The answer is A. (x-1)²/16-(y-1)²/4=1. The standard form of the equation that describes the hyperbola is (x-1)²/16-(y-1)²/4=1.
What is hyperbola?A hyperbola is a two-dimensional, closed-curve shape with two branches, each of which is a mirror image of the other.
This equation is in the standard form of a hyperbola equation, which is
(x-h)²/a² - (y-k)²/b² = 1, where (h,k) is the center of the hyperbola and a and b are the distance from the center to the vertices of the hyperbola.
In this case, the center of the hyperbola is (1,1).
This can be determined by taking the average of the coordinates of the two vertices, (1,-1) and (1,3), which is (1,1).
The distance from the center to the vertices of the hyperbola is 8 for the x-coordinate, and 4 for the y-coordinate.
This can be determined by taking the difference of the coordinates of the vertices, which is 8 for the x-coordinate and 4 for the y-coordinate.
Therefore, the standard form of the equation that describes the hyperbola is (x-1)²/16-(y-1)²/4=1.
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Work out the highest common factor (HCF) of 8 and 20.
Answer: The HCF of 8 and 20 is 4. The factors of 8 are 1, 2, 4, 8, and the factors of 20 are 1, 2, 4, 5, 10, 20.
Step-by-step explanation: Please give Brainlist.
Hope this helps!!!!
find the area of the figure helppp end of the quarter
Answer:
Step-by-step explanation:
if the front says 5ft+5ft so it equals 10ft
12ft+12ft it equals 24ft
the missing area looks alot like the 5ft+5ft so we measure it...
both sides of the back equals to 5ft each 5ft+5ft=10ft
so just put in the end of the quarter equals 10ft
and if he/she wants you to add it all together it all adds up to 44ft...
WILL MARK AS BRAINLIST PLEASE HELP!!
Answer:
a = 125°
Step-by-step explanation:
Angle a and 55° together make up a straight angle (a straight line) that is 180°.
Write an equation.
a + 55° = 180°
subtract 55° from both sides.
a = 180°- 55°
a = 125°
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If A = 68 kilometers and B =51 kilometers, what is c? If necessary, round to the nearest tenth.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{68}\\ o=\stackrel{opposite}{51} \end{cases} \\\\\\ c=\sqrt{ 68^2 + 51^2}\implies c=\sqrt{ 4624 + 2601 } \implies c=\sqrt{ 7225 } \implies c=85[/tex]
Find the quotient. 98.3÷7 7598.3
Find an equation for the line perpendicular to 4x + 36y= 288 and goes through
the point (10,8).
Write your answer in the form y = mx + b.
The equation of the line perpendicular to 4x + 36y = 288 and passing through the point (10, 8) is: y = 9x - 98
Calculating the equation of the perpendicular lineTo find the equation of the line perpendicular to 4x + 36y = 288, we need to first find the slope of the given line.
We can rewrite the equation in slope-intercept form y = mx + b by solving for y:
4x + 36y = 288
36y = -4x + 288
y = (-1/9)x + 8
Therefore, the slope of the given line is -1/9
The slope of a line perpendicular to this line is the negative reciprocal of the slope of the given line.
So, the slope of the line we want to find is:
m = -1 / (-1/9) = 9
The equation is then calculated as
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point.
Plugging in the values, we get:
y - 8 = 9(x - 10)
Simplifying, we get:
y = 9x - 98
Therefore, the equation of the line perpendicular is: y = 9x - 98
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What is the value of the expression below when w=4
Answer:2(3)
Step-by-step explanation: 3w-3w+8
2with a power 3
Answer:
= 44
Step-by-step explanation:
3w² - 3w + 8
When
w = 4
Then:
3*4² - 3*4 + 8
= 3*16 - 12 + 8
= 48 - 12 + 8
= 48 + 8 - 12
= 56 - 12
= 44
.The regression coefficient of Y on X = 1.2 . If
=
−100
2
=
−100
3
, find .
For the regression coefficient, the value of bvu is 0.8.
How to find bvu?Regression coefficient is a measure of the relationship between two variables in a regression analysis. It represents the degree of change in one variable for a unit change in another variable.
