The equation of the parabola with the given focus and directrix is x² = 12( y - 4 ).
What is the equation of the parabola with the given focus and directrix?Since the directrix y = 1, it shows it is vertical, so we use the equation of the parabola that opens up or down.
( x - h )² = 4p( y - k )
Given the data in the question;
Focus: (0,7)directrix y = 1First, we determine the vertex.
The vertex ( h,k ) is half way between the directrix and the focus.
Find the y-coordinate of the vertex using;
y = ( y-coordinate of focus + directrix )/2
y = (7+1)/2 = 8/2 = 4
The x-coordinate of the vertex is the same as that of the focus 0
Hence, the vertex is ( 0,4 )
Next, we determine the distance p from the focus to the vertex.
p = y-coordinate of focus - y-coordinate of vertex
p = 7 - 4
p = 3
Now, plug the known values into the equation and simplify
( x - h )² = 4p( y - k )
( x - 0 )² = 4(3)( y - 4 )
x² = 12( y - 4 )
Therefore, the equation of the parabola with the given focus and directrix is x² = 12( y - 4 ).
Learn more about parabola here: https://brainly.com/question/11911877
#SPJ1
Can you use absolute value when subtracting two negatives?
- 2 1/2 - (-1 2/3)
or does it only work when one number is negative?
Yes, it is possible to use absolute value when subtracting two negatives and as such it does not only work when one number is negative.
How to Interpret Absolute Values?
When adding two negative numbers, add the absolute value of the numbers and keep the negative sign.
For example -1 + -2 = - (||-1| + |-2||), which is -(1 + 2) or -3
The absolute value when subtracting two negatives is -2¹/₂ - (-1²/₃) is possible because when subtracting, we will change the subtraction to addition and change the sign of the number being taken away.
Thus, we can conclude that it is possible to use absolute value when subtracting two negatives.
Read more about Absolute Values at: https://brainly.com/question/24368848
#SPJ1
Can someone help me with these 2 problem
Answer:
Step-by-step explanation:
volume of small cuboid=5×2×4=40 cm³
volume of one small cube=(1/2)³=1/8
so number of cubes=40÷1/8=40×8=320
now width of bigger cuboid=9-5=4 cm
volume of bigger cuboid=4×2×12=96
number of small cubes in this cuboid=96÷1/8=96×8=768
total cubes=768+320=1088
Which numbers have a digit in the ones place that is 1/10 the value of the digit in the tens place? select all that apply
a. 6,044.7
b 6,339.99
c. 8,101.13
d. 8,066.51
e. 9,777.1
The numbers having a digit in the ones place that is 1/10 the value of the digit in the tens place are 6,044.7, 8,066.51 and 9,777.1 . Option A, D , E
What is place value?The place value of a number can be defined as the position of the number is a digit.
Given the digits, we have to determine the numbers of digits in the ones that is 1/10 the value of the digit in the tens place.
⇒ 6044. 7
The ones digit is 4
The tens digit is 40
Take ratio = 4/ 40 = 1/ 10
⇒ 8
The ones digit is 8
The tens digit is 80
Take ratio = 8/ 80 = 1/ 10
⇒ 9,777.1
The ones digit is 7
The tens digit is 70
Take ratio = 7/ 70 = 1/ 10
Thus, the numbers having a digit in the ones place that is 1/10 the value of the digit in the tens place are 6,044.7, 8,066.51 and 9,777.1 . Option A, D , E
Learn more about place value here:
https://brainly.com/question/12386995
#SPJ1
4.30. An internet service provider has two connection lines for its customers. Eighty percent of
customers are connected through Line I, and twenty percent are connected through Line II.
Line I has a Gamma connection time with parameters a = 3 and λ = 2 min-¹. Line II has
a Uniform(a, b) connection time with parameters a = 20 sec and b = 50 sec. Compute the
probability that it takes a randomly selected customer more than 30 seconds to connect to
the internet.
Using the uniform distribution, there is a 0.6667 = 66.67% probability that it takes a randomly selected customer more than 30 seconds to connect to the internet.
What is the uniform probability distribution?It is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
For this problem, the connection time has parameters a = 20 sec and b = 50 sec, as stated in the problem.
