Answer:
[tex]\boxed{\mathrm{view \ explanation}}[/tex]
Step-by-step explanation:
The difference of two cubes formula is given as:
[tex]a^3-b^3 =(a-b)(a^2 +ab+b^2)[/tex]
Step-by-step explanation:
[tex] {(a - b)}^{3} = {(a - b)}^{2} (a - b)[/tex]
[tex] {a}^{3} - 3{a}^{2} b + 3a {b}^{2} - {b}^{3} = {(a - b)}^{2} (a - b)[/tex]
[tex] {a}^{3} - {b}^{3} + 3ab(a - b)= {(a - b)}^{2} (a - b)[/tex]
[tex] {a}^{3} - {b}^{3}= {(a - b)}^{2} (a - b) + 3ab(a - b)[/tex]
[tex] {a}^{3} - {b}^{3} = (a - b)(( {a}^{2} - 2ab + {b}^{2} ) - 3ab)[/tex]
[tex] {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]
What is the square root of 48? what is the square root of 1/49 ? what is the square root of 4/100 ?
Answer:
Step-by-step explanation:
√48 = √(3*16) = 4√3
√1
√(1/49) = ------- = 1/7
√49
√4
√(4/100) = --------------- = ±2/10 =
√100
three people alice , ben , calvin, are conversing at a taxi stand since taxis are the only ride service in this town. although they havent met before ,they realize that all are going the same route to get desire destination. alice destination is 20 miles away , ben destination 30 miles away and calvins destination 40 miles away , the taxi costs 2 dollars per mile with tip included regardless of the number of passengers. how much should each person pay if the three share a cab to their respective destination
Answer:
Alice will have to pay $13.33
Ben will have to pay $23.33
Kelvin will have to pay $43.33
Step-by-step explanation:
Given that
Alice destination is 20 miles away
Ben destination is 30 miles away
Calvin destination is 40 miles away.
For a mile, taxi costs 2 dollars.
To find:
How much each person has to pay if they share the same taxi to their respective destinations?
Solution:
For the first 20 miles, the taxi will be shared by all 3 of them.
Charges for 20 miles = 20 [tex]\times[/tex] 2 = $40
This $40 will be shared among all 3.
Each will pay = [tex]\frac{40}{3} = \$13.33[/tex]
Charges for Alice = $13.33
Charges for Ben = $13.33
Charges for Calvin = $13.33
For the next 10 miles, the taxi will be shared by Ben and Calvin.
Charges for 10 miles = 10 [tex]\times[/tex] 2 = $20
This $20 will be shared between Ben and Calvin.
Each will pay = [tex]\frac{20}{2} = \$10[/tex]
Charges for Alice = $13.33
Charges for Ben = $13.33 + 10 = $23.33
Charges for Calvin = $13.33 + 10 = $23.33
For the next 10 miles, Calvin travels alone.
Charges for 10 miles = 10 [tex]\times[/tex] 2 = $20
This $20 will be paid by Calvin alone.
Charges for Alice = $13.33
Charges for Ben = $23.33
Charges for Calvin = $23.33 + 20 = $43.33
what is the x intercept for y=(2x(x-3))/(x-1). ?
my answer sheet says it is supposed to be -0.5
Answer:
( 0,0) and (3,0)
Step-by-step explanation:
y=(2x(x-3))/(x-1)
Set y = 0
0 =(2x(x-3))/(x-1)
Multiply each side by x-1, which makes x not equal to 1
0 =(2x(x-3))
Using the zero product property
2x=0 x-3 =0
x=0 x= 3
The x intercepts are x=0 x= 3
( 0,0) and (3,0)
Find the common ratio for the geometric sequence for which [tex]a_1[/tex]=3 and [tex]a_5[/tex]=48. A. -3 B. -2 C. 3 D. 2
Answer:
An= A1 * r^n-1
A5= 3 * r^5-1
48= 3*r^4
48÷3=r^4
16=r^4
r=
[tex] \sqrt[4]{16} [/tex]
r=2
The answer is D. 2
Espero que te sirva
hsじぇいrんふぉそ具jんじょおlっっっkjか、
How many planes can be drawn through any three noncollinear points?
Answer:
1 plane
I hope this helps!
