Answers
Answer:
Correct option: First one -> [tex]x^2 = -12y[/tex]
Step-by-step explanation:
The focus and the vertex have the same x-coordinate, so we have a vertical parabola. The standard equation for this parabola is:
[tex]y = a(x-h)^2 + k[/tex]
If the vertex is at the origin, we have that:
[tex](h, k) = (0,0)\\h = 0, k = 0[/tex]
If the focus is at (0,-3), we have that:
[tex](h, k+p) = (0, -3)[/tex]
[tex]p = 1/4a[/tex]
[tex]k + p = -3[/tex]
[tex]1/4a = -3[/tex]
[tex]a = -1/12[/tex]
So we equation of the parabola is:
[tex]y = -x^2/12[/tex]
[tex]x^2 = -12y[/tex]
Correct option: First one
Related Questions
Verify which of the following are identities.
Answers
Answer:
Only the second equation is an identity
Step-by-step explanation:
1)
[tex]1+\dfrac{\cos^2\theta}{\cot^2\theta(1-\sin^2\theta)}= \\\\\\1+\dfrac{\cos^2\theta}{\cot^2\theta(\cos^2\theta)}= \\\\\\1+\dfrac{1}{\cot^2 \theta}= \\\\\\1+\tan^2\theta=\sec^2\theta\neq 2\sec^2 \theta[/tex]
This one is not an identity.
2)
[tex]19\cos \theta\left( \dfrac{1}{\cos \theta}-\dfrac{\tan \theta}{\csc \theta} \right)= \\\\\\19\cos \theta \left( \dfrac{1}{\cos \theta}-\dfrac{\sin^2 \theta}{\cos \theta} \right)= \\\\\\19\cos \theta \left( \dfrac{1-\sin^2 \theta}{\cos \theta}\right)= \\\\\\19\cos \theta \left( \dfrac{\cos^2 \theta}{\cos \theta}\right)= \\\\\\19\cos \theta (\cos \theta)= \\\\\\19\cos^2 \theta = 19\cos^2 \theta[/tex]
This one is an identity. Therefore, only the second equation is an identity. Hope this helps!
Answer:
the person above me is right :)
Step-by-step explanation:
What time is it if half of what has already passed remains until the end of today?
Answers
Answer:
4 p.m.Step-by-step explanation:
We know that a day contains 24 hours in total.
The time already passed will be represented by [tex]x[/tex].
The remaining time would be [tex]\frac{x}{2}[/tex], becasye half of what has already passed remains until the end of the day.
Basically, the sum of these two expression gives 24 hours in total.
[tex]x + \frac{x}{2} =24\\\frac{3x}{2}=24\\ x=16[/tex]
Therefore, the actual time is 4 p.m.
Sue invests £9000 in an account for one year.
At the end of the year, interest is added to her account.
Sue pays tax on this interest at a rate of 20%
She pays £30.24 tax.
Work out the percentage interest rate for the account.
Answers
Answer:
£151.20
Step-by-step explanation:
20%= 100%divided by 5
To find 100% from 20% you x by 5
so you times 30.24 by 5
30.24x 5 = 151.2
So the answer is £151.20
interest percentage rate would be 1.6754%
The interest rate for the account is 1.68%
What is interest rate?The interest rate is the amount a lender charges a borrower and is a percentage of the principal the amount loaned.
Given that,
Sue invests £9000 in an account for one year.
She pays £30.24 at a rate of 20%
So, 20% of the interest = £30.24
Let the interest be x,
X0.2 = 30.24
X = £151.2
The total interest was = £ 151.2
The rate R at which generated this interest =
R = (100 × 151.2)/(1 × 9000)
R = 15120/9000
R = 1.68%
Hence, the interest rate = 1.68%
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An integer is chosen at random from first hundred natural numbers. The probability that the integer chosen the multiple of 5 is
Answers
Answer: 0.2
Step-by-step explanation:
The first hundred natural numbers are 1 to 100.
Now, the numbers that are multiples of 5 are the numbers that end in 5 or 0, so we have:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100
So in the range, we have 20 multiples of 5.
