Answer:
Step-by-step explanation:
Let's answer these questions in an all-encompassing kind of explanation. If you plot the vertex and the directrix, you see that the vertex is below the directrix. Because of the fact that a parabola opens AWAY from the directrix, and wraps itself around the focus, we know it's an upside down parabola of the form
[tex]4p(y-k)=-(x-h)^2[/tex]
The p value from the equation is a distance, specifically the distance between either the vertex and the directrix, or the vertex and the focus. The vertex is exactly in the middle of the directrix and the focus. So that tells us that the focus is 3 units below the vertex (because the directrix is 3 units above the vertex). We also know from this that p = 3.
Filling in the equation with a vertex of (0, 0) which is our h and k respectively:
[tex]4(3)(y-0)=-(x-0)^2[/tex] which simplifies to
[tex]12y=-x^2[/tex] and multiplying both sides by -1:
[tex]-12y=x^2[/tex]. This is not standard form, but it matches what your equation is in the choices. So to sum up:
The focus is located at (0, -3) and the first choice is true.
The parabola opens upside down and the second choice is not true.
The p value is found by counting the units between the vertex and the directrix, so the third choice is not true.
We solved the equation by filling in the values for h, k, and p and got that the equation in the fourth choice is true.
So the fifth choice is not true.
Using concepts from the equation of a parabola, it is found that:
The focus is located at (0,–3).The parabola can be represented by the equation x2 = –12y.--------------------------------------
Equation of a parabola:
The equation of a parabola is given by:
[tex](x - h)^2 = 4p(y - k)[/tex]
The vertex is (h,k).The focus is at (h,k+p).The directrix is y = k - p.--------------------------------------
Vertex at the origin means that [tex]h = 0, k = 0[/tex].Directrix at y = 3 means that [tex]p = -3[/tex].Directrix at the y-axis means the parabola opens upwards.Thus, the focus is: [tex](0, 0 - 3) = (0,-3)[/tex]The p-value is: 4(-3) = -12.The equation of the parabola is:[tex]x^2 = -12y[/tex]
--------------------------------------
The correct options are:
The focus is located at (0,–3).The parabola can be represented by the equation x2 = –12y.A similar problem is given at https://brainly.com/question/15546249
Write a function min that has two str parameters and returns the smallest. (Smallest in the sense of coming first alphabetically, not in the sense of "shortest".)
Answer:
The function written in python is as follows
def min(str1,str2):
if str1 < str2:
return str1
else:
return str2
Step-by-step explanation:
This line defines the function min, along with two parameters str1 and str2
def min(str1,str2):
This line checks if str1 is less than str2
if str1 < str2:
If yes, the function returns str1
return str1
If otherwise,
else:
The function returns str2
return str2
Take for instance
str1 = "abc"
str2 = "cba"
The function will return str1 because str1 is less than str2 in the sense that the first letter of str1 (a) is less than the first letter of str2 (c)
In a certain company, all employees are either beta employees or standard employees. In this company, 25% of the beta employees and 17% of the standard employees participate in the voluntary equity program. Let S be the number of standard employees. If there are 600 employees total, what is the value of S?
In addition to the question, the following conditions must be met:
(1) M > 100
(2) more than 130 employees participate in the voluntary equity program
Answer:
Value of A is 200
Step-by-step explanation:
In this scenario when we divide 100 by the percentage of each employee category we will get a proportion that the number of employees must obey.
This is illustrated below:
For Beta employees 100/25= 4
So the number of employees that are Beta must be divisible by 4
For Standard employees 100/17 = 5.882
Since fractions of employees cannot be obtained, in this case the number of employees must be a multiple of 100
Total employees are 600
The various combinations are:
1. Beta employees 500 and Standard employees 100
Survey participants= (0.25 * 500) + (0.17 * 100) = 142
Number of participants is okay as it is >130 but does not satisfy Standard employees being >100
2. Beta employees are 300 and Standard employees are 300
Survey participants = (0.25 * 300) + (0.17 * 300) = 126
This does not satisfy condition of survey participants >130
3. Beta employees 400 and Standard employees 200
Survey participants = (0.25 * 400) + (0.17 * 200) = 134
This satisfies conditions of >130 survey participants and Standard employees >100
So correct value of S is 200
pls help me with trig! i would rlly appreciate it
Answer:
(4 root 2)/9
Step-by-step explanation:
Sin=opp/hyp
Sin=root 32/9
4 root 2/9
Answer:
sin theta = 4 sqrt(2) / 9
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hypotenuse
We need to find the opposite side using Pythagorean theorem
a^2 + b^2 = c^2
b^2 = c^2 - a^2
b = sqrt( c^2 - a^2)
b = sqrt(9^2 - 7^2) = sqrt(32) = 4 sqrt(2)
sin theta =b/c
sin theta = 4 sqrt(2) / 9
7.
