The equation of the parabola passing through the points (5,-11),(6,-12),(7,-11) is y = x² - 12x - 24
Parabola:
Parabola refers an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. And the fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
Given,
Here we have the following points:
(5,-11),(6,-12),(7,-11)
Now, we need to find the equation of the parabola.
We know that the standard form of the equation of parabola is
y = ax² + bx + c
Here we have to apply each point in order to get the equations,
First we have to take the point (5, -11), then we get the equation,
-11 = 25a + 5b + c ---------------------(1)
Then we have to take the point (6, -12), then we get the equation as,
-12 = 36a + 6b + c ------------------(2)
Finally, we have to take the point (7, -11), then we get
-11 = 49a + 7b + c ------------------------(3)
Now, we have to subtraction, equation (2) from equation (1), then we get,
-12 -(-11) = (36 - 25)a + (6 - 5)b + (c -c)
-1 = 11a + b ---------(4)
Similarly, we have to subtraction equation (3) from equation (2), then we get,
-11 - (-12) = (49 - 36)a + (7 - 6)b + (c-c)
1 = 13a + b -------------------(5)
Now, we have to subtract equation (5) from (4),
1 - (-1) = (13 -11) +(b - b)
2 = 2a
a = 1
If the value of a = 1, then the value of b is,
1 = 13 (1) + b
b = -12
So, the value of c is,
-11 = 25 (1) + 5(-12) + c
-11 = 25 - 60 + c
-11 = -35 + c
c = 24
Therefore, the equation of the parabola is y = x² - 12x - 24
To know more about Equation of parabola here.
https://brainly.com/question/11911877
#SPJ1
NEED HELP ASAPPPPPPP
Answer:
76.93
Step-by-step explanation:
As the area of circle is πr^2
The area of semi-circle is
1÷2×πr^2
0.5×3.14×7×7
76.93
A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drink in 14 minutes?
Camel can drink 21 gallons of water in 14 minutes.
Given in question,
Gallons of water camel can drink in 10 minutes = 15
Gallons of water camel can drink in 1 minutes = 15/10
= 1.5
Gallons of water camel can drink in 14 minutes = 1.5 * 14
= 21
Hence, camel can drink 21 gallons of water in 14 minutes.
To learn more about gallons here:
https://brainly.com/question/9917229
#SPJ1
THE VALUE OF JOHN'S
BASEBALL CARD
INCREASED BY $5. IT IS
NOW WORTH
$158.
(percent change)
The percent change of the worth is 3.26%.
Apples were for sale from a fruit vendor. He has 420 apples and sells 40% of them. How many apples did he have in total when he first started?
Solution: Assume a fruit vendor had x apples in stock.
According to the query,
(100 – 40%) of x = 420
60% of x = 420
60/100 x = 420
X = 700
The fruit vendor, therefore, had 700 apples in all.
Let , the worth is $x.
according to the question, $x + $5 =$158
∴ $x= $153
∴ percent change= (5/153)×100
=3.26%
The percent change of the worth is 3.26%.
to learn more about the percentage from the given link,
https://brainly.com/question/24877689
#SPJ13
Comparing Circles
Here are two circles. Their centers are A and F.
E
C
4 cm
A
B
H
F
8 cm
D
1. What is the same about the two circles? What is different?
G
This is an incomplete question and the complete question is in the image attached.
Both circles A and F have the same radius and diameter.
What is the center of the circle?
It is possible to define a circle as the locus of a point moving in a plane while maintaining a constant distance from a fixed point. The radius of a circle is the distance from any point on the circle to its center. The fixed point is referred to as the center of the circle.
Given:
We have,
Two circles are named A and F.
The radius of circle A is 4cm
So, the diameter of Circle A is 4 x2 = 8 cm
The Diameter of Circle F is 8 cm
Hence, Both circles A and F have the same radius and diameter.
Learn more about the center of the circle here:
https://brainly.com/question/24810873
#SPJ1
Part-Time Job So far this week, you have worked 10 hours at your part-time job.
This is 80% of the number of hours you work each week. How many hours do you
work each week?
