The values of the two original numbers are 7 and 9.
Two numbers when multiplied equal 63 if one number is x and the other number is greater than x by 2.
As per the given phrase, the information given in equation form is as
x × (x + 2) = 63
It expresses as a quadratic equation:
x² + 2x - 63 = 0
Solve the quadratic equation to find possible values of x
x² + 9x - 7x - 63 = 0
x(x + 9) - 7(x + 9) = 0
(x + 9)(x - 7) = 0
(x + 9) = 0 and (x - 7) = 0
x = -9 and x = 7
Since we were told that the two numbers are positive numbers so take x = 7.
Thus, the values of the two original numbers are 7 and 9.
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Suppose that you have 4 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards without replacement.
The probability that two cards will be drawn at random, without replacement, is 13/18.
What is Probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let's look at a straightforward application.
Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.
There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.
According to our answer-
P(at least 1 green) = 1 - P(no green)
P(no green) = draw yellow on both draws
= P(draw yellow on 1st draw) * P( draw yellow on 2nd draw, given draw yellow on 1st draw)
= 5/9 * 4/8 = 20/72 = 5/18
P(at least 1 green) = 1 - 5/18
= 13/18
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Gaspar writes the algebraic expression 5b +3.79.
It represents the total cost, in dollars, of buying 5 bagels
and a container of cream cheese. Identify any variables,
coefficients, and terms in the expression. Tell what
each represents.
Answer:
B is a variable it is a letter
5 is a coefficient because it's in front of the variable
3.79 is a term because it is just numbers by itself
Step-by-step explanation:
Ling must spend no more than $40.00 on decorations for a party. She has spent $10.00 on streamers and wants to buy bags of balloons as well. Each bag of balloons costs $2.50. The inequality below represents x, the number of bags she can buy given the spending limit and how much she has already spent on streamers.
Ling can therefore purchase 0 to 12 bags, but no more is the right decision.
How to calculated the inequality?Ling has been instructed to spend no more than $40.00 on party décor. She has already spent $10.00 on streamers but also plans to purchase bags of balloons. The price of a bag of balloons is $2.50.
Given her spending cap and how much she has already spent on streamers, the inequality 10 + 2.5x ≤ 40 indicates x, the number of bags she can purchase.
Subtracting 10 from both sides of our inequality, let's find x by reversing the inequality.
10 - 10 + 2.5 x ≤ 40 - 10
2.5 x ≤ 30.
We will now divide our inequality by 2.5 on both sides.
2.5 x / 2.5 ≤ 30 / 2.5
x ≤ 12.
Ling can therefore purchase 0 to 12 bags, but no more is the right decision.
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Answer:
Step-by-step explanation:
Ling can therefore purchase 0 to 12 bags, but no more is the right decision.
Write y-2=-1(x+7) in standard form
Y=mx+b is standard form.
y-2= -x-7
+2 +2
y= -x-5
Suppose that you roll two dice. You will be paid $20 if you roll a double. You will not receive anything
for any other outcome. How much should you be willing to pay for the privilege of rolling the dice?
Please round your answer to the nearest cent.
There are 36 possible outcomes when rolling two dice, and only 1 of those outcomes results in a double. Therefore, the probability of rolling a double is 1/36, or approximately 0.028.
If you are willing to pay $20 to roll the dice, then you are effectively paying a premium of $20 for a probability of 0.028 of winning. This means that the expected value of rolling the dice is 0.028 * $20 = $0.56.
Therefore, you should be willing to pay up to $0.56 for the privilege of rolling the dice. Rounded to the nearest cent, this is $0.56.
g(x)=x^4-3x^3-8x^2-6x-20, find zeros
Answer:x=-2,5, -[tex]i\sqrt{2}[/tex], +[tex]i\sqrt{2}[/tex]
Step-by-step explanation:
Determine whether the quadratic function shown below has a minimum or
maximum, then determine the minimum or maximum value of the function.
f(x) = -2(x - 5)(x-7)
The vertex (3, -16) is the maximum point on our quadratic equation.
