Convert y = x2 - 4x + 1 to vertex form by completing the square.
O y= (- 1)2 + 4
O y= (1 - 2)2 +5
O y= (x - 2)2 – 3
O y = (x - 4) + 1
Answer:
vertex: (-2, -3)
Step-by-step explanation:
y = x2 + 4x + 1
y = x2 + 4x + 22 + 1 - 22
y = (x + 2)2 + 1 - 4
y = (x + 2)2 - 3 in y = (x - h)2 + k, (h, k) is the vertex.
Answer:
y = (x - 2)² - 3
Step-by-step explanation:
Given
y = x² - 4x + 1
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² - 4x
y = x² + 2(- 2)x + 4 - 4 + 1
= (x - 2)² - 3
Students was 1: 8. However, this year the ratio of the number of middle school students to the number of high school students changed to 2: 7. If there are 18 middle school students in the band this year, how many fewer high school students are in the band this year compared to last year? Expla
Answer:
Step-by-step explanation:
Last year
Ratio of the number of middle school students to number of high school students = 1 : 8
Total ratio = 9
Middle school = 1
High school = 8
Total students in the band = x
Middle school = 1/9x
High school = 8/9x
Total = 1/9x + 8/9x
This year
Ratio of the number of middle school students to number of high school students = 2 : 7
Total ratio = 9
Middle school = 2
High school = 7
Total students = x
Middle school = 2/9x
High school = 7/9x
Total = 2/9x + 7/9x
If there are 18 middle school students in the band this year
2/9x = 18
x = 18÷2/9
= 18 × 9/2
= 81
x = 81
Last year:
1/9x + 8/9x
= 1/9 * 81 + 8/9 * 81
= 9 + 72
= 81
This year
2/9x + 7/9x
2/9*81 + 7/9*81
= 18 + 63
=81
Change in middle school =this year - last year
= 18 - 9
= 9 (increase)
Change in high school = this year - last year
= 63 - 72
= -9 (decrease)
To encourage recycling many states require a $.70 deposit or drink containers the total deposit di you pay depends on the number of containers N You by the function D =0.07N could be used to describe the situation if you deposit $1.40 how many containers do you buy?
Answer:
20 containers
Step-by-step explanation:
Given:
D = 0.07N
Where,
D = Amount of deposits
N = Number of containers
If D = $1.40 find N
D = 0.07N
1.40 = 0.07N
Divide both sides by 0.07
N = 1.40 / 0.07
= 20
N = 20 containers
if you deposit $1.40, you will buy a total of 20 containers.
If the 16 boys in the classroom are 40% of the class how many students are there in the class
Answer:
56
Step-by-step explanation:
40+16=56
Answer:
40
Step-by-step explanation:
Set up the equation.
Let the full number of people in the classroom = x
(40%) x = 16 Change 40% to a fraction
(40/100) x = 16 Reduce 40/100 to a decimal
0.4 x = 16 Divide by 0.4
0.4/0.4 x = 16/0.4
x = 40
AT&T charges $350 to get a plan with them, plus $60 per month. T-Mobile charges a $275 initial fee, plus $80 per month. Write an equation or inequality that can be used to determine the number of months it would take for T-Mobile to cost the same or more than AT&T.
Given :
AT&T charges $350 to get a plan with them, plus $60 per month.
T-Mobile charges a $275 initial fee, plus $80 per month.
To Find :
Write an equation or inequality that can be used to determine the number of months it would take for T-Mobile to cost the same or more than AT&T.
Solution :
Money-time relation of plan AT&T :
[tex]M_1 = 60x + 350[/tex]
Money-time relation of plan T-Mobile :
[tex]M_2 = 80y + 275[/tex]
( Here, x and y are number of months )
Let, after t months would take for T-Mobile to cost the same or more than AT&T.
So, [tex]M_2\ge M_1[/tex]
[tex]80t+275 \ge 60t + 350\\\\20t \ge 350 - 275\\\\20t \ge 75\\\\t \ge 3.75[/tex]
Hence, this is the required solution.
2. Determine the amount of interest owed after 2 years on a $850 loan at 12.25% if no payments
are made. LTD
Enter your answer
The amount of interest is 208.74$
Here we have given
Amount (P)=850$
Interest (r)=12.25%
Time (t)=2 years
we have to calculate the simple interest
What is the formula for simple interest?
