Answer:
I don't understand the question. Write it again & briefly.
The standard form of a quadratic equation is given as y=ax^2+bx+c and vertex form is given as y=a(x−h)^2+k. Write a formula that relates the values of a,b, and c in y=ax^2+bx+c to the values of a,h, and k in y=a(x−h)^2+k. For instance, h=ax+b would be a formula that relates h to a and b.
Answers:
[tex]h = -\frac{b}{2a}\\\\k = \frac{-b^2+4ac}{4a}\\\\[/tex]
where 'a' cannot be zero.
=========================================================
Explanation:
The vertex is (h,k)
The x coordinate of the vertex is h which is found through this formula
[tex]x = -\frac{b}{2a}[/tex]
For example, if we had the quadratic [tex]y = 3x^2-6x+5[/tex], then we'll plug in a = 3 and b = -6 to get: [tex]h = -\frac{b}{2a} = -\frac{-6}{2*3} = 1[/tex]
------------
To find the value of k, we plug that h value into the original standard form of the quadratic and simplify.
[tex]y = ax^2+bx+c\\\\k = ah^2+bh+c\\\\k = a\left(\frac{-b}{2a}\right)^2+b\left(\frac{-b}{2a}\right)+c\\\\k = a*\frac{b^2}{4a^2}+\frac{-b^2}{2a}+c\\\\k = \frac{b^2}{4a}+\frac{-b^2}{2a}+c\\\\[/tex]
[tex]k = \frac{b^2}{4a}+\frac{-b^2}{2a}*\frac{2}{2}+c*\frac{4a}{4a}\\\\k = \frac{b^2}{4a}+\frac{-2b^2}{4a}+\frac{4ac}{4a}\\\\k = \frac{b^2-2b^2+4ac}{4a}\\\\k = \frac{-b^2+4ac}{4a}\\\\[/tex]
It's interesting how we end up with the numerator of [tex]-b^2+4ac[/tex] which is similar to [tex]b^2-4ac[/tex] found under the square root in the quadratic formula. There are other ways to express that formula above. We need [tex]a \ne 0[/tex] to avoid dividing by zero. The values of b and c are allowed to be zero.
Answer:
The minimum is at (1,-8). In the equation y = (x – 1)2 – 8, h = 1 and c = 8. So, the x-coordinate of the minimum is the same as the h-value in the equation, and the y-value of the minimum is the opposite of the c-value.
Step-by-step explanation:
plato
alex is running in a clockwise direction around a circular track with radius 60 yards. he runs for 20 minutes at a speed of 4 yards per second. find the shortest distance between their starting point and their ending point measured along the track
Answer:
100.9 yards
Step-by-step explanation:
One circuit of the track is a distance of ...
C = 2πr = 2π(60 yd) = 120π yd.
At Alex's running rate, the distance covered in 20 minutes is ...
(4 yd/s)(20 min)(60 s/min) = 4800 yd
The number of circuits will be ...
(4800 yd)/(120π yd/circuit) = 40/π circuits ≈ 12.7324 circuits
The last of Alex's laps is more than half-completed, so the shortest distance to his starting point is 13 -12.7324 = 0.2676 circuits,
That distance is (0.2676 circuits)×(120π yd/circuit) ≈ 100.88 yd
The shortest distance along the track to Alex's starting point is about 100.9 yards.
_____
Additional comment
The exact distance is 120(13π-40) yards. The distance will vary according to your approximation for pi. If you use 3.14, this is about 98.4 yards.
NAME THE PARTS OF THE CIRRCLR
a) Point O
b) [tex]\overline{OB}[/tex]
c) [tex]\overline{AB}[/tex]
4) arc DE (m)
5) [tex]\overline{DE}[/tex]
6) Semicircle AEB
Hanna has 88cm of ribbon and cuts it in the ratio 5 : 6. How much longer is the longest piece and the shortest piece?
Answer:
8 cm
Step-by-step explanation:
sum the parts of the ratio, 5 + 6 = 11 parts
Divide the length of ribbon by 11 to find the value of one part of the ratio
88 cm ÷ 11 = 8 cm ← value of 1 part of the ratio , then
5 parts = 5 × 8 cm = 40 cm
6 parts = 6 × 8 cm = 48 cm
Then difference between lengths is 48 cm - 40 cm = 8 cm
longer piece is 8 cm longer than shortest piece.
can you guys help me?
