The equation for the parabola with a focus at (-4,8) and a directrix at x=-6 is ( y - 8)² = 4( x +5 ).
What is the equation for a parabola with a focus at (-4,8) and a directrix at x = -6?Given that x = -6, it means the directrix is horizontal.
Equation of parabola that opens left or write is expressed as;
( y - k )² = 4p( x - h )
Given that;
Focus: ( -4, 8 )Directrix: y = -6First, we find the vertex.
The vertex( h, k ) is halfway between the directrix and the focus.
Hence, x coordinate of the vertex is;
x = ( x coordinate of focus + directrix ) / 2
x = ( -4 + (-6) ) / 2
x = -10/2
x = -5
y coordinate of the vertex will be the same as that of the focus.
y = 8
Hence vertex will be;
( -5, 8 )
Next, we find the distance p from the focus to the vertex and from the vertex to the directrix.
Subtract x coordinate of vertex from x coordinate of focus.
p = -4 - ( -5 )
p = -4 + 5
p = 1
Now, we substitute these values into the equation.
( y - k )² = 4p( x - h )
( y - (8) )² = 4(1)( x - (-5) )
( y - 8)² = 4( x +5 )
Therefore, the equation for the parabola with a focus at (-4,8) and a directrix at x=-6 is ( y - 8)² = 4( x +5 ).
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What is the product of (5 m superscript negative 2 baseline) (2 m superscript negative 3 baseline)?
Answer:
A
Step-by-step explanation:
Help please !!!!!!! Need helppppp
Answer:
option c
Step-by-step explanation:
option c is a correct answer
13% of a sample of 200 students do not like ice cream. what is the 95% confidence interval to describe the total percentage of students who do not like ice cream?
Using the z-distribution, the 95% confidence interval to describe the total percentage of students who do not like ice cream is:
(8.34%, 17.66%).
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
For this problem, the estimate and the sample size are given, respectively, by:
[tex]\pi = 0.13, n = 200[/tex]
Hence the bounds of the interval are:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.13 - 1.96\sqrt{\frac{0.13(0.87)}{200}} = 0.0834[/tex][tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.13 + 1.96\sqrt{\frac{0.13(0.87)}{200}} = 0.1766[/tex]As a percentage, the interval is:
(8.34%, 17.66%).
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The ball followed a path modelled by the equation h = −0.001! + 0.5 + 2.5 where h is the height of the ball in feet and is the horizontal distance in feet.
1) Represent the distance-height relationship for each player’s ball as an equation, in a table and on a graph. Record each representation and clearly label which player the information belongs to.
2) Supposed there were no obstacles.
a. Whose ball would travel the greatest distance before hitting the ground?
b. Whose ball would travel the shortest distance before hitting the ground?
3) Suppose the fence was 350 ft from home plate. At what height was each ball when it passed over the fence?
The heights the balls hit a fence at 350 ft distance are 65 feet, 38 feet and 30 feet, respectively
Represent the distance-height relationship for each player’s ball as an equation, in a table and on a graph.Juan
Juan's equation is given as:
h = -0.001d^2 + 0.5d + 2.5
h =
Set d to multiples of 50 from 0 to 400.
So, the table of values of Juan's function is:
d (ft) h(ft)
0 2.5
50 25
100 42.5
150 55
200 62.5
250 65
300 62.5
350 65
400 42.5
See attachment for the graph of Juan's function
Mark
A quadratic function is represented as:
h = ad^2 + bd + c
Using the values on the table of values, we have:
c = 3 -- the constant value
So, the equation becomes
h = ad^2 + bd + 3
Using the two other values on the table of values, we have:
23 = a(50)^2 + b(50) + 3
38 = a(100)^2 + b(100) + 3
Using a graphing tool, we have:
a = -0.001
b = 0.45
So, Mark's equation is h(d) = -0.001d^2 + 0.45d + 3
See attachment for Mark's graph.
Barry
From the graph, we have the table of values of Barry's function to be:
d (ft) h(ft)
0 2.5
50 21
100 35
150 44
200 48
250 46
300 41
350 30
400 14
450 0
Using a graphing tool, we have the quadratic function to be:
y = -0.001x^2 +0.4x +2.5
The shortest and the greatest distance before hitting the groundFrom the graphs, equations and tables, the distance travelled by the balls are:
Juan = 505 feet
Mark = 457 feet
Barry = 450 feet
This means that Juan's ball would travel the greatest distance while Barry's ball would travel the shortest.
