Answer:
The coordinates of the focus are [tex]F(x,y) = (-1,0)[/tex] anf the equation of the directrix is [tex]x = 1[/tex], respectively.
Step-by-step explanation:
Let be [tex]y^{2} = -4\cdot x[/tex], which represents a parabola with a horizontal axis of symmetry. To find the location of the focus and to determine the equation of the directrix we must find the distance between focus and vertex ([tex]p[/tex]), dimensionless, a value than can be extracted from the following definition:
[tex](y-k)^{2} = 4\cdot p \cdot (x-h)[/tex] (Eq. 1)
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex, dimensionless.
By direct comparison, we get the following coincidences:
[tex]h = 0[/tex]
[tex]k = 0[/tex]
[tex]4\cdot p = -4[/tex] (Eq. 2)
From (Eq. 2) we get that distance between focus and vertex is:
[tex]p = -1[/tex]
Which is consistent with the fact parabola has an absolute maximum.
Now, the location of the focus is:
[tex]F(x,y) = (h+p, k)[/tex] (Eq. 3)
If know that [tex]h = 0[/tex], [tex]k = 0[/tex] and [tex]p = -1[/tex], coordinates of the focus is:
[tex]F(x, y) = (0-1, 0)[/tex]
[tex]F(x,y) = (-1,0)[/tex]
And the equation of the directrix is represented by:
[tex]x = -p[/tex] (Eq. 4)
([tex]p = -1[/tex])
[tex]x = 1[/tex]
The coordinates of the focus are [tex]F(x,y) = (-1,0)[/tex] anf the equation of the directrix is [tex]x = 1[/tex], respectively.
Answer:
The general formula for this parabola is y2 = 4px.
Therefore, the value of p is
✔ –1
.
The coordinates of the focus are
✔ (–1,0)
.
The equation of the directrix is
✔ x = 1
.
Step-by-step explanation:
help please. no super long answers.
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
So first you have to plug in what you know...
[tex]3x+y>3\\3(\frac{3}{4})+(0)>3\\\frac{9}{4}+0>3\\\frac{9}{4} >3[/tex]
If it's hard to look at it that way you should make it look like this...
[tex]2\frac{1}{4} >3[/tex]
Now when you look at it you can tell that it's false, so [tex](\frac{3}{4},0 )[/tex] is not a solution f this inequality.
N 0 Q. What are the solutions to the graphed system?
A. 0,-2
B. -2,0 and 2,0
C. 3,1
D. 0,-2 and 3,1
Answer:
Answer is D
Step-by-step explanation:
Suppose that you plan on taking a summer job selling magazine subscriptions. The magazine company will pay you 75 cents for selling the first subscription. For each additional subscription sold, the magazine company will pay you 5 cents more than what was paid for the previous subscription. How much will you earn by selling 150 magazine subscriptions?
Answer:
671.25
Step-by-step explanation:
Combine terms: 12a + 26b -4b – 16a.
(a) 4a + 22b,
(b) -28a + 30b,
(c) -4a + 22b,
(d) 28a + 30b.
Answer:
c. -4a + 22b
Step-by-step explanation:
Answer:
c. -4a + 22b
Step-by-step explanation:
Una tienda compra pendrive de diferentes
colores al por mayor, para navidad hizo un
pedido extraordinario de 84 memorias rojas, 196 azules y 252 verdes. Para guardar la
mercancía de forma organizada, exigió que
le enviarán las memorias en cajas iguales,
sin mezclar los colores y conteniendo el mayor número posible de memorias.
Answer:
En síntesis, se requiere utilizar cajas con capacidad para 28 memorias. Al no mezclarse los colores, requerimos utilizar 3 cajas para las memorias rojas, 7 cajas para las memorias azules y 9 cajas para las memorias verdes.
Step-by-step explanation:
La cantidad de cajas es igual a la cantidad de memorias dividida por la capacidad de una caja. Al indicarse que las memorias serán guardadas en cajas de igual capacidad, sin mezclar los colores y con el mayor número posible de artículos, podemos utilizar el concepto de máximo común divisor, cuyo procedimiento mostramos a continuación:
(i) Realizamos la descomposición factorial de cada número:
Memorias rojas:
[tex]84 = 2\times 2 \times 3\times 7[/tex]
Memorias azules:
[tex]196 = 2\times 2\times 7\times 7[/tex]
Memorias verdes:
[tex]252 = 2\times 2\times 3 \times 3 \times 7[/tex]
(ii) Hallamos los números primos en común que tiene cada colección de memorias:
[tex]S=\{2,2,7\}[/tex]
(iii) Calculamos el máximo común divisor al multiplicar los elementos del conjunto S:
[tex]M.C.D. = 2\times 2\times 7[/tex]
[tex]M.C.D. = 28[/tex]
Esto quiere decir que cada caja debe llevar 28 memorias del mismo color. Finalmente, calculamos la cantidad requerida de cajas para cada memoria.
Memorias rojas:
[tex]n_{R} = \frac{84}{28}[/tex]
[tex]n_{R}= 3[/tex]
Memorias azules:
[tex]n_{A} = \frac{196}{28}[/tex]
[tex]n_{A} = 7[/tex]
Memorias verdes:
[tex]n_{V} = \frac{252}{28}[/tex]
[tex]n_{V} = 9[/tex]
En síntesis, se requiere utilizar cajas con capacidad para 28 memorias. Al no mezclarse los colores, requerimos utilizar 3 cajas para las memorias rojas, 7 cajas para las memorias azules y 9 cajas para las memorias verdes.
Tavon has a gist card for $145 that losses $3.50 for each 30-day period is not used. He has another gift card for $125 that losses $3 for each 30-day period it is not used. A. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal. B. What will the value of each card be when they have equal value?
Step-by-step explanation:
A. For Tavon's gift card the equation is
let y be the total amount
let x be the number of 30 day period
y=145-3.5x------1
for Tavon's second gift card the equation is
let y be the total amount
let x be the number of 30 day period
y=125-3x-------------2
B. equating 1 and 2 we have
145-3.5x=125-3x
solve for x we have
145-125=-3x+3.5x
20=0.5x
divide both sides by x we have
x=20/0.5
x= 40
put x=40 in
y=145-3.5*40------1
y=145-140
y=$5
put x=40 in
y=125-3*40------1
y=125-120
y=$5
I need help with geometry
9514 1404 393
Answer:
translate <-6, 0>, reflect over x
Step-by-step explanation:
Point D is at the top in the pre-image and at the bottom in the image, so a vertical reflection is indicated. Only the 1st and 3rd choices show a reflection over the x-axis.
The image is to the left of the pre-image by 6 units, so the translation is in the negative direction. Only the 3rd choice has that.
Which of the following statements does not represent the same value as the others?
the distance between 0 and −9
the absolute value of negative 9
the opposite of 9
the absolute value of 9
the distance between 0 and −9
the absolute value of negative 9
the opposite of 9
the absolute value of 9
please help me out
Answer:
137.5
Step-by-step explanation:
330/12=27.5 miles per gallon of gasoline so 5 times 27.5 you get 137.5 miles.
What is the image of (4, 3) after a dilation by a scale factor of 2 centered at the origin?
What is the quotient of -32/8?
Answer:
Hope it help you
Stayhomestaysafe
Plz mark my answer brainliest✍️✍️
Step-by-step explanation:
[tex] - 32 \div8 = - 4[/tex]Answer is -4
REAL NAME - SHRESTH DUBEY
-4 is the Answer.
-32/8 would be -4
Jessie paid $43.75 for 5 movie tickets. Each ticket cost the same amount. What was the cost of each movie ticket in dollars and cents?
Answer:
$8.75
Step-by-step explanation:
Divide $43.75 by 5 to get the cost of ONE movie ticket like so:
$43.75 / 5 movie tickets = $8.75 per ticket.
Therefore, ONE ticket costs $8.75.
Mr. East is taking his class to see a movie. Student tickets are $10 each and food and beverages will be an additional $4.75 per student. How much will it cost to take his class of 32 students?
Is the number 65.4349224... rational or irrational? Explain.
Answer:
It is irattional because the number keeps changing
Step-by-step explanation:
Answer:
my guess is irrational
Step-by-step explanation:
A rational number is a number that can be express as the ratio of two integers. A number that cannot be expressed that way is irrational. For example, one third in decimal form is 0.33333333333333 (the threes go on forever).
what is x ?
what is y ?
Answer:
y = 100° , x = 80°
Step-by-step explanation:
Two angles on a straight line equal 180°. Therefore, 80° + y = 180°. This means y = 100°.
80° and x are alternate exterior angles. Using that property, we know those angles are congruent. This means x is also 80°.
If a triangle is
rotated 135 degrees
counterclockwise, is
that positive or
negative rotation?
