Answer:
9·x² - 36·x = 4·y² + 24·y + 36 in standard form is;
(x - 2)²/2² - (y + 3)²/3² = 1
Step-by-step explanation:
The standard form of a hyperbola is given as follows;
(x - h)²/a² - (y - k)²/b² = 1 or (y - k)²/b² - (x - h)²/a² = 1
The given equation is presented as follows;
9·x² - 36·x = 4·y² + 24·y + 36
By completing the square, we get;
(3·x - 6)·(3·x - 6) - 36 = (2·y + 6)·(2·y + 6)
(3·x - 6)² - 36 = (2·y + 6)²
(3·x - 6)² - (2·y + 6)² = 36
(3·x - 6)²/36 - (2·y + 6)²/36 = 36/36 = 1
(3·x - 6)²/6² - (2·y + 6)²/6² = 1
3²·(x - 2)²/6² - 2²·(y + 3)²/6² = 1
(x - 2)²/2² - (y + 3)²/3² = 1
The equation of the hyperbola is (x - 2)²/2² - (y + 3)²/3² = 1.
help me please quickly
Answer:
(1) 4
Step-by-step explanation:
Isolate x.
[tex]\frac{x-2}{3}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{5}{6}[/tex]
[tex]\frac{x-2}{3}[/tex] = [tex]\frac{5}{6}[/tex] - [tex]\frac{1}{6}[/tex]
[tex]\frac{x-2}{3}[/tex] = [tex]\frac{2}{3}[/tex]
[tex]\frac{x-2}{3}[/tex] × 3 = [tex]\frac{2}{3}[/tex] × 3
x - 2 = 2
x = 2 + 2
x = 4
10. The hour hand of a clock is 8 cm long.
What area does it cover in:
(a) 12 hours?
List 4 true angle facts about the illustration created by
AD intersects FK at point M.
Find the length of each segment write your answer in simplest radical form. I NEED HELP ASAP
Answer:
1. 5
2. [tex]\sqrt{85}[/tex]
3. [tex]\sqrt{26}[/tex]
Step-by-step explanation:
1. just count the units: 5 units
2. Find the slope = rise/run = -7/6
you now have a right triangle, one side is 7 units (from the rise), and the other is 6 units (from the run)
use the pythagorean theorem to find the hypotenuse.
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]7^{2} + 6^{2} = c^{2}[/tex]
49 + 36 = [tex]c^{2}[/tex]
85 = [tex]c^{2}[/tex]
[tex]\sqrt{85} = \sqrt{ c^{2}[/tex]
[tex]\sqrt{85} = c[/tex]
Simplify the radical, but [tex]\sqrt{85}[/tex] is farthest that it can go, so that is the answer.
3. same process as 2
slope = -1/5
[tex]1^{2} + 5^{2} = c^{2}[/tex]
1 + 25 = [tex]c^{2}[/tex]
26 = [tex]c^{2}[/tex]
[tex]\sqrt{26} = c[/tex]
That is the farthest it can go, so that will be the answer.
Jim went to the playground. He played on the swings for 45 minutes and went on the slide for 55 minutes. It was 4:35 P.M. when Jim left the playground. What time was it when Jim arrived at the playground?
Answer:
2:55 P.M.
Step-by-step explanation:
First, add the amount of time Jim played outside; 45+55=100
100 minutes is equal to 1 hour 40 minutes.
If he left the playground at 4:35 P.M., then you have to subtract in order to find out when he arrived there.
Subtract 1 hour 40 minutes from 4:35 P.M. to then get 2:55 P.M.
To confirm your answer, you can add back the 1 hour and 40 minutes to 2:55 P.M. and you'll get 4:35 P.M.; back with what you started with.
Hope this helped !!!
please help
this is due at noon so anyone who knows this help me.
Answer:
70x+4^2+3
Step-by-step explanation:
Translate the sentence into an equation The sum of 6 times a number and 8 equa's 7 Use the variable b for the unknown number 6 - 0
Answer:
6b + 8 = 7
Step-by-step explanation:
The proper translation of the sentence is 6b + 8 = 7.