Answer:
12.5 hours a week
Step-by-step explanation:
So far this week, you have worked 10 hours at your part-time job. This is 80% of the number of hours you work each week. How many hours do you work each week?
10 hours = 80%
80% = 0.8
10/0.8 = 12.5 hours a week
Volume = 27 ft³
S
8 =
S
feet
S
Answer:
it is 67ft^3
Step-by-step explanation:
5 times 5 times 5 is 67
A specialty shop procures several refrigerators for $400 apiece and offers them to customers for $900 each. What is the mark-up, as a percentage?
The mark-up, as a percentage = 125%
What is Markup?
The term "markup" describes the discrepancy between a product's selling price and its actual cost. It is specified as a percentage over the price. In other words, the seller makes a profit when the price of the commodity.
A unit's gross profit, which is the sales price less the cost to create or buy it for resale, is divided by its cost to determine the markup %. The markup percentage is computed as (12 - 8) / 8 and is equal to 50% if an item costs the business $8 to produce but is sold for $12.
Markup percentage=[(selling price - unit cost)/unit cost]*100
Markup percentage= [(900-400)/400]*100=1.25*100
= 125%
So, the mark-up, as a percentage = 125%
To learn more about Markup percentage from the link
https://brainly.com/question/852329
#SPJ1
A machine costing $450,000 with a four-year life and an estimated $30,000 salvage value is installed by lux company on january 1. The factory estimates the machine will produce 1,050,000 units of product during its life. It actually produces the following units for the first 2 years: year 1, 260,000; year 2, 275,000. What is the depreciation amount for year 2 under the straight line method?.
Depreciation expense in year 2 = 2/4 x $225,000 = $112,500.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
Depreciation expense using the double declining method = Depreciation factor x cost of the assetDepreciation factor = 2 x (1/useful life) Depreciation expense in year 1 = 2/4 x $450,000 = $225,000Book value at the beginning of year 2 = $450,000 - $225,000 = $225,000Depreciation expense in year 2 = 2/4 x $225,000 = $112,500hence,Depreciation expense in year 2 = $112,500.
learn more about unitary method click here:
brainly.com/question/24587372
#SPJ4
Chin has $75.00 in a savings account that earns 5% interest,
compounded annually.
What will the balance be after 4 years?
Round to the nearest cent.
75÷100=0.75
0.75×5=3.75
3.75×4=15
75+15=90
6 3/4divided by 1 2/3
Answers-
7 divided by 2
6 divided by 1
8 divided by 3
3 divided by 2
If a mixed fraction, 6(3/4) is divided by another fraction 1(2/3), then the quotient will be 4.05.
As per the question statement, a mixed fraction, 6(3/4) is divided by another fraction 1(2/3),
And we are required to calculate the quotient of the above mentioned division.
To solve this question, we will first convert the mixed fractions, into improper fractions, and then use the reciprocal rule to obtain our desired answer, that is,
[{6(3/4)}/1(2/3)]
= [{(4 * 6) + 3}/4]/[{(3 * 1) + 2}/3]
= [{(24 + 3)/4}/{(3 + 2)/3}]
= [(27/4)/(5/3)]
= [(27/4) * (3/5)]
= [(27 * 3)/(4 * 5)]
= (81/20)
= 4.05
Hence, when a mixed fraction, 6(3/4) is divided by another fraction 1(2/3), then the quotient will be 4.05
To learn more about about Divisions and Quotients, click on the link below.
https://brainly.com/question/1722234
#SPJ1
Which of the following tables represents the proportional relationship for 6 cups of grape juice for every three fourths cup of rainbow sherbet?
Rainbow Sherbet (cups) 0.75 1.5 2.5
Grape Juice (cups) 6 8 10
Grape Juice (cups) 0.75 1.5 2.5
Rainbow Sherbet (cups) 6 8 10
Grape Juice (cups) 6 8 10
Rainbow Sherbet (cups) 0.75 1 1.25
Rainbow Sherbet (cups) 6 8 10
Grape Juice (cups) 0.75 1 1.25
Answer:
Step-by-step explanation:
D
PLEASE HELP! best answer gets brainiest!!
ONLY QUESTIONS, 51 to 55
please answer in detail!
