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The expression 5x⁶ - x⁴ is a binomial because we have two terms.
Even if they have the same variable x, their exponents are not the same.
Related Questions
solve each system of equations below by graphing, please use my graphy = 1/2x - 3y= 3/2x - 1
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Answer:
(-2, -4)
Explanation:
To solve the system, we need to graph both equations. So, we will find two points for each line.
For y = 1/2x - 3
If x = 0
y = 1/2(0) - 3 = -3
If x = 2
y = 1/2(2) - 3
y = 1 - 3 = -2
For y = 3/2x - 1
If x = 0
y = 3/2(0) - 1 = -1
If x = 2
y = 3/2(2) - 1
y = 3 - 1 = 2
Therefore, we have the points (0, -3) and (2, -2) for the first equation and the points (0, -1) and (2, 2) for the second equation. Now, we can graph the lines as:
The lines intersect at (-2, -4), so the solution of the system is (-2, -4)
that the triangles below are congruent select all options that would provide enough information to prove the triangles are congruent
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The correct options are options C and D;
1) Angle C is congruent to E
2) BA and FD are congruent
Here, we want to select the options that would prove that the triangles are congruent
We can get that from the markings on the diagram
As we can see from the question, we already have two sides being equal as we can see from the markings
Hence, we need an extra information to see through that the two triangles are indeed congruent
If the sides BA and FD are equal, it will simply mean that the three sides of the triangle are equal. In that case, the two triangles are congruent by SSS (side-side-side)
Also, if the angles C and E are congruent, we will have that the two triangles are similar by the SAS (side-angle-side)
So, the correct options are C and D
is (18,302) a solution to the equation y=300?
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No
Explanations:Note that:
the solutions to an equation are the values, if substituted into the equation, that will make the equation true.
The given equation is:
y = 300
(18, 302) means that x = 18, y = 302
Since the equation given is y = 300 and not y = 302, the point (18, 302) is not a solution to the equation.
find its volume. Use 3.14 as the approximate value of a25 m
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we know that
the solid of the figure is a sphere
the volume of the sphere is equal to
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]we have
pi=3.14
r=25 m
substitute
[tex]\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot25^3 \\ V=65,416.67\text{ m\textasciicircum{}3} \end{gathered}[/tex]the volume of the sphere is 65,416.67 cubic metersThere are 14 girls and 12 boys in a class. What is the ratio of gris to students in simplest form
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Number of girls = 14
Number of boys = 12
Number of students = 14 + 12 =26
Ratio of girls to students = 14/26 = 7 : 13
Locker codes at Lincoln High School consist of 4 digits. No digit can be used more than once. How many locker codes are available at Lincoln High School? A 210 B 3,024 C 5,040 D 10,000
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To obtain the number of locker codes available, the following steps are necessary:
Step 1: Create a diagram to represent the slot for each of the digits, as below;
Step 2: State the number ways that each digit can be used to fill any of the spots, as below:
Given that there are the numbers 0,1,2,3,4,5,6,7,8,9 - a total of 10 numbers,
- The first slot can be filled with any of the digits above, and thus can be filled in 10 ways
- The second slot can be filled with any of the remaining 9 numbers after one of them has already been used to fill the first slot. Thus, there are 9 ways the second slot can be filled.
- The same line of reasoning tells us that the third slot will be filled in 8 ways
- Lastly, the fourth slot will be filled in 7 ways
The diagram below gives a better illustration:
Step 3: Multiply the numbers of ways to find the total number of locker codes that are available, as follows:
[tex]10\times9\times8\times7\text{ = 5040}[/tex]Therefore, there are a total of 5040 available locker codes at Lincoln High School
Correct answer = Option C
(4a²b) ?Simplify:(2a3b4)32a5710AB.4ab63с225510D4ab53
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We would apply the following laws of exponents
(x^y)^z = x^(yz)
a^c * a^d = a^(c + d)
a^c / a^d = a^(c - d)
The given expression is
(4a^2b)^2/(2a^3b^4)^3
By applying the first law above, it becomes
[4^2a^(2*2)b^2]/[2^3a^(3*3)b^(4*3)]
= [16a^4b^2]/[8a^9b^12]
by applying the second and third laws, we have
16/8 * a^(4 - 9) * b^(2 - 12)
= 2a^-5b^-10
Also, x^-1 = 1/x
Thus, the final expression would be
2/a^5b^10
Option C is correct
6) 3x2 + 10X - 8We have to find the vertex
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Given:
[tex]3x^2+10x-8[/tex]To find the vertex, use the vertex formula below:
[tex]y\text{ = }a(x-h)^2+k[/tex]Where the vertex is: (h, k)
Thus, we have:
[tex]y=3x^2+10x-8[/tex][tex]\begin{gathered} y+8=3x^2+10-8+8 \\ \\ y+8=3x^2+10 \end{gathered}[/tex]Factorize:
[tex]undefined[/tex]Jessica is a professional baker. She bakes 113 cupcakes in 2 hours How many cupcakes will she make in 6 hours? Jessica can make cupcakes in 6 hours How long will it take her to make 791 cupcakes? It will take Jessica 791 cupcakes hours to make The equation that represents this situation is y Time (hour) Cupcakes 113 2 791
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You know that Jessica can bake 113 cupcakes in 2hours, using this relationship you can calculate the number of cupcakes she can bake in 6 hours using cross multiplication:
2hours_____113cupcakes
6hours_____xcupcackes
[tex]\begin{gathered} \frac{113}{2}=\frac{x}{6} \\ (\frac{113}{2})\cdot6=x \\ 339=x \end{gathered}[/tex]She can bake 339 cupcakes in 6 hours.
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To determine how much time it will take to make 791 cupcakes you can also apply cross multiplication, this time you know the amounts of cupcakes and neet to calculate the time:
So if the can make 113 cupcakes in 2 hours,
Then she will make 791 cupcakes in x hours:
113 cupcakes_____2hours
791 cupcakes_____xhours
[tex]\begin{gathered} \frac{2}{113}=\frac{x}{791} \\ (\frac{2}{113})\cdot791=x \\ 14=x \end{gathered}[/tex]It will take her 14 hours to make 791 cupcakes.
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To determine an equation that represents this situation, first determine the variables.
In this case:
y → will represent the number of cupcakes made
x → will represent the time she spent coocking the cupcakes
Next is to determine how many cupcakes she makes in one hour:
If she makes 113 cupcakes in 2hours, in half the time she will make half the cupcakes, that is
[tex]\frac{113}{2}=56.5[/tex]She makes 56.5 cupcakes per hour, since each passing hour se adds 56.5 cupcakes then this number will represent the coefficient of variation (or slope) of the equation and must multiply x.
Then the equation that represents this relationship is
[tex]y=56.5x[/tex]Tina has earned a total of 9,644 frequent flyer miles by traveling between twin falls and Preston. she has made 4 trip time how many miles is one trip between thses to city's.
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it is given that total miles travelled by tine are 9644 miles in the four trips.
now we calculate the distance travelled in one trip by tina,
[tex]\frac{9644}{4}=2411\text{ miles}[/tex]so tina travels 2411 miles in one trip.
Simplify the following: -(3z)²
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We have the following general rule for exponents:
[tex](a\cdot b)^n=a^n\cdot b^n[/tex]Then, in this case we have:
[tex]-(3z)^2=-(3^2\cdot z^2)=-9z^2[/tex]therefore, the simplifed expression is -9z²
Select the correct choice below and fill in the answer
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Step 1:
Write the function
[tex]g(x)=x^5-16x^3[/tex]Step 2:
Write an inequality equation where g(x) > 0
[tex]\begin{gathered} x^5-16x^3\text{ > 0} \\ \text{Factorize the left hand side of the equation} \\ x^3(x^2\text{ - 16) > 0} \\ x^3(x\text{ - 4)(x + 4) > 0} \end{gathered}[/tex]Step 3:
Identify the intervals
- 4 < x < 0 or x > 4
[tex]\text{Answer in interval notation: }(\text{ - 4 , 0 ) }\cup\text{ ( 4 , }\infty\text{ )}[/tex]Consider the fraction 1/2, if this fraction is divided by 3, will the quotient be more or less than the quotient in the first part?
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Determine whether each linear relationship is a direct variation. If so, state the constant of proportionality. (Example 4) 4. Pictures, x 3 4 5 6 51 Minutes, 185 235 285 335 Profit, y 24 32 40 48 Cost, y 60 100 140 180 7. 6. Game, X 2 5 20 5 15 10 Year, x Polnts, y 4 1 5 6 7 25 50 12.5 37.5 Helght, y
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table 4 . Direct Variation, constant of proportionality =8
Table 5: No. There is not a direct variation, for the growth is not at a constant factor.
1) To state whether there is a direct variation, we need to examine each row to stat how it increases or decreases
2) So for table 4
x y
3 24
4 32
5 40
6 48
For this, we can write a linear function y=8x
Yes. Direct Variation. Constant of proportionality 8
Table 5
x y
185 60
235 100
285 140
335 180
No. There is not a direct variation, for the growth is not at a constant factor.
Table 6
x y
5 12.5
10 25
15 37.5
20 50
We can set a linear function for that y=5/2 x
Yes. Direct Variation. Constant of proportionality 5/2 (2.5)
Table 7
x y
2 4
3 5
4 6
5 7
There is not a direct variation, for the growth is not at a constant factor.
