Answer: (4y-9z)( 16y^2 + 36yz + 81z^2 )
=======================================================
Explanation:
We'll use the difference of cubes factoring rule
a^3 - b^3 = (a-b)(a^2+ab+b^2)
In this case,
a^3 = 64y^3 which leads to a = 4yb^3 = 729z^3 which leads to b = 9zSo,
a^3 - b^3 = (a-b)(a^2+ab+b^2)
64y^3 - 729z^3 = (4y-9z)( (4y)^2 + (4y)(9z) + (9z)^2 )
64y^3 - 729z^3 = (4y-9z)( 16y^2 + 36yz + 81z^2 )
Taylor has nickels and dimes. The number of nickels is 7 less then eight times the number of dimes. If d represents the number of dimes then the number of nickels can be expressed as what
Answer: [tex]8d-7[/tex]
Step-by-step explanation:
Given
Taylor has nickels and dimes
Number of nickels is 7 less than eight times the number of dimes
If d is the number of dimes, then number of nickels is given by
[tex]\Rightarrow \text{Number of Nickels = }8d-7[/tex]
Which of the following equations would not have a solution that is the same as the solution to the system. shown below?
4x+y=7
-2x+5y=1
———————————————
1) 11y = 9
2) 2x + 6y = 8
3) -4x + 10y = 1
4) 12x + 3y = 21
please help asap and thank you in advance to anyone who answers this for me ! :)
Answer:
Step-by-step explanation:
SOMEONEEEE HELPPP MEEEEE PLEASEEEE!!!!
Answer:
[tex]{ \tt{ \tan(x) = \frac{opposite}{adjacent} }} \\ \\ { \tt{ \tan( \theta) = \frac{30}{16} }}[/tex]
An amusement park charges and admission fee of 30 dollars for each person. Let C be the cost (in dollars) of admission for P people. Write an equation relating C to P.
Answer:
14
Step-by-step explanation: B is the midpoint of AC, in other words it is the halfway point.
So A to B should be equal to B to C
Our expression is:
2x + 9 = 37
Subtract 9
2x = 28
Divide by 2
x = 14
A record club has found that the marginal profit,
Upper P prime (x ), in cents, is given by
Upper P prime (x )equals negative 0.0008 x cubed plus 0.20 x squared plus 46.8 x for x less than or equals 200,
where x is the number of members currently enrolled in the club. Approximate the total profit when 120 members are enrolled by computing the sum
Summation from i equals 1 to 6 Upper P prime (x Subscript i Baseline )Upper Delta x with Upper Delta x equals 20.
Solution :
Given :
[tex]$P'(x) = -0.0008x^3+0.20x^2+46.8x,$[/tex] for x ≤ 200
Total profit when 120 members are enrolled is :
[tex]$\sum_{i=1}^6P'(x_i) \Delta x$[/tex] with [tex]\Delta x = 20[/tex]
Using the left end points, we get,
The values of [tex]x_i[/tex] are : { 0, 20, 40, 60, 80, 100}
Therefore,
[tex]$P'(x_1) = P'(0)=-(0.0008)(0)^3+(0.20)(0)^2+(46.8)(0)$[/tex]
= 0
[tex]$P'(x_2) = P'(20)=-(0.0008)(20)^3+(0.20)(20)^2+(46.8)(20)$[/tex]
= 1009.6
[tex]$P'(x_3) = P'(40)=-(0.0008)(40)^3+(0.20)(40)^2+(46.8)(40)$[/tex]
= 2140.8
[tex]$P'(x_4) = P'(60)=-(0.0008)(60)^3+(0.20)(60)^2+(46.8)(60)$[/tex]
= 3355.2
[tex]$P'(x_5) = P'(80)=-(0.0008)(80)^3+(0.20)(80)^2+(46.8)(80)$[/tex]
= 4614.4
[tex]$P'(x_6) = P'(100)=-(0.0008)(100)^3+(0.20)(100)^2+(46.8)(100)$[/tex]
= 5880
[tex]$\sum_{i=1}^6P'(x_i) \Delta x = P'(x_1)\Delta x + P'(x_2)\Delta x + P'(x_3)\Delta x + P'(x_4)\Delta x + P'(x_5)\Delta x + P'(x_6)\Delta x $[/tex]
= (0)(20) + (1009.6)(20) + (2140.8)(20) + (3355.2)(20) + (4614.4)(20) + (5880)(20)
= (20)( 0 + 1009.6 + 2140.8 + 3355.2 + 4614.4 + 5880)
= (20)(17,000)
= 340,000 cents
[tex]$=\frac{340000}{100} \ \text{dollars}$[/tex]
= 3400 dollars
Hence, the required total profit is 3400 dollars.
A football was kicked through the air and it followed the path h\left(s\right)=-3s^2+75h(s)=−3s 2 +75 . Let h\left(s\right)h(s) represent the height of the soccer ball after, s, seconds.
Complete question is;
A soccer ball was kicked through the air and it followed the path. Let h(s) = −3s² +75 represent the height of the soccer ball after s seconds.
