The answer is:
[tex](x+y)(x^{2}-xy+y^{2})=x^{3}+y^{3}[/tex]
Why?To find the resultant expression, we need to apply the distributive property.
It can be defined by the following way:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]
Also, we need to remember how to add like terms: The like terms are the terms that share the same variable and exponent, for example:
[tex]x+x+x^{2}=2x+x^{2}[/tex]
We were able to add only the two first terms since they were like terms (they share the same variable and the same exponent)
So , we are given the expression:
[tex](x+y)(x^{2}-xy+y^{2})[/tex]
Then, applying the distributive property, we have:
[tex](x+y)(x^{2}-xy+y^{2})=x*x^{2}-x*xy+x*y^{2}+y*x^{2}-y*xy+y*y^{2}\\\\x*x^{2}-x*xy+x*y^{2}+y*x^{2}-y*xy+y*y^{2}=x^{3}-x^{2}y+xy^{2}+yx^{2}-xy^{2}+y^{3}\\\\x^{3}-x^{2}y+xy^{2}+yx^{2}-xy^{2}+y^{3}=x^{3}+y^{3}[/tex]
Hence, the answer is:
[tex](x+y)(x^{2}-xy+y^{2})=x^{3}+y^{3}[/tex]
Have a nice day!
Please help me it urgent find the total area.
I'll split this figure up in three sections, 65*60, 70*190, and 95*140.
95*140=13300
70*190=13400
65*60= 3900
Add the three areas of the three figures I have split the original figure into and you get 30600 ft²
what is the measure of major arc MBD
Answer:
The measure of the major arc MBD is 270°
Step-by-step explanation:
we know that
The measure of major arc MBD is equal to the sum of the measure of the arc MB plus the measure of the arc BD
BD is a diameter-----> divide the circle into two equal parts
so
arc BD=180°
arc MB is a quarter of circle
so
arc MB=90°
therefore
arc MBD=180°+90°=270°
8. Kristen borrowed $700 at a
simple interest rate of 15% for 3
years. How much interest will
Kristen pay?
[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$700\\ r=rate\to 15\%\to \frac{15}{100}\dotfill &0.15\\ t=years\dotfill &3 \end{cases} \\\\\\ I=(700)(0.15)(3)\implies I=315[/tex]
What number should be added to both sides of the equation to complete the square?
x2 – 6x = 5
I think 9 should be added to both sides.
cofficient of x = 6
half of it = 6/2 = 3
square the 3
to give 3 squared = 3*3 9
Answer:
9
Step-by-step explanation:
To make it a Perfect Square Trinomial, you can square root 9 and multiply it to get 6, therefore 9 is correct
Can someone help with this plz?
Answer:
Hey No worries. Its very easy.
Step-by-step explanation:
Look,
Volume= 84 in.cube
Length=6 in.
Breadth=2 in.
therefore, Height= Volume/(Length*Breadth)
=84/(6*2)
=84/12
=7
Answer:
h = 7 in
Step-by-step explanation:
The volume (V) of a cuboid is calculated using the formula
V = lbh ( l is length, b is breadth and h is height )
Given V = 84 in³, then
lbh = 84 ← substitute l = 6 and b = 2
6 × 2 × h = 84
12h = 84 ( divide both sides by 12 )
h = 7
This question is very confusing for me can someone please help me
Essentially this question is asking, If we made circle O as big as circle O1, how could we move it to the same spot. Therefore, I would expect the Answer to be D.
A college-entrance exam is designed so that scores are normally distributed with a mean of 500 and a standard deviation of 100. What percent of exam scores are between 400 and 600?
__% of exam scores are between 400 and 600.
Answer:
68% of exam scores lie within one std. dev. of the mean
Step-by-step explanation:
Because the standard deviation is 100, one standard deviation above the mean comes out to 600. Likewise, one std. dev. below the mean comes out to 400. By the Empirical Rule, 68% of exam scores lie within one std. dev. of the mean.
Answer:
[tex]P(400<x<600) = 68.3\%[/tex]
Step-by-step explanation:
We know that the average [tex]\mu[/tex] is:
[tex]\mu=500[/tex]
The standard deviation [tex]\sigma[/tex] is:
[tex]\sigma=100[/tex]
The Z-score is:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
We seek to find
P(400<x<600)
This is:
[tex]P(400<x<600)=P(\frac{400-500}{100}<\frac{x-\mu}{\sigma}<\frac{600-500}{100})\\\\P(400<x<600)=P(-1<Z<1)[/tex]
Looking for the value of z in a normal table we have to:
[tex]P(Z>1) =0.1587\\\\P(Z>-1) = 0.8413[/tex]
So
[tex]P(-1<Z<1)=P(Z>-1) - P(Z>1) =0.8413-0.1587=0.6826\\\\P(400<x<600) = 68.3\%[/tex]
Please help ASAP!!!!
The answer is B i had this problem.
Answer: OPTION B
Step-by-step explanation:
Multiply both denominators to find the Least Common Denominator:
[tex]LCD=(3y-4)(y^2)[/tex]
Now, divide each original denominator by the LCD and multiply the result by each numerator. Then:
[tex]=\frac{(6y^2+2y)(y^2)-(9y-7)(3y-4)}{(3y-4)(y^2)}[/tex]
Applying Distributive property, you get:
[tex]=\frac{6y^4+2y^3-(27y^2-36y-21y+28)}{3y^3-4y^2}\\\\=\frac{6y^4+2y^3-27y^2+36y+21y-28}{3y^3-4y^2}[/tex]
Add the like terms in the numerator:
[tex]=\frac{6y^4+2y^3-27y^2+57y-28}{3y^3-4y^2}[/tex]
Which phrase best describes the translation from the graph y = 2x2 to the graph of y = 2x2 + 5?
ANSWER
5 units up
EXPLANATION
The given function is
[tex]y = 2 {x}^{2} [/tex]
The new graph is
[tex]y = 2 {x}^{2} + 5[/tex]
The new function is obtained by adding 5 to the original function.
This will shift the graph up by 5 units.
The translation is a vertical shift up by 5 units.
Answer:
The translation is 5 units up
Step-by-step explanation:
+5 on the outside means up by 5
Ari’s teacher says he may have his report grade based on either the mean or the median of his last six test scores.
88%, 73%, 97%, 76%, 90%, 80%
Which measure of center would best represent Ari’s grade?
Answer:
Mean because it is the average of all of them combined = best representation of all grades.
84% & Mean
Step-by-step explanation:
88 + 73 + 97 + 76 + 90 + 80 = 504
**divide by how many grades there are** (6 of them)
504 / 6 = 84
Meaning the best center representation would be 84%
Answer: The Mean
The mean is when you add up all of those grades and divide by the amount of exams.
1,580 milliliters (mL) is equal to how many liters (L)?
For this case we must make a conversion. By definition, we have to:
1 liter equals 1000 milliliters.
So, we make a rule of three:
1L ------------> 1000mL
x ---------------> 1580mL
Where the variable "x" represents the amount of liters equivalent to 1580 milliliters.
[tex]x = \frac {1580 * 1} {1000}\\x = 1.58[/tex]
Thus, 1580 milliliters equals 1.58 liters.
Anwer:
1.58 liters
At a local pizza place, the cost of a large cheese pizza is $13.99. Each additional topping is $1.25. The Tigerd family orders a large pizza topped with pepperoni, mushrooms, olives, and sausage. How much did their pizza cost?
Answer:
$18.99
Step-by-step explanation:
Step 1: Take the per topping amount ($1.25) and multiply it by the amount of toppings (4). $1.25x4=$5
Step 2: Add your toppings total ($5) to the base pizza cost ($13.99). $13.99+$5=$18.99
Answer:
18.99
work:
13.99 + (1.25 x 4 )
13.99 + 5
18.99
trust me, 18.99 + (1.25 x 4) will work and the work showing also
c/3 = 30/5 what steps do I take to see what c is?
For this case we must find the value of "c" of the following expression:
[tex]\frac {c} {3} = \frac {30} {5}[/tex]
We solve the right side of the equation:
[tex]\frac {30} {5} = 6[/tex]
Rewriting:
[tex]\frac {c} {3} = 6[/tex]
We multiply both sides of the equation by "3":
[tex]c = 6 * 3\\c = 18[/tex]
Answer:
[tex]c = 18[/tex]
PLEASE HELP!! If the endpoints of have the coordinates A(9, 8) and B(-1, -2), what is the midpoint of ?
A. (5, 3)
B. (4, 5)
C.(5, 5)
D. (4, 3)
M refers to midpoint.
[tex]
A(9, 8) \\
B(-1, -2) \\
M(\frac{x_1-x_2}{2}, \frac{y_1-y_2}{2}) \\
M(\frac{9-(-1)}{2}, \frac{8-(-2)}{2}) \\
M(\frac{10}{2}, \frac{10}{2})\Longrightarrow\boxed{M(5, 5)}
[/tex]
Hope this helps.
r3t40
I need help with this
Answer: Angle 10 and Angle 2
Factor 27a^3 b^9+8c^18
Answer:
(3ab^3+2c^6)(9a^2b^6-6ab^3c^6+4c^12)
Step-by-step explanation:
Given:
Polynomial 27a^3 b^9+8c^18
Factoring the given polynomial
27a^3b^9 can be written as
=3^3.a^3.b^3^3
=(3ab^3)^3
Also 8c^18 can be written as
=2^3.c^6^3
=(2c^6)^3
Hence Polynomial 27a^3 b^9+8c^18 can be written as
=(3ab^3)^3+(2c^6)^3
Applying sum of cubes formula i.e. a^3 + b^3=(a+b)(a^2 – ab + b^2)
=(3ab^3+2c^6)(9a^2b^6-6ab^3c^6+4c^12) !
Complete the square to solve the equation below check all that apply x^2+8x-2=18
x^2+8x-2=18
x^2+8x-2-18= 18-18
x^2+8x-20= 0
(x-2)(x+10)=0
x-2= 0 , x+10=0
x-2+2= 0+2, x+10-10= 0-10
x=2 , x=-10
Answers are x= 2 -B, x=-10 -A.
Answer:
Option A and B
Step-by-step explanation:
Given : Quadratic equation [tex]x^2+8x-2=18[/tex]
To find : Complete the square to solve the equation below check all that apply ?
Solution :
Re-write, [tex]x^2+8x-2=18[/tex]
[tex]x^2+8x-20=0[/tex]
Applying quadratic formula,
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here, a=1 , b=8, c=-20
[tex]x=\frac{-8\pm\sqrt{8^2-4(1)(-20)}}{2(1)}[/tex]
[tex]x=\frac{-8\pm\sqrt{64+80}}{2}[/tex]
[tex]x=\frac{-8\pm\sqrt{144}}{2}[/tex]
[tex]x=\frac{-8\pm12}{2}[/tex]
[tex]x=-4\pm6[/tex]
[tex]x=-4+6,-4-6[/tex]
[tex]x=2,-10[/tex]
The solution of the equation is x=2,-10.
Therefore, Option A,B satisfy the equation.
6.
The higher your credit score, the _____.
lower your savings interest rate
higher your car loan rate
higher risk you are to a creditor
lower your mortgage interest rate
Answer:
lower your mortgage interest rate
Step-by-step explanation:
The higher your credit score, the __lower your mortgage interest rate__.
Because the higher your credit score, the less risk you represent for a lender, so it will most likely grant you a lowest rate for your mortgage/loan.
The "lower your savings interest rate " is not the answer because savings interest rates are not related to the credit score...
"higher your car loan rate " and "higher risk you are to a creditor " are consequences of a low credit score.
HELP! 18 points for the two questions!! urgent will mark brainliest
Answer:
1- none of the choices are correct.
2-none of the answer choices are correct.
Step-by-step explanation:
1- there is no k therefore none are correct because they all offer a solution for k
2- yes the parabola opens upward but none are right in the right mix for the other two. the vertex is at (0,-5) and the axis of symmetry is x = 0 (not only because I calculated it and the graph showed it but because (x,y) And the x spot is a 0)
any time you just see a plain x^2 or really anything like that in the same vanilla sense wether the exponent is changed or there is a coefficient and all it has is a plus or minus whatever it will just be along the y axis where the plus or minus number was. (can't remember any vanilla advice for parabolas sorry)
Answer:
1. a=5,h=0,k=0
2. None of the choices are correct
Step-by-step explanation:
1. The function given is:[tex]f(x)=5x^2[/tex]
We can rewrite this in vertex form as: [tex]f(x)=5(x-0)^2+0[/tex].
Comparing this to [tex]f(x)=a(x-h)^2+k[/tex], we have a=5,h=0 and k=0.
The first choice is correct
2. The function given is: [tex]f(x)=x^2-5[/tex]
This can be rewritten in the vertex form as:
[tex]f(x)=a(x-0)^2-5[/tex]
Comparing this to [tex]f(x)=a(x-h)^2+k[/tex], we have a=1,h=0 and k=-5.
Since 'a' is positive, the parabola opens upwards, and has its vertex at (h,k)=(0,-5), and line of symmetry at x=0.
Based on this, the correct choice is none of the choices are correct
which inequality is equalivalent to |x-4|<9
Answer:
-5 < x < 13Step-by-step explanation:
[tex]|x-4|<9\iff x-4<9\ \wedge\ x-4>-9\qquad\text{add 4 to both sides}\\\\x<13\ \wedge\ x>-5\to-5<x<13[/tex]
Jeremy is recording the weights, in ounces, of different rock samples in a lab. The weights of seven rocks are listed below.
11, 13, 14, 6, 10, 9, 10
The eighth rock that he weighed was 5 ounces. How would the interquartile range of the data be affected if Jeremy includes the weight of the eighth rock?
Answer:
The correct answer is option "C"
"The interquartile range increases"
The value of the (RIC) will increase from 4 to 5.75, that is, 44%
Step-by-step explanation:
The range is defined as the difference between the maximum and minimum value of a series of data. Xmax - Xmin
The interleaving range (RIC) is a measure of dispersion that measures the central range of 50% of the data.
Therefore, if a low value is included, such as five, the variance of the data would be greater and, consequently, the value of the (RIC) will increase from 4 to 5.75, that is, 44%
Annie had 7 apples, she sold 5 of them, and bought 3 more apples. Annie gave 2 apples to her friends, and then lucy gave her 9 apples, annie ate 6 apples, and found 89 more apples. How many apples does annie have now?
Answer:
Annie has 95 apples now
Answer:
Annie has 95 Apples
Step-by-step explanation:
7 Apples - 5 Apples = 2
2 + 3 more apples = 5 Apples
5 Apples - 2 Apples = 3 Apples
3 Apples + 9 more apples = 12 Apples
12 - 6 = 6 Apples
6 Apples + 89 more apples = 95 Apples
Mr. Grocer has 421 dozen eggs valued at $0.59 per dozen. How much are the eggs worth altogether?
248.39
713.56
420.41
421.59
Answer:
248.39
Step-by-step explanation:
421 × .59 =248.39
How much of 10% HCl and 35% HCl would be needed to mix and produce 60 liters of 25% HCl?
About 30 & 30 liters
About 33 & 27 liters
About 36 & 24 liters
About 39 & 21 liters
Answer:
Equation:
HCL + HCL = HCL
0.30x + 0.45(50-x) = 0.35*50
Multiply thru by 100 to get:
30x + 45*50 - 45x = 35*50
-15x = -10*50
x = (2/3)50
x = 33 1/3 liters (amt. of 30% solution needed in the mixture)
50-x = 16 2/3 liters (amt. of 45% solution needed in the mixture)
=============
Step-by-step explanation:
Answer:
about 36 and 24 liters
Step-by-step explanation:
a+b = 60 1
let A multiplied by 10 percent and B multiplied by 35 percent then
10 a + 35 b = 1500 ( 60 * 25 ) 2
add no. 1 to 2 and multiply no.1 by -10
-10 a+ -10 b = -600
10 a+ 35 b = 1500 adding
then 25 b = 900 then b = 36 liter
then a = 24 liter
85 kilometers is equal to how many meters
Answer:
85 kilometers is equal to 85 000 meters
Step-by-step explanation:
1 kilometer is equivalent to 1000 meters. Then to convert from kilometers to meters use the following conversion factor
[tex]x\ kilometers * \frac{1000\ meter}{1\ kilometers }[/tex]
In this case [tex]x=85[/tex]
Then
[tex]85\ km* \frac{1000\ m}{1\ km} =85,000\ m[/tex]
Finally 85 kilometers = 85,000 meters
Answer:
85km = 85,000mStep-by-step explanation:
1km - one kilometer
kilo - 1,000 times more
1km = 1,000m
therefore
85km =85 × 1,000m = 85,000m
Determine the distance between -3 and 6.
A) -9 units
B) -3 units
C) 3 units
D) 9 units
Answer:
9 units
Step-by-step explanation:
Because you start at -3 and go up so you do not add the -9 its just 9
It's 9 units because there's no such thing as -9 units!
What is the answer to 3 √-125/216
Answer:
2.28i
Step-by-step explanation:
u divide the -125/216
then u square root it
and multiply it times 3
YES THE I IS FOR A REASON IT MEANS IT IS IMAGINARY
2.28i I think that’s the answer but I am not sure
The ratio of the lengths of an ellipse is 3:2. If it’s area is 150 cm2, what are the lengths of The major and minor semiaxes respectively?
Answer:
the length of major semiaxes a = 8.45 cm and minor semiaxes b= 5.63 cm.
Step-by-step explanation:
Area of ellipse = π*a*b
Let major semiaxes = a and minor semiaxes = b
then a:b = 3:2
a/b = 3/2
=> a = 3/2 b
Putting in the value of formula
150 = π * (3/2)b * b
150 = 3.14 * 1.5b * b
150= 4.71 b^2
150/4.71 = b^2
=> b^2 = 31.8
b= 5.63
a = 3/2 * b
a = 1.5 * 5.63
a = 8.45
So, the length of major semiaxes a = 8.45 cm and minor semiaxes b= 5.63 cm.
Answer:
Major: 8.5 cm
Minor: 5.6 cm
Step-by-step explanation:
How many hours are there in 1 week, 3 and 1/2 days?
Answer:
252 hours
Step-by-step explanation:
1 day = 24 hours
1 week = 7 days
= 24 * 7
= 168 hours
3 days = 24 * 3
= 72 hours
1/2 day = 24 / 2 = 12 hours
Add up all values/hours:
168 hours + 72 hours + 12 hours = 252 hours
Answer:
1 week- 168 hours
3 days-72 hours
1/2 day-12 hours
Step-by-step explanation:
1 week- 24x7=168
3 days- 24x3=72
1/2 day- 24x.5=12
find the missing angle measure in each figure
Answer:
x = 100°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 7, hence
sum = 180° × 5 = 900°
Sum the given interior angles and equate to 900
x + 155 + 116 + 135 + 135 + 116 + 143 = 900
x + 800 = 900 ( subtract 800 from both sides )
x = 100°