If the directrix of a parabola is the horizontal line y = 3, what is true of the parabola?
a)The focus is at (0, 3), and the equation for the parabola is y2 = 12x.
b)The focus is at (0, –3), and the equation for the parabola is x2 = –12y.
c)The focus is at (3, 0), and the equation for the parabola is x2 = 12y.
d)The focus is at (–3, 0), and the equation for the parabola is y2 = –12x.
Answers
Explanation:
This equation may be written in standard form as
[tex]y=- \frac{1}{12} x^{2} [/tex]
The coefficient in front of x² is negative so the curve is downward.
The vertex has coordinates (0,0).
The vertex is equidistant from the directrix and the focus, so the focus is (0, -3).
Answer: on e2020 it’s b
Step-by-step explanation:
Related Questions
Hector drove 185 miles to a business meeting. His business partner drove 5/4 of this distance to get to the same
meeting. How many miles did the business partner drive?
Answers
5/4(185) = 925/4 = 231 1/4 miles
46.25+185=231.25
The business partner drove 231.25 miles.
The waiter places a bowl of soup in front of Caesar. In a counterclockwise direction, he passes the soup to Jada who then passes it to Haifa. Which two rotations about the center of the table describe passing the soup?
Answers
Answer:
We choose answer C) First 150° and then 60°
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.
The waiter places a bowl of soup in front of Caesar. In a counterclockwise direction, he passes the soup to Jada who then passes it to Haifa. Which two rotations about the center of the table describe passing the soup?
A) First 200° and then 80°
B) First 180° and then 72°
C) First 150° and then 60°
D) First 100° and then 40°
My answer:
From the photo, we can see that there are 12 people or 12 places in the circle. And each person has the same distance to other one.
Hence, we can find the the arch degrees between two members:
360 / 12 = 30 °
So from Caesar to Jada, we have to pass through 5 arches
=> the rotation counterclockwise in this situation is: 30 ° *5 = 150°
So from Jada to Haifa, we have to pass through 2 arches
=> the rotation counterclockwise in this situation is: 30 ° *2 = 60°
We choose answer C) First 150° and then 60°
1.2, 3, 7.5, 18.75, ...
Which formula can be used to describe the sequence?
f(x) = 1.2(2.5)x – 1
f(x) = 2.5(1.2)x – 1
f(x) = 1.2(2.5)x
f(x) = 2.5(1.2)x
Answers
It's geometric sequence:
[tex]a_1=1.2,\ a_2=3,\ a_3=7.5,\ a_4=18.75,\ ....[/tex]
Calculate the common ratio:
[tex]r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{3}{1.2}=2.5[/tex]
The explicit formula of geometric sequence:
[tex]a_n=a_1r^{n-1}\to f(x)=a_1r^{x-1}[/tex]
Substitute:
[tex]a_1=1.2,\ r=2.5\\\\f(x)=1.2\left(2.5)^{x-1}[/tex]
Answer: "f(x) = 1.2(2.5)x-1"
Answer:
AStep-by-step explanation:
100% righttt
Brian needs to paint a logo made using two right triangles. The dimensions of the logo are shown below. What is the difference between the area of the large triangle and the area of the small triangle? 7.5 cm2 15.0 cm2 19.5 cm2 39.0 cm2
Answers
ab/2
ab/2
(6) (2) / 2
12/2
6
;large triangle ;
ab/2
(9) (3)/2
27/2
13.5
------------
13.5 - 6 =7.5
7.5 cm² (A)
ab/2
ab/2
(6) (2) / 2
12/2
6
large triangle:
ab/2
(9) (3)/2
27/2
13.5
13.5 - 6 =7.5
7.5 cm² (A)
Which is not used to reach a conclusion in a formal proof?
Answers
In mathematics especially in verifying certain statements regarding geometry, two column proofs are used. A two-column proof contains a table with a logical series of statements and reasons that reach a conclusion. It is commonly present in geometry. Two column proofs always have two columns: statements and reasons. The other choices don’t fit in the definition of two column proof.
In science, the four ways to incorporate proof into the research paper are:
1. If the research you are investigating has been with other research paper before.
2. There is an experimental proof that the evidence is true.
3. The research published belongs to a reliable source.
4. There are citations of the evidence that you are investigating
A $33$-gon $P_1$ is drawn in the Cartesian plane. The sum of the $x$-coordinates of the $33$ vertices equals $99$. The midpoints of the sides of $P_1$ form a second $33$-gon, $P_2$. Finally, the midpoints of the sides of $P_2$ form a third $33$-gon, $P_3$. Find the sum of the $x$-coordinates of the vertices of $P_3$.