Answer:
[tex]x + ( - 43) = 102 \\ x - 43 = 102 \\ x = 102 + 43 \\ x = 145[/tex]
Step-by-step explanation:
Let the unknown number be represented by x
since sum means addition, we are adding the unknown to -43 and equating it to 102 which is said to be the final answer.
After equating, we find out that we have two symbols and + multiplied by - is always -, giving us an equation as in step 2
after collecting like terms , we get an easy linear equation.
Two angles are complementary to each other. one angle measures 18°, and the other angle measures (8x − 28)°. determine the value of x. 12.5 20 44.5 16
The value of x in complementary angle is 12.5⁰.
We need to know about complementary angles to solve this problem. The complementary angle is the angle that can make another angle has a value of 90⁰. It can be written as
A + B = 90⁰
where A and B are the complementary angles.
From the question above, the given parameters are
A = 18⁰
B = (8x - 28)⁰
By substituting the given parameters, we can calculate the x value
A + B = 90⁰
18⁰ + (8x - 28)⁰ = 90⁰
8x = 90 - 18 + 28
8x = 100
x = 12.5⁰
Find more on complementary angle at: https://brainly.com/question/20428380
#SPJ4
Answer: 12.5
Step-by-step explanation:
18+8x-28=90
18-18
90-18
8x-28=72
28+28
72+28
8x=100
8x/8
100/8
x=12.5
the median of the ordered set of observations 2,3, (4m-3), (3m + 1), 11 and 13 in asending order is 6. Find the value of m.
The value of [m] will be 2.
What is mean, median and mode?The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.Given is the median of the ordered set of observations 2, 3, (4m-3), (3m + 1), 11 and 13 in ascending order is 6.
We have the following data as -
2, 3, (4m-3), (3m + 1), 11, 13
N = 6
So median will be -
{(4m - 3) + (3m + 1)}/2 = 6
(4m - 3) + (3m + 1) = 12
4m + 3m - 3 + 1 = 12
7m - 2 = 12
m = 2
Therefore, the value of [m] will be 2.
To solve more questions on mean, median and mode, visit the link below-
https://brainly.com/question/17160638
#SPJ1
A garden table and a bench cot $572 combined. The garden table cot $78 le than the bench. What i the cot of the bench?
The cost of the bench is $325 and the cost of the garden table is $247.
The situation given in the question can be solved by using equation, with two unknown variables, x is the cost of the garden table and y is teh cost of the bench. Considering the garden table is $78 less than the bench. We get the equation for the value of x, then we substitute it in sum equation 1 to get the value of bench.
x+y=$572 ----------------(1)
x=y-$78 ---------------(2)
Substitute equation 2 in 1, we get.
y-$78+y=$572
2y-$78=$572
2y=$572+$78
2y=$650
y=650/2
y=$325
We got the cost of the bench, we substitute this value in equation 2, to get the value of garden table.
x=y-$78
x=$325-$78
x=$247
Hence, the cost of the bench is $325 and garden table is $247.
To learn more on equation here:
https://brainly.com/question/14686792#
#SPJ4
A line that includes the point (5, 17) has a slope of 1. What is its equation in slope -intercept form?
Answer:
17 = 5 + b
b = 12
y = x + 12
what is 15/16 groups of what size
Step-by-step explanation:
your welcome hope this helps
to can be driven before it would need to be junked is an exponential random variable with parameter smith has a used car that he claims has been driven only 10,000 miles. if jones purchases the car, what is the
Answer:
2334
Step-by-step explanation:
Ephemeral services corporation (esco) knows that nine other companies besides esco are bidding for a $900,000 government contract. Each company has an equal chance of being awarded the contract. If esco has already spent $100,000 in developing its bidding proposal, what is its expected net profit?.
The expected net profit would be $100,000
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
E(X) = (1/9) × $900,000E(X)=0.111111111×$900,000E(X)= $100,000Therefore the expected net profit would be $100,000Hence,The expected net profit would be $100,000
learn more about unitary method click here:
brainly.com/question/24587372
#SPJ4
The y-intercept of the line that is parallel to y=5x-3 that goes through (1,7)
Answer:
y = 5x + 2
Step-by-step explanation:
slope is 5
x = 1
y = 7
Use this to find b for the new equation
y = mx + b
7 = (5)(1) + b
7 = 5 + b Subtract 5 from both sides
2 = b
y = mx + b
y = 5x + 2
in a survey of 2480 golfers, 15% said they were left-handed. the survey's margin of error was 3%. construct a confidence interval for the proportion of left-handed golfers.
