Consider the expression
[tex]\dfrac{x^3-1}{(x+1)^3+1}[/tex]
Factorize the numerator and denominator a difference/sum of cubes:
[tex]\dfrac{(x-1)(x^2+x+1)}{((x+1)+1)((x+1)^2-(x+1)+1)}[/tex]
Expand the denominator:
[tex]\dfrac{(x-1)(x^2+x+1)}{(x+2)((x^2+2x+1)-(x+1)+1)}=\dfrac{(x-1)(x^2+x+1)}{(x+2)(x^2+x+1)}=\dfrac{x-1}{x+2}[/tex]
since x = 2020, and clearly 2020² + 2020 + 1 ≠ 0, so we can cancel the factor of x ² + x + 1. This leaves us with
[tex]\dfrac{2020^3-1}{2021^3+1} = \dfrac{2020-1}{2020+2} = \dfrac{2019}{2022}=\dfrac{673}{674}=\dfrac ab[/tex]
so that a + b = 673 + 674 = 1347.
please help!!
hhhhhh
Step-by-step explanation:
The given equations are
x2+y3=xy9
⟹xy2y+3x=xy9
⟹3x+2y=9 ........(i)
x4+y9=xy21
⟹xy4y+9x=xy21
⟹9x+4y=21 ........(ii)
Now (i)×3⟶9x+6y=27 .....(iii)
Subtracting (iii) from (ii),
−2y=−6⇒y=3.
Putting y=3 in (i),
3x+2×3=9⟹x=1.∴(x,y)=(1,3)
Answer:
i
Step-by-step explanation:
what is 2 × 56 multiplying fraction
Answer:
2 x 56 = 112
This is because 56 + 56 = 112
Hope this helps! :]
HELP LAST ATTEMPT ( get marked brainliest show work
Answer:
10
Step-by-step explanation:
Since we are dealing with area, we need to multiply 16 1/4 by 11 3/4.
If we do that, we get 190 15/16
So, if we divide 190 15/16 by 20:
[tex]190 \frac{15}{16} / 20 = 9.5[/tex]
You cannot have half a bag however. You will need to round the number to 10.
Evaluate; tan^2 60 - sin^2 45.
Answer:
tan^2 60 - sin^2 45
= (√3)^2- (1/√2)^2
= 3-1/2
= 6-1/2
= 5/2
Answer:
[tex]\frac{5}{2}[/tex]
Step-by-step explanation:
The exact value of tan(60) is sqrt(3), and sin(45) is 1/sqrt(2)
tan^2 (60) - sin^2 (45)
[tex]=(\sqrt{3})^2-(\frac{1}{\sqrt{2}} )^2\\=3-\frac{1}{2}\\ = \frac{5}{2}[/tex]
Solve for x
Angles around a point
Answer:
205°
Step-by-step explanation:
The total circle is 360°. The right angle is 90°, and you know the other angle is 64°. 90° + 64° is 154°. 360° -154° is 205°.
Answer:
We know that the angle around any given point is 360°
Therefore, according to the given problem,
[tex]x° + 64° + 90° = 360° \\ x° + 154° = 360° \\ x° = 360° - 154° \\ \boxed{x° = 206°}[/tex]
Hence, the value of x° is 206°
x° = 206° is the right answer.Is 48, 45, 41, 38, 34,... an arthmetic sequence
Answer:
No
Step-by-step explanation:
The change in the sequence is not consistent therefore it cannot be an arithmetic sequence.
If w = 71 + 91, what is the direction of -2w? same direction as opposite direction of
Answer:
opposite
Step-by-step explanation:
it's negative
PLEASE HELP!!!!!
will mark brainliest!!!!!
Answer:
0=0
1=8
2=10
^^^^
I don't know what the graph is asking if you want to graph the equation y=2x+6 the two points are (0,6) and (1,8)
Draw the line of reflection that reflects quadrilateral ABCD onto quadrilateral A'B'C'D'.
The yellow line I drew is the line of reflection.