A cab charges $1.45 for the flat fee and $0.55 for each mile. Write and solve an inequality to determine how many miles Ariel can travel if she has $35 to spend.
answers are:
A. $1.45 + $0.55x ≥ $35; x ≥ 61 miles
B. $1.45 + $0.55x ≤ $35; x ≤ 61 miles
C. $0.55 + $1.45x ≥ $35; x ≥ 23 miles
D. $0.55 + $1.45x ≤ $35; x ≤ 23 miles
9514 1404 393
Answer:
B. $1.45 + $0.55x ≤ $35; x ≤ 61 miles
Step-by-step explanation:
The mileage charge for x miles will be $0.55x, so the total charge will be $1.45+$0.55x. This must be less than or equal to $35 for Ariel to be able to pay for her travel. The appropriate inequality is ...
$1.45 +$0.55x ≤ $35 . . . . . matches choice B
__
Comment on selecting an answer
From a "reasonableness" point of view, any answer choice with "≥ $35" can be eliminated immediately. Further, any answer choice with $1.45x can be eliminated, since the mileage charge is not $1.45, it is $0.55. The leaves only the choice shown above.
What is the equation of this line
Answer:
y = 1/2x - 3
Step-by-step explanation:
Slope: Up 1 over 2
Y-Int: -3
y=mx+b
Please help me estimate the answer of 7987 divided by 39
204.79
Step-by-step explanation:
(-90) + (-20) + 100 =
A-210
B) 10
C) -10
D) 210
Answer:
C.
Step-by-step explanation:
(-90) + (-20) + 100 = -10
Hope I Helped! :)
Answer:
The solution is C. -10
Step-by-step explanation:
Before entering the solution, remember the formula first!
Addition
• (-) + (-) = (-)
• (+) + (+) = (+)
Subtraction
• (+) - (+) = can (-) and (+)
• (+) - (-) = (+)
Multiplication
• (-) x (-) = (+)
• (+) x (-) = (-)
Division
• (-) : (-) = (+)
• (+) : (-) = (-)
Solution:
(-90) + (-20) + 100
= -90 - 20 + 100
= -110 + 100
= -10 (the minus number is greater than the positive, then the result is minus)
PLZ HELP !!!!!!
28x+36y=2520 Write this in slope intercept form or graph!!
Answer:
y= -7/9 x+70
Step-by-step explanation:
28x+36y=2520
36y=-28x+2520
y= -7/9 x+70
Find the value of x.
90°
58°
X
help plz
Answer:
32 degrees
Step-by-step explanation:
90 + 58 = 148
180 - 148 = 32
eternal horizons or doom crossing
Answer:
RIP AND TEAR NEW HORIZON
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
hellllppppp me please
9514 1404 393
Answer:
positive infinitynegative infinityStep-by-step explanation:
The function has a positive leading coefficient (1/3) and is of odd degree (3). These conditions mean the sign of the end behavior of the function will match the sign of x.
x → ∞, m(x) → ∞
x → -∞, m(x) → -∞
What are the points for y=-3x+4 and how do I graph it
Answer:
(-3,13) (-2,10) (-1,7) (0,4) (1,1) (2,-2) (3,5) (4,8) are your graph points.
Step-by-step explanation:
Okay so to find the points, you have to create a table graph with a set of x values.
in this case, your equation y=-3x+4 the x can be replace with a set of numbers and these will be your plots.
-3(-3)+4= 13
-3(-2)+4= 10
-3(-1)+4= 7
-3(0)+4= 4
-3(1)+4= 1
-3(2)+4= -2
-3(3)+4= -5
-3(4)+4= -8
Naturally with these points a shape will form ideally a straight line. Hopefully this helps and good luck!
how many time does 2/3 go into 28/3
Answer:
14 i think
Step-by-step explanation:
Answer:
2/3 goes into 28/3 14 times.
Step-by-step explanation:
Multiply 2 by 14, and you will get 28. That shows you that 2/3 goes into 28/3 14 times.
Y=-x+4
Y=3x (substitution)
Answer:
x=1
Step-by-step explanation:
-x+4=3x
4=4x
x=1
An Apple Pie Was Cut Into 6 Pieces Of Equal Size Jake And Paula Each Ate 1 Piece Apple Pie How Much Apple Pie Was Left?
Answer:
4 slices because 6-2=4
Step-by-step explanation:
pls make me brainliest
what is the answer! i need it nowww !
2+2(6x-3)=10x+ negative4
PLEASE HELP ME IT'S DUE TODAY IF CORRECT I'LL MAKE BRAINYLIST!!!!
Answer:
A
Step-by-step explanation:
