For this case we must factor the following expression:
[tex]27a ^ 3b ^ 9 + 8c ^ 18[/tex]
So, we rewrite the terms like:
[tex]27a ^ 3b ^ 9 = (3ab ^ 3) ^ 3\\8c ^ {18} = (2c ^ 6) ^ 3[/tex]
So, we have:
[tex](3ab ^ 3) ^ 3 + (2c^6) ^ 3 =[/tex]
Being both perfect cube terms, we factorize by applying the cube sum formula:
[tex](a ^ 3 + b ^ 3) = (a + b) (a ^ 2-ab + b ^ 2)[/tex]
Where:
[tex]a = 3ab ^ 3\\b = 2c ^ 6\\(3ab ^ 3 + 2c ^ 6) ((3ab ^ 3) ^ 2- (3ab ^ 3) (2c ^ 6) + (2c ^ 6) ^ 2) =\\(3ab ^ 3 + 2c ^ 6) (9a^2b ^ 6-6ab ^ 3c ^ 6 + 4c ^ {12})[/tex]
Answer:
[tex](3ab ^ 3 + 2c ^ 6) (9a2b ^ 6-6ab ^ 3c ^ 6 + 4c ^ 12)[/tex]
Which equation is y=(x+3)^2 +(x+4)^2 rewritten in vertex form ?
Answer:
option B
Step-by-step explanation:
Given in the question an equation y = (x+3)² + (x+4)²
Step 1
Expand this equation
y = (x+3)² + (x+4)²
y = (x²+9+6x) + (x²+16+8x)
y = 2x² + 14x + 25
Step 2
Find the minimum point of the parabola equation, y = 2x² + 14x + 25
y = ax² + bx +c
x = -b/2a
= -14/2(2)
= -14/4
= -7/2
Step 3
Find the vertex point by plugging value of x in the equation
y = 2(-7/2)² + 14(-7/2) + 25
= 49/2 - 49 + 25
= 1/2
vertex (h,k)
vertex (-7/2 , 1/2)
Step 4
vertex form
y = a(x - h)²+ k
y = 2(x + 7/2)² + 1/2
What is the volume of the figure that can be formed by the net below?
Answer:
125 in³
Step-by-step explanation:
The net will form a cube.
Length of the cube = 5 in.
We will apply the formula for volume, volume = length³, to find the volume of the cube.
Volume = 5 x 5 x 5 = 125 in³
what is 12x4 plz help
Answer:
it is 48 hope this helps
Step-by-step explanation:
The solution of expression is,
⇒ 48
We have to given that,
An expression to solve,
⇒ 12 × 4
Since, To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Hence, We get;
⇒ 12 × 4
⇒ 48
Thus, The solution of expression is,
⇒ 48
Learn more about the multiplication visit:
https://brainly.com/question/10873737
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James found a pair of shoes he wanted at two stores. At store A they are $35 and he had a 20% off coupon. At store B they were $40 and he had a 30% off coupon. Which would be the better deal and by how much?
Answer: They cost the same amount.
Step-by-step explanation:
35(0.20)=7
35-7=28
40(0.30)=12
40-12=28
28=28
Please help with this quiz question!
Using the parallelogram pictured, find the length of the shorter diagonal. Round your answer to the nearest inch.
A) 32.1 in
B) 31.0 in
C) 22.3 in
D) 21.0 in
According to google your answer is c
What is the volume of a rectangular prism that is 120 centimeters by 2 meters by 1.5 meters in cubic meters? 3.6 3,600,00 360 36
Answer: 3,600,000 cm³
Step-by-step explanation: First you have to convert all the units into centimeters,
2 meters = 200 centimeters
1.5 meters = 150 centimeters
To find the volume of a rectangular prism you multiply all the sides.
120 * 200 * 150 = 3,600,000
The answer is 3,600,000 cubic centimeters.
The volume of a rectangular prism with the given dimensions is 3.6 cubic meters.
The dimensions of a rectangular prism are 120 centimetres(1.2 meters) by 2 meters by 1.5 meters.
What is the formula to find the volume of a rectangular prism?The formula to find the volume of a rectangular prism is l×b×h.
Now, volume=1.2×2×1.5=3.6 cubic meters.
Therefore, the volume of a rectangular prism is 3.6 cubic meters.
To learn more about the volume of a rectangular prism visit:
https://brainly.com/question/21308574.
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Zack buys some oranges from a store. The oranges cost $4.00 for 2 pounds. He wants to buy more fruit, but at the same price per pound as the oranges. Which of the following fruits could Zack buy?
A.
bananas at $2.00 for 5 pounds
B.
strawberries at $9.00 for 3 pounds
C.
peaches at $6.00 for 3 pounds
D.
blueberries at $8.00 for 2 pounds
Re
Answer:
C
Step-by-step explanation:
The oranges cost $4 per 2 lbs which is 4/2=$2 per lb. Option C has peaches at $6 for 3 lbs which is 6/3 =$2 per lb.
Answer:
C. Peaches at $6.00 Dollars for 3 pounds
Step-by-step explanation:
find the oranges $ per pound.
4 divided by 2 = 2
match it to each answer (example bellow, correct one)
6 divided by 3 = 2
Oranges per pound = $2.00
Peache per pound = $2.00
C.)
Hope this helped!
Lunar Rose Moon.
What’s 3.24 rounded to the nearest tenth
Answer:
3.2 is the corrext amswr
Step-by-step explanation:
The answer is 3.2 because you only round up if it’s .5 or higher and round down if it’s .4 or lower
Identify the features of the graph solution vertex y-intercept
Answer:
Vertex(3,-4) and y-int (0,5)
Zeroes are (1,0) and (5,0)
Step-by-step explanation:
Answer:
The solutions of the given graph are 1 and 5. The vertex of the graph is (3,-4) and the y-intercept of the graph is 5.
Step-by-step explanation:
From the given graph it is clear that it intersect the x-axis at (1,0) and (5,0).
Therefore the solutions of the given graph are 1 and 5.
Vertex of the parabola is the extreme point of the graph.
From the given graph it is clear that the the turning point or the extreme point of the graph is (3,-4).
Therefore the vertex of the graph is (3,-4).
The given graph intersect the y-axis at (0,5).
Therefore the y-intercept of the graph is 5.
Awire 4 1/2 feet long is been cut into small pieces of wire each one and 1/4 feet long what is the maximum number of smaller pieces of wire that can be cut from the original piece of wire
2,3,4,5
Answer:
3
Step-by-step explanation:
Wire is 4 1/2 feet, or 4.5 feet.
Each smaller wire needs to be 1 1/4 feet, or 1.25 feet.
How many whole 1.25 feet wire can we have from total of 4.5 feet wire?
Let's divide:
\[tex]\frac{4.5}{1.25}=3.6[/tex]
thus we can have 3 whole "1.25 feet long" wire and fractional amount.
Hence, maximum number of smaller pieces is 3
Hi will you plz telp me
Answer:
the mean is 73.4
Step-by-step explanation:
you add all the numbers which equals to 367
then divide by 5
Surface area of prisms and cylinders
Answer:
1. LA = 92 sq. m., SA = 132 sq. m.
2. LA = 460 sq. in., SA = 700 sq. in.
3. LA = 118 sq. in., SA = 168 in. sq.
4. LA = 468 sq. cm., SA = 828 sq. cm.
Step-by-step explanation:
The lateral area is the area of the non-base faces. The surface area is the area of all the faces (so lateral area + area of base).
1.
Lateral area:
There are 2 same triangles each with height and base of 3 and 4, respectively. So
Area of triangle = 1/2 * base * height = 1/2 * 4 * 3 = 6
Since there are 2, so 6 * 2 = 12
Now, the slant height is gotten by using pythagorean theorem on the triangular face.
[tex]4^2+3^2=SlantHeight^2\\16+9=SlantHeight^2\\25=SlantHeight^2\\SlantHeight=5[/tex]
If you look at the side facing away, it is a rectangle with length 10 and width 5, so area of rectangle is length * width = 10 * 5 = 50
The side facing towards us is also a rectangle with dimensions 3 and 10. So area is 3 * 10 = 30
The lateral area is 30 + 12 + 50 = 92
Surface Area:
This is the lateral area we got before (92) + the area of the base.
The base is a rectangle with dimensions 4 and 10. So area = 4 * 10 = 40
The surface area is 92 + 40 = 132
2.
Lateral area:
all the faces are rectangles.
The dimensions of two side faces are 10 and 8. So area would be 2 * (10 * 8) = 2 * 80 = 160
The dimensions of back side and front side is 15 and 10. So area would be 2 * (15 * 10) = 2 * 150 = 300
The lateral area would be 160 + 300 = 460
Surface area:
the surface area is the lateral area (580) + the area of the bases (which is also a rectangle). The dimensions of the bottom and top are 15 and 8. So area of bottom and top is 2(15 * 8) = 240
Thus, surface area = 460 + 240 = 700
3.
Lateral Area:
There are two rectangles (left and right) with dimensions 8 x 5 and 6 x 5. So area would be 8 * 5 = 40 and 6 * 5 = 30. Area = 40 + 30 = 70
There are two triangles (back and front) with base of 6 and height of 8. The area of both are:
(1/2 * 6 * 8 ) * 2 = 48
Lateral area is 70 + 48 = 118
Surface area:
The surface are would be lateral area (118) PLUS the base, which is a rectangle with dimensions 5 and 10. So area = 5 * 10 = 50.
Total surface area = 118 + 50 = 168
4.
lateral area:
there are 2 rectangles (left and right) with dimensions 10 x 12, and 9 x 12. So the total area would be:
(10*12) + (9*12) = 228
The front and back are trapezoids. The area of trapezoid is 1/2 (base1 + base2) * height.
The height is 8 and both the bases are 10 and 20. Plugging it into the formula, we get are of 2 of the trapezoids to be:
2 * (1/2(base1+base2)*height)
2 * (1/2(10+20)*8)
= 240
The lateral area = 228 + 240 = 468
surface area:
it will be 468 (lateral area) PLUS the area of the bases. The bottom base is a rectangle with dimensions 20 and 12. So the area of the base is 20 * 12 = 240
The top is a rectangle with dimensions 12 and 10. So area = 12 * 10 = 120
Surface area = 468 + 240 + 120 = 828
Write an equation of the line that is parallel to 2x + 4y = 6 and passes through the point (6, 4).
A) y = 2x + 4
B) y = 2x - 8
C) y = -2x + 16
D) y = -1/2 + 7
will mark brainliest if correct and give 50 pts.
Answer:
The equation is y = - 1/2 x+7
Step-by-step explanation:
2 x + 4y = 6
4y = -2 x +6
Divide both sides by 4
y = - 1/2 x + 3/2
y=mx+b
slope m = - 1/2
The slope of a line parallel to another line will be the same
The slope of the required line will be - 1/2
m= - 1/2 ,point ( 6 , 4 )
Plugging the values of m and the point in
y=mx+b
4 = -3 + b
b= 7
m= - 1/2
Plug values y = mx +b
y = - 1/2 x+7
Point B is the center of a circle, and AC is a diameter of the circle. Point D is a point on the circle different from A and C. If angle BDA = 20 degrees, then what is the measure of angle CBD?
Answer choices:
a) 70 degrees
b) 120 degrees
c) 140 degrees
d) 40 degrees
Answer:b
Step-by-step explanation:
Please Help Me With This One :-/
So, you want to calculate the interest on $300 at 5% interest per year after 7 years.
The formula we'll use for this problem is:
I = P x r x tWhere:
P is the principal amount, $300.00r is the interest rate, 5% per year, or in decimal form, 5 / 100 = 0.05t is the time involved, 7 yearsTo find the simple interest, we multiply 300 x 0.05 x 7 to get that:
The interest is: $105.00
Answer:
The correct answer is last option
$105.00
Step-by-step explanation:
Points to remember
Simple interest
I = PNR/100
Where P - Principle amount
N - Number of years and
R - Rate of interest
To find the simple interest
Here P = $300, R = 5% and N = 7 years
I = PNR/100
= (300 * 5 * 7)/100
= 3 * 5 * 7
= 105
Therefore simple interest after 7 years = $105
The correct answer is last option
convert 12.5 centimeters into meters
Answer:
0.125 m
Step-by-step explanation:
Answer:
0.125 meters
Step-by-step explanation:
There are 100 cm in a meter. 12.5/100= 0.125
you invest $2800 in an account that pays an interest of 5.5%, compounded continuously. calculate the balance of your account after 12 years. round answer to the nearest hundredth. LAST QUESTION AND I NEED IT CORRECT PLSSS
Hi, hope this helps you. Have a good day. :)
Answer:
A = $5,417.42 (balance of the account)
I = $2,617.42
Answer:
The balance in the account after 12 years is $5417.42
Step-by-step explanation:
* Lets talk about the compound continuous interest
- Compound continuous interest can be calculated using the formula:
A = P e^rt
• A = the future value of the investment, including interest
• P = the principal investment amount (the initial amount)
• r = the interest rate
• t = the time the money is invested for
- The formula gives you the future value of an investment,
which is compound continuous interest plus the
principal.
- If you want to calculate the compound interest only, you need
to deduct the principal from the result.
- So, your formula is:
Compounded interest only = Pe^(rt) - P
* Now lets solve the problem
∵ P = $ 2800
∵ r = 5.5/100 = 0.055
∵ t = 12
∴ A = 2800 e^(0.055 × 12) = $5417.42
* The balance in the account after 12 years is $5417.42
Juan has two machines: one exchanges 1 white token into 4 red tokens, while the other exchanges 1 red token into 3 white one. Juan has 4 white tokens. After exactly 11 exchanges , he has 31 tokens. How many of those are red?
Answer:
14 are red
Step-by-step explanation:
Let's identify the 2 types of transactions Juan machines do:
w : changes 1 white token into 4 red tokens (gain: 3 tokens overall)
r : changes 1 red token into 3 white tokens (gain: 2 tokens overall)
We know that Juan does 11 trades, so we can say:
w + r = 11
Overall, Juan started with 4 tokens and ends with 31... so, gain of 27 tokens.
We can model this as:
3w + 2r = 27
(3w because each w transaction, he gains 3 tokens, 2r because every r transaction, he gains 2 tokens).
From first equation we get r = 11 - w, which we place in the second equation:
3w + 2 (11 - w) = 27
3w + 22 - 2w = 27
w = 5, so r = 6 (from first equation).
Now, we know Juan did 5 w transactions and 6 r transactions. But how many token of each color does he have?
Start: 4W (4 White chips)
He does 4 w transactions, he now has 16R tokens
He does 6 r transactions, he now has 10 (16-6) R tokens, plus 18 W tokens
He does another w transaction, he now has 14 R (10 + 4), plus 17 W(18-1) tokens
He did 11 transactions, and he has 31 tokens at the end, out of which 14 are red.
Find the exact area of a circle having the given circumference.
3pi
A =
2.25
3
9
Answer:
A = 2.25πStep-by-step explanation:
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
r - radius
The formula of a circumference of a circle:
[tex]C=2\pi r[/tex]
We have:
[tex]C=3\pi[/tex]
Substitute:
[tex]2\pi r=3\pi[/tex] divide both sides by 2π
[tex]r=1.5[/tex]
Substitute:
[tex]A=\pi(1.5)^2=2.25\pi[/tex]
This answer is correct, I double checked it and got it right on the assignment in OW. :)
Solve for
2u = 4/9
Simplify your answer as much as possible.
Answer:
2/9
Step-by-step explanation:
If you meant you want to find U,
1) Divide both side by 2. -> U = 4/9 divided by 2
2) You get U = 4/18, which you can further simplify by dividing 2 on top and bottom to get 2/9
What is the approximate length of arc s on the circle below? Use 3.14 for pi round your nearest tenth.
A) 14.1 in.
B) 22.5 in.
C) 42.3 in.
D) 56.5 in.
Answer:
A
Step-by-step explanation:
The arc length is calculated as
arc = circumference × fraction of circle
= 2π × 6 × [tex]\frac{135}{360}[/tex]
= 12π × [tex]\frac{3}{8}[/tex]
= [tex]\frac{36\pi }{8}[/tex] ≈ 14.1 in
Answer
14.1 in
Step-by-step explanation:
Length of the arc formula = circumference of the circle * central angle / 360
circumference of the circle formula = [tex]2\pi r[/tex]
where r is the radius of the circle
Radius = 6 in
central angle = 135 degrees
Length of the arc = [tex]2 \pi * radius* \frac{angle}{360}[/tex]
=[tex]2\pi*6* \frac{135}{360}[/tex]
= 14.137= 14.1 in
Find the volume of the figure.
Answer:
V = 256 mm3
Hope this helps you out!
Answer:
D,256
Step-by-step explanation:
Use multiplication to do 8*10*3.2 you get 256
find the total surface area of this cone. round to the nearest tenth(my last question of my homework and I keep getting it wrong)
Answer:
The surface area is approx. 1017.9 in^2.
Step-by-step explanation:
Total surface area of cone = πrl + πr^2. Since the radius is 12 in. and the slant height is 15 in, substitute 12 for r and 15 for l.
A = π(12)(15) + π(12)^2
= 180π + 144π
= 324π in^2
≈ 1017.9 in^2
Hope this helps!
A farmer can spend no more than $4,000 on fertilizer and seeds. The fertilizer costs $2 per pound and seeds cost $20 per pound. To summarize the situation, the farmer writes the inequality: 2f + 20s ≤ 4,000, where f is the number of pounds of fertilizer and s is the number of pounds of seeds. Which graph's shaded region shows the possible combinations of fertilizer and seeds the farmer can buy?
Answer:
it is the 2nd graph
Step-by-step explanation:
The graph of the linear equation is a right-angle triangle whose height is 2000 units and base is 200 units.
What is the linear system?It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
A farmer can spend no more than $4,000 on fertilizer and seeds. The fertilizer costs $2 per pound and seeds cost $20 per pound.
To summarize the situation, the farmer writes the inequality
[tex]\rm 2 y + 20 x \leq 4,000\\\\y \leq 2000 - 10x[/tex]
where y be the number of pounds of fertilizer and x be the number of pounds of seeds.
Then the graph is shown below.
More about the linear system link is given below.
https://brainly.com/question/20379472
9. A new automobile costs $23,782,
but after one year it is worth
$17,668. What is the approximate
percent of decrease in the value of
the automobile?
Answer:
% decrease in the cost= 6114/23782⋅100=25.71%
Step-by-step explanation:
The decrease in the cost =$23782−$17668=$6114
Hence, % decrease in the cost=6114/23782⋅100=25.71%
the decrease is 23782 - 17668 = 6114.
if we take 23782 to be the 100%, what is 6114 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 23782&100\\ 6114&x \end{array}\implies \cfrac{23782}{6114}=\cfrac{100}{x}\implies 23782x=611400 \\\\\\ x=\cfrac{611400}{23782}\implies x\approx 25.71[/tex]
* don’t mind the marks* please help asap ( 10 points)
Answer:
median:36.5
mean:37
Step-by-step explanation:
to find medain put all of the numbers in order. then find the center number
for the mean add all of the numbers together ad divide it by the amount of data points there are
Answer:
median: 36.5
mean: 37
Step-by-step explanation:
Joel and Sara want to know the combined amount of money they made last week. They both made $9.75 per hour, but Joel also made an $18 bonus. Joel says the combined amount is 9.75j + 18 + 9.75s, where j is the number of hours he worked, and S is the number of hours Sara worked. Sara says the combined amount is 9.75(j + S)+ 18. Who is correct? Explain.
The would both be correct in it's own way depending on how the teacher is teaching.
Both Joel and Sara are correct. Their expressions represent the combined earnings accurately, considering hourly wage and bonus.
To determine who is correct, let's first break down the earnings for each person:
1. Joel:
- Hourly wage: $9.75
- Bonus: $18
Joel's total earnings can be calculated using the formula provided: [tex]\(9.75j + 18\)[/tex], where [tex]\(j\)[/tex] represents the number of hours Joel worked.
2. Sara:
- Hourly wage: $9.75
Sara's total earnings can be calculated using the formula provided: [tex]\(9.75(j + S)\)[/tex], where [tex]\(S\)[/tex] represents the number of hours Sara worked.
Now, let's expand both expressions and see which one correctly represents the combined earnings of Joel and Sara.
Joel's expression: [tex]\(9.75j + 18 + 9.75S\)[/tex]
Sara's expression: [tex]\(9.75j + 9.75S + 18\)[/tex]
Comparing the two expressions, we see that both expressions have the same terms: [tex]\(9.75j\)[/tex], [tex]\(9.75S\)[/tex], and [tex]\(18\)[/tex]. The order of terms is different, but mathematically it doesn't matter since addition is commutative.
So, both Joel and Sara are correct. They just wrote their expressions in a different order, but the mathematical result is the same. They both correctly accounted for their hourly wage and the bonus.
Emily had 75 buttons. She gave 15 buttons to Jake. What percent of the buttons did Emily give to Jake?
20%
My equation:
15*100=1500
1500/75=20
The answer would be 20% off hope this helped!
A company needs 713 slices of pizza for a company party. If each pizza is cut into 8 slices, about how many whole pizzas should the company purchase. A) 60 B) 70 C) 80 D) 90
Answer: D
If there are 713 slices, and each pizza is divided into pieces, then you would divide.
713÷8=89.125. Round up and you get:
90.
Hope this helps and have a great day!!!
For this case we must indicate the number of whole pizzas needed for the company. For this we propose an equation.
Let "x" be the variable that represents the number of whole pizzas, then:
[tex]8x = 713[/tex]
We divide between 8 on both sides of the equation:
[tex]x = \frac {713} {8}\\x = 89,125[/tex]
90 pizzas are needed
ANswer:
Option D
log2-log4
what is the equivalent of the above?
Answer:
[tex\large\boxed{\log2-\log4=\log\frac{1}{2}}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ \log_ab-\log_ac=\log_a\dfrac{b}{c}\\\\==========================\\\\\log2-\log4=\log\dfrac{2}{4}=\log\dfrac{1}{2}[/tex]