Answer:
1) The vertices of the hyperbola are (-8, -15), (-8, 3)
2) The foci of the hyperbola are (11, -7) or (1, -7)
Step-by-step explanation:
1) The vertices of a hyperbola given in the form [tex]\dfrac{\left (y - k\right)^2}{a^2} -\dfrac{\left (x - h\right)^2}{b^2} = 1[/tex] is (h, k ± a)
Therefore, for the given hyperbola with the following equation;
[tex]\dfrac{\left (y + 6\right)^2}{81} -\dfrac{\left (x + 8\right)^2}{49} = 1[/tex], we have;
[tex]\dfrac{\left (y + 6\right)^2}{9^2} -\dfrac{\left (x + 8\right)^2}{7^2} = 1[/tex]
Therefore the vertices are;
(-8, -6 ± 9) = (-8, -15), (-8, 3)
2) The equation of the given hyperbola is presented as follows;
[tex]\dfrac{\left (x - 6\right)^2}{16} -\dfrac{\left (y + 7\right)^2}{9} = 1[/tex]
The given hyperbola is of the form;
[tex]\dfrac{\left (x - h\right)^2}{a^2} -\dfrac{\left (y - k\right)^2}{b^2} = 1[/tex]
We get;
[tex]\dfrac{\left (x - 6\right)^2}{4^2} -\dfrac{\left (y + 7\right)^2}{3^2} = 1[/tex]
The foci is then (h ± c, k)
Therefore, by comparison, the foci of the given hyperbola is (6 ± c, -7)
Where c² = a² + b²
∴ c² = 4² + 3² = 25
c = √25 = 5
∴ The foci; (6 ± 5, -7) = (11, -7) or (1, -7).
Kyle is a satellite radio sales representative. He receives 7% commission on all sales. If
the total sales for the year were $345,000, what would his commission be?
Answer:
24,150
Step-by-step explanation:
7% of 345,000 = 24,150
Please I need all answers ASAP I’ll mark u brainyist
Answer:
I'm pretty sure its A /5
If the shorter rectangle is 1 unit long, how many units long is the longer rectangle?
Answer: 2 units long
Please help !!!!!!!!!!!!!!
The graph of y = cos x is transformed to the graph below. Which statement
about the graph is not correct?
АДА
31
2
A. The midline is y= 1.
B. The phase shift is
C. The period is T.
D. The amplitude is 2.
Answer:
Step-by-step explanation:It’s b
Justin is 12 years older than Agnes in six years timing Johnson will be twice as old as Agnes how old are they now
9514 1404 393
Answer:
Agnes: 6Johnson: 18Step-by-step explanation:
6 years from now, Johnson will be 12 years older than Agnes and twice her age. That means Agnes will be 12 and Johnson will be 24.
Agnes is 6 now, and Johnson is 18 now.
Solve for x and solve for FGI
Answer:
X equals -0.5 in decimal and in fraction it would be negative one half. Im not 100% sure of the answer also I dont know what angle that is...
what makes 3+7+2= ? +2 true? HELP
Answer:
3 + 7 + 2= 12
Step-by-step explanation:
It is made true because the equation adds up to the number. If we take 3+7 it equals to 10. Then we take 10 and add it to 2, which gives us 12.
Hope this helps :)
The value of the missing number x will be 10.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
Let the missing number be x. Then the equation can be written as,
3 + 7 + 2 = x + 2
Simplify the equation, then the value of the variable x will be
3 + 7 + 2 = x + 2
3 + 7 + 2 - 2 = x
x = 3 + 7
x = 10
The value of the missing number x will be 10.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
Raise 1.00203333 to the negative 360 power
Answer:0.4813042802
Step-by-step explanation:
Please help me with this !!
Answer:
Step-by-step explanation:
a = 1
b = 6
c = 6
axis of symmetry = -(6) / 2*1
= -6 /2
= -3
vertex = ( -3, -3 ) :)
Answer:
Step-by-step explanation:
a = 1 because if is not written what x^2 multiply, it means that x^2 multiply 1
b = 6 b is the term that multiply x
c = 6 c is the therm without x
axis of symetry = -6/2 = -3
the x of vertex is same of the axis of the symmetry so it is -3
if we subistute x with this value we can find the y of vertex
(-3)^2 + 6(-3) + 6 = 9 -18 + 6 = -3
Vertex (-3, -3)
6. Kriti has a circular swimming pool in her house. The radius of the swimming
pool is22.5 cm. She walks one round every morning before diving in the pool.
How far does she walk around the pool every morning? *
70.65
141.3
35.33
282.6
Answer:
Total walk she did around the pool every morning = 141.3
Step-by-step explanation:
Given - Kriti has a circular swimming pool in her house. The radius of the swimming pool is 22.5 cm. She walks one round every morning before diving in the pool.
To find - How far does she walk around the pool every morning?
Proof -
Given that, the swimming pool is circular in shape.
So,
1 round of circle = Circumference of circle.
As we know that,
Circumference = [tex]2\pi r[/tex]
= [tex]2*\pi *22.5[/tex]
= 141.3
∴ we get
Total walk she did around the pool every morning = 141.3
Suppose the function:
f(x) = 2.9646 (1.0170)x
models the world population x years after 1948.
Rewrite the exponential equation given above using base e.
f(t) = 2.9646 e ^(0.0169) t
B.
f(t) = 2.9646 (1.0170) e^t
C.
f(t) = 2.9646 + 1.0170e^t
D.
f(t) = 2.9646 e^(1.0170t)
E.
f(t) = 2.9646 e^ln (1.0170t)
Given:
The function is:
[tex]f(x)=2.9646(1.0170)^x[/tex]
To find:
Rewrite the exponential equation given above using base e.
Solution:
The exponential models is:
[tex]f(x)=P(1+r)^x[/tex] ...(i)
Where P is initial values, r is the rate of interest and x is the time period.
The exponential models using base e is:
[tex]f(t)=Pe^{rt}[/tex] ...(ii)
Where, P is initial values, r is the rate of interest and t is the time period.
The given function is:
[tex]f(x)=2.9646(1.0170)^x[/tex]
It can be written as:
[tex]f(x)=2.9646(1+0.0170)^x[/tex] ...(iii)
On comparing (i) and (iii), we get
[tex]P=2.9646[/tex]
[tex]r=0.0170[/tex]
Putting [tex]P=2.9646[/tex] and [tex]r=0.0170[/tex] in (ii), we get
[tex]f(t)=2.9646e^{0.0170t}[/tex]
Therefore, the correct option is D.
45 POINTS!! PLEASE HELP
The scatter plot shows the relationship between the test scores of a group of students and the number of hours they study in a week.
Part A: What is the group of points labeled N called? What is the point labeled M called? Give a possible reason for the presence of point M.
Part B: Describe the association between students’ test scores and the number of hours they study.
Answer:
Step-by-step explanation:
m is called an outlier and it is a positive association
Answer:
Part A) Part N.) is called the cluster of the whole chart. Part M.) is called the outlier because it's not with the rest of the group, therefore, it's the outlier of the group.
Part B.)
The association between the students' test scores and the number of hours they've studied is a positive correlation. That means the longer the students spent time studying for their tests... the better grades they got because of it. It's a lot like a cause-and-effect kind of situation.
Step-by-step explanation:
I hope this helps you!!! Brianlyest please!!! And SO sorry this is so late!
HELP ME PLEASEE Select all of the following that could be classified as a Perfect Square Trinomial.
Son el B el C y el E
High blood pressure has been identified as a risk factor for heart attacks and strokes. The National Health and Nutrition Examination Survey reported that the proportion of U.S. adults with high blood pressure is 0.3. A sample of 38 U.S. adults is chosen. (a) Is it appropriate to use the normal approximation to find the probability that more than 40% of the people in the sample have high blood pressure? If so, find the probability. If not, explain why not. (b) A new sample of 80 adults is drawn. Find the probability that more than 40% of the people in this sample have high blood pressure. (c) Find the probability that the proportion of individuals in the sample of 80 who have high blood pressure is between 0.23 and 0.32.
