It would be your second option. It's the only one that passes the vertical line test.
Answer:
2nd option
Step-by-step explanation:
Write the equation of a parabola with vertex at (0,0) and directrix of y=-3
Answer:
x^2=12y
**C on edge
The equation of a parabola with its vertex at (0,0) and directrix at y=-3 is y = 1/12 x².
Explanation:To write the equation of a parabola, we are given that its vertex is at (0,0) and its directrix is y=-3. The equation of a parabola with the vertex at (0,0) and the focus at (0,p) or a directrix at y=-p is given as y = 1/4p x². Considering the distance from the vertex to the directrix is the same as the distance from the vertex to the focus, the value of p in this case will be 3. Therefore, the equation of this parabola is y = 1/12 x².
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Solve the equation for b. b/2q=h+7
[tex]\dfrac{b}{2q}=h+7\qquad\text{multiply both sides by 2q}\neq0\\\\b=2q(h+7)\qquad\text{use distributive property}\\\\b=(2q)(h)+(2q)(7)\\\\\boxed{b=2hq+14q}[/tex]
a regular size chocolate bar is 5 4/9 inches long. the king size bar is 3 times as long as the regular size bar. how long is the king size bar
Answer:
15 4/9 inches long
Step-by-step explanation:
5 4/9 × 3
When lining them vertically the 3 ends up under 5 in which you multiply and transfer the 4/9 next to the product of 15. Hope that helped!
The king size chocolate bar is three times as long as the regular bar, so given that the regular bar is 5 4/9 inches long, the king size bar is 16 1/3 inches long.
Explanation:The problem involves a regular size chocolate bar that is 5 4/9 inches long and a king size bar that is three times as long. Given the length of the regular bar, our objective is to find out how long the king size bar is.
We start by converting the mixed number 5 4/9 into an improper fraction which gives us 49/9 inches. We then multiply 49/9 by 3 to get the length of the king size bar which is 147/9 inches. Converting this improper fraction back into a mixed number, we get 16 1/3 inches. Therefore, the king size bar is 16 1/3 inches long.
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How many groups of 8 can you make out of 63
Is 2/4 equal to 1/2 cup?
Answer:
yes
Step-by-step explanation:
if you reduce 2/4 and divid both sides by u get 1/2
and 1/2 = 1/2
A pair of parallel lines is cut by a transversal. One of the angles formed measures 58°.
Which statements about the other seven angles formed are true?
There are three more angles with the same measure.
All the other angles have the same measure.
The rest of the angles measure 122°.
Only three of the angles measure 122°.
Four of the angles measure 122°.
Answer:
a and e
Step-by-step explanation:
Urgent
What is the equasion,Can anybody awnser the question attached Please help
Answer:
x=6 ; y=1
Step-by-step explanation:
Let 'y' stand for the speed of the wind and 'x' stand for the speed of Santa. We will use the general equation (distance)=(rate)(time) to write two equations from the given information:
With the wind:
35=(x+y)(5)
Against the wind:
35=(x-y)(7)
Now we have two equations and two unknowns so we can solve for x and y. We get:
x=6 miles/min
y=1 miles/min
Solve the system of equations below by graphing. 2.4x-y=-3.5 x^2+x+y=6 What are the approximate solutions rounded to the nearest tenth? (–6.2, –4) and (5, 0.6) (–4, –6.2) and (0.6, 5) (–2.4, 2.4) and (3.7, –12.8) (2.4, –2.4) and (–12.8, 3.7)
Answer:
(-4.0,-6.2) and (0.6,5)
Step-by-step explanation:
We have been given the system of equations
[tex]
2.4x-y=-3.5........(1)\\x^2+x+y=6 .....(2)[/tex]
Let us graph these equation on the xy-plane.
The intersection point of these two curves will give us the solution of the system of equations.
Equation 1 represents a parabola and equation (2) represents a straight line.
The graph is shown in the attached file.
