Answers
[tex]\bf \sqrt{6x^2}\cdot \sqrt{18x^2}\implies \sqrt{(6x^2)(18x^2)}\implies \sqrt{108x^2x^2}\implies \sqrt{108(x^2)^2} \\\\\\ \begin{cases} 108=&2\cdot 2\cdot 3\cdot 3\cdot 3\\ &2^2\cdot 3^2\cdot 3\\ &(2\cdot 3)^2\cdot 3\\ &6^2\cdot 3 \end{cases}\implies \sqrt{6^2(x^2)^2\cdot 3}\implies 6x^2\sqrt{3}[/tex]
Answer:
the correct answer is option D. 6x²√3
Step-by-step explanation:
It is given that
√6x² * √18x²
To find the value of √6x² * √18x²
√6x² * √18x² = √(6x² ) * (18x²)
= √(6 * 18 x² *x²)
= √(6 * 6 * 3 x² *x²)
= 6x√3
The equivalent of √6x² * √18x² = 6x²√3
Therefore the correct answer is option D. 6x²√3
Related Questions
Find the surface area of the cone. Round your answer to the nearest hundredth
Answers
Basically you do
2 x 3.14 x 8 squared
= 401.92
Then you do
401.92 + 14 x 8
=513.93
Hope this helps :)
Answer:
The correct answer is option option B 606.32 yd²
Step-by-step explanation:
Points to remember
Surface area of cone = πrl + πr²
Where r is the base radius and l is the lateral edge
To find lateral edge
l = √(r²+ h²) = √8² + 14² = 16.12
To find the surface area of given cone
Here r = 8 yd and l = 16.12 yd
Surface area = πrl + π r² = π * 8 * 16.12 + π8²
= 606.32 yd²
What is the answer of number 14?
Answers
Answer:
36
Step-by-step explanation:
Answer:36
Step-by-step explanation:
What is the volume of a cylinder to the nearest whole number? r=7.5 h=20
Answers
Answer:
V = 3533
Step-by-step explanation:
Volume of a cylinder is given by
V = pi r^2 h
Using 3.14 for pi
V = (3.14) (7.5)^2 * 20
V = 3532.5
To the nearest whole number
V = 3533
g(1)=51 g(n)=g(n-1)+2 fina an explicit formula for g(n)
Answers
Answer:
g(n) = 2n+49
Step-by-step explanation:
Since g(1) = 51, then g(1)+2=g(2) or g(2)=53. So the formula for g(n) is
g(n) = 49+2n
The explicit formula for g(n) will be g(n) = 2n + 49.
What is a function?Functions are found all across mathematics and are required for the creation of complex relationships.
g(1) = 51 and g(n) = g(n – 1) + 2
Since g(1) = 51, then g(1) + 2= g(2) or g(2) = 53.
So the formula for g(n) will be
g(n) = 49 + 2n
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Tariq designed the pool shown. The owner of the pool has one square cover to use. Find the area of the space that needs to be covered. (The four corners are squares.)
The area that needs to be covered is
___ ft2.
Answers
Step 1: Find the total area. Since it is a square all the sides are 12 ft so multiply 12 by 12
12 x 12 = 144
^^^This is the total area including the area around the pool. We just need the are of the pool
Step 2: Outside of the pool there are four little 2 ft by 2 ft squares that aren't part of pool, and therefore won't need to be covered. The area of these 2 ft by 2 ft square is 4ft (2 times 2 is 4). Since there are 4 of these squares we multiply 4 by 4 to get 16. This means that 16 ft of the 144 ft we found previously are not part of the pool and we must subtract 16 from 144 to get the total pool area
144 - 16 = 128
This means that the area of the pool is 128 ft
Hope this helped and made sense! Let me know!
Answer:
128
Step-by-step explanation:
Find the inverse of the following function.
Answers
For this case we must find the inverse of the following function:
[tex]f (x) = \sqrt [3] {x + 12}[/tex]
For this, we follow the steps below:
Replace f (x) with y:
[tex]y = \sqrt [3] {x + 12}[/tex]
We exchange the variables:
[tex]x = \sqrt [3] {y + 12}[/tex]
We solve the equation for "and":
[tex]\sqrt [3] {y + 12} = x[/tex]
We raise both sides of the equation to the cube to eliminate the root:
[tex](\sqrt [3] {y + 12}) = x ^ 3\\y + 12 = x ^ 3[/tex]
We subtract 12 on both sides of the equation:
[tex]y = x ^ 3-12[/tex]
Thus, the inverse function is:
[tex]f ^ {- 1} = x ^ 3-12[/tex]
Answer:
Option B
Option: B is the correct answer.
B. [tex]f^{-1}(x)=x^3-12[/tex]
Step-by-step explanation:The inverse function f(x) is calculated in the following steps.
Put f(x)=yInterchange x and y in the equation.Now, solve for y.The function f(x) is given by:
[tex]f(x)=\sqrt[3]{x+12}[/tex]
Now, we keep:
[tex]f(x)=y\\\\i.e.\\\\y=\sqrt[3]{x+12}[/tex]
Now, we interchange x and y
[tex]x=\sqrt[3]{y+12}[/tex]
Now, on taking cube on both side of the equation we have:
[tex]y+12=x^3\\\\i.e.\\\\y=x^3-12[/tex]
i.e.
[tex]f^{-1}(x)=x^3-12[/tex]
Evaluate and simplify the following complex fraction
Answers
Answer:
[tex]\frac{24}{5}[/tex]
Step-by-step explanation:
To evaluate division of fractions, that is
[tex]\frac{9}{-5}[/tex] ÷ [tex]\frac{-3}{8}[/tex]
Leave the first fraction, change division to multiplication and turn the second fraction upside down
[tex]\frac{9}{-5}[/tex] × [tex]\frac{8}{-3}[/tex] ( cancel the 9 and 3) giving
[tex]\frac{3}{-5}[/tex] × [tex]\frac{8}{-1}[/tex]
= [tex]\frac{3(8)}{-5(-1)}[/tex] = [tex]\frac{24}{5}[/tex]
To simplify a complex fraction, multiply both the numerator and the denominator by the same factor to eliminate fraction in the denominator, cancel common factors and follow rules of algebra to maintain equality.
Explanation:To evaluate and simplify a complex fraction, we can use a strategy that involves multiplying the numerator and denominator by the same factor. For example, if our complex fraction had a denominator of 1/2, we could multiply both the numerator and the denominator by 2 to eliminate the fraction in the denominator. This approach ensures the units or variables cancel out where appropriate, leaving us with a simpler expression. When working with fractions, common factors can be identified and cancelled to simplify the fraction further. Always remember that fractions represent division, so when simplifying, divide the digit term of the numerator by that of the denominator and subtract the exponentials accordingly. This process is governed by the rules of algebra, maintaining the equality of the expression.
Liam bought 1 gallon of juice at the grocery how many quarts of juice did he buy?
Answers
Answer:
4 quarts
Step-by-step explanation:
6g-3g+8g-g simplify
Answers
Answer:
Step-by-step explanation:
Bill and Ted are going to order t-shirts for there school clubs. The t-shirts will have the club logo printed on the front. Bill and Ted ask two local t-shirt companies to give them a price. * Patty's Printing charges $21.50 for each t-shirt. * Sandra's shirts has a one-time set up fee for $63 and then charges $18 for each t-sh
Patty's Printing= 21.5x
Sandra's Shirts = 63+ 18x
x=30
Patty's Printing: 21.50 (30) = 645
Sandra's Shirts = 63+ 18 (30) = 603
Sandra's Shirts
37 A recreation center ordered a total of 15 tricycles and bicycles from a sporting goods store
The number of wheels for all the tricycles and bicycles totaled 38.
Write a linear system of equations that models this scenario, where represents the number of
tricycles and b represents the number of bicycles ordered
Answers
Answer:
1) The system of linear equations is equal to
b+t=15 and 2b+3t=38
2) The number of bicycles ordered was 7 and the number of tricycles ordered was 8
Step-by-step explanation:
Let
b----> the number of bicycles ordered
t----> the number of tricycles ordered
we know that
b+t=15 -----> equation A
2b+3t=38 ---> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The solution is the point (7,8)
see the attached figure
therefore
The number of bicycles ordered was 7
The number of tricycles ordered was 8
The number of bicycles ordered was 7 and the number of tricycles ordered was 8.
What is the system of equations?
Systems of equations are sets of equations where the solution is the intersecting point(s) between the equations.
Let, the number of tricycles and b represent the number of bicycles ordered.
A recreation center ordered a total of 15 tricycles and bicycles from a sporting goods store.
[tex]\rm b+t=15[/tex]
The number of wheels for all the tricycles and bicycles totaled 38.
[tex]\rm 2b+3t=38[/tex]
From equation 1
[tex]\rm b+t=15\\\\b=15-t[/tex]
Substitute the value of b in equation 2
[tex]\rm 2b+3t=38\\\\ 2(15-t)+3t=38\\\\30-2t+3t=38\\\\t=38-30\\\\t=8[/tex]
Substitute the value of t in equation 1
[tex]\rm b+t=15\\\\b=15-t\\\\ b = 15-8\\\\b=7[/tex]
Hence, the number of bicycles ordered was 7 and the number of tricycles ordered was 8.
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You are shown either nets or top and side view of three dimensional figures. Match the three dimensional figure to the correct views.
cone
cylinder
rectangular prism
sphere
triangular pyramid
Answers
Answer:
1. rectangular prism
2. cylinder
3. cone
4. triangular pyramid
5. sphere
Step-by-step explanation:
A drawer contains 4 black socks, 3 white socks, and 2 red socks. One sock is drawn from the drawer and kept. The second sock is drawn from the drawer. What is the probability that they are both white?
Answers
The probability that they are both white if the first sock is kept and second is drawn will be 8.33%.
What is probability?Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.
A drawer contains 4 black socks, 3 white socks, and 2 red socks.
One sock is drawn from the drawer and kept.
The second sock is drawn from the drawer.
The total number of the event will be
Total event = 9
Then the probability that they are both white will be
P = (3/9) (2/8)
P = (1/3)(1/4)
P = 1/12
P = 0.0833
P = 8.33%
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The probability of drawing two white socks from the drawer is 2/27.
Explanation:To find the probability that both socks drawn are white, we need to find the probability of drawing a white sock on the first draw and then drawing another white sock on the second draw.
There are a total of 9 socks in the drawer (4 black, 3 white, and 2 red).
The probability of drawing a white sock on the first draw is 3/9 (3 white socks out of 9 total socks).
After replacing the first sock, the total number of socks remains the same, but the number of white socks decreases to 2. So the probability of drawing a white sock on the second draw is 2/9.
Now, to find the probability of both events happening, we multiply the probabilities together: P(First white sock) * P(Second white sock) = (3/9) * (2/9) = 6/81 = 2/27.
Therefore, the probability that both socks drawn are white is 2/27.
What is the arithmetic mean of the following numbers? 8,10,10,10,6,7,8
Answers
Answer:
Step-by-step explanation:
To find the arithmetical mean, add all the numbers togther and divide by the number of numbers.
The sum of all the numbers is ... 59.
There are 7 numbers.
59/7 which is about 8.43 is the arithmetic mean.
Arithmetic mean is 8.42 (Approximately)
Given that;
Values = 8,10,10,10,6,7,8
Find:
Arithmetic mean
Computation:
Arithmetic mean = Sum of all number / Number of term
Arithmetic mean = [8 + 10 + 10 + 10 + 6 + 7 + 8] / 7
Arithmetic mean = 59 / 7
Arithmetic mean = 8.42 (Approximately)
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whats the mode, median, mean and range of 24, 31, 12, 38, 12, 15
Answers
here is your answer young man/lady
The mode is 12, the median is 18.5, the mean is 23.6667, and the range is 26.
The mode is 12 because it appears twice in the list. The median is 18.5 because it is the middle value when the numbers are arranged in ascending order. The mean is 23.6667 which is the sum of all the numbers divided by the total count. The range is 26 which is obtained by subtracting the smallest value (12) from the largest value (38).
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pls help!! 5star and brainliest
Answers
Answer:
C, A, C
Hope This Helps!
What is the measure of angle b
A) 98°
B)108°
C)118°
D)128°
Answers
Answer:
The correct answer is option B). 108°
Step-by-step explanation:
Points to remember
Sum of angles of hexagon is 720°
From the figure we can see a hexagon.
To find the m<B
m<B = 720 - ( m<A + m< C + m<D + m<E + m<F)
= 720 - ( 170 + 133 + 102 + 117 + 90)
= 720 - 612
= 108°
Therefore m<B = 108° Option B is the correct answer
Answer:
B. 108 degrees
Step-by-step explanation:
What is the mean absolute deviation of the data set?
(21, 22, 24, 26, 27, 28, 20, 303
2
3
6
22
Answers
Answer:
3
Step-by-step explanation:
The mean absolute deviation of the data set is approximately 3.09.
The mean absolute deviation (MAD) is a measure of variability that indicates the average distance between observations in a data set and their mean.
To calculate the MAD, you first need to find the mean of the data set. In this case, the mean is 31.375.
Then, you calculate the absolute deviation of each data point from the mean. For example, the absolute deviation of the first data point (21) is 10.375 (|21 - 31.375|).
Once you have calculated the absolute deviation of each data point, you find the average of those absolute deviations. This is the mean absolute deviation.
In the example data set, the mean absolute deviation is approximately 3.
Find the mean of the data set: (21 + 22 + 24 + 26 + 27 + 28 + 20 + 30) / 8 = 31.375
Calculate the absolute deviation of each data point from the mean. For example, the absolute deviation of the first data point (21) is 10.375 (|21 - 31.375|).
Add up the absolute deviations of all the data points. In this case, the sum of the absolute deviations is 24.75.
Divide the sum of the absolute deviations by the number of data points to find the mean absolute deviation. In this case, the mean absolute deviation is 24.75 / 8 = 3.09375.
Therefore, the mean absolute deviation of the data set is approximately 3.09.
The complete question is:What is the mean absolute deviation of the data set?
(21, 22, 24, 26, 27, 28, 20, 303
2
3
6
22
Which is the equivalent of 6 14’ 48” written in decimal form ?
Answers
Answer:
Option A. 6.247°
Step-by-step explanation:
we know that
1°=60'
1'=60"
we have
6° 14' 48"
Convert to decimal form
Convert seconds to minutes
48"=48/60=0.8'
so
6° 14' 48"=6° + 14' +0.8'=6° 14.8'
Convert minutes to degrees
14.8'=14.8/60=0.247°
so
6° 14.8' =6° + 0.247°=6.247°
Answer:
6.247
Step-by-step explanation:
Which are factors of x2 – 4x – 5? Check all that apply.
(x – 5)
(x – 4)
(x – 2)
(x + 1)
(x + 5)
Answers
Answer:
(x + 1) and (x - 5)Step-by-step explanation:
[tex]x^2-4x-5=x^2+x-5x-5=x(x+1)-5(x+1)=(x+1)(x-5)[/tex]
Jennifer's bill for 6 cans of grape juice and 4 cans of apple juice was $13.10. When she got home she found out that she should have bought 4 cans of grape juice and 6 cans of apple juice. Although she mixed up the order, she did save 60 cents. What is the cost per can of apple and grape juice
Solve the problem using substitution and elimination.
Convert your equations to slope intercept form and identify the variables for your x and y axes. Then graph.
SHOW ALL WORK
Answers
Answer:
Part 1) The system is solved using elimination
The cost per can of grape juice is [tex]\$1.19[/tex] and the cost per can of apple juice is [tex]\$1.49[/tex]
Part 2) The system is solved using substitution
The cost per can of grape juice is [tex]\$1.19[/tex] and the cost per can of apple juice is [tex]\$1.49[/tex]
Part 3) The system is solved by graphing
The graph in the attached figure
Step-by-step explanation:
Part 1) Solve the system by elimination
Let
x----> the cost per can of grape juice
y----> the cost per can of apple juice
we know that
[tex]6x+4y=13.10[/tex] -----> equation A
[tex]4x+6y=13.10+0.60[/tex]
[tex]4x+6y=13.70[/tex] -----> equation B
Solve the system by elimination
Multiply the equation A by -6 both sides
[tex]-36x-24y=-78.6[/tex] -------> equation C
Multiply the equation B by 4 both sides
[tex]16x+24y=54.8[/tex] -------> equation D
Adds equation C and equation D
[tex]-36x-24y=-78.6\\16x+24y=54.8\\----------\\-36x+16x=-78.6+54.5\\-20x=-23.8\\x=1.19[/tex]
Substitute the value of x in the equation A
[tex]6(1.19)+4y=13.10[/tex]
[tex]4y=5.96[/tex]
[tex]y=1.49[/tex]
therefore
The cost per can of grape juice is [tex]\$1.19[/tex]
The cost per can of apple juice is [tex]\$1.49[/tex]
Part 2) Solve the system by substitution
Let
x----> the cost per can of grape juice
y----> the cost per can of apple juice
we know that
[tex]6x+4y=13.10[/tex]
[tex]4y=-6x+13.10[/tex]
[tex]y=-1.5x+3.275[/tex] -----> equation A
[tex]4x+6y=13.10+0.60[/tex]
[tex]4x+6y=13.70[/tex]
[tex]6y=-4x+13.70[/tex]
[tex]y=-(4/6)x+13.70/6[/tex]
[tex]y=--0.67x+2.28[/tex] -----> equation B
Substitute equation B in equation A and solve for x
[tex]-0.67x+2.28=-1.5x+3.275[/tex]
[tex]1.5x-0.67x=3.275-2.28[/tex]
[tex]0.83x=0.995[/tex]
[tex]x=1.19[/tex]
Find the value of y
Substitute the value of x in the equation A
[tex]y=-1.5(1.19)+3.275=1.49[/tex]
therefore
The cost per can of grape juice is [tex]\$1.19[/tex]
The cost per can of apple juice is [tex]\$1.49[/tex]
Part 3) Solve the system by graphing
we have
[tex]y=-1.5x+3.275[/tex] -----> equation A
[tex]y=-(4/6)x+13.70/6[/tex] -----> equation B
Remember that
The solution of the system of equations is equal to the intersection point both lines
The solution is the point [tex](1.19,1.49)[/tex]
see the attached figure
therefore
The cost per can of grape juice is [tex]\$1.19[/tex]
The cost per can of apple juice is [tex]\$1.49[/tex]
Over a 30-day period, the mean temperature in Capetown was 98°F with a standard deviation of 1.4°F and the mean
temperature in Three Rivers was 95°F with a standard deviation of 6.5°F.
What statement best describes the data?
A.the temperature was more Consistent in three Rivers
B. The temperatures were more consistent in Cape Town
C. The temperatures were of similar consistency and Cape Town and three rivers
Answers
Answer:
B. The temperatures were more consistent in Cape Town
Step-by-step explanation:
A low standard deviation indicates less variation away from the mean.
Since Cape Town has a lower standard deviation than Three Rivers, it is more consistent
which of the following quadratic equations has the solution (1/2,5)
Answers
(x-5)(2x-1) (-2x+1)(-x+5)=0 and (-2x+1)(x-5)=0 quadratic equation have as solution set.
Answer:
well i got some HOPE THIS WILL HELP
Step-by-step explanation:
To find the solution set of a factored quadratic equation, you should set each one of the factors equal to zero and solve for .
Lets take our first quadratic equation (x+1/2)(x-5)=0 and apply this. First we are our factors equal to zero and ; next we are going to sole for in each factor to find the solution set:
and , so the solution set for the quadratic equation (x+1/2)(x-5)=0 is
Lets do the same for our next one (x-5)(2x-1)=0
and
So, the solution set for the quadratic equation (x-5)(2x-1)=0 is
Next one (x+5)(2x-1)=0
and
So, the solution set for the quadratic equation (x+5)(2x-1)=0 is
Next one (-2x+1)(-x+5)=0
and
So, the solution set for the quadratic equation (-2x+1)(-x+5)=0 is : therefore, we are going the select this one.
Next one (x+1/2)(x+5)=0
and
So, the solution set for the quadratic equation (x+1/2)(x+5)=0 is
Finally, our last one (-2x+1)(x-5)=0
and
So, the solution set for the quadratic equation (-2x+1)(x-5)=0 is ; this is also a correct answer, make sure to select this one too.
We can conclude that both (-2x+1)(-x+5)=0 and (-2x+1)(x-5)=0 quadratic equation have as solution set.
the volume of the Box 4 inches wide 2 inches high and 5 in long is
Answers
Answer:
Volume = 40in^3
Step-by-step explanation:
The volume of a box is:
Volume = width x lenght x height
Where:
width: 4in
Length: 5in
Height = 2in
Then: Volume = width x lenght x height = 4in x 5in x 2in = 40in^3
ANSWER
The volume is 40 cubic inches.
EXPLANATION
The dimensions of the box are ,
width, w=4 inches
height, h=2 inches
and
length, l=5 inches
The box is a rectangular prism.
The formula for finding the volume of a rectangular prism is
[tex]V=l \times b \times h[/tex]
We substitute the values to get,
[tex]V=4\times 5 \times 2 = 40 {in}^{3} [/tex]
The point (-2, -1) satisfies which of the following inequalities?
A) 5x - 2y + 1 > 0
B) -5x + 2y + 1 > 0
C) -2x + 5y - 1 > 0
D) 2x + 5y - 1 > 0
Answers
Ik for s fact the awnser not a
Answer:
B) [tex]-5x + 2y + 1 > 0[/tex]
Step-by-step explanation:
Given point is (-2,-1)
to find out which inequality satisfies this point we plug in x and y value of the given point in each inequality
A) [tex]5x - 2y + 1 > 0[/tex]
x=-2 and y=-1
[tex]5(-2) - 2(-1) + 1 > 0[/tex]
[tex]-10+2+1>0[/tex]
[tex]-7>0[/tex] is False
B) -5x + 2y + 1 > 0
[tex]-5(-2) +2(-1) + 1 > 0[/tex]
[tex]10-2+1>0[/tex]
[tex]9>0[/tex] is True
C) -2x + 5y - 1 > 0
[tex]-2(-2) +5(-1) -1 > 0[/tex]
[tex]4-5-1>0[/tex]
[tex]-2>0[/tex] is False
D) 2x + 5y - 1 > 0
[tex]2(-2) +5(-1) - 1 > 0[/tex]
[tex]-4-5-1>0[/tex]
[tex]-10>0[/tex] is False
One lap around a track is equal to 1/8 of a mile. A horse ran a distance of 9 laps in 2 minutes and 30 seconds. What was the horse's average speed in miles per minute?
Answers
12,450 so yeah your welcome have a fantasist day
Does 2x-5y=-15 represent a linear relationship? please explain
Answers
ANSWER
Yes
EXPLANATION
The given relation is
2x-5y=-15
We solve for y to obtain:
-5y=-2x-15
Divide through by -5.
[tex]y = \frac{2}{5}x + 3[/tex]
This is linear relation.
There is a positive linear relationship between the two variables x and y.
Also we can see that the highest degree of the variables is unity.
Hence it represents a linear relationship between x and y.
what is the quotient when x^3 -5x^2 + 3x -8 is divided by x-3 ?
Answers
For this case, when making the division of polynomials, we must build a quotient that when multiplied by the divisor of the same as the terms of the dividend, the sign is changed and they are eliminated until reaching the remainder of the division.
It must be fulfilled that:
[tex]Dividend = Quotient * Divider + Remainder[/tex]
When observing the attached figure, the quotient is:
[tex]x ^ 2-2x-3[/tex]
Answer:
[tex]x ^ 2-2x-3[/tex]
See attached image
Express the polynomial 5a^2 + 3a^3 + 1 in standard form and then classify it.
A.
A. cubic binomial
B. quadratic monomial
C. cubic trinomial
D. linear trinomial
Answers
Answer: OPTION C
Step-by-step explanation:
To express a polynomial in Standard form, you need to see the exponent of each term of the polynomial and then order the polynomial from highest exponent to lowest exponent.
Therefore, for the polynomial [tex]5a^2 + 3a^3 + 1[/tex], you get:
[tex]3a^3 +5a^2 +1[/tex]
The highest exponent gives you the degree of the polynomial. In this case, the highest exponent is 3, then it is a polynomial of degree 3 or a cubic polynomial.
When a polynomial has three terms, is called "trinomial". Since this polynomial has three terms, it is a trinomial.
Therefore, the you can classify it as:
Cubic trinomial
Answer:
C
Step-by-step explanation:
Polygon Y is a scaled copy of Polygon X using a scale factor of \dfrac13 3 1 start fraction, 1, divided by, 3, end fraction. Polygon Y's area is what fraction of Polygon XXX's area?
Answers
Answer:
Polygon Y's area is one ninth (1/9) of Polygon X's area
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
In this problem
Let
z-----> the scale factor
a-----> Polygon Y's area
b----> Polygon X's area
[tex]z^{2}=\frac{a}{b}[/tex]
we have
[tex]z=\frac{1}{3}[/tex]
substitute
[tex](\frac{1}{3})^{2}=\frac{a}{b}[/tex]
[tex]\frac{1}{9}=\frac{a}{b}[/tex]
[tex]a=\frac{1}{9}b[/tex]
therefore
Polygon Y's area is one ninth (1/9) of Polygon X's area
Answer:
1/9
Step-by-step explanation:
There are 9 players on a baseball team. In how many different ways can the coach choose players for first base, second base, third base, and shortstop?
Answers
There are 3,024 different ways the coach can choose players for first base, second base, third base, and shortstop from a team of 9 players.
Since the positions are distinct (first base, second base, third base, and shortstop), and each position can only be filled by one player, we can use the permutation formula to calculate the number of arrangements.
The coach has 9 players to choose from for the first position.
After selecting one player for first base, there remain 8 players for the second position, 7 players for the third position, and 6 players for shortstop.
The total number of different ways the coach can choose players for the four positions is obtained by multiplying these numbers:
9 x 8 x 7 x 6 = 3,024
Hence, there are 3,024 different ways.
Learn more about the permutations here:
https://brainly.com/question/1216161
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