Answer:
The National Health and Nutrition Examination Survey reported that the proportion of U.S. adults with high blood pressure is 0.3. A sample of 38 U.S. adults is chosen. a. Is it appropriate to use the normal approximation
dos hermanos tienen una cuenta de ahorros de s/1920 lo que le corresponde al hermano mayor es 6 veces mas de lo que le corressponde al hermano menor mas un adicion de s/72 ¿ cuanto le corresponde alk hermano mayor
Answer:
le corresponde s/1656
Step-by-step explanation:
espero y te ayude
Heather has a bag of 15 red, 11 orange, 9 yellow, 12 green, 6 blue and 11 purple markers. how many times would you expect heather to pick a red marker if she picked a marker 90 times?
A.about 11 times
B.about 15 times
C.about 21 times
D.about 64 times
Answer:
B should be the correct answer.
Step-by-step explanation:
15 + 11 + 9 + 12 + 6 + 11 = 64
64<90
Answer:
15 red out of 64 total markers
15 / 64 = .234375
90 x .234375 = 21.09375
so she will pick a red marker about 21 times
Step-by-step explanation:
Lily walks 2 kilometers during each trip to school. Write an equation that shows the
relationship between the number of trips x and the total distance walked y.
Answer:
y = 2x
Step-by-step explanation:
Total distance walked = y
Number of trips = x
Lily walks 2 kilometers during each trip to school
Equation that shows the
relationship between the number of trips x and the total distance walked y:
y = 2x
For example, if the number of trips (x) is 3
Total distance walked,y = 2(3)
y = 6 kilometers
(x+y) (x+y) - (x-y) (x-y)
Answer:
4xy
Step-by-step explanation:
(x+y) (x+y) - (x-y) (x-y)
(x² + xy + xy + y²) - (x² - xy - xy + y²)
(x² + 2xy + y²) - (x² - 2xy + y²)
x² + 2xy + y² - x² + 2xy - y²
x² - x² + 2xy + 2xy + y² - y²
4xy
Answer:
that could literally be anything, as long as the first sum is greater then the second.
example;
(2+4) (3+5) - (6+1) (5+2)
(or, 6+8 = 14, 7+7 = 14, 14 - 14 = 0)
hope this helped :)
Which step comes last when using the divide-center method to find the trend line on a scatterplot? Approximate the center of the cluster located on the left side of the line, and repeat for the right side of the line. Connect the two centers to produce the trend line. Disregard all outliers.Draw a vertical line so that each side has the same number of data points.
Answer:
Is there a picture?
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Look at the drawing of a triangle within a rectangle. The
triangle and the rectangle have the same base, b, and
height, h.
If the area of the triangle is 48 square units, what is the
total area of sections 1 and 2?
square units
) Intro
Answer:
48 square. Units
Step-by-step explanation:
Given that :
Triangle and rectangle have the same base, b and height, h
AREA of triangle = 0.5 * base * height
48 = 0.5 bh
bh = 0.5 * 48
bh = 96
Total area of section 1 & 2 :