The intersection points of the parabola and the line are (0.622,4.992) and (-4.022, -6.152)
Therefore, the solutions rounded to nearest tenth are
(-4.0,-6.2) and (0.6,5)
Answer:
B. (–4, –6.2) and (0.6, 5)
Step-by-step explanation:
Hope this helps!! Have a great day!! : )
what is the domain of f(x) = (1/3)^x ?
Answer:
B
Step-by-step explanation:
There isn't any number that x can't be. Start with a graph to show how this could be so.
It is easy to see that x > 0 gives a line that goes very near the x axis. It is not quite so easy to see that it never touches the x axis. But if you recreate the graph in Desmos, you will see that is true if you spread the x's out.
It is not quite so easy to see that when x<0 the graph tips upward very quickly but again if you move the values of the axis around you will see there is no value that x cannot be.
Answer:
B:All real numbers
Factor the trinomial below 8x^2-12x-8
[tex]8x^2-12x-8=4(2x^2-3x-2)=4(2x^2-4x+x-2)\\\\=4[2x(x-2)+1(x-2)]=4(x-2)(2x+1)\\\\\boxed{ 8x^2-12x-8 =4(x-2)(2x+1)}[/tex]
Answer:
4(2x+1)(x-2)
Step-by-step explanation: I just did it
John must have at least 289 test points to pass his math class. He already has test scores of 72, 78, and 70. Which inequality will tell him at least how many more points he needs to pass the class? A. 72 + 78 + 70 + x 289 B. 72 + 78 + 70 + x > 289 C. 72 + 78 + 70 + x < 289 D. 72 + 78 + 70 + x 289
B. 72 + 78 + 70 + x > 289
The area of a rectangular dog pen is 8 1/2 square feet.if the width is 3 2/5 feet,what's is the length,in feet ?
Answer:
l = 2.5 feet
Step-by-step explanation:
A = lb
8.5 = l * 3 2/5
8.5 = l * 3.4
l = 8.5 / 3.4
l = 2.5 feet (Always remember to put the units, otherwise you may not get points.)
Please give a rating and a thanks.
Thank you.
Answer:
l = 2 1/2 ft
Step-by-step explanation:
Area is given by the formula
A = l*w
We know the area is 8 1/2
Changing this to an improper fraction 8 1/2 = (2*8 +1)/2 = 17/2
The width is 3 2/5 as an improper fraction = (5*3+2)/5 = 17/5
A = l*w
17/2 = l* 17/5
Multiply each side by 5/17
17/2 * 5/17 = l* 17/5 * 5/17
5/2 = l
2 1/2 = l
A tourist starts to walk up a mountain path that is 31 miles long at the rate of 4 miles per hour. After walking for a while, he gets tired and decides to get a taxi. The taxi gets him to the top travelling at a constant speed of 50 mph. If the tourist reaches the destination 2 hours after he started, what distance does he have to pay the cab driver for?
Answer: 25 miles
Step-by-step explanation:
Since, the total distance = 31 miles.
Let he walks x miles at the rate of 4 miles per hour.
⇒ he walks remaining (31-x) miles at the rate of 50 miles per hour.
According to the question,
[tex]\frac{x}{4} + \frac{31-x}{50} = 2[/tex]
⇒ [tex]\frac{25x}{100} + \frac{62-2x}{100} = 2[/tex]
⇒ [tex]\frac{25x+62-2x}{100}= 2[/tex]
⇒ [tex]\frac{23x+62}{100}= 2[/tex]
⇒ [tex]23 x + 62 = 200[/tex]
⇒ [tex]23 x = 200 - 62[/tex] ( by subtracting 62 on both sides )
⇒ [tex]23 x = 138[/tex]
⇒ [tex]x=\frac{138}{23}[/tex] ( Dividing both sides by 23 )
⇒ [tex]x = 6[/tex]
Thus, the distance he pays to the cab driver = 31-x= 31 - 6 = 25 miles.
Therefore, He pays to the cab driver for 25 miles.
