To decrease the area of the circle by $48\pi$, we need to decrease the radius by a factor of $\sqrt{48\pi}$.
Since the original radius of the circle was 8, the radius must be decreased to
$\frac{8}{\sqrt{48\pi}} = \frac{8}{\sqrt{48}\sqrt{\pi}} = \frac{8}{\sqrt{48}} \approx \frac{8}{6.9282} \approx 1.1547$.Therefore, to decrease the area of the circle by $48\pi$, the radius must be decreased by a factor of about 1.1547.
This means that the radius must be decreased by a number that is about 1.1547 times smaller than the original radius of 8, or by about $8 \times (1 - 1.1547) = -0.6158$.
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in the athletics team, tall members tend to win three times as many medals as short members. this year the team has won 60 medals so far. how many of these have been won by short athletes?
in the athletics team, tall members tend to win three times as many medals as short members.20 number of medals have been won by short athletes.
This question can be solved by using the ratio method. Since tall athletes are said to win three times as many medals as short athletes, this means that the ratio of tall athletes' medals to short athletes' medals is 3:1. We can use this ratio to calculate how many medals have been won by short athletes. Since the team has won a total of 60 medals, we can divide this number by 4 (the total number of medals in the ratio) to get 15. We then multiply 15 by the ratio of short athletes' medals (1) to get 15 medals. This means that short athletes have won 20 medals, since 15 multiplied by 3 is 45, leaving 60-45=15 medals for the short athletes. Thus, 20 medals have been won by short athletes.
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Write the fifteenth term of the binomial expansion of (a³+d) 24.
a^45d^9
To find the fifteenth term of the binomial expansion of (a³+d)24, we can use the binomial theorem, which states that the expansion of (a+b)n is given by the sum of the terms in the following formula:
(a+b)^n = a^n + na^(n-1)b + (n(n-1))/2a^(n-2)*b^2 + ... + b^n
Answer: 1,961,256a³⁰d¹⁴
Step-by-step explanation:
[tex]\displaystyle\\(x+y)^n \ is\ the\ binomial\ expansion \\\\The\ k\ term =C_n^{k-1}x^{n-k+1}y^{k-1}\\\\ n - the\ power \ of\ the \ binomial\\\\k - number\ of\ the\ term \ of\ the\ binomial[/tex]
[tex](a^3+d)^{24}[/tex]
[tex]The \ fifteenth\ term=C^{15-1}_ {24}(a^3)^{24-15+1}d^{15-1}\\\\The \ fifteenth\ term=C^{14}_{24}(a^3)^{10}d^{14}\\\\The \ fifteenth\ term=\frac{24!}{(24-14)!14!} a^{30}d^{14}\\\\The \ fifteenth\ term=\frac{24!}{10!14!}a^{30}d^{14} \\\\The \ fifteenth\ term=1,961,256 a^{30}d^{14}[/tex]
Create 4 math problems where the solution is -60
-480 ÷ 8 = -60
2x = -120
-20 × 3 = -60
(2 × 3) × (-5 × 2) = -60
Given 2 and one-eighth times negative 7 times five tenths, determine the product.
negative fourteen and five eightieths
negative 7 and seven sixteenths
fourteen and five fortieths
7 and one eighth
The product of the given numbers is, [tex]-7\frac{7}{16}[/tex].
What is product?
One of the four fundamental arithmetic operations, along with addition, subtraction, and division, is multiplication. A product is the output of a multiplication operation.
The outcome of multiplying two or more numbers together in mathematics is called the product. With the help of examples, learn more about the product of fractions and decimals.
Given:
2 and one-eighth times negative 7 times five tenths.
We have to determine the product.
[tex]2\frac{1}{8} (-7)(\frac{5}{10} )[/tex]
Convert improper fraction into a fraction
[tex]2\frac{1}{8} = \frac{(2)(8)+1}{8} = \frac{17}{8}[/tex]
⇒
[tex](\frac{17}{8} )(-7)(\frac{1}{2}) \\-\frac{119}{16} \\-7\frac{7}{16}[/tex]
Hence, the product of the given numbers is, [tex]-7\frac{7}{16}[/tex].
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Point (25,125) means that the monthly home heating bill was $
for an average monthly temperature of
°F.
The point (25,125) means that the monthly home heating bill was $5 for an average monthly temperature of 1°F.