Answer:
Step-by-step explanation:
1. y = 2x
y = 2*4 = 8 Checks, therefore
y = 20 for x = 10
2. y = 3x
y = 3*(0.3) = 0.9 Checks, therefore:
y = 3*(1.5) = 4.5
y = 3*
3. y = 5/x
y = 5/(1/2) = 10 Checks, therefore:
3 = 5/x
x = 5/3
4 v = wu
7*3 = 21 Checks, therefore:
v = (3/4)*(6) = (18/4) = (9/2)
v = (2/3)wu
v = (2/3)*7*3 = 14 Checks
5 m = Kn/p [Add the K as a constant that will make m = Knp true at some value of K]
9 = K*2/(1/3)
27 = (K*2)
27 = 2K
K = (3/2)
m = (3/2) (n/p)
m = (3/2)*((1/2)/(1/3))
m = (3/2)*(3/2)
m = 1
Students in Mrs. Doyle's classes use 3/4 of a bottle of hand sanitizer every week. Which expression can be used to find how many bottles of hand sanitizer the students will use in 12 weeks?
12 x 3/4
12 + 3/4
12 - 3/4
12 divided by 3/4
Answer:
A. 12 x 3/4
Step-by-step explanation:
Answer:
12 x 3/4
Step-by-step explanation:
Every one week, there is 3/4 used, which is basic multiplication
My Science teacher is named Mrs. Doyle, lol
Koala Airlines carries an average of 272 passengers on its Dallas-Perth flight. It runs 620 such flights each year. How many passengers does it carry on those flights each year?
Answer:
272×620=168,640
Step-by-step explanation:
If koala airlines carries 272 in average then the answer is 168,640
Write 5.4 as a mixed number and as an improper fraction.
Write your answers in simplest form.
Answer:
5.4 as a fraction is 27/5.
Step-by-step explanation:
Learned in 5th grade
need help with this pls
Answer:
Hence y = (5k -3)/ (1 - k)
.... shown
what is the slope of the line 3x-4y=73x4y=7?
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
y = mx + b , "m" is slope and "b" is y-intercept
~~~~~~~~~~~~~
3x - 4y = 7
- 4y = - 3x + 7
y = [tex]\frac{3}{4}[/tex] x - [tex]\frac{7}{4}[/tex] ⇒ m = [tex]\frac{3}{4}[/tex]
Which 2 expressions are equiavalent to -40/9
Answer:
360 is the answer
Step-by-step explanation:
hi
have a good day
hope it helps you
thank me later
carryonlearing
Answer:
Step-by-step explanation: 2\frac{u^2}{8}u^4=10\frac{u^3}{9}u
Please help question in pic
Answer:
7,3
Step-by-step explanation:
for every 5 it goes right it goes 4 up. 2,1+5,4=7,3
Please answer this question Step by Step method.
If it is correct you will get a thank you and 5 stars from me.
Answer:
see explanation
Step-by-step explanation:
The perimeter P is the sum of the 4 sides of the rectangle.
The opposite sides of the rectangle are congruent , then
P = 2x + 1 + 2x + 1 + x + x ← collect like terms
P = 6x + 2
PLEASE HELP. I NEEED THIS BY TOMORROW
PLS HELP ASAP ILL GIVE BRAINLKEST THANKS
Answer:
y = 4/7x
Step-by-step explanation:
(0,0)
(7,4)
up 4 right 7
4/7
y = 4/7x
Answer:
y = 4/7 x
Step-by-step explanation:
using rise/run = slope
rise = 4
run= 7
4/7 = slope
On a coordinate plane, a line is drawn from point A to point B. Point A is at (negative 4, 8) and point B is at (2, negative 4). What are the x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10? Round to the nearest tenth, if necessary. X = y =.
The x and y coordinates of point C are -2.6 and 5.2, respectively
The coordinate of the points are given as:
[tex]A = (-4,8)[/tex]
[tex]B =(2,-4)[/tex]
The ratio is given as:
[tex]m :n = 3 : 10[/tex]
The point at the given ratio is calculated as:
[tex]C = (\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex]
So, we have:
[tex]C = (\frac{3 \times 2 + 10 \times -4}{3+10},\frac{3 \times -4 +10 \times 8}{3+10})[/tex]
Simplify
[tex]C = (\frac{-34}{13},\frac{68}{13})[/tex]
[tex]C = (-2.6,5.2)[/tex]
Hence, the x and y coordinates of point C are -2.6 and 5.2, respectively
Read more about line ratios at:
https://brainly.com/question/11764811
Answer:
a
Step-by-step explanation:
Plz help me! 25 POINTS!
Answer:
g(x) = 24(2^(x-1)) +16
Step-by-step explanation:
A function is stretched vertically by a factor of 'a' by multiplying by 'a'.
g(x) = 4·f(x) = 4(6(2^(x-1) +4)
g(x) = 24(2^(x-1)) +16
5x-6>1+2(4x+1)
I need answers now please and an explanation
NO BOTS I HAVE NO TIME FOR THEM
Answer:
-3
Step-by-step explanation:
I just need 20 characters to help out so yeah
Prove the following
Step-by-step explanation:
Start by multiplying both sides by cosα:
1 + sinα + (cos²α)/(1+sinα) = 2
sinα + (cos²α)/(1+sinα) = 1
Now multiply both sides by 1+sinα:
sinα + sin²α + cos²α = 1 + sinα
sin²α + cos²α = 1 Q.E.D.
