so first off, we know the hyperbola has a horizontal traverse axis, so that means equation wise, the positive fraction is the one with the "x" variable on it, center is the origin, meaning (h,k) is just (0,0), and we know the value for the distances "a" and "c", let's find "b".
[tex]\textit{hyperbola, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ c=71000\\ a=45000 \end{cases}\implies \cfrac{(x- 0)^2}{ 45000^2}-\cfrac{(y- 0)^2}{ b^2}=1 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{c}{71000}=\sqrt{\underset{ a }{45000^2}+b^2}\implies 71000^2=45000^2+b^2 \\\\\\ 71000^2-45000^2=b^2\implies \sqrt{71000^2-45000^2}=b\implies 54918.12\approx b \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(x- 0)^2}{ 45000^2}-\cfrac{(y- 0)^2}{ 54918.12^2}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{ 45000^2}-\cfrac{y^2}{ 54918.12^2}=1 \end{array}}[/tex]
Answer:16000
Step-by-step explanation:
b
PLS HELP RIGHT NOW, IT'S URGENT
which of the following equations has exactly one solution?
A. 3x+5-x-2x=1
B. 8-2(x+1)=6x+6
C. 5x+3+x=3(2x+1)
D. 4(x-4)= 2x+2(x-4)
A. 3x+5-x-2x=1 has only one solution.
To have exactly one solution, the equation must be consistent (have a solution) and not have infinitely many solutions. An equation will have infinitely many solutions if both sides of the equation simplify to the same expression, meaning that any value of x that satisfies one side of the equation will also satisfy the other side. Therefore, we need to simplify each equation and check for consistency and the possibility of infinitely many solutions.
A. 3x + 5 - x - 2x = 1
Simplifying, we get:
0 = -6x - 4
6x = -4
x = -2/3
This equation is consistent and has exactly one solution, x = -2/3.
B. 8 - 2(x + 1) = 6x + 6
Simplifying, we get:
6 - 2x = 6x + 6
-8x = 0
x = 0
This equation is consistent, but it simplifies to -8x = 0, which means that any value of x will satisfy the equation. Therefore, this equation has infinitely many solutions.
C. 5x + 3 + x = 3(2x + 1)
Simplifying, we get:
6x + 3 = 6x + 3
0 = 0
This equation simplifies to 0 = 0, which means that any value of x will satisfy the equation. Therefore, this equation has infinitely many solutions.
D. 4(x - 4) = 2x + 2(x - 4)
Simplifying, we get:
4x - 16 = 4x - 8
-16 = -8
This equation simplifies to -16 = -8, which is not true for any value of x. Therefore, this equation is inconsistent and has no solutions.
Therefore, the only equation that has exactly one solution is A. 3x + 5 - x - 2x = 1.
Learn more about linear equations:
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A. 3x+5-x-2x=1 has only one solution.
To have exactly one solution, the equation must be consistent (have a solution) and not have infinitely many solutions. An equation will have infinitely many solutions if both sides of the equation simplify to the same expression, meaning that any value of x that satisfies one side of the equation will also satisfy the other side. Therefore, we need to simplify each equation and check for consistency and the possibility of infinitely many solutions.
A. 3x + 5 - x - 2x = 1
Simplifying, we get:
0 = -6x - 4
6x = -4
x = -2/3
This equation is consistent and has exactly one solution, x = -2/3.
B. 8 - 2(x + 1) = 6x + 6
Simplifying, we get:
6 - 2x = 6x + 6
-8x = 0
x = 0
This equation is consistent, but it simplifies to -8x = 0, which means that any value of x will satisfy the equation. Therefore, this equation has infinitely many solutions.
C. 5x + 3 + x = 3(2x + 1)
Simplifying, we get:
6x + 3 = 6x + 3
0 = 0
This equation simplifies to 0 = 0, which means that any value of x will satisfy the equation. Therefore, this equation has infinitely many solutions.
D. 4(x - 4) = 2x + 2(x - 4)
Simplifying, we get:
4x - 16 = 4x - 8
-16 = -8
This equation simplifies to -16 = -8, which is not true for any value of x. Therefore, this equation is inconsistent and has no solutions.
Therefore, the only equation that has exactly one solution is A. 3x + 5 - x - 2x = 1.
