The focus of parabola is (4 , -1) and directrix is 5
The general equation of a parabola is: y = a(x-h)²+ k or x = a(y-k)² +h, where (h ,k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.
Focus: The point (a, 0) is the focus of the parabola
Directrix: The line drawn parallel to the y-axis and passing through the point (-a, 0) is the directrix of the parabola. The directrix is perpendicular to the axis of the parabola.
Given equation of parabola is :
y = - 1/12 (x - 4) - 2
Comparing it with standard equation,
h = 4
k = 2
a = -1/12
using Focus: (h, k+ (1/4a)) and Directrix: y = k - 1/4a)
=> focus = (4 , 2+(12/4×-1))
=> focus = (4 , 2-3)
=> focus = (4 , -1)
and directrix is : y = 2-(1/4×-1/12)
y = 2 + 12/4
y=2 + 3 => 5
So, the focus is (4,-1) and directrix is 5
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92≤x≤9? I need help with this fast thankyou
Answer:
yes
Step-by-step explanation:
because 4
Answer:
Step-by-step explanation:
average rate of change
[tex]=\frac{25-(-10)}{9-2} \\=\frac{35}{7}\\=5[/tex]
If angle 1 is 7 degrees in the parallelogram pictured above, what is angle 2
Answer:
m∠2 = 173°Step-by-step explanation:
1 and 2 are supplementary angles and hence sum to 180°.
m∠1 + m∠2 = 180°7° + m∠2 = 180° m∠2 = 180° - 7° m∠2 = 173°differentiate y=in(3-4cosx)
For given equation y = ln(3 - 4 cos(x)),
dy/dx = 4sin(x) / (3 - 4 cos(x))
In this question, we have been given an equation y = ln(3 - 4 cos(x))
We need to differentiate y = ln(3-4cosx)
dy/dx
= d/dx(ln(3 - 4 cos(x)))
= 1/(3 - 4 cos(x)) * d/dx(3 - 4cos(x)) .......(by Chain rule)
= 1/(3 - 4 cos(x)) * [4 sin(x)]
= 4sin(x) / (3 - 4cos(x))
Therefore, for given equation y = ln(3 - 4 cos(x)),
dy/dx = 4sin(x) / (3 - 4 cos(x))
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a packet of crisps weighs 32 grams to the nearest gram. a multipack of crisps contains 10 packets. work out the least and the greatest weights of the multipack. you can ignore the weight of the multipack wrapper
If a multipack of crisps contains 10 packets. the least and the greatest weights of the multipack is 315, 325.
How to determine the least and greatest weight?Range = 31.5≤ x < 32.5
Range = 31.5≤ 10 < 32.5
Hence,
Lowest and greatest possible for 32 grams
Lowest possible = 31.5 grams
Greatest possible =32.4 grams
Since multipack of crisps contain is 10 packets hence.
Least weight = 31.5 grams × 10
Least weight =315
Greatest weight = 32.5 grams × 10
Greatest weight = 325
Therefore 315 and 325 are the weight.
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Consider the equation and the following ordered pairs: (4,y) and (x,2).
y=−2x+4
Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation.
Answer
Keyboard Shortcuts
Complete the table below.
x y
row 14 Answer
row 2 Answer
2
The missing x and y values in the ordered pair of the equation are:
x = 1
y = -4
How to Find the Ordered Pairs of an Equation?Given the ordered pair (x, y) of an equation, y = mx + b, we can find their values by plugging in the given value of either of the x or y coordinates to find the other coordinate value.
The ordered pairs of y = -2x + 4 are given as:
(4, y) and (x, 2)
To find the value of y, substitute x = 4 into the equation y = -2x + 4:
y = -2(4) + 4
y = -8 + 4
y = -4
The value of y is -4.
To find the value of x, substitute y = 2 into the equation y = -2x + 4:
2 = -2x + 4
2 - 4 = -2x
-2 = -2x
-2/-2 = x
1 = x
x = 1
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On what intervals is the function increasing?
