If the first term of an AP is 'a' and the common difference is 'd', then the sum of n terms of an AP is
[tex] \frac{n}{2} \times 2a + (n - 1)d[/tex]
How do i graph the quadratic function f (x)=-(x-3)(x+1)
Answers:
It's basically Inside, Outside, Outside, Inside. (I. O.O.I.)
Explanations:
Given
[tex]f(x)=-(x-3)(x+1)[/tex]
Distribute the (-1) to (x-3)
[tex]f(x)=(-x+3)(x+1)[/tex]
Now let's work the I. O. O. I.
Inside:
[tex](-x)(x)=-x^2[/tex]
Outside:
[tex](-x)(1)=-x[/tex]
Outside:
[tex](3)(x)=3x[/tex]
Inside:
[tex](3)(1)=3[/tex]
Add both the outsides (-x) and (3x) together
[tex]-x+3x=2x[/tex]
Your new equations is now.
[tex]f(x)=-x^2+2x-3[/tex]
The output or possible values you could get as a result from
an expression or equation.
Answer:
The Solution Set
Step-by-step explanation:
Despite missing some context, the output we could get as result of an expression/equation it is what we call a Solution set. A set which makes the initial statement of equation/expression true, therefore valid.
[tex]x^{2} -7x+12=0\\(x-3)(x-4)=0\\S=\{3,4\}[/tex]
Therefore, the elements of the Solution set, 3 and 4 when plugged into the equation make the statement of the quadratic equation true.
[tex](3)^{2}-7(3)+12=0\\-12+12=0\\0=0[/tex]
The output or possible values you could get as a result from an expression or equation is the solution set of the equation
Take for instance, we have the following equation
[tex]x^2 = 4[/tex]
When solved, the equation becomes
[tex]x = \pm 2[/tex]
This can be rewritten as:
[tex]x = \{-2,2\}[/tex]
This means that -2 and are the solution set of the equation [tex]x^2 = 4[/tex]
Hence, the output or possible values are called solution set
Read more about equations at:
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express 0.3°8° in form a/b where by b#0
Answer:
0.3° = 0.3π/180
8° = 2π/45
Multiplying both
0.3π/180×2π/45
3/10π/180 × 2π/45
You will get
π/300 × π/45
= π²/13500 where a = π² b= 13500
Hope this helps.
f(x) is a function true or false
Answer:
Depends on the x value
Step-by-step explanation:
f(x) can only be a function if the x values are not repeating.
36x^2-16 factored. please and thanks
Answer:
(6x+4)(6x-4)
Step-by-step explanation:
a^2 - b^2 = (a+b)(a-b).
sqrt of 36x^2 is 6x; sqrt of 16 is 4.
a = 6x, b = 4.
Answer:
[tex] (6x - 4)(6x + 4) \\ [/tex]
Step-by-step explanation:
[tex]36 {x}^{2} - 16 \\ {6}^{2} {x}^{2} - {4}^{2} \\ (6x - 4)(6x + 4)[/tex]
hope this helps you.
brainliest appreciated
good luck! have a nice day!
What is the quotient when (x + 2) is divided into the polynomial 2x2 - 2x - 12?
Answer:
2(x-3)
Step-by-step explanation:
2x² - 2x - 12= 2(x²-x+6)= 2(x²+2x- 3x+6)= 2(x-3)(x+2)
(2x² - 2x - 12)/(x+2)= 2(x-3)(x+2)/(x+2)= 2(x-3)What proportion results in the equation 9 m = 10 n?
Answer:
it might come from 9/n = 10/m
Answer:
9/m=10/n
Step-by-step explanation:
The radius of a circle is 7.1 cm. Find the circumference to the nearest tenth.
Answer:44.61?
Step-by-step explanation:
Pls help I need these points
Justin Launches a water balloon vertically from a platform on his roof height in feet is represented By the equation H = -16t^2+32t+48,where T is the time (in seconds) after he launch is the water balloon
What is the maximum height of the water balloon?
How long does it take to reach its maximum height?
Answer:
a) 64 feetb) 1 secStep-by-step explanation:
Given the height in feet represented by the equation H = -16t²+32t+48, at maximum height, the velocity of the water balloon is zero.
Velocity = dH/dt = 0
dH/dt = -32t+32 = 0
-32t+32 = 0
-32t = -32
t = -32/-32
t = 1sec
Substituting t = 1sec into the modeled equation of the height
H = -16t²+32t+48
H = -16(1)²+32(1)+48
H = -16+80
H = 64 feet
The maximum height of the water balloon is 64 feet
b) In order to know how long it takes to reach its maximum height, we will substitute H = 64 feet into the equation of the height.