2
a)
An open rectangular box measuring 28 cm by 20 cm
by 12 cm internally is made of woodcm thick. Find:
the capacity of the box in litres,
the volume of wood used in making the box,
the mass of the box if the density of the wood used is
1.25 g/cm3
b)
c)
J
28 82
Answer:
1. Capacity of the box in Litres: 7.917L≈8L
2. Volume of wood used in making the box: 1197cm^3
3. The mass of the box: 1496.25g/cm^3
Step-by-step explanation:
1. 29×21×13=7917cm^3
7917cm^3 → 7.917dm^3→7.917L≈8L
2. Outside Volume: 29×21×13=7917cm^3
Inside Volume: 28×20×13=6720cm^3
7917-6720=1197cm^3
3. 1197×1.25=1496.25g/cm^3
help me i dont get it
Answer:
First one
Step-by-step explanation:
A function only has one y value for every x value.
Which of the following has a solution set of {x | x = 0}?
(x +1<-1) n (x + 1< 1)
(x + 1= 1) n (x + 1 > 1)
(x +1<1) n (x + 1 > 1)
The reason why I'm not entirely sure is because of a potential typo. See below.
Let's go through each answer choice
------------
Choice A
Solve each inequality for x
x+1 < -1 becomes x < -2 after subtracting 1 from both sides
x+1 < 1 becomes x < 0 after subtracting 1 from both sides
We have {x < -2} intersected with {x < 0}. The overlap is x < -2. I recommend using a number line diagram to see how the overlap is working. Basically we're looking for numbers that are both less than -2 AND also less than 0. That simplifies to numbers less than -2 (as anything less than -2 is already smaller than 0).
A number like x = -10 is in the solution set of {x < -2}, but we just wanted 0 and only 0 to be in the solution set. So we can rule out choice A.
------------
Choice B
Solve each for x
x+1 = 1 becomes x = 0
x+1 > 1 becomes x > 0
This is a contradiction as we're talking about numbers that are 0 itself and larger than 0 at the same time. No such number exists. Effectively, these two sets cannot be combined to make anything meaningful. In other words, the solution set here is the empty set. For this reason, we can rule out choice B
------------
Choice C
Again we solve each for x
x+1 < 1 becomes x < 0
x+1 > 1 becomes x > 0
This is also the empty set because there are no numbers both smaller than 0 and larger than 0 at the same time.
If we had "or equal to" as part of the inequality sign, then [tex]x+1 \le 1[/tex] solves to [tex]x \le 0[/tex], while [tex]x+1 \ge 1[/tex] solves to [tex]x \ge 0[/tex]. Combining both [tex]x \le 0[/tex] and [tex]x \ge 0[/tex] will yield exactly one item, and that is [tex]x = 0[/tex]
It seems like your teacher meant for this to be the answer and that there is a typo. Of course, its best to ask him/her about this directly.
3y + 6y - 3x * 10m =
Answer: [tex]9y-30mx[/tex]
Step-by-step explanation:
[tex]3y+6y=9y[/tex]
[tex]9y-3\cdot \:10mx[/tex]
[tex]3\cdot \:10=30[/tex]
[tex]=9y-30mx[/tex]
Please mark Brainliest
Eight people rob a bank: * By what percent does the share of three robbers increase?
Answer:
Step-by-step explanation:
It increase by 2.3
the table shows steves bank account summary fir a month. which two values could be the remaining two debts Chart Credit. $476.35 Debit $ Debit $-93.22 Debit. $ Balance $ 0
f(x)=x^2 what is g(x) PLEASE HELP FAST :)))) THANKS IN ADVANCE!!! YOU'RE THE BEST
Answer:
g(x) = -x² - 3
Step-by-step explanation:
You want to mirror f(x), hence the minus sign.
Then you want to translate it 3 down, hence the -3.
Answer:
g(x) = -x² - 3
Step-by-step explanation:
f(x) is x², so g(x) will be negative because it is on the opposite side of the plane.
g(x) will be -x², it cross the y-intercept at (0, -3)
g(x) = -x² - 3
if x= 3y-2/4, what is the value of y in terms of x?
Answer:
[tex]x = \frac{3y - 2}{4} [/tex]
Multiply through by 4
We have
[tex]3y - 2 = 4x[/tex]
Send 2 to the right side of the expression
That's
[tex]3y = 4x + 2[/tex]
Divide both sides by 3
That's
[tex] \frac{3y}{3} = \frac{4x + 2}{3} [/tex]
We have the final answer as
[tex] y = \frac{4x + 2}{3} [/tex]
Hope this helps you
Answer:
[tex]y = \frac{4x + 2}{3} [/tex]
Step by step explanation
[tex]x = \frac{3y - 2}{4} [/tex](Given)
Multiply by 4 on both sides:
[tex]4 \times x = \frac{3y - 2}{4} \times 4[/tex]
Calculate
[tex]4x = 3y - 2[/tex]
Add 2 on both sides
[tex]4x + 2 = 3y - 2 + 2[/tex]
[tex]4x + 2 = 3y[/tex]
[tex]3y = 4x + 2[/tex]
Divide both sides of the equation by 3
[tex] \frac{3y}{3} = \frac{4x + 2}{3} [/tex]
Calculate
[tex]y = \frac{4x + 2}{3} [/tex]
Hope this helps...
Good luck on your assignment..
100
b)
2. Write the following decimals as common fractions in their simplest forms
a) 0,8
b) 0,03
Answer:
4/5, 3/100
Step-by-step explanation
Let's look at 0.8 first.
0.8 is 8/10, but there's some more.
Let's divide 8 / 2. It is 4.
and, 10 / 2 is 5.
so, 0.8's simplest form is 4/5.
and, 0.03's simmplest fraction is easy.
It is 3/100, cuz 3 is a prime number and 3's integer is only 1 and 3.
Hope this helps!
Please help me find the area of this shape
Answer:
44+50 =94 in²
Step-by-step explanation:
Trapezoid
A= 1/2h(b1+b2)
A= 1/2*4(7+15)
A=1/2*4(22)
A=44
Rectangle
A=l*w
A=5*10
A=50
44+50 =94 in²
Un ciclista debe realizar una ruta a través de una carretera para ir desde una ciudad A hasta una ciudad B en varios tramos. El primer tramo mide dos tercios del tercer tramo, el segundo tramo es dos veces mayor que el tercer tramo y el cuarto tramo tiene la medida del primero más el segundo. Si el último tramo es de 80 km, ¿cuál será la distancia total recorrida de la ciudad A hasta la ciudad B?
Respuesta:
190 km
Explicación paso a paso:
Lo primero es hacer las equivalencias, sea a el primer tramo, b el segundo tramo, c el tercer tramo y el ultimo tramo, el cuarto sería d, entonces:
a = 2/3*c
b = 2*c
d = a + b
Ahora bien sabemos que d = 80, reemplazamos y nos queda:
80 = a + b
tanto a cómo b están en función del tercer tramo es decir de c, reemplazamos:
80 = 2/3*c + 2*c
80 = 8/3*c
c = 80*3/8
c = 30
ahora calculamos tanto a como b:
a = 2/3*30 = 20
b = 2*30 = 60
Ahora, el recorrido total es la suma de todos los tramos:
Total = a + b + c + d
Total = 20 + 60 + 30 + 80 = 190
Quiere decir que la distancia entre la ciudad A y la cuidad B es de 190 km
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each hypotenuse length with the leg lengths that willcreate a right a triangle.
