Answer: It depends on you if it seems easier for you, you should try both and see which one works better for you.
Answer:
Geometry nation helps when you need to go more in depth and need practice problems. While the textbook might give you good definitions it may seem more monotone.
In two or more complete sentences, prove how to find the third term of the expansion of (2x + y)4.
Answer:
The third term is [tex]24x^2y^2[/tex]
Step-by-step explanation:
The formula used to find the third term of the expansion (2x+y)^4 is called Binomial Theorem
The Binomial Theorem is:
[tex](x+a)^n = \sum_{k=0}^{n} {n \choose k}x^ka^{n-k}\\[/tex]
In the given question x = 2x
a = y
n = 4
We have to find the third term, so value of k will be 2 as k starts from 0
Putting the values in the Binomial Theorem
[tex]= {4 \choose 2}(2x)^2(y)^{4-2}\\= {4 \choose 2}4x^2(y)^{2}[/tex]
[tex]{n \choose k}==\frac{n!}{k!(n-k)!}[/tex]
Putting the values:
[tex]= {4 \choose 2}4x^2(y)^{2}\\=\frac{4!}{2!(4-2)!}4x^2(y)^{2}\\=\frac{4!}{2!2!}4x^2y^{2}\\=\frac{4*3*2*1}{2*2}4x^2y^{2}\\=\frac{24}{4}4x^2y^{2}\\=6*4x^2y^{2}\\=24x^2y^2[/tex]
So, the third term is [tex]24x^2y^2[/tex]
Choose the table that represents g(x) = 3⋅f(x) when f(x) = x − 1.
x g(x)
1 2
2 1
3 0
x g(x)
1 2
2 5
3 8
x g(x)
1 5
2 8
3 11
x g(x)
1 0
2 3
3 6
[tex]\bf f(x)=x-1\qquad \qquad g(x)=3\cdot f(x)\implies g(x)=\underline{3(x-1)} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} x&g(x)\\ \cline{1-2} 1&0\\2&3\\3&6 \end{array}\qquad \qquad (\stackrel{x_1}{1}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{6})[/tex]
[tex]\bf slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-0}{3-1}\implies \cfrac{6}{2}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=3(x-1)\implies y=\underline{3(x-1)}[/tex]
The table that represents g(x) = 3⋅f(x) when f(x) = x − 1 is that of Option D;
x g(x)
1 0
2 3
3 6
We are given;f(x) = x − 1
We want to find; g(x) = 3⋅f(x)
This means that; g(x) = 3(x - 1)
Looking at the options, the input values to be used are x = 1, 2 3.
Thus;When x = 1; g(x) = 3(1 - 1 )
g(x) = 0
When x = 2; g(x) = 3(2 - 1)
g(x) = 3
When x = 3; g(x) = 3(3 - 1)
g(x) = 6
Looking at the options, only the table in option D is correct.
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Which is the simplified form of the expression?
Answer:
Step-by-step explanation:
a
Answer:
4/x14y8 - Last Option
Find the value for b.
3x^2– X – 10 = 0
Entor the correct answer
[tex]b=-1[/tex]
.............................
Answer:
X=2, X= -5/3
Step-by-step explanation:
let's solve your equation step-by-step
3x^2-x-10=0
step 1: factor left side of equation.
(3x+5)(x-2)=0
step 2: set factors equal to 0.
3x+5=0 or x-2=0
x= -5/3 or x=2
A direct variation function contains the points (-8,-6) and (12,9) which equation represents the function
Answer:
y = 0.75x
Step-by-step explanation:
Given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k substitute either of the 2 points into the equation
Using (12, 9 ), then
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{9}{12}[/tex] = 0.75, so
y = 0.75x ← equation of variation
Given the coordinates of the vertices of a pre-image figure, describe how to find the coordinates of the image vertices if the figure is translated vertically.
Step-by-step answer:
Step 1:
find out the amount and direction of the vertical translation.
+3 means translating 3 units up, and -6 means translating 6 units down.
Step 2:
to each of the coordinate pairs, add the value of the translation to the y-coordinate (i.e. the second number of the pair).
For example, if the translation is +3, and if one of the vertices is (4,1), then the image of the vertex is (4,1+3) = (4,4).
Repeat for the rest of the vertices.
Step 3:
Check by graphing both image and preimage to see if the shapes are identical. If not, look for a mistake in the translation process.
