The required equation of the hyperbola is expressed as
[tex]\frac{x^2}{10}- \frac{y^2}{15}=1 \\[/tex]
The standard form for calculating the equation of a parabola along the x-axis is expressed as:
[tex]\frac{(x-k)^2}{a^2}-\frac{(y-h)^2}{b^2} = 1 \ ............. 1[/tex] where:
(h, k) is the center
(k±c, h) are the foci
[tex]x=h\pm\frac{a^2}{c}[/tex] is the directrix
From the question given, we can see that foci = (±5, 0)
k±c, h = ±5, 0
k = 0
h = 0
c = 5
From the directrix,
[tex]x=h\pm\frac{a^2}{c}\\x =0\pm\frac{a^2}{5}\\\pm2 = \pm\frac{a^2}{5}\\a^2 = 10\\[/tex]
Also, we need to know that;
a²+b² = c²
10 + b² = 5²
b² = 25 - 10
b² = 15
Substituting the gotten values into the equation of a hyperbola;
[tex]\frac{(x-0)^2}{10}- \frac{(y-0)^2}{15} =1\\\frac{x^2}{10}- \frac{y^2}{15} =1\\[/tex]
This gives the required equation of the hyperbola
Learn more on the equation of hyperbola here: https://brainly.com/question/20409089
Answer:
The answers are between C and D
Step-by-step explanation:
It can't be A or B because they create a horizontal hyperbola, when the directrices are vertical.
PLEEEEASEEE HELP ASAP
In the diagram, the measures of ∠1 and ∠4 are 105°. The measures of ∠5 and ∠8 are 115°. Are lines c and d parallel
a p e x
Answer:
a
Step-by-step explanation:
Answer:
Option A
Step-by-step explanation:
I just got done with this same quiz and i got a 100 .
Chanel found a used bookstore that sells pre-owned DVDs and CDs. DVDs cost $9 each, and CDs cost $6 each. Chanel can spend no more than $108.
The question is incomplete. Kindly see the correct question below
Chanel found a used bookstore that sells pre-owned DVDs and CDs. DVDs cost $9 each, and CDs cost $6 each. Chanel can spend no more than $108 Write an inequality that represents this
Answer:
9D +6C < 108
Step-by-step explanation:
Let the price of Dvd be D
Let the price of CDs be C
Hence the inequality can be represented as follows
9D + 6C < 108
Find the missing values in the Table of Values. Write your numbers from top to bottom in the space below with a comma between each value.
PLEASE DON'T GIVE A LINK OR DELETE THE ANSWER BECAUSE THIS IS MY SECOND TIME POSTING THIS SO PLS PLS PLS GIVE A PROPER ANSWER TO ALL OF THE PICTURES.
Answer:
Alright, with this, its essentially asking for you to plug in X into each equation for the answer.
With the first box, it asks for y = 5 - x, given the x = -2.
y = 5-x
y=5-(-2)
y=5+2
y=7
With the second box down, it wants things a bit differently, it gives you the y value, and wants for you to find the x. Given this, this question can be done backwards for the x value.
y = 5-x
6 = 5-x
x+6= 5
x=-1
With the third one, its the same thing as with the first box.
y = 5-x
y = 5-0
y = 5
Same thing with the fourth one.
y = 5-1
y = 4
If you have any question about the process or the answer, please comment below and I can help explain on what you're stuck on.
Answer:
Picture 1: (-2, 7), (-1,6), (0,5), (1,4)
Picture 2: (-2, -6), (4,6), (0,-2), (1,0)
Picture 3: (-1, -4), (8,5), (1,-2), (5,2)
Jeffrey's recipe for oatmeal muffins calls for 2 3/4 cups of oatmeal and makes one dozen muffins. If he makes 2 dozen muffins for a club meeting and 1 1/2 dozen muffins for a family reunion, how much oatmeal will he use?