Maximum and minimum values of the function:When we compare the given Quadratic function with the general form
ax² +bx +c,
If the value of a is positive then the Quadratic function will have a minimum value, and the graph of the function opens up.
If the value of a is negative then the Quadratic function will have a maximum value, and the graph of the function opens downwards.
Here we have
f(x) = -2(x - 5)(x-7)
f(x) = -2 [x²-7x - 5x + 35 ]
f(x) = -2 [x²-12x + 35 ]
f(x) = -2x² + 12x - 35
Compare f(x) with ax²+ bx + c
=> a = -2, b = 12, and c = - 35
Here,
a = -2 is a negative value then the function f(x) will have maximum value
And the graph of the function opens down.
The formula for the x coordinate of the vertex = -b/2a
The coordinate of x = -(12)/2(-2) = 3
Now substitute x = 3 in f(x) to find y-coordinate
=> f(3) = - 2(3)² +12(3) - 35
=> f(3) = -2(9) + 36 - 35
=> f(3) = - 16
Therefore, y-coordinate = -16
Therefore,
The vertex (3, -16) is the maximum point of the quadratic equation.
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there is a line that includes the point (11,5) and has a slope of 8/11. what is its equation in slope intercept form?
Answer:
[tex]y=\frac{8}{11} x-3[/tex]
Step-by-step explanation:
Plug in the slope and point into the equation y=mx+b to solve for the y-value of the y-intercept. Plug in the x value for x, the y value for y, and the slope for m.
[tex]5=\frac{8}{11} (11)+b[/tex]
[tex]5=8+b[/tex]
[tex]-3=b[/tex]
After solving that, you can plug the slope and y-intercept back into the equation to solve for y.
[tex]y=\frac{8}{11} x+(-3)[/tex]
[tex]y=\frac{8}{11} x-3[/tex]
Answer:
Step-by-step explanation:
Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept. We have all the information we need except for the y-intercept, so we can plug in our point to solve for the y-intercept.
------------------------------------Solving for y-intercept------------------------------------
Plugging in the point gives us [tex]5=8/11*11+b[/tex]. Simplifying this equation results in [tex]5=8+b[/tex]. To solve for b, we subtract 8 from both sides, giving us that [tex]b=-3[/tex]. We now have both the slope and the y-intercept, so our equation is y = 8/11x -3.
Feel free to contact me with any questions about my answer. I hope this helps!
Next O Quiz 6.2
10
Select the correct answer.
According to the Dietary Guidelines for American 2015, you should limit your fat intake to what percentage of your total calories?
OA. Less than 10%
OB. 25-35%
C.
OD.
45-55%
65-75%
Reset
Next
According to the Dietary Guidelines for American 2015, you should limit your fat intake to 25% - 35% of your total calories. The correct option is B.
What is dietary guidelines?Food-based dietary guidelines also known as dietary guidelines are intended to serve as a foundation for public food and nutrition policies, health and agricultural policies, and nutrition education programs aimed at promoting healthy eating habits and lifestyles.
Calories are the units of energy released by your body when it digests and absorbs food. The higher the calorie content of a food, the more energy it can provide to your body. When you consume more calories than you require, your body stores the excess calories as fat. Even fat-free foods can be high in calories. In this case, the fay should not be more than 35%.
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Now let's look at the data from all the Buffalo. If we calculate the 60% confidence interval for every buffalo's count (i.e. data sample), how many Cls do we expect to contain the true mean? Store your answer in theoretical_hits. Then we need to check our theoretical answer with our actual data. Calculate the 60% confidence interval for each buffalo's count. Then commpute how many of those Cls contain the true mean. Assume that the true mean is 25,000. Store this value in sample_hits . Does this value match the theoretical value? It may be helpful to visualize the Confidence Intervals, along with the true mean. Create a plot for the Confidence intervals for the first 40 rows of the dataframe. Also plot true_mean=25000 as a horizontal dotted line. This plot will not be graded, but may help you get a better understanding of different confidence intervals for the same underlying population. We recommend looking into the ggplot package to help with this task.