Now, when we select at random, each number has the same probability of being selected, then the probability of randomly selecting a multiple of 5 is equal to the number of multiples of 5 divided the total number of options in the set.
we have 20 multiples of 5, and in the set we have a total of 100 numbers, then the probability is:
P = 20/100 = 0.2
find the volume of this prism
Answers
Answer:
840cm^2
Step-by-step explanation:
Volume: Area of cross section x length
Area of cross section:(15 x 8 + 4x 5 )
length: 6
So volume:
(15 x 8 + 4x 5 ) x 6 = 120 + 20 X 6 = 140x6 = 840cm^2.
Hope this helps.
Good Luck
There are three people in lee’s family. The range if their shoe sizes are 3. Two people in her family wear size 6. Lee’s size is not 6 or 3. What is Lee’s shoe size?
Answers
Answer:
I would say 9
Step-by-step explanation:
range is the difference between the largest and the smallest values in a data set. the range in this case is 3. so, we have to either add to 6 or subtract from 6.
but we've been told that Lee's shoe size is not three so it 6 + 3 = 9.
hope this helps
When constructing an equilateral triangle, what step comes after six arcs are created on the circle?
Answers
Answer:
Num certo bairro da cidade de Beira após o ciclone Idai, 120 voluntários trabalhavam de
manhã, 130 trabalhavam à tarde, 80 trabalhavam à noite, 60 trabalhavam de manhã e a
tarde, 50 trabalhavam de manhã e a noite, 40 trabalhavam à tarde e a noite e 20
trabalhavam nos três períodos.
(a) Quantos voluntários trabalhavam em 2 períodos?
(b) Quantos voluntários tem o bairro?
(c) Quantos voluntários não trabalhavam á tarde?
(d) Quantos voluntários trabalhavam só de manhã?
Step-by-step explanation:
Find the equation of the circle whose center and radius are given. center ( 7, -3), radius = √7
Answers
Answer & Step-by-step explanation:
The equation of a circle is...
[tex](x-x1)^2+(y-y1)^2=r^2[/tex]
So all we have to do is plug in the numbers we are given.
So, the equation of the circle is (x - 7)² + (y + 3)² = √7²
Answer:
[tex](x - 7)^{2} + (y + 3)^{2} = 7[/tex]
Step-by-step explanation:
Just finished this quiz and checked the answer key.
Hope this helps
Which equation represents the line that passes through (-8.11) and
(4,7/2)?
Answers
Answer:
[tex]y=-5/8x+6[/tex]
Step-by-step explanation:
[tex]m=\frac{7/2 - 11}{4--8}[/tex]
[tex]m=\frac{-15/2}{12}[/tex]
[tex]m=-5/8[/tex]
[tex]y=-5/8x+b[/tex]
[tex](-8,11)[/tex]
[tex]11=-5/8 \times -8+b[/tex]
[tex]b=11-(-5/8)(-8)[/tex]
[tex]b=6[/tex]
What is the greatest common factor of the terms in the expression StartFraction 7 over 3 EndFraction a b minus StartFraction 7 over 6 EndFraction b? One-third b One-third a b 7 b 7 a b
Answers
Answer:
(C)7b
Step-by-step explanation:
Given the expression:
[tex]\dfrac{7}{3}ab-\dfrac{7}{6}b[/tex]
Let us factor the expression:
[tex]=\dfrac{7b}{3}\left(a-\dfrac{1}{2}\right)[/tex]
Since we need the greatest common factor, we can rewrite the expression as:
[tex]7b\left(\dfrac{1}{3}a-\dfrac{1}{6}\right)[/tex]
Therefore, the greatest common factor is 7b.
The correct option is C.
Answer: C. 7 b
Step-by-step explanation:
Got it right on edge
Which expression is equivalent to StartRoot 400h^8 j^4 k^6 EndRoot?
Answers
Answer:
[tex]20h^4j^2k^3[/tex]
Step-by-step explanation:
[tex]\sqrt{400h^8j^4k^6}[/tex]
Since it's square root, you divide the exponents by 2.
[tex]20h^4j^2k^3[/tex]
Answer:
[tex]20h^{4} j^{2} k^{3}[/tex]
Step-by-step explanation:
What is the probability of getting tails 4 times in a row while flipping a coin?
Answers
Answer:
[tex]P=0.0625[/tex]
Step-by-step explanation:
The probability of getting one tails is a half.
The probability of getting another tails given you had a tails is:
[tex]\frac{1}{2}*\frac{1}{2}=(\frac{1}{2})^2=\frac{1}{4}[/tex]
The probability of getting n tails in general is given by:
[tex](\frac{1}{2})^n = \frac{1}{2^n}[/tex]
So, when we have four tails - our value for n is four.
