compare the first factor to the value of the product I did A B C but I don't understand D the question ANSWER FAST PLZ
Answers
The first factor with the value of the product is compared as below.
What are Factors?Factors of a number or an algebraic expression are the numbers or expressions which divides the given number evenly.
For example, 10 = 2 × 5
So we can say that 2 and 5 are factors of 10.
Here there are 3 products.
(a) [tex]\frac{1}{3}[/tex] × 1
Here the first factor is [tex]\frac{1}{3}[/tex].
And the product of the two factors is [tex]\frac{3}{9}[/tex].
[tex]\frac{3}{9}[/tex] = [tex]\frac{1}{3}[/tex] × [tex]\frac{3}{3}[/tex]
Numerator and denominator when take three times gives the product.
(b) First factor is [tex]\frac{2}{3}[/tex] and the product is [tex]\frac{14}{21}[/tex].
[tex]\frac{14}{21}[/tex] = [tex]\frac{2}{3}[/tex] × [tex]\frac{7}{7}[/tex]
Numerator and denominator when multiplied by 7 times gives the [tex]\frac{14}{21}[/tex].
(c) First factor is [tex]\frac{5}{2}[/tex] and the product is [tex]\frac{25}{10}[/tex].
[tex]\frac{25}{10}[/tex] = [tex]\frac{5}{2}[/tex] × [tex]\frac{5}{5}[/tex]
Numerator and denominator when multiplied by 5 gives [tex]\frac{25}{10}[/tex].
Hence the first factor and products are compared.
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Related Questions
What is the following product? 3 sqrt d x 3 sqrt d x 3 sqrt d
Answers
Answer: the first option, d.
Step-by-step explanation:
If the test scores of a class of 34 students have a mean of 73.1 and the test scores of another class of 26 students have a mean of 66.4, then the mean of the combined group is
Answers
= (73.1 * 34 + 66.4 * 26) / (34 + 26)
= (2485.4 + 1726.4) / 60
= 70.2 (rounded)
The Mean of the combined class is 70.19.
MeanMean is the average of a set of two or more numbers. The arithmetic and geometric mean are the types of mean that can be calculated.
Mean formula[tex]\rm Mean = \dfrac{sum\ of\ the\ term}{total\ number\ of\ term}[/tex]
Given
The test scores of a class of 34 students have a mean of 73.1 and
The test scores of another class of 26 students have a mean of 66.4.
To find
The mean of the combined group.
How to get the mean of the combined group?The sum of the total of the test score = Total number of students x Mean
Class 1 sum will be
The sum of the total test score = 34 x 73.1
The sum of the total test score = 2485.4
Class 2 sum will be
The sum of the total test score = 26 x 66.4
The sum of the total test score = 1726.4
Than Mean for the combine will be
[tex]\rm Mean = \dfrac{sum\ of\ the\ term}{total\ number\ of\ term}\\\\Mean = \dfrac{2485.4+1726.4}{34+26} \\\\Mean = \dfrac{4211.8}{60} \\\\Mean = 70.19[/tex]
Thus the Mean of the combined class is 70.19.
More about the Mean link is given below.
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A triangle on a coordinate plane is translated according to the rule T–3, 5(x, y). Which is another way to write this rule?
(x, y) → (x – 3, y + 5)
(x, y) → (x – 3, y – 5)
(x, y) → (x + 3, y – 5)
(x, y) → (x + 3, y + 5)
Answers
the original (x,y) coordinates are being moved to the left by 3 units and up by 5 units.
therefore
the answer is the option
(x, y) → (x – 3, y + 5)
Another way to write the given rule is (x, y) → (x – 3, y + 5).
Given that,
There are the original x and y coordinates that are being moved to the left-hand side by 3 units and go up by 5 units.Based on the information, we can conclude that another way to write the given rule is (x, y) → (x – 3, y + 5).
Hence, the other options are incorrect.
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Which triangle is it ?
