Answer:
f(x)=(x−5)2−16
Set the polynomial equal to y
to find the properties of the parabola.
y=(x−5)2−16
Use the vertex form, y=a(x−h)2+k
, to determine the values of a, h, and k
.
a=1
h=5
k=−16
Since the value of a
is positive, the parabola opens up.
Opens Up
Find the vertex (h,k)
.
(5,−16)
Find p
, the distance from the vertex to the focus.
Tap for more steps...
14
Find the focus.
Tap for more steps...
(5,−634)
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
x=5
Answer:
x > -1 or x < -9
Step-by-step explanation:
(x + 5)^2 must be > 16 for f(x) to be positive.
(x + 5)^2 > 16
Taking square roots:-
x + 5 > 4
x > -1 (answer)
or x + 5 < -4
x < -9 (answer)
a soccer team practiced 3 times a week. each practice lasts for 110 minutes. the team practices for 14 weeks during the season. how many minutes did he team practice during the season? how many hours did the team practice during the season? ( Hint: remember that there are 60 minutes in one hour)
Answer:
3 weeks x 110 minutes = 330 minutes
330 minutes a week x 14 weeks = 4620 minutes
4620 divided by 60 minutes = 77 hours
77 hours is your answer
Step-by-step explanation:
Team practices for 4620 minutes or 770 hours during the season.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Soccer team participates 3 times a week,
One practice lasts for 110 minutes,
And The team practice for total 14 weeks.
Total time practice in one week = 3 x 110 = 330 minutes
Since, total week are 14,
So total duration for practice = 14 x 330 = 4620 minutes
Total time duration in hours = 4620 / 60 hours = 770 hours.
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a 33 m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 36m Find the length of the shadow
Answer:
14.39
Step-by-step explanation:
a^2 + b^2 = c^2
33^2 + b^2 = 36^2
1089 + b^2 = 1296
1089 - 1089 + b^2 = 1296 - 1089
b^2 = 207
b = 14.39
What is the value of cos 0 given that (-2,9) is a point on the terminal side of 0?
Answer:
The value of cos 0 = - 2 sqrt(85) / 85 = - 0.216930458
Step-by-step explanation:
cos 0 = ?
Point on the terminal side of 0 : (-2,9)=(x,y)→x=-2, y=9
cos 0 = x/r
r=sqrt(x^2+y^2)
Replacing the known values:
r=sqrt( (-2)^2+(9)^2)
r=sqrt(4+81)
r=sqrt(85)
cos 0 = x/r
cos 0 = -2 / sqrt(85) = -2/9.219544457 = -0.216930458
Rationalizing:
cos 0 = -[2 / sqrt(85)] [sqrt(85) / sqrt(85)]
cos 0 = - 2 sqrt(85) / [sqrt(85)]^2
cos 0 = - 2 sqrt(85) / 85
Arrange the systems of equations that have a single solution in increasing order of the x-values in their solutions.
2x + y = 10
x − 3y = -2
x + 2y = 5
2x + y = 4
5x + y = 33
x = 18 − 4y
y = 13 − 2x
8x + 4y = 52
x + 3y = 5
6x − y = 11
2x + y = 10
-6x − 3y = -2
y = 10 + x
2x + 3y = 45
Answer:
6 , 2 , 5 , 7 , 4 , 1 , 3
Step by Step:
1) x - 3(10 - 2x) = -2
x - 30 + 6x = -2
7x - 30 = -2
7x = 28
x = 4
2) x + 2(4 - 2x) = 5
x + 8 - 4x = 5
-3x + 8 = 5
-3x = -3
x = 1
3) 5(18 - 4y) + y = 33
90 - 20y + y = 33
90 - 19y = 33
-19y = -57
y = 3
x = 18 - 4(3)
x = 18 - 12
x = 6
4) 8x + 4(13 - 2x) = 52
8x + 52 - 8x = 52
52 = 52
5) x + 3(-11 + 6x) = 5
x - 33 + 18x = 5
19x - 33 = 5
19x = 38
x = 2
6) -6(5 - 2y) - 3y = -2
-30 + 12y - 3y = -2
-30 + 9y = -2
9y = 28
y = 3
2x + 3(3) = 5
2x + 9 = 5
2x = -4
x = -2
7) 2x + 3(10+x) = 45
2x + 30 + 3x = 45
5x + 30 = 45
5x = 15
x = 3
Answer:
The order for the systems is 2), 5),7), 1) and 3)
Step-by-step explanation:
To find the solution for ecah system first you have to choose a method, for example you can isolate one of the variables (x or y) in both equations and then equal each other.