The height the balls hit a fence at 350 ft distanceTo do this, we set d = 350
From the graphs, equations and tables, the height at 350 ft by the balls are:
Juan = 65 feet
Mark = 38 feet
Barry = 30 feet
The above represents the height the balls hit the fence
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Gustavo is in a contest where he will win one of four possible prizes. he creates a four-part spinner to represent the four prizes that he has an equal chance of winning: a video game system, a bicycle, a watch, and a gift card. he spins the spinner several times to demonstrate the likelihood of winning a certain prize. what is true about gustavo’s method of data collection and his data on the possible prizes?
Answer:
Gustavo used a simulation where the data is quantitative’
i need help with this
The value of the x from the given equation is 1 and 6/7.
According to the statement
we have given that the quadratic equation and we have to find the solve for the value of the x.
So, For this purpose we know that the
A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers.
So, The given equation is
7x^2 -x -6 =0
Find the factors of the equation
7x^2 -7x + 6x -6 =0
7x(x-1) -6(x-1) = 0
(x-1)(7x-6) =0
here the values of x becomes 1 and 6/7.
So, The value of the x from the given equation is 1 and 6/7.
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Solve for x.
x/3 ≤ −6
x / 3 ≤ -6
---Multiply both sides by 3 to cancel out the denominator on the left side
x ≤ -18
Hope this helps!
Answer:
x=18 we multiply both 6and33. What kind of triangle is represented by the triangle shown below?
Isosceles
Right
O Equilateral
Scalene
Answer:
Isosceles
Step-by-step explanation:
An Isosceles triangle has an acute angle (less than 45°), and this photo shows a triangle with two matching sides with one side being longer.
A right triangle would have a 90° angle which this photo doesn't have
An Equilateral triangle has all 60° sides, since it doesn't have all matching sides, it cannot be the answer.
A Scalene triangle is similar to this photo except it has 30° 60° and 90° angles, which this photo doesn't have.
I hope this helps!
please help! look at the phot linked
Answer: C
Step-by-step explanation: the other two options are both wrong, 0.13 is larger than 0.125 and she did order by volume per fish.
y=2x + 9
3x + 2y = 4
Answer:
The answer is: (x,y) = (-2,5)
Match each quadratic function given in factored form
with its equivalent standard form listed on the left.
-f(*) = (x + 2)(x - 6)
f(x) = (x - 4)(x + 3)
f(x) = (x - 12)(x 1)
f(x) = (x -3)(x + 4)
The standard form of the given quadratic equation in factored form is
(x+2) (x-6) = x²-4x-12
(x-4) (x+3) = x²-x-12
(x-12) (X+1) = x²-11x-12
(x-3) (x+4) = x²+x-12
what are quadratic equations?
A quadratic function can be defined as a function having the highest degree 2. The standard form of a quadratic function is ax²+bx+c where a and b are not equal to zero
To convert a factored quadratic function into the standard form, we first need to open the brackets by multiplying the integers. Then carry out addition or subtraction operations to obtain the equation.
f(x) = (x+2) (x-6)
x²+2x-6x-12
x²-4x-12
similarly, the standard form of equations 2,3 and 4 are :
(x²-x-12)
(x²-11x-12)
(x²+x-12)
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Answer:
B, D, A, C
Step-by-step explanation:
f(x) = (x + 2)(x – 6)
✔ B
f(x) = (x – 4)(x + 3)
✔ D
f(x) = (x – 12)(x + 1)
✔ A
f(x) = (x – 3)(x + 4)
✔ C
At a sale this week, a desk is being sold for $336. This is a 36% discount from the original price.
What is the original price?