Thats the answer and method i used
The coach for a basketball team wants to buy new shoes for her 12 players.
Super Sports is offering a 20\% discount on each pair of shoes, which were originally priced $72.50. A 6.5\% sales tax will be applied to the discounted price.
The same shoes are also available on Double Dribble's web site for $54.75. A 9\% processing fee will be applied to the cost of the shoes, plus a shipping fee of $5.99 for each pair.
What is the difference in the total costs of the 12 pairs of shoes between the two stores?
(please show ur work)
Answer:
$46.8
Step-by-step explanation:
Price for Super Sports:
$72.5*0.8=$58 (20% discount so price is 80% of original price)
$58+$58*0.065=$61.77 (6.5% sales tax added after discounted price)
$61.77*12=$741.24
Price for Double Dribble:
$54.75+$54.75*0.09=$59.6775≈$59.68 (9% processing fee added to cost; round to 2 decimal places)
$59.68+$5.99=$65.67 (shipping fee)
$65.67*12=$788.04
Difference in price:
$788.04-$741.24=$46.8
If you have questions please ask in the comments; also please give this answer brainliest if you found it useful!
given:f(x)=3x-5,find f(x+2)
ans=3x+1
Step by step solution
=3(x+2)-5
=3x+6-5
=3x+1
Which number line shows the estimate of V47 in the correct interval of integers?
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
Answer:
B (the second number line)
Step-by-step explanation:
[tex]\sqrt{49}[/tex] = 7, so [tex]\sqrt{47}[/tex] would be close to 7
A stairway handrail has a rise of 12 feet and a run of 24 feet. What is the slope of the handrail?
Answer:
1/2
Step-by-step explanation:
12 / 24 = 1/2
Answer:
12/24
Step-by-step explanation:
use the stander rise over run since the rise is 12 it goes over the run which is 24
i really need your help on this
Answer:
That is an improper fraction
Step-by-step explanation:
When the numerator (the top) is greater than the denominator (The bottom) then the fraction is improper
Hope this helps!
Answer:
Improper fraction
Step-by-step explanation:
Easy question, Worth 80 points, PLEASE HELP!! What are the angles and the side measurements for this triangle?
Answer:
the angles are 89.2°, 34.5°, 56.3° and the sides are √26units, √8units, √18units respectively
Step-by-step explanation:
Distance between points (2,5) and (-1,2)
Using the formula, √(X2 - X1)² + (Y2 - Y1)²
= √(-1-2)²+(2-5)²
=√(-3)²+(-3)²
=√9+9
=√18 or 3√2
Distance between points (-1,2) and (4,3)
=√[4-(-1)]²+(3-2)²
= √5²+1²
=√25+1
=√26
Distance between points (2,5) and (4,3)
=√(4-2)²+(3-5)²
=√2²+(-2)²
=√4+4
=√8
Using Cosine rule/formula, C²= A²+B²-2abcosc
Let C be √18, A be √26 and B be √8
√18²=√26²+√8² - 2√26.√8cosc
18= 26+8 - 2√208cosc
18= 34 -2√208cosc
2√208cosc= 34-18
Cosc = 16/2√208
Cosc= 0.5546
c= Cos`¹(0.5547)
c= 56.3°
Using sine rule/formula
Sinc/C= Sina/A=Sinb/B
Sin56.3/√18= Sina/√26
Sina= (0.8320 × √26)/ √18
Sina= 0.9999
a= Sin`¹(0.9999)
a= 89.2
56.3+89.2+b= 180°( sum of angles in a triangle)
145.5 + b =180
b=180-145.5
b= 34.5
In science class, the girl to boy ratio is 3 to 7.
If there are 50 students total in the class, how many are boys?
Answer:
There are 35 boys in the class.
Step-by-step explanation:
Girls to Boys ratio = 3:7
Total number of students in class = 50
Let total number of girls be '3x' and total number of boys be '7x'
Total number of girls + Total number of boys = Total number of students
3x + 7x = 50
10x = 50
x = 50/10
x = 5
[tex] \therefore [/tex]
Total number of girls = 3 × 5 = 15
Total number of boys = 7 × 5 = 35
(1)Pradnya had 5 dozen copies. She gave half of the copies to Anushka and 1/5 times of the copies to Prajwal. How many copies are remaining with her ?
