The function f(t) = t2 + 6t − 20 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your work.
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know?
Part C: Determine the axis of symmetry for f(t)
PART A:
The function in vertex form by completing the square is:
[tex]f(t)=(t+3)^2-29[/tex]
PART B:
The vertex is located at (-3,-29)
and the vertex is the minimum point of the graph.
PART C:
The axis of symmetry of f(t) is:
t= -3
Step-by-step explanation:The function f(t) is given by:
[tex]f(t)=t^2+6t-20[/tex]
We know that the vertex form of a equation is given by:
[tex]f(t)=a(t-h)^2+k[/tex]
where a,h and k are real numbers.
and the vertex is located at (h,k)
The function is given by:
[tex]f(t)=(t+3)^2-29[/tex]
Hence, the vertex is given by:
(-3,-29)
Also, as the leading coefficient is positive.
Hence, the parabola is upward open parabola.
Hence, the vertex will be the minimum point of the graph.
Also, the axis of symmetry of a graph is given by:
t=h
Hence, here the axis of symmetry is: t= -3
Stacy bought a skateboard at a local sporting goods store. The skateboard was on sale for 10% off the original price. The store then charges 10% sales tax.
a. how does the original price compare to the final price?
b. would the final price be different if the 10% sales tax was added first and then the 10% discount was applied to this new amount
What is the value of ?
What is m∠PTS??????????
11(y-10) = 4y-5
11y-110 = 4y-5
7y -110 = -5
7y =105
y = 105/7 = 15
PTS = 11(15-10) = 11*5 = 55 degrees
Answer:
55
Step-by-step explanation:
We are given with two lines that intersects each other .
the vertical opposite angles are same.
So we equate the angles and solve for y
[tex]11(y-10)= 4y-5[/tex]
[tex]11y-110=4y-5[/tex]
Subtract 4y from both sides
[tex]7y-110=-5[/tex]
Now we add 110 on both sides
[tex]7y=105[/tex]
Now we divide by 7 on both sides
y=15
now we find m∠PTS
m∠PTS=[tex]11(y-10)[/tex]
Plug in 15 for y
m∠PTS=[tex]11(15-10)=55[/tex]
HELP ME OUT PLEASE I REALLY NEED SOME HELP ON THIS QUESTION PRETTY PLEASE !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Identify a reflection about the x-axis or a reflection about the y-axis of ƒ(x) = x^4 + x by observing the equation of the function g(x) = x^4 – x.
I think it might be on the y axis
The ratio of boy to girls in a class is 3 : 2. there are 15 boys in the class. how many total boys and girls are in the class?
a.15
b.23
c.25
d.35
the answer is c. 25
expalnation: A 3:2 ratio can be used in a proportion.
3/2=15/girls, girls =15*2÷3=10.
10÷15=25
The legs of a right triangle are 12 centimetres and 16 centimeters. What is the length of the hypotenuse?
15 centimeters
17 centimeters
20 centimeters
28 centimeters
The length of the hypotenuse is 20 centimeters.
In order to solve this question, we'll use the Pythagoras formula which will be:
a² + b² = c²
where,
First leg = a = 12 centimeters
Second leg = b = 16 centimeters
Hypothenuse = c = Unknown
It should be noted that the hypothenuse is the longest side and therefore the formula will be:
a² + b² = c²
12² + 16² = c²
144 + 256 = c²
400 = c²
Therefore, c = ✓400
c = 20
Therefore, the length of the hypotenuse is 20 centimeters.
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George's page contains twice as many typed words as Bill's page and Bill's page contains 50 fewer words than Charlie's page. If each person can type 70 words per minute, after one minute, the difference between twice the number of words on Bill's page and the number of words on Charlie's page is 220. How many words did Bill's page contain initially?
Need help Identify three solutions of the graph shown
what transformations change the graph of f(x) to the graph of g(x)?
f(x)=x^2
g(x)=(x+3)^2-7
Answer:
B. The graph of g is the graph of f translated to the left 3 units and down 7 units.
Step-by-step explanation:
f(x) = x² to g(x) = (x + 3)² - 7
Notice the difference:
from 'x' to 'x + 3'
and then from 'x²' to '(x+3)² - 7'
The transformation that changes 'x' to 'x + 3' is the translation across the x-axis, three units to the left. The transformation that changes 'x²' to (x + 3)² - 7' is the translation across the y-axis, seven unit down. Refer to the graph attached below to visualize the transformation. Take the vertex of f(x) = x² and translate it three unit left and seven unit down to get g(x).
