Answer:
1) Expression is
[tex](n+1)+(n^3+3n^2+2n)=n^3+3n^2+3n+1[/tex]
2) The standard form of the expression is
[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]
3) The expression is
[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]
Where [tex](n+1)^3[/tex] is the cube of the middle integer
Step-by-step explanation:
1) Given three consecutive integers are n. n+1, and n+2
Now multiplying the three consecutive integers
[tex](n)(n+1)(n+2)=(n^2+n)(n+2)[/tex]
[tex]=n^3+2n^2+n^2+2n[/tex]
[tex]=n^3+3n^2+2n[/tex]
Therefore [tex](n)(n+1)(n+2)=n^3+3n^2+2n[/tex]
Now adding the middle integer to the result of the multiplication.
ie, adding (n+1) to the result of the multiplication [tex]n^3+3n^2+2n[/tex]
[tex](n+1)+(n^3+3n^2+2n)=n+1+n^3+3n^2+2n[/tex]
[tex]=3n+1+n^3+3n^2[/tex]
Therefore [tex](n+1)+(n^3+3n^2+2n)=n^3+3n^2+3n+1[/tex]
2) Expression is [tex]n^3+3n^2+3n+1[/tex]
Now we simplify the above expression
[tex]n^3+3n^2+3n+1=n^3+3n^2(1)+3(n)(1)^2+1^3[/tex]
[tex]=(n+1)^3[/tex] (by using [tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex] , Here a = n and b=1)
[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]
3) The expression is
[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]
Where [tex](n+1)^3[/tex] is the cube of the middle integer.
ie, expression is equivalent to the cube of the middle integer
Miquel created the table below to show how he uses the money he earns at work
how much will he save if he earns $120.00
$30.00
$45.00
$90.00
$75.00
Complete Question with table is attached
Answer:
Miguel will save money of $90 if he earns $120.00
Step-by-step explanation:
The figure attached clearly shows the ratio of his earnings and savings. We have to find what would be the savings amount if he earn $120.00. So, first we have to calculate the percentage of ratio of his earnings and savings. As per the data given in the figure,
If he earns $10.00, he saves $7.50, calculate %amount he saves as below,
[tex]\frac{\$ 7.50}{\$ 10.00} \times 100=0.075 \times 100=75 \%[/tex]
Likewise, calculate for all given data. If he earns $50.00 then he saves $37.50
[tex]\frac{\$ 37.50}{\$ 50.00} \times 100=0.75 \times 100=75 \%[/tex]
If he earns $150.00 and save $112.50,
[tex]\frac{\$ 112.50}{\$ 150.00} \times 100=0.75 \times 100=75 \%[/tex]
So, from all above, it clearly tells that Miguel saves 75% of amount from his earnings. Now, given earnings as $120.00. By finding 75% of $120.00, we can find his savings in that amount. So,
[tex]\frac{75}{100} \times \$ 120=0.75 \times 120=\$ 90[/tex]
Answer:
D. $90.00
Step-by-step explanation:
To describe a specific arithmetic sequence, Elijah wrote the recursive formula:
{ f(0)=30
{f(n+1)= f(n)+7
Write a linear equation that models this sequence using the sketchpad below.
You can earn up to 3 points, 1 for each correct value/variable in the equation.
Format: Y=_________
Answer:
Y(n) = 7n + 23
Step-by-step explanation:
Given:
f(0) = 30
f(n+1) = f(n) + 7
For n=0 : f(1) = f(0) + 7
For n=1 : f(2) = f(1) + 7
For n=2 : f(3) = f(2) + 7 and so on.
Hence the sequence is an arithmetic progression with common difference 7 and first term 30.
We have to find a general equation representing the terms of the sequence.
General term of an arithmetic progression is:
T(n) = a + (n-1)d
Here a = 30 and d = 7
Y(n) = 30 + 7(n-1) = 7n + 23
The length of a rectangle is 4 units more than its width. The area of the rectangle is 25 more than 4 times the width.
What is the width of the rectangle?
A 9
B. -5
C. 3
D.-5
Answer:
B or D ( answer = 5 => Two options is one! One of the options should be 5)
Note: The width of a rectangle will never be negative.
Answer:
its d. 5
Step-by-step explanation:
PLEASE HELP!! WILL MARK BRAINLIEST AND THANK YOU!!!