The confidence interval for the proportion of left-handed golfers is of:
(0.12, 0.18).
How to obtain a confidence interval?A confidence interval is calculated as the sample mean plus/minus the margin of error, hence the bounds of the confidence interval are given as follows:
Lower bound: sample mean - margin of error.Upper bound: sample mean + margin of error.In the context of this problem, these parameters are given as follows:
Sample mean: 15% as a percentage, 0.15 as a proportion.Margin of error: 3% as a percentage, 0.03 as a proportion.Hence the lower bound of the confidence interval for the proportion of left-handed golfers is:
0.15 - 0.03 = 0.12.
The upper bound of the confidence interval for the proportion of left-handed golfers is:
0.15 + 0.03 = 0.18.
Then the interval is:
(0.12, 0.18).
More can be learned about confidence intervals at https://brainly.com/question/25890103
#SPJ1
please solve this question
Answer 2
Step-by-step explanation and no not writing out how to do it.
Brayden is saving up to buy a new video game. He already has $25 and can save an additional $5 per week using money from his after school job. How much total money would Brayden have after 4 weeks of saving? Also, write an expression that represents the amount of money Brayden would have saved in ww weeks.
A school is arranging a field trip to the zoo. the school spends 683.47 dollars on passes for 38 students and 3 teachers. the school also spends 334.78 dollars on lunch for just the students. how much money was spent on a pass and lunch for each student?
Answer:
1018.25
----------------------------------------------------------------------
hope you do well on the quiz/test/assignment!
Find the lengths of PR and QS
The length of PR and QS will be 20 units. And the area of the rectangle will be 173.21 square units.
What is the area of the right-angle triangle?The area of the right-angle triangle is given as
A = 1/2 x B x H
Where B is the base and H is the height of the right triangle.
The length of PT is 10 and the angle ∠TPS is 60°.
The length of PR is given as,
PR = PT + TR
PR = 10 + 10
PR = 20
And the length of QS is given as,
QS = QT + TS
QS = 10 + 10
QS = 20
The area of the rectangle is given as,
A = Area of triangle ΔPQR + Area of triangle ΔPSR
A = 2 [(1/2) x (20 cos 60°) x (20 sin 60°)
A = 173.21 square units
The length of PR and QS will be 20 units. And the area of the rectangle will be 173.21 square units.
More about the area of the right-angle triangle link is given below.
https://brainly.com/question/16653962
#SPJ1
an inverted cone has a radius of 4 cm and a height of 16 cm. initially, the cone is full of water, and it flows from the bottom of the cone at a rate of 50 $\text{cm}^3$ per minute. find the rate at which the height of water is decreasing (in cm per minute) when the height of the water is 5 cm.
The flowrate of decreasing water is 3.98 cm/min after the water reaches 5cm of its height.
We need to know about the flowrate to solve this problem. The rate can be described as how much water flows in a unit of time. It can be represented by this equation
Q = V / t
where Q is flowrate, V is volume and t is time.
From the question above, the given parameters are
Inverted cone with
Q = 50 cm³/min
R = 4 cm
h = 5 cm
Hence, the rate of decreasing water is
Q = V / t
50 = A . h / t
50 = π . R² . h / t
50 = 22/7 . 4 . h / t
h/t = 3.98 cm/min
Find more on the flowrate at: https://brainly.com/question/21630019
#SPJ4
A statistics student from a large high school takes a random sample of 200 students and finds that 123 are actively
involved in a political party. A 99% confidence interval for the proportion of students at this school who are actively
involved in a political party is (0.526, 0.704). Which statement correctly interprets the interval?
O The statistics student can be 99% confident that 62% of students from this school are actively involved in a
political party.
O There is a 99% probability that the proportion of students at this school who are actively involved in a political
party lies between 0.526 and 0.704.
