The values of a, h and k for the given quadratic function are:
a = -6, h = -5 and k = -1
What is vertex form?
This is one way of writing a quadratic function:
f(x) = a(x-h)² +k
(h, k) = vertex
a = vertical stretch
According to the given question:
We're given:
f(x)= -6x² - 60x - 151
To write a quadratic function in vertex form, we must complete the square.
⇒ Put parentheses around the first two terms containing x and x²:
f(x)= (-6x² - 60x) - 151
⇒ Factor out -6 (keeping the x's in the parentheses):
f(x)= -6(x² + 10x) - 151
⇒ To complete the square, add, inside the parentheses, the square of half the coefficient of x.
⇒ In this case, the coefficient of x is 10.
⇒ Half of this value is 5.
⇒ The square of 5 is 25.
⇒ Add this inside the parentheses:
f(x) = -6(x² + 10x + 25) - 151
⇒ Now, we cannot randomly introduce a new value into a function. To balance the +25, subtract -6(25) outside the parentheses:
f(x) = -6(x² + 10x + 25) - 151 - (-6 x 25)
f(x) = -6(x² + 10x + 25) - 151 - (-150)
f(x) = -6(x² + 10x + 25) - 151 + 150
f(x) = -6(x² + 10x + 25) - 1
⇒ Finally, complete the square.
Remember: (a + b)² = a² + 2ab + b²
In this case, a is x, and b is 5:
f(x) = -6(x + 5)² - 1
On comparing with f(x) = a(x-h)² +k we get the values of a, h and k as:
a = -6
h = -5
k = -1
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Jon Begins jogging at a steady 3 m/sec down the middle of lane one of a straight track. Laura starts even with him in the cneter of lane two but moves at 4 m.sec. At the instant they begin, Ellis is loacted 100 meters down the track in lane four, and is heading towards them in his at 6 m.sec. After how many seconds will the runners lie in a straight line?
a) Let t be the number of seconds the three have been running. Write expressions for the number of meters each has run after t seconds.
b) Consider the location of each runner as a point on a graph. What quantity might you use as the x-coordinate? What quantity might you use as the x-coordinate? What quantity might you use as the y-coordinate?
c) How can you tell if three points are on a line? Use this to solve the problem.
Answer:
The runners will be in a straight line after 1/2 seconds.
To solve this problem, we can set the y-coordinates of each runner equal to each other and solve for t. The y-coordinate represents the lane number, and if the lane numbers are equal, the runners are on a straight line.
Jon: y = 1
Laura: y = 2
Ellis: y = 4
Jon: 3t = 1
Laura: 4t = 2
Ellis: 6t = 4
Solving these equations simultaneously, we find that t = 1/2 seconds. This means that after 1/2 seconds, the runners will be in a straight line.
1. On a journey from Dover to Sheffield, Liam drove at an average speed of 40mph
for the first three hours of his journey.
The remaining 120miles of his journey were completed at an average speed of
30mph.
According to the given statement Liam is incorrect because average speed is 34.28 miles per hour.
Why do people use average speed?The average scores of a body's speed over a duration of time is its average speed. Because a moving body's speed is not constant over time and fluctuates, the average speed formula is required.
What does "average speed" actually mean?The overall distance the thing travels in a given amount of time is its average speed. A scalar value symbolizes the average speed. It has no direction and therefore is indicated by the magnitude.
Distance covered in first three hours = 40 × 3 = 120 miles
Time taking to covered remaining 120 miles = 120/30
= 4 hours
Total time = 4 hours + 3 hours = 7 hours
Total distance = 120 miles + 120 miles
= 240 miles
Average speed = total distance / total time
Average speed = 240 miles / 7 hours = 34.28 miles per hour
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evaluate 2n if n = 9
Answer:
18
Step-by-step explanation:
If n=9, then plug in 9 for n in the equation and solve. You should get 2•9, which is 18 when you simplify. Hope this helps and please mark brainliest!
C-Town is advertising a Back-to-School sale on pencils. Pack A has 30 pencils and sells for $7.50, while Pack B has 12 pencils and costs $4.25. Find the unit price for each and determine which pack is the better buy.
The rate for Pack A and Pack B
The unit price for Pack A and Pack B
Which pack is the better buy? Explain your reasoning.