[tex]I=\frac{PRT}{100}[/tex]
Plug the given value in above formula
[tex]I=\frac{850*12.25*2}{100}[/tex]
Simplify above equation we get
[tex]I=\frac{850*12.25*2}{100}\\\\I=\frac{20874}{100}\\\\I=208.74[/tex]
Therefore the amount of interest is 208.74$
To learn more about the interest visit:
https://brainly.com/question/25793394
Write the linear equation in slope intercept form y-2=1/2(x+4)
Answer:
y = 1/2x + 4
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
m - slope
b - y-intercept
Step 1: Define
Point-slope form; y - 2 = 1/2(x + 4)
Step 2: Rewrite
Distribute 1/2 to both sides: y - 2 = 1/2x + 2Add 2 to both sides: y = 1/2x + 4Answer:
y=1/2x+4
Step-by-step explanation:
y-2=1/2(x+4)
(distribute the 1/2)
y-2=1/2x+2
(add 2 to both sides)
y=1/2x+4
There are (64)2 ⋅ 60 pigs on a farm. What is the total number of pigs on the farm?
Answer:
If the question is (64)2 x 60, then the answer is 7,200
Step-by-step explanation:
What is the value for y
When x=20
Y=-2x+8
Answer:
y = -32
Step-by-step explanation:
Y=-2x+8
Let x= 20
y = -2 * 20 +8
y = -40+8
= -32
Exercise 1. A truck has the capacity to transport up to 8 tons of a material at a time. If 104 tons of the material should be transported, how many trucks like this will be needed?
Answer:
how many trucks ?
Step-by-step explanation:
It is solved using the rule of three simple ones, where the number of trucks is for the quantity of material transported. We have that 1 is for 8 as X is for 104 (Look attached).
Multiplying cross, we have to:
8X = 104
X = 104/8
X= 13
8c + 20 = -180
c =
can some one help me please
Answer:
c = -25
Step-by-step explanation:
8c + 120 = -180
Subtract 20 from both sides.
8c = -200
Divide both sides by 8.
c = -25
Answer:
C = -25
Step-by-step explanation:
Start by getting C alone, subtract 20 from the left side of the equal sign and subtract 20 from the right. (what you do on one side you MUST do to the other) this gives you 8c= -200. Divide 8 from 8c on the right side and divide 8 from -200 on the left side. This will give you c= -25
Which of the following situations have a sum of zero? Select all that apply.
1. Shawna spends $20 on materials to make bracelets for her friends. She then earns $20 from selling the bracelets.
2. A diver dove down 20 1/4 feet under water and then descended 20 1/4 feet.
3. A golfer shot 2 over par (+2) on a hole. They then then shot 2 under par (−2) on the next hole.
4. You have $5.50 in your pocket and then you receive $5.50 for doing your chores.
Calculate the reciprocal of -0.013, correct to 1 decimal
Answer:
Step-by-step explanation:
-0.013 = [tex]\frac{-13}{1000}[/tex]
Reciprocal = [tex]\frac{-1000}{13} =-76.9[/tex]
A and \angle B∠B are supplementary angles. If m\angle A=(5x-19)^{\circ}∠A=(5x−19)
∘
and m\angle B=(2x+10)^{\circ}∠B=(2x+10)
∘
, then find the measure of \angle B∠B.
Answer: 52
Step-by-step explanation:
4x+8 = 5x-3 by the Vertical Angles Theorem that states the vertical angles are congruent.
Subtract 4x from both sides and get:
8=1x -3
Add 3 to both sides:
11= 1x
if x =11, plug that in to angle A.
4x+ 8 becomes 4(11)+8 =
44+ 8=
52
Please help!!!!
Carol's class has ninestudents on roll. newstudents join her class and the number of
students increases to 16. Which equation
represents Carol's class roster.
o 16 + X = -9
oX - 16 = 9
o 16X = 9
09 + X = 16
Answer:
9 + X = 16
Step-by-step explanation:
Given parameters:
Number of students on the roll = 9
Unknown:
The equation representing the class roster = ?
Solution:
Let the number of additional students that joined the class = x
Carol's class roster:
New number of students = number of students + additional students
16 = 9 + x
The solution of the problem is 9 + x = 16
14.) George is designing a pool that will be 34 feet long. He plans to make
a scale drawing of the pool by letting 1/4 inch represent 1 foot. How long
should the line representing the length of the pool in the diagram be?
Answer:
I believe the answer is 8.5 inches long
Step-by-step explanation:
we have to find out how long 1/4 × 34 is, since each 1/4 represents one of the 34 feet of the pools length.
34×.25 = 8.5
Substitute the given value for x into each equation to determine the value of y.
1. y = 3x + 6; x = -4
2.3.2 - 8y = 12; x = 4
3. y = -43; x = -2
Answer:
Y=-6
Y= -1.1
Y=-43
Step-by-step explanation:
Which equation represents a line that passes through (5, 1) and has a slope of 1/2?
y-5= 1/2(x-1)
y-1/2=5(x-1)
y-1=1/2(x-5)
y-1=5[x-1/2]
Step-by-step explanation:
Hey there!
The given point is (5,1) and slope is 1/2.
Let's use one point formula for finding the eqaution.
[tex](y - y1) = m(x - x1)[/tex]
Keep all values.