15000 Cls should we expect to include the true mean if we compute the 60% confidence interval for each buffalo count (i.e., data sample).
Given that,
We have to calculate let's now examine the Buffalo's collective data. How many Cls should we expect to include the true mean if we compute the 60% confidence interval for each buffalo count (i.e., data sample).
We know that,
Theoretical hits= confidence interval × total no. of buffaloes
= 0.6×(buffaloes)
Sample hits = count among total no. of buffaloes, from which how many of inside 25000, that will be sample hits.
So,
=0.6×25000
=15000
Therefore, 15000 Cls should we expect to include the true mean if we compute the 60% confidence interval for each buffalo count (i.e., data sample).
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CHALLENGE:
3. There are less than 30 students in Mr. Klein's math class. On a
test, % of the class received a "B", %4 received a "C", % received a "D",
and % failed. How many more students received a "B" than received
an "A"?
Answer: ???
Step-by-step explanation:
You have to put in the numbers for the percentages.
[tex]\frac{1}{3}+\frac{1}{105}-\frac{1}{21}[/tex]
Nancy's pack of pens had 80% red pens. If
there were 55 pens total in the pack, how
many were red?
Answer:
44
Step-by-step explanation:
80*55/100 = 44
Answer:78
Step-by-step explanation:
WORD PROBLEM:
You have 200 meters of fencing to enclose two adjacent rectangular pens for livestock. The total area of the enclosed region is 1400 square meters. What are the dimensions of each pen?
The dimensions of each of the rectangular pens are given as follows:
8.41m and 41.58 m.
How to obtain the dimensions of the pen?The pen have rectangular format, as shown by the image given at the end of the answer, hence the dimensions are obtained from the area and the perimeter of the pen.
For each pen, the dimensions are given as follows:
Length: x.Width: y.For the entire pen, the dimensions are given as follows:
Length: 2x.Width: y.You have 200 meters of fencing to enclose two adjacent rectangular pens for livestock, hence the perimeter is given as follows:
2(2x + y) = 200
2x + y = 100.
The total area of the enclosed region is 1400 square meters, hence:
2xy = 1400.
From the first equation, we have that:
y = 100 - 2x.
Replacing in the second, the length x is obtained as follows:
2x(100 - 2x) = 1400
-4x² + 200x - 1400 = 0
4x² - 200x + 1400 = 0.
The solutions are of:
8.41m and 41.58 m.
Which gives the dimensions of the pen.
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Probability and Statistics Question
we want to find the number of hours (or rather days) until only 4.25% of the drives fail.
that means for an exponential distribution we have
P(X < x) = 1 - e^(-Lx)
L = 1/mean = 1/12500
and we need to find x, so that P(X <x) = 0.0425 (that is 4.25% converted into a probability).
so, we get
0.0425 = 1 - e^(-x/12500)
0.0425 - 1 = -e^(-x/12500)
-0.9575 = -e^(-x/12500)
0.9575 = e^(‐x/12500)
ln(0.9575) = -x/12500
-x = ln(0.9575)×12500
x = -ln(0.9575)×12500 = - -0.043429558...×12500 =
= 0.043429558...×12500 = 542.8694741... hours
after 542.8694741... hours = 22.61956142... days
it is expected that 4.25% of the hard drives fail.
you left out to what decimal this should be rounded. and if you need hours or days. in case of doubt use hours (as the only other time information is given in hours).
please round yourself as you need.
prove that for every integer exists a multiple of that number that is composed of only ones and zeros in the decimal system
Let n be a positive integer. Consider the n+1 integers 1,11, 111,1111,... (where the last integer in this list is the integer with n+1 - 1s in its decimal expansion).
Note that there are n possible remainders when an integer is divided by n. Because there are n+1 integers in this list, by the pigeonhole principle there must be two with the same remainder when divided by n. The larger of these integers the smaller one is a multiple of n, which has a decimal expansion consisting entirely of 0s and 1s.
