The value of a, b, c, h, k, and foci coordinates are 4, 3, 5, 2, -1, and (5, 0) and (-5, 0) respectively.
What is hyperbola?It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.
We have given a hyperbola equation:
[tex]\rm \dfrac{(x-2)^2}{16}-\dfrac{(y+1)^2}{9}=1[/tex]
We know the standard form of a hyperbola is given:
[tex]\rm \dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]
After comparing:
a² = 16 ⇒ a = 4
b² = 9 ⇒ b = 3
[tex]\rm c^2 = a^2+b^2\\\\\rm c^2 = 16+9 \Rightarrow 25[/tex]
c = 5
(h, k) is the center of the hyperbola:
(h, k) = (2, -1)
Vertices will be (a, 0) and (-a, 0):
(4, 0) and (-4,0)
Foci will be at (c, 0) and (-c, 0):
(5, 0) and (-5, 0)
Thus, the value of a, b, c, h, k, and foci coordinates are 4, 3, 5, 2, -1, and (5, 0) and (-5, 0) respectively.
Learn more about the hyperbola here:
brainly.com/question/12919612
#SPJ1
The value of a=4 , b=3 , k=-1 and h=2 for the hyperbola having the equation
[tex]\dfrac{(x-2)^2}{16}-\dfrac{(y+1)^2}{9}=1[/tex]
What is hyperbola?A hyperbola is the symmetrical open curve formed by the combination of a circular cone with a plane at a minimum angle with its axis than the side of the cone.
Here the general form of the equation of hyperbola will be:
[tex]\dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=1[/tex]
And we have a equation given as:
[tex]\dfrac{(x-2)^2}{16}-\dfrac{(y+1)^2}{9}=1[/tex]
By comparing the equation we the solutions
[tex]a=4 , b=3 , k=-1 \ and\ h=2[/tex]
To know more about hyperbola follow
https://brainly.com/question/2351925
#SPJ1
8 - 3(2-(3 + 1)2 = 8.2)
Solve for x, then find the missing side of the lengths.
Answer:
Here are the examples!
Step-by-step explanation:
15 45 X +3 5x + 1 15 = 45 5x + 1 = 3x + 9 x+3 5x + 1 5x - 3x = 9-1 1 … 5( 5x + 1) = 45(x+3) 2x = 8 5x + 1 = 3( x + 3) x :) ...
thrill drop to nearest food. Number of minutes
slope for y=2x+3 and y intercept
Answer:
slope = 2, y-intercept = 3
Step-by-step explanation:
» Concepts
All straight lines can follow the slope-intercept form, y = mx + b, where y = y-coordinate, m = slope, x = x-coordinate, and b = y-intercept. The slope is the constant rate of change, and the y-intercept is where the line intersects at the y-axis.
» Application
We are asked to find the slope and y-intercept of the equation, y = 2x +3, given the form y = mx + b. As you can see, in the place of m (the slope), there is the number 2, making the slope 2. Then, in the place of b (the y-intercept), there is the number 3, making the y-intercept 3.
5. What is the difference between each term to the next of this number sequence: 14, 11, 8, 5? A. 3 B. 5 C. 7 D. 10
A: 3
if you subtract 11 from 14 you get three, and the pattern is repeated and works with the other consecutive numbers
Yesterday, there were 80 problems assigned for math homework. Deb got 72 problems
correct and 8 problems incorrect. What percentage did Deb get correct?
Answer:
90%
Step-by-step explanation:
Do 72/80 to find the decimal
72/80=0.9
Then to convert decimal to percent move the decimal point two times to the right.
0.9=90%
The volume of a box is 9cm³ and its base area is 20cm². What is the height of the whole box
Answer:
0.45 cm
Explanation:
In order to find the height of any shape given the volume and base area.
Simply divide the volume by the base area.
Here given:
Volume: 9 cm³Base area: 20 cm²Height:
volume ÷ base area = 9 ÷ 20 = 0.45 cm5. A square on the coordinate plane has vertices
at A(-3,0), B(1, 2), C(2,-1), and D(-2,-4). After a
dilation using a scale factor of 3, what are the
new coordinates of D'?
Reason:
Multiply each coordinate of D(-2,-4) by the scale factor 3 to get (-6, -12)
In other words, triple each coordinate of point D.
This trick only works if the center of dilatioin is the origin.
100 POINTS!! NEED ANSWER WITH WORK ASAP!!
Coach Bennet’s high school basketball team has 14 players, consisting of six juniors and eight seniors. Coach Bennet must select three players from the team to participate in a summer basketball clinic.
How many different groups of three players are possible for Coach Bennet to select?
Answer:
See below ~
Step-by-step explanation:
This is a combination because the order in which the players are selected is not important.
