Answer:
(a) [tex]3x^2 + 27y^2 + z^2 - 18xy + 6 \sqrt{3} yz -2 \sqrt{3} zx[/tex]
this can be written as
[tex](-x\sqrt{3})^2 + (y3\sqrt{3})^2 + (z)^2 +2 ( -x\sqrt{3} )( y3\sqrt{3}) + 2( y3\sqrt{3})(z) + 2(z)( -x\sqrt{3})[/tex]
which is equivalent to
[tex]a^2+ b^2 + c^2 + 2ab + 2bc + 2ac = (a+b+c)^2[/tex]
[tex](-x\sqrt{3} + y3\sqrt{3} + z)^2 = (-x\sqrt{3} + y3\sqrt{3} + z)(-x\sqrt{3} + y3\sqrt{3} + z)[/tex]
(b)[tex]27 x^3 + 125y^3[/tex] = [tex](3x)^3 + (5y)^3[/tex]
which is same as [tex]a^3 + b^3 = (a+b)(a^2 +b^2 -ab)[/tex]
= [tex](3x + 5y)(9x^2 + 25y^2 -15xy)[/tex]
(c) [tex](2a - 3b + c )^2[/tex] = (2a -3b +c)(2a -3b+c)
(d) [tex]a^3 + b^3 + 125 c^3 - 15 a b c[/tex]
this is same as
[tex]a^3 + b^3 +c^3 - 3abc[/tex] = [tex](a+b+c)( a^2+b^2+c^2 -ab-bc-ac)[/tex]
= [tex](a + b + 5c)(a^2+b^2 +25c^2 -ab -5bc -5ac)[/tex]
(e) [tex](x - 1/x y)^3[/tex] = [tex](x - 1/xy)(x - 1/xy)(x - 1/xy)[/tex]
(f) [tex]x^4 y^4 - x y64^4 = xy( x^3y^3 - 64^4) = xy( x^3y^3 - (256)^3) \\ = xy( xy - 256 )(x^2y^2 + 65536 + 256xy)[/tex]
(using the property of [tex]a^3 -b^3 = (a-b)(a^2+b^2 +ab)[/tex] )
(g) [tex]8x^3 - (2x - y)^3 = (2x)^3 - (2x-y)^3 \\ = (2x - 2x + y)(4x^2 + (2x-y)^2 + 2x(2x-y))\\ = y(8x^2 + y^2 -6xy +4x)[/tex] using the same property above
(h)
[tex]a^6 -b^6 = (a^2)^3 - (b^2)^3 = (a^2-b^2)( a^4+b^4 +a^2b^2)\\ = (a-b)(a+b)( a^4+b^4 +a^2b^2)[/tex]
Jasmine wants to use her savings of $1,128 to buy video games and movies. The total price of the movies she bought was $72. The video games cost $43 each. Choose the inequality that would be used to solve for the maximum number of video games Jasmine can buy with her savings.
A. 43 + 72x ≤ 1,128
B. 43 + 72x ≥ 1,128
C. 43x + 72 ≥ 1,128
D. 43x + 72 ≤ 1,128
Answer:
D. 43x + 72 ≤ 1,128
Step-by-step explanation:
She has $1,128
Total price $72
43x since its unit rate for each
43x + 72 is less than or equal to $1,128
Answer:
D. 43x + 72 ≤ 1,128
Step-by-step explanation:
Good luck! Hope this helped :)
3. You purchase a car using a $20,000 loan with a 5% simple interest rate.
(a) Suppose you pay the loan off after 4 years. How much interest do you pay on your loan? Show your work.
(b) Suppose you pay the loan off after 2 years. How much interest do you save by paying the loan off sooner? Show your work.
Answer:
Answer:
a) $4000
b) $2000
Step-by-step explanation:
a)
interest = Principal x rate as decimal x time
interest = 20,000 x 0.05 x 4
interest = 4000
b)
interest = Principal x rate as decimal x time
interest = 20,000 x 0.05 x 2
interest = 2000
you save $2000 if you pay after 2 years
Answer:2,500
Step-by-step explanation:
Miguel sells boxes of cookies for $8 each. Donna sells boxes of cookies for $10 each. Each of them sold the same dollar amount. It was the smallest dollar
amount for which this was possible.
Answer the following questions.
How many boxes did Miguel sell?
Answer:
$40
Step-by-step explanation:
You find the LCM (least common multiple). To do this, you can use prime factorization.
(there is an below that shows the prime factorization tree for 8 and 10)
so, the only common prime factor is 2. you use the 2 and multiply with the remaining prime factors.
5*2 --> for 10
2*2*2 -->for 8
becomes
5*2*2*2
if you multiply that out, it becomes 40.
Another method is to just think: "What can they both become after being multiplied by a number?" or "What can 8 and 10 both be?"
Anyway, the answer is 40. Hope this helps!
The ordered pairs is a
solution to the
inequality
8x – 3y > 24
A.2,6
B.0,-8)
C.-4,-6
D. 4,1
E. 8,2
Answer:
D,E
Step-by-step explanation:
Consider the rates 45 mile in 8 minutes and 4 minutes to travel 25 mile. Select the statement(s) that are true. Multiple select question. Cross out A) The rate 45 mile in 8 minutes has a unit rate of 10 miles per minute. Cross out B) The rate 45 mile in 8 minutes has a unit rate of 110 mile per minute. Cross out C) The rate 4 minutes to travel 25 mile has a unit rate of 10 minutes per mile. Cross out D) The rate 4 minutes to travel 25 mile has a unit rate of 110 minute per mile. Cross out E) Both rates are equivalent. Cross out F) The rates are not equivalent.
Answer:
F) The rates are not equivalent.
Step-by-step explanation:
Consider the rates 45 mile in 8 minutes and 4 minutes to travel 25 mile. Select the statement(s) that are true. Multiple select question.
We find the unit rates
a) 45 mile in 8 minutes , we find the unit rate in miles per minute
8 minutes = 45 miles
1 minute = x
8 × x = 45 miles × 1 minute
x = 45 miles/8 minutes
x = 5.625 miles/ minute
b) 4 minutes to travel 25 miles. Find the unit rate is minutes per mile
25 miles = 4 minutes
1 mile = x
25miles × x = 4 minutes × 1
x = 4 minutes/25 miles
x = 0.16 minutes/mile
Hence, the correct option is
F) The rates are not equivalent.
How can I get better at math so I don't flunk?
Answer:My suggestion is practice what you learned after each class for like 10-20 min and pay close attention in class. Wish you the best of luck.
Step-by-step explanation:
{PLEASE ANSWER}
g(7)=
Answer:
g(7) = 4
General Formulas and Concepts:
Algebra I
Reading a Cartesian PlaneWriting CoordinatesStep-by-step explanation:
What g(7) is saying is that we are trying to find the y-value when x = 7. According to the graph, when x = 7, y would equal 4. Therefore, g(7) = 4 and our coordinate would be (7, 4).
You need to know that g(7) means that x = 7. Look at the graph. When x is 7, what is the value of y?
The point (7,4) indicates that g(7) = 4.
Please help! It's about systems of equations. Answer correctly i will mark brainliest
Answer:
Step-by-step explanation:
Y= -6
X=-2
Which one is correct
Answer:
2ft
Step-by-step explanation:
Answer:
2 ft
Step-by-step explanation:
The triangle has a dilation of 1/3 and we can assume that the triangles are congruent
So we take 6 and divide it by 3 and get 2
The answer is 2 ft
5/12 = 8/n
What is N
Answer:
19.2
Step-by-step explanation:
Cross multiply to get 96=5n
n=19.2
Answer:
n= 96/5 or 19.2 or 19 1/5
Step-by-step explanation:
Help! How many points per star does Jayce earn from gold stars?
Which of the equations below represents a line perpendicular to the y-axis?
A.
x = 6
B.
y = -6
C.
y = 6x
D.
y = x
Answer:
B. y = -6
Step-by-step explanation:
As you can see the graph I done is perpendicular
Answer:
B
Step-by-step explanation:
A line perpendicular to the y- axis is a horizontal line parallel to the x- axis, with equation
y = c ( where c is the value of the y- coordinates the line passes through )
The only equation in this form is
y = - 6 → B
Complete the table for the function y=f(1/3x)
Answer:
Step-by-step explanation:
In AOPQ, m2O = (2x – 5)º, m P = (3x – 8)°, and mZQ = (10x – 17).
What is the value of x?
9514 1404 393
Answer:
x = 14
Step-by-step explanation:
The sum of angles in a triangle is 180°:
∠O +∠P +∠Q = 180°
(2x -5)° +(3x -8)° +(10x -17)° = 180°
15x -30 = 180 . . . . . divide by °, collect terms
x -2 = 12 . . . . . . . . . divide by 15
x = 14 . . . . . . . . . . . .add 2
What is the area of ABC?
Answer:
Area of triangle ABC = 10
Option C is correct.
Step-by-step explanation:
We need to find area of triangle ABC
We are given A(2,1) B(4,7) and C(6,3)
The formula used to find [tex]Area \ of \ triangle=\frac{1}{2}base\times height[/tex] ABC is:
In the given triangle base= AC and height = BC
First we need to find the distance between A and C and B and C
The formula used to find distance between AC [tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have [tex]x_1=2, y_1=1, x_2=6, y_2=3[/tex]
Putting values and finding distance
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(6-2)^2+(3-1)^2}\\Distance=\sqrt{(4)^2+(2)^2}\\Distance=\sqrt{16+4}\\Distance=\sqrt{20}[/tex]
find distance between BC [tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have [tex]x_1=4, y_1=7, x_2=6, y_2=3[/tex]
Putting values and finding distance
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(6-4)^2+(3-7)^2}\\Distance=\sqrt{(2)^2+(4)^2}\\Distance=\sqrt{4+16}\\Distance=\sqrt{20}[/tex]
So, We have height = [tex]\sqrt{20}[/tex] and base = [tex]\sqrt{20}[/tex]
Finding area of triangle
[tex]Area \ of \ triangle=\frac{1}{2}base\times height\\Area \ of \ triangle=\frac{1}{2}\sqrt{20} \times \sqrt{20} \\Area \ of \ triangle=\frac{1}{2}\times 20\\Area \ of \ triangle=10[/tex]
So, Area of triangle ABC = 10
Option C is correct.
PLS HELP ASAP!! WILL GIVE BRAINLIEST!!
Which system of inequalities has the following graph as its solution?
Answer:
x>3
y≥2x-5
Step-by-step explanation:
graph them
Name a point NOT on line l or m
0.000487 an Scientific Notation
Answer:
4.87 to the fourth power
Step-by-step explanation:
0.000487 in Scientific Notation:
4.87 * 10^-4
what is the value of b in the equation 45 x -b
Answer:
Step-by-step explanation:
if 45x-b is an equation then b value is the y coordinate of y-intercept (where graph touches the y axis)
Can i please get some help :)
ales tax is calculated as a percentage of the sales price. If sales tax is 7%, what is the sales tax on clothing that costs $150
Answer:
7% of 150= 10.5 :)
Step-by-step explanation:
150/x=100/7
(150/x)*x=(100/7)*x - we multiply both sides of the equation by x
150=14.2857142857*x - we divide both sides of the equation by (14.2857142857) to get x
150/14.2857142857=x
10.5=x
x=10.5
now we have:
7% of 150=10.5
Any help would be appreciated(brainly for best answer)
Answer:
a. x=100 b. x=30
Step-by-step explanation:
A: <1 and <2 are supplementary by consecutive interior angles theorem
x + x-20 = 180
2x-20=180
2x=200
x=100
B: <1 and <2 are congrunt by corresponding angles postulate
3x-5=x+55
2x=60
x=30
What is the equation of the line in slope-intercept form?
Answer:
y=mx+b :)
Step-by-step explanation:
1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7
ques #1: What happens to the mean and standard deviation of the data set when the 7 is changed to a 70?
ques #2: For the data set with the value of 70, why would the median be a better choice for the measure of center than the mean?
Answer:
The mean would get bigger becuase you are adding in a bigger number there for the mean would increase.The standard deviation would change as well because then again you are adding a bigger number and standard diviation is basically the difference between the gratest and least. For #2 no the median wouldn't chnage becuase the 70 is going in place for the 7 so it would just fill it's spot and wouldn't effect the data set.
Step-by-step explanation:
The median would be a better choice for the measure of center becuase the mean is telling you the average and the median is actully telling you where the middle of the data set is.
The mean is the average of a group of data. The data set added up and divided by the number of data. The mean is sensitive to extreme data.
When 7 is changes to a 70 then mean and standard deviation both changes.
For the given data set median be a better choice for the measure of center than the mean because mean is sensitive to extreme data and median is the point at which half the data are above and half the data are below.
The median is the point at which half the data are above and half the data are below. Medians are less sensitive to extreme scores . Therefore, median is center point of data set.
Standard deviation shows how much variation there is from the mean. A low SD indicates that the data points tend to be close to the mean, whereas a high SD indicates that the data are spread out over a large range of values.
Learn more:
https://brainly.com/question/14532771
can someone help me ?
36 + 3w = -36, w = ?
4 – 9g = -23, g = ?
Answer:
1. w=-24
2. g=3
Step-by-step explanation:
In 1999 there were 4076 J.C. Penney
stores and in 2003 there were 1078 stores. Write a linear
equation that gives the number of stores in terms of the
year. Let i = 9 represent 1999. Then predict the numbers
of stores for the years 2008 and 2010. Are your answers
reasonable? Explain.
Answer:
- 749.5i + 10821.5
−2669.5
−4168.5
Step-by-step explanation:
Given tgat:
Number of stores in 2003 (y2) = 1078
Number of stores in 1999 (y1) = 4076
1999 = i = 9
2003 = 13
y - y1 = m(x - x1)
m = slope = (y2 - y1) / (i2 - i1)
m = (1078 - 4076) / 13 - 9
m = - 2998 / 4
m = - 749.5
y - 4076 = - 749.5(i - i1)
y - 4076 = - 749.5(i - 9)
y - 4076 = - 749.5i + 6745.5
y = - 749.5i + 10821.5
Prediction for 2008 and 2010
2008 ; i = 18
y = - 749.5(18) + 10821.5
y = −2669.5
2010 ; i = 20
y = - 749.5(20) + 10821.5
y = − 4168.5
Frank drove from New York City to Los Angeles. The distance between the two cities is 2,760 miles. After 16 hours, he still had to drive 1,400 miles to reach Los Angeles. How far did he drive per hour?
Answer:
fghjgfvgh
yguhyu
Step-by-step explanation:
Answer:
frank traveled 2760-1400 = 1360 miles
traveled 16 hours
This means he drove: 1360 miles / 16 hours = 85 miles per hour.
The amount of time it takes an ice cube to melt varies inversely to the air temperature. At 30 degrees Celsius, the ice will melt in 10 minutes. How long will it take the ice to melt if the temperature is increase to 40 degrees Celsius?
It will take 7 minutes and 30 seconds to melt at a temperature of 40°C.
What is proportion?Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, The amount of time it takes an ice cube to melt varies inversely to the air temperature this can be written as,
Time ∝ 1/(Temparature).
Time = K(1/Temp).
At 30 degrees Celsius, the ice will melt in 10 minutes.
10 = K(1/30).
K = 300.
Now, the time required to melt the ice at 40°C is,
Time = 300(1/40).
Time = 7.5 minutes or 7 minutes 30 seconds.
learn more about proportion here :
https://brainly.com/question/7096655
#SPJ2
8 students is ?% of 20 students.
Finish the missing percent
Answer:
40%
Step-by-step explanation:
Choose the equations in which n=100
will make the equation true.
1:12.4 divided by n=0.124
2:3.8 divided by n=0.038
3:52350divided by n=52.35
4:850.4 divided by n =85.04
5:0.41 divided by n =0.0041
Answer: 1, 2, 5
Step-by-step explanation: Move the decimal two times to the left if you divide by 100.