Complete the square to determine if the equation is a circle, quadratic (parabola) or other. Show all work and graph the circles and quadratics on a grid. A. 16^2 + 4^2 + 96 − 8 + 84 = 0
The conic equation 16 · x² + 4 · y² + 96 · x - 8 · y + 84 = 0 is equivalent to (x + 3)² / 4.75 + (y - 2)² / 19 = 1, that represents an ellipse.
How to derive the nature of a conical by algebraic means
Mathematically speaking, conics are described by quadratic equations of the form A · x² + B · y² + C · x + D · y + E = 0, where A, B, C, D, E are real coefficients of the conic.
We can infer if a conic is a circle, a parabola, an ellipse or a hyperbola by modifying the expression into its standard form by algebra properties. First, write the equation of the conic:
16 · x² + 4 · y² + 96 · x - 8 · y + 84 = 0
Second, complete the square in the equation of the previous step:
16 · (x² + 6 · x) + 4 · (y² - 2 · y) = - 84
16 · (x² + 6 · x + 9) + 4 · (y² - 2 · y + 4) = - 84 + 16 · 9 + 4 · 4
16 · (x² + 6 · x + 9) + 4 · (y² - 2 · y + 4) = 76
Third, factor the polynomial and simplify the expression until standard form is derived:
16 · (x + 3)² + 4 · (y - 2)² = 76
(x + 3)² / 4.75 + (y - 2)² / 19 = 1
The conic equation represents an ellipse.
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Riley and her children went into a movie theater and she bought $51 worth of bags of popcorn and drinks. Each bag of popcorn costs $5 and each drink costs $6. She bought twice as many drinks as bags of popcorn. Determine the number of bags of popcorn and the number of drinks that Riley bought.
Solving a system of equations we can see that she bought 3 bags of popcorn and 6 drinks.
How many bags of popcorn and drinks she bought?We can define the two variables:
x = number of bags of popcorn.y = number of drinks.Knowing that each bag of popcorn costs $5 and each drink costs $6, and the total cost was $51, we can write:
x*$5 + y*$6 = $51
And we also know that she bought twice as many drinks as bags of popcorn, then:
y = 2x
So we have a system of equations:
y = 2x
x*$5 + y*$6 = $51
Replacing the first equation into the second one:
x*$5 + (2x)*$6 = $51
x*$17 = $51
x = $51/$17 = 3
So she bought 3 bags of popcorn and 2*3 = 6 drinks.
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Complete the congruence statement, if possible.
theorem you used.
(9) AAB
(10)
B
A
D
C
If so, state the postulate or
EFG =
E
G
FN
M
(9) The triangle ABD ≅ triangle CDB by SAS Congruence Postulate ,
(10) The triangle EFG ≅ triangle LNM by SAS Congruence Postulate .
In the question ,
(9)
a figure is given where AD = CB
In the Triangle ABD and triangle CDB ,
side AD = CB ....given
angle ADB = angle CBD .... given
side AB = CD .......because opposite sides of parallelogram are equal .
hence ΔABD ≅ ΔCDB by SAS Congruence Postulate .
(10)
a figure is given where EF = LN
In the Triangle EFG and triangle LNM ,
side EF = LN ....given
angle G = angle M .... because both are 90°
side FG = NM .....given
hence ΔEFG ≅ ΔLNM by SAS Congruence Postulate .
Therefore , (9) The triangle ABD ≅ triangle CDB by SAS Congruence Postulate ,
(10) The triangle EFG ≅ triangle LNM by SAS Congruence Postulate .
The given question is incomplete , the complete question is
Complete the Congruence Statement for the figure given below , If possible . If so , state the Postulate / Theorem you used .
(9) ΔABD ≅ (10) ΔEFG ≅ .
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i-Ready
» Rewrite the expression 110.3-5 using only positive exponents.
First rewrite 11º.
11⁰.3-5
=
The new form of 11^0.3^(-5) is 1/3^5 with positive exponent.
What is exponent of a number?
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For example: a^b, where b is the exponent of a.
What is negative exponent?
The negative exponent indicates how many times the base number must be divided. In other words, the negative exponent indicates how many times the reciprocal of the base must be multiplied.
If the exponent of a number is zero, then the value of the number is 1.
Given expression is
11^0.3^(-5)
The value of 11^0 is 1.
Rewrite 3^(-5) into positive exponent 1/3^5.
The new form of 11^0.3^(-5) is 1×(1/3^5) = 1/3^5.
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No idea how to do this
Answer:
Add them together and you have your answer I think
A chemist needs 50 mL of a 16% salt solution for an experiment. She can only find a 13% salt solution and an 18% salt solution in the supply room. How many milliliters of the 13% solution should be mixed with the 18% solution to produce
the desired amount of the 16% solution?
