Find the focus. y= -1/12 (x)² - 6
Answers
Answer:
[tex]\Large \boxed{\sf\ \ (0,-9) \ \ }[/tex]
Step-by-step explanation:
Hello,
We know that when the parabola equation is
[tex]y=a(x-h)^2+k[/tex]
the vertex is (h,k) and the focus is
[tex](h,k+\dfrac{1}{4a})[/tex]
Here, the equation is
[tex]y=-\dfrac{1}{12}x^2-6[/tex]
so
[tex]a=-\dfrac{1}{12}\\\\h = 0\\\\k =-6[/tex]
So,
[tex]k+\dfrac{1}{4a}=-6-\dfrac{12}{4}=-6-3=-9[/tex]
Then, the focus is
[tex]\large \boxed{\sf\ \ (0,-9) \ \ }[/tex]
I attached the graph, included the focus so that you can see it :-)
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Related Questions
Use the linear combination method to solve this system of equations. What is the value of x? Negative 2.4 x minus 3.6 y = 1.2. 2.4 x + 1.2 y = 1.2. Negative 1 0 1 -4.8
Answers
Answer:
x=1/4
y=1/2
Step-by-step explanation:
Given:
-2.4x+3.6y=1.2
2.4x + 1.2y=1.2
-2.4x+3.6y=1.2
Divide through by 1.2
-2x+3y=1
2.4x + 1.2y=1.2
Divide through by 1.2
2x+y=1
-2x+3y=1 (1)
2x+y=1 (2)
From 2
y=1-2x
Substitute y=1-2x into (1)
-2x+3y=1
-2x+3(1-2x)=1
-2x+3-6x=1
-8x=1-3
-8x=-2
Divide both sides by -8
x=1/4
Substitute x=1/4 into (2)
2x+y=1
2(1/4)+y=1
2/4+y=1
1/2+y=1
y=1-1/2
y=1/2
x=1/4
y=1/2
Answer:
x=1
Step-by-step explanation:
edge 2021
You have 0.895 m of ribbon to hang the “Grand Opening” sign. You need 100 cm to hang it correctly. Do you have enough ribbon? If not,how much more do you need?
Answers
Answer:
no you need 10.5cm
Step-by-step explanation:
so convert 0.895m to cm by multiplying it by 100 to get 89.5 which is less
so take the required 100-89.5
Subtraction is a mathematical operation. The ribbon is not enough. 10.5 cm of ribbon is more needed.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
It is known that 1 meter is equal to 100cm, therefore, the length of the ribbon will be equal to,
[tex]\rm 1\ m =100\ cm\\\\0.895\ m = 0.895 \times 100 = 89.5\ cm[/tex]
Now, as the ribbon needed is 100 cm, therefore, the length of ribbon that is needed more is
[tex]\rm \text{length of the ribbon needed} = 100\ cm - 89.5\ cm = 10.5\ cm[/tex]
No, the ribbon is not enough. 10.5 cm of ribbon is more needed.
Learn more about Subtraction:
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Given the coordinates for the function below, which of the following are
coordinates for its inverse?
Gallons Cost, in
of Gas Dollars
1
2
5
15
20
1.25
2.50
6.25
18.75
25.00
Answers
The coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
How to determine the inverse coordinates?The table of values is given as:
Gallons Cost
1 1.25
2 2.50
5 6.25
15 18.75
20 25.00
The inverse of the above table would have the following header
Cost Gallons
When the inverse table is populated, we have:
Cost Gallons
1.25 1
2.50 2
6.25 5
18.75 15
25.00 20
The coordinates are: (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
Hence, the coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
Read more about coordinates at:
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How much does a composition notebook weigh?
Answers
Answer:
11.2 ounces
Step-by-step explanation:
A village P is 10km from a lorry station,Q on a bearing 065°.another village R is 8km from Q on a bearing 155°.calculate;1.the distance of R from P to the nearest kilometer and 2.the bearing of R from P to the nearest degree.