[tex](\frac{1}{2})^4=\frac{1}{2^4}=\frac{1}{16}=0.0625[/tex]
What is the equation of a line, in general form, that passes through point (1, -2) and has a slope of 1/3. 1.x - 3 y - 7 = 2.x - 3 y + 7 = 0 3. 3 x - y - 7 = 0
Answers
Answer:
x- 3y - 7=0
Step-by-step explanation:
the line in the slope-intercept form:
y= mx+bm= 1/3 and point given (1, -2) by using which we find y-intercept:
b= y-1/3xb= -2- 1/3*1= - 7/3y= 1/3x- 7/3General form of a line is: ax+by+c= 0
converting:
y= 1/3x- 7/3 ⇒ 3y= x- 7 ⇒ x- 3y - 7=0Answer:
x- 3y - 7=0
Step-by-step explanation:
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To test the effectiveness of a diet cat food, scientists divided a group of overweight cats into a control and treatment group. The cats in the control group ate their regular food. The cats in the treatment group received a measured portion of diet cat food twice a day. After two months, the cats in the treatment group had lost an average of 1.2 lb, and the cats in the control group had gained an average of 0.1 lb. State the Subjects:
Answers
Answer:
Step-by-step explanation:
The subject in a statistical research work usually refer to the participants involved in the experiment which is usually a quantitative research.
The subjects in this study are all the overweight cats including those in the control and treatment groups.
What is the equation of the following line? Be sure to scroll down first to see all answer options.
Answers
Answer:
C
Step-by-step explanation:
Since the graph hits 0 at x = 0, your y intercept is 0.
The graph is decreasing which means you have a negative slope.
They gave you a coordinate so use it to find the slope.
[tex]\frac{1-0}{-3-0} = \frac{-1}{3}[/tex]
That's your slope.
C is the correct answer.
y=-1/3x
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A piece of timber is x cm long. how long would 10 pieces of timber be put together in a line?
Answers
Answer:
10x cm
Step-by-step explanation:
e.g.
5cm cm x 10 = 50cm
--> 10x cm
The length of the 10 pieces together will be, 10x.
What is length?The length is the distance between the extreme ends of the object.
It is known that the length of one piece of timber is x cm.
Multiply 10 and x to determine the total length of 10 pieces of timber together.
10·x=10x
Thus, the total length of 10 pieces of timber will be 10x cm.
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The measure of one angle of a triangle is 105°. What do you know about the measures of the other two angles? Check all that apply.
Both angles are acute.
The sum of the measures of the two angles is 75°.
The sum of the measures of the two angles is 155°.
One of the angles is a right angle.
The measure of neither angle is more than 75°.
The measures of the other angles must be 105° too.
The measure of one of the other angles equals 75°.
The measure of one of the other angles must be 45°.
Answers
Step-by-step explanation:
The sum of the measures of the two angles is 75° because of the sum of angles in a triangle which means that both angles are acute. This also means that the measure of neither angle is more than 75°.
Answer:
A, B, E
Step-by-step explanation:
both angles are acute
The sum of the measures of the two angles is 75°
The measure of neither angle is more than 75°
What is the slope of the line represented by the points in the table? x y –2 –0.35 –1 –0.3 0 –0.25 1 –0.2 2 –0.15 Negative 0.05 Negative .005 0.005 0.05
Answers
Answer:
its a
Step-by-step explanation:
the slope goes from point a to , in this case is subtracting -.05
Answer:
its A - 0.05
Step-by-step explanation:
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You are renting some tables for a party and have to choose between two different rental companies. The first charges $15 per table. The second charges $40 plus $11 per table. Based on this information , the second company is cheaper if you rent more than _____ tables.
Answers
Answer:
10
Step-by-step explanation:
15x = 40 + 11x
4x = 40
x = 10
10 tables they would cost the same, so more than 10 tables would make the second company cheaper
Please help! Correct answer only!
For a fundraiser, there is a raffle with 100 tickets. One ticket will win a $150 prize, and the rest will win nothing. If you have a ticket, what is the expected payoff?