Answer:
5
Jeffrey will use 9 __ cups of oatmeal
8
Step-by-step explanation:
2.75 cups of oatmeal per 1 dozen
2.75 x 2 = 5.5
2.75 + 2.75(1/2) = 4.125
add
5.5 + 4.125 =
9.625 cups of oatmeal
or
9 5/8 cup
A hospital recorded the weights, in ounces, of newborn babies for two weeks. The
results are listed below.
Weights of babies born during week one: 128, 105, 80, 82, 96, 98, 87, 100, 112, 126
Weights of babies born during week two: 75, 85, 90, 97, 89, 105, 110, 127, 129, 130
Which statement is true?
Answer:
The standard deviation for week two was about 3 ounces more than the standard deviation for week one
Step-by-step explanation:
Given
[tex]Week\ 1: 128, 105, 80, 82, 96, 98, 87, 100, 112, 126[/tex]
[tex]Week\ 2: 75, 85, 90, 97, 89, 105, 110, 127, 129, 130[/tex]
See attachment for options
Required
The true statement
Checking the standard deviation
For week 1
Calculate the mean:
[tex]\bar x = \frac{\sum x}{n}[/tex]
[tex]\bar x = \frac{128+ 105+ 80+ 82+ 96+ 98+ 87+ 100+ 112+ 126}{10}[/tex]
[tex]\bar x = \frac{1014}{10}[/tex]
[tex]\bar x_1 = 101.4[/tex]
Then standard deviation
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{(128 - 101.4)^2 +............+ (126- 101.4)^2}{10}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{2522.4}{10}}[/tex]
[tex]\sigma_1 = \sqrt{252.24[/tex]
[tex]\sigma_1 = 15.88[/tex]
For week 2, we have:
[tex]\bar x = \frac{75+ 85+ 90+ 97+ 89+ 105+ 110+ 127+ 129+ 130}{10}[/tex]
[tex]\bar x = \frac{1037}{10}[/tex]
[tex]\bar x_2 = 103.7[/tex]
Then standard deviation
[tex]\sigma_2 = \sqrt{\frac{(75 - 103.7)^2 +................+ (130- 103.7)^2}{10}}[/tex]
[tex]\sigma_2 = \sqrt{\frac{3538.1}{10}}[/tex]
[tex]\sigma_2 = \sqrt{353.81[/tex]
[tex]\sigma_2 = 18.81[/tex]
Compare the standard deviations
[tex]\sigma_1 = 15.88[/tex]
[tex]\sigma_2 = 18.81[/tex]
Calculate the difference:
[tex]d = \sigma_2 - \sigma_1[/tex]
[tex]d = 18.81 - 15.88[/tex]
[tex]d = 2.93[/tex]
[tex]d \approx 3[/tex]
This implies that option (b) is true
A. 65
B. 30
C. 10
D. 50
Answer:
50
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
D. 50
Step-by-step explanation:
∠CGF and ∠AFG add up 180° because they are same side interior angles. We can write an equation to model the situation:
m∠CGF + m∠AFG = 180°
And, we can substitute:
3x - 20 + x = 180
4x - 20 = 180
4x = 200
x = 50
What is the solution to the inequality -3x - 5 < -20?
Answer: x>5
Step-by-step explanation: Hope this help :D
What is the probability of rolling a 6 and then a 7 on a number cube?
NO LINKS PLEASE!
Answer:
the probability of rolling 6 is 16 or 16.7%.
the probability of rolling 7 is 0.
Step-by-step explanation:
7 is 0 because its impossible to roll a 7 on one number cube.
Evaluate the expression for a = 10 and b = 12.
a+4(b−3)
Answer:
46
Step-by-step explanation:
a + 4(b - 3)
Substitute the values for a and b.
10 + 4(12 - 3)
Subtract inside the parenthesis.
10 + 4(9)
Multiply.
10 + 36
Add.
46
PLS HELP DUE ASAP! WILL MARK BRAINLIEST
Answer:
24º
Step-by-step explanation:
C = (1/2)(56 + 116)
C = 86
4x - 10 = 86
4x = 96
x = 24
PLEASEEEE HELPPP MEEE.
DUE RIGHT NOW!!
Topic: Math
Solve all the questions
Answer:
1. x= 9
2. x= −2
3. 51 inches
4. $213.11 each month
Step-by-step explanation:
1. Simplify both sides of the equation.
x + 7 + 7x= 25 + 6x
Combine Like Terms
(x + 7x) + (7)=6x + 25
8x + 7= 6x + 25
8x + 7= 6x + 25
Subtract 6x from both sides.
8x + 7 − 6x= 6x + 25 − 6x
2x + 7= 25
Subtract 7 from both sides.
2x + 7 − 7= 25 − 7
2x= 18
Divide both sides by 2.
2x/2= 18/2
2. Subtract 5x from both sides.
x − 5x= 5x + 8 − 5x
−4x= 8
Divide both sides by -4.
−4x/−4= 8/−4
3. First find the perimeter of the trapezoid
4 + 3 + 4 + 8= 19
A square has all equal sides
8 * 4= 32
Add them together
19 + 32 = 51 inches
4. Subtract the amount she put for finance from the total
1598.66 - 320 = 1278.66
Then divide that amount by the 6 months
1278.66 divided by 6 = 213.11
$213.11 each month
Solve log2 x = log5 3+1 by graphing. round to the nearest tenth
Answer:
the answer is 3.2
Step-by-step explanation:
x≈3.2
Help me ASAP!!
Find the area of the whole blue triangle.
8.5 m
10 m
8 m
3 m
6 m
it is multiple choice and i know 100% that the answer is no, but i dont know the answer for the solution part
Answer:
NO
NO SOLUTION
Step-by-step explanation:
2t + 2e = 11 eqn 1
t + e = 6.5 eqn 2
this can be solved using simultaneous equation
Multiply eqn 2 by 2
2t + 2e = 13
subtract eqn 1 from2
0 + 0 = 2
there is no solution
If a town with a population of 2000 doubles in size every 89 years what will the population be 267 years from now
Answer:
8,000 or 8·10³
Step by Step:
2000+2000=4000
4000+4000=8000
8000 or 8·10³
Answer:
16000
Step-by-step explanation:
This is essentially is asking 'What is 2000 * 2 * 2 * 2?'.
May I have Brainliest?
Hope that this helps!
Can someone help me
Answer:
b. the slopes of both functions are positive
Step-by-step explanation:
hope this helps :)
Answer:
C. The slope of function A is positive and the slope of function B is negative.
Step-by-step explanation:
For this problem, you need to determine the slope of each function.
For function A:
You're given y = (1/4)x - 2/3, which is in slope-intercept form y = mx + b. The slope of an equation in slope intercept form is given by m.
So the slope for function A is 1/4.
For function B:
You're given a list of (x, y) points, so use the definition of the slope = [tex]\frac{y2-y1}{x2-x1}[/tex], which gives you the slope from any two (x, y) points on the line. Let's take the first and second points (2, -8) and (4, -9)
Slope = [tex]\frac{-9-(-8)}{4-2} = \frac{-1}{2}[/tex].
Therefore, the slope of function A is positive and the slope of function B is negative.
please find the missing side of this triangle
please help me dont add a link you'll get reported
Answer:
D, 245.0 in^2
Step-by-step explanation:
Formula for the surface area of a cylinder: A=2πrh+2πr^2
A = 2πrh + 2πr^2
A = 2π(3)(10) + 2π(3)^2
A = 60π + 18π
A = 245.044
Answer:
???/
Step-by-step explanation:
Lena has two coupons for pants.
Coupon A: 45% off of $47 pants
Coupon B: $25 rebate on $47 pants
Choose the coupon that gives the lower price.
