The required vertices of hyperbola is given as (3, 5±√38).
What is an hyperbola?Hyperbola is part of conic section, and its equation is given as,
[tex](x - h)^2/a^2 + (y - k)^2/b^2 = 1[/tex], where h,k is center and a and b are the lengths of the semi-major and the semi-minor axes.
Here,
Given equation of hyperbola,
36x²-y^²-216x+10y+261=0
Equation of hyperbola in vertex form is given as,
(x - 3)²/(19/18) - (y - 5)²/38 = 1
From above equation,
h = 3 k = 5 a = √38/6 and b = √38
Vertices of the hyperbola is given as,
(h, k ± b) = (3, 5±√38)
Thus, the required vertices of hyperbola is given as (3, 5±√38).
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Use the number line to answer the question. A number line is shown with end points marked at the 2 and 2 tenths and 2 and 3 tenths. There are 9 tick marks between the two end points. Point H is on the third mark after 2 and 2 tenths. What is the decimal value of point H? Enter the answer in the box.
The decimal value of point H is then approximately 0.033333.
How to solve:
We must translate the position of the third mark after 2 and 2 tenths into a decimal value in order to determine the decimal value of point H.
We can determine the distance between each tick mark by dividing the distance between the two end points (2.3 - 2.2 = 0.1) by the total number of tick marks (9) because there are nine tick marks between the end points.
To get to point H, we can multiply the distance between each tick mark by the number of ticks: 0.1 / 9 = 0.011111.
The decimal value of point H is then approximately 0.033333.
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100000+10000000000000=
Answer:
Step-by-step explanation:
The sum of 100,000 + 10,000,000,000,000 is 10,000,100,000,000.
What is the probability that either event will occur?
Now, find the probability of event A and event B.
A
B
6
6
20
20
P(A and B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Enter
The probability that either event will occur is 0.62
What is the probability that either event will occur?From the question, we have the following parameters that can be used in our computation:
Event A = 6 + 6 = 12
Event B = 20 + 6 = 26
Both A and B = 6
Other Events = 20
Using the above as a guide, we have the following:
Total = A + B + C + Others - Both
So, we have
Total = 12 + 26 - 6 + 20
Evaluate
Total = 52
So, we have
P(A) = 12/52
P(B) = 26/52
Both A and B = 6/52
For either events, we have
P(A or B) = (12 + 26 - 6)/52
Evaluate
P(A or B) = 0.62
Hence, the probability that either event will occur is 0.62
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Jai spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 5375 feet. Jai initially measures an angle of elevation of 15° to the plane at point A. At some later time, he measures an angle of elevation of 30° to the plane at point B. Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary.
The distance that the plane traveled from point A to point B is given as follows:
10,750 ft.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.The altitude of 5375 feet is the opposite angle, hence the position A is obtained as follows:
tan(15º) = 5375/A
A = 5375/tangent of 15 degrees
A = 20060 ft.
The position B is obtained as follows:
B = 5375/tangent of 30 degrees
B = 9310 ft.
Hence the distance is of:
20060 - 9310 = 10,750 ft.
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What is the sum of the interior angles of the polygon shown below?
Answer: 360 degrees.
Step-by-step explanation: The sum of the interior angles in a quadrilateral is always 360.
(you can check using the formula 180(n-2), where n is the number of sides.)
select all answers that are similar to polygon K
Answer:
B, C, D
Step-by-step explanation:
You want to identify the shapes that are similar to polygon K.
Right trianglePolygon K is a right triangle that has leg lengths in the ratio 4:2 = 2:1.
Polygons B, C, and D are right triangles similar to polygon K:
B is a dilation by a factor of 1/2C is a reflection of BD is a rotation of KOthersPolygons A and E are also right triangles, but have different ratios of leg lengths. In A they are 1/1, and in E they are 4/3. These triangles are not similar to triangle K.
__
Additional comment
Polygons similar to the same polygon are similar to each other. Rigid transformations such as reflection and rotation result in figures congruent to the original. Congruent figures are also similar.
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Work out the integer values
Please help, I attached a photo.
Step by step explanation if possible :)))
The integers that satisfy the inequality are -1, 0, 1, and 2.
To find the integer values that satisfy the inequality x < 6/(x - 1), we can start by analyzing the domain of the expression.