Find the measures of two complementary angles if the difference in the measures of the two angles is 14
If you know that a line has a slope of 2/3 and a y-intercept of 7, what is the equation for that line in slope-intercept form?
the equation for a line is y = mx+b
m = slope
b = y intercept
you know the slope is 2/3 and the y intercept is 7 so just replace them in the equation:
y =2/3x +7
A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 5 tables is $39 . The total cost to rent 9 chairs and 7 tables is $63 . What is the cost to rent each chair and each table?
The temperature dropped 3 °C every hour for 5 hours.
Write an integer that represents the change in temperature.
If 10 miles is about 16 kilometers and the distance between two towns is 45 miles, use a ratio table to find the distance between the towns in kilometers
Problem page the ratio of men to women working for a company is 5 to 8 . if there are 169 employees total, how many women work for the company?
How do you write "the difference between twenty and a number and four is six" as an algebraic expression?
|5v-10|=0 solve for v
M is the midpoint of CF for the points c(3,7) and f(5,5). Find MF
To find the length of MF, the distance formula is used after calculating the midpoint M of CF with coordinates C(3,7) and F(5,5), resulting in MF being √2 units.
Explanation:The question asks to find the distance MF, where M is the midpoint of segment CF given the coordinates of the points C(3,7) and F(5,5). To find the coordinates of M, we need to use the midpoint formula:
Midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2)
Using the given points C(3,7) and F(5,5), we get:
M = ((3 + 5)/2, (7 + 5)/2) = (4, 6)
Now, we will use the distance formula to calculate MF:
Distance formula: D = √((x2 - x1)² + (y2 - y1)²)
Since M(4,6) and F(5,5) are the points in question, plugging in these values yields:
MF = √((5 - 4)² + (5 - 6)²) = √((1)² + (-1)²) = √(1 + 1) = √2
So, the length of segment MF is √2 units.
PLEASE HELP ME !!
Abigail has $30.00 to buy groceries. She needs to buy some apples, some bananas, and 3 pounds of potatoes. Fuji apples are $1.79 a pound, bananas are $0.36 each, and potatoes are $2.99 for a 3 lb. bag. If a represents the number of pounds of apples Abigail buys and b represents the number of bananas she buys, which expression represents the amount of change she receives after her purchases? Choices are
A. 30.00-a-b
B. 1.79a + 0.36b+2.99
C. 30.00 – (1.79a + 0.36b + 2.99)
D. 30.00 + (1.79a + 0.36b + 2.99)
Answer:
[tex]30-(1.79a+0.36b+2.99)[/tex]
Step-by-step explanation:
Let a represents the number of pounds of apples Abigail buys
Cost of 1 pound of apple = $1.79
So, Cost of a pounds of apple = 1.79a
Let b represents the number of bananas she buys,
Cost of 1 pound of banana = $0.36
Cost of b pounds of banana = 0.36b
Abigail buys 3 pounds of potatoes
Cost of 3 pounds of potatoes = $2.99
So, Total cost = [tex]1.79a+0.36b+2.99[/tex]
Abigail has $30.00 to buy groceries.
So, the amount of change she receives after her purchases=[tex]30-(1.79a+0.36b+2.99)[/tex]
So,Option C is correct.
Hence The expression represents the amount of change she receives after her purchases is [tex]30-(1.79a+0.36b+2.99)[/tex]
A data set includes the entries 2, 5, 7, 9, 9, and 12. complete the data set with an entry between 1 and 12 so that the median and mode of the set are equal.
The complete data set will be 2, 5, 7, 9, 9, 9, 12. When the number 9 is added to the collection, the median and mode are both 9.
What is the median of data?The median is defined as the value range. To get it, arrange the numbers in ascending order from smallest to largest, then hide one number on either end until you reach the center.
The median of a set is the middle number when the numbers are arranged in numerical order.
The mode of a set is the number that appears most frequently.
To find an entry that will make the median and mode equal, we first need to arrange the given numbers in numerical order: 2, 5, 7, 9, 9, 12.
The median of this set is the middle number, which is 9.
The mode is 9, since it appears twice while the other numbers appear only once.
To make the median and mode equal, we need to find a number that is between 1 and 12 and that is equal to 9. The only such number is 9.
Therefore, if we add the number 9 to the set, the median and mode will both be 9. The complete data set will be 2, 5, 7, 9, 9, 9, 12.
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44cm is rounded to the nearest whole cm. Write down the maximum possible length it could have been.