Indicate intervals on the x-axis using the Ray tool for intervals that extend to infinity and the Segment tool for bounded intervals.
Graph a ray by selecting the endpoint followed by a point on the ray. Graph a segment by selecting an endpoint followed by the other endpoint.
Answer:
[-7, - 2] and [3, 7]--------------------------------------
The graph has two local maximums and two local minimums.
The intervals between those points are the increasing intervals.
Refer to the attached, where the intervals are marked.
The intervals are
x = [-7, - 2] and [3, 7]Use a table of areas to obtain the shaded area under the standard normal curve.
The shaded area under the standard normal curve is 2.58%.
According to z-score table,
Area for < 2.23 = 0.9871
Area for >2.23 = 1 - 0.9871
= 0.0129
Area for < 2.23 = 0.0129
Total area = 0.0129 + 0.0129
= 0.0258
Area percent = 0.0258*100
= 2.58%
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How many ways can the letters in the word CHEWY be arranged to form a five letter code
Answer:
60 ways;
GOOD LUCK!
Step-by-step explanation:
The word CHEWY has 5 letters, Therefore, it can be arranged in 5!/2! = 120/2 = 60 ways.
Select the equation of the graph line above. (A) y = x + 5 (B) y = 3x + 5 (C) y = x - 5 (D) y = 3x - 5
Answer: (D) [tex]y=3x-5[/tex]
Step-by-step explanation:
Using the points (0, -5) and (2, 1), the slope of the line is [tex]\frac{-5-1}{0-2}=3[/tex].
Since the y-intercept is -5, the equation is [tex]y=3x-5[/tex].
The sum of a number and 4 times the number
Write two equivalent expressions for each statement.
Let the number be n.
Then the expression is:
The sum of a number and 4 times the numbersum = n + 4nsum = 5nAnswer:
4x + x5xStep-by-step explanation:
Forming the expression,
→ 4x + x
Let's solve the expression,
→ 4x + x
→ 5x
Hence, the answer is 5x.
p=(-3,7); m=-1 graph line containing the point p and having slope m.
The equation of the line is x+y-4=0.
What is an equation?
A formula known as an equation uses the equals sign (=) to express how two expressions are equal.
Main Body:
we know that one point form of a line is
y-y₁= m(x-x₁) , where m= slope
now given is a point (-3,7) and m=-1
y-7 =(-1)(x+3)
x+y-4=0
Hence the answer is x+y-4 =0
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A manufacturer of fax machines find that the cost (in dollars) generated by manufacturing x
units per week is given by the function C(x) = 0.15x²-39x+4500. How many units should
be manufactured to minimize the cost?
130 units should be manufactured to minimize the cost.
How to solve a quadratic equation using quadratic formula?Only a factorable quadratic expression can be solved using the factoring approach, and a quadratic equation with real roots can be solved using the graphing method, etc. However, the quadratic formula can be used to solve any kind of quadratic problem and gets over all these restrictions. step 1: Get into the standard form as the first step.step 2: Determine the values of a, b, and c by comparing the equation to [tex]ax^{2} +bx+c=0[/tex]Step 3: Replace the numbers in the quadratic equation, which is written as[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex] step 4: simplifyCalculation
by using the quadratic formula
[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex]
where, a = 0.15, b = -39 and c = 4500
x= [tex]\frac{-b}{2a} = \frac{39}{0.3} =130[/tex]
Hence, 130 units should be manufactured to minimize the cost of fax machines
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130 units should be manufactured to minimize the cost.