Answers
Answer:
Step-by-step explanation:
find the difference between the two angles first:
155-65=90 degrees
d is the distance d:
d^2=a^2+b^2-2ab cos(90)
d^2=10^2+8^2-2(10)(8)cos(90)
d^2=164
d=√164=12.81
the bearing of R from P to the nearest degree:
180-155=35 degrees
A, B, and C are midpoints of ∆XYZ. What is the length of ? YZ
Answers
Answer:
[tex]YZ = 48[/tex]
Step-by-step explanation:
Given
[tex]AB = 24[/tex]
[tex]XZ = 60[/tex]
Required
Find YZ
From the attachment, AB is parallel and equal to YC;
This implies that
[tex]AB = YC = 24[/tex]
Given that C is the midpoint of YZ;
This implies that
[tex]YC = CZ = 24[/tex] and [tex]YZ = YC + CZ[/tex]
Substitute values for YC and CZ
[tex]YZ = 24 + 24[/tex]
[tex]YZ = 48[/tex]
Answer:
48
Step-by-step explanation:
Write each as a decimal. Round to the thousandths place. 0.2%, 756%, 762%, and 90%. Please answer i need it by tonight >~
Answers
Answer:
0.2%=0.200%
756%=756.000%
762%=756.000%
90%=90.000%
( plz mark me as brainliest, that wold be most appreciated! )
756%=7.56
762%=7.62
90%=0.9
Solve. x2+5x−2=0 Enter your answers, as exact values, in the boxes. x = or x =
Answers
Answer:
[tex]x=\frac{-5+\sqrt{33} }{2}[/tex]
[tex]x=\frac{-5-\sqrt{33} }{2}[/tex]
Step-by-step explanation:
Using the quadratic formula in which a=1, b=5 and c=-2
[tex]x_1=\frac{-b+\sqrt{b^{2}-4ac } }{2a} \\x_2=\frac{-b-\sqrt{b^{2}-4ac } }{2a}\\x_1=\frac{-5+\sqrt{5^{2}-4(1)(-2) } }{2(1)}\\x_1=\frac{-5+\sqrt{33} }{21}\\x_2=\frac{-5-\sqrt{25+8 } }{2}\\x_2=\frac{-5-\sqrt{33} }{2}[/tex]
Elton is a candle maker. Each 15 \text{ cm}15 cm15, start text, space, c, m, end text long candle he makes burns evenly for 666 hours. If Elton makes a 45 \text{ cm}45 cm45, start text, space, c, m, end text long candle, how long would it burn?
Answers
Answer:
18
Step-by-step explanation:
cm 15 -> 14
hours 6 ->?
cm 15 x3->45
hours 6 x3->18
the 45 cm long candle is 3 times as long ,so it would burn for 3 times as long A 45cm long candle would burn for 18 hours
What the answer now and answer fast correct answer
Answers
Answer:
Using the given information in the problem, the value of f is 9
Step-by-step explanation:
In this problem, we will be using tangent, Tangent is the opposite side divided by the adjacent side from the given angle. The given angle that we will be using for this problem is the measurement of ∠F which is 58°. We will use this for our equation.
Let's set up our equation for tangent.
[tex]Tan(58)=\frac{15}{f}[/tex]
Since we are looking for f , then we will rearrange the equation.
[tex]f=\frac{15}{tan(58)}[/tex]
Now, we will solve for x. You can use a calculator to do these calculations.
[tex]f=9[/tex]
So, the value of f in the triangle is 9.
Answer: f=9
Because quick mafs says so
1. Robert and Casey added the following values shown below. Who solved
correctly?
ROBERT
CASEY
5 1/8+ 2 1/3 = 7 1/2
-4 1/2+ 6 3/4= 2 1/4
Answers
Answer:
Casey is correct.
Step-by-step explanation:
Robert's 5 1/8 + 2 1/3 = 7 1/2 is wrong because if 5+2 = 7, I would have to change the denominator of both fractions so they are both the same. The denominator would have to be 24. That would make the fractions 3/24 and 8/24. If you added them together, it would not be able to simplify to 1/2.
Casey's -4 1/2 + 6 3/4 = 2 1/4 is correct because —4 - 6 = 2. In order to make the fractions have the same denominator, you would have to multiply -1/2 by 2 on both numerator and denominator wich would equal -2/4. Now add -2/4 and 1/4 and you get 1/4. If my explaining is confusing, I'm sorry!☜(ﾟヮﾟ☜)
Casey is correct and he will get the correct solution.