Solving for b, we get 6b = -1 and b = -1/6
How is "6 - 0" part of this problem?
Find the unknown value .
45%=54/⬛️
Answer:
12
Step-by-step explanation:
54/12=4.5 then move the decimal once
expand and simplify (x-4)(x-1)
Step-by-step explanation:
(x - 4)(x - 1)
= x² - x - 4x + 4
= x² - 5x + 4.
Answer:
[tex]\huge(x - 4)(x - 1) \\ \huge= {x}^{2} - x - 4x + 4 \\ \huge = {x}^{2} - 5x + 4[/tex]
(x^2-5x+4) is the right answer.please help for bainlest
Answer:
[tex]\frac{5}{12}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4} -\frac{1}{3}[/tex]
Find the common denominator and multiply each side by that number
[tex]\frac{9}{12} -\frac{4}{12}[/tex]
[tex]\frac{5}{12}[/tex]
For bolded part in explanation: 4·3=12 3·3=9
3·4=12 1·4=4
Miguel designs a square garden. Each side length is 3x + 5. Write an expression to find the perimeter of Miguel’s garden.
Answer:
12x+20
Step-by-step explanation:
Perimeter of a garden = 4s, s being the length of the side
In this case, s = 3x+5
substitute the equation
4(3x+5)
=12x+20
100 POINTS! SOLVE FOR X. PIC ATTACHED. Random answers will be reported.
Answer:
x = 29Step-by-step explanation:
The angles (2x- 10) and (4x+ 16) are consecutive interior angles and therefore are corresponding
Corresponding angles sum to 180
(2x - 10) + (4x + 16) = 1806x + 6 = 1806x = 174x = 174/6x = 29Suppose that a person's peak blood alcohol level is0.04 (grams per 100 mL) and that this level decreases by 20% each hour.
Answer:
Step-by-step explanation:
incomplete question
A recipe for grape Gatorade calls for 1 1/2 quarts of sparkling water and 3/4 quart of grape juice.
1. How much sparkling water would you need to mix with 9 quarts of grape juice?
(Please help)
Answer: 3 1/2
Step-by-step explanation:
Yes
Answer:3 1/2
Step-by-step explanation:
Four friends share 10 fruit bars equally. How many fruit bars does each friend get?
Answer:
2.5
Step-by-step explanation:
10 / 4 = 2.5
The shadow of a building is 72 feet long. At the same time, John, who is 5 feet tall, casts a shadow that's 6 feet long. How tall is the building?
Answer:82feet tall
Step-by-step explanation:
Select the equation that is true.
Answer:
you didnt attach anything
Step-by-step explanation:
Look at the image bel9w
Answer:
it's your answer
Step-by-step explanation:
60+5(6÷2)
60+30÷10
60+3
63
18+(10-6)square
18+(100-36)
18+64
82
John builds a wooden box. ∙ The box is 3 feet long. ∙ The height is half the width. ∙ The volume is 4 times the width. Which equation can be used to find the width, w , of the box?
Answer:
4w=w*3*1/2w
Step-by-step explanation:
4w=w*3*1/2w
If y = 3x^4 -2x^3-7x+5, find dy/dx.
The derivative of [tex]y = 3x^4 - 2x^3 - 7x + 5[/tex] with respect to x is
dy/dx = 12x³ - 6x² - 7.
We have,
The power rule states that if we have a term of form a[tex]x^n[/tex], the derivative with respect to x is given by [tex]d/dx(ax^n) = nax^{n-1}.[/tex]
Applying the power rule, we differentiate each term as follows:
[tex]d/dx(3x^4) = 3 \times 4x^{4-1} = 12x^3\\d/dx(-2x^3) = -2 \times 3x^{3-1} = -6x^2\\d/dx(-7x) = -7 \times 1x^{1-1} = -7[/tex]
d/dx (5) = 0 (since 5 is a constant)
Combining these derivatives, we get:
dy/dx = 12x³ - 6x² - 7
Therefore,
The derivative of [tex]y = 3x^4 - 2x^3 - 7x + 5[/tex] with respect to x is
dy/dx = 12x³ - 6x² - 7.