bh = area of triangle + x
X = bh - area of triangle
X = 96 - 48
Area of se tion 1&2 = 48
3. What is Total Surface Area?
4 in
3 in
10 in
O 82
O 140
O 164
O 120
Answer:
120in. ezy
Step-by-step explanation:
3x^2+bx+24=0 if one of its root is 3
Answer:
Other root of equation, [tex]\frac{8}{3}[/tex]
Value of ([tex]b[/tex]), [tex]-17[/tex]
Step-by-step explanation:
The given quadratic equation is in standard form. Standard form is the basic format of representing a quadratic equation, a quadratic equation in standard form would use the following format,
[tex]y=ax^2+bx+c[/tex]
To solve this problem, one could use Vieta's theorems. Vieta's theorems state the following, let ([tex]x_1[/tex]) and ([tex]x_2[/tex]) represent the roots of the equation,
[tex](x_1)+(x_2)=-\frac{b}{a}[/tex]
[tex](x_1)(x_2)=\frac{c}{a}[/tex]
Substitute the given values into the equation,
[tex]3+(x_2)=-\frac{b}{3}[/tex]
[tex](3)(x_2)=\frac{24}{3}[/tex]
Simplify,
[tex](3)+(x_2)=-\frac{b}{3}[/tex]
[tex](3)(x_2)=8[/tex]
Inverse operations,
[tex](3)+(x_2)=-\frac{b}{3}[/tex]
[tex]x_2=\frac{8}{3}[/tex]
Substitute in the value of ([tex]x_2[/tex]),
[tex](3)+(\frac{8}{3})=-\frac{b}{3}[/tex]
Simplify, convert to improper fractions and combine like terms,
[tex]\frac{9}{3}+\frac{8}{3}=-\frac{b}{3}[/tex]
[tex]\frac{17}{3}=-\frac{b}{3}[/tex]
Multiply both sides of the equation by ([tex]3[/tex]) to remove the denominator,
[tex]17=-b[/tex]
The price per share of a professional sports team increased from $58 to $65 over the past year. What is the stock’s percent increase during this time? Round your answer to the nearest percent.
Answer:
95.7%
Step-by-step explanation:
i think im not too sure im sorry if you get it wrong
Please help me. Very important please show work
Please help! Solve the following:
Answer:
n=10.
Step-by-step explanation:
[tex]\frac{45}{n^{2}-3n-4 }[/tex] - [tex]\frac{3}{n-4}[/tex] = [tex]\frac{2}{n+1 }[/tex]
[tex]\frac{45}{n^{2}-3n-4 }[/tex] - [tex]\frac{3(n+1)}{(n+1)(n-4)}[/tex] = [tex]\frac{2(n-4)}{(n+1)(n-4) }[/tex]
[tex]\frac{45}{n^{2}-3n-4 }[/tex] - [tex]\frac{3n+3}{n^{2} -3x-4}[/tex] = [tex]\frac{2n-8}{n^{2} -3x-4 }[/tex]
45-3n-3=2n-8
45-3+8=5n
n=50/5=10
What's the ratio? please help! Urgent!
Answer:
13:5
Step-by-step explanation:
Messy played 65 minutes while the substitute played 25 minutes. This ratio is 65:25 and can be simplified to 13:5.
b) Factorise 4(x + y) + (x + y)?
Terms & Conditions
Answer:
5(x+y)
Step-by-step explanation:
4×x+4×y+x+y
4x+4y+x+y
5x+5y
5(x+y)
A worker places tape around a rectangular shipping label that is 2 times longer than it is wide. How much tape does the worker need? The width is 74mm
Answer:
444 :) (angel number, haha)
Step-by-step explanation:
it needs 74 times 2 mm which is 148 I think, which will also be the length since 148 is 2 times more than 74
so it's : 74 + 74 + 148 + 148 which is basically just 148 times three, so the answer is 444!
Given the function h(x) = -x2 -X2 – 5x + 8, determine the average rate of change of the function over the interval -4 < x < -2
Hi there!
[tex]\large\boxed{\text{Average rate = 1}}[/tex]
We can calculate the average rate of change using the following:
[tex]ARC = \frac{f(b)-f(a)}{b-a}[/tex]
Thus, we can plug in the endpoints of -4 and -2. Find the corresponding y-values for these x-values:
f(-2) = -(-2)² - 5(-2) + 8 = -4 + 10 + 8 = 14
f(-4) = -(-4)² - 5(-4) + 8 = -16 + 20 + 8 = 12
Plug in the solved for values into the ARC equation:
[tex]ARC(slope) = \frac{14-12}{-2(-4)} = \frac{2}{2} = 1[/tex]