To translate a figure vertically, add the translation value to the y-coordinates of each vertex. For a translation of 'k' units, the new vertices will be (x, y + k). This keeps the shape the same and only changes its position vertically.
To find the coordinates of the image vertices when a figure is translated vertically,
you need to follow these simple steps:
Identify the translation value: Determine the distance by which the figure is to be translated vertically. Let's say the translation value is 'k' units.Add the translation value to the y-coordinates: For each vertex of the pre-image figure, a translation involves modifying only the y-coordinate.If the original vertices of the pre-image are (x, y), then the new vertices (image) will be (x, y + k).Suppose you have a triangle with vertices A(2,3), B(5,4), and C(1,7). If the figure is translated vertically by 3 units up, the coordinates of the image vertices will be:This method ensures that the shape of the figure remains unchanged and it is only shifted up or down vertically.
Solve for y. Py + qy = -4y + 8
[tex]\bf Py+qy=-4y+8\implies Py+qy+4y=8\implies \stackrel{\textit{common factor}}{y(P+q+4)}=8 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=\cfrac{8}{P+q+4}~\hfill[/tex]
Answer:
y = 8 / (P + q + 4)
Step-by-step explanation:
Group ALL y terms on the left side: Py + qy + 4y = 8.
Factor y out of the left side: y(P + q + 4) = 8
Divide both sides by (P + q + 4): y = 8 / (P + q + 4)
6. A quadrilateral has three acute angles, each measuring 75°. Find the fourth angle
Answer:
Heya mate here's the answer
let the 4th angle be x
so 75°+ 75°+75° +x= 360°
=> x= 360 - 225
=> x = 135°
therefore the 4th angle= 135°
hope this helps
Step-by-step explanation:
A flute is on sale for 20% off. Including the discount and 8% tax, the sales price is $216.
Answer:
Before Tax: $240
After Tax: $259.20
Step-by-step explanation:
If we are trying to find the original price then here:
216/1.08 = 200
This took away the tax now we need to take away the discount:
200 x 1.2 = 240
Before Tax: $240
After Tax: $259.20
The original after tax price of the flute is $259.20.
Determining the original after tax price of the flute.
The first step is to remove tax from the sales price. In order to remove tax, divide the sales price by (1 + tax): $216 / 1.08 = $200
The second step is to remove the effect of discount. In order to do this multiply 200 by (1 + discount): 200 x 1.2 = $240.
The after tax original price = $240 x 1.08 = $259.20
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Sorry for all the questions
Jerod will need 19 pages to display all his 112 photos.
If you divide 112 by 12 you get 18.6667.
Since Jerod cannot break his paper into a half for the .6667 space, he would need to use 19 pages in total. All his 18 pages will have 6 photos each but his last 19th will have 1 photo left on it.
Hope this helps!!!
Mark as Brainliest Please!!!
What is the surface of a sphere with a radius of 9 units
Answer: 324π units²
Step-by-step explanation:
The formula for the surface area of a sphere is: A=4πr²
Now we just plug in 9 for r:
A = 4π(9)²
A = 4π*81
A = 324π
Answer:
1018 units^2
Step-by-step explanation:
The surface area of a sphere is given by A = 4pi(r)^2, where r is the radius.
Here, A = 4(3.14159)(9 units)^2 = 1018 units^2, to the nearest integer.
How do you find the same y intercept
Answer:
D
Step-by-step explanation:
The y-intercept is the number or constant at the end of the equation.
D sets both of their y-intercepts to -6, so it's correct.
=============================================
Explanation:
Plug x = 0 into f(x)
f(x) = 4x + 1
f(0) = 4(0) + 1
f(0) = 1
The y intercept of f(x) is 1
----------
Now plug x = 0 into g(x)
g(x) = 3^x - 2
g(0) = 3^0 - 2
g(0) = -1
The y intercept of g(x) is -1
----------
Note how the y intercepts are 2 units apart.
Each of the answer choices are in the form of f(x) + M and g(x) + N. The goal is to see which M and N values will be 2 units apart. In this case, that would be choice C where M = -1 and N = 1
We see that f(x) - 1 = f(0) - 1 = 1 - 1 = 0 and g(x) + 1 = g(0) + 1 = -1 + 1 = 0
Therefore, f(x) - 1 and g(x) + 1 have the same y intercept of 0.
if it takes one hour to paint 85ft then how long will it take to paint 410.2ft?