For example, take n=7
we have, 1,11, 111,1111,...,11111111
The remainder possible when any number is divided by 7 is 0,1,2,3,4,5,6
These are the remainders when the numbers in the first list are divided by 7 gives 1,4,6,5,2,0,1,4.
Now you can see that we have 7 pigeonholes {0,1,2,3,4,5,6} and 8 pigeons {1,11, 111,1111,...,11111111} so there needs to be at least one pigeonhole where 2 pigeons will reside.
In this case, we have 11%7=4 and 11111111%7=4
Their difference, i.e. 11111111-11=11111100 is divisible by 7.
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Steve buys last year's best-selling novel, in hardcover, for $26.35. This is with a 15% discount from the original price. What was the original price of the novel?
Step 1 of 2 : Use the variable x to set up an equation to solve the given problem. Set up the equation, but do not take steps to solve it.
Answer:
$30.30
Step-by-step explanation:
$26.35*15%=$3.95
Then you add $26.35 and $3.95 to get $30.30
1. Write two expressions that are equivalent to the expression listed below. You can use the equation editor to input your answers.
(x^{1/3)²
Two index that are equivalent to the index (x^{1/3)² are:- 1) X⁽²/³⁾, 2) (∛X)²
What are index ?
An index can be assigned to a number or variable. A value raised to the power of a variable's (or a constant's) value is its index. The exponents or powers are other names for the indices. It displays how many times a particular number must be multiplied. It takes the following form:
a(m) = a × a × a ×……× a (m times)
The base in this case is a, and the index is m.
The index instructs a certain integer (or base) to be multiplied by itself a specified number of times, where the number of times is determined by the index raised to the base. It is a condensed way of expressing large sums of information and calculations.
[tex]X^b . X^A. X^n = X^b^a^n[/tex]
Example: 2^3 = 2 × 2 × 2 = 8
[tex][X^\frac{1}{3} ]^2[/tex][tex]= X^\frac{2}{3}[/tex]
We can also write the same index as;
[tex]A^\frac{1}{n}=\sqrt[n]{A}[/tex]
[tex]X^\frac{2}{3}=[\sqrt[3]{x}]^2[/tex]
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A rectangle piece of metal has an area of 32 square centimeters. Its perimeter is 24 centimeters. What are the dimensions of the piece
The dimensions of the piece are l = 8 and b =4.
What are dimensions?
The minimal set of coordinates required to specify any point within a mathematical space is the dimension of that space. Because only one coordinate is required to specify a point on a line, it has a dimension of one.
Here,
Let the length of a rectangular piece of metal = l cm
And the breadth of a rectangular piece of metal = b cm
Perimeter of a rectangular piece of metal = 2(l+b) = 24 cm
Or, l+b = 24/2
Or, l+b = 12 -------- (1)
Area of a rectangular piece of metal = l×b = 32 cm²
Or, l×b = 32 ------- (2)
We know that,
(l - b)² = (l+b)² - 4×l×b
(l - b)² = (12)² - 4×32
(l - b)² = 144 - 128
(l - b)² = 16
(l - b)² = 4
l - b = 4 --------- (3)
Adding equations (1) and (3), we get
l+b+l-b = 12 + 4
2l = 16
l = 8
Now, we put the value of l in equation(1) and we get
8 + b = 12
b =4
Hence, the dimensions of the piece are l = 8 and b =4.
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If quadrilateral A' B' C' D' = D8 (ABCD), which of the following statements are true? Select all that apply.
So the correct statement is A and D
Quadrilateral A'B'C'D' and ABCD will be similar only if s>= 1 The corresponding side lengths are Related by AB = s.A'What is a Quadrilateral?
A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
A quadrilateral is a flat shape with four edges and four corners, also known as vertices. The quadrilateral has angles at each of its four vertices, or corners.
The Latin words quadra, which means four, and latus, which means sides, are combined to form the English term quadrilateral. A quadrilateral does not always have to have equal lengths on each of its four sides.