Learn more about linear equations:
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Solve and show each step
Answer: C
Step-by-step explanation:
Let's check each one:
A-
The graph is linear, but it says non-linear
B- Lets take point 4, 10
Y=-x+18
-4+18=14
So, y[tex]\neq[/tex]-x+18
C- Let's take point 4,10
Y=-2x+18
-8+18=10
y does =-2x+18
D- wrong since C is right
Answer:
The correct answer is C.
Step-by-step explanation:
First off, identify the y-intercept. In this case, the y-intercept, or b, is 18. Now that we got the y-intercept, we have to identify if the slope is going up or down. In this particular case, the slope is going down, so the slope is negative. Slope is always delta y over delta x, rise over run in how they teach this in schools, so we have to find two points in particular. I chose (0, 18) and (2, 14) since they're the easiest to find out. We do 18 minus 14, which gives us 4. We then do 0 minus 2, giving us negative 2. 4 over negative 2 is negative 2, which is our slope. We try to match this with one of our answers, and C gives us an exact replica. C is the correct answer.
Use the graph to answer the question.
Graph of polygon ABCDE with vertices at negative 3 comma 3, negative 3 comma 6, 1 comma 6, 1 comma 3, negative 1 comma 1. A second polygon A prime B prime C prime D prime E prime with vertices at negative 5 comma 3, negative 5 comma 6, negative 9 comma 6, negative 9 comma 3, negative 7 comma 1.
Determine the line of reflection.
Reflection across x = −4
Reflection across y = 1
Reflection across the x-axis
Reflection across the y-axis
Answer:
The line of reflection is x = 4, since the line x = 4 divides the original polygon and its image into congruent halves.
Step-by-step explanation:
ABCDE polygon graph with vertices at bottom 1 comma 6, 1 comma 3, negative 1 comma 1, 3 commas, 3 commas, and 1 comma. cross-axis reflection.
A polygonal shape is what?A polygon is a two-dimensional, closed structure that is flat or planar and has straight sides. It lacks crinkled sides. The edges of a polygon are also referred to as its sides.
Describe polygons with an example.Any two-dimensional form that can be made entirely of straight lines is referred to be a polygon. Polygons include forms like triangles, hexagons, pentagons, and quadrilaterals. The name of the shape has a side count indication.
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Determine the line of reflection.
Reflection across the x-axis
Reflection across the y-axis
Reflection across x = 6
Reflection across y = −4
Answer:
The answer is the 4th option! (Reflection across y = -4)
Step-by-step explanation:
If you have any questions please ask me! :)
Polygon JKLM is drawn with vertices J(−4, −4), K(−4, −6), L(−1, −6), M (−1, −4). Determine the image coordinates of L′ if the preimage is reflected across y = −2.
L′(−3, 6)
L′(−1, 6)
L′(−1, 2)
L′(1, 2)
Answer:
The answer is L'(-1, -2)
Step-by-step explanation:
If you have any questions ask me please! :)
(25 POINTS) Use the drop-down menus and enter values to complete the statements below.
Answer:
1. Greater than or equal to
2. a. 4 b. 4 or anything above four
3. Greater than or equal to
4. a. -4 b. -4 or anything above -4
Step-by-step explanation:
Hope this helps
Solve and show each step
Answer:
A. Slope = 5/2 , y-intercept = -10
Step-by-step explanation:
To find the y-intercept, it is always at the point on the y-axis where x=0. In the graph, the function crosses over -10 at x=0. So the y=intercept would be -10.
The slope "equation" is rise/run, aka y / x. In this case, an easy way to find it is by taking the y-intercept and seeing how far it is away from the origin. It is 10 away from the origin. Since this graph is heading right and upwards, it is increasing, resulting in the slope being positive. To find the "x" portion, from the origin, find when the graph crosses the x-intercept (the point where the line crosses through the x-axis). In this case, it will be 4.
Now that we know our y value and x value, put them into the slope formula.
Slope = rise/run --> 10/4 ---> 5/2
The net of a right circular cylinder is shown.
net of a cylinder where the radius of each circle is labeled 5 meters and the height of the rectangle is labeled 8 meters
What is the surface area of the cylinder? Use π = 3.14 and round to the nearest whole number.
220 m2
283 m2
408 m2
628 m2
Answer: Your answer is 408 m2
Step-by-step explanation: I've done that before in middle school.
Hope it helped :D
PLSSS LOOK AT IMAGE, I NEED HELP
Answer: 33.3%
Step-by-step explanation:
Since you want numbers less than 3, that would mean you want the sides with #1 and #2. And since there are six sides on the dice, you would put the number of sides you wish over the total number of sides. This would be 2/6 which could be simplified to 1/3 and if you want a decimal answer divide 1/3 to get a repeating decimal then move two decimal places to the right to make it 33.3% (This is rounded to the nearest tenth decimal place)
find the probability of drawing a black face card on the first draw, replacing it, and drawing a red card on the second draw. please show work.