How to interpret the meaning of the point?From the question, we have the following parameters that can be used in our computation:
Point (25, 125)
This point can be expressed as
(x, y) = (25, 125)
The average monthly temperature bill is then calculated using the following equation
Average monthly temperature bill = y/x
Substitute the known values in the above equation, so, we have the following representation
Average monthly temperature bill = 125/25
Evaluate
Average monthly temperature bill = 5
Hence, the average monthly temperature = 5
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Which bank would be best for Gerard to use, I need this today please
Answer:
Step-by-step explanation:
The best bank depends on the amount that Gerard will deposit. He can open an account with My bank and receive $100, or he can open with New bank and deposit lets say $5000 and he would receive an additional $250 because of the 5% bonus. It depends on the amount that Gerard is putting into the bank account when he opens it.
PLEASE HELP!!! Make sure to show your work.
1)How many triangles can be constructed
with angles measuring 16˚, 38˚ and 126˚?
Circle one answer:
A) None
B) One
C) Infinite (More than one)
A triangle has three angles that measure 16˚, 38˚ and 126˚ will lead to
C) Infinite (More than one)How to know when infinite number of triangles are formedThere are an infinite number of triangles produced when no side is specified.
The three angles produce an unlimited number of distinct triangles if side lengths are not provided.
The option that offered just angles—namely, angles of 16˚, 38˚ and 126˚—and no sides—meets the requirement for the production of an infinite number of triangle sides.
When there are options have sides or a side is provided, but not in accordance with that, to form an infinite number of triangles.
This condition forms infinite number of triangles
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Answer:
C) Infinite (More than one)
Step-by-step explanation:
Applications of Basic Equations:
97.) An isosceles triangle has two congruent sides that measure 3x + 8 in. and - 9x-5 over 2 in. respectively. The third sidle
28 over 2y-1
measures in. If the perimeter of the triangle is 72 in., find the length of all three sides. Find the value of y. Hint:
solve for x first.
Answer:
Step-by-step explanation:
Let the congruent sides of an isosceles △ be x.
Let the base of the isosceles △ be y
According to the 1st condition,
x+x+y=30
2x+y=30
According to the 2nd condition
x=y+3
x−y=3
Solving equation (1) and (2)
2x+y=30
x−y=3
-------------------
3x=33
x=
3
33
x=11
By substituting x=11 in equation (1)
2x+y=30
2(11)+y=30
22+y=30
y=30−22
=8
∴ The length of the sides of a △ are 11cm,11cm and 8cm.
Mr. Torre tell hi cla that when they have completed the aignment, they may read. Eleven tudent are reading, which i about 40
The students that still need to complete their assignments = 14
According to the given question,
The total number of students in Mr. Torres's class = 24
Now as the question tells us,
Mr. Torres instructed the students to read only if they have finished their assignments.
The percentage of the class that is reading = is 40% which means that 40% of the class has completed their assignments.
Now we have to calculate the number of students that are still doing their assignments,
⇒ 40 % of the 24
⇒ [tex]\frac{40}{100}[/tex] x 24
⇒ 0.4 x 24
⇒ 9.6 ≈ 10
So the students that have completed their assignments = 10
Students that are still doing their assignments,
⇒ 24 - 10
⇒ 14
Therefore, The students that still need to complete their assignments = 14
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Mr. Torres tells his class of 24 that when they have completed their assignment they may read at the end of class 40% of the class is reading how many students still need to complete their assignment
john is moving from portland to sacramento, which is 600 miles away. he is traveling at an average speed of 55 miles per hour. jon stops for gas after a couple of hours and wonders how much further he needs to go. if y represents distance from sacramento and x represents time, which linear equation would indicate the amount of miles jon still has to travel to sacramento? a.) y equals short dash 55 x plus 600 b.) y equals short dash 600 x plus 55 c.) y equals 55 x minus 600 d.) y equals 600 x minus 55
Jon still needs to travel miles to Sacramento, according to a linear equation: Y=-55x +600 .
What is EQUATIONS?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The meanings of the word equation and its cognates in various languages can vary slightly.
For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.
Finding the values of the variables that result in the equality is the first step in solving an equation with variables.
The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions.
Equations come in two varieties: identities and conditional equations.
Hence, Jon still needs to travel miles to Sacramento, according to a linear equation: Y=-55x +600 .
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what is the probability a randomly selected 30 year old in 1970 earned more than his or her parents at age 30?
In 1970, 92% of American 30-year-olds earned more than their parents did at age 30 (adjusted for inflation). In 2014, only 51% of American 30-is The probability is. 83
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
How is probability determined?
picture for "probability"
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood that something will occur by the likelihood that it won't.
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a fair coin is tossed n times, and the number of heads, n, is counted. the coin is then tossed n more times. find the expected total number of heads generated by this process.