Answers
Given any 2 points P(a, b) and Q(c, d), the midpoint [tex]M_P_Q[/tex] of PQ is given by [tex]( \frac{a+c}{2}, \frac{b+d}{2} )[/tex].
2.
Let the x coordinates of the vertices of P_1 be :
[tex]{x_1, x_2, x_3....x_3_3}[/tex]
the x coordinates of P_2 be :
[tex]{z_1, z_2, z_3....z_3_3}[/tex]
and the x coordinates of P_3 be:
[tex]{w_1, w_2, w_3....w_3_3}[/tex]
3.
we are given that
[tex]x_1+ x_2+ x_3....+x_3_3=99[/tex]
and we want to find the value of [tex]w_1+ w_2+ w_3....+w_3_3[/tex].
4.
According to the midpoint formula:
[tex]z_1= \frac{x_1+x_2}{2} [/tex]
[tex]z_2= \frac{x_2+x_3}{2} [/tex]
[tex]z_3= \frac{x_3+x_4}{2} [/tex]
.
.
[tex]z_3_3= \frac{x_3_3+x_1}{2} [/tex]
and
[tex]w_1= \frac{z_1+z_2}{2} [/tex]
[tex]w_2= \frac{z_2+z_3}{2} [/tex]
[tex]w_3= \frac{z_3+z_4}{2} [/tex]
.
.
[tex]w_3_3= \frac{z_3_3+z_1}{2} [/tex]
5.
[tex]w_1+ w_2+ w_3....+w_3_3=\frac{z_1+z_2}{2}+\frac{z_2+z_3}{2}+...\frac{z_3_3+z_1}{2}= \frac{2(z_1+z_2+ z_3....+z_3_3)}{2}[/tex]
[tex]=(z_1+z_2+ z_3....+z_3_3)=\frac{x_1+x_2}{2}+\frac{x_2+x_3}{2}+...\frac{x_3_3+x_1}{2}[/tex]
[tex]=\frac{2(x_1+x_2+ x_3....+x_3_3)}{2}=(x_1+x_2+ x_3....+x_3_3)=99[/tex]
Answer: 99
The odds against a spinner showing an even number are 3:8. What is the probability of the spinner showing an even number?
Answers
Probability: yes/total
3:8 represents odds of 'not even' which is the same as odds of an odd number being spun.
There are 3 odd numbers and 8 even numbers.
P(even) = 8/11
Probability is the likelihood or chance that an event will occur. If the probability of the spinner showing an even number if the odds against a spinner showing an even number are 3:8 is 8/11
What is probability?Probability is the likelihood or chance that an event will occur. The formula for calculating probability is expressed as:
Probability = expected/total outcome
If the odds against a spinner showing an even number are 3:8, the total number of spins is 11 spins
From the ratio
Number of odd spin = 3
Number of even spin = 8
Find the probability of spinning even
pr(even spin) = 8/11
Hence the probability of the spinner showing an even number if the odds against a spinner showing an even number are 3:8 is 8/11
Learn more on probability here: https://brainly.com/question/24756209
An image point after a 180° rotation is Z'(3, 7). What were the coordinates of the pre-image point?
Z(-3, -7)
Z(7, 3)
Z(-7, -3)
Z(7, -3)
Answers
The rule for 180 degree rotations is (x, y) -> (-x, -y). There is no change in the order of the coordinates; they just become negative. The pre-image point's coordinates are (-3, -7), because (-(-3), -(-7)) = (3, 7), which are the coordinates of Z'.
The graph below represents the price of sending picture messages using the services of a phone company.What is the constant of proportionality?
10
11
21
22
Answers
What is the degree of this polynomial 5y2+y+1
Answers
[tex]~~\downarrow \\ 5y^2+ y +1 ~~~~\text{(See arrow)} \\\\ \texttt{Degree of this polynomial } = \boxed{2}[/tex]
Answer:
Degree = 2
Step-by-step explanation:
Given: [tex]5y^2+y+1[/tex]
We are given a polynomial with variable y.
Polynomial: It is an expression with positive number exponent of same variable.
Degree: It is highest power of variable.
In the given polynomial, [tex]5y^2+y+1[/tex].
It has three term with variable y.
The highest power of y is 2.