64 = -16t²+32t+48
-16t²+32t = 16
16t²-32t+16 = 0
t²-2t+1 = 0
t²-t-t+1 = 0
t(t-1)-1(t-1) = 0
(t-1)² = 0
t-1 = 0
t = 1sec
It took the water balloon 1 sec to reach its maximum height.
Can someone plz help me solved this problem! I really need help ASAP! Will mark you as brainiest!
Answer:
a) k = 3 b) k = 4
Step-by-step explanation:
a) 3 x 7 = 21
b) 4 x 3 = 12
Answer:
1) k=3 (2) k=4
Step-by-step explanation:
[tex]21=k\cdot \:7\quad \\\mathrm{Switch\:sides}\\k\cdot \:7=21\\\frac{k\cdot \:7}{7}=\frac{21}{7}\\k=3\\2)\\12=k\cdot \:3\\Switch\:sides\\k\cdot \:3=12\\\frac{k\cdot \:3}{3}=\frac{12}{3}\\k=4[/tex]
if f(x) is 5x-4 and g(x) is 4x+1 then what is (f-g)(x)
Answer:
Step-by-step explanation:
5x - 4 - (4x + 1)
5x - 4 - 4x - 1
x - 5
Q1.work out the sum of the interior angles of a pentagon.
Q2.work out the size of one interior angle of a regular octagon.
Q3.work out the size of one exterior angle of a regular hexagon
Answer:
Question 1:
The sum of interior angles of a polygon can be found by the following formula:
(n-2) × 180
Where n is the no. of sides
A pentagon has 5 sides
So,
= (5-2) × 180
= (3) × 180
= 540 degrees
Question 2:
Since The sum of interior angles of a regular octagon is 1080 and the total interior angle are 8
So, Measure of interior angle = [tex]\frac{1080}{8}[/tex]
Measure of interior angle = 135 degrees
Question 3:
Since, one interior angle in a hexagon measures 120 degrees.
So,
The interior angle should be subtracted by 180 to get the exterior angle.
Exterior angle = 180-120
Exterior Angle = 60 degrees
Which of these is an example of a literal equation?
A. 12 = 9 + 3x
B. 6 + 30 = 62
C. ax - by = k
D. 3x - 4y
Richard's Rental Car charges a $55 rental fee and $0.25 per mile. Freddy's Rental Car charges a
$45 rental fee and $0.35 per mile. For how many miles, X, will the total charge of Richard's
Rental Car be no more than the total charge of Freddy's Rental Car?
2 < 10
> 10
> 100
2 < 100
Answer:
Correct option: third one -> X > 100
Step-by-step explanation:
The equation for the price of Richard's Rental Car is:
P1 = 55 + 0.25*X
The equation for the price of Freddy's Rental Car is:
P2 = 45 + 0.35*X
To find for how many miles will the total charge of Richard be less than Freddy, we have that P1 < P2, so:
55 + 0.25*X < 45 + 0.35*X
0.25*X - 0.35*X < 45 - 55
-0.1*X < -10
0.1*X > 10
X > 100
Correct option: third one
PLEASE HELP ASAP How many solutions does this system have? (photo below)
Answer: I got b., no solutions
Step-by-step
3x-5y=15
6x-10y-30x
times the top by-10 and the bottom by 10
-30x+50=-150
60x-50=300
crossing out the 50's cause they cancel out. also, subtract the others -30-60 giving -90x. and -150-300= -140
-90x=-450
divide -450 by -90
x=5.
Put 5x in either equation. Either one you do. it cancels out the answer in the equation. then you would subtract and get zero. divide and still get zero.
Sounds really confusing but hope it helps. Please give me a brainliest. Thanks :)
Prove that
(1 + cot A + tan A) (sin A - cos A) = sin A tan A - cot A cos A
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
tan A = [tex]\frac{sinA}{cosA}[/tex] , cot A = [tex]\frac{cosA}{sinA}[/tex]
Consider the left side
(1 + cotA + tanA)(sinA - cosA)
each term in the second factor is multiplied by each term in the first factor.
1(sinA - cosA) + cotA(sinA - cosA) + tanA(sinA - cosA)
= sinA - cosA + cosA - [tex]\frac{cos^2A}{sinA}[/tex] + [tex]\frac{sin^2A}{cosA}[/tex] - sinA ( collect like terms )
= [tex]\frac{sin^2A}{cosA}[/tex] - [tex]\frac{cos^2A}{sinA}[/tex]
= ( sinA × [tex]\frac{sinA}{cosA}[/tex] ) - ([tex]\frac{cosA}{sinA}[/tex] × cosA )
= sinAtanA - cotAcosA
= right side ⇒ proven
A baseball team won 9 games, which was 60% of the total number of games the team played. How many total games did the team play?