$ ___
Answers
Answer:
Expected Payoff ⇒ $ 1.50 ; Type in 1.50
Step-by-step explanation:
Considering that 1 out of the 100 tickets will have a probability of winning a 150 dollar prize, take a proportionality into account;
[tex]100 - Number of Tickets,\\1 - Number of Tickets You Can Enter,\\\\1 / 100 - Probability of Winning,\\$ 150 - Money Won,\\\\Proportionality - 1 / 100 = x / 150, where x - " Expected Payoff "\\\\1 / 100 = x / 150,\\100 * x = 150,\\\\Conclusion ; x = 1.5 dollars[/tex]
Thus, Solution ; Expected Payoff ⇒ $ 1.50
Please help! Correct answer only please! I need to finish this assignment by today.
Doug is birdwatching at the coast. He records each bird he sees.
What is the experimental probability that the next bird Doug sees will be a cormorant?
Simplify your answer and write it as a fraction or whole number.
Answers
Answer:
1/2
Step-by-step explanation:
During his time bird watching, he sees 1+1+5+8+1=16 different birds in total. Out of those, 8 are cormorant, which means that the experimental probability that the next one is is 8/16=1/2. Hope this helps!
At a sale , dresses were sold for 35% of their original price. If the dresses originally cost 40$ each how much did a dress cost on sale
Answers
Answer:
$ 14
Step-by-step explanation:
$ 40 --- 100%
$ x --- 35%
x = 40*35/100 = 14
The queen received a diamond brooch for her birthday. The largest gem weighed 5.1 carats. There were three other gems that weighed 0.7 carats, 1.4 carat, and 2.6 carats. What was the total weight of the gems?
Answers
Answer:
9.8 carats.
Step-by-step explanation:
5.1 + 0.7 + 1.4 + 2.6
= 9.8
Please answer correctly !!!!! Will mark brainliest !!!!!!!!!!!
Answers
Answer:
no
Step-by-step explanation:
I really need help with this question
Answers
Step-by-step explanation:
∠1 = ∠4 = 57° (vertical angles)
∠6 = 123° (same side interior angles are supplementary)
Answer:
The answer is 123
Step-by-step explanation:
Angle 5 is the same measure as angle one, and a straight line measures 180 degrees. Subtract 57 from 180, and you get the remaining angle. 123 degrees.
I need help please I need to get the right answer
Answers
Answer:
33
Step-by-step explanation:
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Sierra Movie Theater sold 189
tickets for $9.25 each on Friday
night. What was the total amount
of ticket sales for that night?
Answers
Answer:
$1748.25
Step-by-step explanation:
Multiply:
($9.25/ticket)(189 tickets) = $1748.25 (total amount of ticket sales)
If f(x) = 5x + 40, what is f(x) when x = –5? pls help a. -9 b. -8 c. 7 d, 15
Answers
Answer:
D.
Step-by-step explanation:
f(5) = -25 + 40
f(5) = 15
Answer:
The answer is D) 15
Step-by-step explanation:
F(x)= 5x + 40 (substitute -5 for x)
= F(x)= 5(-5)+ 40
= F(x)= -25+40
F(x)= 15
What is 2 with an exponent of -2 equal to?
Answers
Answer:
[tex] \boxed{\frac{1}{4} } [/tex]
Step-by-step explanation:
[tex]{2}^{ - 2} = \frac{1}{ {2}^{2} } \\ \\ \: \: \: \: \: \: \: \: \: = \frac{1}{4} [/tex]
[tex] Negative \: exponent \\ \\ = > {a}^{-x} = \frac{1}{{a}^{x}} [/tex]
Answer:
[tex]=\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]2^{-2}\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}\\2^{-2}=\frac{1}{2^2}\\=\frac{1}{2^2}\\2^2=4\\=\frac{1}{4}[/tex]
What is the image of (9,-5) after a dilation with the scale factor of 2.5?
O (23, 12)
O (22.5, -12.5)
O (-22.5, 12.5)
O (18, 12)
Answers
Answer:
(B) (22.5, -12.5)
Step-by-step explanation:
When the point [tex](9,-5)[/tex] is dilated by with a scale factor of 2.5
In a dilation, when its scale factor is less than 1, the pre-image will be lesser than the image.
However, when the scale factor is greater than 1, the pre-image will be greater than the image.
The Image of the dilation of [tex](9,-5)[/tex] with a scale factor of 2.5 is therefore:
[tex](9*2.5,-5*2,5)\\=(22.5, -12.5)[/tex]
The correct option is B.