Answers
we know that
sin(30°)=0.5 cos(30°)=√3/2
sin(60°)=√3/2 cos(60°)=0.5
sin(60)=BC/AC=5√3/10=√3/2-------------- is ok
cos (60)=AB/AC=5/10=0.5---- is ok
sin(30)=BA/AC=5/10=0.5-------------- is ok
cos (30)=BC/AC=5√3/10=√3/2-------------- is ok
if angle B is 90°
then
AB²+BC²=AC²------------> 5²+(5√3)²=10²=(25+75)=100------------- > is ok
the solution in the attached figure
The scale on a map is 1 cm:35 mi. The distance on the map between Los Angeles, CA, and San Francisco, CA, is 10.8 cm. What is the actual distance between Los Angeles and San Francisco?
Answers
this is answer
Step 1: Let us assign variable for the unknown that we need to find.
' x ' be the actual distance between Los Angeles and San Francisco
Step 2: Set up an equation based on the given statement "The scale on a map is 1 cm:35 mi. The distance on the map between Los Angeles, CA, and San Francisco, CA, is 10.8 cm."
[tex] \frac{distance \; in \; cm}{distance\; in\; miles}=\frac{1}{35}=\frac{10.8}{x} \\ \\ Cross \; Multiply\\ \\ 1 \cdot x = 35 \cdot 10.8\\ \\ x = 378 [/tex]
Conclusion:
The actual distance between Los Angeles and San Francisco is 378 miles.
8. The U.S. population was 309 million in 2010. If the U.S. had had the same firearm death rate as Australia in 2010, how many firearm deaths would the U.S. have expected to have that year? Australia’s population was 22.3 million people in 2010. Australia had 236 firearm deaths in 2010. (round to the nearest person)
Answers
As per linear equation, in 2010 the expected firearm death U.S. had is 3270.
What is a linear equation?A linear equation represents an equation that has one or multiple variables with the highest power of the variable is 1.
Australia’s population was 22.3 million people in 2010.
Australia had 236 firearm deaths in 2010.
Therefore, portion of Australian population had firearm deaths is
[tex]= \frac{236}{22.3(10)^{6} } \\= 0.000011[/tex]
The U.S. population was 309 million in 2010.
Therefore, the expected firearm deaths in U.S. in 2010 was
[tex]= (309) (10^{6}) (0.000011)\\= 3270.13\\= 3270[/tex]
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Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 – 4x = 5
Answers
x^2 - 4 x = 5
Subtract 5 from both sides:
x^2 - 4 x - 5 = 0
x = (4 ± sqrt((-4)^2 - 4 (-5)))/2 = (4 ± sqrt(16 + 20))/2 = (4 ± sqrt(36))/2:
x = (4 + sqrt(36))/2 or x = (4 - sqrt(36))/2
sqrt(36) = sqrt(4×9) = sqrt(2^2×3^2) = 2×3 = 6:
x = (4 + 6)/2 or x = (4 - 6)/2
(4 + 6)/2 = 10/2 = 5:
x = 5 or x = (4 - 6)/2
(4 - 6)/2 = -2/2 = -1:
Answer: x = 5 or x = -1
Answer:
x = 5 or x = -1
Step-by-step explanation:
x^2 – 4x = 5
Solve it by completing the square method
In completing the square method, we take the coefficient of x that is -4, divide it by 2 and then square it
-4/2 = -2
square it (-2)^2 = 4
Now add 4 on both sides
x^2 – 4x +4 = 5+4
x^2 – 4x +4 = 9
Now factor the left hand side
(x-2)(x-2)=9
(x-2)^2 = 9
Take square root on both sides
x-2 = +-3
x-2 = 3 , so x= 5
x-2 = -3, so x= -1
Find geometric mean of the pair of number 6 and 10
Answers
6 x 10 = 60
2nd step find the square root
sqrt(60) = 7.745
round the answer as needed.