Number of ways
14! / 11! 3!14 x 13 x 12 x 11! / 11! x 3 x 214 x 13 x 2364 waysApply combination
[tex]\\ \rm\Rrightarrow ^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
So
[tex]\\ \rm\Rrightarrow ^{14}C_3[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{14!}{3!(14-3)!}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{14(13)(12)(11!)}{3!11!}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{14(13)(12)(11)}{6}[/tex]
[tex]\\ \rm\Rrightarrow 14(13)(2)(11)[/tex]
[tex]\\ \rm\Rrightarrow 4004[/tex]
What’s the answer to this question
Answer:I guess
represent
expression
degree of 4
math please help me
Answer:
1, 3
Step-by-step explanation:
1. 2.3 - 2.3 = 0
2. -3.7 + -4.1 = -7.8
3. -2.6 - (-12/4) = 0.4 = 4/10 = 2/5
4. 5/2 + (-2.5) = 0
5. 72- (-100)
72+100 = 172
Find and interpret the mean absolute deviation of the data. $4.6,8.5,7.2,6.6,5.1,6.2,8.1,10.3$ The mean absolute deviation is . The values differ from the mean by an average of .
Using it's concept, it is found that:
The mean absolute deviation is 1.45.The values differ from the mean by an average of 1.45.What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the number of observations.The mean absolute deviation of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.In this problem, the mean of the data-set is given by:
M = (4.6 + 8.5 + 7.2 + 6.6 + 5.1 + 6.2 + 8.1 + 10.3)/8 = 7.075.
Hence, the mean absolute deviation is given by:
MAD = (|4.6-7.075| + |8.5-7.075| + |7.2-7.075| + |6.6-7.075| + |5.1-7.075| + |6.2-7.075| + |8.1-7.075| + |10.3-7.075|)/8 = 1.45
Then:
The mean absolute deviation is 1.45.The values differ from the mean by an average of 1.45.More can be learned about the mean absolute deviation at https://brainly.com/question/3250070
#SPJ1
I NEED HELP URGENTLY
Answer:
30 square millimeters
Step-by-step explanation:
3 x 3 = 9
3 x 1 = 3
there are two sides with the area 9 therefore...
9 x 2 = 18
There are four sides with the area 3 therefore...
3 x 4 = 12
Therefore the suface area is
12 + 18 = 30
Which expression is equivalent to [4(x + 9)]/ 2/3
Answer:
36+2.67
Step-by-step explanation:
I hope this is correct
What is the sum of a seven-term geometric series if the first term is -2, the last term is
-31,250, and the common ratio is -5?
Answer:
-26042
Step-by-step explanation:
sum of a finite geometric series =
[tex]\frac{a_1(1-r^n)}{1-r}[/tex]
here, a1 is the first term, r is the common ratio, and n is the number of terms
a1 = -2
r = -5
n = 7
[tex]\frac{a_1(1-r^n)}{1-r} = \frac{-2(1-(-5)^7)}{1-(-5)} = -26042[/tex]
There are 30 days in November.
It’s rains on 3/5 of them
Work out the number of days when it does not rain.
(3/5) × 30 = 3 × 6 = 18 days it won't rain
30 - 18 = 12 days it will rain
hope it helps...!!!
In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achieve the graph of g(x) = log(-2x-4) + 5
Please solve this for me!!!!
Step-by-step explanation:
Howdy there :)
To describe the transformation of the parent logarithmic function, you just need to follow these rules
1. A + on the outside of the parentheses will mean a vertical shift upwards. As such, the transformation is moved 5 units up. If it was -, it would move 5 units down.
2. The inside of the parentheses will result in a horizontal shift right 4 units. The rule to remember is that these kinds of functions follow x(a - b) rules, meaning that when the 4 is subtracted, we are really talking about a positive four, unlike in standard arithmetic. Vice versa, a + 4 will mean a -4 four, since a - -4 is the same as a + 4. As such, we will move in the positive direction (right) on the y axis.
3. Since x is now -2x, we are reflecting about the y axis, meaning the function will switch from left to right or right to left.
4. The 2 in front of it represents a vertical dilation by a factor of 2. This is because our constant, 2, is greater than 1. If the number were in between 0 and 1, it would represent a vertical compression by the constant number.
Why is dividing a fraction by 3 and then multiplying by 2 the same as multiplying by 2/3?
please i need it now
press the link and tell the answers pls
Answer:
wE NEED MORE CLARIFICATION
Step-by-step explanation:
What is the equasion
What is the link
Answer:
im passing this concept trust me answer is 34.8
Step-by-step explanation:
Identify the range of the exponential function?
Answer:
The range of an exponential function, or any function is all the possible y values the function can spit out.
In MOST exponential functions they will be x>0
I am talking about the standard form: y = a * b^x
I cannot tell you the range for YOUR exponential function without seeing it first.