X= ____________
Y= ____________
Answer:
x = 11, y = 3
Step-by-step explanation:
9x + 25 and 13x - 19 are corresponding angles and congruent, thus
13x - 19 = 9x + 25 ( subtract 9x from both sides )
4x - 19 = 25 ( add 19 to both sides )
4x = 44 ( divide both sides by 4 )
x = 11
Thus
13x - 19 = (13 × 11) - 19 = 143 - 19 = 124°
13x- 19 and 17y + 5 form a straight angle and are supplementary, thus
13x - 19 + 17y + 5 = 180, that is
124 + 17y + 5 = 180
129 + 17y = 180 ( subtract 129 from both sides )
17y = 51 ( divide both sides by 17 )
y = 3
BRAINLIEST!!
A bin contains seven red chips, nine green chips, three yellow chips, and six blue chips. Find each probability.
selecting two blue chips without replacement
Answer:
[tex]\frac{1}{20}[/tex]
Step-by-step explanation:
First, we need to look at the # of chips. There are a total of 25, 6 of which are blue.
This means that the chance of getting the first blue chip would be [tex]\frac{6}{25}[/tex]
As there is no replacement, the total number of chips is 24 and there are only 5 blue left. This gives us the chance of [tex]\frac{5}{24}[/tex]
Now all we need to do is mulitply these two and then simplify
[tex]\frac{6}{25} *\frac{5}{24} =\frac{30}{600} =\frac{1}{20}[/tex]
Answer:
1/20
Step-by-step explanatio
pick without replacement must mean pick it two times without put back the first chip
6/25 x 5/24 = 1/20
Line segment AB with endpoints A(4, 16) and B(20,4) lies in the coordinate plane. The segment will be dilated with a scale factor of 3/4 and a center at the origin to create A'B'. What will be the length of A'B'?
Answer:
The length of A'B' is 15 units
Step-by-step explanation:
As line segment AB has end points
A(4, 16)B(20, 4)The distance formula to calculate the distance between two points is given by:
[tex]{\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}}[/tex]
[tex]{\displaystyle d={\sqrt {(20-4)^{2}+(4-16)^{2}}}}[/tex]
[tex]d=\sqrt{16^2+(-12)^2}[/tex]
[tex]d=\sqrt{256+144}[/tex]
[tex]d=\sqrt{400}[/tex]
[tex]d=20[/tex]
[tex]d=20[/tex] is also the length of the line segment AB.
As segment will be dilated with a scale factor of 3/4 and a center at the origin to create A'B'.
So,
The length of A'B' can be obtained by multiplying the length of AB by 3/4
Therefore,
The length of A'B' = 3/4 × 20 = 15
So, the length of A'B' is 15 units.
Keywords: dilation, distance formula, length, line segment
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Use number line to show numbers in the solution set of the inequality 2s+ 36 greater than 50.
s>7
So, all values greater than 7 are included in the number line.
Step-by-step explanation:
We need to use number line to show numbers in the solution set of the inequality 2s+ 36 greater than 50
Solving and finding value of s:
2s+36>50
Adding -36 on both sides
2s+36-36>50-36
2s>14
Divide both sides by 2
s>7
So, all values greater than 7 are included in the number line.
The number line is shown in figure attached below
Keywords: Solving inequalities
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Answer:
A
Step-by-step explanation:
Took the test in edge
What is the acceleration of this object? The object's mass is 2 kg. 11 m/s2 4 m/s2 0 m/s2 7 m/s2
Answer:
The acceleration of the object is 4 [tex]m/s^2[/tex]
Step-by-step explanation:
Given:
The mass of the object is = 2 kg
To Find:
Acceleration of the object = ?
Solution:
From the diagram below we know that
The resultant force is 8N along the east Direction
we know the acceleration is the"Rate of change of Velocity"
And Expressed as
F = ma
Where
F is the Force
m is the mass
Now substituting the known values we get
[tex]8 = 2 \times a[/tex]
[tex]a =\frac{8}{2}[/tex]
a=4 [tex]m/s^2[/tex]
Answer:
b the object is 4 m/s
Step-by-step explanation:
According to the graph, what is the value of the constant in the equation
below?
10
3,9.6)
Height = Constant.Width
12, 6.4)
Height
(1,3.2)
(0.5,1.6)
Width
The question is missing the graph. So, it is attached below.
Answer:
(D) 3.2
Step-by-step explanation:
Given:
A graph of height versus width.