Answer:
Half the cards in the deck are black. Your chance of drawing one is 1/2.
Step-by-step explanation:
Four cards in the deck are jacks. Your chance of drawing one is 4/52, which is 1/13.
The chance of you doing so on two draws, with replacement, is 1/2*1/13, or 1/26.
3. Write an expression to represent "6 more than y"
Answer: y+6
Step-by-step explanation:
In order to do this, we do 6 more than y. More than is going to be addition, and we get y+6 since it is 6 more than y.
PLEASE HELP NOW!!!!!
1 in 1/2 + 2 in 2/1 + 2 in 4/2 + 3 in 1/2 + 3 in 4/2 +?
Need an answer ASAP!
Answer:
74%
Step-by-step explanation:
$1983.20/ $2680 ×100= 74
=74%
Answer:26%
Step-by-step explanation:
HELP ME WITH THESE LAST 3 PLEASE
number each with answer
Thank you so much for people who helped me with my work because I really need it I’m behind
Answer:
Step-by-step explanation:
First image:
.0000625 m/s
.0003125 m
Second image:
1080
4320
Third
2240 g
Answer: First image:.0000625 m/s.0003125 mSecond image:10804320Third2240 g
Step-by-step explanation:
yo bro need help with assigments
Write the equivalent percent for each fraction.
7/2
4/1,000
10/25
3/8
Please help
Answer:
[tex]\frac{7}{2}[/tex] = 350%
[tex]\frac{4}{1000}[/tex] = 0.4%
[tex]\frac{10}{25}[/tex] = 40%
[tex]\frac{3}{8}[/tex] = 37.5%
How to change a fraction into a percentage?
To change a fraction to a percentage, you can divide the numerator by the denominator then multiply the result by 100. Alternatively, you can multiply the numerator by 100 first then divide the result by the denominator of the fraction.
Hope this helps :)
Pls brainliest...
Last one!! thank you
Answer: 30 60
Step-by-step explanation:
30 mi/hr
60 mi
Answer:
30 mph
60 miles in 2 hours
Step-by-step explanation:
(Comparing Data MC)
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 10,16,20, and 28. There are two dots above 8 and 14. There are three dots above 18. There are four dots above 12. The graph is titled Bus 14 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.
Bus 14, with an IQR of 6
Bus 18, with an IQR of 7
Bus 14, with a range of 6
Bus 18, with a range of 7
Answer:im not too sure but I think it was b
Step-by-step explanation:
Replace the question mark with the answer.
√(5/6)^2 = ?
Answer:
0.83333333333 or 5/6
Step-by-step explanation:
Always do the parenthesis first
Then engage with the ^2
Then take the sq root of that answer
Answer:
0.833333.... or 5/6
Step-by-step explanation:
There are 2 ways to do this:
1) Since you have a square root followed by an immediate square, they cancel each other out, so you are left with 5/6
2) Take the long way and actually take the square root of 5/6 then square it, which would still give you 5/6
hope this helps :)
50 PTS HURRY PLS PLS PLS
Match each description to its example.
1. (2, -3) → (-2, -3)
reflection across the y-axis
2. (2, -3) → (-3, 2)
reflection across the x-axis
3. (2, -3) → (-2, 3)
not a reflection
4. (2, -3) → (2, 3)
reflection across both axes
Answer:
1. a
2. d
3. c
4. b
Step-by-step explanation:
Answer:
1. reflection across the y axis
2. not a reflection
3. reflection across both axes
4. reflection across x axis
8th grade math i mark as brainliest
Answer: 1/16
Step-by-step explanation:
Answer: 1/16
Step-by-step explanation:
probability of 4
P(4)=1/4
probability of 6
P(6)=1/4
Because there is an "and" in the question and not an or you mulitiply the 2 probabilities
P(4 and 6)=(1/4)(1/4 = 1/16
Match the following.
