Answer:
[tex]a^3 + b^3 = -4[/tex]
Step-by-step explanation:
Given
[tex]a + b = 3ab = 2[/tex]
Required
Solve: [tex]a^3 + b^3[/tex]
Rewrite the expression as:
[tex]a^3 + b^3 = a^3 - a^2b +ab^2 + a^2b - ab^2 + b^3[/tex]
Factorize
[tex]a^3 + b^3 = a(a^2 - ab +b^2) + b(a^2 - ab + b^2)[/tex]
[tex]a^3 + b^3 = (a + b)(a^2 - ab + b^2)[/tex]
Rewrite as:
[tex]a^3 + b^3 = (a + b)(a^2 + b^2- ab)[/tex]
[tex]a^3 + b^3 = (a + b)(a^2 + b^2+2ab - 3ab)[/tex]
Factorize
[tex]a^3 + b^3 = (a + b)((a + b)^2 - 3ab)[/tex]
Open brackets
[tex]a^3 + b^3 = (a + b)^3 - 3ab(a + b)[/tex]
Given that:
[tex]a + b = 3ab = 2[/tex]
This means that:
[tex]a + b = 2[/tex] and [tex]3ab = 2[/tex]
So, we have:
[tex]a^3 + b^3 = (a + b)^3 - 3ab(a + b)[/tex]
[tex]a^3 + b^3 = 2^3 - 3 * 2 * 2[/tex]
[tex]a^3 + b^3 = 8 - 12[/tex]
[tex]a^3 + b^3 = -4[/tex]
NEED HELP ASAP! WILL CRY OR SOMETHING
The scatter plot shows the relationship between the test scores of a group of students and the number of hours they play computer games in a week:
On a grid, Label Hours Playing Computer Games on x axis and Test Scores on y axis. The title of the graph is Test Scores and Computer Games. The scale on the x axis shows the numbers from 0 to 10 at increments of 1, and the scale on the y axis shows numbers from 0 to 100 at increments of 10. Dots are made at the ordered pairs 0, 90 and 0, 100 and 0.5, 89 and 1, 81 and 1, 95 and 1, 100 and 1.1, 85 and 2, 90 and 3, 81 and 3.5, 65 and 3.5, 75 and 5, 70 and 6, 55 and 6.5, 65 and 7, 52 and 7.5, 95 and 9, 65. The ordered pair 7.5, 95 is circled and labeled as B. All the other points are put in an oval and labeled as A.
Part A: What is the group of points labeled A called? What is the point labeled B called? Give a possible reason for the presence of point B. (5 points)
Part B: Describe the association between students' test scores and the number of hours they play computer games. (5 points)
Part A: Group A is a cluster of points. Group B Is not even a group this point is an outlier. A possible reason Point B is involved is because there could be a student that although played a lot of video games, he studied too and got a good score.
Part B: The association is a negative linear association. Also as students play more video games the test scores tend to go down.
Hope This Helps!
Answer:
Part A: A is a cluster and B is an outlier. I think it is there to show that even kids who play lots of games can get good grades.
Part B: So, if they play too many games, the grades go down, but not all the time
Which symbol correctly compares the fractions below?
1/8 ? 1/2
Answer:
<
Step-by-step explanation:
140 apples increased by 45%
Answer:
The answer is 196 apples
Step-by-step explanation:
Write what you know about this phrase.
Preview: constant of proportionality
Answer:
Constant - A symbol having a fixed numerical value.
Proportionality - Equality between two ratios.
can some help me its number 2
W: (5,9)
X: (7,8)
Y: (9,2)
Z: (2,5)
hope this helps! tell me if i got anything wrong!
The endpoints of the directed line segment AB are A(−3, 4) and B(5, 10). Find the coordinates of point P along AB¯¯¯¯¯¯¯¯ so that the ratio of AP to PB is 1 to 3.