What are the solutions to the equation (2x – 5)(3x – 1) = 0? x = or x = 3 x = x = 5 or x = 1
Answer:
x = 5/2 x=1/3
Step-by-step explanation:
(2x – 5)(3x – 1) = 0
Using the zero product property
2x-5 =0 3x-1 =0
2x=5 3x =1
x = 5/2 x=1/3
Answer:
C on edg 2021
Step-by-step explanation:
In a local kickball league, the ratio of college graduates with a graduate degree to non-college graduates is 1:8, and the ratio of college graduates without a graduate degree to non-college graduates is 2:3. If one random college graduate is picked, what is the probability that they hold a graduate degree
Answer:
3 / 19
Step-by-step explanation:
Given the following :
ratio of college graduates with a graduate degree to non-college graduates = 1:8
ratio of college graduates without a graduate degree to non-college graduates is 2:3
If college graduate with a degree = A
College graduate without a degree = B
Non-college graduate = C
College graduate to non college graduate = A:C
College graduate without degree to non college graduate = B:C
A:C = 1:8 - - - (1) ; B:C = 2:3 - - - (2)
Combining the two ratios :
To do so : the proportion of non college graduate should be the same in both ratios
To do this, multiply (1) by 3 and (2) by 8
A:C = 3 : 24
B:C = 16 : 24
combining both, we have :
A:B:C = 3:16:24
If one random college graduate is picked, what is the probability that they hold a graduate degree?
Total proportion of college graduate : (college graduates with degree + college graduates without degree)
A + B = (3 + 16) = 19
Proportion who hold a graduate degree = A = 3
Probability = require outcome / Total possible outcomes
Thus :
P = A / (A +B)
= 3/19
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
9.6km
Step-by-step explanation:
Do 6x1.6 ÷1= 9.6km
Answer:9.6km
Step-by-step explanation: Recall BSM(big-small-multiply),so
1.6km×6
Factorise using suitable identities (0.1x-0.2y)^2
Answer:
Step-by-step explanation:
(a - b)² = a² - 2ab + b²
a = 0.1x
b = 0.2y
(0.1x - 0.2y)²= (0.1x)² - 2*0.1x*0.2y + (0.2y)²
= (0.1)²x² - 0.04xy + (0.2)²y²
= 0.01x² - 0.04xy + 0.04y²
The graph represents revenue in dollars as a function of greeting cards sold. A coordinate plane showing Greeting Card Revenue, Number of Cards Sold on the x-axis and Revenue in dollars on the y-axis. A line starts at (0. 0) and passes through (2, 8), (4, 16), and ends at (5, 20). Which equation represents the function shown on the graph? y = x y = x y = 2x y = 4x
Answer:
D
Step-by-step explanation:
Just did it
A function assigns the values. The equation that represents the function shown on the graph is y=4x.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that the graph represents revenue in dollars as a function of greeting cards sold. Therefore, we can write the function as,
Revenue ∝ Number of cards sold
Since the Number of Cards Sold on the x-axis and Revenue in dollars on the y-axis. Therefore, we can write,
y ∝ x
Removing the proportionality, we will get,
y = k x
Now, substitute any point through which the graph of the function passes to get the value of k,
20 = k × 5
20/5 = k
k = 4
Thus, the function can be represented as,
y = kx
y = 4x
Hence, the equation that represents the function shown on the graph is y=4x.
Learn more about Function here:
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There is a regular dodecahedron with all the points connected to each other. What is the area if each of the shales formed if the distance between each Point is x?
Answer:
18581.16
Step-by-step explanation:
The area of each of the shale can be calculated as
distance between each point = x
The area of the regular Dodecahedron
A = [tex]\sqrt[3]{25+10\sqrt{5} } a^{2}[/tex]
where a = number of edges = 30
hence the area of the regular dodecaheron = 18581.16
Find all values of $x$ such that \[\frac{2x}{x + 2} = -\frac{6}{x + 4}.\]If you find more than one value, then list your solutions, separated by commas.
Greetings from Brasil...
2X/(X + 2) = 6/(X + 4)
2X(X + 4) = 6(X + 2)
2X² + 2X - 12 = 0 ÷2
2X²/2 + 2X/2 - 12/2 = 0/2
X² + X - 6 = 0Δ = 25
X' = 2X'' = - 3S = {-3, 2}
By using factorization, [tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex] , values of x are -2, 3.
What is factorization?Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number. These numbers are broken down into factors or divisors.
Given
[tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex]
⇒ 2x(x + 4) = 6(x + 2)
⇒ [tex]2x^{2} +8x = 6x + 12[/tex]
⇒ [tex]2x^{2} +8x-6x-12=0[/tex]
⇒ [tex]2x^{2} +2x -12=0[/tex]
Divide above equation by 2, we get
⇒ [tex]x^{2} +x -6=0[/tex]
⇒ [tex]x^{2} +2x-3x-6=0[/tex]
⇒ [tex]x(x+2)-3(x+2)=0[/tex]
⇒ [tex](x+2)(x-3)=0[/tex]
⇒ x = -2, 3
By using factorization, [tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex] , values of x are -2, 3.
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The equation of line WX is 2x + y = −5. What is the equation of a line perpendicular to line WX in slope-intercept form that contains point (−1, −2)?