The anticipated total number of heads produced by this method is 1/2n=N when fair coin is tossed n times, and the results are tallied by counting the heads.
Given that,
A fair coin is tossed n times, and the results are tallied by counting the heads. The coin is then thrown a further n times.
We have to calculate the anticipated total number of heads produced by this method.
We know that,
Either head or tail will appear when a coin is tossed.
The sample space of a random experiment is the collection of all feasible results. Therefore, if your random experiment involves flipping a coin, the sample space is "Head, Tail," or more tersely, "H, T."
So,
1/2n=N
Therefore, the anticipated total number of heads produced by this method is 1/2n=N when fair coin is tossed n times, and the results are tallied by counting the heads.
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Find the average acceleration of a bus that reaches a top speed of 14.2 m/s from rest in 22.8 seconds.
The average acceleration of a bus that reaches a top speed of 14.2 m/s from rest in 22.8 seconds is 0.62 m/s².
What is the average acceleration?Acceleration is the amount by which the velocity of something changes over a set period of time.
The formula to find the acceleration is a=(v-v₀)/t, where a=average acceleration, v=final velocity, v₀=initial velocity and t=time.
Given that, final velocity =14.2 m/s, initial velocity=0 and t=22.8 seconds.
Now, the average acceleration is
a=(14.2-0)/22.8
= 14.2/22.8
= 0.62 m/s²
Therefore, the average acceleration of a bus that reaches a top speed of 14.2 m/s from rest in 22.8 seconds is 0.62 m/s².
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The worldwide population is estimated to be around _______ by the year 2050.
a. 9 million
b. 9 trillion
c. 9 billion
d. 9.9 trillion
please select the best answer from the choices provided a b c d
Answer:
option c
Step-by-step explanation:
c. 9 billion people
Answer:
B. 9 Billion people
Step-by-step explanation:
Please help with this question, if you can thank you
C. The slope of the graph is 1/3
Slope = (y2 - y1) ÷ ( x2- x1)
y2= 5, y1=2, x2=9, x1=0
y2-y1 = 5-2 = 3
x2-x1 = 9-0 = 9
Slope = 3/9 = 1/3
calculate the margin of error of a confidence interval for the difference between the two population means.
A 95% confidence interval with a 4% margin of error suggests that your statistic will be 95% of the time within 4 percentage points of the true population value.
A survey, may reveal that the 98% confidence interval is between 4.88 and 5.26. So, if the poll is repeated using the same methods, the true population parameter (parameter vs. statistic) will fall 98% of the time within the interval estimates (i.e. between 4.88 and 5.26).
The formal definition, on the other hand, includes a little more information. The margin of error in a confidence interval is defined as the range of values below and above the sample statistic. The confidence interval is a tool for demonstrating the level of uncertainty associated with a certain statistic (i.e. from a poll or survey).
In 2012, a Gallup poll (incorrectly) predicted that Romney would win the election, with Romney polling at 49% and Obama polling at 48%. The declared level of confidence was 95%, with a margin of error of 2. We can conclude that the results were computed to be 95% accurate within 2 percentage points.
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PLEASE HELP ASAP, 100 POINTS FOR ANSWER
6.For the Raleigh company, create a table to represent the cost of the cab ride given the number of miles provided for miles 5, 10, 15 and 20. List the cost for the cab ride for 15 miles
7.For the Raleigh company write an equation in slope-intercept form to represent the amount charged, y, for x number of miles.
8.For the Raleigh company write an equation in point-slope form to represent the amount charged, y, for x number of miles for the company in Raleigh, NC.
9. Write an equation in standard form to represent the amount charged, y, for x number of miles for the company in Raleigh.
10.What does the slope mean in the context of the problem?
6) A table that represents the cost of the cab ride is;
5 15.25
10. 28.95
15. 42.45
20. 55.95
7) The equation in slope intercept form is;
y = 2.70x + 1.95
8) The equation in point slope form is; y - 15.25 = 2.70(x - 5)
9) The equation in standard form is; -2.70x + y = 1.95
10) What the slope indicates is the amount of money charged per mile driven by each cab ride.
How to express a linear equation?6) A table that represents the cost of the cab ride given the number of miles provided for miles 5, 10, 15 and 20.
5 15.25
10. 28.95
15. 42.45
20. 55.95
7) The general equation of a line in slope intercept form is y = mx + b
where;
m is slope.
b is y-intercept
The slope will be 2.70 since that is how much we go up for a mile
Similarly, 1.95 is y-intercept since it is where we start no matter what and we have to add that constant fee every time.