The equation given is:
Height = constant × Width
Rewriting in terms of 'constant'. This gives,
[tex]\textrm{Constant}=\frac{Height}{Width}[/tex]------------- (1)
The width is plotted on the X-axis and the corresponding height is plotted on the Y-axis.
The four points plotted on the line are:
[tex](x, y) = (0.5, 1.6), (1, 3.2), (2, 6.4)\ and\ (3, 9.6)[/tex].
Now, any point will satisfy equation (1).
Consider the point (0.5, 1.6). So, height = 1.6 and width = 0.5. Therefore,
[tex]\textrm{Constant}=\frac{Height}{Width}\\\\\textrm{Constant}=\frac{1.6}{0.5}=3.2[/tex]
Also, we observe that for all the remaining points,
[tex]\dfrac{3.2}{1}=\dfrac{6.4}{2}=\dfrac{9.6}{3}=3.2[/tex].
Hence, the value of the constant is 3.2.
Option (D) is correct.
In right triangle JKL, ZL is a right angle, mZJ = 62°, and JK = 17.
sin 62° 0.88
cos 62° 0.47
tan 62° 1.88
© 2019 StrongMind. Created using GeoGebra.
What is the measurement of JL?
If necessary, round your answer to one decimal place, like this: 42.5
Please the attachment for question.
Answer:
Measurement of JL=8
Step-by-step explanation:
Given:-
[tex]\triangle JKL\ is\ right\ angle\ triangle[/tex]
[tex]m\angle J=62\ degree[/tex]
JK=17
[tex]sin\ 62\ degree= 0.88[/tex]
[tex]cos\ 62\ degree= 0.47[/tex]
[tex]tan\ 62\ degree= 1.88[/tex]
To find measurement of JL=?
Now,
[tex]cos\theta=\frac{adjacent\ side}{hypotenuse}[/tex]
[tex]cos\ 62\ degree=\frac{JL}{17}[/tex]
[tex]0.47=\frac{JL}{17}[/tex]
[tex]JL=0.47\times 17[/tex]
[tex]JL=7.99[/tex]
[tex]JL=8[/tex]
Therefore measurement of JL=8
help with question 7 part i & ii
Answer:
(i) [tex]k\in (-\infty,-16)\cup (0,\infty)[/tex]
(ii) [tex]p\in (9,\infty)[/tex]
Step-by-step explanation:
(i) Given equation
[tex]2x^2+4x+2=k(x+3)[/tex]
Rewrite this equation as quadratic equation in the standard form:
[tex]2x^2+4x+2=kx+3k\\ \\2x^2+4x+2-kx-3k=0\\ \\2x^2+(4-k)x+(2-3k)=0[/tex]
If the equation has two distinct real roots, then its discriminant is greater than 0. Find the discriminant:
[tex]D=(4-k)^2-4\cdot 2\cdot (2-3k)=16-8k+k^2-16+24k=k^2+16k[/tex]
Solve the inequality [tex]D>0:[/tex]
[tex]k^2+16k>0\\ \\k(k+16)>0\Rightarrow k\in (-\infty,-16)\cup (0,\infty)[/tex]
(ii) The quadratic expression is always greater than 0 when:
[tex]p>0\\ \\D<0[/tex]
Find the discriminant:
[tex]D=6^2-4\cdot p\cdot 1=36-4p[/tex]
Solve the inequality [tex]D<0:[/tex]
[tex]36-4p<0\\ \\-4p<-36\\ \\4p>36\\ \\p>9[/tex]
Assuming that [tex]p>0[/tex] and [tex]p>9,[/tex] you get
[tex]p>9\Rightarrow p\in (9,\infty)[/tex]
If m1 + m2 = 137°, what is m3?
Answer:
m3=43°
Step-by-step explanation:
The total has to add up to 180° so 180-137 = 43°
a bag contains 5 red, 6 white, and 5 blur marbles. a marble is drawn from the bag and replaced 32 times. the table shows the results. for which color is the experimental probability of drawing the color the same as the theoretical probability?
red:12 white: 12 blue:8
Answer:
White.
Step-by-step explanation:
Theoretical probabilities are:
Red: 5 / ( 5 + 6 + 5) = 5/16
White: 6/16 = 3/8.
Blue: 5/16.
The answer is white because it is drawn 12 times which equals its theoretical probability: 12/32 = 3/8.
The probability of drawing the color the same as the theoretical probability is 3/8.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
A bag contains 5 red, 6 white, and 5 blue marbles.
Theoretical probabilities for the colors are:
Red:
= 5 / ( 5 + 6 + 5)
= 5/16
White:
= 6/16
= 3/8.
Blue: 5/16.
So, the probability of drawing the color the same as the theoretical probability is white because the theoretical probability is 3/8.
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Find the value of x when y = 6 and z = -1/2, If
Answer:
[tex]x=-\frac{261}{46}[/tex]
Step-by-step explanation:
we have the expression
[tex]\frac{3x+2y-5z}{y-4z}=\frac{x}{3y}[/tex]
we have
[tex]y=6,z=-\frac{1}{2}[/tex]
To find the value of x, substitute the given values of y and z in the expression
[tex]\frac{3x+2(6)-5(-\frac{1}{2})}{6-4(-\frac{1}{2})}=\frac{x}{3(6)}[/tex]
solve for x
[tex]\frac{3x+12+\frac{5}{2}}{6+2}=\frac{x}{18}[/tex]
[tex]\frac{3x+12+\frac{5}{2}}{8}=\frac{x}{18}[/tex]
Multiplying in cross
[tex](3x+12+\frac{5}{2})18=8x[/tex]
[tex]54x+216+45=8x[/tex]
[tex]54x-8x=-216-45[/tex]
[tex]46x=-261[/tex]
[tex]x=-\frac{261}{46}[/tex]
The first three steps of completing the square to solve the quadratic equation x² + 4x - 6 = 0, are
shown below.
Step 1: x2 + 4x = 6
Step 2: x2 + 4x + 4 = 6 + 4
Step 3: (x + 2)2 = 10
What are the next 3 steps?
Answer:
The next 3 steps are
Step 4: [tex](x+2)=\pm \sqrt{10}[/tex]
Step 5: [tex]x=-2\pm \sqrt{10}[/tex]
Step 6: [tex]x=-2+\sqrt{10}\ or\x=-2-\sqrt{10}[/tex]
Step-by-step explanation:
Given:
Quadratic Equation is
x² + 4x - 6 = 0
To Find:
x = ?
Solution:
Step 1: x2 + 4x = 6
Step 2: x2 + 4x + 4 = 6 + 4
Step 3: (x + 2)2 = 10
Step 4: [tex](x+2)=\pm \sqrt{10}[/tex]
Step 5: [tex]x=-2\pm \sqrt{10}[/tex]
Step 6: [tex]x=-2+\sqrt{10}\ or\x=-2-\sqrt{10}[/tex]
Maria finds a local gym that advertises 101 training sessions for $626. Find the cost of 124 training sessions.
Answer:
$768
Step-by-step explanation:
Let x bet the cost of 124 training session.
Given:
Maria finds a local gym that advertises 101 training sessions for $626.
Find the cost of 124 training sessions.
Solution:
cost for each training sessions [tex]=\frac{626}{101}[/tex]
cost for each training session = $6.19
So, we get cost of 124 training sessions by multiplication of cost of each training sessions and number of training sessions.
[tex]x=cost\ of\ each\ training\ session\times number\ of\ training\ session[/tex]
[tex]x=6.19\times 124[/tex]
[tex]x=767.56[/tex]
round 767.56≅768
[tex]x=768[/tex]
Therefore, the cost of 124 training sessions is $768
Lashonda drove 225 miles using 10 gallons of gas. At this rate, how many gallons of gas would she to drive 441 miles?
Answer:
19.6 gallons.
Step-by-step explanation:
She drives 225/ 10 = 22.5 miles per gallon of gas.
So driving 441 miles she will use 441/22.5
= 19.6 gallons.
9263 divided by 88 I’m really confused on how to do this
Answer: 105.26
Step-by-step explanation: 9263/88=105.26
Do you have or own a calculator?
What is 68−−√ in simplest radical form?
I think you mean [tex]\sqrt{68}[/tex] so I will just simplify that.
[tex]\sqrt{68}=\sqrt{4}*\sqrt{17}=2\sqrt{17}[/tex]
answer: [tex]2\sqrt{17}[/tex]
the answer is 2√17
hope this helps :)))
A kilogram of seawater contains 1/40 kg of salt. How much salt is there in two buckets of seawater, which contain 500 liters of seawater each, if 1 liter of seawater weighs 1 12/125 kg?
