the equation 3x^2-6x=8 is rewritten in a form of 3(x-p)^2+q=0.
Answer:
[tex]3(x - 1)^2 - 11= 0[/tex]
Step-by-step explanation:
Given
[tex]3x^2 - 6x = 8[/tex]
Required
Rewrite in form of [tex]3(x - p)^2 + q = 0[/tex]
[tex]3x^2 - 6x = 8[/tex]
Subtract 8 from both sides
[tex]3x^2 - 6x - 8 = 8 - 8[/tex]
[tex]3x^2 - 6x - 8 = 0[/tex]
Express -8 as 3 - 11;
So, we have:
[tex]3x^2 - 6x + 3 - 11= 0[/tex]
Expand [tex]3x^2 - 6x + 3[/tex]
[tex]3(x^2 - 2x + 1) - 11= 0[/tex]
Factorize the expression in the bracket;
[tex]3(x^2 - x -x + 1) - 11= 0[/tex]
[tex]3(x(x - 1) -1(x - 1)) - 11= 0[/tex]
[tex]3((x - 1)^2) - 11= 0[/tex]
[tex]3(x - 1)^2 - 11= 0[/tex]
By comparison: [tex]3(x - p)^2 + q = 0[/tex]
[tex]p= 1[/tex]
[tex]q = -11[/tex]
A 20 gallon tank is full. How many gallons are in the tank?
Answer:
20???
Step-by-step explanation:
what is 200 digits of pi
Answer:
3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000568127145263560827 785771342757789609173637178721468440901224953430146549585371050792279689258923 542019956112129021960864034418159813629774771309960518707211349999998372978049 951059731732816096318595024459455346908302642522308253344685035261931188171010 003137838752886587533208381420617177669147303598253490428755468731159562863882 353787593751957781857780532171226806613001927876611195909216420198938095257201 065485863278865936153381827968230301952035301852968995773622599413891249721775 283479131515574857242454150695950829533116861727855889075098381754637464939319 255060400927701671139009848824012858361603563707660104710181942955596198946767 837449448255379774726847104047534646208046684259069491293313677028989152104752 162056966024058038150193511253382430035587640247496473263914199272604269922796 782354781636009341721641219924586315030286182974555706749838505494588586926995 690927210797509302955321165344987202755960236480665499119881834797753566369807 426542527862551818417574672890977772793800081647060016145249192173217214772350 141441973568548161361157352552133475741849468438523323907394143334547762416862
Step-by-step explanation:
Answer:3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196
Step-by-step explanation:teehee
Charlie and Kathy want to borrow $21254 to make some home improvements. Their bank will lend them the money for 9 years at an interest rate of 5.07%. How
much will they pay in interest?
Answer:
$ 9698 will be paid paid in interest. hope this helps.
Step-by-step explanation:
interest= prn/100
i= 21254x9x5.07/100
i= $ 9698.2
Find the equation of the line passing through the point (–1, 0) and parallel to the line y = –1∕2x + 3∕7
Answer:
y = -1/2x - 1/2
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
m - slope
b - y-intercept
Step 1: Define
y = -1/2x + 3/7
Point (-1, 0)
Step 2: Find parallel line
Parallel lines have the same slope as the original but different y-intercepts.
m = -1/2
y = -1/2x + b
0 = -1/2(-1) + b
0 = 1/2 + b
b = -1/2
Step 3: Write parallel line
y = -1/2x - 1/2
If f(x) = -2 cos x, findf(-300 º). Do not use a calculator.
Answer:
- 1
Step-by-step explanation:
Using the trigonometric identity
cos(- x) = cosx and exact value cos60° = [tex]\frac{1}{2}[/tex]
Given
f(x) = - 2cosx , then
f(- 300° )
= - 2cos(- 300)°
= - 2cos(300)°
= - 2cos(360 - 300)°
= - 2cos60°
= - 2 × [tex]\frac{1}{2}[/tex]
= - 1
X^2+ 17x+91=0
Help please!!
Answer:
x^2+17x+91=0
a = 1; b = 17; c = +91;
Δ = b2-4ac
Δ = 172-4·1·91
Δ = -75
Delta is less than zero, so there is no solution for the equation
Step-by-step explanation:
You are a car salesperson and make $17.50 per hour. You are paid on a biweekly basis. Your boss encourages a competition between employees by letting you know that you will receive $100 for each new car you sell. In the first week, you work 20 hours and sell 2 cars. In the second week, you work 30 hours and sell 3 cars. How much will your pay be at the end of the these two weeks?
Answer:
Your pay at the end of the these two weeks will be $1,375
Step-by-step explanation:
In the first place, it is convenient to calculate your salary each week, and then simply add the salary for each week and obtain the fortnightly pay.
In the first week you work 20 hours and sell 2 cars. Knowing that you earn $ 17.50 per hour and you receive $ 100 for each new car that you sell, then to obtain the payment in this first week you perform the calculation:
20 hours* $17.50 per hour + 2 cars * $100 for each car= $350 + $200 = $550
In the second week you work 30 hours and sell 3 cars. Then to obtain the payment in this second week you perform the calculation:
30 hours* $17.50 per hour + 3 cars * $100 for each car= $525 + $300 = $825
Then your salary at the end of these two weeks is calculated by:
Payment of the first week + Payment of the second week
$550 + $825 = $1,375
Another way to solve this problem is, first, add the total number of hours you did during these two weeks and the number of cars sold:
hours= number of hours in the first week + number of hours in the second week= 20 hours + 30 hours= 50 hourscars= number of cars sold in the first week + number of cars sold in the second week= 2 cars + 3 cars= 5 carsThen your salary at the end of these two weeks is calculated by:
50 hours* $17.50 per hour + 5 cars * $100 for each car= $525 + $300 = $1,375
Note that either way you get the same result.
Your pay at the end of the these two weeks will be $1,375
Can someone please help me with this? I would appreciate it <3
Answer:
i kinda see its test or not?
Step-by-step explanation:
you have to divided it.
HEY CAN ANYONE PLS ANSWER DIS MATH QUESTION RQ!!!!!!
Answer: 6 i thank
Step-by-step explanation:
So three quarters is 1/3. So 1/3 of 18 is 6.
And the average size of an Gecko is 18in
And a Iguanas is 1/3 that of an Gecko
Hopefully that helps
What number would go into the box?
Identify the domain of these ordered pairs from least to greatest:
Answer:
(0,5)
Step-by-step explanation:
you are supposed to take the lowest and highest numbers of the x values and then that would be your domain
Need helps with 45 , picture above
Answer:
Ok:
Step-by-step explanation:
We know Josh buys 3 oranges for $2 and sells 2 oranges for $3. Let's take the LCM (least common multiple) of 2 and 3. It is 6. If he buys 6 oranges, he needs $4. When he sells 6 oranges he makes $9. That is a total profit of $5. In total that means, if we multiple by 10, that means that if he sells 60 oranges, he would make $50. Thus C is the answer
Polly stacked the tins from five boxes of cat food onto an empty shelf in a supermarket. There were 15 tins of cat food in each box. At the end of the week there were 20 tins left on the shelf. The rest of the tins had been sold. Write the number of boxes of cat food that had been sold, as: (a) A mixed number (b) An improper fraction
Answer:
(a) [tex]3\frac{2}{3}[/tex] boxes of cat food had been sold.
(b) [tex]\frac{11}{3}[/tex] boxes of cat food had been sold.
Step-by-step explanation:
From the question,
Polly stacked the tins from five boxes of cat food onto an empty shelf and there were 15 tins of cat food in each box. That is,
5 × 15 tins of cat food were stacked onto the empty shelf.
5 × 15 = 75
Hence, 75 tins of cat food were stacked onto the empty shelf.
Also, from the question,
At the end of the week there were 20 tins left on the shelf and the rest of the tins had been sold, that is
75 - 20 tins had been sold
75 - 20 = 55
Hence, 55 tins of cat food had been sold.
To determine the number of boxes of cat food that had been sold,
Since there are 15 tins of cat food per box, then
we will divide 55 tins of cat food that had been sold by 15 tins of cat food per box
55 ÷ 15 = [tex]\frac{55}{15}[/tex]
Hence, [tex]\frac{55}{15}[/tex] boxes of cat food had been sold
(a) As a mixed number
[tex]\frac{55}{15} = 3\frac{2}{3}[/tex]
Hence, [tex]3\frac{2}{3}[/tex] boxes of cat food had been sold.
(b) As an improper fraction
[tex]\frac{55}{15} = \frac{11}{3}[/tex]
Hence, [tex]\frac{11}{3}[/tex] boxes of cat food had been sold.
Find the distance between V (4.4) and X (5.8). Round to the nearest tenth, if necessary. about units
Answer:
V= 5 X=6
Step-by-step explanation:
Please answer! Thank you so so much and you will be rewarded in points!!
If the line passes through (-4,-7) and (4,9), what is the equation of the line in standard form?
2x - y = 1
2x + y = -1
2x + y = 1
2x - y = -1
Answer:
Step-by-step explanation:
Y=2x+1??
Answer:
2x - y = -1
Step-by-step explanation:
hope this helps
PLZ ANSWER THE QUESTION 50 POINTS!!!!!!!
(-4,3) m=2 make this in point slope form
Answer:
y-3=2(x-(-4))
Or
y-3=2(x+4)
Step-by-step explanation:
What is the solution to 4 x + 6 less-than-or-equal-to 18?
help
<3
Answer:
x is less-than-or-equal to 3
Step-by-step explanation:
4(3)+6 =18
Which equation in standard form has a graph that passes
through the point (-5,11) and -2.5 is the slope.
What is the solution to 8x - 3(2x - 4) = 3x - 18?
Answer:
X=30
Step-by-step explanation:
The answer is X=30
do you guys know this by any chance
Answer:
[tex]10^{17}[/tex]
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
10
. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
400+90+7,000+ blank =7,495
Answer:
The answer is for this question is 5.
solve this equation
6x+13=9x-8
Step-by-step explanation:
Hey there!
Given;
6x + 13 = 9x - 8
Shift "6x" to right side and "-8" to left side and simplify it to get answer.
13+8 = 9x-6x
21 = 3x
x= 21/3
Therefore, x= 7.
Hope it helps...
You need at least 30 cubic feet of sand to fill a sand box. Each box contains 2.5 cubic feet of sand. Write and solve an inequality that represents the number of bags “b” that you need to buy
Answer:
2.56 = 30
b = 12
(Sorry if I’m wrong! I speeded on it.)
Step-by-step explanation:
A restaurant charged Ms. Smith $120 for dinner,
while at dinner she met with a friend and they had a
great conversation about the 25 animals at the zoo.
When dinner was over she left a 15% tip. How much
was the tip amount?
help = brainleist
please help
Answer:
The answer is D
Step-by-step explanation:
Hope this helps
please mark as brainlist
The volume, V, of a certain gas varies inversely with the amount of pressure, P. placed on it. The volume of this gas is 175
cm' when 3.2 kg/cm² of pressure is placed on it. What amount of pressure must be placed on 400 cm' of this gas?
2.86 kg/cm2
1.31 kg/cm?
7.31 kg/cm2
1.40 kg/cm2
Answer:
1.3 kg/cm
Step-by-step explanation:
What is the range of the function shown in this table? х3 4 5 6 y4 4 2 5 A. (3, 4), (4, 4), (5, 2), {6, 5{ B. {3,4,5,6} C. {3, 4} D. {2,4,5}
The answer fam is............ D. {2,4,5}
1+2x6+7= -13
where do i have to put the parenthesis so its correct
Answer:
you have to but it back 2 times
Step-by-step explanation:
ir is because it should be back 2 rimes
what is the siope of a line that passes through the points (2, 3) and (4.-12)?
Answer:
-7.5
Step-by-step explanation: