Answers
Answer:
[tex](-9.5,2.63)[/tex]
Step-by-step explanation:
In essence, this problem asks one to find the vertex of the given equation. An easy way to find the vertex of a quadratic equation in standard form is to complete the square.
Completeting the square involves grouping the quadratic and linear term, then factoring out the coefficient of the quadratic term. After doing so, one will add a term to make the grouped terms a perfect square trinomial and then balance the equation. Finally, one will simplify the equation and get the quadratic equation in vertex form. From there, finding vertex is quite easy, the x-coordinate is the additive inverse of the quadratic term, and the y-coordinate is the constant.
Once a quadratic equation in standard form has been converted to vertex form by the process of completing the square, its equation is amongst the lines of the following,
[tex]a(x-k)^2+h[/tex]
(k, h) is the vertex of the parabola.
The quadratic equation in standard form,
[tex]2x^2+19x+42.5[/tex]
Group the quadratic and linear terms,
[tex](2x^2+19x)+42.5[/tex]
Factor out the coefficient of the quadratic term,
[tex]2(x^2+9.5x)+42.5[/tex]
Add a term to make the grouped part a perfect square trinomial, then balance the equation,
[tex]2(x^2+9.5x+22.5625)+42.5-2(22.5625)[/tex]
Simplify,
[tex]2(x^2+9.5x+22.5626)+42.5-45.125[/tex]
[tex]2(x+9.5)^2+2.625[/tex]
The vertex of the equation is the following,
[tex](-9.5,2.625)[/tex]
Rounded,
[tex](-9.5,2.63)[/tex]
Related Questions
I need the correct answer please and thank you.
Answers
Answer:
1,156 I think that’s right
Step-by-step explanation:
Solve for x please help me
Answers
Answer:
4
Step-by-step explanation:
By intersecting chords theorem:
[tex]12x = 3(x + 12) \\ \\ 12x = 3x + 36 \\ \\ 12x - 3x = 36 \\ \\ 9x = 36 \\ \\ x = \frac{36}{9} \\ \\ x = 4[/tex]
Which representation shows y as a function of x?
Answers
Please help me hurry!! 8
Answers
Answer:
r = 7
Step-by-step explanation:
[tex]a =5\\\\a_{3}=245\\\\a_{n}=ar^{n-1}\\\\a_{3}= 5*r^{2} \\\\5*r^{2} = 245\\\\r^{2}=\frac{245}{5}\\\\r^{2}=49 = 7^{2}\\\\r = 7[/tex]
Explanation I just calculate it
1. A rubber ball consists of a sphere with 150 small cones protruding from the surface. The volume of the sphere is 50 cubic centimeters. Each cone has a radius of 0.2 centimeters and a height of 0.4 centimeters. What is the total volume of the ball? Round to the nearest hundredth.
A. 60.05 cm3
B. 2.51 cm3
C. 52.51 cm3
D. 50.02 cm3
2. A baker fills a piping bag with frosting to decorate a cake. The bag has the shape of a cone, and the frosting fills the bag to a height of 12 inches and diameter of 5 inches. Approximately what volume of frosting in cubic inches does the piping bag contain? Round to the nearest tenth.
A. 117.8 in3
B. 314.2 in3
C. 78.5 in3
D. 235.6 in3
3. A ski resort creates a three-dimensional model of its logo consisting of two cones. One of the cones has a radius of 6 feet and a height of 12 feet, and the other has a radius of 5 feet and is 23 the height of the first. What is the volume of the model? Round to the nearest hundredth.
A. 661.83 ft3
B. 496.37 ft3
C. 766.55 ft3
D. 1,985.49 ft3
Answers
Answer:
1. C. 52.51 cm3
2. C. 78.5 in3
3. A. 661.83 ft3
Step-by-step explanation:
just finished the quick check
Drag each tile to the correct box. Amanda, Derrick, and Todd attend the same high school. Each student works as the cashier one night a week at the school's concession stand. The number of items sold at the concession stand to the first 20 customers on three different nights is represented on the dot plots below. Find the interquartile range, IQR, for each dot plot. Then, place the students in order from greatest to least IQR.
Answers
Answer:
Amanda > Todd > Derrick
Step-by-step explanation:
Amanda's IQR- 3.5
Derrick's IQR- 2
Todd's IQR- 3
The solution is, ordering the IQR in descending order :
Emma, Sally, Olivia
What is IQR?The interquartile range (IQR) contains the second and third quartiles, or the middle half of your data set. Whereas the range gives you the spread of the whole data set, the interquartile range gives you the range of the middle half of a data set.
here, we have,
Writing out the points obtained from the dot plot, and applying the relevant formula, the Interquartile range of each dot plot is given below ;
Writing out each score on the dot plot to calculate the statistical values :
Emma's Scores:
6 , 7 , 8 , 8 , 9 , 9 , 9 , 10 , 10 , 11 , 11 , 11 , 11 , 11 , 12 , 13 , 13 , 13 , 13 , 14
Q1 = 1/4(n+1)th term
Q1 = (5th + 6th) terms
Q1 = (9 + 9) / 2 = 9
Q3 = 3/4(n+)th term
Q3 = (12 + 13) ÷ 2 = 12.5
IQR = Q3 - Q1
IQR = 12.5 - 9 = 3.5
Sally's Scores:
6 , 6 , 6 , 7 , 7 , 8 , 8 , 8 , 9 , 9 , 10 , 10 , 10 , 10 , 10 , 10 , 11 , 11 , 12 , 12 , 14
Q1 = 1/4(n+1)th term
Q1 = (7 + 8) ÷ 2 = 7.5
Q3 = 3/4(n+1)th term
Q3 = (10 + 11) ÷ 2 = 10.5
IQR = Q3 - Q1
IQR = 10.5 - 7.5 = 3
Olivia's Scores:
6 , 6 , 7 , 7 , 7 , 8 , 8 , 8 , 8 , 9 , 9 , 9 , 9 , 9 , 10 , 10 , 12 , 12 , 13 , 14
Q1 = 1/4(n+1)th term
Q1 = (7 + 8) ÷ 2 = 7.5
Q3 = 1/4(n+1)th term
Q3 = (10 + 10) ÷ 2 = 10
IQR = Q3 - Q1
IQR = 10 - 7.5 = 2.5
Therefore, ordering the IQR in descending order :
Emma, Sally, Olivia
Learn more on IQR :
brainly.com/question/18006476
#SPJ3
complete question:
Drag each tile to the correct box.
Emma, Sally, and Olivia play for the school basketball team. The dot plots show the number of points each of them scored in 20 games.
Find the interquartile range, IQR, for each dot plot. Then, place the basketball players in order from greatest to least IQR.
If the ratio of baseballs to golf balls is 2:3 and there are 30 baseballs in the box, how many golf balls are in the box
Answers
Answer:
45
Step-by-step explanation:
Ratio is 2 baseballs to 3 golf balls you have 30 baseballs.
2×15= 30
3x15= 45
Ira walked 20 miles last week and 22 miles this week. Raj walked 1/3 the distance that Ira walked. Write an expression for the distance Raj walked
Answers
Answer:
Multiply your pace by your distance; If your pace is 9.5 minutes per mile and you ran 3 miles: 9.5 min per mi × 3 mi = 28.5 minutes = 28 minutes, 30 seconds How to calculate running speed. Divide your run distance by your run time; If you ran 2.5 miles and you ran for 20 minutes
Step-by-step explanation:
What is the axis of symmetry for the quadratic equation 4x^2-16x+5 plz help
Answers
Answer:
x=2
Step-by-step explanation:
use completeting the square
[tex]4x^2-16x+5=4(x-2)^2-11[/tex]
please help me rn!! no links!
Answers
Answer:
D
Step-by-step explanation:
Clark is conducting and expermint in which he drains water form buckets. The buckets do not have the same amount of water. Bucket A loses water at the rate of 10 ml per minute. The table represents the water in bucket B. The graph represents the water in bucket C
Answers
Answer:
A - B - C
Step-by-step explanation:
I NEED HELP ASAP IM TRYING TO STUDY FOR MY STAAR TEST TOMORROW *NO LINKS ALLOWED*
Answers
Answer:
C
Step-by-step explanation:
equations for each:
A) y - x = 25
B) y = 25x
C) x = 25y
D) y = 25 + x
PLEASE ANSWER I NEED LOTS OF HELP!!!!!!!!!!!!!!