Leading coefficient is 5
Hence, The degree of given polynomial is 2
Learning about system of equations, please give a VERY DETAILED explanation! I'm having a lot of trouble with this. :(
Answers
P=190x
5=m+x
P=H+270
P stands for Polish
H stands for Hungarian
M stands for the time she can speak in H
X stands for the time she can speak in P
Plug in H and P
190x=150m+270
5=m+x
Solve for X
-m both sides
X=-m+5
Plug in x
190 (-m+5)=150m+270
Distribute
-190m+950=150m+270
+190m both sides
950=340m+270
-270 both sides
680=340m
÷340 both sides
M=2
5=x+2
-2 both sides
X=3
She spoke 2 minutes in Hungarian and 3 minutes on Polish
Graph the following inequality. Then click to show the correct graph. 3x - 2y ≤ 6
Answers
Solution:
The given inequality is :
3 x - 2 y ≤ 6
To draw the graph we will first draw the graph of line : 3 x - 2 y = 6
The graph of this function i.e 3 x - 2 y = 6 will be a straight line.
Then we will check whether origin lies on which side of line .
Put x=0, and y = 0 in the inequality 3 x - 2 y ≤ 6, we obtain
LHS = 0 ≤ 6
It means the line will contain the Origin.
Equation of line in Intercept form is : [tex]\frac{x}{2} -\frac{y}{3}\leq 1[/tex]
How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally
Answers
each person will get 1/6 lb of chocolate
Each person will get 1/6 lb of chocolate.
Here,
Number of people = 3.
Quantity of chocolate = 1/2 lb
What is equally divide?
The law recognizes that both spouses contribute to child care, household management and financial support.
Now,
Quantity of chocolate dividing equally in 3 person = [tex]\frac{\frac{1}{2} }{3}[/tex]
= [tex]\frac{1}{6}[/tex]
Hence, Each person will get 1/6 lb of chocolate.
Learn more about the equally divide rule visit:
https://brainly.in/question/16410598
#SPJ2
Given the function y-4=5/6(x-2), complete the table of values by entering the missing value.
Table:
X: -10 | -4 | -1 | ?
----------------------------
Y: -6 | -1 | 3/2 | 9
And how did you find the that Answer?
Answers
9 - 4 = 5/6 (x - 2)
Then, you subtract on the left side
5 = 5/6 (x - 2)
Then, you multiply by 6 on both sides
30 = 5 (x - 2)
Then, divide both sides by 5
6 = x - 2
Then, at 2 on both sides to isolate x
& your final answer is
x = 8 (this would be the missing value)
Three cube-shaped boxes are stacked one above the other. The volumes of two of the boxes are 1,331 cubic meters each, and the volume of the third box is 729 cubic meters. What is the height of the stacked boxes in meters?
Answers
So if we are given the volume V of a cube-shaped box, the side length of thit is [tex] \sqrt[3]{V} [/tex].
So we calculate the cubic roots of the volumes we have, and we add their heights.
To calculate the cubic root of 729, we can factorize it, and group the perfect cubes together, as follows:
[tex] \frac{729}{3}= \frac{600}{3} + \frac{120}{3} + \frac{9}{3}=200+40+3=243 [/tex]
[tex] \frac{243}{3}= \frac{240}{3}+ \frac{3}{3}=80+1=81 [/tex], which we recognize as [tex] 3^{4} [/tex]
so [tex]729=3*3* 3^{4}= 3^{6}= ( 3^{2} )^{3}= 9^{3} [/tex]
similarly 1,331 can be found to be [tex]11^{3}[/tex].
Thus we have 2 boxes with side length equal to 11 m and one with side length equal to 9 m.
Answer: h= 11+11+9 = 31 (meters)
Answer: The height of the stacked boxes is 31 meters.
Step-by-step explanation:
Since, the Volume of a cube = (side)³
The volume of first box = 1331 cubic meters,
⇒ (side)³ = 1331
⇒
Similarly, the side of second box = 11 meters ( Because, both boxes have the same volume )
Now, the volume of third box = 729 cubic meters
⇒ ⇒ (side)³ = 729
⇒
Thus, the height of the stacked boxes = Side of first box + side of second box + side of third box
= 11 + 11 + 9
= 31 meters.
What is the slope of a line that is perpendicular to the line whose equation is
2y = 3x - 1 ?????
Answers
Nancy and Gabe had a pizza with 12 pieces. Brent ate 1/3 of a pizza and Kayla ate 1/4 of a pizza. How much of the whole pizza is left? Explain how you got your answer please!
Answers
1/4=3/12
4/12+3/12=7/12
1-7/12=5/12
then 1/4 of 12 is=3
4+3=7
12-7=5
5 slices remain
brainliest if were calm:))))))))))))
Chang is participating in a 4-day cross-country biking challenge. He biked for 70, 63, and 66 miles on the first three days. How many miles does he need to bike on the last day so that his average (mean) is
65miles per day?