Choose the median for the set of data. 99 95 93 92 97 95 97 97 93 97 a. 7b. 95.5 c. 96d. 97
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The median is the middle of a sorted list of number. So, we need to place the number in value order, that is,
[tex]92,93,93,95,95,97,97,97,97,99[/tex]then, the middle is between the 5th and 6th number:
then, we need to find the mean value of these numbers. So, the median is
[tex]\text{ median=}\frac{95+97}{2}=96[/tex]Therefore, the answer is option C.
Suppose that f is an even function whose domain is the set of all real numbers. Then which of the following can we claim to be true?
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If f is an even function, then f can't have an inverse, because even functions don't have inverses. Therefore the correct answer is A.
What is the zero of function f?f(x)=3 square root of x+3 -6
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Solution:
Given:
[tex]f(x)=3\sqrt{x+3}-6[/tex]The zeros of a function are the values of x when f(x) is equal to 0.
Hence,
[tex]\begin{gathered} 0=3\sqrt{x+3}-6 \\ \\ Collecting\text{ the like terms,} \\ 0+6=3\sqrt{x+3} \\ 6=3\sqrt{x+3} \\ \\ Divide\text{ both sides by 3;} \\ \frac{6}{3}=\sqrt{x+3} \\ 2=\sqrt{x+3} \\ \\ Taking\text{ the square of both sides;} \\ 2^2=x+3 \\ 4=x+3 \\ \\ Collecting\text{ the like terms;} \\ 4-3=x \\ 1=x \\ x=1 \end{gathered}[/tex]Therefore, x = 1
The correct answer is OPTION A.
if the measure of the angles of a triangle are represented by 2x, 3x - 15 , and 7x + 15, the triangle is
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Answer:
D An isosceles triangle
Explanation:
Given that the angles of a triangle are represented by;
[tex]\begin{gathered} 2x \\ 3x-15 \\ 7x+15 \end{gathered}[/tex]Recall that the sum of angles in a triangles is equal to 180 degrees.
Summing up the given angles we have;
[tex]\begin{gathered} (2x+3x-15+7x+15)^{\circ}=180^{\circ} \\ 2x+3x+7x-15+15=180 \\ 12x=180 \\ x=\frac{180}{12} \\ x=15 \end{gathered}[/tex]We have calculated the value of x.
We now need to calculate the value of each angle;
[tex]\begin{gathered} 2x=2(15)=30^{\circ} \\ 3x-15=3(15)-15=30^{\circ} \\ 7x+15=7(15)+15=120^{\circ} \end{gathered}[/tex]Therefore, the angles of the triangle are;
[tex]30^{\circ},30^{\circ},120^{\circ}[/tex]From the derived angles, we can notice that the triangle has two equal angles.
So it is an Isosceles triangle.
Simplify the expression below. Share all work/thinking/calculations to earn full credit. You may want to do the work on paper and then upload an image of your written work rather than try and type your work. \sqrt[4]{ \frac{162x^6}{16x^4} }
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On a hike, each hiker carries the items shown. Write an expression in simplest form that represents the weight (in pounds) carried by x hikers. sleeping bag: 3.4lb bag: 4.6lb water bottle: 2.2lb
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ok
Weight(x) = 3.4x + 4.6x + 2.2x or
W(x) = 3.4x + 4.6x + 2.2x
or
W(x) = 10.2x this is the expression
Hello, May I please get some assistance with this homework question? I posted an image below. Question A has already been answered, but do need help with the other questions. Q2 (part b)
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ANSWER
• (g o f)(x) = ,16x² + 24x + 9
,• B., the domain of g o f is all real numbers
EXPLANATION
The composition is,
[tex](g\circ f)(x)=g(f(x))[/tex]This means that, to find the composition, we have to replace x with f(x) in the function g(x),
[tex]g(f(x))=(f(x))^2[/tex]Now, replace f(x) with its expression,
[tex]g(f(x))=(4x+3)^2[/tex]We can expand this binomial squared to write it in standard form. The composition is,
[tex](g\circ f)(x)=16x^2+24x+9[/tex]As we can see, this is a polynomial function. Therefore, the domain is all real numbers.
The volume of a large tank is 350 ft. It is 65 ft wide and 4 ft high. What is the length of the tank?