Recall that:
u = (x – a)/p
v = (y – c)/q
b[tex]_{yx}[/tex] = q/p × bvu
Given: u = (x-100)/2 and v = (y-200)/3
Thus, q = 3 and p = 2
Since the regression coefficient of Y on X = 1.2.
Thus, b[tex]_{yx}[/tex] = 1.2
b[tex]_{yx}[/tex] = q/p × bvu
1.2 = 3/2 * bvu
bvu = 1.2 * 2/3
Therefore, the value of bvu is 0.8
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Complete Question
The coefficient of regression on Y on X = 1.2.
If U = (x-100)/2 and V = (y-200)/3 .
Find bvu.
Determine the length of FE.
18
20
21
26
Using the concept of similar triangles, the length of FE is: 26
How to find the length of similar triangles?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. Thus, if two triangles are similar, then it means that their corresponding angles are congruent and corresponding sides are in equal proportion.
Using the concept of similar triangles and trigonometric ratios, we can apply that to the given diagram and say that:
tan E = 4/8 = 1/2
tan E = DF/FE
Thus:
1/2 = 13/(FH + HE)
1/2 = 13/(FH + 8)
FH = 18
FE = FH + HE
FE = 18 + 8
FE = 26
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thanks froggy for all the help i need more help
Answer:
∠KRL is 34°.
Hope this helps!
Step-by-step explanation:
∠KRL is a vertical angle to ∠QRP ( meaning they have the same angle ).
∠HM is a 180° angle and ∠PRM is a 90° angle which means ∠HRP is also a 90° angle. ∠HRQ plus ∠QRP is equal to 90°, ∠HRQ is 56° which means ∠QRP is 90° - 56° which is 34°. That means ∠KRL is also 34°.
What is the volume of the cone in cubic feet?
hope you understood the answer
option A
Solve For B. 47.5 degrees, 79.5 degrees
53 is the answer
47.5 + 79.5= 127
180-127=53
Scenario:
JRJ Corporation recently issued 10-year bonds at a price of $1,000. These bonds pay $60 in interest each six months. Their price has remained stable since they were issued, that is, they still sell for $1,000. Due to additional financing needs, the firm wishes to issue new bonds that would have a maturity of 10 years, a par value of $1,000, and pay $40 in interest every six months. If both bonds have the same yield, how many new bonds must JRJ issue to raise $4,000,000?
5190 new bοnds must be JRJ issued tο raise $4,000,000.
What is the interest rate?The amοunt οf interest due each periοd expressed as a percentage οf the amοunt lent, depοsited, οr bοrrοwed is knοwn as an interest rate. The tοtal interest οn a lοaned οr bοrrοwed sum is determined by the principal amοunt, the interest rate, the frequency οf cοmpοunding, and the periοd οf time the lοan, depοsit, οr bοrrοwing tοοk place.
Here, we have
Given: JRJ Cοrpοratiοn recently issued 10-year bοnds at a price οf $1,000. These bοnds pay $60 in interest every six mοnths. Their price has remained stable since they were issued, that is, they still sell fοr $1,000.
Cοupοn rate = 8.0%
Face value = 1000
Year tο maturity = 10
NPER = 20
PMT = Face value × Cοupοn rate / 2 =(1000 × 0.08) / 2 = 80/2 = 40
Yield = 12%
Rate = Yield / 2 = 12% / 2 = 6%
We then calculate the net prοceeds which will be:
= PV(rate, NPER, PMT, FV)
= PV(6%, 20, 40, 1000)
= $770.60
We shοuld nοte that the amοunt that needed tο be raised is $4,000,000. Therefοre, the bοnd that will be needed tο be sοld will be:
= $4,000,000 / 770.60
= 5190bοnds
Hence, 5190 new bοnds must JRJ issued tο raise $4,000,000.
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Replace each * with a digit that makes the solution of the equation a whole number. Find all possibilities.
5x – 124=10*
Answer:* = 50
Step-by-step explanation:
x = 75.2 5x -124 =500
10 times 50 =500
In a cross-country race, Duante took 8/9 as long as James to finish. Kofi took 7/8 as long as James to finish. Who took the longest to finish the race?
