°
(12x+8)°
Answer:
sorry
Step-by-step explanation:
Where is the figure?
Help please I really need it
Answer:
40%
Step-by-step explanation:
it ads up to 90, so 50+x=90 x=40
Answer:
40° as it is a right angle
then 90 - 50= 40
What is the x-intercept of the graph of Y= 4x-36
The x - intercept of the line is at Point X(9, 0).
We have the following equation of a straight line -
y = 4x - 36
We have to find the x - intercept of the of this line.
What is the general equation of a straight line ?The general equation of a straight line is as follows -
y = mx + c
where -
m - slope of line
c - intercept of line on y - axis.
According to the question, we have -
y = 4x - 36
Now, comparing this line with the general equation of line - y = mx + c, we get -
m = 4
c = - 36
for the x - intercept of the line, substitute y = 0. We get -
0 = 4x -36
4x = 36
x = 9
Hence, the x - intercept of the line is at Point X(9, 0).
Refer to the graph attached for more clarity.
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Help the sista out cause it boring
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
4/5 your dividing 4 by 5, so answer is B :)
URGENT
Explain:
Answer the following questions using 125 words or more:
1. Write about the similarity of the original comic to the enlargement. How similar are they and how can you tell? What
would cause differences in the two pictures? If you drew another comic using a grid, is there anything you would do
differently?
2. What would happen if you reduced the comic's size rather than enlarged it? Would the process be the same? What
would you do differently?
The way in which the original comic would be similar to the enlargement is that they have the same proportion.
How is the original comic similar to the enlargement?Based on the fact that when a comic is enlarged, the original and enlargement would remain the same and the only difference would be a larger size.
Hence, we can see that because they have the same proportion, each individual pixel in the original is more visible and the enlargement displays the image in a small number of large pixels.
The use of a grid would likely reduce the effect of pixelation and if there is a reduction in the size of the comic, there would be the same effect, only that it would be smaller, but have the same proportion.
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1. Use the triangle below to determine the values indicated:
Answer:
A. Sine Y = 20 / 29
B. Cos Y = 21 / 29
C. Tan Y = 20 / 21
D. Sine Z = 21 / 29
E. Cos Z = 20 / 29
F. Tan Z = 21 / 20
Step-by-step explanation:
A. Determination of Sine Y
Opposite = 20
Hypothenus = 29
Sine Y =?
Sine Y = Opposite / Hypothenus
Sine Y = 20 / 29
B. Determination of Cos Y
Adjacent = 21
Hypothenus = 29
Cos Y =?
Cos Y = Adjacent / Hypothenus
Cos Y = 21 / 29
C. Determination of Tan Y
Opposite = 20
Adjacent = 21
Tan Y =?
Tan Y = Opposite / Adjacent
Tan Y = 20 / 21
D. Determination of Sine Z
Opposite = 21
Hypothenus = 29
Sine Z =?
Sine Z = Opposite / Hypothenus
Sine Z = 21 / 29
E. Determination of Cos Z
Adjacent = 20
Hypothenus = 29
Cos Z =?
Cos Z = Adjacent / Hypothenus
Cos Z = 20 / 29
Determination of Tan Z
Opposite = 21
Adjacent = 20
Tan Z =?
Tan Z = Opposite / Adjacent
Tan Z = 21 / 20
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!
Answer:
105
Step-by-step explanation:
17.5÷2.5=7
7x15=105
if you need extra points (50 points) and brainiest answer this correctly plz
Answer:
D) 500 square feet
Step-by-step explanation:
20x40=800
30x10=300
800-300=500
Answer:
500 square feet
Step-by-step explanation:
Walk way A=bh
A=40 times 20
A=800
garden
A=30 times 10
A=300
Now subtract walkway from the garden. 800 - 300= 500
A__ function is a function in the form f(x) = ax? + bx+c, where a, b, and care real
numbers and a 70, that will graph as a parabola.
is it
a) quadratic
b) first
c) parabolic
d) second
There are 26 songs in a playlist. Jackson adds some more
songs to the playlist. Which equation models how many
songs a are in the playlist after Jackson adds s more songs
to the playlist?
Pls I need help with it
Last month,Marco's neighbors paid him to take care of their fish when they went on vacation. He spent $5 on his earnings on an after snack and $16 on a new book. Afterward,he had no more then $9 left. How can you beat describe how much Marco's neighbors paid him?