Answer:
Step-by-step explanation:
X+Y = 50
0.13X + 0.18Y = 0.16*50 = 8
0.13X + 0.18(50-X) = 8
0.13X + 9 - 0.18X = 8
-0.05X = -1
5x = 100
x=20
20 mL of the 13% salt solution
30 mL of the 18% salt solution
calculate the area of the following triangle (round off answers to one decimal point)
Answer:
Step-by-step explanation:
Since it is an isosceles triangle the opposite side of that with 35mm is equal to 35mm.
Area of triangle =. ½b x h
. =. ½ x 35 x 35
. = 612.5mm²
. =. 613mm²(1.d.p)
I have 10 blue marbles, 4 green marbles, and 7 red marbles. Find the probability that, randomly, I will pick: A green marble A marble that is not red 2 blue marbles in a row.
The probability of randomly picking a green marble, a marble that is not red and 2 blue marbles in a row is 0.03 approximately to 2 decimal places
What is probabilityProbability of an event is the fraction of the required outcome of event divided by the number of possible outcomes of events. The probability that an event will not occur is one minus the probability of the event occurring.
The total marbles are 21 in number with;
the probability of picking a green marble = 4/21
the probability of picking a marble that is not red = 1 - (7/21) = 14/21
the probability of picking two blue marbles = (10/21) × (10/21)
probability of randomly picking a green marble, a marble that is not red and 2 blue marbles in a row = (4/21) × (14/21) × (10/21) × (10/21)
probability of randomly picking a green marble, a marble that is not red and 2 blue marbles in a row = 5600/19481 = 0.03
Therefore, considering it is a random pick without replacement, the probability of the event for picking a green marble, a marble that is not red and 2 blue marbles in a row is approximately 0.03.
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Help help help hurry
Answer: (-2m)-10
3x+11
9xy+2z-16
-7x-11
6m^2-m+8
Step-by-step explanation:
×= 5484883929292922882829
What is the mean of 7 5 4 5 6 9
Answer:
The mean is 6
Step-by-step explanation:
To find the mean, add all the numbers and then divide by the number of data points
( 7+5+4+5+6+9)/ 6
36/6
6
The mean is 6
What is 2+2? I'm having a hard time figuring out this complex equation and cannot seem to find anybody who know it either. If your could send me a picture of the work on a doc or paper I would greatly appreciate it.
Answer:
Step-by-step explanation:
4
Answer:4
Step-by-step explanation: I have 2 apples and my friend gives me 2 more it'll give me 4. Also you put up 2 fingers and and you add 2 more that will also give me 4.
a crate is 24cm by 18cm by 15cm. it is to be packaged with boxes that are 8cm by 6cm by 5cm . what is the largest number of boxes that can fit into the crate. someone help please
The rectangular crate will be able to carry a maximum of 27 boxes
Volume of CuboidThe crate carries a shape of a cuboid which can be said to be a rectangle in three-dimensional side. To solve this problem, we have to find the volume of the crate and then the volume of the box and divide the volume of the crate by the volume of box.
The volume of a cuboid = L * W * H
This can be calculated as V = 24 * 18 * 15 = 6480cm³
The volume of the box = 8 * 6 * 5 = 240cm³
Number of boxes that can fit in the cuboid = 6480 / 240
Number of boxes = 27 boxes
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Is r = 10 a solution to the equation 3 (r+5) + 55?
The value of the expression 3(r+5) when r = 10 is 100
Algebraic ExpressionAlgebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
In this problem, we are to substitute the value of r which is 10 int the expression.
3(r + 5) + 55 = 3(10 + 5) + 55 = 3(15) + 55 = 45 + 55 = 100
The expression is equal to 100.
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1. A landscaper can rent a backhoe for $45,000 a year. He could purchase the equipment for
monthly costs of $2,500 plus $20 for each hour it is used. How many hours per year must
the equipment be used to justify purchasing it rather than renting it?
The number of hours per year that the equipment be used to justify purchasing it rather than renting it is 2125 hours.
What is an expression?It should be noted that an expression is used to illustrate the relationship between the variables.
Let the number of hours be illustrated as h.
The landscaper can rent a backhoe for $45,000 a year and he could purchase the equipment for
monthly costs of $2,500 plus $20 for each hour it is used.
This will be:
2500 + 20h = 45000
Collect like terms
20h = 45000 - 2500
20h = 42500
Divide
h = 42500 / 20
h = 2125
The number of hours is 2125 hours.
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Express the confidence interval 653.1 ± 130.3 in interval form.
The confidence interval form of the given question will be (783.4,522.4).
What is a confidence interval?
A confidence interval (CI) in frequentist statistics is a range of estimates for an unknown parameter. A confidence interval is calculated at a specified degree of confidence; the most popular level is 96%, but other values, such 90% or 99%, are occasionally used. The confidence level is the percentage of corresponding CIs over the long run that actually contain the parameter's true value. As an illustration, 96% of all intervals produced at the 96% level should have the parameter's actual value.