Column A
1. How should a polygon be constructed triangle?
2. How can you relate construction of polygons to your every day life?
3. Why is it important to know the different kinds of polygons?
4. What do we need to know for polygon?
5. What is the basic construction of polygons?
Column B
A. Three edges of equal legth and tree angles between each pair of edges to be bo degree.
B. The squared form of the tiles you walk on indicates that they are polygons.
C. They teach us how to make patterns, how to use polygons to make other shape.
D. The side must be straight.
E. A regular polygon is a polygon that us equiangular and equilateral.
Question 1 — Answer E
Question 2 — Answer B
Question 3 — Answer C
Question 4 — Answer D
Question 5 — Answer A
Step-by-step explanation:COLUMN — A (Questions) COLUMN — B (Answers)How should a polygon be construct a triangle?ANSWER — A regular polygon is a polygon that is equiangular and equilateral.
How can you relate construction of polygons to your every day life?ANSWER — The squared from of the tiles you walk on indicate that they are polygons.
Why is it important to know the different kinds of polygons?ANSWER — They teach us how to make patterns, how to use polygon is to make other shape.
What do we need to know for a polygon?ANSWER — The side must be straight.
What is the basic construction of polygons?ANSWER — Three edges of equal length and three angles between each pair of edges to be 60 degree.
Hope my answer helps you.
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I will add you as my friend if you mark my answer as the BRAINLIEST.
Mrs. Williams has a prize box with different colored tickets.
Each ticket results in a different type of prize.
Pedro will randomly select a ticket, replace it, and then select another ticket.
What is the probability that he chooses a yellow ticket and then a purple ticket? This problem is based on Independent event problems.
Answer:
The probability that Pedro chooses a yellow ticket and then a purple ticket is A. 3/25
Answer:
The probability that Pedro chooses a yellow ticket and then a purple ticket is A. 3/25
pls help.....HEEEEELP
I think the answer is 29 cubic units.
12 on the bottom, 9 in the middle, and 8 on the top.
HELLOO HELPP PLSS!!!!!!!!!!!!
Answer: 1
Step-by-step explanation:
factors mean numbers that multiply to make other number
1, 2, 3, and 4 are all factors of 36 because thye all go in evenly os
4/4=1
FIRST ANSWER=BRAINLIEST ANSWER :))
Need an answer ASAP!!!
Answer:
C) 25%
Step-by-step explanation:
68.75 - 51.56 = 17.19
17.19 / 68.75 = .2500 estimated
0.2500 x 100 = 25.00%
25%
Need an answer ASAP!
Answer:
C) 11.5%
Step-by-step explanation:
5. A number cube with the numbers 1-6
on its sides is rolled twice. What is the
probability of rolling ________
(a) a 1 and then a 6
(b) an even number and then an odd
number
(c) a number less than 3 and then a
number greater than 3
Write the probability as a reduced fraction
Part - A = 1/36
Part - B = 1/4
Part - C = 1/6
Step-by-step explanation (Part - A):The numbers on the cube are, 1 , 2 , 3 , 4 , 5 and 6.
Formula to calculate probability =
Total Number of the particular number / Total Number of Numbers
The probability of rolling 1 is 1/6 as there is only one 1 in a numbered cube.
The probability of rolling 6 is 1/6 as there is only one 6 in a numbered cube.
So, the probability of rolling 1 and 6 is 1/6 * 1/6.
The probability of rolling 1 and 6 = 1/36.
The numbers on the cube are, 1 , 2 , 3 , 4 , 5 and 6.
Formula to calculate probability =
Total Number of the particular number / Total Number of Numbers
The probability of rolling an even number is 3/6 = 1/2 because there are 3 even numbers in a numbered cube.
The probability of rolling an odd number is 3/6 = 1/2 because there are 3 odd numbers in a numbered cube.
So, the probability of rolling an even and an odd number is 3/6 * 3/6 = 1/2 * 1/2.
The probability of rolling an even and an odd number = 9/36 = 1/4.
The numbers on the cube are, 1 , 2 , 3 , 4 , 5 and 6.
Formula to calculate probability =
Total Number of the particular number / Total Number of Numbers
The probability of rolling a number that is less than 3 is 2/6 = 1/3 because there are 2 numbers that are less than 3 in a numbered cube.
The probability of rolling a number that is greater than 3 is 3/6 = 1/2 because there are 3 numbers that are greater than 3 in a numbered cube.
So, the probability of rolling a number that is less than 3 and a number that is greater than 3 is 2/6 * 3/6 = 1/3 * 1/2.
The probability of rolling a number that is less than 3 and a number that is greater than 3 is 6/36 = 1/6.
Hope my answer helps you.
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Answer:
pls mark "harendraganesh" as brainlist that was the best answer I have ever seen