Answer:
$30
Step-by-step explanation:
5+16=21+9=30
Sofie makes and sells scarves. Her profit depends on what price she charges for a scarf.
She writes the expression (−5)(50−2) to represent her profit based on the price per scarf,
Use the drop-down menus to complete the statements about Sofie's profit.
Answer:
The first part is 5
The maximum it can be is 200
Step-by-step explanation:
Because I said So
Sofie will not make a profit if she sells her scarves for $5 or less.
The maximum profit Sofie can make is $200.
What is a parabola?A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.
According to the given problem,
y = (x - 5)(50 - 2x)
⇒ y + (-(x - 5)(50 - 2x) = (x - 5)(50 - 2x) + (-(x - 5)(50 - 2x)
⇒ y - (x - 5)(50 - 2x) = (x - 5)(50 - 2x) - (x - 5)(50 - 2x)
⇒ y - (x - 5)(-2x + 50) = 0
⇒ y - (-x *2x + x*50 + 5*2x -5*50) = 0
⇒ y - ( -2x² + 50x + 10x - 250) = 0
⇒ y - ( - 2x² + 60x - 250 ) = 0
⇒ y + 2x² - 60x + 250 = 0
⇒ 2x² -60x + y + 250 = 0
⇒ ( 2x² - 60x ) + y + 250 = 0
⇒ 2 ( x² - [tex]\frac{60}{2}[/tex]x) + y + 250 = 0
⇒ 2 ( x² - [tex]\frac{2^{2} *3*5}{2}[/tex]x) + y + 250 = 0
⇒ 2 ( x² - 30x ) + y + 250 = 0
⇒ 2( x² + 2(-15)x + 225 -225 +y + 250 = 0
⇒ 2( x - 15 )² + 2(-225) + y + 250 = 0
⇒ 2( x - 15 )² + y = -2(-225) - 250
⇒ 2( x - 15 )² + y = 450 - 250
⇒ 2( x - 15 )² + y = 200
⇒ y = -2( x - 15 )² + 200
This equation is in the form of y = a(x - h)² + k where the vertex of the parabola is (h , k).
Therefore the vertex of the parabola is at (15 , 200)
Hence, we can conclude that Sofie will maximum profit of $200 if she sells a scarf at 15$ and will make the least profit if she sells the scarf at $5 or less.
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Can someone help me plz
njjjwer:
jajajajaj
Step-by-step explanation:
yessolve for x -5(x-4)=-30
Answer:
-5x + 20 = -30
-5x = 10
x = -2
22:4 :: x : 16, what is the value of x, if all the four numbers are in proportion.
Answer:
= 22:4 :: x : 16
22*16 = 4x
352 = 4x
x = 352/4
x = 88
Hope this helps you. Do mark me as brainliest.
s + 10.7 = 7.2
s = ?
how do i solve
An exponential distribution is formed by the waiting times for a patient in the emergency room. The average waiting time for this distribution is 38 minutes. Given that it has already taken 37 minutes, what is the probability that the wait time will be more than an additional 41 minutes? Round your answer to three decimal places.
Answer:
0.207 = 20.7% probability that the wait time will be more than an additional 41 minutes
Step-by-step explanation:
To solve this question, we should understand the exponential distribution and conditional probability.
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
The average waiting time for this distribution is 38 minutes.
This means that [tex]m = 38, \mu = \frac{1}{38} = 0.0263[/tex]
Given that it has already taken 37 minutes, what is the probability that the wait time will be more than an additional 41 minutes?
Event A: Taking more than 37 minutes.
Event B: More than 37 + 41 = 78 minutes.
Probability of taking more than 37 minutes:
[tex]P(A) = P(X \leq 37) = 1 - e^{-0.0263*37} = 0.6221[/tex]
More than 37 minutes and more than 78 minutes:
The intersection is more than 78 minutes, so:
[tex]P(A \cap B) = P(X > 78) = e^{-0.0263*78} = 0.1286[/tex]
The probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1286}{0.6221} = 0.207[/tex]
0.207 = 20.7% probability that the wait time will be more than an additional 41 minutes
From the top of a lighthouse the angle of depression of a speed
boat is 35º. The boat is 134 meters from the base of the
lighthouse. Find the distance from the top of the lighthouse to the
boat.
Answer:
164m (to 3 s.f.)
Step-by-step explanation:
Please see the attached picture for the full solution.