The Geometric mean of the pair of number 6 and 10 is [tex]7.74[/tex]
Geometric mean :The geometric mean of two number m and n is given as,
[tex]G.M=\sqrt{m*n}[/tex]
Geometric mean of the pair of number 6 and 10 is,
[tex]G.M=\sqrt{6*10} =\sqrt{60} \\\\G.M=7.74[/tex]
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describe the graph of y=3/4x-12 as compared to the graph of y=1/x
Answers
Answer:
Parent function is compressed by a factor of 3/4 and shifted to right by 3 units.
Step-by-step explanation:
We are asked to describe the transformation of function [tex]y=\frac{3}{4x-12}[/tex] as compared to the graph of [tex]y=\frac{1}{x}[/tex].
We can write our transformed function as:
[tex]y=\frac{3}{4(x-3)}[/tex]
[tex]y=\frac{3}{4}*\frac{1}{(x-3)}[/tex]
Now let us compare our transformed function with parent function.
Let us see rules of transformation.
[tex]f(x-a)\rightarrow\text{Graph shifted to the right by a units}[/tex],
[tex]f(x+a)\rightarrow\text{Graph shifted to the left by a units}[/tex],
Scaling of a function: [tex]a*f(x)[/tex]
If a>1 , so function is stretched vertically.
If 0<a<1 , so function is compressed vertically.
As our parent function is multiplied by a scale factor of 3/4 and 3/4 is less than 1, so our parent function is compressed vertically by a factor of 3/4.
As 3 is being subtracted from x, so our parent function is shifted to right by 3 units or a horizontal shift to right by 3 units.
Therefore, our parent graph is compressed by a factor of 3/4 and shifted to right by 3 units to get our new graph.
Final answer:
The equation y=3/4x-12 represents a linear function with a straight line graph, while y=1/x depicts a rectangular hyperbola with a curved graph showcasing an inverse relationship. These graphs exhibit fundamentally different behaviors, one being constant and the other varying.
Explanation:
The student's question involves comparing the graph of y=3/4x-12 to the graph of y=1/x. The first equation, y=3/4x-12, describes a linear function with a slope of 3/4 and a y-intercept of -12. This means it is a straight line that increases as x increases, crossing the y-axis at (0, -12).
On the other hand, the graph of y=1/x is a rectangular hyperbola. This curve approaches the x-axis and y-axis but never touches them, known as asymptotes. The hyperbola is divided into two parts, one in the first quadrant where both x and y are positive, and another in the third quadrant where both x and y are negative. This graph does not resemble a straight line at any part.
Comparatively, the key difference lies in the nature of their graphs - one is a straight line and the other a curved hyperbola, showcasing completely different behaviors. The linear equation reflects constant change, whereas the hyperbola’s rate of change varies with x, indicating an inverse relationship.
factor, x^4y+8x^3y-6x^2y^2-48xy^2
Answers
[tex]\boxed{\boxed{((((x^4)*y)+((8*(x^3))*y))-((6*(x^2))*(y^2)))-(24*3xy^2)}} \\ \\ (let's \ simplify \ some \ number's \ down) \\ \\ \boxed{\boxed{ ((((x4)*y)+((8*(x3))*y))-((2*3x2) *y2))-(24*3xy2)}} \\ \\ \\ Pull \ out \ like \ factors : \\ \\ \boxed{\boxed{ x4y + 8x^3y - 6x2y^2 - 48xy^2 = xy * (x3 + 8x^2 - 6xy - 48^y) }} \\ \\ \\ (TAKE \ NOTICE) \swarrow\swarrow\swarrow\swarrow \swarrow\swarrow\swarrow\swarrow\swarrow\swarrow \\ \\ \\ [/tex]
[tex]\boxed{\boxed{\boxed{ (((((x^4)*y)+(23x^3*y))-(2*3x2y2))}}} \\ \\ \\ \boxed{\boxed{\boxed{-(24*3xy2))-xy*(x3+8x2-6xy-48y) = \boxed{0}}}}}[/tex]
I hope this helps you!
see attached picture for steps:
HELP ME ANSWER THIS QUESTION!