Find the time at which the soccer ball hits the ground.
Answer:
s = 5 seconds.
Step-by-step explanation:
We are given the function;
h(s) = −3s² +75
Where;
h(s) is height at time s
s is the time taken
Now, the time at which the time at which the soccer ball hits the ground would be at h(s) = 0 since height is at 0 point.
Thus;
−3s² +75 = 0
−3s² = -75
s² = 75/3
s² = 25
s = √25
s = 5 seconds.
The measures of a rectangle are 8 inches by 15 inches. Find the length of the diagonal.
Answer:
17
Step-by-step explanation:
The diagonal forms a triangle.
Use the Pythagorean theorem
Diagonal = sqrt(8^2 + 15^2)
Diagonal = sqrt(64 + 225)
Diagonal = sqrt( 289)
Diagonal = 17
Answer: 17 inches
Determining if a Relationship Is a Function
Which represents a function?
Answer:
only the first one...
a "FUNCTION" has a UNIQUE relation between each input and output...
notice the middle one the -2 goes to BOTH th2 10 & -7 that makes it NOT a FUNCTION
Step-by-step explanation:
Help and please explain I don't get khan academy
Answer:
same y intercept
Step-by-step explanation:
The y intercept is when r = 0
Function 1
p = -3/2 r - 5
Let r = 0
p = 0-5
p = -5
Function 2
When r = 0 p = -5
They both equal -5, so they both have the same y intercept
How to find the exact answer of the area and circumference
I know how to find the approximate answer for both but i don’t know how to find the exact answer. Pi should be included in the exact fraction.
Can someone explain pls:)
Answer:
[tex]\pi \\[/tex] is irrational so any attempt to use 3.14... is never EXACT...
do not try to convert it ... if it asks for exact..
write 81[tex]\pi \\[/tex] or 9 [tex]\pi \\[/tex] etc. don't put in 63.62 like answers
Step-by-step explanation:
I’m stuck on this one help anyone?
Answer:
just add a small amount to the 2.8 and square the result
Step-by-step explanation:
x x^2
2.8 7.84
2.81 7.8961
2.82 7.9524
2.83 8.0089
2.84 8.0656
2.85 8.1225
2.86 8.1796
2.87 8.2369
Find the value of x for the right triangle.
Mr Lorenzo must make a minimum of 48 circuit boards per day. On Wednesday he made 60. What percent of required minimum did he make
Answer:
He made 125% of the required minimum.
Step-by-step explanation:
Percentage:
The percentage that a number b is of a is given by:
[tex]P = \frac{100b}{a}[/tex]
In this question:
Minimum of 48, made 60. The percentage 60 is of 48 is:
[tex]P = \frac{100(60)}{(48)} = 100(1.25) = 125[/tex]
He made 125% of the required minimum.
what is the approximate area of the shaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question.
a. 0.02
b. 0.14
c.0.34
d.0.84
You want to find Pr[-2 < Z < -1].
The table tells you that
• Pr[Z < 0] = 0.5000
• Pr[Z < 1.00] = 0.8412
• Pr[Z < 2.00] = 0.9772
• Pr[Z < 3.00] = 0.9987
We have
Pr[-2 < Z < -1] = Pr[Z < -1] - Pr[Z < -2]
(because the distribution of Z is continuous)
… = Pr[Z > 1] - Pr[Z > 2]
(by symmetry of the distribution about its mean)
… = (1 - Pr[Z < 1]) - (1 - Pr[Z < 2])
(by definition of complement)
… = Pr[Z < 2] - Pr[Z < 1]
… = 0.9772 - 0.8412
… = 0.1360 ≈ 0.14 … … … (B)
Answer:
it's B aka 0.10.14
Step-by-step explanation:
Two legs of a right triangle measure 23 inches and 38 inches. What is the length of the hypotenuse, to the nearest
inch?
Answer:
hypotenuse ≈ 44 inches
Step-by-step explanation:
Using Pythagoras' identity
The square on the hypotenuse is equal to the sum of the squares on the other two sides.
let the hypotenuse be h , then
h² = 23² + 38² = 529 + 1444 = 1973 ( take square root of both sides )
h = [tex]\sqrt{1973}[/tex] ≈ 44 inches ( to the nearest inch )
Find the measure of each angle indicated.
890
50°
A) 44°
C) 47°
B) 51°
D) 71°
Answer:
51
Step-by-step explanation:
See the other answer
Answer:
(B). 51°
Step-by-step explanation:
Examine circle O, where chords AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯ are congruent.
Point P lies on AB¯¯¯¯¯¯¯¯ and point Q lies on CD¯¯¯¯¯¯¯¯.
Angles APO and DQO are right angles.
The diagram as described in the problem.
Which congruence statement is true?
CD≅AP
QD≅QO
OP≅OQ
OP≅AB
What is sin 28°?
62
8
17
90
15
28
A.
Sooden
O c.
O
Answer:
the sin of 28 degree is 28
Step-by-step explanation:
it's the same degree in radians I hope this help
Can someone help me please
Answer:
ok
Step-by-step explanation:
Somebody give the answer to the question attached please
Sophia pays £222 for a plane ticket.