Two buckets of seawater contain [tex]13\frac{28}{40}[/tex] kg of salt.
Step-by-step explanation:
Amount of salt in 1 kg water = [tex]\frac{1}{40}\ kg[/tex]
It is given that;
1 liter = [tex]1\frac{12}{125} = \frac{137}{125}\ kg[/tex]
500 liters = [tex]500*\frac{137}{125} = \frac{68500}{125}[/tex]
500 liters = 548 kilogram
As,
1 kg of seawater = [tex]\frac{1}{40}\ kg[/tex] of salt
548 kilograms = [tex]\frac{1}{40}*548[/tex]
548 kilograms = [tex]13\frac{28}{40}[/tex] kilograms of salt
Two buckets of seawater contain [tex]13\frac{28}{40}[/tex] kg of salt.
Keywords: unit rate, multiplication
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A wooden block measures 2 inches by 2 inches by 3 inches. A wedge is cut off from each corner of the block by slicing at points that are 1 inch from each corner. How many edges does the resulting solid have?
Final answer:
The resulting solid will have four edges.
Explanation:
To find the number of edges in the resulting solid, let's first determine the dimensions of the solid after the wedges are cut off.
The original wooden block measures 2 inches by 2 inches by 3 inches. After cutting off the wedges, each side will be reduced by 2 inches (1 inch from each corner), resulting in a solid with dimensions of 2 - 2(1) = 0 inches by 2 - 2(1) = 0 inches by 3 - 2(1) = 1 inch.
A solid with dimensions of 0 inches by 0 inches by 1 inch is essentially a rectangular prism with one dimension equal to zero. Such a solid has six faces, eight vertices, and four edges.
Therefore, the resulting solid will have four edges.
Help me with this math problem
Answer:
Weight of each large box [tex]x=15.75kg[/tex]
Weight of each small box [tex]y=13.75kg[/tex]
Step-by-step explanation:
Given:- Two equations are given,
Equation 1 :- [tex]7x+9y=234[/tex]
Equation 2:- [tex]5x+3y=120[/tex]
let,
x=weight of large box in Kilogram.
y=weight of small box in Kilogram.
Now,
multiply Equation 1 by 2 and Equation 2 by 6,
So we get 2 new equations,
Equation 3:- [tex]14x+18y=468[/tex]
Equation 4:- [tex]30x+18y=720[/tex]
Now after subtracting Equation 3 from Equation 4 we will get a new equation,
i.e. Equation 5:- [tex]16x=252[/tex]
therefore [tex]x=15.75[/tex]
now, put the value of x in Equation 1, so we will get
[tex](7x15.75)+9y=234[/tex]
[tex]110.75+9y=234[/tex]
[tex]9y=234-110.75[/tex]
[tex]9y=123.75[/tex]
[tex]y=123.75/9[/tex]
[tex]y=13.75[/tex]
So, weight of each large box i.e. [tex]x=15.75 kilogram[/tex]
and weight of each small box i.e. [tex]y=13.75 kilogram[/tex]
12 Points ASAP Will mark BRAINLEIST
Given the formula for an arithmetic sequence f(5) = f(4) + 3 written using a recursive formula, write the sequence using an arithmetic explicit formula.
f(5) = f(1) + 3
f(5) = f(1) + 4
f(5) = f(1) + 12
f(5) = f(1) + 15
Answer:
[tex]f(5)=f(1)+12[/tex]
Step-by-step explanation:
If [tex]f(5) = f(4) + 3,[/tex] then
[tex]f(n)=f(n-1)+3[/tex]
So,
[tex]f(2)=f(2-1)+3=f(1)+3\\ \\f(3)=f(3-1)+3=f(2)+3=f(1)+3+3=f(1)+6\\ \\f(4)=f(4-1)+3=f(3)+3=f(1)+6+3=f(1)+9\\ \\f(5)=f(5-1)+3=f(4)+3=f(1)+9+3=f(1)+12[/tex]
Answer:f(5) = f(1) + 12
Step-by-step explanation:
I WILL GIVE BRAINLIEST!!!! PLZ HELP!!!! ASAP!!!!
m - 7 < 6
A. m < -1
B. m ? 1
C. m < 13
D. < - 13
Find the measure of 3. Help Plz
Answer:
∠3 = 135°
Step-by-step explanation:
∠3 = ∠1 = 135° ( corresponding angles are congruent )
1. 4/5 - (-3/10)=
2. 5.5 - 8.1=
3. -5 - 5/3=
4. -8 3/8 - 10 1/6=
5. -4.62 - 3.51=
Answer:
11/10
Step-by-step explanation:
4/5-(-3/10)=4/5+3/10=8/10+3/10=11/10
Which table shows a proportional relationship between x and y?
x 1 3 4 7
y 2 5 8 14
x 7 14 28 35
y 1 2 4 5
x 1 2 3 4
y 4 10 12 16
x 2.5 3 5 6
y 5 6 10 15
Which table shows a proportional relationship between x and y?
x 1 3 4 7
y 2 5 8 14
x 7 14 28 35
y 1 2 4 5
x 1 2 3 4
y 4 10 12 16
x 2.5 3 5 6
y 5 6 10 15
Which table shows a proportional relationship between x and y?
x 1 3 4 7
y 2 5 8 14
x 7 14 28 35
y 1 2 4 5
x 1 2 3 4
y 4 10 12 16
x 2.5 3 5 6
y 5 6 10 15
Which table shows a proportional relationship between x and y?
x 1 3 4 7
y 2 5 8 14
x 7 14 28 35
y 1 2 4 5
x 1 2 3 4
y 4 10 12 16
x 2.5 3 5 6
y 5 6 10 15
Which table shows a proportional relationship between x and y?
x 1 3 4 7
y 2 5 8 14
x 7 14 28 35
y 1 2 4 5
x 1 2 3 4
y 4 10 12 16
x 2.5 3 5 6
y 5 6 10 15
Which table shows a proportional relationship between x and y?
PLS HELP!!!!
Answer:
Second table
Step-by-step explanation:
Proportional relationships between x and y satisfied the following equation y = k*x, where k is some constant. Rearranging we get: k = y/x. So, if we take every pair y-x and divided them, we have to find the same k.
- Division y/x for the first table:
2/1 = 2
5/3
8/4 = 2
14/7 = 2 It is not a proportional relationship
- Division y/x for the second table:
1/7
2/14 = 1/7
4/28 = 1/7
5/35 = 1/7 It is a proportional relationship
- Division y/x for the third table:
4/1 = 4
10/2 = 5
12/3 = 4
16/4 = 4 It is not a proportional relationship
- Division y/x for the fourth table:
5/2.5 = 2
6/3 = 2
10/5 = 2
15/6 = 5/2 It is not a proportional relationship
Which equation represents this number sentence to more than 1/3 of a number is eight?
Answer:
The equation [tex]2+\frac{1}{3}n=8[/tex] represents the corresponding statement ' two more than 1/3 of a number is eight'.
Step-by-step explanation:
As the sentence statement is
"Two more than 1/3 of number is eight".
Lets decode this sentence and write the corresponding mathematical expression.
Let's suppose n is the number.[tex]\frac{1}{3}[/tex] of n will be expressed as [tex]\frac{1}{3}n[/tex]Two more then 1/3 of n will be expressed as [tex]2+\frac{1}{3}n[/tex]As two more than 1/3 of a number is eight. Therefore, this statement can be easily expressed as [tex]2+\frac{1}{3}n=8[/tex]Hence, the equation [tex]2+\frac{1}{3}n=8[/tex] represents the corresponding statement ' two more than 1/3 of a number is eight'.
Keywords: equation, algebraic expression
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How many squares will be in the fifth figure
Answer: 30
Step-by-step explanation:
see photo for work
Which of the following is the best use for the sign chart when graphing
rational functions?
The best use of a sign chart when graphing rational functions involves identifying critical points, determining function values within each interval, and using this information to sketch the graph. The sign chart is a valuable tool for analyzing the behavior of a rational function on the x-axis.
The sign chart is a useful tool when graphing rational functions because it helps identify the intervals where the function is positive, negative, or undefined. This information is crucial for accurately sketching the graph of a rational function. Here is how to use a sign chart:
Identify the critical points of the function by setting the numerator and denominator equal to zero and solving for the variables.
Choose a value from each interval determined by the critical points and evaluate whether the function is positive or negative at that value.
Record the signs in a table or chart to visualize the pattern.
Use the sign chart to determine the intervals on the x-axis where the function is positive, negative, or undefined.
Plot any vertical asymptotes, holes, and x-intercepts on the graph.
Sketch the graph by using the information from the sign chart and locating the appropriate points.
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