Boyd (B) is trapped in a soccer training circle. Albert (A) and Carlos (C) kick the ball to Boyd in rotation. Determine how far Boyd needs to kick the ball to Carlos if he is located in the center of his training circle and Carlos is located at the outer rim.
Answers
AB = 19+x
BC= x
AC= 30
From the picture we can see that side AB is hypothenuze. We are given number 19 as part of length of that hypothenuze. Other part is equal to distance from center to edge of circle. This length is same as side BC.
We will use Pythagorean theorem to solve this:
[tex] (AB)^{2} = (BC)^{2} + (AC)^{2} \\ (19+x)^{2} = x^{2} + 30^{2} \\ 361+38x+ x^{2} = x^{2} +900 \\ x^{2} - x^{2} +38x=900-361 \\ 38x=539 \\ x=14.2yard[/tex]
Which simplified equation is equivalent to the equation shown below?
4x+x-3-9+4x=6
a.5x-8=6
b.-3x=6
c. 9x-12=6
d. 8x-12=6
Answers
9x-12=6
Answer C
We need to group the like terms and combine like terms to get the simplified equation.
[tex] 4x+x-3-9+4x=6\\ \\ Step \; 1: \; Group \; like\; terms\\ \\ 4x+x+4x-3-9=6\\ \\ Step \; 2: \; Combine \; like\; terms\\ \\ 9x-12=6 [/tex]
Conclusion:
Option C is the right answer !!
If you take out a loan that costs $130.50 over nine years at an interest rate of 10%, how much was the loan for?
Answers
The original loan amount for which the final amount payable is $130.50 over nine years at an interest rate of 10% was approximately $55.39.
Explanation:To find out the original amount of the loan for which the final amount payable is $130.50 over nine years at an interest rate of 10%, we will use the formula for the present value of a loan.
The formula given is P = A / (1 + r/n)^nt, where P is the principal (initial loan amount), A is the final amount, r is the annual interest rate (expressed as a decimal), n is the number of times that interest is compounded per year, and t is the time the money is borrowed for in years.
As the question doesn't specify how many times the interest is compounded per year, we will assume it is compounded once a year (n=1).
We have:
A = $130.50,r = 10% or 0.10,n = 1,t = 9 years.Plugging these values into the formula:
P = $130.50 / (1 + 0.10/1)^(1*9)
P = $130.50 / (1 + 0.10)^9
P = $130.50 / (1.10)^9
P = $130.50 / 2.35794769
P = $55.39 approximately
Therefore, the original loan amount was approximately $55.39.
1.Write equatios to represent the distances the family drove on the given days.
2. construct a math argument to explain why your answer to 5 is correct.
3. How can you check that your answer is reasonable?
Answers
i think this is correct because you need morning and evening combined to know a exact answer.
you can check this by calculating you equations and u will end up with Wednesday as the longest amount of miles
which of the following is equivalent to the polynomial below
Answers
1. to find the roots of the equation (D=-36):
[tex] \left[\begin{array}{ccc}x=5+6i\\ x=5-6i\end{array}\right[/tex]
2. to simplify the polinom:
x²-10x+61=(x-(5-6i))(x+(5+6i))
Answer: 1
Can you answer this one for my plz I need before Monday ty
Answers
.. -x^2 -4x +1
.. = -(x^2 +4x) +1
.. = -(x^2 +4x +(4/2)^2) +1 -(-(4/2)^2) . . . . complete the square
.. = -(x +2)^2 +5
The vertex is (-2, 5).
The axis of symmetry is x = -2.
The perimeter of a quilt is 34 ft. If the quilt is 8 ft long, what is the area
Answers
2 x 8 = 16 (Finding out the length)
16 + 2w = 34 (Problem with the length)
-16 -16 (Using the subtraction property of equality to isolate the variable)
2w = 18 (New problem)
/2 /2 (Using division property of equality)
w = 9. (Width is found)
9 x 8 = 72. The area is 72 squared feet.
18÷2=9
8x9=72
Which shows how the distributive property can be used to evaluate 7×84/5?
Answers
84/5 gives 16 4/5. I don't know how much saving in work there is in doing this but you could do this.
7 ( 16 + 4/5)
You still have to do something with 28/5 when you get done, but it is one way to do it.
How to start the problem off. (substitution)
Answers
HELP PLEASE
Translate the answer, T2 = A3, into words:
The BLANK of the orbital period, T, of a
planet is equal to the BLANK of the average distance, A, of the planet from the Sun.
Square
Square Root
Cube
Answers
Answer: The square of the orbital period, T, of a planet is equal to the cube of the average distance, A, of the planet from the Sun.
Step-by-step explanation:
In mathematics, A number or variable 'a' to its second power is said to be square of 'a' i.e. [tex]\ a^2[/tex] is the square of a.
A number or variable 'b' to its third power is said to be cube of 'b' i.e. [tex]\ b^3[/tex] is the cube of b.
In the given equation: [tex]T^2 = A^3[/tex]
Here, [tex]T^2 [/tex] is square of T.
And [tex]A^3[/tex] is cube of A.
Therefore, The square of the orbital period, T, of a planet is equal to the cube of the average distance, A, of the planet from the Sun.
The answer should be a fraction
Answers
4y2/5y3..
now apply the exponent rule, which is : xa /xb = 1/ xb-a
so...y2/y3 = 1/ y3 - 2 = 1/y
ANSWER : 4/5y
The correct answer to your question is... [tex] 2^{3} y^{5} [/tex]
Evidence:
Step 1: Simplify [tex] y^{2} [/tex]/5
( 40 multiplied by [tex] y^{2} [/tex]/5 multiplied by [tex] y^{3} [/tex] )
Step 2: [tex] y^{2} [/tex] multiplied by [tex] ^{3} [/tex] = y(2 + 3) = [tex]y^{5} [/tex]
So the correct answer is... [tex] 2^{3} y^{5} [/tex]
I hope this helped! : )
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A bank runs a contest to encourage new customers to open accounts. In the contest, each contestant draws a slip representing a different reward—$5, $3, or $x—from a jar. At the beginning of the contest the jar contains 60 slips for $5, 40 slips for $3, and 50 slips for $x.
If the expected value of the first draw from the jar is $5.8, the value of x is__
At one point in the contest, the jar contains 3 slips for $5, 7 slips for $3, and y slips for $x. If the expected value on the next draw is $6, the value of y is __
Answers
We'll use x = 9 from part 1.
Again let,
A = event that the $5 reward is drawn
B = event that the $3 reward is drawn
C = event that the $x reward is drawn (x is some positive number)
We can update event C to say
C = event that the $9 reward is drawn
The probabilities change to
P(A) = 3/(10+y)
P(B) = 7/(10+y)
P(C) = y/(10+y)
where y is some positive whole number. It represents the number of slips in jar C
The net values are
V(A) = 5
V(B) = 3
V(C) = x = 9
Like before, multiply the probabilities and net values to get
P(A)*V(A) = (3/(10+y))*5 = 15/(10+y)
P(B)*V(B) = (7/(10+y))*3 = 21/(10+y)
P(C)*V(C) = (y/(10+y))*9 = (9y)/(10+y)
The results add up to
[ 15/(10+y) ] + [ 21/(10+y) ] + [ (9y)/(10+y) ]
(15+21+9y)/(10+y)
(36+9y)/(10+y)
That last expression is the expected value. The expected value is also given to be 6, so set the two expressions equal to each other and solve for y.
(36+9y)/(10+y) = 6
36+9y = 6(10+y)
36+9y = 6(10)+6(y)
36+9y = 60+6y
9y-6y = 60-36
3y = 24
3y/3 = 24/3
y = 8
The statement "y slips of $x" turns into "8 slips of $9" since x = 9 and y = 8.