First, note that the denominator (x - 1) cannot be equal to zero since division by zero is undefined. Therefore, we must exclude x = 1 from the domain.
Next, consider the sign of the expression 6/(x - 1). When the denominator (x - 1) is positive, the expression will be positive. Similarly, when the denominator is negative, the expression will be negative.
Considering the inequality x < 6/(x - 1), we can divide the problem into two cases based on the sign of (x - 1):
Case 1: (x - 1) > 0
In this case, the expression 6/(x - 1) is positive. To satisfy the inequality x < 6/(x - 1), x must be less than the positive value of 6/(x - 1). Since the denominator is positive, we can drop the absolute value sign. Therefore, the inequality becomes:
x < 6/(x - 1)
Case 2: (x - 1) < 0
In this case, the expression 6/(x - 1) is negative. To satisfy the inequality x < 6/(x - 1), x must be greater than the negative value of 6/(x - 1). Since the denominator is negative, we need to flip the inequality sign and change the direction. Therefore, the inequality becomes:
x > 6/(x - 1)
Now, let's solve each case separately:
Case 1: (x - 1) > 0
Since the denominator (x - 1) is positive, we can multiply both sides of the inequality by (x - 1) without changing the direction of the inequality. This gives:
x(x - 1) < 6
Expanding the left side:
x² - x < 6
Rearranging the inequality:
x² - x - 6 < 0
Now we can factorize the quadratic:
(x - 3)(x + 2) < 0
To determine the solution, we need to consider the sign of the expression for different intervals:
When x < -2, both factors are negative, so the expression is positive.
When -2 < x < 3, the first factor (x - 3) is negative, and the second factor (x + 2) is positive, so the expression is negative.
When x > 3, both factors are positive, so the expression is positive.
Therefore, the solution to Case 1 is:
-2 < x < 3
Case 2: (x - 1) < 0
Since the denominator (x - 1) is negative, we need to flip the inequality sign. Multiplying both sides of the inequality by (x - 1) changes the direction of the inequality. This gives:
x(x - 1) > 6
Expanding the left side:
x² - x > 6
Rearranging the inequality:
x² - x - 6 > 0
Factoring the quadratic:
(x - 3)(x + 2) > 0
Considering the sign of the expression for different intervals:
When x < -2, both factors are negative, so the expression is positive.
When -2 < x < 3, the first factor (x - 3) is negative, and the second factor (x + 2) is positive, so the expression is negative.
When x > 3, both factors are positive, so the expression is positive.
Therefore, there are no solutions in Case 2.
Combining the solutions from both cases, we find that the integer values satisfying the inequality x < 6/(x - 1) are:
-2 < x < 3
In other words, the integers that satisfy the inequality are -1, 0, 1, and 2.
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Now, let’s rewrite our point-slope equation in slope-intercept form.
y−6=−2(x+2)
y−6=
x−4
y=−2x+2
Is this the same equation we got when we wrote it in slope-intercept form earlier? YES!
Any equation written in point-slope form can be rewritten in slope-intercept form and most of the time, we will rewrite them. Slope-intercept form is the most popular and used form of linear functions/equations. In Slope-intercept form, all like terms have been combined, therefore it is in simplified form. Remember that we always want the most simplified answer possible, unless otherwise directed!
The equation in slope-intercept form is,
y = - 2x + 2
We have to given that;
The point-slope equation is,
y - 6 = - 2 (x + 2)
Now, We can rewrite the equation in slope-intercept form as;
y - 6 = - 2 (x + 2)
y - 6 = - 2x - 4
y = - 2x - 4 + 6
y = - 2x + 2
Thus, the equation in slope-intercept form is,
y = - 2x + 2
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48 as a tree diagram prime factor
Answer:
48 prime factors are: 2 x 2 x 2 x 2 x 3
Can someone please me with this question.
Correct form of the area of compound shape is:
Given,
Compound shape including triangle and rectangle.
Firstly , calculate the area of rectangle:
Area of rectangle = l* b
l= length of rectangle
b = breadth of rectangle
Thus,
Area of rectangle = 12*m
Secondly, area of triangle,
Area of triangle = 1/2 *b * h
b = base of triangle
h = height of triangle
Base of triangle = 12 - n
Then,
Area of triangle = 1/2* (12 - n) *m
Area of triangle = 6m - 0.5mn
Now to calculate the total area of the compound shape,
Total area = Area of rectangle + Area of triangle
Total area = 12m + (6m - 0.5mn)
Total area = 18m - 0.5mn
Hence option 3 satisfies the area of the compound shape .