Answer:
coupon A
Step-by-step explanation:
coupon A 45%÷100=0.45 so 0.45×47= gives 21.15. coupon B 25÷2=23.50 so that the solution the lower price is coupon A $21.15
Liam bought a sandwich for $4.75, a bag of chips for $2.30, and a drink for $1.15. The tax was $0.65. He gave the cashier $10.00. How much change should Liam have receive
URGENT THIS IS FOR FINALS CAN SOMEONE PLZ SOLVE IT I will brain list
Answer:
were is the line
Step-by-step explanation:
Answer:
1- y=2x-5
2- y=-1/6x-5
Hope this helps you!!
Rocco has a weekly reading schedule, reading for 4.5 hours per day on some days and 3.5 hours per day on the other days. He reads a total of 25.5 hours in a seven-day week. On how many days does he read for 4.5 hours?
Answer:
x = days he reads for 4.5 hours = 1 day
y = days he reads for 3.5 hours = 6 days
Step-by-step explanation:
Let
x = days he reads for 4.5 hours
y = days he reads for 3.5 hours
x + y = 7 (1)
4.5x + 3.5y = 25.5 (2)
From (1)
x = 7 - y
Substitute x = 7 - y into (2)
4.5x + 3.5y = 25.5 (2)
4.5(7 - y) + 3.5y = 25.5
31.5 - 4.5y + 3.5y = 25.5
- 4.5y + 3.5y = 25.5 - 31.5
-y = -6
y = 6
Substitute y = 6 into (1)
x + y = 7 (1)
x + 6 = 7
x = 7 - 6
x = 1
x = days he reads for 4.5 hours = 1 day
y = days he reads for 3.5 hours = 6 days
Help me plsssssssssssssssss
Jenna multiplied four numbers together and then divided by -2. The result was a positive value.
Which of the following statements MUST be true?
A) An odd number of factors were negative.
B) None of the factors were negative.
C) An even number of factors were negative.
D) All of the factors were negative.
Answer:
c
Step-by-step explanation:
problem of volume that equals 9 work please
Step-by-step explanation:
l=1
b=3
h=3
l×b×h
9 is the vol
Logan has $63 and would like to purchase as many packs of baseball cards as possible to add to her collection. Part A An advertisement in the newspaper shows that each pack of cards costs $1.75. At this price, how many packs of cards can Logan buy? Write the answer in the box. packs
Answer:
36 card
Step-by-step explanation:
because 1 card cost $1.75 and Logan has $63, just divide 63 by 1.75 to get the answer
63÷1.75 =36
HELP IM GOING TO HAVE A MENTAL BREAKDOWN
Find the values of x and y that make these triangles congruent by the HL Theorem.
Answer:
x = 3 ; y=2
Step-by-step explanation:
to simplify the work we can build a system of two equations
2x+3 = 3y+3
x = y+1
we can now substitute the value of x in the first equation
2(y+1)+3 = 3y+3
2y + 2 + 3 = 3y+3
2y + 5 = 3y+3
y = 2
now we can subisitute the value of y in the first equation
x = 2 + 1 = 3
Verify
2(3)+3 = 6+3 = 9
3(2) + 3 = 6 + 3 = 9
3
2+1 = 3
Can you solve this for x? 7x-1
-2/3m = 12 solve for m
Step-by-step explanation:
[tex]\\ \:\:\:\:\sf {:}\dashrightarrow \dfrac{-2}{3m}=12[/tex]
use cross multiplication[tex]\\ \:\:\:\:\sf {:}\dashrightarrow -2=3m\times 12[/tex]
[tex]\\ \:\:\:\:\sf {:}\dashrightarrow -2=6m[/tex]
[tex]\\ \:\:\:\:\sf {:}\dashrightarrow m=\dfrac{-2}{6}[/tex]
[tex]\\ \:\:\:\:\sf {:}\dashrightarrow{\underline{\boxed{\bf{ m=-\dfrac{1}{3}}}}}[/tex]
Can someone help me out my grads are bad
Answer:
50 m^2
Step-by-step explanation:
3cm = 5 m
6 cm = 10 m
5 x 10 = 50 m^2
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
50 [tex]m^{2}[/tex]
Step-by-step explanation:
3cm = 5m
6cm = 10m
5x10 = 50