Answer: The team played 15 games total
Step-by-step explanation: 9 is 60 percent of 15.
Find the range of the graphed function
Answer:
-9 ≤ y ≤ 5
Step-by-step explanation:
The range is all the values of y. In this case, the values of y are any number in between -9 and 5. So -9 ≤ y ≤ 5.
Answer:
x ≥ 0
Step-by-step explanation:
I need help showing my work for the picture I've attached! I already have the answer as you can see below :)
Answer:
3x²y∛y
Step-by-step explanation:
∛27x⁶y⁴= ∛3³(x²)³y³y= 3x²y∛y
Which is equivalent to 3 square root of 8 1/4 x
Answer:
3
√
33
x
2
Step-by-step explanation:
Simplify
(Something is wrong with my keyboard hopefully you can put this together I'm sorry)
PLS HELP ASAP!!!
Figure RST is reflected about the x-axis and then translated down 1 unit to obtain figure R′S′T′:
A coordinate plane is shown. Triangle RST has vertices R at 4 comma negative 2, S at 7 comma negative 2, and T at 5 comma negative 5. Triangle R prime S prime T prime has vertices R prime at 4 comma 1, S prime at 7 comma 1, and T prime at 5 comma 4.
Which statement best describes the relationship between the two figures? (4 points)
Figure RST is congruent to figure R′S′T′.
Figure RST is bigger than figure R′S′T′.
The measure of angle R is equal to the measure of angle S′.
The measure of angle R is equal to the measure of angle T′.
A) Figure RST is congruent to figure R′S′T′.
Answer:
a
Step-by-step explanation:
What is the decimal multiplier to increase by 39%?
The decimal multiplier to increase by 39% is 1.39
A decimal multiplier is used when determining the percentage of a particular amount.
From the information given:
the decimal multiplier required to increase by 39% can be determined as follows:
[tex]\mathbf{=\dfrac{100}{100} + \dfrac{39}{100}}[/tex]
[tex]\mathbf{=1 +0.39}[/tex]
= 1.39
Learn more about decimals here:
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Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the area of land mowed in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points?
Answer:
Aaron;s rate for mowing lawns is 0.5 acres per hour."as1.5 acres / 3 hours = 0.5 acres an hour2.5 acres / 5 hours = 0.5 acres an hour Option (B)
Step-by-step explanation:Aaron;s rate for mowing lawns is 0.5 acres per hour."as1.5 acres / 3 hours = 0.5 acres an hour2.5 acres / 5 hours = 0.5 acres an hour
Write Successor of 999 please help me
Answer:
1000
Step-by-step explanation:
The successor of 999 is 1000
999+1=1000
SUCCESSOR
The number which comes immediately after a particular number is called its successor. The successor of a whole number is the number obtained by adding 1 to it. Clearly, the successor of 0 is 1; successor of 1 is 2; successor of 2 is 3 and so on.
what is the c value?
answer in x= form
7. A shopkeeper can buy 36 toys for $20.52. What will be
for 120 toys?
Answer:
$68.40
Step-by-step explanation:
Let x represent the required cost.
Since the number of toys is directly proportional to the cost:
x : $20.52 = 120 : 36
i.e. x/$20.52 = 120/36
x = ([tex]\frac{120 * $20.52}[/tex])/36
x = $2462.40/36
x = $68.40
Hope this helps!!!
What is the value of p?
Answer:
Step-by-step explanation:
Expand 3x(2 + 11x) please answer
Answer:
6x + 33x²
Step-by-step explanation:
3x × 2 = 6x
3x × 11x = 33x²
which law would you use to simplify the expression (p/q)^3
Answer:
Step-by-step explanation:
Can anybody help me solve for surface area?
(Formula=add all the areas of the faces)
Answer:
230.3cm^2
Step-by-step explanation:
surface area: sum of all faces
base: 12 x 2.5 = 30cm^2
back: 84 cm ^2
cross section x 2 = 7 x 2.5 = 17.5
use Pythagoras theorem to find the width of slope: 7^2 + 2.5^2 = 49 + 6.25 = 55.25. square root of 55.25 = 7.4
so, area of slope : 7.4 x 12 = 88.8cm^2
sum of all areas: 114 + 106.3 = 230.3