How to solve a quadratic equation using quadratic formula?Only a factorable quadratic expression can be solved using the factoring approach, and a quadratic equation with real roots can be solved using the graphing method, etc. However, the quadratic formula can be used to solve any kind of quadratic problem and gets over all these restrictions. step 1: Get into the standard form as the first step.step 2: Determine the values of a, b, and c by comparing the equation to [tex]ax^{2} +bx+c=0[/tex]Step 3: Replace the numbers in the quadratic equation, which is written as[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex] step 4: simplifyCalculation
by using the quadratic formula
[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex]
where, a = 0.15, b = -39 and c = 4500
x= [tex]\frac{-b}{2a} = \frac{39}{0.3} =130[/tex]
Hence, 130 units should be manufactured to minimize the cost of fax machines
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Solve for x.
Please !!!
Step-by-step explanation:
6x-4+60=14x-8
6x+56=14x-8
8x=64
x=8
The Roxbury CC Tigers basketball team scored 12 points in the first 6 minutes of a game. If they continue at the same pace, how much will they score during the entire 40 minute game?
84 i think?
im not sure if i did my math properly
Answer:
80
Step-by-step explanation:
40 ÷ 6 = 6.66666667 x 12 = 80
Alan has 229 songs on a playlist. He's categorized them in the following manner: 11 rock, 21 Latin American, 46 gospel, 30 country, 39 rap, 25 classical, and 57 pop. If Alan begins listening to his playlist on shuffle, what is the probability that the first song played is a rock song?
The probability of the event that the first song played by Alan is a rock song is 0.01.
What is probabilityThe probability of an event occurring is the ratio of the number of required outcome divided by the total number of possible outcomes. But the probability of an event say event "a" not occurring is 1 - a.
We shall calculate for the probability of the event that Alan's first song to be played is a rock song as follows:
probability of playing a rock song = 11/229
probability of not playing a Latin American song = 208/229
probability of not playing a gospel song = 183/229
probability of not playing a country song = 199/229
probability of not playing a rap song = 190/229
probability of not playing a classical song = 204/229
probability of not playing a pop song = 172/229
So,
The probability that the first song played is a rock song = (11/229) × (208/229) × (183/229) × (199/229) × (190/229) × (204/229) × (172/229)
The probability that the first song played is a rock song = 0.05 × 0.91 × 0.80 × 0.67 × 0.83 × 0.89 × 0.75
The probability that the first song played is a rock song = 0.01
Therefore the probability of the event that Alan's first song played is calculated to be 0.01 approximated to 2 decimal places.
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y varies inversely with the square x. If y =
-4 when x =
-2, find y when x= 7.
The value of y is - 0.326 when x = 7.
What are ratio and proportion?A ratio is a divisional comparison of two quantities, and a proportion is the equality of two ratios. A ratio is typically expressed as x: y or x/y, although it may alternatively be read as x is to y.
Comparatively speaking, a proportional equation states that two ratios are comparable. A ratio is expressed as x: y: : z: w and is understood to mean that x is to y as z is to w. Here, w and y are not equal to 0, therefore x/y Equals z/w.
A connection between two quantities is said to be in inverse proportion if one quantity rises while the other falls, and vice versa. As a result, an inverse ratio is expressed as y ∝ 1/x.
The general equation of proportion is given by
y = k/x²
-4 = k/(-2)²
k = -4(4)=-16
y = -16/x²
When x=7, then
y= -16/49
y= - 0.326
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brainliest points whatever you want please
Annual rate of return earned when the share was sold at $50 per share is 20%
Annual rate of return earned when the share was sold at $60 per share is 40%
How to calculate annual rate of returnAnnual rate of return is given by the formula
let end of the year price = eyp
let beginning of the year price = byp
= {(eyp - byp) / byp} * 100
Annual rate of return at share price of $50 per share
when there is paying of dividends the value is added to the the eyp
eyp = 50 * 100 + 2 * 100 * 5 = 6000
byp = 50 * 100 = 5000
= {(6000 - 5000) / 5000} * 100
= 20%
Annual rate of return at share price of $60 per share
eyp = 60 * 100 + 2 * 100 * 5 = 7000
byp = 50 * 100 = 5000
= {(7000 - 5000) / 5000} * 100
= 40%
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An object is launched directly in the air at a speed of 32 feet per second from a platform located 20 feet above the ground. The position of the object can be modeled using the function f(t)=−16t2+32t+20, where t is the time in seconds and f(t) is the height, in feet, of the object. What is the maximum height, in feet, that the object will reach?