Answer:
$525
Step-by-step explanation:
We can find the original price by using the formula x - 0.36x = 336, where x is the original price, 0.36 is the discount percentage (converted to decimal form), and 336 is the total amount paid after the discount is applied:
[tex]x-0.36x=336\\0.64x=336\\x=525[/tex]
To check and further understand why the formula works, we can simply apply the discount to the original price and subtract the number from the original price:
525 * 0.36 = 189
525 - 189 = 336
Modeling the first formula gives us:
525 - (0.36 * 525) = 336
525 - 189 = 336
6. Solve the system of equations.
x = 3y + 1
2x+4y= 12
O (10,3)
O (4,1)
(1,4)
(3,10)
Answer:
(4, 1 )
Step-by-step explanation:
x = 3y + 1 → (1)
2x + 4y = 12 → (2)
substitute x = 3y + 1 into (2)
2(3y + 1) + 4y = 12
6y + 2 + 4y = 12
10y + 2 = 12 ( subtract 2 from both sides )
10y = 10 ( divide both sides by 10 )
y = 1
substitute y = 1 into (1)
x = 3(1) + 1 = 3 + 1 = 4
solution is (4, 1 )
A large container holds 4 gallons of chocolate milk that has to be poured into 1-pint bottles. if the ratio of gallons to pints is 1 : 8, how many bottles are needed? a. 2 bottles b. 4 bottles c. 8 bottles d. 32 bottles e. 40 bottles
32 bottles are needed to poured 4 gallons of chocolate milk.
The correct option is D.
What do you know about volume?A closed surface's volume, which is expressed as a scalar quantity, measures how much three-dimensional space is enclosed. The area that a material or 3D object takes up or contains, for instance. The SI-derived cubic metre is a common unit for quantifying volume quantitatively.
According to the given information:Pints to Gallons Ratio: 1:8
Permit x bottles to be present.
There are x bottles required for 4 gallons of chocolate milk.
Because of the direct proportion
4/x = 1/8
x = 4 x 8
x = 32
As a result, 32 bottles are required.
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giving brainliest to right answer tyy
Answer:
B
Step-by-step explanation:
Original form:
y=mx+b
m=slope
b=y interecept
By replacing those variables with the given we come up with the equation of:
y=3/2x-7
Answer:B
Step-by-step explanation:
Solve the following system using the algebraic method of substitution. Verify your solution.
x + 2y = -5
3x - y = -1
Solve the following linear system using the algebraic method of elimination. Verify your solution.
x + 2y = 2
3x + 5y = 4
Solve the following linear system algebraically. State why you chose the method you used.
x + 3y = 7
2x + 4y = 11
Answer: Look into step by step
Step-by-step explanation:
1. Multiply the second equation by 2; 6x - 2y = -2 then add to first equation
7x = -7 so x = -1, substitute x = -1 into the first equation -1 + 2y = -5 so y = -2
2. Multiply the first equation by 3; 3x + 6y = 6 then subtract it by second equation
y = 2, substitute y = 2 into first equation, x + 4 = 2, x = -2
3. Multiply the first equation by 2; 2x + 6y = 14 then subtract it by second equation
2y = 3 so y = 1.5, substitute y = 1.5 into the first equation x + 4.5 = 7, x = 2.5
I chose this method as it is easy
What is the twentieth term in the sequence 23, 43, 63, 83 …?
Answer:
403 (hope this helps)
Step-by-step explanation:
Here are the scores of 18 students on a history test. 55, 57, 58, 61, 62, 66, 68, 68, 71, 75, 75, 78, 82, 83, 85, 86, 88, 89. Notice that the scores are ordered from least to greatest. Make a box-and-whisker plot for the data.
The box-and-whisker plot for the given data is given below:
A box and whisker plot is defined as a graphical method of displaying variation in a set of data.
The results of a history test taken by 18 students: 55, 57, 58, 61, 62, 66, 68, 68, 71, 75, 75, 78, 82, 83, 85, 86, 88, 89.
Take note of how the scores are listed from lowest to highest.
The median for the given data is 73.
The Lower Quartile and the Upper Quartile would be found after that.
These represent the lower and higher halves' medians.
Lower quartile = 61.75
Upper quartile = 83.5
Make a number line. Mark your median, quartiles, and smallest and largest values.
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Ben invests Nu 125,000 in a bank shares with a face value of Nu 100 but they are being sold at a premium of 25%. How many shares can he buy?
Answer:
This is your answer!
Step-by-step explanation:
Rearrange the equation so w is the independent variable.
u-5=-4(w-1)u−5=−4(w−1)u, minus, 5, equals, minus, 4, left parenthesis, w, minus, 1, right parenthesis
u=u=
u = - 4w + 9 is the rearranged equation so that w is the independent variable given that the equation is u - 5= - 4(w - 1). This can be obtained by simplifying the equation and taking w to one side of the equation with other constants.