The best buy is pack of 30 .
What is cost and division ?
A cost function is a mathematical formula used to chart how production expenses will change at different output levels.
The general form of the cost function formula is C(x)=F+V(x) C ( x ) = F + V ( x ) , where F is the total fixed costs, V is the variable cost, x is the number of units, and C(x) is the total production cost.
Division is the opposite of multiplication.
A division is a process of splitting a specific amount into equal parts.
Pack A has 30 pencils
sells for $7.50.
pack of 30:
7.97/30 = 0.27 per pencil
Pack B has 12 pencils
costs of $4.25.
pack of 12:
4.77/12 = 0.40 per pencil
The best buy is pack of 30 because:
0.27 < 0.40
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melissa's null hypothesis is that the average calories in frozen mac n cheese is 350 (that is, the population average is 350). since she only has one sample, she uses the bootstrap to estimate the average and ultimately decides to create a confidence interval. she also chooses an 8% p-value cutoff. what kind of confidence interval should she use?
For 8% p-value cutoff , Melissa should use 92% confidence interval
A confidence interval calculated for a treatment effect measure shows the range in which the true treatment effect is likely to fall.
A smaller sample size or higher variability will result in a wider confidence interval with a larger margin of error. The interval width is also influenced by the level of confidence. If you want a higher level of certainty, the interval should be wider.
The width of the confidence interval and the size of the p value are related.
The narrower the interval, the smaller the p value. The confidence interval, on the other hand, provides useful information about the likely magnitude of the effect under consideration as well as the accuracy of the estimate.
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(c) The sum of the ages of two brothers is 31 years and the age of older brother is 5 years more than the younger brother. Find their present ages.
Answer:
Here is your answer,
Step-by-step explanation:
(c)
x + y = 31 ------ (i)
x - y = 5 ------ (ii)
We have subtract eqn (ii) from eqn (i). Here we get the equation as,
2y = 26
y = 13 ------(iii)
Put eqn (iii) in eqn (i), we get -
=> x + y = 31
=> x = 31 - 13
=> x = 18
Therefore, their present ages of younger brother & older brother is 13 yrs & 18 yrs respectively.
pleaseee help me ill give brainliest IM BEING TIMED
-STATISTICS question!!!-
Answer:
The data given from the graph proves that Catherine and Ana's suspicions were correct and the athletes at their school do indeed have a quicker reaction time than other students at their school. The average reaction time for the athletes ranges from 240 - 300, while the normal student's reaction time ranges from 260 - 330. There still should be more experiments to test this theory to get more detailed and accurate results because there are still athletes that have the same reaction time as normal students and the dot away from the boxes shows that there is a athlete that has a slower reaction rate than all of the normal students. So it is safe to say there is indeed a difference in reaction times, but not a drastic one.
study results indicate that the mean amount of time people live in the same house s between 5.5 and 13.5 years. what is the study's margin of error?
Answer:4.25
Step-by-step explanation: because it is daddy
A new club sent out 192 coupons to boost sales for next year's memberships. They provided 5 times as many to potential members than to existing members. How many coupons did they send to existing members? A. 37 B. 6 C. 32 D. 5
They send 32 coupons to existing members. Option C is correct.
What is a linear equation in two variables?
A Linear equation in two variables x and y is of the form
Ax + By = C.
Given,
They provide 5 times as many to potential members than existing members.
Let, there are y potential members and x existing members.
Therefore, x + 5y = 192
Also, x and y are whole numbers.
Hence, x=32 satisfy the equation.
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The legs of a right triangle are 3 units and 5 units. What is the length of the hypotenuse? Round your answer to the nearest hundredth. (5 points)
Question 4 options:
1)
4.00 units
2)
2.83 units
3)
5.83 units
4)
8.00 units
Answer:
bom é a soma dos algarismos se for matemática
a researcher studying malnutrition among children in a developing country collected weights of a random sample of children using a scale that she had set to give weights 2.5 kilograms less than the actual weight. which statement best describes this situation? measurement error has not occurred, and the researcher is not guilty of unethical statistical practice. measurement error has occurred, and the researcher is guilty of unethical statistical practice. measurement error has occurred, but the researcher is not guilty of unethical statistical practice. measurement error has not occurred, but the researcher is guilty of unethical statistical practice.
Therefore the the best statement that describes this situation is Measurement error has occurred, and the researcher is guilty of unethical statistical practice.
As per the details share in the above question are as follow,
A researcher collected weights of a random sample of children using a scale that she had set to give weights 2.5 kilograms less than the actual weight.
We have to determine the best statement that describes this situation?
It measured precisely 2.5 kg less, which is a systematic inaccuracy, thus there has been a measuring error.
The statistician was guilty because she purposefully gave them less weight in order to support her argument.
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The diameter of a circle divides the circle into two equal sectors true or false
Answer:
NO
FALSE
Step-by-step explanation:
The diameter divides the circle into two equal part called semi– circles( the image on white)
A sector is the plane figure enclosed by two radii of a circle or ellipse and the arc between them.
( the image that is dark)
i hope this helped
Answer: No, the diameter of a circle divides the circle into two equal halves called semi circle.
Step-by-step explanation:
The line that splits a circle into two identical halves is its diameter. The widest chord that divides the circle in half exactly is called the diameter. Each component is known as a semicircle.
Given the following data calculate the correlation coefficient. Then describe the correlation based on the correlation coefficient.
0 11
3 26
9 17
4 22
6 18
The correlation coefficient is -7.44, which shows a strong negative correlation.
To calculate the correlation coefficient, you can use the following formula:
r = (n Σ(xy) - Σ(x) Σ(y)) / √((n Σ(x²) - (Σ(x))²) (n Σ(y²) - (Σ(y))²))
Where n is the number of data points, x is the variable on the x-axis, y is the variable on the y-axis, Σ(xy) is the sum of the products of x and y, Σ(x) is the sum of x, Σ(y) is the sum of y, Σ(x²) is the sum of the squares of x, and Σ(y²) is the sum of the squares of y.
Plugging in the values from the data, we get:
r = (5 x 198 - 39 x 91) / √((5 x 114 - 39²) x (5 x 187 - 91²))
Simplifying this equation gives us:
r = (-179) / √((-97) x (-6))
r = (-179) / √(582)
r = (-179) / 24.07
r = -7.44
The correlation coefficient is -7.44, which indicates a strong negative correlation. This means that as the value of x increases, the value of y decreases. Conversely, as the value of x decreases, the value of y increases.
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Please help NOWWW!!!
Write y=2/3x+7 in standard form using integers.
A. -2x+3y=7
B. -2x+3y=21
C. 3x-2y=21
D. -2x-3y=21
Ava’s pet pig is older than Izzy’s pet pig, which is 2 years old. Ava adopted her pig when it was 1 year old, and she has had it for x years.
Write a one-step inequality to represent the situation, where x is the time, in years, since Ava adopted her pet pig.
Enter the correct answers in the boxes in the form of x+p ? q, where p and q are rational numbers and ? is replaced by >, ≥, <, or ≤.
The inequality that represents this situation is, (1 + x) > 2.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Ava’s pet pig is older than Izzy’s pet pig, which is 2 years old.
Ava adopted her pig when it was 1 year old, and she has had it for x years.
∴ The inequality that represents this situation is,
(1 + x) > 2.
x > 2 - 1.
x > 1.
Ava adopted her pig for more than one year.
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a tank has the shape of an inverted circular cone with height 10 m and base radius 4 m. it is filled with water to a height of 8 m. find the work done to empty the tank by pumping the water out of the top of the tank.
The work done to empty the tank by pumping the water out of the top of the tank is 3.4 * 10^6 .
Given :
a tank has the shape of an inverted circular cone with height 10 m and base radius 4 m. it is filled with water to a height of 8 m. find the work done to empty the tank by pumping the water out of the top of the tank .
Formula :
[tex]W=\int_a^bpA(y)D(y)dy[/tex]
Using the base radius of 4, I found the equation of the line which was y = 5x / 2 and by solving for x gives us x = 2y / 5 .
Work = [tex]9.8*1000\int_0^{8} (\pi(\frac{2y} 5)^2)(10-y)dy[/tex]
= 3.4 * 10^6
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What are the missing parts that correctly complete the proof? W/ picture
1. Reason: Since QA divides ∠PQR into two different parts so it is a bisector∠PQA≅∠RQA.
2. The line which divides an angle into two different angles is known as a bisector.
4. ∠QXA≅∠QYA and they are situated opposites to each other so we can say that right angles are conjugate.