A family membership at a tennis club cost a flat fee of $150, plus $25 per person. If n stands for the number of people, then the membership cost is modeled by ?
Answer:
total cost = 150 + 25n
Step-by-step explanation:
total cost = flat fee + cost per person* number of people
total cost = 150 + 25n
To complete such a customer at your store needs to purchase vertical brackets to attach to the wall the customer wants to show them to be at least 48 inches in 60 in section 248 inspection cost 1295 to 16 section cost 6095 the brackish if you want switch from each end and no more than 24 inches apart what will the total cost of the brackets before tax
Answer:
67
Step-by-step explanation:
you have to divide
Answer
Step-by-step explanation:$149.50 is the answer
At a competition with 6 runners, medals are awarded for first, second, and
third places. Each of the 3 medals is different. How many ways are there to
award the medals?
Decide if this is a permutation or a combination, and find the number of ways
to award the medals.
Answer: 120 different ways. It is a permutation.
Step-by-step explanation:
Because 1st, 2nd, and 3rd are different positions and the order of placing matters, this is a permutation. (In Combinations, the order doesn’t matter, like in choosing people to be on a team without any positions). The calculation is 6x5x4 because there are 6 competitors who could get first, 5 who could get second (the 6th already has first place), and 4 who could get 3rd ( the other two already have 1st and 2nd place).
The number of ways to award the medals in 120 different ways.
What is permutation?When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.
Given
Because 1st, 2nd, and 3rd are different positions and the order of placing matters, this is a permutation. (In Combinations, the order doesn’t matter, like in choosing people to be on a team without any positions). The calculation is 6x5x4 because there are 6 competitors who could get first, 5 who could get second (the 6th already has a first place), and 4 who could get 3rd ( the other two already have 1st and 2nd place).
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Heather has $45.71 in her savings account. She bought six packs of markers to donate to her school. Write an expression for how much money she has in her bank account after the donation.
Answer: 45.71 - 6x = y
Step-by-step explanation:
45.71 - 6x = y
x= the amount 1 pack of markers cost
y= how much money Heather has after the donation
Answer: The required expression for amount left in her bank after the donation is given by [tex]Amount\ left=45.71-6x[/tex]
Step-by-step explanation:
Since we have given that
Amount of her saving = $45.71
Number of packs of markers to donate to her school = 6
Let the cost of each pack of markers be 'x'.
So, Amount left in her bank account after the donation is given by
[tex]Amount\ left=45.71-6x[/tex]
Hence, the required expression for amount left in her bank after the donation is given by
[tex]45.71-6x[/tex]
Perform the indicated operation.
Answer : The correct answer is, [tex]29\frac{62}{7}[/tex]
Step-by-step explanation :
The given expression is:
[tex]10\frac{3}{7}+19\frac{5}{9}[/tex]
Step 1 : Convert mixed fraction into fraction.
[tex]\frac{73}{7}+\frac{176}{9}[/tex]
Step 2 : Taking L.C.M
[tex]\frac{(9\times 73)+(176\times 7)}{63}[/tex]
[tex]\frac{(657)+(1232)}{63}[/tex]
[tex]\frac{1889}{63}[/tex]
Step 3 : Convert fraction into mixed fraction.
[tex]=29\frac{62}{7}[/tex]
Thus, the correct answer is, [tex]29\frac{62}{7}[/tex]
The largest possible circle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square feet, of the remaining board?
Answer:
=13.73 ft²
Step-by-step explanation:
The diameter of the largest possible circle that can be cut out of a square is equal to the length of the side of the square.
Therefore the diameter of the circle cut from a square of side 8ft =8ft
r=4ft
Area of the remaining board= Area of square- area of circle
=side²-πr²
=8²-π×4²
=64-16π
=13.73 ft²
What is the value of this limit?
Answer:
a
Step-by-step explanation:
athy's customer base is 2/3 residential and 1/3 business . if she has 350 residential customers, how many total customers does she have?
Answer: She has 525 costumers.
Step-by-step explanation:
We know that the costumer base is [tex]\frac{2}{3}[/tex] residential and [tex]\frac{1}{3}[/tex] business. This means that:
[tex]\frac{2}{3}=350[/tex] residential customers
Let be "x" the total costumers Athy has and "y" the number of business costumers.