Find the product
-3.5(5/7)
A. -2.5
B. -2.1
C.-4.9
D. 2.5
Answer:
A. -2.5
hope that helped <3
Answer the question below
Answer:
[tex]s = 19z - 7 - (5z - 9) - (8z + 3) \\ = 19z - 7 - 5z + 9 - 8z - 3 \\ = (19z - 5z - 8z) + (9 - 7 - 3) \\ \therefore \: third \: side \: s= 6z - 1[/tex]
add or subtracr 3/8 + 1/16
Answer:
7/16
Step-by-step explanation:
change 3/8 to have a common denominator with 1/16 then add the numerators. 6/16 + 1/16 which is 7/16.
I’ll give BRAINLIEST
Answer:
-3/2
Step-by-step explanation:
Slope: (y₂ - y₁) / (x₂ - x₁)
Plug the given points into this formula:
(-4 - 5) / (8 - 2) =
(-9) / (6)
-3/2
what is the area of a rectanglewith a lenght of 5.6cm and a width of 6 cm?
Answer:
A= wl = (6)5.6 = 33.6cm²
Answer:33.6
Step-by-step explanation:
A=wl=6·5.6≈33.6cm²
find (f.g)(-3)when f(x)=-5x-7 and g(x)= 7x^2-2x+9
Answer:
[tex]f(7 {x}^{2} - 2x + 9) \\ = - 5(7 {x}^{2} - 2x + 9) - 7 \\ = - 35 {x}^{2} + 10x - 45 - 7 \\ = - 35 {x}^{2} + 10x - 38 \\ f.g( - 3) = - 35 {( - 3)}^{2} + 10( - 3) - 38 \\ f.g( - 3) = -383[/tex]
A real estate office pays its salespeople a weekly retainer of $220 plus commission of 2.5% for the first
$200 000 of the value of each property sold and 2% of each amount after that. Calculate the commission
received if the following houses are sold.
7- The commission for the sale of a $ 540,000 house was $ 12,020.
8- The commission for the sale of a $ 795,600 house was $ 17,132.
9- The commission during the 4 weeks of February was $ 24,690.
10- The commission during the 4 weeks was $ 27,754.
11- The house was worth $ 440,000.
Given that a real estate office pays its salespeople a weekly retainer of $ 220 plus commission of 2.5% for the first $ 200,000 of the value of each property sold and 2% of each amount after that, to determine the commission received if the following houses are sold, the following calculations must be performed:
7- a $ 540,000 house 540,000 - 200,000 = 340,000 220 + (200,000 x 0.025) + (340,000 x 0.02) = X 220 + 5000 + 6800 = X 12020 = X
8- a $ 795,600 house 795,600 - 200,000 = 595,600 220 + 5000 + (595,600 x 0.02) = X 5220 + 11912 = X 17132 = X
9- a $ 472,500 house and a $ 618,000 house 472,500 - 200,000 = 272,500 618,000 - 200,000 = 418,000 220 x 4 + 5000 + (272,500 x 0.02) + 5000 + (418,000 x 0.02) = X 880 + 10,000 + 5,450 + 8,360 = X 24,690 = X
10- a $ 384,000 unit, a $ 216,000 unit and a $ 593,700 house 384,000 - 200,000 = 184,000 216,000 - 200,000 = 16,000 593,700 - 200,000 = 393,700 880 + 5000 x 3 + (184,000 x 0.02) + (16,000 x 0.02) + (393,700 x 0.02) = X 15880 + 3680 + 320 + 7874 = X 27.754 = X
11- the value of a house whose commission is $ 9800 200,000 x 0.025 = 5000 9800 - 5000 = 4800 2 = 4800 100 = X 100 x 4800/2 = X 240,000 = X 240,000 + 200,000 = 440,000
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If 5^x= 1 over 125 what is the value of x
Can someone plz help me
9514 1404 393
Answer:
(C) Mr. Dixon saved about $500
Step-by-step explanation:
The prices can be rounded to hundreds to give ...
regular price: $2500sale price: $2000The sale price is about 20/25 = 4/5 of the regular price. It is about 2500-2000 = 500 dollars lower.
The true description is ...
Mr. Dixon saved about $500
need help on my homework plz and thank u :)
Answer:
Vertex: (-7/2, -27/2), opens upward
Step-by-step explanation:
I used Desmos to graph this function, as you can see in the attached photo. The vertex was (-3.5, -13.5) and the parabola opened upward.
How do you transpose a number
Answer:
Transposing a number is a type of error where two digits swap position in the sequence. An example would be to enter 13 instead of the desired 31. It could also be the error of dropping a needed zero as in writing 15 instead of the desired 150.
Step-by-step explanation:
Unless by "number" you mean musical score. Then transposing is rewriting the score in a new key.
3 × 10d what is this please I. In a math test
Answer:
30d
Step-by-step explanation:
The original price of a computer was reduced by 120 dollars. The new,
discounted price is 899 dollars.
Mathematical sentence?
Answer:
x-120=899
Step-by-step explanation:
(x=1019)
A dose of 2g of medication has been ordered for patient.The medication comes in 4g/0.4ml.What volume will you give the patient?
To give the patient a dose of 2g medication with a strength of 4g/0.4ml, you should administer 50 ml of the medication.
Given that,
Dose ordered: 2g of medication
Medication strength: 4g/0.4ml
Conversion factor: 10
To calculate the volume of medication you need to give the patient,
Use a simple formula:
Volume (in ml) = (Dose ordered / Strength) x Conversion factor
In this case,
The dose ordered is 2g and the strength is 4g/0.4ml.
To find the conversion factor,
Divide 4g by 0.4ml, which equals 10.
So, using the formula,
The volume of medication you need to give the patient would be:
Volume (in ml) = (2g / 0.4ml) x 10
Now, calculating this:
Volume (in ml) = 5 x 10
Hence, you should give the patient 50ml of medication.
Learn more about the multiplication visit:
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#1: mZGKH =
O*
1 point
G
H
(9x + 3)
(13x – 11°
к
Your answer
This is a required question
a
pls help!!!! you’ll get a lot of points
[tex]\\ \sf\longmapsto a_1=3(1)-9=3-9=-6[/tex]
And
[tex]\\ \sf\longmapsto a_5=3(5)-9=15-9=6[/tex]
A car travels 240 km on 20 liters of petrol. how many litres of petrol is needed to travel 600 km
Answer:
50 L of petrol is needed to travel 600 km.
Step-by-step explanation:
The car travels 1 km in 20/240 L of petrol.
Then,
Petrol needed to travel 600 km
20/240 × 600
20/24 × 60
20/4 × 10
5 × 10
= 50 L
Answer:
50 liters
Step-by-step explanation:
Petrol needed to travel 240 Km = 20 liters
Petrol needed to travel 1 Km = 20/240
Petrol needed to travel 600 Km = [tex]\frac{20}{240} * 600[/tex]
= 50 liters
Find the domain and solve: √(6+x−x2)=9
Step-by-step explanation:
√(6+x−x²)=9
the domain :
6+x-x² ≥ 0
(3-x)(2+x) ≥0
-2 ≤ x ≤ 3
problem solving:
√(6+x−x²)=9
6+x−x²=81
-x²+x+6-81 = 0
-x²+x-75 = 0
x²-x+75 = 0
D = 1² -4(1)(75) = 1-300 = -299
since D < 0, the equation doesn't have any real numbers solution
. M is the midpoint 'of RS, and
M has coordinates (2,6).
R has coordinates (-10, 6).
Find the coordinates of S.
Answer:
the answer is of mid piont (4&6)
P(AB)
=
P(A n B)
P(B)
Freshmen
Sophomores
Juniors
Seniors
Boys
3
1
4
2
Girls
7
9
6
5
P(Girl|Senior) =
P (Girl|Senior) = P(Girl n Senior) / P(Senior)
P(girl n senior) = 5 / 37
P(senior) = 7/37
P(girl | senior) = 5/7
Determine the percent of the figure that is unshaded(there are 360 in a circle)
Answer:
Approx 41.7%
Step-by-step explanation:
150/360=0.41.666666667
0.417*100=41.7%