Answer:
The properties and characteristics of the sum of two cubes
1) In the sum of two cubes, the middle sign of the binomial factor on the right hand side of the equation is positive
2) The trinomial factor has a middle sign that is opposite to the middle sign in the question on the sum of two cubes
The properties and characteristics of the difference of two cubes
1) In the difference of two cubes, the middle sign of the binomial factor on the right hand side of the equation is always negative
2) The trinomial factor has a middle sign that is opposite to the middle sign in the question on the difference of two cubes
Step-by-step explanation:
The sum and difference of two cubes are;
a³ + b³, and a³ - b³
Factorizing the expressions for the sum and difference of two cubes can be shown as follows;
Sum of two cubes; a³ + b³ = (a + b) × (a² - a·b + b²)
Difference of two cubes; a³ - b³ = (a - b) × (a² + a·b + b²).
While sailing, Jacob is 150 feet from a lighthouse. The angle of elevation from his feet on the boat (at sea level) to the top of the lighthouse is 48°
What can you conclude about the height of the lighthouse, with respect to Jacob's distance from the lighthouse? Explain your answer.
Answer:
The height of the lighthouse is approximately 166.6 feet.
Step-by-step explanation:
Let the height of the lighthouse be represented by s, then;
Tan 48° = (opposite) ÷ (adjacent)
Tan 48° = s ÷ 150
⇒ s = 150 × Tan 48°
= 150 × 1.1106
= 166.59
s ≅ 166.6 feet
Therefore, the height of the lighthouse is approximately 166.6 feet.
Answer:
The height of the lighthouse is approximately 42.
Step-by-step explanation:
This situation forms a right triangle so the angles would be 90 and 48
90+48+x=180
138+x=180
x=180-138
x=42
If AC = 40, find the length of JK.
Answer:
JK = 24
Step-by-step explanation:
Δ BKJ and Δ BCA are similar triangles and ratios of corresponding sides are equal, that is
[tex]\frac{JK}{AC}[/tex] = [tex]\frac{BK}{BC}[/tex] , substitute values
[tex]\frac{JK}{40}[/tex] = [tex]\frac{3}{5}[/tex] ( cross- multiply )
5JK = 120 ( divide both sides by 5 )
JK = 24
the triangles are all similar, because they have proportional sides and equal angles.
if you assume the smallest, equal part of side to be x
the biggest triangle has "5 parts" so BC=5x and BK has 3 parts so BK=3x .
since they're similar, ratio of their corresponding sides is constant or equal.
[tex] {BK\over BC}={JK \over AC}[/tex]
BK/BC=3/5
and AC=40
so JK = 40*3/5=24
Question 9(Multiple Choice Worth 4 points)
(02.05 LC)
Which of the following statements best describes the effect of replacing the
graph of y = f(x) with the graph of y = f(x - 9)?
The graph of y = f(x) will shift up 9 units.
The graph of y = f(x) will shift down 9 units.
The graph of y = f(x) will shift left 9 units.
The graph of y = f(x) will shift right 9 units.
Answer: D) right 9 units
Step-by-step explanation:
The Vertex form of a quadratic equation is: y = a(x - h)² + k where
a is the vertical stretch or shrink(x, h) is the vertex→ h is the horizontal shift (+ is right, - is left)
→ k is the vertical shift (+ is up, - is down)
y = f(x - 9)
↓
h=9
Since h is positive, the graph moves 9 units to the RIGHT
Answer:
The graph of y = f(x) will shift right 9 units.
Step-by-step explanation:
If the -9 is inside the parenthesis, the graph g(x) shifts 9 points to the right.
Someone please help! Thank you
Answer:
Hey there!
We can write a equations here:
3x+y=180
Also, since all of the angles have 3x on the outside, then y must be constant.
3y=180
y=60
Thus, for x, we have 3x+60=180, 3x=120, x=40.
2x+6y
2(40)+6(60)
80+360
440.
Let me know if this helps :)
If there is a positive correlation between salary and education, then based on the table shown, which of the following careers requires the most education? A graph titled Average Salaries of Various Careers, 2008 to 2009. Veterinarian, 56,000 dollars; personal trainer, 18,000 dollars; accountant, 43,000 dollars; paralegal, 34,000 dollars; architect, almost 50,000 dollars; photographer, 19,000 dollars; pharmacist, 44,000 dollars; secretary, 30,000 dollars; surveyor, 36,000 dollars; webmaster, 49,000 dollars. a. accountant b. paralegal c. photographer d. surveyor
Answer:
The correct option is;
a. Accountant
Step-by-step explanation:
The given data are;
Career, Average Salary
Veterinarian, $56,000
Personal trainer, $18,000
Accountant, $43,000
Paralegal, $34,000
Architect, $50,000
Photographer, $19,000
Pharmacist, $44,000
Secretary, $30,000
Surveyor, $36,000
Webmaster, $49,000
Among the options given, which are, accountant (salary, $43,000), paralegal (salary, $34,000), photographer (salary, $19,000), and surveyor (salary, $36,000), the accountant, with a salary of $43,000, requires the most education.