5. Given, Both are situated in the same plan so QA≅QA
6.ΔQXA≅ΔQYA, by the AAS Postulate.
8. Definition of equidistant. XA=XY.
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In need of help like rn pls nd thanks!!!!!!!!!!!!!!!
Answer: His work shows that the answer is an F. E. Which means a False Equation.
Step-by-step explanation:
This happens when an equation cannot be solved. Here is an example of a false equation answer:
Let's say that 3=6, in the equation or expression, all the letters like "x, y, z..." have been undone.
Therefore we can no longer undo, so the answer to your question is a False Equation.
Solve the simultaneous equation 4x+6y=21;7x-3y=3
The solution of the equations 4x + 6y = 21 and 7x - 3y = 3 will be (1.5, 2.5).
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The linear equation is given below.
4x + 6y = 21 ...1
7x - 3y = 3 ...2
From equation 2, then we have
7x - 3y = 3
3y = 7x - 3
y = (7/3)x - 1
Put in equation 1, then we have
4x + 6[(7/3)x - 1] = 21
4x + 14x - 6 = 21
18x = 27
x = 3/2
x = 1.5
Then the value of the variable 'y' is calculated as,
y = (7/3)(3/2) - 1
y = 7/2 - 1
y = 3.5 - 1
y = 2.5
The solution of the equations 4x + 6y = 21 and 7x - 3y = 3 will be (1.5, 2.5).
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18. Higher Order Thinking The student council was
preparing for the school bake sale. The members divided
each type of donated item equally on plates. Each plate
contained only one type of item, and every plate had
exactly the same number of items. There were no leftovers.
What is the greatest number of items that could have been
placed on each plate?
Bake Sale Donations
Muffins
Breadsticks
Rolls
96
48
84
3-2 Find Greatest Common Factor and Least Common M
We need 8 plates for muffins, 4 plates for breadsticks, and 7 plates for rolls, with this arrangement, all plates will have the same amount of items, 12 per plate.
What are the denominator and numerator?
A fraction's top digit is always referred to as the numerator. It displays the number of our parts. A fraction's numerator—the lowest digit—is referred to as the denominator. It displays the overall number of pieces that something can be broken down into.
we have to divide each item in a way that gives us equal groups on each plate,
we have to find a divisor for each item that gives us the same result.
Muffins.
96/2=48
96/3=32
96/4=24
96/8=12
That is, by dividing all muffins into 8 plates we would have 12 muffins per plate.
Breadsticks.
48/2=24
48/4=12
That is, by dividing all breadsticks into 4 plates we would have 12 breadsticks per plate.
Rolls.
84/2=42
84/3=28
84/4=21
84/6=16
84/7=12
By dividing all rolls in 7 plates, we would have 12 rolls per plate.
Therefore, we need 8 plates for muffins, 4 plates for breadsticks, and 7 plates for rolls, with this arrangement, all plates will have the same amount of items, 12 per plate.
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Hi, I need help solving quadrilateral problems.
The value of x in quadrilateral JKLM is 29
What is a quadrilateral?A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points. The sum of interior angles of quadrilaterals is always equal to 360 degrees.
The sum of the interior angles in a quadrilateral is 360°
∠J + ∠K + ∠L + ∠M = 360
3X + 90 + 2X + 8 + 4X + 1 = 360
9x + 99 = 360
9x = 360 - 99
9x = 261
x = 261/9
x = 29
In conclusion 29 is the value of x in the quadrilateral.
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Please help, I don't really understand.
Answer:
y = [tex]\frac{2}{3}[/tex] x + [tex]\frac{26}{3}[/tex]
y = [tex]\frac{-3}{2}[/tex] x
Step-by-step explanation:
y = [tex]\frac{-3}{2}[/tex] x - 6
The slope of this line is -3/2
A perpendicular slope is the opposite reciprocal. That means you flip it upside down and take the opposite sign. Since this slope is negative, the perpendicular slope will be positive. If I turn this fraction upside down it will be 2/3, so the perpendicular slope is 2/3.