Answer:
Step-by-step explanation:
y = -2x - 5
perp. slope: 1/2
y + 2 = 1/2(x + 1)
y + 4/2 = 1/2x + 1/2
y = 1/2x - 3/2
what is the image (-9,-2) after a reflection over the x-axis ?
Answer:
(-9,2)
Step-by-step explanation:
The rule for reflecting over the x axis is
(x,y)→(x,−y)
(-9, -2) becomes ( -9, - -2) = (-9,2)
Answer:
(-9,2)
Step-by-step explanation:
It will be -9,2 because when you reflect across x axis you change the y axis not the x axis because if you imagine it it works like that
Isabelle bought some stationery. 1/3 of them were pencils. 5/8 of the remainder were erasers and the rest were ruler.The cost of the stationery is ,Pencil: $1.20 ,Eraser :$1 ,Ruler: $0.50 She spent a total of $169.50 on all the stationery. How much more did she spend on erasers than rulers.
Answer:
She spend[tex]\frac{7}{24}[/tex] more on erasers than rulers.
Step-by-step explanation:
We are given that Isabelle bought some stationery.
Fraction of pencil = [tex]\frac{1}{3}[/tex]
Remaining stationary =[tex]1-\frac{1}{3}=\frac{2}{3}[/tex]
5/8 of the remainder were erasers
So, part of eraser in stationary=[tex]\frac{5}{8} \times \frac{2}{3}=\frac{5}{12}[/tex]
Remaining stationary(rulers)=[tex]\frac{2}{3}-\frac{5}{12}=\frac{1}{4}[/tex]
Cost of ruler = $0.50
Cost of [tex]\frac{1}{4}[/tex]rulers =[tex]0.50 \times \frac{1}{4}=\frac{1}{8}[/tex]
Cost of eraser=$1
Cost of [tex]\frac{5}{12}[/tex] eraser=[tex]\frac{5}{12}[/tex]
Difference in cost of eraser and rulers =[tex]\frac{5}{12}-\frac{1}{8}=\frac{7}{24}[/tex]
Hence She spend[tex]\frac{7}{24}[/tex] more on erasers than rulers.
Hey please help me with Math!
There’s a bicycle that runs 45km in 1 hour and 15 minutes.
1) What is the speed of this bicycle? (__km/ph)
2) How far will this bicycle get in 2 hours and 40 minutes?
Step-by-step explanation:
Hello!!!!
According to the question,
distance covered (d)= 45km.
time taken (t)= 1 hr and 15 mins.
now,
let's find answer of this question no. i).
》answer :
speed (s)= distance by time taken
= 45 /1.25
so, the speed is 36 km/hr.
now, for 2nd question,
time (t)= 2hrs and 40 mins.
speed (s)= 36km / hr
now,
distance (d)= s×t
= 36×2.6666666667
= 96km....is yourrequired answer.
Hope it helps...
Look at the figure below: Triangles ABC and BDC have a common base BC. E is the point of intersection of BD and AC. AE = EC and ED = BE Based on the figure, which pair of triangles is congruent by the Side Angle Side Postulate? HELPPPPP MEEEEEE WILL GIVE BRAIN POINTS
Answer:
AEB and CED
Step-by-step explanation:
Given the two pairs of congruent sides, you now use the vertical angles as the pair of congruent included angles, <AEB and <DEC.
The congruent triangles are:
AEB and CED
Answer:
B- Triangle AEB and triangle CED
Step-by-step explanation:
I took the test and it was correct
6 sqrt (x-2) +4 < 28
How do you solve? Btw.. x-2 is under sqrt sign.
Answer:
Step-by-step explanation:
[tex]6\sqrt{x-2}+4<28\\6\sqrt{x-2}<28-4\\\sqrt{x-2}<\frac{24}{6}\\\sqrt{x-2}<4\\\\x-2 <16\\x<16-2\\x<14x-2 \geq 0\\x\geq 2\\so~2 \leq x < 14[/tex]
Find m∠WVT. A. 40 B. 45 C. 53 D. 50
Using the formula for the angle of a secant and tangent line
Angle V = (TW - UW)/2
Write the formula with the given information:
3x+4 = (14x+7 - 7x+11)/2
Simplify:
3x+ 4 = (7x -4)/2
Multiply both sides by 2:
6x + 8 = 7x-4
Add 4 to both sides:
6x+12 = 7x
Subtract 6x from both sides:
X = 12
Now replace x with 12 in angle v:
3(12) +4 = 35 + 4 = 40
The answer is A) 40
Simplify to create an equivalent expression. 8-4(-x+5)
Answer:= -12+4x
Step-by-step explanation:
Distribute -4 through the parentheses
8+4x=20
Calculate the difference
-12+4x
Which of the following expressions demonstrates the distributive property?