Answer:
√8 - 2 units and 2 units,
√7 - √5 units and √2 units,
√5 - 1 units and 2 units,
3 - 2 units and √5 units,
Explanation;
To get each hypotenuse length with the leg lengths that will create a right a triangle., we need to use the pythagoras theorem. According to the theorem;
hypotenuse² = opposite² + adjacent²
The given two lengths are the opposite and adjacent sides of the right angled triangle.
For the triangle with lengths √5 units and √2 units,
hyp² = (√5)² + (√2)²
hyp² = 5+2
hyp = √7 units
For the triangle with lengths √3 units and 4 units,
hyp² = (√3)² + 4²
hyp² = 3+16
hyp = √19 units
For the triangle with lengths 2 units and √5 units,
hyp² = (2)² + (√5)²
hyp² = 4+5
hyp = √9 units
hyp = 3 units
For the triangle with lengths 2 units and 2 units,
hyp² = (2)² + (2)²
hyp² = 4+4
hyp = √8 units
For the triangle with lengths 1 units and 2 units,
hyp² = (1)² + (2)²
hyp² = 1+4
hyp = √5 units
Answer:
the guy above me is correct
Step-by-step explanation:
he smart
30 Points!! Vivian is at a fair in Coachella Valley, California. Much of the valley lies below sea level. Vivian has brought along an altimeter to measure her elevation at different places in the valley. Vivian’s first ride was on the Ferris wheel. When she sat on the wheel at its lowest point, her altimeter read -9.6 feet. When she reached the top of the wheel, her altimeter read 12.3 feet.
Is the change in Vivian's elevation from the bottom of the Ferris wheel to the top a positive number or a negative number? Why?
Answer:
Its a postive number
Step-by-step explanation:
If you look it says she is at sea leveal wicth is 0 and she is going up 12.3 feet so its postive.
The change in elevation from the bottom of the Ferris wheel to the top is 21.9 feet, which is a positive number.
What is subtraction?The process of subtracting one number from another is known as subtraction.
Given that, the lowest point of the Ferris wheel is -9.6 feet, and the highest point is 12.3.
The change in elevation from the bottom of the Ferris wheel to the top of the Ferris wheel is,
12.3 - (-9.6)
=12.3 + 9.6
= 21.9
Hence, the change in elevation from the bottom of the Ferris wheel to the top is 21.9 feet, which is a positive number.
To learn more about subtraction, click here:
https://brainly.com/question/2346316
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Can I get the awnser to this please?
Answer:
151.320046 m^2
150 m^2
Hope it helped!!!!!
Step-by-step explanation:
Area of the circle is:
pi * r^2
Therefore:
= pi * 17^2
= 289 * pi
Now Area of the sector:
= 289 * pi * (60/360)
= 289 * pi * 1/6
= 48.1666667 * pi
= 151.320046 m^2
= 150 m^2 (rounded)
Riley has a farm on a rectangular piece of land that is 200200200 meters wide. This area is divided into two parts: A square area where she grows avocados (whose side is the same as the length of the farm), and the remaining area where she lives.
Every week, Riley spends \$3$3dollar sign, 3 per square meter on the area where she lives, and earns \$7$7dollar sign, 7 per square meter from the area where she grows avocados. That way, she manages to save some money every week.
Write an inequality that models the situation. Use lll to represent the length of Riley's farm.
Answer:
The inequality that models the situation for her to have money to save is
7L² > 3(200L - L²)
On simplifying and solving,
L > 60 meters
Step-by-step explanation:
The length of her farm = L meters
The farm where she grows avocados is of square dimension
Area of the farm = L × L = L²
The piece of land is 200 m wide.
Total area of the piece of land = 200 × L = (200L) m²
If the area of her farm = L²
Area of the side where she lives will be
(Total area of the land) - (Area of the farm)
= (200L - L²)
= L(200 - L)
Every week, Riley spends $3 per square meter on the area where she lives, and earns $7 per square meter from the area where she grows avocados.