Answers
(199 + x) / 4 = 65
199 + x = 65 * 4
199 + x = 260
x = 260 - 199
x = 61 <== he would need a 61
Chang needs to bike 65 miles on the last day to have an average of 65 miles per day.
Explanation:To find how many miles Chang needs to bike on the last day, we need to find the total miles he has biked so far. So, we add up the miles he has biked on the first three days: 70 + 63 + 66 = 199 miles.
To find the average of 65 miles per day, we need to divide the total miles by the number of days: 199 / 4 = 49.75 miles per day.
Since Chang wants to have an average of exactly 65 miles per day, he needs to bike 65 miles on the last day. Therefore, he needs to bike 65 miles on the last day.
For how many positive integer values of x is the sum x^2+4x+4 less than 20?
Answers
2^2 is 4+4 times 2 is 12 plus 4 is 16
3^2 is 9+ 4 times 3 is 21 XXXXXXX==> 2 times
Answer:
2 times
Step-by-step explanation:
Note that since we can only use positive integers for , the minimum will be x = 1. Testing x = 2, we get . Since , we know that only will work, thus, there are positive integer values of such that this function is less than 20.
Meg described four triangles as shown below:
Triangle P: All sides have length 7 cm.
Triangle Q: Two angles measure 55°.
Triangle R: Two sides have length 8 cm, and the included angle measures 60°.
Triangle S: Base has length 8 cm, and base angles measure 55°.
Which triangle is not a unique triangle? PLEASE HELP
Answers
The triangle which is not a unique triangle is:
Triangle Q.
Step-by-step explanation:As we know that with the help of given three side lengths a unique triangle is constructed.Hence, Triangle P will be unique.
Also, with the help of the given three angle measure infinite number of triangles could be constructed as the side lengths may be different.'Hence, Triangle Q is not unique.
( Since we are given two angles and the measure of the third angle could be known with the help of property that:
Sum of all the angles of a triangle is 180° )
Also, with the help of a given two side lengths and a included angle measure a unique triangle is constructed.( Since, we make a line segment of given length and then keep the compass at one of end point and make a 60 degree angle and cut that side into length 8 cm and finally join the other end point and the constructed line to get a triangle)
Hence, Triangle R is also unique.
Similarly Triangle S will also be unique by construction.( First draw a line segment of length 8 cm and at both the ends of the line make a 50 degree angle and extend the line over the arc of the angle and see where two lines intersects.
By such a way we obtain a unique triangle)
What are the solutions of the following equation? 5∣x+6∣+8=−6∣x+6∣+8
Answers
Julia spent 1/3 of her birthday money then she lost half of the rest now she has only $10 left how much did she get for her birthday
Answers
Final answer:
Working backwards from the $10 Julia has left after spending and losing money, we calculate that she initially had $30 for her birthday.
Explanation:
To find out how much birthday money Julia initially had, we can work backwards from the $10 she has left. Julia lost half of her money after spending 1/3 of it, which means that the $10 is half of what remained after spending 1/3. Therefore, before she lost half, she must have had $20 (since $10 is half of $20). We can then calculate the original amount by understanding that $20 is 2/3 (the remaining amount after spending 1/3) of the original amount. To find the full amount, we divide $20 by 2/3.
Here's the calculation step-by-step:
Let the original amount of birthday money be X.
Julia spent 1/3 of X, leaving her with 2/3 of X.
She then lost half of the remaining money, leaving her with (1/2)(2/3)X, which equals $10.
Solving for X: (1/2)(2/3)X = $10 -> (1/3)X = $10 -> X = $10 / (1/3) -> X = $10 × 3 -> X = $30.
Julia originally had $30 for her birthday.
Write what the expressions below best represent within the context of the word problem How many quarts of water must be added to 4 quarts of an 80% mixture to obtain a 50% mixture?
Answers
Answer:
80%
50%
Step-by-step explanation:
Question: In the diagram below, point O is the center of the given circle. What is the measure of arc DE.
Answers
FDE = 49 degrees
so arc FE = 49x2 =98
arc DF = 180
so arc DE = 180 -98 = 82
answer
arc DE = 82
Answer:
[tex]82^{o}[/tex]
Step-by-step explanation:
I assumed you are asking about the angle size of minor arc DE.
OD and OE are radii and therefore are equal.
So triangle ODE must be isosceles. That makes angle OED also 49 degrees.