Answer:
The coordinates of P is (-1,5.5)
Step-by-step explanation:
Here, we want to find the coordinates of the point that divides the segment into the ratio 1 to 3
To do this, we are going to use the section formula
We have this as;
(x,y) = (nx1 + mx2)/m+ n, (ny1 + my2)/m + n
where m = 1 , n = 3
(x1,y1) = (-3,4)
(x2,y2) = (5,10)
Substituting these values, we have;
(x,y) = (3(-3) + 1(5)/4 , (3(4) + 1(10)/4
(x,y) = (-9+ 5)/4 , (12 + 10)/4
(x,y) = (-1, 5.5)
What is the Volume of a hexagonal pyramid shown if the hexagon has a side length of 4 inches and the height of the pyramid is 12 inches?
Answer:
166.24 in³Step-by-step explanation:
Volume formula:
V = 1/3 Bh, B-base area, h- heightBase area:
B = 3√3a² / 2 = 3√3*4² / 2 = 41.57 in (rounded)Volume:
V = 1/3*41.56*12 = 166.24 in³3. During the period of October 1 to 15, Cathy Powers spent the following: October 1, rent, $540;
October 6, electricity, $48.55; October 7, food, $34.15; October 6, dinner at the China Palace,
$12.80; October 12, blouse, $18.95, October 14, food, $38.60; October 15, magazine, $2.00,
and batteries, $6.50. Make a cash record of her expenses and total them.
Answer: Cathy spent a total of $701.55.
Step-by-step explanation:
The wallpaper is sold in rolls that are 18 in wide and 33 ft. long
What is the area of one roll of wallpaper?
Answer:
49.5 ft²Step-by-step explanation:
Dimensions:
w = 18 in = 18*1/12 ft = 1.5 ftl = 33 ftArea is:
A = lw = 1.5*33 = 49.5 ft²Help pls and no links
Answer:
The answer is A. 4+y^2/2y^2
Please answer honestly and I will give brainleyest
Answer:
I select the third option and the last linear equation
find w to find the measure of the exterior angle
The angle that has nothing in it is going to be 54, leaving x to be 78
x=78 degrees
write an inequality for the given graph
What is the volume of this solid?
Answer:
175 in³
Step-by-step explanation:
First the area of the triangle:
S: ½a×b×SinC
½×7in×10in×Sin90°===> 35in²
and now the volume
35 in²×5 in=175 in³
What is -4/5 + 4/5 = ?
Answer:
0.
Step-by-step explanation:
I can't really explain it, but think of it is 4/5 - 4/5 instead of -4/5 + 4/5.
HELLLP!!! Which of the following is a true statement?
A) 3/4 > 13/16
B) 6/7 < 5/8
C) 1/3 < 24/72
D) 3/5 > 4/7
Answer:
C is the correct answer.
Step-by-step explanation:
All you have to do is divide 72 by three to get it into thirds and 1/3 is 24.
Answer:
D
Step-by-step explanation:
3/5>4/7
find the common denominator
the common denominator is 35
so since you multiply 7 to 5 to get 35 multiply 7 to 3
3/5 = 21/35
since you multiply 5 to 7 to get 35 multiply 5 to 4
4/7 = 20/35
21/35 > 20/35
Find the angle with a tangent ratio of 0.9325.
a. 77°
b. 43°
C. 13°
d. 47°
Answer:
B = 43
Step-by-step explanation:
Answer:B
Step-by-step explanation:
Write the number 0.00004 in scientific notation.
Answer:
4.0 x 10^-5
Step-by-step explanation:
Answer:
4*10^-5
Step-by-step explanation:
Start by counting the zeros to the right of the decimal if 0<x<1. Stop when you hit a digit between 1 and 9Add 1 to the number of zerosThis is the powerExpress the number as one between 1 and 9 The power is changed to a negative, if 0<x<10.00004 has 4 zeros. Add 1 = 5
The power on 10 becomes negative (-5)
4 is a number between 1 and 9 inclusive.
4 * 10^-5
In ΔXYZ, ∠Y=90° and ∠X=24°. ∠ZWY=81° and XW=7.1. Find the length of WY to the nearest 10th.
Answer:
0.5
Step-by-step explanation:
delta math
How many years will it take for $136,000 to grow to $468,000 if it is invested in an account with an annual interest rate of 8%?
Answer:
=21.29%(Approx).
Step-by-step explanation:
We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
a.
468,000=136,000*(1.08)^n
(468,000/136,000)=(1.08)^n
Taking log on both sides;
log (468,000/136,000)=n*log 1.08
n=log (468,000/136,000)/log 1.08
=16.06 years(Approx).
b.
475,000=10,000*(1+r/100)^20
(475,000/10,000)^(1/20)=(1+r/100)
(1+r/100)=1.2129
r=1.2129-1
=21.29%(Approx).
2. What is the surface area of the triangular prism below?
The surface area of triangular prism is 281.68 square cm
What is the triangular prism?Triangular Prism is a pentahedron and has nine distinct nets. The edges and vertices of the bases are joined with each other via three rectangular sides. The sides of the triangular prism, which are rectangular in shape are joint with each other side by side. All cross-sections parallel to the base faces are the same as a triangle. A triangular pyramid has four triangular bases unlike the triangular prism, joined with each other and all are congruent to each other.
We have,
The length of triangular prism(l)=13 cm
The height of triangular prism(h)= 5.1 cm
The base of triangular prism(b)= 6.8 cm
S1, S2, and S3 are the three edges (sides) of the base triangle=6.1 cm,6.8 cm and 6.1 cm
Perimeter of base(p)=S1+S2+S3
=6.1cm+6.8cm+6.1cm
=19cm
According to question,
We know the formula of The surface area of prism=(perimeter of base× length of prism)+(2×base area of prism)
=(P ×l)+(2×[tex]\frac{1}{2}[/tex]×b ×h)
=(19×13)+(6.8×5.1)
= 247+34.68
=281.68 square cm
To learn more about surface area of prism here
https://brainly.in/question/7707474
#SPJ2
A parallelogram has one angle that measures 5°. What are the measures of the other three angles in the parallelogram?
Step-by-step explanation:
hope this help the other angles are 5 degrees, 175degrees and 175 degrees
Answer:
jwbeeivrievtidtvidvtirvtjrvtitthtirht
Choose the best term from the box.
The
?
of an object is how heavy the object is.
Answer:
mass
Step-by-step explanation:
because that is how heavy it is
Negative five times two
Answer:
-10
Step-by-step explanation:
When multiplying a negative number by a positive number, you multiply the numbers normally and then add on a negative sign. When dealing with signs in multiplication/division, two positives make a positive, two negatives make a positive, and one negative and one positive make a negative.
Which scenario could be best represented by the graph?
A a ballon descending
B a car increasing speed
C a person climbing up the stairs
D a child swinging on a swing
Answer:
I think swinging.
Step-by-step explanation:
I think this because that is the only one that would explain why the distance decreases and increases.
Help and Plz make sure it’s right
Answer:
8.6
Step-by-step explanation:
Use the pythagorean therom for this
(5.9)^2 + (6.3)^2 = c
c= 74.5
square root of 74.5 is 8.631 or 8.6
hope this helps
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quv-xypc-xhm
Answer:
oh i will what is that code of yours
Step-by-step explanation:
quv-xypc-xhm ←what is this
Varies directly as m
A)k=dm
B)d=k/m
C)m=k/d
D)d=km
Answer:
d = km
Step-by-step explanation:
d Varies directly as m
This is written mathematically as :
d ∝ m
d = km
Where k is the constant k of proportionality
Option D)d=km is the correct option.
15.4 = -2.1 + a
0.2
help pleasee
Answer:
a = 3.5
Step-by-step explanation:
[tex]15.4=-2.1+\frac{a}{0.2} \\\\\frac{a}{0.2} =15.4+2.1\\\\\frac{a}{0.2} =17.5\\\\a=3.5[/tex]
What are all of the steps to get 17=5y-3
Answer:4
Step-by-step explanation: 17 = 5y-3
Add 3 to both sides
17 turns into 20
3 is gone
20=5y
Divide by 5 on both sides
20 divided by 5 =4
5 crossed out
4=y