Thus, the equation is;
y = 2.70x + 1.95
8) The general equation for a line in point slope form is;
y - y₁ = m(x - x₁)
Thus, the equation by taking the first coordinate is;
y - 15.25 = 2.70(x - 5)
9) The equation in standard form will be;
y = 2.70x + 1.95
Thus;
-2.70x + y = 1.95
10) What the slope indicates is the amount of money charged per mile driven by each cab ride.
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a bridge hand consists of 13 cards dealt at random from the deck of 52. the probability that a bridge hand will have exactly 2 queens is:
The probability that a bridge hand will have exactly 2 queens is 0.45%.
To find the probability of getting a bridge hand with exactly 2 queens, we need to use the binomial probability formula. The formula is:
P(exactly k successes) = (n choose k) * p^k * (1-p)^(n-k)
Where:
n is the total number of trials
k is the number of successes in the trials
p is the probability of success in a single trial
In this case, the total number of trials is 13 (since a bridge hand consists of 13 cards), and the number of successes we want is 2 (since we want exactly 2 queens). The probability of success in a single trial is the probability of drawing a queen, which is 4/52 (since there are 4 queens in a deck of 52 cards).
Plugging these values into the formula, we get:
P(exactly 2 queens) = (13 choose 2) * (4/52)² * (48/52)¹¹
= (78) * (1/169) * (4/13)¹¹
= (4/169) * (4/13)¹¹
This simplifies to:
P(exactly 2 queens) = (4/169) * (4/13)¹¹
= (4/169) * (4/169)¹¹
= (4/169)¹²
The final probability is approximately 0.0045 or 0.45%. This means that the probability of getting a bridge hand with exactly 2 queens is quite low.
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Avery invested $4,700 in an account paying an interest rate of 5 1/8% compounded
continuously. Jayden invested $4,700 in an account paying an interest rate of 5 1/2%
compounded quarterly. After 12 years, how much more money would Jayden have in
his account than Avery, to the nearest dollar?
Answer:
20090089$
Step-by-step explanation:
Answer: $359
Step-by-step explanation:
I got the same problem on DeltaMath- You use the formula A = P ( 1 + r/n ) ^nt
P = 4700
R = 0.055
T = 12
N = 4
You plug it in to get 9052.7283 and then subtract 8693.386 to get 359.3423 which rounds to 359
You tie a spherical balloon that is 2 feet in diameter to a
stake in the ground. The string is 15 feet long. The wind
blows and you observe that the top of the balloon is
8 feet over from the stake, as shown in the diagram.
What is the height, b, of the balloon?
Show your work.
15 ft
2 ft
8 ft
Answer:
Step-by-step explanation:
15. Gerald’ average core for nine tet wa 96. If the um of the core of two of hi tet wa 178, then what wa hi average for the other even tet
Let x is average for rest of seven test. Then average for remaining test is x= 2.27
What is average?The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
Why is average called mean?The middle point of the set of values is the mean. It represents the mean of the data set's values. In statistics, the centre number, also known as the mean, is referred to as the average.
We want the TOTAL average to equal 94
4/9 of the 5 scores have an average of 178
Let x = average of the 5 remaining test, which is worth 5/9 of the total average.
We get: 94 = (4/9)(178) + (5/59)(x)
94=712/9+59x/9
846=712+59x
846-712=59x
134=59x
134/59=x
Solve: x = 2.27
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Janie's goal is to spend no more than
$13 each week on coffee. The graph
shows the amount she has spent on
coffee over the last several weeks.
The unit rate of the graph that represents the proportional relationship is $12.5, which is below $13 per week. Therefore, Louis made the correct statement.
How to Interpret the Graph of a Proportional Relationship?The graph of a proportional relationship is typically a straight line that runs through the point of origin (0, 0).
The slope of the graph gives the unit rate, which is calculated as m = y/x.
Given the graph that shows the proportional relationship between the number of weeks and the amount spent on coffee, we can use one point on the line, (4, 50) to find the unit rate, which will given us how much is spent per week.
Therefore:
Slope/unit rate or amount spent per week = y/x = 50/4 = $12.5.
Based on this, we can state that Louis is correct by saying Janie has not met her goal, because $12.5 per week is below the target of $13 each week.
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Please help me I’m struggling
The percentage of 12-month-old baby boys who weigh is 0.5.
What is mean and standard deviation?