What is the mean of the values in the stem-and-leaf plot? Enter your answer in the box.Key: 2|5 means 25
Enter your answer in the box.
Key: 2|5 means 25
A stem-and-leaf plot with a stem value of 1 with leaf values of 5 and 8, a stem value of 2, a stem value of 3, a stem value of 4 with a leaf value of 6, a stem value of 5 with leaf values of 0, 0, 0, 0, 7, a stem value of 6, a stem value of 7, a stem value of 8, and a stem value of 9.
Answers
The mean of the values in the stem-and-leaf plot is 42.
To find the mean of the values in the stem-and-leaf plot, we first need to interpret the plot correctly. Here's the stem-and-leaf plot description:
Stem | Leaves
1 | 5, 8
2 |
3 |
4 | 6
5 | 0, 0, 0, 0, 7
6 |
7 |
8 |
9 |
Let's list the individual values from the plot:
- From stem 1: Leaves are 5 and 8
- From stem 4: Leaf is 6
- From stem 5: Leaves are 0, 0, 0, 0, 7
Now, we calculate the mean (average) of these values.
Step-by-step calculation:
1. List of values:
- Values from stem 1: 15, 18
- Values from stem 4: 46
- Values from stem 5: 50, 50, 50, 57
2. Count the number of values:
- There are 2 values from stem 1, 1 value from stem 4, and 5 values from stem 5.
- Total count = 2 + 1 + 5 = 8
3. Calculate the sum of all values:
- Sum = 15 + 18 + 46 + 50 + 50 + 50 + 50 + 57
- Sum = 336
4. Calculate the mean:
- Mean = Sum / Count
- Mean = 336 / 8
- Mean = 42
Therefore, the mean of the values in the stem-and-leaf plot is [tex]{42} \).[/tex]
What is the measure of angle z in this figure?
Enter your answer in the box.
z = ___°
Answers
I've attached a photo for reference.
Lines A and B form straight angles, which measure 180 degrees. That means that -
m∠x + m∠y = 180°
m∠y + m∠z = 180°
m∠z + 43° = 180°
43° + m∠x = 180°
Since you're trying to find z, use the solvable equation with z in it:
m∠z + 43° = 180°
180 = z + 43
137 = z
Answer:
m∠z = 137°
A triangle has one 60 degree angle and one 20 degree angle. The third angle in the triangle must be
a.acute
b.obtuse
c.commplementary
d.straight
Answers
A circular city park has a sidewolk directly through the rmiddle that is 111- feet long. I each bag of fertilizer covers 50 square feet, then determine how many bags of tertilizer the Parks and Recreation department needs to use to cover the circular park. Ignore oll the sidewalks around and through the park.
Answers
.. A = (π/4)d^2
.. = (π/4)*(111 ft)^2 ≈ 9676.9 ft^2
The number of bags of fertilizer required will be
.. (9676.9 ft^2)*(1 bag)/(50 ft^2) = 193.5 bags
Parks & Rec needs to use 193.5 bags of fertilizer to cover the park.
_____
No doubt, P&R has half a bag left over from a previous use of fertilizer in the park, so they will not have to purchase a whole bag to cover the fraction.
How many bits are required to represent the decimal numbers in the range from 0 to 999 in straight binary code?
Answers
[tex]2^0=1_2[/tex]
[tex]2^1=10_2[/tex]
[tex]2^2=100_2[/tex]
and so on. Observe that [tex]n+1[/tex] digits are required to represent the [tex]n[/tex]-th power of 2 in binary.