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Jackson bought 17 eggs from each farmer at the farmers’ market. Each farmer had an equal number of eggs.
Is this sample of eggs at the farmers market likely to be representative?
Without this information, it is not possible to determine if the sample accurately represents the overall distribution of eggs at the farmers' market.
It is impossible to say if the sample of eggs at the farmers' market is likely to be representative based on the information supplied. Jackson appears to have bought 17 eggs from each farmer, which suggests that he did so in an equal amount. It does not, however, provide data on the total number of farmers present at the market or their overall distribution of eggs.
Additional data, such as the total number of farmers present at the market, the average number of eggs each farmer generally has, and the variability in the number of eggs among the farmers, would be required to evaluate the sample's representativeness.
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(50 points) Please help me i would really appreciate it
calculate the value of x and y
(multiple choice)
x = [select]
- 140
-120
-160
-100
y= [select]
-50
-60
-80
70
The values of the angles x and y are ∠x = 110 and ∠y = 70
How to calculate the values of x and yFrom the question, we have the following parameters that can be used in our computation:
The lines (parallel, transversal and others)
The measure of angle 1 is calculated as
∠1 = 180 - 140 -- angle on a straight line
So, we have
∠1 = 40
Next, we have
∠2 = 180 - 40 - 80 --- corresponding angles
So, we have
∠2 = 60
This means that
∠y = 180 - 60 - 50 -- angle on a straight line
So, we have
∠y = 70
This also means that
∠x = 180 - 60 - 10 -- angle in a triangle
So, we have
∠x = 110
Hence, the values of x and y are ∠x = 110 and ∠y = 70
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What is the equation for the given graph expressed in the form of y = a|x – h| + k?
The equation of the graph in the required form is y = 5|x| - 5
How to determine the equation for the graphFrom the question, we have the following parameters that can be used in our computation:
The graph (see attachment)
The graph is an absolute value graph
And it can be expressed in the form of y = a|x – h| + k
Where
Vertex = (h, k)
The vertex of the graph is (0, -5)
So, we have
y = a|x| - 5
Using the point on the graph, we have
a|1| - 5 = 0
So, we have
a = 5
This means that the equation of the graph is y = 5|x| - 5
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What is the unit rate if you drove a go-kart 9 miles in 36 minutes?
Answer:
Step-by-step explanation:
To find the unit rate, we need to divide the distance traveled by the time taken.
In this case, the distance traveled is 9 miles, and the time taken is 36 minutes.
Unit rate = distance/time
Unit rate = 9 miles / 36 minutes
Simplifying the above expression by dividing both numerator and denominator by 9, we get:
Unit rate = 1 mile / 4 minutes
Therefore, the unit rate at which the go-kart is traveling is 1 mile per 4 minutes.
the area of a trapizoid is 150 square millimeters 7mm 16mm 13mm what is the trapezoids height
The height of the trapezoid is approximately 13.043 mm.
Understanding How to Solve TrapezoidTo find the height of a trapezoid, you can use the formula:
Area = 1/2 * (base1 + base2) * height
Given:
Area = 150 square millimeters
base1 = 7 mm , w
base2 = 16 mm
150 = 1/2 * (7 + 16) * height
150 =1/2 * 23 * height
Make height the subject of the formula
300 = 23 * height
height = 300 / 23
height = 13.043 mm (rounded to three decimal places)
Therefore, the height of the trapezoid is approximately 13.043 mm.
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If D = 2w? - w - 7 and C = 3w - 6, find an expression that equals D + 3C in
standard form.
The expression that equals D + 3C in standard form is 2w² + 8w - 25.
To find an expression that equals D + 3C in standard form, we first need to simplify D and C.
Starting with D = 2w² - w - 7, we can rearrange the terms to put it in standard form:
D = 2w² - w - 7
D = 2w² - 2w + w - 7
D = 2w(w - 1) + (w - 7)
Next, simplifying C = 3w - 6:
C = 3w - 6
Now, we can substitute these expressions into D + 3C:
D + 3C = (2w² - w - 7) + 3(3w - 6)
Expanding and simplifying:
D + 3C = 2w² - w - 7 + 9w - 18
D + 3C = 2w² + 8w - 25
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Find the measure of AB.