1) 2x + y = 10 ⇒ y= 10 - 2x
x - 3y = -2 ⇒ -3y = -2 - x ⇒ y = (-2 - x)/-3 ⇒ y = 2/3 + (1/3)x
Now you have to equal both equations
10 - 2x = 2/3 + (1/3)x ⇒ 10 - 2/3 = (1/3)x + 2x ⇒28/3 = (7/3)x
⇒ (28/3)/(7/3) = x ⇒ 4.
With the "x" value obtained we return to the original equations and replace it there to find "y".
2x + y = 10 ⇒ 2(4) + y = 10 ⇒ y= 10 - 8 ⇒ y =2
The solution to the system is (4,2).
If you do the same for all the systems you will find that the solutions are
2) x + 2y = 5
2x + y = 4
Solution = (1, 2)
3) 5x + y = 33
x = 18 − 4y
Solution = (6,3 )
4) y = 13 − 2x
8x + 4y = 52
Solution = ∅, no solution
5) x + 3y = 5
6x − y = 11
Solution = (2, 1)
6) 2x + y = 10
-6x − 3y = -2
Solution = ∅, no solution.
7) y = 10 + x
2x + 3y = 45
Solution = (3, 13)
What is median of this histogram
Answer: You take the 2 middle columns in this case the purple gray looking one and the brown one and add them together divide them by 2
Step-by-step explanation:
After working 60 hours at his job, Tyler earned a total of $1500. How much does Tyler earn per hour?
[ Answer ]
$25 An Hour
[ Explanation ]
We already know the total amount he has right now. We also know how long he has worked at his job. To solve, we can use division.
Divide 1500 by 60
1500 / 60
= 25
<> Arsenal <>
Answer:
1500 ÷ 60 = 25
Step-by-step explanation:
He worked for 60 hours and got $1500, 1500 divided by 60 equals 25 dollars each hour.
URGENT NEED HELP, Titus works at a hotel. Part of his job is to keep the complimentary pitcher of water at least half full and always with ice. When he starts his shift, the water level shows 4 gallons, or 128 cups of water. As the shift progresses, he records the level of the water every 10 minutes. After 2 hours, he uses a regression calculator to compute an equation for the decrease in water. His equation is W –0.414t + 129.549, where t is the number of minutes and W is the level of water. According to the equation, after about how many minutes would the water level be less than or equal to 64 cups?
A)150 minutes
B) 160 minutes
C)170 minutes
D)180 minutes
The number of minutes the water level would be less than or equal to 64 cups is t ≥ 158.33. option B, C, D
How many minutes would the water level be less than or equal to 64 cups?
The regression equation:
W = -0.414t + 129.549
Where,
t is the number of minutes and
W is the level of water.
When w ≤ 64
W ≤ -0.414t + 129.549
64 ≤ -0.414t + 129.549
Subtract 129.549 from both sides
64 - 129.549 ≤ -0.414t
-65.549 ≤ -0.414t
Divide both sides by -0.414
t ≥ -65.549 / -0.414
t ≥ 158.3309178743961
Approximately, t ≥ 158.33
Therefore, the water level would be less than or equal to 64 cups when t is greater than or equal to 158.33
a ferris wheel can accumulate 75 people in 30 minutes how many people could ride the ferris wheel in 4 hours what was that rate per hour
Answer:
600 people
Step-by-step explanation:
We can use ratios to solve this problem.
Change the 30 minutes in to hours
30 minutes = .5 hours
75 people x people
---------------- = -----------------------
.5 hours 4 hours
Using cross products
75*4 = .5 *x
300 = .5x
Divide each side by .5
300/.5 = .5x/.5
600 =x
Given f(x)=5x+5, find f(-4)
f(-4) This means that x is -4, so you can plug in -4 for "x" in the equation
f(x) = 5x + 5
f(-4) = 5(-4) + 5
f(-4) = -20 + 5
f(-4) = -15
3+2(2p+4t) some one plz HELP ME.
Answer:
3+4p+8t
Step-by-step explanation:
We have been given an expression:
3+2(2p+4t)
We will simplify the equation:
Firstly, we will open the parenthesis by multiplying it with the 2 given outside of the parenthesis we get:
3+4p+8t
Since, we have two variables so it can not be further solved therefore,
This is the maximum simplification of the given expression.
Bennie blinko Owns a small bookstore in Cambridge MA.Bennie is ordering some copies of Veronica Roth’s new book. Printer a sells the book at $350 per 100 and printer be sells the books at 1:50 $ per 40 which company offer the lower price
Divide the total price by the total number of books from each printer to find the price per book:
Printer A: $350 / 100 books = $3.50 per book
Printer B: $150 / 40 books = $3.75
Printer A has the lowest price.