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The volume of a rectangular prism can be calculated by the formula
[tex]V=l\cdot w\cdot h[/tex]in which l, w and h represent the length, width, and heght respectively.
clear the equation for l
[tex]l=\frac{V}{w\cdot h}[/tex]replace with the data given
[tex]undefined[/tex]3, -9, 27, -81,..... common difference/ratiod = 3r = 9r = -3 d = 12
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To find the common ratio we divide the terms by the previous one. In this case we have:
[tex]-\frac{9}{3}=-3[/tex][tex]\frac{27}{-9}=-3[/tex][tex]-\frac{81}{27}=-3[/tex]Therefore, the common ratio is r=-3.
Find the slope of the line that passes through each pair of points. (4,3) and (-6-5)
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Answer:
4/5
Explanation:
Given the points (4,3) and (-6,-5), the slope of the line that passes through the two points is:
[tex]\begin{gathered} Slope=\frac{Change\text{ in y}}{\text{Change in x}} \\ =\frac{-5-3}{-6-4} \\ =\frac{-8}{-10} \\ =\frac{4}{5} \end{gathered}[/tex]The slope of the line is 4/5.
Two Column Proof. If you could write it on a piece of paper and send a picture, that would be great.
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Let's suppose
∠1 =∠5 and ∠2 = ∠4
then
180° - ∠1 - ∠2 = ∠3
180° - ∠1 - ∠2 =
Harry took a loan from the bank.D represents Harry's remaining debit (In dollars) after t months.D = -200t + 9000
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D = His remaining debt in dollars
t = number of months
[tex]\begin{gathered} D=-200t+9000 \\ D=9000-200t \end{gathered}[/tex]The size of the loan will be $9000 . From the equation you can notice the product of 200 and t is always subtracted at t months from the amount he borrowed($9000)
Pl3ase help me with Geometry. right angles and perpendicular angles
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(Question 3)
Because of the definition of a perpendicular bisector, we know that angle B is a right angle (90°) an that
[tex]\bar{DB}=\bar{BE}[/tex]Note that AB is a segment that is shared by both triangles in the image. By using SAS (Side-Angle-Side), we can find that both the triangles are congruent (they are equal). Therefore,
[tex]\begin{gathered} 3x-9=x+21\rightarrow3x-x=21+9\rightarrow2x=30 \\ \rightarrow x=\frac{30}{2} \\ \rightarrow x=15 \end{gathered}[/tex]We know that
[tex]AE=x+21[/tex]We'll just have to plug in the value of x we calculated to find the lenght of AE
[tex]AE=15+21\rightarrow AE=36[/tex]Therefore, AE = 36
(Question 4)
Because of the definition of a perpendicular bisector, we know that XY splits TS right by the middle. So if TS = 10, RS would be worth half of that
Therefore, RS = 5
Joe’s parents are making sandwiches for the class picnic they have 7230 size is 48 two slices and 96 tomato sauce is Y
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We have to calculate the maximum common divisor of these 3 numbers in order to know what is the maximum ammount of sandwiches they can make.
We can list the factors of each number:
72: 1, 2, 3, 4, 6, 8, 12, 18, 24, 36, 72.
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 96.
To calculate this factors, we start by dividing by 2 and 3, and so on, and checking if the result is a whole number. If it is, the denominator is a factor.
The maximum common divisor is 24, so they can make 24 sandwichs, each one with 72/24=3 slices of turkey, 48/24=2 slices of cheese and 96/24=4 slices of tomatoes.
George's boxes
He has bought boxes at different prices.
3 boxes at $3.50 and 4 boxes at $3.00.
The cost of the first group of boxes is 3 boxes x 3.50 $/boxes = $10.50.
The cost of the second group is 4 boxes x 3.00 $/boxes = $12.
Then, if we add the cost, it is 10.50 + 12 = $22.50.
If we write it in the blanks we have:
3 boxes * 3.50 = 3 * 3.50
4 boxes * 3.00 = 4 * 3.00
(3 * 3.50) + (4 * 3.00) = 22.50
(underlined is what goes in the blanks)
The value of the surface area (in square centimeters) of the cone is equal to the value of the volume (in cubic centimeters) of the cone. The formula for the surface area S of the cone S=piR2+piRL where R id the radius and the base and L is slant higher find the hight of the cone
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hello
to find the height of the cone, we can simply use pythagorean theorem here since we know two sides of the triangle formed
using pythagorean theorem,
[tex]\begin{gathered} x^2=y^2+z^2 \\ 15^2=y^2+6^2 \\ 225=y^2+36 \\ \text{collect like terms } \\ y^2=225-36 \\ y^2=189 \\ \text{take square roots of both sides} \\ y=\sqrt[]{189} \\ y=13.747\approx13.75 \end{gathered}[/tex]from the calculations above, the height of the cone is 13.75cm
need to show 1,242 ÷ 23 = and 732 x 268 = show answers on graph
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1,242 ÷ 23 = 54
and
732 x 268 = 196, 176