She also pays 100 euros airport tax.
The exchange rate is £1 = 1.38 euros.
What percentage of the total cost of the ticket and the airport tax does Sophia pay
for the
airport tax?
Give your answer correct to 1 decimal place.
9514 1404 393
Answer:
24.6%
Step-by-step explanation:
The cost of the ticket in euros is ...
£222 × €1.38/(£1) = €306.36
Then the ratio of the tax to the to the total cost is ...
€100/(€306.36 +100) = 100/406.36 ≈ 24.6%
Seventy of Myra’s classmates are traveling by bus to a football game in another town. They hired 2 buses, but there were only 64 seats. The remaining 6 students had to travel in a separate van.
The equation 2b + 6 = 70 represents the given scenario. What does b represent?
Answer:
seats in each bus
Step-by-step explanation:
total no.of seats = 64
so, the no.of seats in each bus = 64/2 =32
therefore , b denotes the no.of seats in each bus
PLEASE MARK ME AS BRAINLIEST .
In a shipment of airplane parts, 6% are known to be defective. If 42 parts are found to be defective, how many parts are in the shipment?
Answer:
700 parts
Step-by-step explanation:
To find the total amount of parts in the shipment, all we need to do is divide.
6% = 0.06
42 / 0.06 = 700
Best of Luck!
someone help me solve this pls !!
Answer:
9 (or 18)
9 (or 18)
18 (or 36)
Step-by-step explanation:
If B is midpoint if AC, then AB = BC
AB = 3x
BC = 5x - 6
So...
3x = 5x - 6
==> 2x = 6
==> x = 3
AB = BC = 3×3 = 5×3 - 6 = 9
And...
AC is AB + BC (since B is midpoint)
==> AC = 9 + 9 = 18
((Answer may be twice this. Picture is unclear if "3x" and "5x - 6" are values of AB and BC (resp.) or if they are midpoint values of AB and BC, in which case everything would just be doubled (except for x, the 2's would cancel out).))
Select the correct answer.
Function h is a transformation of the parent exponential function, f(x) = 2^x.
.h(x)=-3.2^x
-
Which statement is true?
A certain forest covers an area of 2300 km. Suppose that each area decreases by 5.75%. What will be the area after 12 years?
Answer:
The correct answer is 2043 km².
Step-by-step explanation:
Given:
Starting area,
A = 2300 km²
Rate of decreasing,
r = 5.75%
Time,
t = 12 years
As we know,
⇒ [tex]y = A(1-r)^t[/tex]
By substituting the values, we get
[tex]=2300(1-0.0575 )^{12}[/tex]
[tex]=2300(0.9425)^{12}[/tex]
[tex]=2300\times 0.8883[/tex]
[tex]=2043 \ km^2[/tex]
How much money invested at 3% compounded monthly for 3 years will yield $520?
$179.42
$475.30
$358.84
$148.78
Answer:
Step-by-step explanation:
Use this formula:
[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex] where A(t) is the amount after the compounding is done, P is the initial investment (our unknown), r is the interest rate in decimal form, n is the number of compoundings per year, and t is the time in years. Filling in:
[tex]520=P(1+\frac{.03}{12})^{(12)(3)}[/tex] and simplifying that a bit:
[tex]520=P(1+.0025)^{36[/tex] and a bit more:
[tex]520=P(1.0025)^{36[/tex] and even bit more:
520 = P(1.094551401) and divide to get
P = $475.30
Someone help me pls ..
Answer:
because they are both in the circle
Step-by-step explanation:
shanika has a lamp that she wants to send to her sister in baltimore.the lamp is in the shape of a rectangular prism.it measures 14 high, 9 wide, and 3 long.she wants to buy a box so that there is 1 all around the lamp for bubble wrap
Consider we need to find the dimensions and volume of the box.
Given:
The shape of the lamp is a rectangular prism.
It measures 14 high, 9 wide, and 3 long.
There is 1 all around the lamp for bubble wrap
To find:
The dimensions and volume of the box.
Solution:
Length of the box is:
[tex]3+2=5[/tex]
Width of the box is:
[tex]9+2=11[/tex]
Height of the box is:
[tex]14+2=16[/tex]
Therefore, the dimensions of the box are 5 by 11 by 16 units.
The volume of the box is:
[tex]V=l\times w\times h[/tex]
Where, l is length, w is width and h is height.
Putting [tex]l=5, w=11, h=16[/tex], we get
[tex]V=5\times 11\times 16[/tex]
[tex]V=880[/tex]
Therefore, the volume of the box is 880 cubic units.
Find the value of x.
B
X+2
3
D
E
х
2
А
x = [?]
Answer:
x = 4
Step-by-step explanation:
The line DE is parallel to AC and divides the sides proportionally, that is
[tex]\frac{BD}{AD}[/tex] = [tex]\frac{BE}{CE}[/tex] , substitute values
[tex]\frac{x+2}{x}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )
3x = 2(x + 2) = 2x + 4 ( subtract 2x from both sides )
x = 4