20,
E
61%
D
B
A
21. B
65°
D
C
22. A
B
E
D
91
To find the measure of angle AB, we can use the fact that the sum of the angles in a triangle is 180 degrees.
Given:
Angle A = 65 degrees
Angle B = 91 degrees
We can subtract the sum of these two angles from 180 degrees to find angle AB:
Angle AB = 180 - (Angle A + Angle B)
Angle AB = 180 - (65 + 91)
Angle AB = 180 - 156
Angle AB = 24 degrees
Therefore, the measure of angle AB is 24 degrees.
face pard He then decides to push the brick like a loy car 311 Mention the transformation of the brick when it is flipped or turned sideways $72 When the key is pushing the brick, without using or flipping the brick, what * What are the two differences between a rectangle and a paralelogram?
1. All angles of a rectangle are right angles (90 degrees), while the angles of a parallelogram can be any angle other than 90 degrees.
2. The opposite sides of a rectangle are equal in length, whereas in a parallelogram, opposite sides are of equal length as well, but they may not be perpendicular to each other.
The questions are a bit unclear and have some spelling errors, but I will try my best to provide an answer:
- Mention the transformation of the brick when it is flipped or turned sideways:
If the brick is flipped over, the transformation it undergoes is called a reflection. This can also be thought of as a mirror image of the original brick. If the brick is turned sideways, the transformation it undergoes is called a rotation. In a rotation, the object is turned about a point, and the image of the object appears to have been rotated around that point.
- When the key is pushing the brick, without using or flipping the brick, what... (I'm not sure what the question is asking for, as it seems incomplete or there is some text missing.)
- What are the two differences between a rectangle and a parallelogram?
In summary, the transformation of a flipped brick is a reflection, while a turned sideways brick undergoes a rotation. The differences between a rectangle and a parallelogram include the angles (all right angles for a rectangle and any angle other than 90 degrees for a parallelogram) and the opposite sides (equal length and perpendicular for a rectangle, equal length but not necessarily perpendicular for a parallelogram).
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A student’s course grades and their corresponding weights are given in the table.
What is the minimum grade needed on the final exam to earn an overall grade of 85% in the class?
The minimum grade needed to have overall grade of 85% in the class is 90%
What is percentage?A percentage is a number or ratio expressed as a fraction of 100. It is represented by by the symbol %.
Percentage can also be said as per 100
For example if there are total of 100 students in a class and their are 40 girls, the percentage of girls in the class is
40/100 × 100
= 40%
For the student to have a overall grade of 85%, the minimum grade in exam is calculated as
(100+70+80+x)/4 = 85
250+x = 340
x = 340 - 250
x = 90%
Therefore the minimum graded needed is 90%
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What formula would be used to find the future value? Return on balance 7.00% Monthly rate of return 0.583% Monthly payment -$200 Number of payments 120
Answer:
To calculate the future value (FV) of an investment with a given return on balance, monthly rate of return, monthly payment, and number of payments, you can use the future value of an ordinary annuity formula:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future value
P = Monthly payment
r = Monthly rate of return (expressed as a decimal)
n = Number of payments
In this case, the return on balance and the monthly rate of return are provided separately. To incorporate the return on balance into the monthly rate of return, you can use the following formula:
Effective Monthly Rate of Return = (1 + Monthly Rate of Return) * (1 + Return on Balance) - 1
Let's calculate the effective monthly rate of return using the given values:
Return on Balance = 7.00% (expressed as a decimal) = 0.07
Monthly Rate of Return = 0.583% (expressed as a decimal) = 0.00583
Effective Monthly Rate of Return = (1 + 0.00583) * (1 + 0.07) - 1
= 1.00583 * 1.07 - 1
= 1.0761281 - 1
= 0.0761281
Now that we have the effective monthly rate of return, we can use the future value formula to calculate the future value:
FV = -$200 * ((1 + 0.0761281)^120 - 1) / 0.0761281
Please note that since the monthly payment is negative (-$200), it indicates that it is an outgoing payment or an investment with regular withdrawals.
Calculating the above formula will give you the future value of the investment.
I hope I was helpful
help with geometry please‼️‼️
which of the decimals below are less than 0.7? select all that apply.