The probability that it takes a randomly selected customer more than 30 seconds to connect to is P(X > 30).
Hence, applying the formula, with the bounds, we have that:
P(X > 30) = (50 - 30)/(50 - 20) = 2/3 = 0.6667.
The measure above is the desired probability.
More can be learned about the uniform distribution at https://brainly.com/question/24321725
#SPJ1
PLS HELP!! MIDDLE SCHOOL 8TH GRADE MATH QUESTION!! The school cafeteria serves portions of fried rice that are 140 grams each.
A. If 64 portions of rice are served, how many grams of rice would that be?
B. Write an expression for the total weight in grams of rice needed for p portions.
C. One day, the total weight of rice served was 11,340 grams. How many portions were served that day?
D. Write an expression for the number of portions served if the total rice weighed t grams.
Answer:
a: 8960
b: I suck at proportions even though im in hs. srry i cant answer that.
c: 177.1875, if you have to round than 177.
d: im so srry lol
Step-by-step explanation:
Solve. Round your answer to the nearest tenth.
90.97 ÷ 8.6
Please show all of your work
Answer:
10.6
Step-by-step explanation:
Answer:
10.6
Step-by-step explanation:
90.97 divided by 8.6 = 10.57790697
rounded to the nearest tenth = 10.6
A lighthouse casts a 72-yard shadow at the same time as a 32-foot tall billboard casts a 19-foot
shadow.
What is the height of the lighthouse?
The quotient of x^2 − 16/ x − 4 is x+4 .
Compute each quotient using the identities you discovered in this module.
The quotient of x^3 − 64/x − 4 is x^2+
.
The quotient of x^4 − 256/x − 4 is x3+
.
The quotient of x^5 − a^5/x − a is x4+
The quotient of x³ - 64/x - 4 is (x² + 4x + 16).
The quotient of x⁴ − 256/x − 4 is (x³ + 4x² + 16x + 64).
The quotient of x⁵ - a⁵ /x - a is (x⁴ + ax³ + a²x² + a³x + a⁴).
What is Division method?
Division method is used to distributing a group of things into equal parts.
We have to given that;
The quotient of x² − 16/ x − 4 is x + 4.
Now, We have compute each quotient as;
The quotient of x³ - 64/x - 4 is;
[tex]\frac{x^{3} - 64}{x-4} = \frac{x^{3} - 4^{3} }{x-4} = \frac{(x-4) (x^{2} +4x+16)}{(x-4)} = (x^{2} +4x+16)[/tex]
Hence, The quotient of x³ - 64/x - 4 is (x² + 4x + 16).
And, The quotient of x⁴ − 256/x − 4 is;
[tex]\frac{x^4-4^4}{x-4} = \frac{((x^2)^2-(4^2)^2)}{(x-4)} = \frac{(x^{2} -4^4) (x^{2} + 4^2)}{(x-4)} = \frac{(x-4)(x+4)(x^{2} +4^2)}{(x-4)} = (x+4)(x^{2} + 16)[/tex]
[tex](x+4)(x^{2} + 16) = x^{3} + 4x^{2} +16x + 64[/tex]
Hence, The quotient of x⁴ − 256/x − 4 is (x³ + 4x² + 16x + 64).
The quotient of x⁵ - a⁵ /x - a is;
_______
x - a ) x⁵ - a⁵ ( x⁴ + ax³ + a²x² + a³x + a⁴
x⁵ - ax⁴
- +
-------------------
ax⁴ - a⁵
ax⁴ - a²x³
- +
-------------------
a²x³ - a⁵
a²x³ - a³x²
- +
-----------------
a³x² - a⁵
a³x² - a⁴ x
- +
--------------------------
a⁴ x - a⁵
a⁴ x - a⁵
- +
-----------------------
0
Hence, The quotient of x⁵ - a⁵ /x - a is (x⁴ + ax³ + a²x² + a³x + a⁴).
Therefore, The quotient of x³ - 64/x - 4 is (x² + 4x + 16).
The quotient of x⁴ − 256/x − 4 is (x³ + 4x² + 16x + 64).