Here this question, it is given in the interval form.
Now we can find out the minimum and maximum value of the value.
Maximum value is 653.1+130.3 = 783.4
Minimum value is 653.1 - 130.3 = 522.4
So The confidence interval can be written as (783.4,522.4).
Hence the answer will be (783.4,522.4).
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Graph the linear inequality.
y >25x
Answer:mum
Step-by-step explanation: mom
Is It Reasonable?
Your friend says the
quotient of 3,627 and 9 is 43. Is your
Friend's answer reasonable?
Answer: No, the answer is not reasonable because 3,627/9 doesn’t equal 43, it equals 387.
Answer:
No, you friend's answer is not reasonable.
Step-by-step explanation:
3,627 x 9 does not equal 43
3,627 x 9 =32643
Therefore your friend is incorrect
A sample with the sample proportion of 0.4 and which of the following sizes will produce the widest 95% confidence interval when estimating the population parameter?
A. 45
B. 35
C. 55
D. 65
The size 50 will produce the widest 95% confidence interval when estimating the population parameter.
What is a confidence interval for population standard deviation?It is defined as the sampling distribution following an approximately normal distribution for a known standard deviation.
It is given that, a sample with the sample proportion of 0.4 and which of the following sizes will produce the widest 95% confidence interval.
The margin of error provides an estimate of the percentage of errors in real statistical data.
The formula for finding the MOE:
[tex]\rm MOE = Z\times \dfrac{s}{\sqrt{n}}[/tex]
Where,
Z is the z-score at the confidence interval
s is the standard deviation
n is the number of samples.
An interval is broader the bigger the margin of error.
The margin of error reduces with increasing sample size. The smallest confidence interval should be chosen if we want the widest possible interval.
Thus, the size 50 will produce the widest 95% confidence interval when estimating the population parameter.
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Answer:
B. 35
Step-by-step explanation:
I got it correct :D
2 + b ( a to the power of 2 + 4 ) when a =2 and b=4
Answer:
ez
Step-by-step-
ezzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Answer:
34
Step-by-step explanation:
2+b(a^2+4)
2+4(2^2+4)
2+4(4+4)
2+4(8)
2+32
34
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Which associations best describe the scatter plot?
Select each correct answer.
Select 2 correct answer(s)
Question 5 options:
Positive association
Nonlinear association
Linear association
Negative association
The associations that best describe the scatter plot is Option A and C
Positive associationLinear associationWhat characteristics mark a strong connection?When below-average values also tend to occur together and above-average values of one variable tend to be accompanied by below-average values of the other, there is a positive association between the two variables. When the average values of two variables tend to be below average, two variables have a negative connection.
Note that a statistical term used to describe a straight-line relationship between two variables is a linear relationship (or linear association).
Additionally, a straight line connecting the spots indicates a linear association. As a result, the scatter plot indicates that as practice time increases, giving off also rise.
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The association that describe the scatter plot is
Positive associationLinear associationWhat is scatter plot ?A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities or events (called variables).
The connection is positive if the variables tend to rise and fall together. When one variable tends to rise while the other falls, there is a negative connection.
The connection between the variables demonstrates a straight line in the positive direction. hence the option having linear and positive association is the correct choice
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Which of the following is an advantage to using equations?
A. You can forget what an equation represents when it is used by
itself.
B. Every problem needs an equation if you want to solve it.
C. When given two names for the same quantity can use algebra
to solve the equation.
If two names are given for the same quantity then we can use algebra
to solve the equation thus option (C) is correct.
What is the equation?There are many different ways to define an equation.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
In another word, the equation must be constrained with some constraints.
If we have a problem in word formate.
And the same quantity is used two times with two different names.
Then by algebra, the variable defines the quantity remains the same but the value of the variable changes according to the given value.
By this the problem can be easily solved.
Hence "If two names are given for the same quantity then we can use algebra to solve the equation".
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What value of coefficient b makes the equation true for any real number x?
Answer:
x=58
Step-by-step explanation:
Find the quotient. 5 divided by 1/4 thanks
Answer:
20
Step-by-step explanation:
we turn 5 into a fraction to make it easier
[tex]\frac{5}{1}[/tex]÷[tex]\frac{1}{4}[/tex]
Now to figure it out we keep the first fraction 5/1 the same and then flip the second one 1/4 to make it 4/1 and multiply
[tex]\frac{5}{1}[/tex]×[tex]\frac{4}{1}[/tex]
[tex]\frac{20}{1}[/tex]
20
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A triangle is dilated by a scale factor of 5. How will this affect the perimeter and the area of the new image?
The area of triangle is 25.
and, The perimeter of triangle is 5.
Given,
In the question:
A triangle is dilated by a scale factor of 5.