If this procedure is repeated many, many times, the true proportion of students at this school who are actively
involved in a political party will be captured 99% of the time.
O The statistics student can be 99% confident that the interval from 0.526 to 0.704 captures the true proportion of all
students at this school who are actively involved in a political party.
The last option is correct.
The statistics student can be 99% confident that the interval from 0.526 to 0.704 captures the true proportion of all students at this school who are actively involved in a political party.
What is political party?
A political party is a group that arranges candidates to run in elections in a certain nation. It is typical for party members to share similar political viewpoints, and parties may support particular ideologies or policy objectives.
Given: A statistics student from a large high school takes a random sample of 200 students and finds that 123 are actively involved in a political party.
A 99% confidence interval for the proportion of students at this school who are actively involved in a political party is (0.526, 0.704).
Hence, the statistics student can be 99% confident that the interval from 0.526 to 0.704 captures the true proportion of all students at this school who are actively involved in a political party.
To know more about the political party, click on the link
https://brainly.com/question/633543
#SPJ1
find the volume of a sphere, if it has a radius of x-1
The volume of the sphere is [tex]\frac{4}{3}\pi (x-1)^3[/tex]. It can be obtained by using the formula of the volume of the sphere.
What is the formula of the volume of the sphere?
Volume of any object is the amount of 3 dimentional space occupied by that object. Volume of the sphere is given by the following expression:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Here, V is the volume of the sphere and r is the radius of the sphere.
Substitute x-1 for r in the above formula.
[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}\pi (x-1)^3[/tex]
This is the simplest form.
In the above equation, you can apply the formula [tex](a-b)^3=a^3-3a^2b+3ab^2-b^3[/tex] but that will make the equation difficult and lenthy. Hence, there is no need to apply this formula.
Hence, the volume of the sphere is [tex]\frac{4}{3}\pi (x-1)^3[/tex].
Learn more about the volume of sphere from the following link:
https://brainly.com/question/22807400
#SPJ1
a new pyramid has been found in south america. the pyramid has a rectangular base that measures by 180 yd, and has a height of 90 yd. the pyramid is not hollow like the egyptian pyramids and is composed of layer after layer of cut stone. the stone weighs 456 lb per cubic yard. how many pounds does the pyramid weigh?
Answer:
443,232,000 lb
Step-by-step explanation:
You want the weight in pounds of a pyramid 180 yd square and 90 yd high made of material weighing 456 lb/cubic yard.
VolumeThe volume of the pyramid is given by the formula ...
V = 1/3s²h . . . . . . . . where s is the side length and h is the height
V = 1/3(180 yd)²(90 yd) = 972000 yd³
WeightAt a weight of 456 pounds per cubic yard, the weight of the pyramid is estimated to be ...
(456 lb/yd³)×(972,000 yd³) = 443,232,000 lb
The pyramid weighs about 443,232,000 pounds.
__
Additional comment
At 456 lb per cubic yard, the stone is less dense than most wood and will float high in water.
Steve claims that the points (-4,8) (8,8) and (-4,3) form a right triangle. Use the distance formula and the Pythagorean theorem to determine if Steve is correct. Show your work and explain your reasoning.
(question 7)
Yes, the points are the vertices of a right triangle and we will prove that by using the Pythagorean theorem.
Are these the vertices of a right triangle?
Remember that the distance between two points (a, b) and (c, d) is:
distance = √( (a - c)² + (b - d)²)
The distance between (-4, 8) and (8, 8) is:
d₁ = √( (-4 - 8)² + (8- 8)²) = 12
The distance between (8, 8) and (-4, 3) is:
d₂ = √( (8 + 4)² + (8- 3)²) = 13
The distance between (-4, 8) and (-4, 3) is:
d₃ = = √( (-4 + 4)² + (8 - 3)²) = 5
if the Pythagorean theorem is true, then the sum of the squares of the two shorter sides must be equal to the square of the larger side, then we must have that:
5² + 12² = 13²
Solving that we get:
25 + 144 = 169
169 = 169
This is true, so yes, the vertices are the vertices of a right triangle.
Learn more about right triangles:
https://brainly.com/question/2217700
#SPJ1