Then "x" must be:
[tex]x=350+y[/tex]
Then, in order to find "y" , we need to multiply the number of residential costumers by [tex]\frac{1}{3}[/tex] and divide the product by [tex]\frac{2}{3}[/tex] :
[tex]y=\frac{(350)(\frac{1}{3})}{\frac{2}{3} }\\\\y=175[/tex]
Substituting we get that "x" is:
[tex]x=350+175=525[/tex] costumers
pls can someone help me with this, and please explain why?
Answer:
C
Step-by-step explanation:
recall the property [tex]a^{1/b}= \sqrt[b]{a}[/tex]
if we apply this to this case,
[tex]x^{1/4} = \sqrt[4]{x}[/tex]
- [tex]x^{1/4} = - \sqrt[4]{x}[/tex]
True or False
1/5^-2=25
That is true for sure!!!
The statement 1/5⁻² =25 is true.
Explanation:The statement 1/5⁻² = 25 is true.
To simplify the expression, we can rewrite 1/5⁻² as 5²/1. When we have a negative exponent in the denominator, it moves to the numerator and becomes positive.
Therefore, 1/5⁻² is equivalent to 5²/1.
Since 5² equals 25, we can conclude that 1/5⁻² is indeed equal to 25.
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Colette took a speed reading class, and afterward she was able to read a 368-page book in 46 minutes. At what rate did Colette read?
Answer:
8 pages/ minute
Step-by-step explanation:
To find the rate, we take the pages and divide by the minutes
368 pages / 46 minutes
8 pages/ minute
can somebody help me
Explain why 1 cm3 = 1000 mm3.
Answer:
The answer in the procedure
Step-by-step explanation:
Remember that
[tex]1\ cm=10\ mm[/tex]
Elevated to the cube both sides
[tex](1\ cm)^{3}=(10\ mm)^{3}[/tex]
[tex](1)^{3}\ cm^{3}=(10)^{3}\ mm^{3}[/tex]
[tex]1\ cm^{3}=1,000\ mm^{3}[/tex]
28lbs is what % of 58
Answer:
48.28
Step-by-step explanation:
2800:58 = 48.28
y = x^2+ 7x - 5 can be written in the form y = (x + a)^2+b
Find the value of a and the value of b
Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = (x - h)² + k (h, k) are the coordinates of the vertex
Given y = x² + 7x - 5
To express in vertex form use the method of completing the square
add/subtract ( half the coefficient of the x- term )²
y = x² + 2( [tex]\frac{7}{2}[/tex] )x +[tex]\frac{49}{4}[/tex] - [tex]\frac{49}{4}[/tex] - 5
y = (x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{49}{4}[/tex] - [tex]\frac{20}{4}[/tex]
y = (x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{69}{4}[/tex]
Hence
a = [tex]\frac{7}{2}[/tex] and b = - [tex]\frac{69}{4}[/tex]
(-5+1)(((3+6)*2-2)(5)-1) evaluate.
Answer:
-316
Step-by-step explanation:
Each operation shown in bold is done on the next line.
(-5+1)(((3+6)*2-2)(5)-1) =
= (-4)((9*2-2)(5)-1)
= (-4)((18-2)(5)-1)
= (-4)(16(5)-1)
= (-4)(80-1)
= (-4)(79)
= -316
Use the given information to determine the exact trigonometric value.
Answer: [tex]\bold{a.\quad -\dfrac{2\sqrt{6}}{5}}[/tex]
Step-by-step explanation:
[tex]sin\theta=\dfrac{y}{h}\implies y=-1, h=5\\\\\\\text{Use Pythagorean Theorem to find x:}\\x^2 + y^2 = h^2\\x^2 + (-1)^2=5^2\\x^2+1=25\\x^2=24\\x=\sqrt{24}\\x=2\sqrt{6}[/tex]
[tex]\text{Since }\theta\text{ is between }\pi\text{ and }\dfrac{3\pi}{2} \text{ (Quadrant III)},\text{ then x and y are negative.}\\\implies x=-2\sqrt{6}\\\\\\cos\theta = \dfrac{x}{h}\quad =\boxed{-\dfrac{2\sqrt{6}}{5}}[/tex]
What is the quotient of 3,968 ÷ 32?
Answer:
124
Step-by-step explanation:
Answer:
124
Step-by-step explanation:
32 goes into 39 one time, 39-32= 7
bring down the 6
32 goes into 76 two times, 76 - 64= 12
bring down the 8
32 goes into 128 four times, 128 - 128 = 0
So 3968/32 = 124