(2) Shrikant bought a watch at Rs. 900. He gave equal number of notes of denomination Rs. 10, Rs. 20, Rs. 50 and Rs. 100. Find the number of notes of Rs. 20 that he gave to the shopkeeper.
(3) Mangalakaku purchased 6016 saplings of lemon. She planted 47 saplings in each row. How many rows will be formed of those saplings?
Explanation:
(i)Total number of copies are at Pradnya = 5 dozen
We know that 1 dozen = 12
⇛5×12 = 60
Given copies to Anushka = half of 60
⇛60/2 = 30 copies
Given copies to Prajwala = 1/5 the copies
⇛ (1/5)×60
⇛60/5
⇛12 copies
Total number of given copies = 30+12 = 42
Remaining copies = 60-42 = 18
Answer: Remaining copies = 18
(ii)Let the number of Rs. 10 notes be X
So given that
all are equal in number
So, Number of Rs 20 notes = Number of Rs. 50 notes = Number of Rs. 100 = X
Total number of notes
= X+X+X+X = 4X
Value of Rs. 10 = 10X
Value of Rs. 20 = 20X
Value of Rs. 50 = 50X
Value of Rs. 100 = 100X
Total amount = Rs. 900
⇛10X +20X +50X+100X = 900
⇛180X = 900
⇛X = 900/180
⇛X = 5
Number of Rs. 10 notes = Number of Rs. 20 notes = Answer: number of Rs. 50 notes = Number of Rs. 100 = 5
(iii) Let the number of rows be X
Number of saplings per each row = 47
Total number of saplings of X rows = 47X
According to the given problem,
Total number of saplings purchased by Mangalakaku = 6016
⇛47X = 6016
⇛X = 6016/47
⇛X = 128
Answer: Total number of rows = 128
Put the numbers in order from least to greatest.
39% , 0.42 , 11/25
Answer:
39%, 0.42, 11/25
Step-by-step explanation:
First, let's convert the percentage and the fraction into decimals, to make out lives so much easier.
39% = 0.39
11/25 = 0.44
Now, we reorder.
0.39, 0.42, 0.44
Finally, we convert the percentage and the fraction back into their original forms, and adjust the order.
39%, 0.42, 11/25
-hope it helps
how do i do this?? i really need help !!
Answer:
angles: 150°, 108°, 90°, 12°
Step-by-step explanation:
The size of each sector of a pie chart is proportional to the size of the data item being represented. Here, the total of all frequency numbers is ...
25 +18 +15 +2 = 60
These 60 are represented in the chart by 360°, so each unit of frequency is represented by 360°/60 = 6°.
The 25 destinations in France are represented by a sector that is ...
25 × 6° = 150°
The 18 destinations in Spain are represented by a sector that is ...
18 × 6° = 108°
The 15 destinations in Greece are represented by a sector that is ...
15 × 6° = 90°
The remaining (Other) destinations are represented by the remaining part of the circle:
2 × 6° = 12°
You can draw the sector dividers in the circle using a protractor or geometry application, or you can let a spreadsheet draw the entire pie chart for you.
__
The attachment is roughly what the finished product would look like. We have included the angle measures, so you can see what they are. Ordinarily, those would not be present. The labels might include data values or percentages, as you may decide. The purpose is to communicate, so you need to figure what message you want the chart to communicate, and label it appropriately.
Answer:
angles: 150°, 108°, 90°, 12°
Step-by-step explanation:
The size of each sector of a pie chart is proportional to the size of the data item being represented. Here, the total of all frequency numbers is ...
25 +18 +15+2 = 60
These 60 are represented in the chart by 360°, so each unit of frequency is represented by 360` = 6°.
The 25 destinations in France are represented by a sector that is ...
25 x 6° = 150°
The 18 destinations in Spain are represented by a sector that is ...
18 x 6° = 108°
The 15 destinations in Greece are represented by a sector that is ...
15 x 6° = 90°
The remaining (Other) destinations are represented by the remaining part of the circle:
2 x 6° = 12°
You can draw the sector dividers in the circle using a protractor or geometry application, or you can let a spreadsheet draw the entire pie chart for you.
The attachment is roughly what the finished product would look like. We have included the angle measures, so you can see what they are. Ordinarily, those would not be present. The labels might include data values or percentages, as you may decide. The purpose is to communicate, so you need to figure what message you want the chart to communicate, and label it appropriately.
12>-2(y-4) solve the inequality
[tex]12>-2(y-4)\\\\\implies -\dfrac{12}2 <y-4~~~;[\text{Dividing by a negative number, so reverse the inequality.}]\\\\\implies -6<y-4\\\\\implies -6+4<y\\\\\implies -2<y\\\\\implies y>-2\\\\\text{Interval,}~ (-2,\infty)[/tex]