The term standard deviation refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.Z-scores are calculated using the formula z = (x-μ)/σ, where x represents the raw score, the population mean, and the population standard deviation. The z-score is simply the raw score less the population mean, divided by the population standard deviation, as the calculation demonstrates.Mean=22.5; Standard deviation=2.2
The z-score for the given weight is
z−score = Blood pressure reading−Mean / Standard deviation
= 23.6−22.5/2.2
= 1.1/2.2
=0.5
Hence, the percentage of 12-month-old baby boys who weigh is 0.5
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Coefficient of x^5 in expansion of (2x-1)^6
The coefficient x⁵ in expansion of (2x - 1)⁶ is; -192
How to solve Binomial expansion?We are given the expression;
(2x - 1)⁶
Using Pascals triangle, the coefficient of the terms here are;
1 6 15 20 15 6 1
The general formula for binomial expansion is;
(x + y)ⁿ = ⁿC₀xⁿy⁰ + ⁿC₁xⁿ⁻¹y¹ + ⁿC₂xⁿ⁻²y²+......+ ⁿCₙx⁰yⁿ
Thus, we can find the expansion of (2x - 1)⁶ as;
1[(2x)⁶ * (-1)⁰] + 6[(2x)⁵ * (-1)¹] + 15[(2x)⁴ * (-1)²] + 20[(2x)³ * (-1)³] + [15(2x)² * (-1)⁴] + [6(2x)¹ * (-1)⁵] + [1(2x)⁰ * (-1)⁶]
= 64x⁶ - 192x⁵ + 240x⁴ - 160x³ + 60x² - 12x + 1
The coefficient we are looking for is -192
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The graph of a function f(x) passes through the following points: (0, 2), (1, 0), ( – 1,0) Which of the following could be f(x)?
A possible definition for function f(x) is given as follows:
y = -2x² - 2.
How to define the function f(x)?According to the Factor Theorem, the function f(x) can be defined according to it's zeros, as follows:
f(x) = a(x - x')(x - x'').
In which:
a is the leading coefficient.x' and x'' are the zeros of the function.Two of the points of the function are (1,0) and (-1,0), hence the zeros are given as follows:
x' = 1, x'' = -1.
Then the function can be defined as follows:
f(x) = a(x - 1)(x + 1)
f(x) = a(x² - 1).
When x = 0, y = 2, hence the leading coefficient a is obtained as follows:
2 = a(0 - 1)
-a = 2
a = -2.
Thus the complete definition of the function is of:
y = -2(x² - 1)
y = -2x² - 2.
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lanson biked 1 13/14 miles to the library, the. 1 4/9 miles to the park. how far did he bike altogether
Answer: 3 47/126
Step-by-step explanation: You have to find the common denominator to make the problem easy and make sense. I highly recommend using a fraction calculator if you aren't sure how to do it.
What is the expression in rational exponent form? (∜8³)⅓
Answer:
2 is the answer
Step-by-step explanation:
(∜8³)⅓
the (⁴√8) is 2 { 2×2×2×2 = 8}
= (2³)⅓
= 2³×⅓
= 2
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Penny earned a 74% on her first test. If each test has 100 points, what must she earn on her next test to achieve an average of at least 80%?
Step-by-step explanation:
the mean value is average is the sum of all data divided by the number of data points.
with the second test she will have 2 data points.
the first was 74 points (74% of 100 points = 74 points).
x = 2nd test result
(74 + x)/2 = 80
74 + x = 160
x = 86
she must earn 86% on her second test to achieve an average score of 80%.
Thi month, Kami old 70 figurine in 2 ize. The large figurine old for $12 each, and the mall figurine old for $8 each. The amount of money he received from the ale of the large figurine wa equal to the amount of money he received from the ale of the mall figurine. How many large figurine did Kami ell thi month?
The large figurine old for $12 each, and the mall figurine old for $8 each. The amount of money he received from the ale of the large figurine wa equal to the 42
Let x represent the number of large figurines that Kami sold.
Let y represent the number of small figurines that Kami sold.
This month kami sold 70 figurines in 2 sizes. This means that
x + y = 70 - - - - - - - - - - 1
The large figurines sold for $12 each and the small figurines sold for $8 each. The amount of money he received from the sales of the large figurines was equal to the amount of money he received from the sales of the small figurines. This means that
12x = 8y
y = 12x/8
y = 1.5x
Substituting y = 1.5x into equation 1, it becomes
x + 1.5x = 70
2.5x = 70
x = 70/2.5 = 28
y = 1.5x = 1.5 × 28 = 42
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What is the vertex of the quadratic function?
(-6,1)
(6,-1)
(1,6)
(1.-6)
Answer:
(1,-6)
Step-by-step explanation:
Ordered pairs are (x,y)
The vertex of the quadratic formula is its lowest point if opening up, and its highest point if opening down
This one opens up so it is the lowest point
The x value of the vertex is x=1
the Y value of the vertex is y=-6