Answers
Answer:
40%
Step-by-step explanation:
Rachael liked 36/90 books movies that she watched. This simplifies to 2/5 which is 0.4. To find the percentage, we multiply 0.4 by 100 to get 40%.
Herbert has three lawn-mowing jobs. One lawn is shaped like a trapezoid,
one like a triangle, and one like a rectangle. The trapezoidal lawn has bases that are 90 feet and 126 feet and a height of 75 feet. The triangular lawn has a height of 80 feet and a base of 105 feet. The rectangular lawn has a length of 120 feet and width of 90 feet. If Herbert can cut a 160 ft × 70 ft lawn in 2 hours, how long will it take him to mow all three lawns?
Answers
Answer:
4.125 hours
Step-by-step explanation:
Trapezoid shaped lawn :
Bases : 90 ; 126 ; height = 90
Area of trapezium = 1/2(a+b) h ; a and B are the bases and h = height
Area of trapezium = 1/2(90 + 126) * 75
Area = 108 * 90 = 8100 feets
Triangular lawn :
Height = 80 feets ; Base = 105 feets
Area of triangle = 1/2 base * height
Area = 1/2 * 80 * 105 = 4200 feets
Rectangular lawn :
Length = 120 feets ; width = 90 feets
Area of rectangle = Length * width
Area = 120 * 90 = 10800 feet²
Area of all 3 lawns = (8100 + 4200 + 10800) = 23100
In 2 hours ; Herbert can now (160 * 70) = 11200 feets
23100 / 11200 = 2.0625
Tine required to mow all three lawns :
2 hours * 2.0625 = 4.125 hours
= 4 hours, 7 minutes, 30 seconds
2
Which point on this number line best represents 10?
point A
point B
point C point D
Answers
Answer:
probably 5 because thats half of 10 i guess
Step-by-step explanation:
don bought the bookshelf for 42 dollars this was 3/4 of the regular price
Answers
Answer:
Regular Price = $56
Step-by-step explanation:
3/4 x = 42
42/3 * 4 = x
14 * 4 = 56
x - 56
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
NEED HELP ASAP
there are 16 ounces in 1 pound. Juan is mailing a package that weighs 96 ounces. He wants to know the weights of the package in pounds
Answers
Answer:
Divide, 16.
Step-by-step explanation:
So, lets look at the unit scale.
For every 16 ounces, there are 1 pound.
To convert ounces to pounds, the number must be divide by 16, since there are 16 ounces in one pound.
The first fill in box answer is division.
Next we must ifnd the actual amount of pounds.
We know that the box weights 96 ounces.
Now lets divide this by ounces per pound, and see what we get:
96/16
=
6
So the box weighs 6 pounds.
This is the answer to the second fill in question.
Hope this helps!
Answer: MULTIPLY N AND 16 THE OTHER GUY IS WRONG
Step-by-step explanation:
DID IT ON I-READY
Mr chow is buying rolls of paper for the school. This is a lost of the suppliers, the size of their rolls, and their cost per roll. supplier x sells 25 meter rolls for 18.98, supplier y sells 30 meter rolls for 21.89, supplier z sells 40 meter rolls for 29.59 to the nearest cent what is the cost per meter for a roll of paper from the least expensive supplier
Answers
Answer:
0.73
Step-by-step explanation:
cost per meter for a roll of paper = total cost / total meter of rolls sold
Supplier x = 18.98 / 25 = 0.76
Supplier y = 21.89 / 30 = 0.73
supplier z = 29.59 / 40 = 0.74
the lowest per unit cost is 0.73
PLEASE HURRY!!!
NO LINKS OR FILES, JUST THE CORRECT ANSWER AND I WILL GIVE BRAINLIEST IF THERE ARE ANY LINKS I'LL REPORT YOUU
Answers
Answer:
so the 2 questions i see are surveys so... you have to answer them with truth on your own self
Step-by-step explanation:
Answer:
hi i am the person that you are talking to with all the comments give him brainliest
Step-by-step explanation:
The probability distribution for a
random variable x is given in the table.