The quotient of x⁵ - a⁵ /x - a is (x⁴ + ax³ + a²x² + a³x + a⁴).
Learn more about the division method visit:
https://brainly.com/question/2053526
#SPJ1
Grandpa Mayowa and Grandma Quetta gave money to their 5 grandchildren to divide evenly among themselves. Grandpa Mayowa gave 500 dollars and Grandma Quetta gave d dollars. How much money did each grandchild receive? Write your answer as an algebraic expression.
6. The Edwards's Theater chain has studied its movie customers to determine how much money they spend on concessions. The study revealed that the spending distribution is approximately normally distributed with a mean of $4.11 and a standard deviation of $1.37. What percentage of customers will spend less than $3.00 on concessions? a. 2.09% b. 20.9% c. 81.0% d. 209.0%
The percentage of customers will spend less than $3.00 on concessions is which is option (d).
Z-scores can be placed on a normal distribution curve. Z-scores range from -3 standard deviations (leftmost part of normal distribution curve) to +3 standard deviations (rightmost part of normal distribution curve). To use the z-score, we need to know the mean μ and the population standard deviation σ. A Z-score is a way to compare results to a "normal" population. Test or poll results have thousands of possible outcomes and units. These results often seem meaningless. A sample basic Z-score formula is z = (x - μ) / σ ...(1)It is given that mean is $4.11 , standard deviation is $1.37 and value is $3.00
Putting above values in equation (1) , we get
[tex]z=\frac{3-4.11}{1.37} \\\\z=-0.810[/tex]
P(x<3) = 0.20891
Percentage will be 209. %
Learn more about normal distribution here :
https://brainly.com/question/4079902
#SPJ9
Order the square root of 70, negative 8.2 repeating, twenty five thirds, and negative eight and four sevenths from least to greatest. negative eight and four sevenths, negative 8.2 repeating, square root of 70, twenty five thirds negative eight and four sevenths, negative 8.2 repeating, twenty five thirds, square root of 70 negative 8.2 repeating, negative eight and four sevenths, twenty five thirds, square root of 70 negative 8.2 repeating, negative eight and four sevenths, square root of 70, twenty five thirds
Answer:
[tex]\textsf{B)} \quad -8 \frac{4}{7} \quad -8.\.{2} \quad \dfrac{25}{3} \quad \sqrt{70}[/tex]
Step-by-step explanation:
Given:
[tex]\sqrt{70} \quad -8.\.{2} \quad \dfrac{25}{3} \quad -8 \frac{4}{7}[/tex]
Convert the given numbers into decimals:
[tex]\sqrt{70}=8.366...[/tex]
[tex]-8.\.{2} =-8.222...[/tex]
[tex]\dfrac{25}{3}=8.333...[/tex]
[tex]-8 \frac{4}{7}=-8.571...[/tex]
Order the decimals from least to greatest:
[tex]-8.571... < -8.222... < 8.333... < 8.366...[/tex]
Therefore:
[tex]-8 \frac{4}{7} < -8.\.{2} < \dfrac{25}{3} < \sqrt{70}[/tex]
Answer:
negative eight and four sevenths, negative 8.2 repeating, twenty five thirds, square root of 70
PLEASE HELP FIND FOR X QUICK PLEASE!!!!
Greetings from Brasil...
Assuming that the line segments CE and FH are parallel, then:Angle W
Here we have Opposite Angles by Vertex, so
W = 14
According to the attached figure, the angle W is also corresponding, so in the triangle CEG one of the angles will be 14°
Angle Z
The sum of the interior angles of a triangle is 180°, so for triangle CEG:
Z + W + 78 = 180
Z + 14 + 78 = 180
Z = 88
Angle X
Z and 4X are complementary angles, then
Z + 4X = 180
88 + 4X = 180
X = 23
___________________________________
see something similar in
https://brainly.com/question/28649713
ANSWER THE FOLLOWING WITH COMPLETE SOLUTIONS:
The solution of the rational inequality are-
x ≤ 9 x > 1What is meant by the rational inequality?A rational inequality is one that includes a rational expression.