We have given that,
ROBERT CASEY
5 1/8+ 2 1/3 = 7 1/2 -4 1/2+ 6 3/4= 2 1/4
Robert's 5 1/8 + 2 1/3 = 7 1/2 is wrong because if 5+2 = 7, I would have to change the denominator of both fractions so they are both the same.
What is the equation?A statement that the values of two mathematical expressions are equal.
The denominator would have to be 24.
That would make the fractions 3/24 and 8/24.
If you added them together, it would not be able to simplify to 1/2.
Casey is correct.
-4 1/2 + 6 3/4 = 2 1/4 is correct
because 4 - 6 = 2.
In order to make the fractions have the same denominator, you would have to multiply -1/2 by 2 on both numerator and denominator which would equal -2/4.
Now add -2/4 and 1/4 and you get 1/4.
To learn more about the equation visit:
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A ladder is placed 8 feet away from the base of a tree. If the ladder forms a 57° angle
with the ground, how high up the tree will the ladder reaach
Answers
Answer:
3.88 feet
Step-by-step explanation:
let the length the ladder reaches be x
[tex] \tan(57) = \frac{x}{8} [/tex]
[tex]x = 8 \tan(57) [/tex]
x = 3.8775938143
Please help as soon as possible
Answers
Your question has been heard loud and clear.
Answer is option d or the fourth option.
thank you
if sade can be 12 years and his mother senior him with 24 years and his dad senior him with 30 yearshow old is the sum of the both parents
Answers
Answer:
88
Step-by-step explanation:
mother's age = 12+24
= 36
father's age = 12+40
=52
add the parent age= 36+52
= 88
3 ( 1 - 20 ) + 10 = 4
Answers
Answer:
3(1 - 20) + 10 = 4
3 * (-19) + 10 = 4
-57 + 10 = 4
-47 = 4
Since the two are not equal, this statement is false/invalid.
Hope this helps!
Dora bought a bottle of nail polish that was marked down by 20 percent from its original price of $4.50. Including a 9 percent sales tax, what is the final cost of the bottle of nail polish?
Answers
Answer:
3.92$
Step-by-step explanation:
The first step is to deduct 20% of 4.50 from 4.50.
20% of 4.50 is 0.2 x 4.50 = .90
4.50 - 0.90 = 3.60
That's the new price without the sales tax.
Now we need to add 9% of 3.60 to 3.60 to get the final cost.
9% of 3.60 is .09 x 3.60 = 0.32
3.60 + .32 = $3.92
Hope it helps.. If yes mark me BRAINLIEST
Tysm!
Answer:
$3.92
Step-by-step explanation:
Hello! For this question we need to gather up all the facts before we could answer it!
The original nail polish cost was $4.50
But the bottle was marked down by 20%
Then has a sales tax of 9%
So let's multiply 4.50 x 0.2 = 0.9
With that we need to subtract off of the original price because it is decreasing.
4.50 - 0.9 = 3.60
But that is not the final price because the bottle has a sales tax! We need to multiply the price after the 20% mark down, so, 3.60 x 0.09 = 0.324
And Then because we are dealing with money, we are going to make sure that we are only adding a decimal that goes up to the hundredths place.
Add: 3.60 + 0.32 = 3.92
The Final price of the nail polish that Dora bought would be $3.92. Which is actually a 0.58 cents drop!
I hope this helped!
An actor invests some money at 8% simple interest, and $21 comma 000 more than four times the amount at 10% simple interest. The total annual interest earned from the investment is $49 comma 140. How much did he invest at each amount? Use the six-step method.