Learn more about derivatives here:
https://brainly.com/question/29020856
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Mr. Tang gives a math test worth 90 points that contain 25 questions. Multiple-choice questions are worth 3 points and word problems are worth 4 points. How many of each type of question are there?
Answer:
m=10
w=15
Step-by-step explanation:
m + w = 25
3m + 4w = 90
Let's do substitution, first by solving the first equation for m.
m = 25 - w
Substitute!
3(25 - w) + 4w = 90
75 - 3w + 4w = 90
w = 15
m = 25 - 15 = 10
Find the value of "c". 4c + 18 = 74 *
[tex]4c \: + 18 = 74[/tex]
[tex] \implies \: 4c = 74 - 18[/tex]
[tex] \implies \: 4c = 56[/tex]
[tex] \implies \: c = \cancel \dfrac{56}{4} [/tex]
[tex] \implies \: c = 14[/tex]
The value of c is 14 .
Answer:
14
Step-by-step explanation:
move all terms that don't contain c then solve.
how to solve 2 divided by 1/7
Answer:
14
Step-by-step explanation:
You can put it as a fraction like so:
2/1 divided by 1/7
Use the strategy KCF (Keep, Change, Flip)
2/1 x 7/1
=2x7
=14
What would be the new set of numbers if the Scale Factor was 2? 3:4:5:6
Answer:
6:8:10:12
Step-by-step explanation:
Scale factor of 2-
3:4:5:6
multiply each number by 2
6:8:10:12
1. Yolanda has a 30%-off coupon from her favorite clothing store. She wants to buy a coat that regularly costs $85.40 How much will the coat cost after the coupon is applied?
Answer:
59.78
Step-by-step explanation:
Lol I use the calculator and find the cost of 30 of 85.40 than the number of the percent is 25.62 so I subtract them both and got 59.78 as an answer hope this help
Walking Robert walks 7 blocks east from his home and arrives at his favorite restaurant. When he arrives, he discovers that he dropped his wallet along the way. He retraces his steps for 5 blocks until he finds his wallet. An expression for how many blocks east Robert is from his home after finding his wallet is the sum 7+(−5).
Answer:
2 block east from home
Step-by-step explanation:
Given an expression for how many blocks east Robert is from his home after finding his wallet as the sum 7+(−5),
Simplifying the given expression
7+(-5) = 7-5 (note that the product of a plus and minus sign will give a minus sign)
7-5 = 2
Hence Robert will be 2 block east from home
Write an equation for the line in standard form
Answer:
The equation of the line in standard form is y = -1/2·x - 3
Step-by-step explanation:
From the given graph, the "x" and "y" coordinates points through which the line of the graph passes are;
(-4, -1), (-2, -2), and (2, -4)
The slope, m, of the graph is given as follow;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Therefore, by substituting the values of the coordinates for two known points, we have;
[tex]Slope, \, m =\dfrac{(-4) -(-1)}{2-(-4)} = \dfrac{(-4) + 1}{2+4 } = \dfrac{-3}{6} = -\dfrac{1}{2}[/tex]
The slope of the graph, m = -1/2
The equation of the graph on point and slope form is given as follows;
y - (-4) = -1/2(x - 2)
y = -x/2 + 1 - 4 = -x/2 - 3
The equation of the line in standard form, y = m·x + c is y = -1/2·x - 3.
Here is a list of numbers:
10, 3, -2, 19, -19, 4, 13, 6, 7
State the median.
Answer:
the answer is 6
Step-by-step explanation:
When factored completely, x3+ 3x2 - 4x-12 equals?
Answer:
(x - 2) (x + 2) (x + 3)
Step-by-step explanation:
Dont know the full thing but hope some of this helps!
Answer:
(x - 2) (x + 2) (x + 3)
Step-by-step explanation:
7 candes cost £45.29,
how much would 25 candles cost?
Answer:
161.75
Step-by-step explanation:
45.28 divided by 7 = 6.47
6.47 per cande
6.47 times 25 = 161.75