Also observe that
[tex]\log_2(2^n)=n\log_22=n[/tex]
so we need only add 1 to the logarithm to find the number of binary digits needed to represent powers of 2. For any other number (non-power-of-2), we would need to round down the logarithm to the nearest integer, since for example,
[tex]2_{10}=10_2\iff\log_2(2^1)=\log_22=1[/tex]
[tex]3_{10}=11_2\iff\log_23=1+(\text{some number between 0 and 1})[/tex]
[tex]4_{10}=100_2\iff\log_24=2[/tex]
That is, both 2 and 3 require only two binary digits, so we don't care about the decimal part of [tex]\log_23[/tex]. We only need the integer part, [tex]\lfloor\log_23\rfloor[/tex], then we add 1.
Now, [tex]2^9=512<1024=2^{10}[/tex], and 999 falls between these consecutive powers of 2. That means
[tex]\log_2999=9+\text{(some number between 0 and 1})[/tex]
which means 999 requires [tex]\lfloor\log_2999\rfloor+1=9+1=10[/tex] binary digits.
Your question seems to ask how many binary digits in total you need to represent all of the numbers 0-999. That would depend on how you encode numbers that requires less than 10 digits, like 1. Do you simply write [tex]1_2[/tex]? Or do you pad this number with 0s to get 10 digits, i.e. [tex]0000000001_2[/tex]? In the latter case, the answer is obvious; [tex]1000\times10=10^4[/tex] total binary digits are needed.
In the latter case, there's a bit more work involved, but really it's just a matter of finding how many number lie between successive powers of 2. For instance, 0 and 1 both require one digit, 2 and 3 require two, while 4-7 require three, while 8-15 require four, and so on.
Final answer:
To represent the decimal numbers from 0 to 999 in binary code, we require 10 bits. This is determined by finding the binary equivalent of the largest number, 999, which necessitates at least 10 powers of 2 (from [tex]2^0 \ to \ 2^9[/tex]).
Explanation:
To determine how many bits are required to represent the decimal numbers in the range from 0 to 999 in straight binary code, we need to find the binary equivalent of the largest number in that range, which is 999. In binary, this would require the highest power of 2 that is less than or equal to 999. The largest power of 2 less than 999 is 512 (29), and we continue to add powers of 2 to represent the number:
512 (29)
256 (28)
128 (27)
64 (26)
32 (25)
16 (24)
8 (23)
4 (22)
2 (21)
1 (20)
Adding these up, we see that we need at least 10 bits to represent the number 999 in binary, because adding powers of 2 from 20 to 29 will give us the required range. Therefore, we need 10 bits to represent any number from 0 to 999 in binary.
Evaluate g(n-5) if g(x)=x^2-6/2x
Answers
g( n-5) = ( [n-5]^2 -6) / 2(n-5)
= ( n^2 -10n +25 -6 ) / 2(n-5) or ( n^2 -10n +25 -6 ) / (2n-10)
Your Answer
I did foil first and got n^2-10n+25
then did 25-6 to get 19.
so n^2-10n+25 is on top.////// should have been n^2 -10n +19
and the bottom is 2(n-5) so I distributed the 2 and got 2n-10
so n^2-10n+25
2n-10
= (n^2 -10n +19) / 2(n-5)
Answer: We want to evaluate g(x) in x = n -5, where g(x) = (x^2-6)/2x
then, doing it step by step: [tex]g( n- 5)= \frac{(n-5)^{2} - 6 }{2*(n-5)}= \frac{(n^{2} - 2*5*n + 25) - 6 }{2n - 10} = \frac{n^{2} - 10n + 19 }{2n - 10}[/tex]
where i used that (a - b)^2 = a^2 -2ab + b^2
So the correct option is C.
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let f(x)=4x+3 and g(x)=-2+5. find (fog) (5)
Answers
let f(x)=4x+3 and g(x)=-2x+5. find (fog) (5)
we have that
f(x)=4x+3
g(x)=-2x+5
(fog) (x)---------> f(g(x))------> 4*[-2x+5]+3---------> f(g(x))=-8x+20+3
f(g(x))=-8x+23
then
(fog) (5)=-8*5+23---------> (fog) (5)=-40+23
(fog) (5)=-17
the answer is (fog) (5)=-17
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