a) Show that x² - 8x + 20 can be written in the form (x - a)² + a where a is an integer.
b) Hence explain how you know that x² - 8x + 20 is always positive.
I have worked out the first bit of the question and the answer is:
x²-8x+20
x²-8x+16-16+20
(x-4)²+4
(x-a)²+a
a= 4
I just need help with part b and I'm struggling to do it. Please help.
Answer:
Step-by-step explanation:
b) x^2 - 8x + 20 is always positive because in part a, you figured out that it could also be written as (x-4)^2 + 4.
You know that (x-4)^2 is greater than or equal to 0 so by adding 4, the result will always be positive
An object has an acceleration of 12.0 m/s/s. If the mass of this object were tripled (with no change in its net force), then its new acceleration would be m/s/s.?
Answer:
ummm
Step-by-step explanation:
I believe it's A2=8m/s^-2
plz help itz a hard question
Answer:
Lol, that is easy.
Step-by-step explanation:
PLZ HURRY IT'S URGENT!!!
The USC basketball team scored over 100 points in its last game. Some baskets, x, were worth 2 points and other baskets, y, were worth 3 points. Write an inequality to represent the score.
options:
2x+3y 100
2x+3y≤100
2. For the inequality y
options:
True
False
Answer:
its 2x+3y>100
Step-by-step explanation:
BTW the greater than sign is greater than or equal to I just cant input that sign so make sure the sign is > with a line underneath it.
helpppppp pleaseeeee
Answer:
A: 24
B: 40.04
Step-by-step explanation:
A=L*W
8*3=24
5.2*7.7=40.04
rearrange the following numbers in order from greatest (top)to least (bottom) -1, 2, -2,-4
Answer:
2,-1,-2,-4
Step-by-step explanation:
5+3*3x-2 let x=2 i need help please
Answer:
21
Step-by-step explanation:
a shark begin at 172 M below sea level and then swim up hunting 37 meters where is the Sharks location now in relation to sea level
Answer:
135 meters
Step-by-step explanation:
172 minus 37 equals 135
Is m || n? Which theorem (which tool) did you use to decide?
Answer:
Yes. m is parallel to n. Since the 2 angles labelled are equal, by alternate angles rule, m is parallel to n.
Step-by-step explanation:
This is a question on angles. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)
Answer:
yes
Step-by-step explanation:
Yes m is parallel to n because the alternate interior angles are equal .
The height (in feet) of a certain rocket t seconds after it leaves the ground is modeled by
h(t) = - 16t^2 + 48t. What is the shortest time it takes the rocket to reach a height of 35feet. Be
sure to include units. Round to the hundredths place.
Answer:
The answer is 1/2 second
Step-by-step explanation:
Hope this helps
The ratio of pizza to nachos sold during A-lunch is 4 to 3. There was 48 nachos sold. What number of pizzas sold during A-lunch?
Answer:
64 pizzas
Step-by-step explanation:
4:3 * x:48
x resembles the amount of pizzas sold,
what times 3 = 48?
x=16
4 * 16 is 64
64 pizzas were sold
* Let me know if you have any questions*
9. Alan invests £425 in a savings account paying 4.14% compound interest.
a. How much will his investment be worth after three years?
b. Express the amount paid as a percentage of the amount invested
Find the missing fraction that would make each equation true. Explain how you got the answer.
*Please check if the ones I did are right
Answer:
1 1/6
Step-by-step explanation:
Solve using standard algorithm 12.2 * 4.
Answer and Step-by-step explanation:
12.2
* 4
____
48.8
4 times 2 is 8.
4 times 2 is 8.
4 times 1 is 4.
Remember to place the decimal.
#teamtrees #WAP (Water And Plant)
Answer:
48.8
Step-by-step explanation:
help help helpe help !!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Yes it is a right triangle
Step-by-step explanation:
Brainliest pls
Jamie recorded vehicle turning choices at the intersection near his house. He organized the results in the table shown.
Based on Jamie’s results, what is the probability of a vehicle turning versus continuing straight?
Answer:
There is no table or picture and nice Uzumaki clan picture.
I know this question so here
It is less likely the vehicle will turn left asgoing straight
Step-by-step explanation:
plz mark brainliest
Please help it due today at 11:59pm 6 minutes left plz help me anybody plz
Answer:
b=0
Step-by-step explanation:
Please help I will brainliest!! Really urgent!!
and tell you me how you go it, not just the answer please!❤️
For the terms and like terms just put:
T:
LT:
Answer:
T: x^2 & 3 LT: -x & -3x
Step-by-step explanation:
x^2 has no other like term like: -x^2, 8x^2 or basically no longer "x^2"
3 is the same ^ there is no other single integer
(We cannot use -3x because it has an x attached to it)
-x & -3x are like terms because they both have an x to it a single x, not a x with an exponent like x^2
so -x + (-3x) would equal -4x if we wanted to solve it
Answer:
Terms: 3, (-x), x², (-3x)
Like terms: (-x) and (-3x)
Step-by-step explanation:
A term is a single number (positive or negative), a single variable (a letter), or several variables multiplied but not added or subtracted.
Like terms are terms that have the same variables and power like -x.
Which description describes the transformation from y= x to y=x +3
Shift up 3
Shift left 3
Shift right 3
Shift down 3
Answer:
three units to the right
In a group of 50 children, 11 cannot swim. What percentage can swim?
Answer:
78% of the children can swim
Step-by-step explanation:
There are 50 children, 11 of them cannot swim. The fraction of children that cannot swim is 11/50. We have to change that into a percentage.
11/50 x 2 will equal our percentage
11 x 2 = 22
50 x 2 = 100
22/100 or 22%
We have the percentage of the children who cannot swim, now we have to find the percentage of children who can swim.
100% - 22% = 78%
I Hope That This Helps! :)
Input in standard form the equation of the given line. The line that passes through (-3, 5) and (-2, -6)
Answer:
The equation in standard form is 11x + y = -28.
Step-by-step explanation:
Let's start with y = mx + b
5 = -3m + b
-6 = -2m + b
Let's take the second less the first.
m = -11
Plug back in the first equation to calculate b.
5 = 33 + b
b = -28
So y = -11x - 28
11x + y = -28
Let L1 be the line through the origin and the point (6, 0, −1). Let L2 be the line through the points (1, −1, 1) and (7, 1, 7). Find the distance between L1 and L2.
Answer:
6
Step-by-step explanation:
Determine if the following system of equations has no solutions, infinitely many
solutions or exactly one solution.
- 2x + 3y = 7
- 4x + 9y = 27
the number if baskets nikki can make varies directy with the time she spends making the baskets she can make 4 baskets in 1/2 an hour how many baskets can nikki make in 5 hours
Answer:
40 baskets
Step-by-step explanation:
Find out how many baskets she can make in an hour. Since she makes 4 in 1/2 an hour, multiply 4 by 2 to find out how much she makes in an hour. She makes 8 baskets an hour, so multiply 8 by 5. 8 x 5 = 40.
Answer:
40 Baskets
Step-by-step explanation:
4 x half an hour = 8 baskets an hour. 8 x 5 = 40
Solve.
Question in a triangle, the measure of the first angle is four times the measure of the second
angle. The measure of the third angle is 78° more than the second angle. What is the
measure of the first angle?
17°
95°
68°
43°
< Previous
Next >
No new data to save last checked at 10:16 nm
Answer:
The first angle is 68.
Step-by-step explanation:
[tex]x_{1}+x_{2}+x_{3}=180\\x_{1} = 4*x_{2}\\x_{3}=x_{2}+ 78\\4*x_{2} + x_{2} + x_{2}+ 78 = 180\\6*x_{2}=102\\x_{2} = 17\\[/tex]
So [tex]x_{1}=68[/tex] and [tex]x_{3}=95[/tex]
in how many distinct ways can the letters in philosophy be arranged
Answer:
3 Letters Word: 6 Distinct Ways: 4 Letters Word: 24 Distinct Ways: 5 Letters Word: 120 Distinct Ways: 6 Letters Word: 720 Distinct Ways: 7 Letters Word: 5,040 Distinct Ways: 8 Letters Word: 40,320 Distinct Ways: 9 Letters Word: 362,880 Distinct Ways: 10 Letters Word: 3,628,800 Distinct Ways
Step-by-step explanation:
The number of ways in which the word 'PHILOSOPHY' can be arranged is 453,600.
What is a factorial?The product of a whole number 'n' with every whole number until 1 is called the factorial. The factorial of 4 is, for example, 43221, which equals 24.
As we can see that the word 'PHILOSOPHY' has 10 letters therefore, the letters of the word can be arranged in the 10! manner, but it contains the letter P, H and O twice therefore, there will be words that will look the same and are counted twice. Thus, the number of ways the word PHILOSOPHY can be arranged are,
[tex]\text{Number of ways} = \dfrac{10!}{2! \times 2! \times 2!} = 453,600[/tex]
Hence, the number of ways in which the word 'PHILOSOPHY' can be arranged is 453,600.
Learn more about Factorial:
https://brainly.com/question/16674303
Carmen is designing an intersection of the rail line and four streets. She wants to know which streets are parallel.
Transversal t crosses lines c, d, e, f forming 16 angles. Clockwise from top left, the angles formed with line c are blank, blank, blank, 114 degrees; with line d are blank, blank, 68 degrees, blank; with line e are blank, 112 degrees, blank, blank; with line f are blank, blank, 66 degrees, blank.
Which streets are parallel? Check all that apply.
c || d
c || e
c || f
d || e
d || f
e || f
Answer:
c || f d || e
step-by-step explanation:
Answer:
C and D
or
c || f
d || e
Hope this Helps!
9
What is the range of the numbers?
12,
27, 34, 9, 29, 28, 9
OA.
23
OB. 24
OC.
25
D. 28
Answer:
it is c
Step-by-step explanation:
tje biggest is 34-9 which is smallest and get 25
-8k + 6 = -10k + 10 SOMEONE HELP QUICKKKK
Answer:
k = 2
Step-by-step explanation:
-8k + 6 = -10k + 10
-8k = -10k +4
2k = +4
2k / 2 = 4 / 2
k = 2
Does anyone know the answer to this?
Answer:
by Alternate Intererior Angles Theorem
Step-by-step explanation:
1. Line L || Line M
1. Given
2. ∠4≅∠6
2. Alternate Interior Angles Theorem