Using the LCM formula, it is deduced that James took the longest to finish the race.
What is LCM?
In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple. The smallest number among all the common multiples of the provided numbers is the least common multiple of two or more numbers.
Let's assume that James took time "J" to finish the race. Then -
Duante took 8/9 of James' time, which is (8/9)J
Kofi took 7/8 of James' time, which is (7/8)J
To determine who took the longest to finish the race, we need to compare their times.
Let's start by comparing Duante and James -
Duante's time = (8/9)J
James' time = J
Since Duante took less time than James, we can conclude that James did not take the longest to finish the race.
Now let's compare Kofi and James -
Kofi's time = (7/8)J
James' time = J
To compare these times, we need to express them with a common denominator.
The least common multiple of 8 and 1 is 8, so we can rewrite James' time as (8/8)J:
Kofi's time = (7/8)J
James' time = (8/8)J
Now we can compare the times -
Kofi's time = (7/8)J < (8/8)J = James' time
Therefore, Kofi took the least time to finish the race, and James took the longest.
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help now pls !!!!!!!!!!!!!!!!!!!!!
Answer: it was another reason for the United States to join the war in the side of the Allie’s.
Step-by-step explanation:
Give one example of matrix of order 2 and 3 in which industrial
World problem is mentioned. Also solve them by using matrix
Inversion method.
It would take 90 hours on the first machine, 20 hours on the second machine, and 0 hours on the third machine to produce 100 units of Product A and 50 units of Product B.
What is matrix ?
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.
Here is an example of a 2x3 matrix that represents a problem in industrial engineering:
Suppose a company produces two types of products, Product A and Product B, and they use three different machines to manufacture these products. The number of hours required to produce each unit of each product using each machine is given by the following matrix:
| 2 3 4 |
| 4 2 3 |
This matrix represents a system of linear equations that can be solved using matrix inversion to find the number of hours required to produce a given number of units of each product. For example, suppose the company needs to produce 100 units of Product A and 50 units of Product B. To find the number of hours required for each machine, we can set up the following system of equations:
2x + 3y + 4z = 100
4x + 2y + 3z = 50
where x, y, and z represent the number of hours required for each machine.
To solve this system of equations using matrix inversion, we can first write the system in matrix form:
| 2 3 4 | | x | | 100 |
| 4 2 3 | * | y | = | 50 |
| 0 0 0 | | z | | 0 |
Next, we need to find the inverse of the coefficient matrix:
| 2 3 4 |^-1 = 1/10 | -6 12 -3 |
| 4 2 3 | | 9 -6 4 |
| 0 0 0 | | 0 0 0 |
Finally, we can solve for x, y, and z by multiplying both sides of the equation by the inverse of the coefficient matrix:
| x | | -6 12 -3 | | 100 | | 90 |
| y | = | 9 -6 4 | * | 50 | = | 20 |
| z | | 0 0 0 | | 0 | | 0 |
Therefore, it would take 90 hours on the first machine, 20 hours on the second machine, and 0 hours on the third machine to produce 100 units of Product A and 50 units of Product B.
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Find the solution of
{Y≤-x² - 4x +3
Y>x^2+3
Thus, shaded region bounded between the interval (-2,7) and (0,3) are the solution of the given linear inequalities.
Explain about the graphical method?The 2 linear programming is optimised using the graphical approach. Finding the ideal answer is best done using a graphical approach when there are two choice factors in the problem. The collection of inequalities are bound by limitations in this method. The disparities are then shown using an XY plane graphic.
To represent the data visually, there are two different sorts of graphs. As follows: Time Series Graphs - Line Graph as an example. Frequency Polygon Graph is an illustration of a frequency distribution graph.For charting linear functions, there are three fundamental techniques. The first method involves tracing a line through a set of points that have been plotted. The second method makes use of the slope and y-intercept. The third method involves changing the identity function f(x)=x.Given linear inequalities are:
Y ≤ -x² - 4x +3
Y > x² + 3
Plot the graph of each equation using the graphing tool to get he solution.