Final answer:
The question is a mathematics problem comparing the cost per book from two different printers. By calculating and comparing, we see that Printer A offers a lower price at $3.50 per book compared to Printer B's $3.75 per book.
Explanation:
The student is asking a math question related to finding the lower price between two options for purchasing books. To determine which printer offers the better deal, we need to calculate the cost per book for each printer.
Printer A: $350 per 100 books, which is $3.50 per book.
Printer B: $150 per 40 books, which equates to $3.75 per book.
By comparing the costs, we see that Printer A offers the lower price at $3.50 per book, while Printer B's price is higher at $3.75 per book. Therefore, Bennie Blinko should order from Printer A to get the best deal.
Layla and Carson work at the same store. Last week, Layla worked 8.75 hours, which was 25% of the amount of the time that Carson worked. How many hours did Carson work last week
Divide 8.75 by 35 and multiply the result by 100 to get 25 hours.
Someone please help!!!!!
I'm bad at math!!!
(5b - 9) - 3(8 - 2b)
Also, could you give me tips on how to solve these kind of problems?
Thanks.
- A Math Disaster
Evaluate (precalculus)
Answer:
Option 4 which is 1,430.
Step-by-step explanation:
Step 1
In this this step we will break up the terms in the summation symbol using the rules for manipulation summations.
[tex]\sum_{i=1}^{n}(aX^2_i+k)=\sum_{i=1}^{n}(aX)+\sum_{i=1}^{n}k\\\\\sum_{i=1}^{n}(aX^2_i+k)=a\sum_{i=1}^{n}X^2+nk.[/tex]
This means that for our case, the sum can be simplified to be,
[tex]\sum_{i=1}^{11}(3i^2_i-8)=3\sum_{i=1}^{11}i^2+11\times(-8)\\\\\sum_{i=1}^{11}(3i^2_i-8)=3\sum_{i=1}^{11}i^2-88[/tex]
Step 2
In this step we use the formula for the sum of the first n squares to evaluate the first part of the sum in step 2. The formula for the sum of the first n squares is,
[tex]\sum_{i=1}^{n}n^2=\frac{n(n+1)(2n+1)}{6} \\\\\implies\sum_{i=1}^{11}i^2=\frac{11(11+1)(2\times 11+1)}{6} =506[/tex]
Step 3
In this step we use the result from step 1 to evaluate the sum.[tex]3\sum_{i=1}^{11}i^2-88=3(506)-88=1,430.[/tex]
The correct answer is Option 4,which is 1,430.
Answer:
[tex]\boxed{\boxed{\sum_{i=1}^{11}(3i^2-8)=1430}}[/tex]
Step-by-step explanation:
The given expression is,
[tex]\sum_{i=1}^{11}(3i^2-8)[/tex]
[tex]=\sum_{i=1}^{11}(3i^2)-\sum_{i=1}^{11}(8)[/tex]
[tex]=3\sum_{i=1}^{11}(i^2)-\sum_{i=1}^{11}(8)[/tex]
we know that,
[tex]\sum_{i=1}^{n}i^2=\dfrac{n(n+1)(2n+1)}{6}[/tex] and
[tex]\sum_{i=1}^{n}c=cn,\text{ Where c is a constant}[/tex]
Hence,
[tex]3\sum_{i=1}^{11}(i^2)-\sum_{i=1}^{11}(8)=3\left(\dfrac{11(11+1)(2(11)+1)}{6}\right)-8(11)[/tex]
[tex]=3\left(\dfrac{11(12)(23)}{6}\right)-8(11)[/tex]
[tex]=3\left(506}\right)-8(11)[/tex]
[tex]=1518-88[/tex]
[tex]=1430[/tex]
plz help meeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
Your answer should be D.
Step-by-step explanation:
this is because the points being represented have a posotive slope that is up 3 over 1 so therefore you slope is 3
Answer:
D) y = 3x - 7
Explanation:
Just plug in the x values for x in the function, if you get the y number every time, then it is correct.
For example I did, (3 · 4) - 7 = 5 and (3 · 3) - 7 = 2 and so on, getting the y number every time. With the other functions, when you do this, you don't get the y number EVERY time.
I hope this helps!
Good luck on ur quiz!!
:)
the show the work for these problems
Answer:
Part A $150.00
Part B $140.00 because you would do 35 x 4 = 140.
Part C, He will have $17 left over. You would take 167 - 140 = 17
Question 5, The would have gathered $150 because you would take 30 x 5 = 150.
Will give lots of points/write a rule to describe each transformation
Step-by-step explanation:
What number(s)?
Jim earns $140 during the summer doing chores. He bought 2 sets of pens worth $25 each using his chore money. How much money was left after he bought the pen sets?