For which function is the ordered pair (4, 12) not a solution? y = 3 x y = 16 - x y = x + 8 y = 8 - x
if an ordered pair is a solution, it should satisfy the equation.
see the first option
[tex]y=3x[/tex] , if you put $x=4$ and $y=12$
you'll get $12=12$ which is true.
now the last option, $y=8-x$ put $x=4$ and $y=12$
$12=8-4\implies 12\ne4$ thus it is not a solution.
So option 4 is correct
Answer:
Last one:
y = 8 - xStep-by-step explanation:
y = 8 - x
Replace x and y in this function12 = 8 - 4
12 = 4 (impossible)
So, (4 , 12) is not solution for: y = 8 - xAnswer ASAP, will give brainliest!!
Answer:
Step-by-step explanation:
77; The formula to calculating the area of a trapezoid is (a+b)/2 * c. a+b are the 2 parallel lines, and c is the height or the altitude. So, it is (10+12)/2 * 7, which is 22/2 * 7 = 11*7=77 :)
$10,000 for 20 years at 5% compounded annually
Answer:
$26532.98
Step-by-step explanation:
Given:
Principal = $10000Profit rate = 5% PA compoundedTime = 20 yearsCompounds = 20*1 = 20Sum is:
10000*(1 + 5/100)²⁰ ≈ 26532.98inscribed angles. need answers asap , thank u!
Answer:
40°
Step-by-step explanation:
The circumference of a circle is equal to 360°
The arc AB is 180°, the arc AC is given as 100° so the arc CB is 80° and since <A is an inscribed angle it is equal to the half of the arc it sees
80 ÷ 2 = 40
Write 3.6 as a percent.
Answer:
360%
Step-by-step explanation:
You have to multiply 3.6 by one hundred to get the percentage. When you multiply decimals by numbers that are multiples of ten, you move the decimal place to the right of the number by the number of zeroes that is in your number. Sorry if its confusing.
Examples: 3.76 * 100 = 376. You move the decimal to the right two spaces
46.263 * 1000 = 46263. You move the decimal to the right three spaces. Hope you understand.
Type the correct answer in the box. Use numerals instead of words.
Find the area of this shape.
4 cm
2 cm
4 cm
4 cm
5.75 cm
The area of the shape is
square centimeters.
Answer:
35 cm squared
Step-by-step explanation:
Triangle area = bxh 2 = 5.75 x 8 / 2 = 23
Trapezium Area = a+b /2 x h = 8 + 4 /2 x 2 = 12
23 + 12 = 35
Hope that helped!!! k
what is the GCF of 100x squared - 250xy+75x
Answer:
25x
Step-by-step explanation:
100x^2 -250xy +75x
Rewriting
25*4*x*x -25*10 *x*y + 25*3*x
As we can see each term contains 25x
The greatest common factor is 25x
25x( 4x -10y+3)
Answer:
25x
Step-by-step explanation:
GCF means the greatest common factor.
First, we write the factors of these numbers.
=> 100x^2 = 2 * 2 * 5 * 5 * X * X
=> 250xy = 5 * 5 * 5 * 2 * X * Y
=> 75x = 5 * 5 * 5 * x
=> Next, we need to take the numbers that come in all sets.
=> 5 , 5 , x
Next, we multiply these numbers.
=> 25x
So, the GCF of these numbers are 25x
A carpenter has a 10 1/2 foot wood plank. He cuts off 4 1/4 feet to replace a deck board as well as 3 2/3 feet to repair a step. He uses the rest of the plank for a shelf. How many feet of wood does the carpenter have for the shelf? PLEASE SHOW YOUR WORK AND EXPLAIN HOW YOU GOT THE ANSWER PLEASE I WILL MARK YOU BRAINIEST.