Using sum of interior angles of a triangle DOE = 180 - (49+49)= 82 degrees.
Note: Your question is ambiguous. There are two arc DE's in this question:
The minor arc, straight from D to E along the circumference
The major arc, from D along the circumference to F then E. That is also arc DE
Zoe is making a quilt using 15 red squares and 30 green squares. Which combination shows the same ratio of red squares to green squares
Answers
if x is equal 1 what number is y
Answers
Our equation is this:
y = [tex] \frac{5}{ x^{2} + 1} [/tex] - 1
If x = 1, we can plug it in and then try to solve for y.
Let's plug in 1 for x.
y = [tex] \frac{5}{ 1^{2} + 1} [/tex] - 1
y = [tex] \frac{5}{1 + 1} [/tex] - 1
y = [tex] \frac{5}{2} [/tex] - 1
y = 2.5 - 1
y = 1.5
I hope this helps!
y = 5/ (1)² + 1 -1
y = 5/ 1 + 1 -1
y = 5/2 -1
y = 2.5 -1
y = 1.5
Simplify: (64x^5y^9z^8)^3/7
Answers
= ( 64 )^(3/7) ( x^5)^(3/7) ( y^9 )^(3/7) ( z^8 )^(3/7) =
= ( 2^6 ) ^(3/7) * x^(15/7) * y^(27/7) * z^(24/7) =
= 2^(18/7) * x^(15/7) * y^(27/7) * z^(24/7) =
= 2^2 * 2^(4/7) * x^2 * x^(1/7) * y^3 * y^(6/7) * z^3 * z^(3/7) =
= 4 * x^2 * y^3 * z^3 * ( 16 * x * y^6 * z^3 )^(1/7) =
= [tex]4 x^{2} y ^{3} z^{3} \sqrt[7]{16 x y^{6} z ^{3} } [/tex]
Easy math question help asap
Answers
Combine like terms to get
1/2z+1=1/2z+1
Subtract one from both sides to get
1/2z=1/2z
Multiply both sides by 2 to get
z=z.
This is D, has infinitely many solutions because any number you enter as z will equal itself.
Ex. 5 as z would be 5=5 which is true with any number.
Hope this helped!
Answer:
3/4z-1/4z+1=2/4z+1
Combine like terms to get
1/2z+1=1/2z+1
Subtract one from both sides to get
1/2z=1/2z
Multiply both sides by 2 to get
z=z.
This is D, has infinitely many solutions because any number you enter as z will equal itself.
Ex. 5 as z would be 5=5 which is true with any number.
Determine which system below will produce infinitely many solutions.
−6x + 3y = 18
4x − 3y = 6
2x + 4y = 24
6x + 12y = 36
3x − y = 14
−9x + 3y = −42
5x + 2y = 13
−x + 4y = −6
Answers
-9x + 3y = -42...divide by -3
3x - y = 14...same as first equation....means same line...means infinite solutions
answer is : 3rd answer choice
Answer:
The answer is C
[tex]3x-y=14\\-9x+3y=-42[/tex]
Step-by-step explanation:
In order to determine the system, we have to know the condition to produce infinitely solutions. A solution of a system is the coordinate (x,y) which is common between two lines ( in a 2D plane). A system does not have solution when the lines do not intercept each other, that it means, they are parallele. When two lines are coincident in all points, there are infinitely solutions.
I have attached an image that shows different systems of two lines.
So, to find the system, we have to find two equal equation. If we multiply by 3 the third system:
[tex]3x-y=14\\-9x+3y=-42\\\\(-3)*(3x-y)=(-3)*14\\(1)*(-9x+3y)=(1)*-42\\\\-9x+3y=-42\\-9x+3y=-42[/tex]
This system has infinitely solutions.
Jason has two bags with 6 tiles each.
Without looking, Jason draws a tile from the first bag and then a tile from the second bag. What is the probability of Jason drawing the tile numbered 2 from the first bag and the tile numbered 3 from the second bag?
Answers
assuming the tiles are numbered 1, 2, 3, 4, 5, 6
there is one tile with the number 2 on it in the first bag
and 1 tile with the number 3 on it in the second bag
so you have a 1/6 probability of picking the 2 and a 1/6 probability of picking the 3
so 1/6 * 1/6 = 1/36 probability of picking them both
Answer:
1/36
Step-by-step explanation:
first bag, 1/6 probability of taking 2 from the bag with 6 tabs
second bag, 1/6 probability of taking 3 from the bag with 6 tabs
Multiply 1/6 and 1/6 = 1/36