-5
3
-2
0
2
3
Probability
.17
.13
33
(16
.10
Find the probability that xs-3
Answers
There are only two possible outcomes in the table that satisfy x ≤ -3; either x = -5 or x = -3. Then
P(x ≤ -3) = P(x = -5) + P(x = -3) = 0.17 + 0.13 = 0.3
PLS HELP ASAP
Function g is shown on the graph
Which function represents g
Answers
Answer:
Step-by-step explanation:
Can someone plz help me out with this I will really appreciate it no links plz
Answers
Answer:
B
Step-by-step explanation:
1) use a proportion to find how many students chose pizza
30 : 100 = x : 80
x = (80 x 30)/100 = 24
2) use a proportion to find how many students chose salad
10 : 100 = x : 80
x = (80 x 10)/100 = 8
3) solve the question
24 - 8 = 16
Answer:
12 STUDENTS CHOSE HAMBURGERS
24 STUDENTS CHOSE PIZZA
16 STUDENTS CHOSE SANDWHICHES
20 STUDENTS CHOSE HOT DOGS
8 STUDENTS CHOSE SALAD
24 = PIZZA
8 = SALAD
8 - 24 = 16 SO B
i dont know why everything i capitilized sorry haha
Step-by-step explanation:
Please help me with this
Answers
Answer:
128
Step-by-step explanation:
they are parralel
Answer:
the answer is 128 they are parallel
5) A real estate agent sells condominiums for $90,000 each. She earns 4% 6 points
commission. In May, she sold 9 condominiums. How much commission
does she make on each condominium?*
$86,400
$93,600
$32,400
$3,600
Answers
Isabelle and Brenda are selling bunches of tulips.
→ Each bunch has 7 tulips.
→ Isabelle sold 7 bunches.
→ Brenda sold 3 bunches
What is the total number of tulips the friends sold?
A. 21
B. 42
C. 49
D. 70
PLEASE HELP!!!
Answers
It’s asking the TOTAL- 7(7) = 49 + 7(3) =70 total tulips sold combined
Which is the expression 4 x 4 x4 x 3 x 3 x 2 x 2 x 2 x 2 written using
exponents?
Answers
A canister contains 12 ounces of flour. When the canister is full, it holds 6 times as much flour.
How many ounces of flour does the canister hold when it is full?
Answers
Answer:
72
Step-by-step explanation:
Answer:
72
Step-by-step explanation:
Given A canister = 12 ounces of flour. When full = 6 times more.
To find: How many ounces of flour does the canister hold when it is full?
Solution: With the given data, all that is needed to be done in order to find how many ounces can be held by the canister at its full potential, simply multiply the given data:
12 × 6 = 72
Hence, the canister can hold 72 ounces of flour when it is full.
What is -7 + 1/3?
Answers:
-7 1/3
-6 2/3
6 2/3
7 1/3
Answers
Answer:
-6 2/3
Step-by-step explanation:
Answer
- 6 2 / 3
Step-by-step explanation:
answer is - 6 2/ 3
Extend to find solutions that fit a second constraint in the formx *a, where inequality symbol and a is an integer. For example solve 3x + 4 >10, then find integers that satisfy bothx < 6 and 3x +4 >10.
Answers
Answer:
[tex]x = \{3,4,5\}[/tex]
Step-by-step explanation:
Given
[tex]3x + 4 > 10[/tex]
[tex]x < 6[/tex]
Required
Solve
We have:
[tex]3x + 4 > 10[/tex]
Collect like terms
[tex]3x > 10 - 4[/tex]
[tex]3x > 6[/tex]
Divide by 3
[tex]x > 2[/tex]
So, we have:
[tex]x > 2[/tex] and [tex]x < 6[/tex] i.e. between 2 and 6 (exclusive)
This implies that:
[tex]x = \{3,4,5\}[/tex]
Arun walked the 6 2/3 kilometre the first day, 5 5/6 kilometre the second day ,and 5 1/3 km the third day .how much did he walk in all ?
Answers
Answer:
17 5/6 is the answer.
Step-by-step explanation:
6+5+5=16 + 2/3+5/6+1/3
2/3=4/6
1/3=2/6
2+4+5=11/6=1 5/6
1 5/6+ 16=17 5/6
I did this stuff in like 4th grade