To solve a rational inequality, first locate the zeroes (from the denominator) and also the undefined points (from the denominator). These zeroes and undefined points are used to divide this same number line into intervals. Then you locate the rational's sign on each interval.1. (3x - 1)/(x + 4) ≤ 2
Solving the equation.
3x - 1 ≤ 2(x + 4)
3x - 1 ≤ 2x + 8
Placing the constants and the variable on different side.
3x - 2x ≤ 8 + 1
x ≤ 9
Thus, the value of 'x' is less than equal to 9.
2. 2x/(x + 1) > 1
Simplifying;
2x > x + 1
Placing the constants and the variable on different side.
2x - x > 1
x > 1
In this, the value of the x is less than 1.
To know more about the rational inequality, here
https://brainly.com/question/10653224
#SPJ9
Suppose the average yearly salary of an individual whose final degree is a master's is $40 thousand less than twice that of an individual whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn $113 thousand. Find the average yearly salary of an individual with each of these final degrees.
In linear equation 109333.2 dollars is the average yearly salary of an individual with each of these final degrees .
What is a linear equation ?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.let x be the salary of individual with bachelor degree
Then the average salary of individual with Masters degree is:
(2x-40000)
the combined of two salaries is 130000:
x+(2x-40000)=130000
3x-40000=130000
3x=130000+40000
x=170000/3
x = 56,666.66
x= 56,666.6 dollars ( the average salary of bachelor degree)
the average salary of Masters degree = 2x - 40000
2(56666.6)-40000 = 109333.2 dollars
Learn more about linear equation
brainly.com/question/11897796
#SPJ9
4.) Connor went to the fair with $22. He bought a hot dog and a coke for $5 and planned to spend the rest of his money on rides that cost $1.50 each. Write and solve an inequality to represent the number of rides that Connor can afford.
The inequality represents the number of rides that Connor can afford is 1.50x+5≤22 and he can ride 11 rides
The amount Connor had when he went to the fair = $22
The cost of a hotdog and coke = $5
The cost of each ride = $1.50
Consider then number of rides he ride as x
Then, the equation of the inequality is
1.50x+5≤ 22
Solve the inequality
1.50x+5≤ 22
1.50x ≤ 17
x ≤ 11.33
He can afford 11 rides with the money he has
Hence, the inequality represents the number of rides that Connor can afford is 1.50x+5≤22 and he can ride 11 rides
Learn more about inequality here
brainly.com/question/20383699
#SPJ1
you have a $3125 student loan. suppose you pay the loan off in two and a half years(30 months). estimate your monthly payment by ignoring interest and rounding down the amount owed. (round your answer to the nearest dollar.)
The monthly payment by ignoring intrest and rouning down the amount owed is $104
Given that "you have a $3125 student loan. suppose you pay the loan off in two and a half years(30 months)" and asked to find out the monthly payment by ignoring the intrest and round off the amount to nearest integer.
Total loan=$3125 .
Total time given= two and a half years(30 months)
The monthly payment=[tex]\frac{3125 }{30}[/tex]
The monthly payment=$104
To complete the student loan monthly payment of $104 is required.
Therefore,The monthly payment by ignoring intrest and rouning down the amount owed is $104
Learn more about intrest here:
https://brainly.com/question/28170884
#SPJ9
Given the function: f(x) = 2x³-3/2x, find f(-4).
The sets you can form using only the elements in the set (5, 7, 9)
Can you do a Step-by-step explanation:
Unknown Numbers
Consider the following problem.
One number is 3 less than 6 times a second number.
Their sum is 46. Find the numbers
If × represents the second number, which equation is
correct for solving this problem?
Step-by-step explanation:
y is the second number. This means we can define it as the following equations where x is the second number:
y=6x-3
y+x=46
we have a system of equations, let's move all x to the right side
y=6x-3
y=46-x
this means that 6x-3=46-x
6x+x=46+3
7x=49
x=7
now that we know x we can calculate the y through one of the equations above:
y=39
mals
For how many animals is (p V q) Ar true?
O 15
O 17
O 20
O 22
Answer:
17
Step-by-step explanation:
A pool cleaner uses 3/5 pound of liquid chlorine for each pool she services. She has 5 pounds of liquid chlorine available. Determine how many whole pools can be serviced with the available liquid chlorine.