For which value of a does Limit of g(x) as x approaches alpha not exist?
The value of a where the Limit of g(x) as x approaches alpha not exist are -1 and 1
Limit of a functionThe limit of a function is the limit of a function as x tends to a value.
From the given graph, you can see that the function g(x) goes large at the point where the arrows orange and purple point down from the x-coordinates -1 and 1.
Hence the value of a where the Limit of g(x) as x approaches alpha not exist are -1 and 1
Learn more on limit of a function here: https://brainly.com/question/23935467
#SPJ1
I need the answer urgently please !!
Answer:
y = 2x
Step-by-step explanation:
Parallel line share the same slope, therefore we can put any parallel line of y = 2 (x + 1) in equation as: y = 2x + k
As the parallel has to intercept with point (2/3, 1/3), simply put the coordinate into the equation to get value of k
2/3 = 2(1/3) + k
k = 0
Therefore the equation of this parallel line is y = 2x
Assume the spinner wedges are the same size. Find the probability of the spinner landing on a section that contains he number - 16
Answer:
find the probability of rolling a 4, take the number of possible ways of rolling a 4 and divide it by the total number of possible outcomes.
Write an equation of the line that passes through the point (6,-9) with the given slope m= 3
Answer:
[tex]y = 3x - 27[/tex]
Step-by-step explanation:
[tex]y - y0 = m(x - x0) \\ y - ( - 9) = 3(x - 6) \\ y + 9 = 3x - 18 \\ y = 3x - 27[/tex]
89 90 91 92 96 96 99 99 find the median
Answer: The median is 96
Step-by-step explanation:
calculate the number of subsets and the number of proper subsets for the set.
{1/6, 1/7,1/8,1/9 }
A. 16;15
B.15;16
c.14;15
D.15;14
A set of n elements has 2ⁿ subsets. One of these subsets is the set itself, so this set would have 2ⁿ - 1 proper subsets.
The given set has 4 elements, so it has 2⁴ = 16 subsets and 2⁴ - 1 = 15 proper subsets.
Just to illustrate the claim, we have
• subsets of size 0 (1 of these):
{ } (empty set)
• subsets of size 1 (4 of these):
{1/6}, {1/7}, {1/8}, {1/9}
• subsets of size 2 (6 of these):
{1/6, 1/7}, {1/6, 1/8}, {1/6, 1/9}, {1/7, 1/8}, {1/7, 1/9}, {1/8, 1/9}
• subsets of size 3 (4 of these):
{1/6, 1/7, 1/8}, {1/6, 1/7, 1/9}, {1/6, 1/8, 1/9}, {1/7, 1/8, 1/9}
• subsets of size 4 (1 of these):
{1/6, 1/7, 1/8, 1/9}
and the last one is the only subset that is not a proper subset, because that subset = the set.
The number of subsets are 16 and number of proper subsets for the set are 15. So, correct option is A.
The set {1/6, 1/7, 1/8, 1/9} has 4 elements.
To calculate the number of subsets, including both the proper and improper subsets, you can use the formula 2ⁿ, where n is the number of elements in the set.
So, for this set, there are 2⁴ = 16 subsets.
To calculate the number of proper subsets, you subtract 1 from the total number of subsets (to exclude the empty set).
So, the number of proper subsets is 16 - 1 = 15.
Hence, option A is correct, the number of subsets are 16 and number of proper subsets for the set are 15.
To learn more on Sets click here:
https://brainly.com/question/30705181
#SPJ3
Which of the following are NOT organizational structure for an informative essay?
A. cause and effect
B. chronological
C. equal parts
D. problem solving
find the equaton of the line passing through the points (2,11) and (-8, -19) y= ?x ?
Find the slope:
(-19 - 11) / (-8 - 2) = (-30/-10) = 3
Find the y intercept:
y = mx + b
11 = 3(2) + b
b= 5
So equation is:
y = 3x + 5
Carmen has 4 baby bunnies. Each bunny weighs 1/5 of a pound. How much do the bunnies weigh all together?
Step-by-step explanation:
The answer is 0.8 as a fraction is 4/5
PLEASE HELP ME! For a geometric sequence, if a1 = 2 and a5 = 1250, what is the value of r?
Answer: r = 5
Steps:
[tex]a_n=ar^{n-1}[/tex]
1. add Values to formula
[tex]1250=2r^{5-1}[/tex]
2. get r alone
[tex]\frac{1250}{2}=\frac{2r^{4}}{2}[/tex] ➜ [tex]625= r^4[/tex]
3. get rid of the exponents
[tex]\sqrt[4]{625}= \sqrt[4]{r^4}[/tex] ➜ [tex]\sqrt[4]{625}= r=5[/tex]
r = 5