Find the rearranged equation:Simplifying an equation can be done by using the following steps:
Add/subtract the terms from the equation on both sides Multiply/divide the coefficients of the variable in order to isolate the variable Solve for the variable Substitute the variable in the original equation for finding other variables (if any)Here it is given that the equation is,
⇒ u - 5= - 4(w - 1)
We have to find an equation in which w is taken to one side of the equation with other constants.
First by adding both side of the equation with 5 we get,
⇒ u - 5 + 5 = - 4(w - 1) + 5
By opening the bracket we get,
⇒ u = - 4w + 4 + 5
Finally by adding the constants we get,
⇒ u = - 4w + 9
Hence u = - 4w + 9 is the rearranged equation so that w is the independent variable given that the equation is u - 5= - 4(w - 1).
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In the circle below, if < B = 39 °, what is the measure of arc AB?
From my analysis, the answer is likely to be D. I don't have a formula to prove it though.
Answer: 78 degrees.
Step-by-step explanation:
The other guy is wrong don't listen to him.
Area=
Help me please asap.
Thanks so much :)
The area of the given parallelogram is 8 square units
Area of a parallelogramA parallelogram is a 2 dimensional figure with 4 sides and angles. From the given diagram, the opposite sides are equal and the sum of the adjacent angles are supplementary
The formula for calculating the area of a parallelogram is expressed as:
A = base * height
From the given diagram
Base = (4, 0) = 4 units
Height. = (2, 0) = 2 units
Substitute the given values into the formula to have:
A = 4 units * 2 units
A = 8 square units
Hence the area of the given parallelogram is 8 square units
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Look at the equation shown below. 19 - 5 = 3 z - 11 Which of these expressions gives the value of Z
If the equation is 19-5=3z-11 then the value of z is 15/3.
Given an equation in terms of z is 19-5=3z-11.
We are required to find the value of variable z which exist in equation.
Equation is like a relationship between two or more variables expressed in equal to form. Equations of two or more variables look like ax+by=c. It may be linear equation, quadratic equation,cubic equation,or many more depending on power of the variable.
The value of z can be find as under:
19-5=3z-11
4=3z-11
3z=4+11
3z=15
z=15/3
Hence if the equation is 19-5=3z-11 then the value of variable z is 15/3.
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The long division below shows the first term of the quotient. which polynomial should be subtracted from the dividend first? x 2 startlongdivisionsymbol x cubed 3 x squared x endlongdivisionsymbol to get a quotient of x squared
The polynomial that should be subtracted from the dividend first is; x³ + 2x²
How to carry out polynomial long division?
The long division we are given is;
__________
x + 2 ) x³ + 3x² + x
Now, when we divide the polynomial by (x + 2), it means that the first quotient will be x².
Then by the multiplication of (x + 2) and x², we get a polynomial which will be subtracted from the dividend. Thus, we have;
(x + 2) * (x²) = x³ + 2x²
Thus, the polynomial to be subtracted is x³ + 2x²
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Everyone in Sandy's class has to do a science project. Out of 50 students, 56% have completed their projects.
How many students still need to do their projects?
Pls help ASAP
Answer:
22
Step-by-step explanation:
100 - 56 is 44. 44% have still not done the project
.44 x 50 = 22
Answer:
22 coz 56% of 50 which is the total is 28. Then the remaining 44%is22
Step-by-step explanation:
Question 1 (essay worth 4 points) (h2.02 mc) the cost of attending an amusement park is $15 for children and $40 for adults. on a particular day, the attendance at the amusement park is 5,000 attendees, and the total money earned by the park is $100,000. use the given matrix equation to solve for the number of children’s tickets sold. explain the steps that you took to solve this problem. a matrix with 2 rows and 2 columns, where row 1 is 1 and 1 and row 2 is 15 and 40, is multiplied by matrix with 2 rows and 1 column, where row 1 is c and row 2 is a, equals a matrix with 2 rows and 1 column, where row 1 is 5,000 and row 2 is 100,000.
Using a system of equations, it is found that there were 4,000 children tickets sold.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given by:
Variable x: Number of children tickets sold.Variable y: Number of adult tickets sold.The attendance at the amusement park is 5,000 attendees, hence:
x + y = 5000 -> y = 5000 - x.