[tex](y - 1) = \frac{1}{2} (x - 5)[/tex]
This matches with Option C,
So, your answer is Option C.
Hope it helps...
8.
Which of the following is a negative
rational number that is not an integer?
А -pi
B -4.5
C -2
D 5 squared
PLEASE HELP WILL MARK BRAINLIEST FOR RIGHT ANSWER!!
Answer:
Population 2 pattern is that every year the population goes down by 2
Step-by-stepation:
plz help i dont know the answer
Answer:
Im not 100 percent sure but I think you have to do this
Step-by-step explanation:
Add all numbers together to find total students
Then add the students in Chemistry and Physics and both together
Then find what that number is in percent to the total students
Al saves pennies. He agreed to give 3/7 of his pennies to Bev if she would give 3/7 of what she got from Al to Carl and if Carl in turn would give 3/7 of what he got from Bev to Dani. Bev, Carl, and Dani agreed and Dani received pennies. How many pennies did Al have initially
Answer:
2744
Step-by-step explanation:
Let Al had x pennies initially.
Al agreed to give 3/7 of his pennies to Bev if she would give 3/7 of what she got from Al to Carl and if Carl in turn would give 3/7 of what he got from Bev to Dani.
So, as per the given condition,
The number of Pennies received by Ben from Al [tex]= \frac{3}{7} x[/tex]
The number of Pennies received by Carl from Bev
[tex]=\frac{3}{7} \times \frac{3}{7} x=\frac{9}{49}x[/tex]
The number of Pennies received by Dani from Carl
[tex]= \frac{3}{7}\times \frac{9}{49}x=\frac{27}{343} x[/tex]
Now, as Dani received 216 Pennies, so
[tex]\frac{27}{343} x =216[/tex]
[tex]\Rightarrow \frac{216\times 343}{27}=2744.[/tex]
Hence, initially, Al had 2744 Pennies.
Which is equal to 0.47?
CLEAR
SUBMIT
47
1,000
47
100
47
10
47
Answer: 47/100
Step-by-step explanation: 47/100 = 0.47.
bailey ran 0.674 times aound her school track. what percentage of the track did she run around?
f: 0.0674%
G: 6.74%
H:64.4%
j: 674%
Answer:
0.674 as a percent. 0.674 is equivalent to 67.4%.
Hope this helps!
Answer for brainliest.
Answer:
t > 28
Step-by-step explanation:
Given
[tex]\frac{t}{4}[/tex] > 7 ( multiply both sides by 4 to clear the fraction )
t > 28
Answer:
[tex]t>28[/tex]
Step-by-step explanation:
[tex]\frac{t}{4} >7\\[/tex]
Times both sides by 4
[tex]t>28[/tex]
Hope this helps and pls do mark me brainliest:)
determine the unit rate for each ratio.
The gas station charges $180 for 3 hours of work. How much
they charge for 1 hour of work?
Answer:
$60
Step-by-step explanation:
180/3 = 60
I hope this helps :)
Answer:60 per hour
Step-by-step explanation: you divide 180 by 3
Hummingbirds beat their wings very fast. The smaller the
hummingbird is, the faster its wings beat. The average hummingbird beats its
wings about 3 x 10 3 times a minute. How many times a minute is that, written as
a whole number?
Pls help me! I will give brainliest
Answer:
A hummingbird's heart beats from 225 times per minute when it's at rest and more than 1,200 times per minute when it is flying. Its wings beat about 70 times per second in regular flight and more than 200 times per second while diving.
Answer: A hummingbird's heart beats from 225 times per minute when it's at rest and more than 1,200 times per minute when it is flying. Its wings beat about 70 times per second in regular flight and more than 200 times per second while diving.
Step-by-step explanation:
3/4 change 3/4 to a decimal show work
Answer:
0.75
Step-by-step explanation:
You just need to convert 3/4 into a decimal.
For example: If you get 3 out of 4 problems right on a quiz, in percent form it will be a 75%, in decimal form 0.75 because you'll move the percent sign 2 spaces to the left. That will then be a decimal if you're converting 75% to 0.75.
3 divided by 4 is also going to give you 0.75. Because, a "fraction slash" is the dividing point. So,
3/4 = 0.75
a population of bears is decreasing the population this year is 200 bears after 1 year it is estimated that the population will be 160 bearsafter 2 years it is estimated that the population will be 128 bears what equation describes the bear population in any year x?
Answer:
200x-160
Step-by-step explanation:
This recipe makes 15 cupcakes.
Deepak only wants to make 12 cupcakes.
How much of each ingredient does he need?
Recipe: Makes 15 cupcakes
12 ounces butter
10 ounces sugar
15 ounces flour
5 eggs
I WILL GIVE BRAINLIEST TO THE BEST ANSWER IF ITS RIGHT