Answer:
8 pools
Step-by-step explanation:
5 ÷ 3/5
5 x 5/3 = 35/3 = 8 1/3
If f(x) = 4x² -3 and g(x) = x+1, find (f - g)(x)
The value of (f - g)(x) = 4x² - x - 4.
Function - A function is a relationship or expression involving one or more variables. It has a set of input and outputs. Each input has only one output. The function is the description of how the inputs relate to the output.
We have been given that -
f(x) = 4x² - 3
g(x) = x + 1
Find out (f - g)(x) = ?
(f - g)(x) = 4x² - 3 - (x + 1)
(f - g)(x) = 4x² - 3 - x - 1
Output of
(f - g)(x) = 4x² - x - 4
Hence , for the given function f(x) = 4x² - 3 and g(x) = x + 1 the relationship of (f - g)(x) is 4x² - x - 4.
To learn more about Function
Visit - https://brainly.com/question/11624077
#SPJ9
Find the values of x and y.
PLEASE HELP ME I DONT GET THIS
Answer:x=60 y=61
Step-by-step explanation:
lmk if you want an explanation
How to write one billion,three hundred million,two hundred and sixty six thousand in figure
Answer:
1,300,266,000
Step-by-step explanation:
Billion - 1
Hundred Million - 3
Ten Million - 0
Million - 0
Hundred Thousand - 2
Ten thousand - 6
Thousand - 6
Hundred - 0
Tens - 0
Unit - 0
Which of these is not a technique that can be used to randomly assign
students to a treatment group?
OA. Flipping a coin
B. Winning an election for class president
C. Rolling a die
D. Choosing a card from a fair deck
What is 9 divided 2.43
eight to the fourth power increased by six
Answer: 4102
Step-by-step explanation:
8^4 + 6=
4096+6=4102
If Ef bisects CD, CG = 9x - 4, GD = 2x + 31, EF = 4x - 1, and GF = 7, find EG
The value of EG is 12
In geometry, the term line segment is defined as the part of a line segment used to join two points in a plane. When segments join the midpoints of two sides of a triangle, the segments are parallel to the other side and represent one half of it.Given equations of line are :
CG = 9x -4
GD = 2x+31
EF = 4x-1
GF = 7
We are asked to find the length of EG. We can start by analyzing the bisector, CD. Since the segment is the bisector, So CG = GD.
CG = GD
9x -4 = 2x+31
7x = 35
x = 5
Analyzing EF
EF = EG + GF
4x-1 = EG +7
20 - 1 -7 = EG
EG = 12
The value of EG is 12
Learn more about line segment here
https://brainly.com/question/2437195
#SPJ9
Kaili is training for a marathon. For the first five days of her training plan, she will need to walk 5.431 miles each day. For the next four days she will to increase her mileage and walk 6.749 per day. How many miles total did Kaili run during her training?
The total mile Kaili ran during her training was 54.151 miles
Calculating total distanceFrom the question, we are to calculate the total miles Kaili ran during her training
From the given information,
" For the first five days of her training plan, she will need to walk 5.431 miles each day"
That is,
She ran 5 × 5.431 miles
5 × 5.431 miles = 27.155 miles
Also, from the information,
"For the next four days she will to increase her mileage and walk 6.749 per day"
That is,
She ran 4 × 6.749 miles
4 × 6.749 miles = 26.996 miles
Thus,
The total mile Kaili ran = 27.155 miles + 26.996 miles
The total mile Kaili ran = 54.151 miles
Hence, the total mile Kaili ran during her training was 54.151 miles
Learn more on Calculating distance here: https://brainly.com/question/14330664
#SPJ1
greatest common factor 2a and 4ab
Answer: [tex]2a[/tex]
Step-by-step explanation:
So let's say you're adding [tex]2a+4ab[/tex] and you want to factor that...
well you can take a 2 out of that...
[tex]2(a+2ab)[/tex]
Next, you can take an "a" out of that..
[tex]2a(1+2b)[/tex]
So the greatest monomial factor is 2a... Hope this helps!! Please rate it 5 stars!