3 + 4 + 5 = 4 + 3 + 5
-2(5 + 7) = -2(7 + 5)
O 3(-8 + 1) = 3(-8) + 3(1)
6[(7)(-2)] = [(6)(7)](-2)
Answer:
3(-8 + 1) = 3(-8) + 3(1)
Step-by-step explanation:
The distributive property is quite literally when you distribute numbers. This is the only instance of that happening here
The first two are the communitive property of addition, and the last one is the communitive property of multiplication.
Cheers.
Answer:
c
Step-by-step explanation:
Jak policzyc: [tex](2x^2)^2[/tex] ?
Nimisha wants to draw a wheel like the one shown. Each shaded part of the wheel should be one-third of each unshaded part. What should be the degree measure of the angle formed at the center by each shaded part?
Answer:
Each shade has a 22.5 degree angle from the middle
Each unshaded has a 67.5 degree angle from the middle.
Step-by-step explanation:
You can solve this by making each unshaded part equal to x and each shaded part equal 1/3x it is a circle so it has to equal 360 so you end up with:
x + 1/3x + x + 1/3x + x + 1/3x + x + 1/3x = 360
Combine Like terms:
16/3x = 360
Multiply both sides by the opposite:
(3/16) (16/3x) = (360) (3/16)
x=135/2 or x=67.5
Then you can plug 67.5 in for x:
1/3x ---> 1/3(67.5) = 22.5
Based on the image below, if you know that , find the following:
a) sin A
b) cos A
c) tan A
d) tan B
Answer:
A. Sine A = 4/5
B. Cos A = 3/5
C. Tan A = 4/3
D. Tan B = 3/4
Step-by-step explanation:
We'll begin by calculating the value of b in the attached photo.
This can be obtained as follow:
Cos B = 4/5
Cos B = Adjacent /Hypothenus
Adjacent = 4
Hypothenus = 5
Using pythagoras theory, the value of b can be obtained as follow:
b² = 5² – 4²
b² = 25 – 16
b² = 9
Take the square root of both side.
b = √9
b = 3
A. Determination of Sine A
Sine A =?
Opposite = 4
Hypothenus = 5
Sine A = Opposite /Hypothenus
Sine A = 4/5
B. Determination of Cos A
Cos A =?
Adjacent = 3
Hypothenus = 5
Cos A = Adjacent /Hypothenus
Cos A = 3/5
C. Determination of Tan A.
Tan A =?
Opposite = 4
Adjacent = 3
Tan A = Opposite /Adjacent
Tan A = 4/3
D. Determination of Tan B
Tan B =?
Opposite = 3
Adjacent = 4
Tan B = Opposite /Adjacent
Tan B = 3/4
Find the sum of the geometric sequence. 1, 1/2,1/4,1/8,1/16
Answer:
31/16
or
1 15/16
Step-by-step explanation:
1/8 = 2/16
1/4 = 4/16
1/2 = 8/16
1 = 16/16
then:
1 + 1/2 + 1/4 + 1/8 + 1/16
= 16/16 + 8/16 + 4/16 + 2/16 + 1/16
=(16+8+4+2+1)/16
= 31/16
31/16 = 16/16 + 15/16 = 1 + 15/16 = 1 15/16
A gallon of paint covers 400 square feet. How many square feet will 2 3/8 gallons of paint cover. How do you solve this problem.
Answers
(A) 950 sq ft
(B) 986 sq ft
(C) 1,040 sq ft
(D) 1,068 sq ft
Answer:
Hey there!
1 gallon=400 square feet
2 3/8 gallon= 400 (2 3/8) square feet
2 3/8 gallon= 950 square feet.
Let me know if this helps :)
Estimate. Then determine the area. Please please please, need help!
Estimate:
2.3 rounds down to 2
So after multiplying by 2, the area is estimated to be 4 cm squared.
Actual Area:
2.3 x 2 = 4.6
The actual area of the shape is 4.6 cm squared.
Hope this helped!
Answer:
4.6
Step-by-step explanation:
Convert the mixed number to an improper fraction 1 13/15
━━━━━━━☆☆━━━━━━━
▹ Answer
28/15
▹ Step-by-Step Explanation
[tex]1\frac{13}{15} \\\\1 * 15 = 15\\15 + 13 = 28\\\\\\= \frac{28}{15}[/tex]
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
HELP PLSSSSSSSS ( needed 20 characters)
Answer:
A
Step-by-step explanation:
It have the same sides!
Solve the equation. Do not put "x = "in your answer, just type the number.
Ex: -8 3x - 5 = 13*
Answer:
6
Step-by-step explanation:
3x - 5 = 13
3x = 18 (Add 5 to both sides; 13 + 5 = 18)
x = 6 (Divide both sides by 3; 18 / 3 = 6)