Answers
Answer:
First investment = $98000
Second = $413,000
Step-by-step explanation:
Given the following :
Investment 1:
Let first investment = f
Rate = 8% = 0.08
Investment 2:
$21,000 more than 4 times of investment 1:
4f + 21000
Rate = 10% = 0.1
Total annual interest earned from both :
$49,140
Interest on investment 1 + interest on investment 2 = $49,140
To solve:
Simple Interest = principal * rate * time
Time = 1 year
Total interest = (f * 0.08 * 1) + ((4f + 21000) * 0.1 * 1)
49140 = 0.08f + 0.4f + 2100
0.48f = 47040
f = 47040 / 0.48
f = 98000 = first investment
Second investment :
4f + 21000
= 4(98000) + 21000
= $413,000
What is the slope of a line that contains the points (4, -2) and (-1, 4)
Answers
Answer:
-6/5
Step-by-step explanation:
The slope is (4 - (-2)) / (-1 - 4) = (4 + 2) / (-5) = 6 / -5 = -6/5.
Answer:
-6/5
Step-by-step explanation:
We can find the slope by using the slope formula
m = (y2-y1)/(x2-x1)
= (4 - -2)/(-1 -4)
= (4+2)/ ( -1-4)
=-6/5
What is the circumference of a circle with a diameter of 100m. A 100m B 157m C 300 m D 314m
Answers
Answer:
C = 314 m
Step-by-step explanation:
The circumference of a circle is given by
C = pi * d
Using 3.14 for pi
C = 3.14 * 100
C = 314 m
Answer:
The answer is option D.
314mStep-by-step explanation:
Circumference of a circle = πd
Where d is the diameter
From the question
d = 100m
Circumference of the circle is
100π
= 314.2
Which is 314m to the nearest whole number
Hope this helps you
The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Select two options. $8 $9 $11 $13 $14
Answers
Answer:
The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Select two options.
$8 . YES
$9 . HELL NO
$11 . DEFINITLY NOT
$13 . GET OUTTA HERE
$14 . MMM YES
Step-by-step explanation:
Answer:
A and E or 8, 14
Step-by-step explanation:
I need Help!!! Will give Brainliest ABC≅DEF Find the following: 1. x = 2. CB = 3. FE = 4. y = 5. ED = 6. FD = 7. AB = 8. AC = 9. Area =
Answers
Answer:
ABC≅DEF
x = 2
CB = 3
FE = 4
y = 5
ED = 6
FD = 7
AB = 8
AC = 9
In triangle ABC=
Side AC= 9 cm
Side CB= 3 cm
Area= [tex]\frac{1}{2}[/tex]×[tex]b[/tex]×[tex]h[/tex]
=13.5 cm^2
In triangle DEF=
Side FE= 4 cm
Side FD= 7 cm
Area= [tex]\frac{1}{2}[/tex]×[tex]b[/tex]×[tex]h[/tex]
=14 cm^2
Are the following angle relationships possible? Explain.
Answers
Answer:
no
Step-by-step explanation:
The 5x+30 is the supplementary angle of the interior one:
180 - 5x - 30 = -5x + 150
Then they have to add up to 180:
4x-9 + 2x+3 -5x + 150 = 180
which simplifies to x = 36
So the angles would be 135, 75 and -30, which is impossible!
pls help me with this (ill give brainliest)
Answers
Answer:
72.96
Step-by-step explanation:
Let the first circle's radius be r and quarter circle's radius be R
Area of circle = π[tex]r^{2}[/tex]
= 3.14 × 8 × 8
= 200.96 [tex]cm^{2}[/tex]
Area of quarter circle = π[tex]R^{2}[/tex]/4
= 3.14 × 16 × 16
= 803. 84/4
=200.96
Area of shaded portion = (Area of Quarter circle - Area of semi-circle ACD - Area of triangle ABC) + (Area of the circle - Area of semi-circle ACD - Area of triangle ABC)
Area of Semi-circle = Area of the circle divided by 2
= 100.48
Area of triangle = [tex]\frac{bh}{2}[/tex]
= [tex]\frac{16 * 8}{2}[/tex]
= 64
Therefore, The area of shaded portion= (200.96-100.48-64) + (200.96 - 100.48 - 64)
= 36.48 +36.48
=72.96
Multiply (3x-2) (2x+3)
Answers
Answer:
6x^2 + 5x + 6
Step-by-step explanation:
Distributive property
Answer:
=6x^2+5x−6
Step-by-step explanation:
Using the foil method, 3x*2x+3x*3+-2*2x+-2*3
A number is 30% of 20% of the number x.
Answers
Answer:
6/100x
Step-by-step explanation:
Answer:6/100x
Step-by-step explanation:
X*2+1=10 then x=? Tell me the value of x
Answers
Answer:
4.5Step-by-step explanation:
[tex]x \times 2 + 1 = 10[/tex]
[tex]2x + 1 = 10[/tex]
Move constant to R.H.S and change its sign
[tex]2x = 10 - 1[/tex]
Subtract the numbers
[tex]2x = 9[/tex]
Divide both sides of the equation by 2
[tex] \frac{2x}{2} = \frac{9}{2} [/tex]
Calculate
[tex]x = 4.5[/tex]
Hope this helps..
Best regards!!
sin theta = x , sec theta =y . find cot theta pls answer fast i need to verify my answer . you can directly write the answer no issues
Answers
Answer:
[tex]\huge\boxed{\cot\theta=\dfrac{1}{xy}}[/tex]
Step-by-step explanation:
[tex]\bold{METHOD\ 1}[/tex]
[tex]\sin\theta=x\\\\\sec\theta=y\\\\\cot\theta=?\\\\\text{We know:}\\\\\sec x=\dfrac{1}{\cos x};\ \cot x=\dfrac{\cos x}{\sin x}\\\\\sec\theta=y\to\dfrac{1}{\cos \theta}=y\to\dfrac{\cos\theta}{1}=\dfrac{1}{y}\to\cos\theta=\dfrac{1}{y}\\\\\cot \theta=\dfrac{\frac{1}{y}}{x}=\dfrac{1}{xy}[/tex]
[tex]\bold{METHOD\ 2}[/tex]
[tex]\text{We know}\\\\\tan x=\dfrac{\sin x}{\cos x}\\\\\cot x=\dfrac{\cos x}{\sin x}=\dfrac{1}{\tan x}\\\\\sec x=\dfrac{1}{\cos x}\\\\\text{therefore}\\\\(sin x)(\sec x)=(\sin x)\left(\dfrac{1}{\cos x}\right)=\dfrac{\sin x}{\cos x}=\tan x\\\\\dfrac{1}{(\sin x)(\sec x)}=\dfrac{1}{\tan x}=\cot x[/tex]
[tex]\\\sin \theta=x;\ \sec\theta=y\\\\\text{substitute}\\\\\cot\theta=\dfrac{1}{xy}[/tex]
Please helpppp!!!
Solve: x^2 - 4x-5=0
Answers
Answer:
[tex]x=-1,5[/tex]
Step-by-step explanation:
[tex]x^2-4x-5=0[/tex]
In order to solve this quadratic, we have many methods. We can factor, complete the square, or use the quadratic formula. I'm going to factor since it's the easiest method.
To factor, find two numbers that when multiplied equal a(c) and when added equal b.
a=1, b=-4, and c=-5.
So we want two numbers that when multiplied equals 1(-5)=-5 and when added equals -4.
-5 and 1 are the possible numbers. Therefore:
[tex]x^2-4x-5=0\\x^2+x-5x-5=0\\x(x+1)-5(x+1)=0\\(x-5)(x+1)=0\\x=5, -1[/tex]
Justin weighed 8 lb 12 oz when he was born. At his two-week check-up, he had gained 8 ounces. What was his weight in pounds and ounces?
Answers
Answer:
9 lb 4 oz
Step-by-step explanation:
Justin weighed 8 lb 12 oz at birth. He gained 8 ounces by his two-week checkup. So,
8 lb 12 oz + 8 oz = 8 lb 20 oz
But, 16 oz equals one pound. So,
20 oz = 1 lb with 4 oz remaining
Now add them together.
8 lb + 1 lb 4 oz = 9 lb 4 oz
Justin's weight is 9 lb 4 oz.
Hope that helps.
Which of the following is not a congruence theorem or postulate A. SSA B. SAS C. AAS D. SSS
Answers
Answer:ITS A
Step-by-step explanation:
SAS: side angle side
SSA: is not a congruence theorem
AAS:angle angle side
SSS:side side side
Answer:
The answer is A.
Step-by-step explanation:
Just took the test