A) 0.65
B) 0.71
C) 0.54
D) 0.31
E) 0.84
Ace Autos sell cars and pay Sue each month as follows.
• a salary of £1410
• 26% of the total profit the company makes from her sales
• a £390 bonus if she sells at least 16 cars
The table shows information about the cars she sold last year.
Total cost to the
Total income for
Number of months when she
company
the company
sold at least 16 cars
£473 500
£549 000
4
Work out Sue's total pay for the year.
Sue's total pay for the year based on the values will be £38110
How to calculate the amountSue's total pay of year will have three parts
Fixed Salary for 12 months
one month salary = £1410
so 12 month salary = £1410 x 12 = £16920
26% of total profit
Total cost to the company- £473,500
Total income for the company - £549,000
Profit = Total income for the company - Total cost to the company
= £549,000 - £473,500 = £75500
Sues income from profit = 26% of £75500 = (26 × 75500)/100 = £19630
Bonus if Sue sells at least 16 cars
Given number of months when sue solds atleast 16 cars = 4
So bonus income = 4 × 390 = £1560
Adding the three above parts
Sue's total pay for the year = £16920 + £19630 + £1560 = £38110
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Complete question
Ace autos sell cars and pay sue each month as follows
-salary of £1410
-26% of the total profit the company makes from her sales
- a £390 bonus if she sells at least 16 cars
The table shows information about the cars she sold last year
Total cost to the company- £473,500
Total income for the company - £549,000
Number of months when she sold at least 16 cars - 4
work out sues total pay for the year
100 Points! Algebra question. Photo attached. Graph the function. Thank you!
The graph of the function is attached and the amplitude and the period are 5 and 2π
How to determine the amplitude and period of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 5cos(θ)
A sinusoidal function is represented as
f(x) = Acos(B(x + C)) + D
Where
Amplitude = APeriod = 2π/BSo, we have
A = 5
Period = 2π/1
Evaluate
A = 5
Period = 2π
Hence, the amplitude is 5 and the period is 2π
The graph of the function is attached
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area of a rectangular piece of cloth 3 1/4m by 25 cm
Answer:
8125 cm² (or 0.8125 m²)
Step-by-step explanation:
area of a rectangular piece of cloth 3 1/4m by 25 cm
the area of the rectangle is found by making the base by the height, we convert the meters into centimeters
3 1/4 m = 3.25m = 325 cm
we find the area
325 × 25 = 8125 cm² (or 0.8125 m²)
What is the amount of discount
Answer: 26.40
Step-by-step explanation:
Please help me important question in image
The following property must be given to prove that ΔCJG ~ ΔCEA: B. GJ║AE.
What are the properties of similar triangles?In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Additionally, the lengths of three (3) pairs of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.
Based on the side, side, side (SSS) similarity theorem, we can logically deduce the following congruent and similar triangles:
ΔCJG ≅ ΔCEA (line segment GJ is parallel to line segment AE)
ΔBIJ ≅ ΔBDF (line segment IJ is parallel to line segment DF).
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help me please with this question
Answer:A
Step-by-step explanation:
Which of these values for P and a will cause the function f(x)= Pa to be an
exponential growth function?
○ A. P= 1/2;a=1
OB. P = 2; a = 1
OC. P = 2; a = 3
O D. P = 1/2; a= 1/3
The values of P and a such that [tex]f(x) = Pa^x[/tex] is an exponential growth function are given as follows:
C. P = 2; a = 3.
How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The conditions for an exponential growth function are given as follows:
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What is the volume of a square based pyramid with based side lengths of 6cm, a slant height of 7 cm, and a height of 5cm
Answer:
60 cm^3
Step-by-step explanation:
The formula for volume of a pyramid is
V = 1/3Bh, where B is the area of the base and h is the regular height (aka the altitude that connects the top of the pyramid and the base so we can simply ignore the slant height in the problem)
Step 1: The base of a square pyramid is a square and the formula for area (A) of a square is A = s^2, where s is the side.
Since we're told that the length of the base side length is 6 cm, we can find the area of the base:
A = 6^2 = 36
Step 2: Now, we can plug in 36 for B and 5 for h in the volume formula to find the volume:
V = 1/3(36)(5)
V = 12 * 5
V = 60 cm^3