Considering the cost of parking and that the total money earned by the park is $100,000, we have that:
15x + 40y = 100000
Applying the multiplication of the matrices, these equations are the same that the system gives. Replacing the second equation into the first:
15x + 40(5000 - x) = 100000
25x = 100000
x = 100000/25
x = 4000.
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A blimp is 1600 meters high in the air and measures the angles of depression to two stadiums to the east of the blimp. if those measurements are 71.7° and 25.2°, how far apart are the two stadiums?
The two stadiums are 2,871 meters
A blimp = point A
stadium 1 = point B
stadium 2 = point C
height of the blimp , AD = 1600
depression angle of stadium 1 , ∠y = 71.7°
depression angle of stadium 2 , ∠x = 25.2°
distance between the two stadiums = d
So, it forms 2 triangles ABD and ACD,
Using the trigonometric ratios,
tan θ = Altitude / Base
DC = AD × tan (90° - x)
= 1600 × tan( 90° - 25.2° )
= 1600 × cot(25.2°)
= 1600 × 2.13
DB = AD × tan (90° - y)
= 1600 × tan( 90° - 71.7° )
= 1600 × cot(71.7°)
= 1600 × 0.33
∴ d = DC - DB
= 1600 * [ tan( 90° - 25.2° ) - tan( 90° - 71.7° ) ]
= 2,871 meters
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40 POINTS AND BRAINLIEST!! Solve for x in the following equations..
a) 6x +3 +21
b) 15(x - 5) = 75
c) 3/4 x +5 = 26
Answer:
a) x = 3
b) x = 10
c) x = 28
Explanation:
a)
[tex]\sf 6x + 3 = 21[/tex]
collect term
[tex]\sf 6x = 21-3[/tex]
simplify
[tex]\sf 6x = 18[/tex]
divide both both sides by 6
[tex]\sf x = 3[/tex]
b)
[tex]\sf 15(x - 5) = 75[/tex]
distribute
[tex]\sf 15x - 75 = 75[/tex]
collect terms
[tex]\sf 15x = 75 + 75[/tex]
combine
[tex]\sf 15x = 150[/tex]
divide both sides by 15
[tex]\sf x = 10[/tex]
c)
[tex]\sf \frac{3}{4} x +5 = 26[/tex]
collect like terms
[tex]\sf \frac{3}{4} x = 26-5[/tex]
combine
[tex]\sf \frac{3}{4} x = 21[/tex]
cross multiply
[tex]\sf x = \frac{ 21 (4)}{3}[/tex]
simplify
[tex]\sf x =28[/tex]
Isabelle is mixing red paint with blue paint to make purple paint. She adds 3/10 of a fluid ounce of red to 11/15 of a fluid ounce of blue to make 1 1/30fluid ounces of purple. How many fluid ounces of red paint will she need to make 3 fluid ounces of purple paint?
Answer:
27/31
Step-by-step explanation:
FIrst, construct a ratio. Isabelle needs 3/10 red to make 31/30 purple. So, we can divide red by purple to form a fraction to determine how much red paint for 1 fluid oz of purple. (3/10)/(31/30)=(9/30)/(31/30)=9/31. For every 1 oz of purple, we need 9/31 oz of red. Because we found how much red paint for 1 oz purple paint, we simply multiply by 3 to find how much red paint for 3 fluid oz of purple paint. (9/31)*3=27/31
For what value of x is 3 − x equal to x − 3?
Answer:
x = 3
Step-by-step explanation:
Given the information from the question, we can deduce that:
3 - x = x - 3
Now our goal here is to find x.
3 - x = x -3
3 - x - 3 = x - 3 - 3
- x = x - 6
- x - x = x - 6 - x
- 2x = - 6
x = [tex]\frac{-6}{-2}[/tex] = 3
Answer: 3
Step-by-step explanation: The only value for x in which 3 - x is the same as x - 3 is where x does not affect the value of 3 whatsoever. We can also set this up algebraically to find this out algebraically.
x - 3 = 3 - x
Adding 3 to both sides, we have
x = 6 - x
Adding x to both sides we have
2x = 6
Dividing by 2 from both sides, we get
x = 3