The maximum possible length it could have been 44.49cm.
What is round off?Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.
here, we have,
44cm is rounded to the nearest whole cm.
as, it is rounded to the nearest whole cm.
so, we get,
The maximum possible length it could have been 44.49cm.
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Olivia's work and solution to the equation -6x+ 11 =43 is shown. identify each error in Olivia's work and explain what she should have done instead . please help
-6x + 11 = 43
+ 11 +11
-6x =54
-6x/6 = 54/6
x =9
Kai calculates that he spends 75 minutes of a school day in science class. if he spends 500 minutes in school, what percent of his school day does kai spend it science class
How many significant digits are in 4.0×10^4
I need to find the equation for this.. I keep getting confused please explain
What are the quotient and remainder when 6x3 + 13x2 + x − 2 is divided by x − 1?
Final answer:
The quotient when dividing 6x³ + 13x² + x - 2 by x - 1 is 6x² + 19x + 20, and the remainder is 18. This solution can be found using synthetic division.
Explanation:
The question asks to find the quotient and remainder when the polynomial 6x³ + 13x² + x - 2 is divided by x - 1. To solve this, we can use polynomial long division or synthetic division. As the divisor is in the form of x - a, where a is 1, synthetic division is a streamlined approach.
We set up our synthetic division with 1 as our key number outside the division symbol and the coefficients of our polynomial (6, 13, 1, -2) inside:
Bring down the 6.
Multiply 1 by 6 to get 6, add this to the next coefficient 13 to get 19.
Continue the process: Multiply 1 by 19 to get 19, add this to 1 to get 20.
Repeat: Multiply 1 by 20 to get 20, add this to -2 to get 18.
The numbers now inside the division symbol represent the coefficients of the quotient polynomial, giving us 6x² + 19x + 20 with a remainder of 18. Therefore, the quotient is 6x² + 19x + 20, and the remainder is 18.
The Sum of 3 consecutive integers is 1,623
divide 1623 by 3
1623 / 3 = 541
now subtract 1 from that
541-1=540
then add one to 541, 541+1 = 542
540 + 541 + 542 = 1623
the numbers are 540, 541, 542
A restaurant compiled the following information regarding 40 of its employees. Of these employees, 9 cooked food, 14 washed dishes, 22 operated the cash register, 4 cooked food and washed dishes, 2 cooked food and operated the cash register, 7 washed dishes and operated the cash register, and 1 did all three jobs. Complete parts a) through e) below.
a) How many of the employees only cooked food?
Answer: 2
Step-by-step explanation:
Let Set A represents the number of employees cooked food.
Set B represents the number of employees washed dishes.
Set C represents the number of employees operated the cash register .
Given : n(A)=9 ; n(B)=14 ; n(C)=22
n(A∩B)=4 ; n(A∩C) = 2 ; n(B∩C)=7 ; n(A∩B∩C)=1
Using the given information, we have made a Venn diagram below.
Using Venn diagram , we have
n(only A)= n(A)-(n(A∩B)+n(A∩C)+n(A∩B∩C))
⇒n(only A)=9-(4+2+1)=9-7=2
Hence, 2 employees only cooked food.
If the maximum acceleration that is tolerable for passengers in a subway train is 1.74 m/s2 and subway stations are located 930 m apart, what is the maximum speed a subway train can attain between stations?
To calculate the maximum speed a subway train can reach between stations, given the maximum tolerable acceleration, we use the equation Vmax = sqrt(2 × a × d), resulting in a maximum velocity of approximately 40.21 m/s.
To find the maximum speed a subway train can attain between stations, given a maximum tolerable acceleration for passengers, we need to use the equations for uniformly accelerated motion. Since the train starts and ends at rest at the stations and because the stations are 930 meters apart, we can think of the train's trip as two identical parts: an acceleration phase and a deceleration phase.
Let's denote the maximum speed as Vmax, the acceleration as a, and the distance for each phase as d (half the distance between stations). We have:
Acceleration: a = 1.74 m/s2Total distance to the halfway point: d = 930 m / 2 = 465 mUsing the equation Vmax2 = 2ad, we can solve for the maximum speed (Vmax) as follows:
Vmax = sqrt(2 × a × d)
Substituting the values, we get:
Vmax = sqrt(2 × 1.74 m/s2 × 465 m)
Vmax ≈ sqrt(1617) m2/s2 ≈ 40.21 m/s
Therefore, the maximum speed the subway train can attain between stations is approximately 40.21 m/s.