Answer:
The carpenter used 2 7/4 feet of plank for the shelf
Step-by-step explanation:
Total length of plank =10 1/2 foot
He used
For Deck board=4 1/4 feet
Step=3 2/3 feet
Shelf=x feet
Total plank=deck board + step + shelf
10 1/2 = 4 1/4 + 3 2/3 + x
Change the fractions
21/2 = 17/4 + 11/3 + x
Add 17/4 + 11/3
21/2 =51+44/12 + x
21/2= 95/12 + x
Collect like terms
21/2 - 95/12 =x
126-95/12 = x
31/12=x
2 7/12 =x
Therefore, the carpenter used 2 7/4 feet of plank for the shelf
Answer:
Step-by-step explanation:
Total length of plank =10 1/2 foot
He used
For Deck board=4 1/4
Step=3 2/3
Shelf=x
Total plank=deck board + step + shelf
10 1/2 = 4 1/4 + 3 2/3 + x
Flying against the wind, a jet travels 1650 miles in 3 hours. Flying with the wind, the same jet travels 3480 miles in 4 hours. What is the rate of the jet in still air and what is the rate of the wind?
Step-by-step explanation:
Let the rate of the plane be x
The rate of the wind be y
Against the wind
Resultant velocity = x-y
1650/3 = x - y
550 = x - y
With the wind
Resultant velocity = x + y
3480/4 = x + y
870 = x + y
Solve equation simultaneously
Add both equations
870+550 = x+y+x-y
1420 = 2x
x = 710
x + y = 870
y=870 - 710
y = 160
The rate of jet in still air = 710 mph
The rate of wind = 160 mph
HOPE IT HELPS!
PRETTY PLEASE MARK ME BRAINLIEST :-)
What type of number is 17?
There may be more than one correct answer.
Select all that apply.
If only one answer is correct, select "only" and the answer that applies.
rational
only
integer
natural
whole
Rational Numbers
Answer:
Rational, integer, natural, whole, rational numbers
Step-by-step explanation:
17 is a rational, integer, natural, whole, and is a rational number. I'm not totally sure why rational is on there, since rational and rational number should be the same thing. Basically it's everything but "only". If rational is supposed to mean irrational, then it's not irrational.
Simplify:
[tex] \frac{ {a}^{5} {b}^{8} }{ {a}^{4} {b}^{10} } [/tex]
HELP! answer if you can !
Answer:
a^5b^8/a^4b^10
= a^5-4 b^8-10
= a^1 b^-2
= a/b^2
I hope this helps
if u have question let me know in comments ^_^
HE SODA MACHINE
The soda machine at your school offers several types of soda. There are two buttons for your favorite drink, Blast,
while the other drinks (Slurp, Lemon Twister, and Diet Slurp) each have one button.
Describe the input and output of this soda machine.
While buying a soda, Ms. Whitney pushed the button for Lemon Twister and got a can of Lemon Twister.
Later she went back to the same machine, again pushing the Lemon Twister button, but this time she got a can
of Blast. Is the machine functioning consistently? Why or why not?
BLAST
BLAST
BLUSO
ooo
Students, write your resnonsel
Answer:
yes and no
Step-by-step explanation:
if a machine is work a lot lot LOT, then it might be jamed
or the teacher might have accidentally pressed blast and you might have not seen the buttons correctly
( also i am not a student of yours )
How do -11.5 and -9.5 compare? Choose the correct symbol.
-11.5 _ -9.5
A.<
B.=
C.>
Answer:
A. <
Step-by-step explanation:
-9.5 is greater than -11.5
Answer:
A) <
less than
Step-by-step explanation:
-11.5 < -9.5
The graph of function f is shown. Function g is represented by the equation. Look at the graph and picture!
Answer: B) different y intercepts; same end behavior
=======================================================
Explanation:
The graph shows the y intercept is 4 as this is where the green curve crosses the vertical y axis.
The y intercept of g(x) is 6 which can be found by plugging x = 0 into the g(x) function
g(x) = 4(1/4)^x + 2
g(0) = 4(1/4)^0 + 2
g(0) = 6
So we can see the y intercepts are different.
----------
However, the end behaviors are the same for each function. The left side of f(x) goes up forever to positive infinity. The same is true for g(x). You could use a graphing calculator or a table to see this. As x heads to negative infinity, y goes to positive infinity.
In terms of symbols, [tex]x \to -\infty, y \to \infty[/tex]
----------
For the right side of f(x), it slowly approaches the horizontal asymptote y = 2. It never actually reaches this y value. The same happens with g(x). The portion 4(1/4)^x gets smaller but never gets to 0 so overall 4(1/4)^x+2 gets closer to 2. We can say that as x approaches infinity, y approaches 2.
In terms of symbols, [tex]x \to \infty, y \to 2[/tex]
What is the center of a circle with the equation (x - 6)2 + (y + 2)2 = 9?