From the graph:
Blue Region : Y ≤ -x² - 4x +3
green region: Y > x² + 3
Thus, shaded region bounded between the interval (-2,7) and (0,3) are the solution of the given linear inequalities.
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Find the perimeter of the triangle whose vertices are the following specified points in the plane.
(-9,-5), (-6,1) and (5,8)
After calculating the lengths of all 3 sides, we need to add them together to get the perimeter, which is 32.
Perimeter = 32
To find the perimeter of a triangle whose vertices are specified points in the plane, we need to first calculate the lengths of the 3 sides of the triangle. To do this, we need to use the distance formula, which is the square root of (x2 - x1)^2 + (y2 - y1)^2. To calculate the first side, we need to calculate the distance between (-9,-5) and (-6,1), which is 7.14. For the second side, we need to calculate the distance between (-6,1) and (5,8), which is 11.18. For the last side, we need to calculate the distance between (5,8) and (-9,-5), which is 14.86. After calculating the lengths of all 3 sides, we need to add them together to get the perimeter, which is 32.
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The circle below is centred at O.
a) Work out the size of angle X.
b) Which of the circle theorems below allows you to calculate this angle?
Answer:
61∘
Step-by-step explanation:
Isosceles triangle property:
The triangle in the circle is an isosceles triangle, so that means the lateral sides of the triangle are equal, and so are the angles;
x = 90∘ - 29∘ = 61∘ (90∘, because the tangent and the radius form a right angle (that the b) part, I think))
Neeed helpppp pleaseeee
Answer:
b. 840
Step-by-step explanation:
7!/3! is the same thing as saying (7*6*5*4*3*2*1)/(3*2*1). The 3*2*1 simplifies to 1 so the simplified expression is 7*6*5*4. If you compute that, you will get the answer is 840, b.
slove the trig problems using the ratios. Remember to use SOH-CAH-TOA
1. solve for side x x = ___
2.solve for side x x = ___
3. solve for angle x x = ____
4. solve for angle x x = ____
thank you
Answer:
Step-by-step explanation:
1/3 ÷ 4 show your work
Answer:
Forma exacta:
1
12
Forma decimal:
0.083
Step-by-step explanation:
Answer:
[tex] \frac{1}{12} [/tex]
[tex]0.8333... [/tex]
as decimal form
A company starts to track the number of phone calls recived each month. Infromation about the number of phone calls the company recived the first three months of tracking is listed below.
-During the first month, the company recieved 4,264 phone calls.
-during the second months, the company recieved 25% more phone calls than in the first month.
-during the third month, the company recived 6,396 phone calls
What was the percent in crease in the number of phone calls from the second month to the third month?
The number of phone calls received in the second month is 25% more than the first month, which means:
Number of phone calls in second month = 1.25 x 4,264 = 5,330
To find the percent increase from the second month to the third month, we can use the percent increase formula:
Percent increase = (New value - Old value) / Old value x 100%
Using this formula, the percent increase from the second month to the third month is:
Percent increase = (6,396 - 5,330) / 5,330 x 100%
= 20%
Therefore, the percent increase in the number of phone calls from the second month to the third month is 20%.
Hunter's math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit. Based on the line of best fit, what quiz score should someone who studied 6 hours expect?
Therefore, we can say that after studying 2.5 hours, a student should expect a quiz score of 81.6 based on the line of best fit.
What is line of best fit?A line of best fit, also known as a trend line, is a straight line that is drawn through a scatter plot to represent the general trend or pattern of the data. It is used to show the relationship between two variables, usually the independent variable (x) and the dependent variable (y), by fitting a line that comes as close as possible to all the data points. The line of best fit can be used to make predictions about future data points or to estimate values of the dependent variable for certain values of the independent variable. The most common method for finding the line of best fit is the method of least squares, which minimizes the sum of the squared differences between the actual data points and the predicted values of the dependent variable on the line.
Here,
The point (2.5, 81.6) represents a data point on the coordinate axes, where the x-coordinate of 2.5 represents the number of hours studied and the y-coordinate of 81.6 represents the quiz score earned by a student who studied for 2.5 hours.
Based on the line of best fit that the math teacher drew, we can use this point to estimate the quiz score for other students who also study for 2.5 hours. The line of best fit is a straight line that passes through the average point of all the data points and is used to predict one variable (quiz score) based on another variable (hours studied).
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Complete question:
Hunter's math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit. What does the point (2.5,81.6) represent?
After studying 81.6 hours, a student should expect a score of 2.5. A student who actually spent 81.6 hours studying and got a score of
2.5. A student who actually spent 2.5 hours studying and got a score of 81.6. After studying 2.5 hours, a student should expect a score of 81.6.
how do you solve this?
Answer:
Step-by-step explanation:
a 3.75 kg stone hanging from a rope
vector or scalar? and why?
The object represented by a 3..75 kg stone is scalar object
How to determine if the object is scalar or vectorThe quantity "3.75 kg" is a scalar because it is a single value that only has magnitude, and it does not have a direction associated with it.
On the other hand, the force of gravity acting on the stone and the tension force of the rope holding the stone up are vector quantities because they have both magnitude and direction.
It is important to note that the stone itself does not have a direction associated with it, but the forces acting on it do have direction.
Therefore, when describing the motion of the stone, both scalar and vector quantities are involved.
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Is 92 divisible of 3
Answer:No but it is 30.7
Step-by-step explanation:
Answer: No, 92 isn't divisible of 3.
Step-by-step explanation: We can see that the sum of the digits in this case is 11 and this number is not divisible by 3, which means that 92 is also not divisible by 3.
A packaging employee making $20
per hour can package 160 items
during that hour. The direct
material cost is $.50 per item. What
is the total direct cost of 1 item?
Answer:
To find the total direct cost of one item, we need to calculate the sum of the direct labor cost and the direct material cost.
Direct labor cost per item = (hourly rate)/(number of items per hour) = $20/160 = $0.125 per item
Direct material cost per item = $0.50 per item
Total direct cost per item = direct labor cost per item + direct material cost per item
= $0.125 + $0.50 = $0.625
Therefore, the total direct cost of one item is $0.625.
Type the correct answer in each box.
Compete the statement about these similar cylinders.
Figure 1
D.
9 in
E 4.5 in
5 in
Figure 2
P.
R
The circumference of the base of figure 2 is
(Hint: The circumference of a circle = 2rr and the area of a circle = n², where r is the radius.)
and the area of a
It inches, and the area of the base of figure 2 is
[]
π square inches.
Therefore, the completed statement is: The circumference of the base of Figure 2 is 9π inches, and the area of the base of Figure 2 is 20.25π square inches.
What is area?Area is a measure of the size of a two-dimensional surface or region, typically expressed in square units. It is the amount of space inside a closed shape, such as a square, rectangle, triangle, circle, or any other shape with a well-defined boundary. The concept of area is used in many areas of mathematics, science, and engineering, such as geometry, calculus, physics, and architecture. For example, engineers need to calculate the area of materials, such as the cross-sectional area of a pipe or the surface area of a building, in order to design structures that are strong, efficient, and safe.
Here,
The missing information in the statement can be found by using the given dimensions of the cylinders.
Figure 1 has a height of 9 inches and a radius of 4.5 inches.
Figure 2 is similar to Figure 1, so its height and radius are proportional to those of Figure 1. Let the height of Figure 2 be h inches and the radius be r inches. Then we have:
h/r = 9/4.5 = 2
So the height of Figure 2 is twice the radius.
The circumference of the base of Figure 2 is 2πr, which is equal to 2π(4.5) = 9π inches.
The area of the base of Figure 2 is πr², which is equal to π(4.5²) = 20.25π square inches.
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Answer:
The circumference of the base of figure 2 is 5 π inches, and the area of the base of figure 2 is 6.25 π square inches.
Hope this helps!
Step-by-step explanation:
The cylinders are similar, not congruent. That means the shape is the same but the values are not. The radius of figure 1 ( 4.5 in ) is half of figure 1's height ( 9 in ). That means we can figure out that figure 2's radius will also be half its height ( 5 in ), figure 2's radius is 2.5 in. Plug 2.5 into the circumference and area formulas and you have figure 2's circumference and circle area.