Total amount she earns from the side she grows the avocados = 7 × L² = 7L²
Total amount she spends on the side where she lives = 3 × (200L - L²) = 3(200L - L²)
For her to save money, the amount she earns must be greater than the amount she spends, hence the inequality had to be
(Amount she earns) > (Amount she spends)
7L² > 3(200L - L²)
To simplify,
7L² > 3L(200 - L)
Since L is always positive, we can divide both sides by L
7L > 3(200 - L)
7L > 600 - 3L
10L > 600
L > 60 meters
Hope this Helps!!!
Answer:
Answer is in attached image.
what is the answer? The 8x-1x confused me.
10+ 8x -1x
Answer:
7x + 10
Step-by-step explanation:
10 + 8x - 1x
Add or subtract like terms.
10 + (8 - 1)x
10 + (7)x
Rearrange.
7x + 10
Answer:
7x+10
Step-by-step explanation:
start by rewriting the problem
10+8x-1x
now, you can subtract 8x from 1x, because they are like terms
10+7x
arrange the terms
7x+10
now, that is your final answer!
Which of the following are identities?
1. x2 + 2xy + y2 = (x + y)2
II. 2x + 2 = 2(x + 1)
III. O + a = a
Answer:
The answer is 2 because they are similar it is just that the one at the side is factorised
Combine the like terms to create an equivalent expression: r+(-5r)
Answer:
-4r
Step-by-step explanation:
r + -5r
Factor out r
r( 1-5)
r(-4)
-4r
Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function, and rank the functions based on their axis of symmetry (from smallest to largest).
f(x) = -4(x − 8)2 + 3
g(x) = 3x2 + 12x + 15
(graph attatched= h(x) )
Answer:
1. x=8 is the line of symmetry for f(x) = -4(x − 8)2 + 3
2. x=-2 is the line of symmetry of g(x) = 3x2 + 12x + 15
3. x=3 is the line of symmetry of h(x), shown in the graph.
Step-by-step explanation:
To find the line of symmetry of a vertical parabola (second degree polynomial), find the value of x that sets the squared term to zero. This is a vertical line passing through the vertex of the second degree function.
1. f(x) = -4(x − 8)2 + 3
setting x=8 will give f(8) = 3, so x=8 is the line of symmetry
2. g(x) = 3x2 + 12x + 15
here, we need to complete the squares,
g(x) = 3x2 + 12x + 15
g(x) = 3(x^2+4x+5)
g(x) = 3(x^2 + 2(2x) +4 +1)
g(x) = 3((x+2)^2 +1)
So setting x=-2 will anihilate or cancel the squared term, therefore
x= -2 is the line of symmetry.
3. the curven shown in graph,
we see that the vertex is at x=3, so x=3 is the line of symmetry.
The axes of symmetry of the functions f(x), g(x), and h(x) will be x = 8, x = -2, and x = 3, respectively.
What is the axis of symmetry?Axial symmetrical is similarity around an axis; an item is internally symmetric if it retains its appearance when turned around an axis.
Three capabilities are given underneath: f(x), g(x), and h(x).
f(x) = -4(x − 8)² + 3
The axis of symmetry of the function f(x) will be given as,
x − 8 = 0
x = 8
g(x) = 3x² + 12x + 15
Convert the expression into a vertex form.
g(x) = 3x² + 12x + 15
g(x) = 3(x² + 4x + 5)
g(x) = 3(x² + 4x + 4) + 3
g(x) = 3(x + 2)² + 3
The axis of symmetry of the function g(x) will be given as,
x + 2 = 0
x = −2
From the graph, the axis of symmetry of the function h(x) will be given as,
x = 3
More about the axis of the symmetry link is given below.
https://brainly.com/question/22495480
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A triangle has angles that measure 107°, 20°, and 53°. What kind of triangle is it?
Answer:
Scalene triangle
Step-by-step explanation:
Let's first cancel out the obvious.
This is not a equilateral triangle because the angles are not equal.
Now if you draw out the triangle, you can see that the triangle is a little weird. Not at all a equilateral triangle.
It's also not a iscosles because no two angles are the same.
Thus we end up with scalene triangle.
Hope this helps!
This box has the same length, width, and height as the two tennis balls. Which expression gives the volume of the empty space encircling the tennis balls inside the box?
Formala : Times bottom row with side row with the height.