A)
(6,2)
B)
(6,-2)
0)
(-6, 2)
D)
(-6, -2)
Answer:
B. (6,-2)
Step-by-step explanation:
The equation of a circle is (x-h)^2+(y-k)^2=r^2
The center of the circle is (h,k)
So, in this problem, h is 6 and k is -2, so the center of this circle is (6,-2).
Four witches are making a brew.Patricia puts in x frogs legs.sheila puts in five more than patricia.Anne puts double the amount that Sheila adds,and Winifred adds three times the number Sheila adds.
write down an algebraic expression for:
Sheila. Anne. Winifred
Answer:
see explanation
Step-by-step explanation:
Given Patricia puts in x frogs legs, then
Sheila puts in x + 5 ( 5 more than Patricia )
Anne puts in 2(x + 5) ( double the amount of Anne )
Winifred puts in 3(x + 5) ( three times the number of Sheila )
how many are 9 raised to 2 ???
Answer:
[tex]\boxed{81}[/tex]
Step-by-step explanation:
9 raised to 2 is
=> [tex]9^2[/tex]
=> 9 * 9
=> 81
What is the value of x in the equation 3x-4y=65, when y =4 will give brainliest
Hello!
Answer:
[tex]\huge\boxed{x = 27}[/tex]
Given:
3x - 4y = 65 where y = 4;
Substitute in 4 for "y":
3x - 4(4) = 65
Simplify:
3x - 16 = 65
Add 16 to both sides:
3x - 16 + 16 = 65 + 16
3x = 81
Divide both sides by 3:
3x/3 = 81/3
x = 27.
Hope this helped you! :)
Answer:
x=27
Step-by-step explanation:
3x-4y=65
Let y=4
3x - 4(4) = 54
3x -16 = 65
Add 16 to each side
3x -16+16 = 65+16
3x = 81
Divide each side by 3
3x/3 =81/3
x =27
find the sum of partial fraction for x^4/(x-1)(x²-4)
Answer:
see attachment
Step-by-step explanation:
A sprinter run 400 meter in 54 second.what about s the runner's average running rate in meter per second?round to the nearest tenth
Answer:
7.4
Step-by-step explanation:
400 ÷ 54 =7.407407...
7.407407... rounded to the nearest tenth is 7.4
I hope this helps... and plz mark me brainliest!!!
I got this wrong please help me get the right answer in the first little box marked in red. thx
Answer:
The inverse is 1/2x +2
Step-by-step explanation:
f(x) = 2x-4
y= 2x-4
To find the inverse
Exchange x and y
x = 2y-4
Solve for y
Add 4 to each side
x+4 = 2y
Divide by 2
x/2 + 4/2 = 2y/2
1/2x +2 = y
The inverse is 1/2x +2
Find the distance between the two points (8, 3) and (0, -3)
Answer:
10
Step-by-step explanation:
d is the variable for distance
√(0−8)2+(−3−3)2=
√(−8)2+(−6)2=
√64+36=
√100=
10
Answer:
10
Step-by-step explanation:
help me with guys plzzzzz
Answer:
C
Step-by-step explanation:
So the lion weighs more than the ant right?
And we wish to figure out how much greater the lion's weight is compared to the ant's weight.
So only thing we have to do is divide.
[tex]\frac{1 * 10^5}{2*10^-3} = \frac{10^5}{2*10^-3} = \frac{10^8}{2} = 50000000 = 5 * 10^7[/tex]
Answer:
5×10^7
Step-by-step explanation:
2×10^-3 1×10^5
(1×10^5)/(2×10^-3)=
5×10^7
to scheck :(2*10^-3)(5*10^7)=(1*10^5)
Write an expression to represent the product of 6 and the square of a number plus 15.
Answer:
6x^2 + 15
Step-by-step explanation:
We don't know what the square of a number is, so we represent it as x^2
The first part tells us to find the product of 6 and the square of a number, so
6x^2
The second part tells us to add 15 so,
6x^2 + 15
The expression that should be represented is [tex]6x^2 + 15[/tex]
Given that
The product of 6.The square of number + 15.Based on the above information,
Let us assume the number should be x
So, from the above information, the expression should be [tex]6x^2 + 15[/tex]
Therefore we can conclude that The expression that should be represented is [tex]6x^2 + 15[/tex]
Learn more about the equation here:brainly.com/question/21105092?
Please help I did the first 2 already.
The answer to C is 1.5 or 3/2
Since we know that 2x is equal to 3 because the solution is three and 3+3=6 then we divide 3 by 2 to get 3/2