A.) $58
B.)$90
C.)$190
D.)$255
Answer:
B) $90!
I hope this helped :D
Answer:
90 is the answer
Step-by-step explanation:
90+50=140
140-50=90
Which of the following is an arithmetic sequence? -2, 4, -6, 8,...; -8, -6, -4, -2,...; 2, 4, 8, 16, ...
Answer: -8, -6, -4, -2
Step-by-step explanation:
This would be the ideal choice because an arithmetic sequence is something that progresses, and in this case, the correct answer choice increases by 2 each time.
Answer:
-8,-6,-4,-2 .... is Arithmetic series.
Step-by-step explanation:
Since common difference is 2 in the -8,-6,-4,-2....
or we can get next term on adding 2 in each term
so it is arithmetic series.
six less than the product of 13 and a number use the variable n to represent the unknown number
Answer:
13n - 6 is your correct answer
The written statement 'six less than the product of 13 and a number' is translated into the algebraic expression 13n - 6, where 'n' represents the unknown number.
The student is asking to translate a written statement into a mathematical expression using a variable. The statement is 'six less than the product of 13 and a number' and we are using the variable n to represent the unknown number. To form this expression, first consider the 'product of 13 and a number', which is written as 13n. Then, to represent 'six less than' this product, you would subtract 6 from it, resulting in the expression 13n - 6.
What is the coefficient of the fourth term in the expression? 5 − 10x + 15y − 20xy
A) −
B) 20
C) −20
D) −20xy
Answer:
C
Step-by-step explanation:
the coefficient of a term is the numeric value including the sign in front of the variable/ s
the fourth term in the expression is - 20xy
The coefficient of this term is - 20 → C
What is 341/1000 in words
List these fractions from least to greatest: 1/8, 3/16, 3/4
Candice recorded outdoor temperature of -5°C -1°c,and -2°C which following correctly compares the three temperature
-5°C < -2°C < -1°C
Look at the picture.
The soccer team collected $800 at a car wash fundraiser. They charged $5.00 for small vehicles and $10.00 for larger vehicles. The amount collected can be modeled by the equation , where x represents the number of small vehicles and y represents the number of larger vehicles. If the number of larger vehicles washed was 50, how many small vehicles were washed in total?
55
60
130
150
Answer:
60
Step-by-step explanation:
Which equation represents the following word sentence? The opposite of g times the quantity 2 plus 5.
Answer:
-g * (2+5)
Step-by-step explanation:
The opposite of g times the quantity 2 plus 5
Opposite means put a negative sign
times means multiply
Quantity means parenthesis
plus means addition
-g * (2+5)
The problem 'The opposite of g times the quantity 2 plus 5' translates into the mathematical equation -g*(2+5) or -g*7 in which g is multiplied by 7, and the result is negated.
Explanation:The word sentence 'The opposite of g times the quantity 2 plus 5' can be represented by the equation -g*(2+5) or -g*7, where * denotes multiplication, + denotes addition, and - denotes opposite or negation. Therefore, the interpretation of the sentence is 'multiply g by 7 and then take the opposite or negative of the result'. The use of parentheses ( ) in the equation ensures we first perform the addition within, according to the order of operations in math, most commonly known as BIDMAS/BODMAS or PEMDAS rules.
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PLEASE HELP
Which value represents the slope of a line perpendicular to the equation?
[tex]\text{Let}\ k:y=m_1x+b_!\ \text{and}\ y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\\text{We have}\ y=\dfrac{9}{11}-\dfrac{5}{4}x\to m_1=-\dfrac{5}{4}.\\\\m_2=-\dfrac{1}{-\frac{5}{4}}=-\left(\dfrac{4}{5}\right)=\dfrac{4}{5}\\\\Answer:\ \boxed{D.\ \dfrac{4}{5}}[/tex]
help thx so much for ur help
Answer:
$352.33
Step-by-step explanation:
100% Rep. $334.60
105% Rep. 334.60/100 * 105%
=$351.33
The number of fruit tarts that a baker makes each day is 40% of the total number of desserts she makes. On Monday, the baker makes 90 desserts total. What is the number of fruit tarts the baker makes on Monday?
Question 1 options:
36
50
54
225
Answer:
36 fruit tarts
Step-by-step explanation:
90 x .40 = 36 fruit tarts
Emma,brandy,and Damian will cut a rope that is 29.8 feet long into 3 jump ropes. Each of the 3 ropes will be the same length.Write a division sentence using compatible numbers to estimate the length of each rope
Answer:
30 ÷ 3 = 10 ft each
hope it helps :)))
Step-by-step explanation:
29.8 you can estimate it to 30
so you would divide 30 ÷ 3 = 10