Example: A box has the same length, width, and height as two tennis balls.
Times the bottom row with side row with the height.
On a coordinate plane, kite W X Y Z is shown. Point W is at (negative 3, 3), point X is at (2, 3), point Y is at (4, negative 4), and point Z is at (negative 3, negative 2). What is the perimeter of kite WXYZ?
2√53+2 units
2√53+5 units
2√53+10 units
2√53+14 units
Answer:
2√53+10 units
Step-by-step explanation:
We know the diagonal segments have an irrational length. All answer choices agree those two segments total 2√53 units.
The two orthogonal sides each have a length of 5 units, so their total length is 10. (You can count the grid squares, or subtract coordinates.)
Then the perimeter is ...
2√53 +10 units
Answer:
10
Step-by-step explanation:
TRUST ME PLEASE FAM
Solve: -7 < 2x+5 < 7
Answer:
[tex] - 6 < x < 1[/tex]
Step-by-step explanation:
first things first:
[tex] - 7 < 2x + 5 \\ - 7 - 5 < 2x + 5 - 5 \\ - 12 < 2x \\ - 6 < x[/tex]
now:
[tex]2x + 5 < 7 \\ 2x + 5 - 5 < 7 - 5 \\ 2x < 2 \\ x < 1 [/tex]
now the intersection is:
[tex] - 6 < x < 1[/tex]
The length of the smaller rectangle at the right is 1 inch less than twice its width. Both the dimensions of the larger rectangle are 2 inches longer than the smaller rectangle. The area of the shaded region is 86 square inches. What is the area of the larger rectangle? PLEASE its important
Answer: 464 square inches is the area of the larger rectangle.
Step-by-step explanation: Assuming that the shaded area is the part of the large rectangle outside the small rectangle, you can set up dimensions from the information given.
The small rectangle's Area = w (2w -1) which is 2w² -w
The large rectangle's Area = (w + 2)(2w + 1) which is 2w² + 5w +2
Now figure out the equation for the "shaded area" (probably outside the small rectangle) 2w² + 5w +2 -(2w² -w) = 86 (The 2w² terms cancel)
6w + 2 = 86, so 6w = 84, w=14
Substitute 14 for w in the dimensions of the large rectangle: (w + 2)(2w + 1)
(14+2)(2[14] + 1) = Area
16 × 29 = 464
(I think I deserve Brainliest for figuring this out, but I see the question has been red-flagged, so We'll see!)
Please answer please please
Answer: T
Step-by-step explanation: The vertex is where the two lines meet at the endpoint, meaning that the vertex is always where the lines begin to spread out.
If α and β are the zeroes of the polynomial 2x2 + 3x – 7, then find a polynomial whose zeroes are and .
Answer:
[tex]\frac{-\sqrt{65} - 3 }{4}, \frac{\sqrt{65} + 3}{4}[/tex]
Step-by-step explanation:
Since we cannot factor the expression, we must use quadratic formula: [tex]x = \frac{-b +/-\sqrt{b^2 - 4ac} }{2a}[/tex]
Plug in a for 2, b for 3, and c for -7 and you should find your roots.
expresa como monomio Cos7x +Sen5x Sen2x
plis lo necesito urgente
Answer:
El monomio equivalente es [tex]\cos 5x \cdot \cos 2x[/tex].
Step-by-step explanation:
Un monomio es una entidad algebraica consistente en un componente, el polinomio dado puede ser transformado mediante el uso de la siguientes propiedades trigonométricas:
[tex]\cos (\alpha + \beta) = \cos \alpha \cdot \cos \beta - \sin \alpha \cdot \sin \beta[/tex]
Es decir:
[tex]\cos 7x + \sin 5x \cdot \sin 2x[/tex] Dado
[tex]\cos (5x+2x) + \sin 5x\cdot \sin 2x[/tex]
[tex]\cos 5x \cdot \cos 2x - \sin 5x \cdot \sin 2x + \sin 5x \cdot \sin 2x[/tex]
[tex]\cos 5x \cdot \cos 2x[/tex]
El monomio equivalente es [tex]\cos 5x \cdot \cos 2x[/tex].