Answers
4x[tex] ^{7} [/tex] + 5x[tex] ^{6} [/tex] - 4x[tex] ^{4} [/tex] + 1.
So the first term would be 4x^7. Second is 5x^6. Third is -4x^4. Fourth is 1.
The coefficients are the numbers in front of each variable.
Related Questions
The sum of three numbers is 45 the second of the three numbers is three more than twice the first number, ×. The thurd number is two more than the first number, ×. Which equation can be used to solve the first number
Answers
Answer:
Step-by-step explanation:
We know that the 1st equation + 2nd equation + 3rd equation = 45. Now we just need to identify from the infor given what these equations are, then set them to equal 45.
It has already been determined that the 1st equation is x.
The second equation is "3 more than twice the first". Twice the first is 2x, and 3 more is +3; therefore, the second equation is: 2x + 3.
The third equation is "2 more than the first". 2 more than is +2, so the third equation is x + 2.
Now we have all 3:
1st: x
2nd: 2x + 3
3rd: x + 2
Add them all up and set them equal to 45:
x + 2x + 3 + x + 2 = 45.
You don't have choices listed, so it's either that one above, or simplified down to:
4x + 5 = 45
After that, any simplification done will be solving the equation.
Which of the following functions are homomorphisms?
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Given [tex]f:Z \rightarrow Z, [/tex] defined by [tex]f(x)=-x[/tex]
[tex]f(x+y)=-(x+y)=-x-y \\ \\ f(x)+f(y)=-x+(-y)=-x-y[/tex]
but
[tex]f(xy)=-xy \\ \\ f(x)\cdot f(y)=-x\cdot-y=xy[/tex]
Since, f(xy) ≠ f(x)f(y)
Therefore, the function is not a homomorphism.
Part B:
Given [tex]f:Z_2 \rightarrow Z_2, [/tex] defined by [tex]f(x)=-x[/tex]
Note that in [tex]Z_2[/tex], -1 = 1 and f(0) = 0 and f(1) = -1 = 1, so we can also use the formular [tex]f(x)=x[/tex]
[tex]f(x+y)=x+y \\ \\ f(x)+f(y)=x+y[/tex]
and
[tex]f(xy)=xy \\ \\ f(x)\cdot f(y)=xy[/tex]
Therefore, the function is a homomorphism.
Part C:
Given [tex]g:Q\rightarrow Q[/tex], defined by [tex]g(x)= \frac{1}{x^2+1} [/tex]
[tex]g(x+y)= \frac{1}{(x+y)^2+1} = \frac{1}{x^2+2xy+y^2+1} \\ \\ g(x)+g(y)= \frac{1}{x^2+1} + \frac{1}{y^2+1} = \frac{y^2+1+x^2+1}{(x^2+1)(y^2+1)} = \frac{x^2+y^2+2}{x^2y^2+x^2+y^2+1} [/tex]
Since, f(x+y) ≠ f(x) + f(y), therefore, the function is not a homomorphism.
Part D:
Given [tex]h:R\rightarrow M(R)[/tex], defined by [tex]h(a)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right) [/tex]
[tex]h(a+b)= \left(\begin{array}{cc}-(a+b)&0\\a+b&0\end{array}\right)= \left(\begin{array}{cc}-a-b&0\\a+b&0\end{array}\right) \\ \\ h(a)+h(b)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)+ \left(\begin{array}{cc}-b&0\\b&0\end{array}\right)=\left(\begin{array}{cc}-a-b&0\\a+b&0\end{array}\right)[/tex]
but
[tex]h(ab)= \left(\begin{array}{cc}-ab&0\\ab&0\end{array}\right) \\ \\ h(a)\cdot h(b)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)\cdot \left(\begin{array}{cc}-b&0\\b&0\end{array}\right)= \left(\begin{array}{cc}ab&0\\-ab&0\end{array}\right)[/tex]
Since, h(ab) ≠ h(a)h(b), therefore, the funtion is not a homomorphism.
Part E:
Given [tex]f:Z_{12}\rightarrow Z_4[/tex], defined by [tex]\left([x_{12}]\right)=[x_4][/tex], where [tex][u_n][/tex] denotes the lass of the integer [tex]u[/tex] in [tex]Z_n[/tex].
Then, for any [tex][a_{12}],[b_{12}]\in Z_{12}[/tex], we have
[tex]f\left([a_{12}]+[b_{12}]\right)=f\left([a+b]_{12}\right) \\ \\ =[a+b]_4=[a]_4+[b]_4=f\left([a]_{12}\right)+f\left([b]_{12}\right)[/tex]
and
[tex]f\left([a_{12}][b_{12}]\right)=f\left([ab]_{12}\right) \\ \\ =[ab]_4=[a]_4[b]_4=f\left([a]_{12}\right)f\left([b]_{12}\right)[/tex]
Therefore, the function is a homomorphism.