Using differentiation, 36 feet is the maximum height, in feet, that the object will reach.
In the given question,
An object is launched directly in the air at a speed of 32 feet per second from a platform located 20 feet above the ground.
The position of the object can be modeled using the function [tex]f(t)=-16t^2+32t+20[/tex], where t is the time in seconds and f(t) is the height, in feet, of the object.
We have to find the maximum height, in feet, that the object will reach.
The given function is [tex]f(t)=-16t^2+32t+20[/tex].
To find the maximum height we differentiate the function with respect to t
[tex]\frac{df}{dt}=-32t+32[/tex]
As we know that at the maximum point the slope of the tangent is zero.
So df/dt = 0
So -32t+32=0
Subtract 32 on both side
-32t+32-32=0-32
-32t=-32
Divide by -32 on both side
-32/-32 t = -32/-32
t=1
Therefore at t=1 the function have maximum value. So we put t=1 in the given equation.
[tex]f(1)=-16(1)^2+32\times1+20[/tex]
f(1)=(-16)×1+32×1+20
Simplifying
f(1)=-16+32+20
f(1)=36 feet.
Hence, 36 feet is the maximum height, in feet, that the object will reach.
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8 (x + 2 ) when x = 6
Answer:
64
Step-by-step explanation:
8(x+2) when x=6
replace x with 6
8(6+2)
distribute 8
48+16= 64
help with this pls! Lol
Answer:
3y+3y-12
Step-by-step explanation:
we can add the coefficients of y to make 6y-12
And that is equivalent
Hopes this helps please mark brainliest
will reward brainliest please help!!!
Dianelys accepted a new job at a company with a contract guaranteeing annual raises. In the first year, Dianelys' salary will be $40000, and she will get a raise of $2500 every year. Make a table of values and then write an equation for S,S, in terms of n,n, representing Dianelys' salary after working nn years for the company.
1. Dianely's salary can be represented with the following table of values for 5 years as follows:
Year Salary
1 $40,000
2 $42,500
3 $45,000
4 $47,500
5 $50,000
2. The equation to model Dianely's salary after n years is S = 40,000 + 2,500n.
What is an equation?An equation is a mathematical statement equating two or more mathematical expressions.
Equations use variables, numbers, mathematical operands, and the equation symbol (=).
Dianely's initial salary = $40,000
Salary raise per year = $2,500
Dianely's salary after n years in equation form, S = 40,000 + 2,500n.
Table of Values for Dianely's Salary:Year Salary
1 $40,000
2 $42,500 (40,000 + 2,500)
3 $45,000 (42,500 + 2,500)
4 $47,500 (45,000 + 2,500)
5 $50,000 ($47,500 + 2,500)
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In which of these cases should the mean be used
At the beginning of a journey, the fuel tank of a car was 34 full. When the car reached its destination, it had consumed 60% of the gasoline in the tank. The full capacity of the fuel tank was w gallons.
a Enter an algebraic expression for the amount of gasoline left in the fuel tank.
gal
b If w = 15.5, how much gasoline was left in the tank at the end of the journey?
gal
a) An algebraic expression for the gasoline left in the fuel tank is L = 0.4w.
b) If w = 15.5, the amount of gasoline left in the tank at the end of the journey was 6.2 gallons.
What is an algebraic expression?An algebraic expression is a mathematical statement that combines constants and variables together with mathematical operands.
The mathematical operands include addition, subtraction, division, multiplication, etc.