These are the several kinds of quadrliaterals:
Trapezium ParallelogramSquares Rectangle Rhombus KiteQuadrilateral A'B'C'D' = D8(ABCD) as we know two quadrilateral will be congruent in case of unit length scaling factor and corresponding side length corresponds like AB,BC,CD,DA
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Window Rock Recruitment Agency just placed Alejandro Rivera in a job as an assistant
pharmacist. The job pays $71,500 annually. The agency fee is equal to 40% of the first
5 weeks' pay. Demonstrate and explain how you would be able to determine what he will
earn during the first 4 weeks if he pays the agency fee weekly?
Answer: To determine Alejandro's earnings for the first 4 weeks, we first need to calculate his weekly pay. To do this, we divide his annual salary by the number of weeks in a year:
Annual salary / 52 weeks/year = weekly pay
$71,500 / 52 weeks/year = $1,375/week
Next, we need to determine the agency fee that Alejandro will pay each week. The agency fee is equal to 40% of the first 5 weeks' pay, so we multiply Alejandro's weekly pay by 40% to get the agency fee:
Weekly pay * 40% = agency fee
$1,375/week * 40% = $550/week
Finally, to determine Alejandro's earnings for the first 4 weeks, we multiply his weekly earnings by the number of weeks:
Weekly pay * number of weeks = earnings
$1,375/week * 4 weeks = $5,500
So, Alejandro will earn $5,500 during the first 4 weeks of his new job, after paying the agency fee each week.
SWIMMING Yukio is keeping track of the number of calories she
burns while swimming freestyle laps. The number of calories she
burns can be represented by a function. Sketch a graph that shows
the number of calories burned y as a function of time x, in hours.
y-Intercept: No calories burned when she has swum for 0 hours.
Linear or Nonlinear: The graph of the function is linear.
Positive: for time greater than 0
Increasing: for time greater than 0
End Behavior: As the number of hours she has swum increases, the
number of calories burned increases.
The proportional relationship y = 200x, showing the number of calories y burned as a function of the time swimming of x hours, is given as follows:
What is a proportional relationship?A proportional relationship is a special case of a linear function, as even though it has a constant rate of change, the intercept is of zero.
The general format of a proportional relationship is given as follows:
y = kx.
In which the constant of proportionality k represents the constant rate of change.
Supposing that for each hour swimming, the person spends 200 calories, the constant is given as follows:
k = 200.
Hence the proportional relationship that gives the number of calories y burned as a function of the time swimming of x hours is given as follows:
y = 200x.
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Bonds Payable has a balance of $810,000, and Premium on Bonds Payable has a balance of $8,910. If the issuing corporation redeems the bonds at 102, what is the amount of gain or loss on redemption?
a. $8,910 gain
b. $8,910 loss
c. $7,290 loss
d. $7,290 gain
To determine the gain or loss on the redemption of the bonds, you need to compare the redemption price to the carrying value of the bonds. The carrying value of the bonds is the amount that the bonds are recorded as being worth on the issuing corporation's balance sheet. This is calculated by adding the Bonds Payable balance and the Premium on Bonds Payable balance.
In this case, the carrying value of the bonds is $810,000 + $8,910 = $818,910. If the bonds are redeemed at a price of $102, the gain or loss on the redemption can be calculated as follows:
Gain or loss on redemption = Redemption price - Carrying value of bonds
= $102 - $818,910
= -$817,810
Since the gain or loss on the redemption is a negative number, this indicates that the redemption price was lower than the carrying value of the bonds, resulting in a loss. The correct answer is therefore: c. $7,290 loss.
Select the correct answer. What is the range of y = sin 0 ? Ο Α. B. C. D. [-1.1] [0,⁰0) all real numbers 277
The range of the sine function is:
R: {x ∈ R| -1 ≤ x ≤1}
It can also be written as [-1, 1], so that is the correct option.
What is the range of the sine function?For a function y = f(x) we define the range as the set of the outputs, this is, the set of the possible values of y.