To find the how will this affect the perimeter and the area of the new image?
Now, According to the question:
The perimeter of triangle is X + Y + Z, where X, Y, and Z are the sides.
So if we shrink all the sides by 5, we change the perimeter by 5.
However, because the area of the triangle involves 0.5 × Base × Height,
if we shrink all of the sides by 5, the area is shrunk by 5 * 5 (once for base, once for height).
Hence, The area of triangle is 25.
and, The perimeter of triangle is 5.
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A plane flies 420 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 15 mph, find the speed of the plane in still air.
The Speed of the plane in still air is 165 miles per hour.
What is speed?
The rate that an object travels a certain distance is what is meant by the speed formula. The amount of distance a body moves in a certain amount of time is referred to as speed. The metric unit of speed is the m/s. For example, m/s, km/hr, miles/hr, and other units can be used to express speed.
Let x be the speed of the plane in the still air, and w be the wind speed.
Using speed formula Balancing by the time,
=> Time = Distance/ Speed
=> 420/(x+w) = 350/(x-w)
Then ,
=>420/(x+15)=350/(x-15)
=> 420(x-15)=350(x+15)
=> 420x-6300=350x+5250
=> 420x-350x=5250+6300
=>70x=11550
=>x=11550/70
=>x=165mph.
Hence speed of the plane in still air is 165 miles per hour.
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Two parts: Make sure to answer EACH part:
1. What is the rate of change for each shop shown below?
2. Which shop has the GREATEST rate of change?
Rate of change for Carol's = 4.99
Rate of change for Wilma's:
line passes through (0, 0) and (2, 15)
slope = m = (15 - 0) / (2 - 0) = 7.5
Rate of change for Wilma's = 7.5
7.5 > 4.99
So Wilma's has the greatest rate of change.
A camera has a listed price of $722.95 before tax. If the sales tax rate is 9.75%, find the total cost of the camera with sales tax included.
Round your answer to the nearest cent, as necessary.
The total cost of the camera with sales tax included is $793.44
The listed price of camera = $722.95
The sales tax rate = 9.75%
The amount of tax = The listed price of camera × (The sales tax rate / 100)
Substitute the values in the equation
The amount tax = 722.95 × (9.75 / 100)
Divide the terms first
= 722.95 × 0.0975
Multiply the terms
= $70.49
The cost of the camera including tax = The listed price of camera + The amount tax
Substitute the values in the equation
= 722.95 + 70.49
= $793.44
Hence, the total cost of the camera with sales tax included is $793.44
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How many 5-letter code words can be formed from the letters T, Q, G, E, B if no letter is repeated? If letters can be repeated? If adjacent letters must be different?
The number of codes that can be made using the 5 letters given is 120 as calculated using permutation and combination.
Now when no letters are repeated:
5 letter codes to be made.
Possible options for each space = 5
so first digit has 5 options, second digit has 4 options , third digit has 3 options , fourth digit has 2 options and the final digit will have only 1 option left.
So total number of codes = 5 × 4 × 3 × 2 × 1 = 120 codes
if letters can be repeated
5 letter codes to be made.
Possible options for each space = 5
so first digit has 5 options, second digit has 5 options , third digit has 5options , fourth digit has 5 options and the final digit will have only 5 options also.
So total number of codes = 5 × 5 × 5× 5× 5= 3125 codes
if adjacent letters cannot be repeated
5 letter codes to be made.
Possible options for each space = 5
so first digit has 5 options, second digit has 4 options , third digit has 4 options , fourth digit has 4 options and the final digit will have only 4 options also.
So total number of codes = 5 × 4 × 4× 4× 4 = 1280 codes
Hence the total number of codes as calculated by permutation and combination is 1280.
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93 qt= ____gal ____gt
A bag contains 39 U.S. quarters and eleven Canadian quarters. (The coins are identical in size.) If four quarters are randomly picked from the bag, what is the probability of getting at least one Canadian quarter? (Round your answer to one decimal place.)
The probability of getting at least one Canadian quarter is 0.6
How to determine the probability of getting at least one Canadian quarter?
This is a binomial probability experiment. We are going to use the binomial distribution formula for determining the probability of x successes:
P(x = r) = nCr . p^r . q^n-r
Where n = number of trials, p = probability of success and q = probability of failure, x = number of Canadian quarters
39 U.S. quarters + 11 Canadian quarters coins = 50 coins
Given: n = 4 (four quarters picked), p = 11/50 = 0.22, q = 1-p =1-0.22 = 0.78
Probability at least one Canadian quarter = 1 - Probability of no Canadian quarter
P(x≥1) = 1 - P(x = 0)
= 1 - (4C0×0.22⁰× 0.78⁴⁻⁰ )
= 1 - 0.4
= 0.6
Therefore, the probability of getting at least one Canadian quarter is 0.6
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