Let L = the amount of gasoline left
Let the full capacity of the fuel tank = w gallons
Gasoline consumed on the journey = 60% = 0.6
Equation:L = w - 0.6w
L = 0.4w
Solution:If w = 15.5
L = 0.4(15.5)
= 6.2 gallons
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The regression equation for 2 variables is y = -2.6 x + 10 If the value of R2 is 0.810, what is the value of R?
If the value of R² in the regression equation is 0.810, the value of R is 0.9
How to determine the value of r?From the question, we have the following parameters that can be used in our computation:
Regression equation: y = -2.6x + 10
Value of R2 = 0.810
Rewrite the above parameters properly
So, we have the following representation
y = -2.6x + 10
R² = 0.810
The variable r² represents the coefficient of determination
Recall that
R² = 0.810
This gives
r² = 0.810
Take the square roots of both sides
r = 0.9
Hence, the value of r is 0.9
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a piece of pipe is 40in. long. It is cut in to 3 pieces. the longest piece is 3 times as long as the middle sized piece and the shortest piece is 23 in. shorter than the longest piece. Find the lengths of all 3 pieces of pipe.
The length of shortest piece is 4 inches, middle sized piece is 9 inches and that of longest piece is 27 inches.
According to the question,
We have the following information:
A piece of pipe is 40in. long. It is cut in to 3 pieces. The longest piece is 3 times as long as the middle sized piece and the shortest piece is 23 in. shorter than the longest piece.
Let's take the length of middle sized piece to be x inches.
Length of longest piece = 3x inches
Length of shortest piece = (3x-23) inches
Now, we have the following expression:
x+3x+3x-23 = 40
7x-23 = 40
Adding 23 on both the sides:
7x = 40+23
7x = 63
Dividing by 7 on both the sides:
x = 63/7
x = 9 inches
Length of longest piece = 3*9 inches
Length of longest piece = 27 inches
Length of shortest piece = (27-23) inches
Length of shortest piece = 4 inches
Hence, the length of shortest piece is 4 inches, middle sized piece is 9 inches and that of longest piece is 27 inches.
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BD = 5, CX = 3, CD = 5
what is BC
Answer:
need more information to answer
If Tomas divides his stack of programs between himself and his 3 friends, what fraction of the original stack will each of his friends have? can someone help me.
As per the given information, Tomas divides one program among four people then each person will get fraction of ( 1/ 4) of the original stack if divided equally .
As given in the question,
Number of stacks of program to be divided = 1
Number of friends = 3
Number of people among whom stack of program is to be divided = 4
Let us consider stack of program divided equally
Fraction of stack of program each friend will get = 1 /4
As
( 1 / 4 ) + ( 1 / 4 ) + ( 1 / 4 ) + ( 1 / 4 )
= ( 1+ 1+ 1+ 1) / 4
= 4/4
= 1
Therefore, for the given information, Tomas divides one program among four people then each person will get fraction of ( 1/ 4) of the original stack if divided equally .
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not really sure what to do here??
Answer:
[tex]d=-6[/tex]
[tex]a_9=-49[/tex]
Step-by-step explanation:
If the first term of a sequence is [tex]-1[/tex] and the second term is [tex]-7[/tex], then each successive term in the sequence is [tex]6[/tex] less than the previous term. The common difference is [tex]-6[/tex] ( [tex]d=-6[/tex] ).
The formula representing the arithmetic sequence is:
[tex]a_n=-6n+5[/tex]
Therefore, the ninth term in the sequence is:
[tex]a_9=-6(9)+5[/tex]
[tex]a_9=-54+5[/tex]
[tex]a_9=-49[/tex]
Which inequality is represented by the graph?
5 - 3 -2 -1 0 1 2 3
-3
(1) x>-1
(3) *<-1
(2) x≤-1
D
(4) x ≥-1
4
gering
5
Answer:
answer,(2)x≥-1
Step-by-step explanation:
it was right
a bakery worker uses 175 cups of sugar to make 100 cinnamon rolls. at this rate, how many cups of sugar would be needed to make 1 cinnamon roll?