In this case, our function is y = sin(θ)
Remember that the maximum value of the sine is sin(π/2) = 1
And the minimum is sin(3π/2) = -1
So the maximum value of y is 1 and the minimum is -1, thus, the range is the set of all real numbers between these two, then we can write the range as:
R: {x ∈ R| -1 ≤ x ≤1}
It can also be written as [-1, 1]
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Kiana delivers sandwiches for a restaurant that charges $8.25 for each sandwich plus a $10 delivery fee. Kiana has an order that totals $59.50. Write an equation to describe this situation.
Answer: 59.50=8.25x + 10
Step-by-step explanation: so we know that It is 8.25 per sandwich making it the constant. Then we know that 10 is the the deléguente fee making it the y-intercept. Finally this all has to equal to 59.50. X represents how many sandwiches the person ordered.
A scientist uses a submarine to study ocean life. She begins at sea level, which is an elevation of 0 feet. She travels down 21.1 feet. She then ascends 19.1 feet. Next, she travels down a second time, 80.7 feet. How many feet must she now ascend to get back to sea level?
Based on the elevation of the scientist after descending and traveling directly up, the number of feet she needs to ascend to get to sea level will be; 82.7 feet.
How to find the elevation?To find the number of feet that the scientist needs to travel up to get back to sea level, you need to find her current elevation.
The current elevation of the scientist is:
= 0 - 21.1 + 19.1 + 80.7
= 82.7 feet
In other words, the scientist is 82.7 feet below sea level.
To get back to sea level therefore, the scientist will need to travel 82.7 feet directly up.
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Preeti discovers that her roommate Shari recently experimented with methamphetamine. Preeti, worried about her roommate, informs Shari that there are risks associated with methamphetamine use, such as the induction of symptoms associated with ____.
psychosis
Preeti informs Shari that there are risks associated with methamphetamine use, such as the induction of symptoms associated with Psychosis
Psychosis is a combination of symptoms resulting in an impaired relationship with reality. It can be a symptom of serious mental health disorders. People who are experiencing psychosis may have either hallucinations or delusions.
If someone is experiencing an episode of psychosis, the main symptoms include:
hallucinationsdelusionsdisorganized behaviorAccording to the question,
Preeti discovers that her roommate Shari recently experimented with methamphetamine. Preeti, worried about her roommate, informs Shari that there are risks associated with methamphetamine use, such as the induction of symptoms associated with Psychosis
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A line has a slope of 14/19 and passes through the point 0,15 what is its equation in slope intercept form
Answer: y = 14/19x+15
Step-by-step explanation: using the equation y = mx+b, m is your slope and b is the y-intercept. plug your slope (14/19) and y-intercept (15) into the equation and you’ve got your answer in slope-intercept form
Which point shows the approximate location of [tex]\sqrt{7}[/tex] plotted on the number line
The position of the √7 on the number line is slightly right of the 2.6.
What is a number line?
A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.
Here,
In general conclusion,
√4< √7 < √9
2 < √7 < 3
So, the value of the √6 lies between 2 and 3.
√6 = 2.6457
Hence, the position of the √7 on the number line is slightly right of the 2.6.
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in a certain hyperbola, the center is at $(-2,0),$ one focus is at $(-2 \sqrt{34},0),$ and one vertex is at $(-5,0).$ the equation of this hyperbola can be written as\[\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2}
The equation of certain hyperbola with center ( -2,0) is (x+ 2)²/25 - (y)²/ 9 = 1
According to the question,
Equation of hyperbola is given : (x-h)²/a² - (y-k)²/b² = 1
Center of hyperbola = (-2,0)
Focus = (-2√34 , 0)
vertex = (-5,0)
This hyperbola is from left to right
As center is (-2,0) means h = -2 and k = 0
Hyperbola are symmetric ,
Second focus = (-2√34 , 0)
Second vertex = ( 5,0)
Vertex are (a,b) => a = 5
Foci of general hyperbola are ( h ± ck)
=> ( h ± c, k) = (-2√34 , 0)
=> -2 ± c = -2√34
=> c = ± √34
Also , c^2 = a^2 + b^2
=> 34 = 25 + b^2
=> b^2 = 9
=> b = 3
Substituting all the values ,
Equation of Hyperbola is (x+ 2)²/25 - (y)²/ 9 = 1
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