For the equation of the line we need the slope (m) and the y intercept. To find that we will use the point that goes through this line.
m = (2/3)
x = -4 from the point given (-4, 6)
y = 6 from the point given (-4,6)
y = mx + b
6 = [tex]\frac{2}{3}[/tex] [tex](\frac{-4}{1})[/tex] + b
6 = [tex]\frac{-8}{3}[/tex] + b Add [tex]\frac{8}{3}[/tex] to both sides
[tex]\frac{6}{1}[/tex] + [tex]\frac{8}{3}[/tex] = b
[tex]\frac{18}{3}[/tex] + [tex]\frac{8}{3}[/tex] = b
[tex]\frac{26}{3}[/tex]
y = [tex]\frac{2}{3}[/tex] x + [tex]\frac{26}{3}[/tex]
Parallel lines have the same slope.
m = [tex]\frac{-3}{2}[/tex]
x = -4 from the point (-4,6)
y = 6 from the point (-4,6)
y = mx + b
6 = [tex]\frac{-3}{2}[/tex][tex](\frac{-4}{1})[/tex] + b
6 = 6 + b Subtract 6 from both sides
0 = b
y = [tex]\frac{-3}{2}[/tex] x
Attachment 1 is answer options, attachment 2 is questions, answer all please 30 points
Any quality that pertains to a certain set is referred to in mathematics as a property. A property p that is rigorously specified for every component of a set X is typically defined as a function p: X → {true, false}.
What are the 4 properties of equality?The four properties of equality addition, subtraction, multiplication, and division can be used to solve an equation. To get the value of an equation's unknown variable, we can easily add, subtract, multiply, or divide the two sides of the equation.
The qualities of equality are those characteristics that have no effect on an equation's truth value, i.e., those characteristics that do not affect the equality of two or more values. These equality-related qualities enable us to define an equivalence relation and solve a number of algebraic equations.
9/2 x - 3 = 1/2 x + 2 Addition property of equality
9/2 x - 1/2 x - 3 = 1/2 x - 1/2 x + 2 Addition property of equality
1/4 * 4x = 1/4 * 5 Multiplication property of equality
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Daphne wants to buy some apples. An advertisement says that she can get $2$ apples for $1.24$. What is the price of $5$ apples?
Answer:
The price of 5$ worth of apples will be $3.10.
Step-by-step explanation:
5 dollars worth of apples would be 2 and a half apples. So, you would multiply 1.24 by 2.5. that gives you 3.1. Then, change those into change and you have your answer. Hope this helps!
How do I Solve this:
Answer:
x = 20
Step-by-step explanation:
x + 2x + 6x = 9x / 180
x=20
triangles = 180
angle 1 = ?
angle 2 = 160?
angle 3 = 20
Please help me respond this question.
Answer:
Apples are least preferred
75% don’t prefer oranges
40 people prefer bananas
Answer:
Step-by-step explanation:
a) apples
b)
(40+ 20 + 15)
75% do not prefer oranges
c)
20% prefer bananas
20% as decimal is 0.2
0.2 * 200 =
40 people prefer bananas
There are 5,280 feet in a mile. There are 3 feet in a yard. How many yards are there in a mile? Please help this is due tomorrow
In mile there are 63360 inches.
The number of inches in a mile is equal to the number of inches in a foot times the number of feet in a mile
We multiply 528 by 12 and add one zero to the right of the result.
Use vertical form to perform the multiplication.
So. 12 × 5280=63360
∴ 5280/6336
= 1056
The number of inches in a mile = 12 × 5280
We multiply 528 by 12 and add one zero to the right of the result.
Use vertical form to perform the multiplication:
528 × 12 = 1056
1056 + 5280 = 6336
So, 12 × 5280 = 63360 miles
Therefore, in mile there are 63360 inches.
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Find the y-intercept of the line y=10x+ 7/13
Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.
Answer: 7/13 is the y intercept
What is the proportional relationship?
6
3.75
20
1/5
3
1/8
1.12
5/2
5
1/2
8
2
Answer:
I think multiples of 4
I hope this helps
Two ladders are leaning against a wall at the same angle, as shown. How long is the short ladder?
Answer:
15 ft
Step-by-step explanation:
60 divide by 40 equal 1.5
1.5 x 10 = 15