Distance that must be paid to the taxi = 25 miles
Further explanationLinear motion consists of 2: constant velocity motion with constant velocity and uniformly accelerated motion with constant acceleration
• At constant velocity motion:
the speed of vo = v = constant
acceleration = a = 0
Δx = vt or x = xo + vtAn equation of constant velocity motion
[tex]\large {\boxed {\bold {x = v \times \: t}}}[/tex]
x = distance = m
v = speed = m / s
t = time = seconds
so
[tex]\rm t=\dfrac{x}{v}[/tex]
A mountain path is 31 miles long
The distance traveled by tourists = x1
The distance traveled taxi = x2, such that
x1 + x2 = 31
x1 = 31-x2
total travel time (t) = 2 hours
tourist speed = v1 = 4 mph
taxi speed = v2 = 50 mph
time taken by tourists = t1
[tex]\rm \dfrac{x1}{v1}=\dfrac{x1}{4}[/tex]
the time taken by taxi = t2
[tex]\rm \dfrac{x2}{v2}=\dfrac{x2}{50}[/tex]
total time = t1 + t2
[tex]\rm 2=\dfrac{x1}{4}+\dfrac{x2}{50}\\\\2=\dfrac{25x1+2x2}{100}\\\\200=25(31-x2)+2x2\\\\200=775-25x2+2x2\\\\575=23x2\\\\x2=\boxed{\bold{25~miles}}[/tex]
Learn more
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Solve the system of equations by subtraction. What is the solution for x? 2x+y=1 4z+2y=-1
[tex]\left\{\begin{array}{ccc}2x+y=1&|\text{subtract 2x from both sides}\\4x+2y=-1\end{array}\right\\\\\left\{\begin{array}{ccc}y=-2x+1&(*)\\4x+2y=-1&(**)\end{array}\right\\\\\text{substitute}\ (*)\ \text{to}\ (**):\\\\4x+2(-2x+1)=-1\qquad\text{use distributive property}\\\\4x+(2)(-2x)+(2)(1)=-1\\\\4x-4x+2=-1\\\\2=-1\qquad\text{FALSE}\\\\Answer:\ \boxed{NO\ SOLUTION}[/tex]
You have just accepted a job at Wonders Day Camp for the summer. The camp will pay you $48.23 each day for 8 weeks. If you work 5 days each week, how much money will you make this summer?
Answer:
$192.20
Step-by-step explanation:
8 x 5=40 48.32x40=192.20
Answer:
You will make $1929.20 this summer.
Step-by-step explanation:
You have just accepted a jab at Wonders Day Camp for the summer.
The camp will pay for each day for 8 weeks = $48.23
You work 5 days each week.
So total days of work = 8 × 5 = 40 days
You earn $48.23 for one day.
For 40 days you will earn = 40 × 48.23 = $1,929.20
You will make $1929.20 this summer.
A radio station have free tickets to 10% of the people attending a concert. The radio station gave 640 people free tickets. What is the total number of people who attended the concert?
Answer:
6400 people.
Step-by-step explanation:
If 640 is 10%. You multiply 640 by 10 to get 6400 or 100% of the people.
The area of a square is (4x + 3)^2 square inches. The perimeter of the square is 172 inches. What is the value of x?
Answer:
x = 10
Step-by-step explanation:
the area of a square = s² ( s is the side length )
s² = (4x + 3)² ( take the square root of both sides )
s = [tex]\sqrt{(4x+3)^2}[/tex] = 4x + 3
perimeter = 4s = 172, that is
4(4x + 3) = 172 ( distribute left side )
16x + 12 = 172 ( subtract 12 from both sides )
16x = 160 ( divide both sides by 16 )
x = 10
In a rectangle the length is 2 cm longer than the width. If its length and width are both increase by 4 cm it's area is increased by 56 cm. Find the original length and width.
Answer:
Length = 6 cm and width = 4 cm.
Step-by-step explanation:
Let the width be x, then the length is x + 2 cm and its area = x(x + 2).
The new width and length are x + 4 and x + 6, and the new area is
(x + 4)(x + 6).
So we have the equation:-
(x + 6)(x + 4) = x(x + 2) + 56
x^2 + 10x + 24 = x^2 + 2x + 56
10x - 2x = 56 - 24
8x = 32
x = 4 cm = width
and length = 4 + 2 = 6 cm
Can you help?
: 46 × 12 = 46 × (10 + ? )
= ( ? × 10 ) + ( ? × 2)
= ? + 92
= ?
Thank you :D
46 × 12 = 46 × (10 + 2) =
= (46 × 10 ) + (46 × 2)
= 460 + 92
= 552
I'm very confuesed where to start this problem:
Graph −18x+9y=72
Answer:
Plug in x=0 and plot the point, then plug in y = 0 and plot the point.
Answer:
y=-2x+8
Step-by-step explanation:
first you have to -18x on both sides because you want to get y by itself
9y=-18x+72
then divide 9 by both sides
9y/9=-18x+72/9.....-18/9=-2 and 72/9=8
y=-2x+8
-2x is your slope and 8 is your y intercept
36x+45y=123
46x+15y=23
Elimination Method
[tex]\left\{\begin{array}{ccc}36x+45y=123&\text{divide both sides by (-3)}\\46x+15y=23\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-12x-15y=-41\\46x+15y=23\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad34x=-18\qquad\text{divide both sides by 34}\\.\qquad\qquad x=-\dfrac{18}{34}\to\boxed{x=-\dfrac{9}{17}}\\\\\text{Put the value of x to the second equation.}\\\\46\left(-\dfrac{9}{17}\right)+15y=23[/tex]
[tex]-\dfrac{414}{17}+15y=\dfrac{391}{17}\qquad\text{add}\ \dfrac{414}{17}\ \text{to both sides}\\\\15y=\dfrac{805}{17}\qquad\text{divide both sides by}\ 15\\\\y=\dfrac{805}{255}\\\\\boxed{y=\dfrac{161}{51}}\\\\Answer:\ \boxed{x=-\dfrac{9}{17}\ and\ y=\dfrac{161}{51}}[/tex]
Write the coordinates for the given dilation
Answer:
D[tex]_o[/tex] of Y = (-3/2, -1)
Step-by-step explanation:
We are given three points on the graph:
X (4, 0)
Y (3, 2)
Z (2, 2)
and the scale factor of dilation which is [tex]-\frac{1}{2}[/tex].
Given that, we are to find the coordinates of Y after dilation. To find that, we will multiply the coordinates of the point Y with the scale factor.
Y = [tex](-\frac{1}{2}[/tex] × [tex]3[/tex] , (-\frac{1}{2}[/tex] × [tex]2)[/tex]
Y = [tex](-\frac{3}{2} , -1)[/tex]
Rohan invested in a precious mineral. The value of the mineral tends to increase by about 9% per year. He invests $12,000 in 2018.
How much more will his investment be worth by 2025?
Enter your answer in the box.
Round to the nearest whole dollar.
Answer:
$9,936.47
Step-by-step explanation:
Similarly to the other problem I helped you with we have:
[tex]A_{final}=A_{initial}(1+r)^t[/tex]
Where A is amount, r is rate and t is time.
In this case A=12000, r=9%=0.09 and 9% in decimals is 0.09 (9÷100=0.09), and t=7 since 2025 -2018 = 7 years. So how much is this investment worth in 7 years? Let's plug those values in and we obtain:
[tex]A_{final}=12000(1+0.09)^7=12000(1.09)^7=21936.47[/tex]
So the investment will be worth $21,936.47. Now we must calculate how much more will this precious mineral be worth so we get the difference of the final amount and the initial amount the mineral was worth and so:
[tex]A_{final}-A_{initial}=21936.47-12000=9936.47[/tex]
And so the mineral will be worth $9,936.47 more than it originally was worth after 7 years.