For a certain bathtub, the hot water faucet can fill the tub in 13 minutes. The cold water faucet can fill the tub in 12 minutes. If both faucets are used together, how long will it take to fill the tub?
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It will take approximately 6.24 minutes for both faucets to fill the bathtub when used simultaneously.
To solve this problem, we need to find the combined rate at which both faucets can fill the bathtub. The hot water faucet can fill the tub in 13 minutes, and the cold water faucet can fill it in 12 minutes. We can express their rates as fractions of the tub they can fill per minute as 1/13 and 1/12, respectively.
When we add these rates together, we get the combined rate:
Rate of hot water faucet + Rate of cold water faucet = combined rate
1/13 + 1/12 = (12 + 13) / (13 imes 12) = 25 / 156
The combined rate is 25/156 tubs per minute. To find out how long it will take for both faucets to fill the tub together, we take the reciprocal of the combined rate:
Time to fill the tub = 1 / (combined rate) = 156 / 25 = 6.24 minutes
Therefore, it will take approximately 6.24 minutes for both faucets to fill the bathtub when used simultaneously.
Describe two situations in which opposite quantities combine to make zero
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In the situation, x + (-x) is combined making zero and other y + (-y) is making zero.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.
Summation = addition of two or more numbers or variable
Subtraction = Minus of any two or more numbers with each other called subtraction.
Division = divide any two numbers or variable called division.
Multiplication = to multiply any two or more numbers or variables called multiplication.
If we combine any two opposite quantities then their summation must be zero.
For example,
if you combine 5 and -5 then it will be 0.
If you combine 10 and -10 then it will be 0.
So,
The first situation ⇒
Combining x and -x
x + (-x) = 0
The second situation ⇒
Combining y and -y
y + (-y) = 0
Hence, In the situation, x + (-x) is combined making zero and other y + (-y) makes zero.
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Number of solutions to equations -2+10+7z=16z+7
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The given equation resulting in one solution, which is z = 1/9.
To find the number of solutions to the equation -2 + 10 + 7z = 16z + 7, we first simplify and solve for z. Start by combining like terms on the left side:
-2 + 10 = 8, so the equation becomes 8 + 7z = 16z + 7.
Next, we get all the terms with z on one side and the constants on the other:
Subtract 7z from both sides:
8 = 16z - 7z + 7
Combine z terms:
8 = 9z + 7
Subtract 7 from both sides:
1 = 9z
Divide both sides by 9:
z = 1/9
What is 4 - ( -h ) = 68?
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h = 68 - 4
h = 64
hope this helps
Next subtract 4 from both sides
And lastly subtract 68 - 4 and u have your answer which is 64.
A television game has 6 shows doors, of which the contests must pick 2. behind two of the doors are expensive cars, and behind the other 4 doors are consolation prizes. Find the probability that the contestant wins exactly 1 car? no car? or atleast one car?
what if they had to pick 3 doors? and all of the other information wast the same
Answers
One car probability 82/120
No car probability = 24/120
At least one car probability= 96/120
I will focus answering the 3 doors probability since the 2nd door problem is solved in the previous problem. (https://brainly.com/question/5761449)
No car condition
1. 1st door consolation, 2nd door consolation=, 3rd door consolation= 4/6 * 3/5 * 2/4= 24/120
This was also can be found by: (4!/1!)/ (6!/3!) = 24/120
(At least one car probability) is the opposite of (no car probability) In this case, the easier way is
100% - (no car probability) = 120/120 - 24/120= 96/120
One car probability is (At least one car probability) - (2 car probability). It will be easier to count the 2 car probability and subtract the (At least one car probability)
Two car condition:
1. 1st door car, 2nd door car, 3rd door consolation = 2/6 * 1/5 * 4/4 =8/ 120
2.1st door car, 2nd door consolation, 3rd door car =2/6 * 4/5 * 1/4 = 8/120
3. 1st door consolation, 2nd door car, 3rd door car= 4/6 * 2/5 * 1/4= 8/120
The total probability will be 8/120+ 8/120 + /120= 24/120
This was also can be found by: (2!) (4!/2!)/ (6!/3!) = 24/120
One car probability = (At least one car probability) - (2 car probability)= 96/120-24/120= 82/120
''Please Help!!'' says Kuku and Yaya
A middle-school band holds a car wash to raise money. The sixth-grade band members wash 16 cars. The seventh-grade band members wash 75% as many cars as the sixth-graders. The eighth-grade band members wash half as many cars as the sixth- and seventh-grade band members combined.
If the band charges $5 per car, how much money did the members raise altogether?
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7th grade was 75% as many as 6th grade....0.75(16) = 12 cars washed
8th grade wash half as many as 6th and 7th combined...(12 + 16) / 2 =
28/2 = 14 cars washed
total cars washed : (16 + 12 + 14) = 42 cars
at $ 5 per car.....42 * 5 = $ 210 <===
Estimate how many times larger 7 x 10^10 is than 13 x 10^8. A.50 B.100 c.200 d.400
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13 x 10^8 = 1,200,000,000
70,000,000,000/1,200,000,000 = 58.3333333
I would go with A :)
6% sales tax, hotel charges $265 find cost before tax?
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265 - 15.9 = 249.1
249.1 is your answer
hope this helps
What is the difference between –4 and 6?
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Hope this helps!
Answer:
2
Step-by-step explanation:
Took the test ;)
100.6 - 30.06 show me it in vertically form (show work)so I can understand how to regroup it.
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To vertically subtract 30.06 from 100.6, start by borrowing 1 from the tens place and adding it to the ones place. Then, borrow 10 from the hundreds place and add it to the tens place. Finally, combine the result to get 70.54.
Explanation:To vertically subtract 30.06 from 100.6, you'll need to line up the decimal points vertically. Start by subtracting the hundredths place (0.06) from the hundredths place (0.00). Since 6 is bigger than 0, you'll need to regroup. Borrow 1 from the tens place by making it 9, and add it to the ones place, making it 10. Then, you can subtract 6 from 10, which gives you 4. Next, subtract the whole number part (30) from the whole number part (100). Since 0 is smaller than 3, regroup again by borrowing 10 from the hundreds place and adding it to the tens place, making it 20. Then, subtract 3 from 10, which gives you 7. Finally, combine the result by placing the decimal point in the correct position, which gives you the answer: 70.54.
Write an equation of a line that does not have a y intercept
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the formula of the area of a triangle is A=1/2bh what is the length of the base if the area is 22cm and the height is 8cm
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Kristin jogs around a park that has a perimeter of 12 mile. Kristin jogged around the park 4 times in 50 minutes.
What is the unit rate of Kristin's speed?
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12 *4 = 48 total miles in 50 minutes
48 / 50/60 = 57.6 miles per hour
Will the standard form 3.2 × 10^–4 be more or less than 1? Explain what effect the negative exponent has.
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Translate the following into a mathematical equation:
The density D of a material is directly proportional to the mass of the object M and inversely proportional to its volume V.
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The density of a material is equal to its mass divided by its volume.
Explanation:The equation that represents the relationship between density (D), mass (M), and volume (V) is: D = M/V.
This equation shows that the density of a material is equal to its mass divided by its volume.
For example, if you have an object with a mass of 10 grams and a volume of 2 cubic centimeters, you can calculate its density by dividing the mass by the volume: D = 10g / 2cm³ = 5g/cm³.
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The density (D) of a material is directly proportional to the mass (M) and inversely proportional to its volume (V). The mathematical equation for this relationship is D = k * (M / V).
Explanation:The density (D) of a material is directly proportional to the mass (M) and inversely proportional to its volume (V). To translate this into a mathematical equation, we can write:
D = k * (M / V)
Where D represents the density, M represents the mass, V represents the volume, and k represents the proportionality constant.
This equation demonstrates that as the mass of the object increases, the density also increases, while as the volume increases, the density decreases.
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Where is the hole for the following function located? mc005-1.jpg
Answers
The holes of the graph are located at (5, 3) and (-1, 11)
How to determine the hole of the graph
From the question, we have the following parameters that can be used in our computation:
The graph
The holes of the graph are at (5, 3) and (-1, 11)
This is so because the function is not defined at this value
Also, we can see that
The function has it vertical asymptotes are x = 2 and x = -2
how would i write y= -7x+25 In Standard form?
please help:)
Answers
nohpihot7 ggyfffffff
Isolate the constant to write is in standard form.
You want it in the form
Ax + By = C
7x + y = 25
Done!
Simplify (4.5)(5)(−2).
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a pet store has 30 animals. some are cats the rest are dogs. the cats cost $50 each. the dogs cost $100 each. if the total for all 30 animals is $1900, how many cats are there?
Answers
Cats= Y
X + Y = 30
100x + 50y= 1900
Easiest way is to solve by substitution.
[Looking for Y]
x+y=30
[subtract Y]
X= 30- Y
—————
Next, plug that into the next equation.
100 (30-y) + 50y= 1900
[Distribute]
300- 100y + 50y= 1900
[Combine Like Terms]
300- 50y= 1900
[subtract 300]
-50y= 1600
[divide by -50]
Y= ANSWER
This is Systems of Equations.
Answer:
There are 22 cats and 8 dogs.
Step-by-step explanation:
Let the cats be represented by = c
Let the dogs be represented by = d
Given, that the pet store has 30 pets.
First equation forms :
[tex]c+d=30[/tex] ........(1)
Also given, the cats cost $50 each and dogs cost $100 each and the total for all is $1900. Now second equation forms:
[tex]50c+100d=1900[/tex] .........(2)
From equation (1) we get [tex]c=30-d[/tex]
Putting this value of c in equation 2:
[tex]50(30-d)+100d=1900[/tex]
[tex]1500-50d+100d=1900[/tex]
=> [tex]50d=400[/tex]
=> [tex]d=8[/tex]
Now,[tex]c+d=30[/tex]
So, [tex]c=30-8[/tex]
[tex]c=22[/tex]
Hence, there are 22 cats and 8 dogs.
what is the 3sqaure root of 0.027y^9 = ?
Answers
three times the quantity five less than x, divided by the product of six and x
Answers
———- that would be it
6•x
The simplified expression is (x - 5) / (2x).
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The expression given is 3 (x - 5) / (6x)
We can simplify this expression by following the order of operations, which is a set of rules that tells us which operations to perform first in a mathematical expression.
The order of operations.
Perform any calculations inside parentheses first.
Exponents (ie: powers and square roots, etc.)
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)
Using the order of operations, we can simplify the expression as follows:
We start by simplifying the expression inside the parentheses.
x - 5 represents five less than x.
Next, we multiply the result of step 1 by 3.
= 3 (x - 5)
= 3x - 15
Finally, we divide the result of step 2 by the product of 6 and x.
= (3x - 15) / (6x)
= (3(x - 5)) / (6x)
= (x - 5) / (2x)
Therefore,
The simplified expression is (x - 5) / (2x).
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14x25x4=
Using the common core showing your work.
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The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. 8. Time (days) Cost ($) 3 75 4 100 5 125 6 150
Answers
Answer:
The rate of change is 25. It means the cost increased by $25 per day.
Step-by-step explanation:
The given table is
Time (days) Cost ($)
3 75
4 100
5 125
6 150
It means the graph of this constant function passing through the points (3,75) and (4,100).
If a line passing through two points, then the slope of the line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{100-75}{4-3}[/tex]
[tex]m=\frac{25}{1}[/tex]
[tex]m=25[/tex]
Therefore the rate of change is 25. It means the cost increased by $25 per day.
A running cheetah begins to slow down. For each meter the cheetah travels, its speed changes by −3.4 kilometers per hour. The cheetah travels a total of 21.5 meters.
What is the total change in the cheetah's speed during this time?
Drag and drop the correct answer into the box.
73.1.
71.9.
-71.9.
-73.1.
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help pleeeaaase this............... ..... .... .
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Higher order thinking if 1/2 is multiplied by 1/2 will the product be greater than half explain
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Find an equation for the line perpendicular to the line −7x−9y=−6 having the same y-intercept as 2x−6y=6
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-9y = 7x - 6
y = -7/9x + 2/3...slope here is -7/9....a perpendicular line will have a negative reciprocal slope. So the perpendicular line will have a slope of 9/7
2x - 6y = 6
-6y = -2x + 6
y = 1/3x - 1....the y int here is -1
so ur equation is : y = 9/7x - 1 <==
Algebraically determine if the relation y = x3 − 4x is symmetric with respect to the x-axis, y-axis, the origin or has no symmetry.
Answers
notice, if you replace x = -x and y = -y accordingly for each test for symmetry, if the resulting function, is equal to the original function, then it has that type of symmetry.
Final answer:
Algebraically, the relation y = x^3 - 4x is not symmetric to the x-axis or y-axis but is symmetric with respect to the origin when both x and y are replaced with their negatives.
Explanation:
To determine if the relation y = x3 − 4x is symmetric with respect to the x-axis, y-axis, or the origin, we perform a series of tests substituting -x for x (to test y-axis symmetry), -y for y (to test x-axis symmetry), and both -x for x and -y for y (to test origin symmetry).
Y-axis symmetry test:
Replace x with -x:
y = (-x)3 - 4(-x)
y = -x3 + 4x ≠ x3 − 4x (not symmetric to y-axis)
X-axis symmetry test:
Replace y with -y:
-y = x3 - 4x ⇒ y = -x3 + 4x ≠ x3 − 4x (not symmetric to x-axis)
Origin symmetry test:
Replace both x with -x and y with -y:
-y = (-x)3 - 4(-x)
-y = -x3 + 4x
y = x3 − 4x (symmetric to origin)