What is the full price of 90 tablets of "Drug Y", assuming your cost for 500 tablets is $425.00 with a 28% markup and a dispensing fee of $4.85 ?
Answer: Full price of Drug Y = $98.793
Step-by-step explanation:
Cost of 500 tablet = $425
28% markup = 425 * 28/100
= $119
Cost + markup = $425 + $119 = $544
Cost + markup + dispensing fee = $544 + $4.85 = $548.85
Full price of 500 tablet = $548.85
Full price of 1 tablet = $548.85/500
=$1.0977
Full price of 90 tablet = $1.0977 * 90
= $98.793
Please show steps so I understand.
Rearrange the equation so X is the independent variable. 6x+y=4x+11
Y=______________
6x+y=4x+11
y=4x+11-6x
y=-2x+11
[tex]\(y = 11 - 2x\)[/tex] is the rearranged equation with [tex]\(x\)[/tex] as the independent variable.
To rearrange the equation [tex]\(6x + y = 4x + 11\)[/tex] so that (x\) is the independent variable and (y) is dependent, we need to isolate (y) on one side of the equation.
Start with the given equation: [tex]\(6x + y = 4x + 11\)[/tex].
Subtract (4x) from both sides to move all terms involving (y) to one side: [tex]\(6x - 4x + y = 11\).[/tex]
Simplify the left side by combining like terms: 2x + y = 11.
To isolate y, subtract 2x from both sides: 2x + y - 2x = 11 - 2x.
Simplify: [tex]\(y = 11 - 2x\)[/tex].
So, the rearranged equation with (x) as the independent variable is y = 11 - 2x.
Detailed calculation:
Starting equation: (6x + y = 4x + 11)
Subtract (4x) from both sides:
[tex]\(6x - 4x + y = 4x - 4x + 11\)[/tex]
[tex]\(2x + y = 11\)[/tex]
Subtract (2x) from both sides:
[tex]\(2x + y - 2x = 11 - 2x\)[/tex]
[tex]\(y = 11 - 2x\)[/tex]
Therefore, [tex]\(y = 11 - 2x\)[/tex] is the rearranged equation with [tex]\(x\)[/tex] as the independent variable.
solve equation for n
Simplify 2/3 + n + 6 to n + 20/3
n + 20/3 = 3/4
Subtract 20/3 from both sides
n = 3/4 - 20/3
Simplify 3/4 - 20/3 to - 71/12
n = -71/12
SOMEONE FILL IN THE BLANK PLEASE!! The diameter of a sphere is 16 cm. The volume of the sphere is _____
Answer:
2144.66cm I think
Step-by-step explanation:
The functions f(x) and g(x) are defined below.
Which expression is equal to f(x) · g(x)?
none of the above
Step-by-step explanation:This question wants you to see that the radical can be simplified because it is ...
[tex]f(x)=\sqrt{(x+6)^2}[/tex]
The answer choices show you are expected to simplify this to ...
... f(x) = x +6
Then
... f(x)·g(x) = (x+6)(x³ -12) = x⁴ +6x³ -12x -72 . . . . . matches choice C
_____
However,
... f(x) = |x+6| . . . . . . . √(x^2) = |x|, the positive root regardless of sign of x
so the product f(x)·g(x) only matches selection C for x≥ -6. It matches the opposite of selection C for x ≤ -6.
The attached graph shows this. It graphs f(x), g(x), f(x)·g(x) (as a purple curve), and selection C (as orange dots).
The endpoints of are A(1, 4) and B(6, -1). If point C divides in the ratio 2 : 3, the coordinates of C are
Answer
The answer is C=(4,2). Let me know if you need an explanation.
Step-by-step explanation:
Doreen is flipping two fair coins. What is the probability that both coins land on heads?
Answer:
There are four different possible outcomes: both coins are heads, the red coin is heads and the blue coin is tails, the red coin is tails and the blue coin is heads, or both coins are tails. Each outcome has equal probability. So the probability of both being heads is 1/4.
Step-by-step explanation: