I need some explanation on how to do piece wise functions? Where do I even start with this equation, can you explain this step by step? Including breaking down the graphing of absolute functions?
Answers
A piecewise function is basically a function that behaves differently at different domain intervals.
The given piecewise function is
[tex]\begin{cases}2x\quad \quad \quad \quad \quad \quad x\le3 \\ \frac{1}{3}x^2-2x+9\quad x>3\end{cases}[/tex]As you can see, the function has a different expression for the interval x is less than or equal to 3 and a different expression for the interval x is greater than 3.
The easiest way to determine which graph corresponds to the given piecewise function is to evaluate the piecewise function at different values of x and graph it.
Evaluate the piecewise function for the interval x is less than or equal to 3.
[tex]\begin{gathered} 2x \\ x=1\rightarrow2(1)=2 \\ x=2\rightarrow2(2)=4 \\ x=3\rightarrow2(3)=6 \end{gathered}[/tex]Evaluate the piecewise function for the interval x is greater than 3.
[tex]\begin{gathered} \frac{1}{3}x^2-2x+9 \\ x=4\rightarrow\frac{1}{3}(4)^2-2(4)+9=6.33 \\ x=6\rightarrow\frac{1}{3}(6)^2-2(6)+9=9 \\ x=8\rightarrow\frac{1}{3}(8)^2-2(8)+9=14.33 \end{gathered}[/tex]Now, let us graph these points
As you can see from the graph, it matches with the graph of the 2nd option.
Therefore, the correct graph of the given piecewise function is the 2nd graph.
Related Questions
It takes Allie 456
minutes to drive to the store. From the store, it takes her 734
minutes to drive to the car wash. How many minutes does it take Allie to drive to the store and then to the car wash?
Answers
It takes 1190 minutes for Allie to drive to the store and then to the car wash.
According to the question,
We have the following information:
Time taken by Allie to drive to the store = 456 minutes
Time taken by Allie to drive to the car wash from the store = 734 minutes
Now, we have to find the total time in minutes. So, we will add the total time taken by Allie to drive to the store and then to the car wash.
(Note that the time asked in the question is in minutes. So, we do not need to change the units of given time.)
Now,
The total time taken by Allie to drive to the store and then to the car wash = Time taken by Allie to drive to the store + Time taken by Allie to drive to the car wash from the store
The total time taken by Allie to drive to the store and then to the car wash = (456 + 734) minutes
The total time taken by Allie to drive to the store and then to the car wash = 1190 minutes
Hence, the total time taken by Allie to drive to the store and then to the car wash is 1190 minutes.
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Berti is the Shape Factory's top employee. She has received awards every month for having the top sales
figures so far for the year. If she stays on top, she will receive a $5000 bonus for excellence. She currently has
sold 16, 250 shapes and continues to sell 340 per month.
EMPL
Since there are eight months left in the sales year, Sarita is working hard to catch up. While she has only sold
8,830 shapes, she is working overtime and on weekends so that she can sell 1, 082 per month. Will Sarita
catch up with Berti before the end of the sales year? If so, when?
Answers
No, Sarita will not be able to catch up with Berti before the end of the sales year.
Berti currently has sold 16, 250 shapes
She continues to sell 340 per month.
In eight months she will be able to sell
16250 + 8 x 340
= 16250 + 2720
= 18970
Sharita has only sold 8,830 shapes
Working overtime and on weekends so that she can sell 1, 082 per month
In eight months she will be able to sell
8830 + 8 x 1082
8830 + 8656
17486
No, Sarita will not be able to catch up with Berti before the end of the sales year.
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If z = 1 istartroot 3 endroot, what is z5? 16 16istartroot 3 endroot â€"16 16istartroot 3 endroot 16 â€" 16istartroot 3 endroot â€"16 â€" 16istartroot 3 endroot
Answers
Complex number z has a power of 5 represented by (-16√3 + 16) + 4(-√3 + 3)i
Given that,
z = 1 + StartRoot 3 EndRooti, what is z5? 16 + 16StartRoot 3 EndRoot i –16 + 16StartRoot 3 EndRoot i –16 – 16StartRoot 3 EndRoot i 16 – 16StartRoot 3 EndRoot i
What is a complex number?
It is characterized as a number that can be expressed as x+iy, where x is a real number or the real portion of the complex number, y is the imaginary portion of the complex number, and I is the iota, which is just the square root of -1.
We have:
z = 1 + √3i
We have to find: z⁵
z⁵ = (1 + √3i)(1 + √3i)(1 + √3i)(1 + √3i)(1 + √3i)
z⁵ = (-2 + 2√3)(1 + √3i)(1 + √3i)(1 + √3i)
z⁵ = (-16√3 + 16) + 4(-√3 + 3)i
Therefore, the complex number z's power of 5 is -16√3 + 16) + 4(-√3 + 3)i
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HELP ASAP!!! (100 POINTS!!!) GIVING BRAINIEST
PLEASE HELP SOLVE ALL OF THEM!!!
Use the idea of partial quotients to solve each of the
division problems below. You can use the powers of 10 or grouping,
whichever makes the problem go faster.
1. 1,085/7
2. 7,104/32
3. 2,244/51
4. 1,584/12
5. 1,467/9
6. 2,830/28
7. 9,090/45
8. 7,000/62
9.1,150/15
HELP ASAP!!!
PLEASE HELP SOLVE ALL OF THEM!!!
Answers
Answer:
I gotchu
Step-by-step explanation:
1= 155
2= 222
3= 44
4= 132
5= 163
Determine the point (x, y) on the unit circle associated with the following real numbers. Write the exact answer as an ordered pair. Do not round.S = 30
Answers
Remember that
In a unit circle, the radius of the circle is 1
see the figure below to better understand the problem
we have that
[tex]\sin (30^o)=\frac{y}{1}[/tex]and we know that
[tex]\sin (30^o)=\frac{1}{2}[/tex]so
[tex]\begin{gathered} \frac{y}{1}=\frac{1}{2} \\ y=\frac{1}{2} \end{gathered}[/tex][tex]\cos (30^o)=\frac{x}{1}[/tex]and we know that
[tex]\cos (30^o)=\frac{\sqrt[]{3}}{2}[/tex]so
[tex]x=\frac{\sqrt[]{3}}{2}[/tex]therefore
the coordinates (x,y) are
[tex](\frac{\sqrt[]{3}}{2},\frac{1}{2})[/tex]Let x represent the unknown value, then write an algebraic expression for: double a quantity increased by nine
Answers
Answer:
2(x + 9)
Explanation:
Let x represent the unknown value.
Double a quantity increased 9 means;
*We'll multiply the quantity by 2
*Increased by signifies addition
*Quantity means we'll put the expression after it in brackets
Let's go ahead and write the required algebraic expression;
[tex]2(x+9)[/tex]A school is arranging a field trip to the zoo. The school spends 564.16
Answers
Suppose the function f and g are defined as follows.
Answers
In this session we will focus on calculating the composition of f and f.
given the function f, the composition f composition f is obtained by taking the definiton of f and replace the varaible x with the function f itself. So we are given that
[tex]f(x)=\frac{8}{5x}[/tex]So
[tex]f\circ f(x)=\frac{8}{5(\frac{8}{5x})}=\frac{8}{\frac{8}{x}}=\frac{8x}{8}=x[/tex]So we have that f composition f is the function x.
What is the wavelength of a gamma ray with a frequency of 1.0 × 10¹⁹ Hz? 19 x [?] x 10?] m c = 3.0 x 108 m/s
Answers
The wave length of the gamma ray with a frequency of 1.0 x 10¹⁹ is 3 x 10⁻¹¹
Wave length:
Wavelength refers the distance between two peaks (or troughs) of a wave, and is therefore measured in meters.
The formula for calculating wave length is,
λ = c/v
where,
c = 3.0 × 10⁸, i.e. the speed of light, and
λ = wavelength , and
ν = frequency .
Given,
Here we have the frequency as 1.0 x 10¹⁹.
Now we need to find the wave length of the gamma ray.
Here we know that value of c = 3 x 10⁸
And the value of v = 1.0 x 10¹⁹
Wen we apply the value on the formula then we get,
λ = ( 3 x 10⁸) / ( 1.0 x 10¹⁹)
When we simplify it, then we get,
v = 3 x 10⁻¹¹
Therefore, the wavelength of the gamma ray is 3 x 10⁻¹¹.
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Select all ratios equivalent to 13.14
52:56. 39:42. 3:4
Answers
wkskskskskkakakskskskksmwkwkwkwksskks
SLook at point in the coordinate grid.If a line contains both points and the origin, which point would the line also contain? *(2 points)DS(12,8)(14,7)(15,9)(20, 12)5tvAle--AR
Answers
the point which will fall in the line is (14, 7)
Explanation:
The coordinates o f S = (2, 1)
When we draw a line from the origin (0, 0) touching the point S, we will see the next point will be (4, 2). Followed by (6, 3).
So when we look at the trend, we see that the x axis is the double of the y axis:
(2y, y) = (x, y)
(2,1 ) , (4, 2), (6, 3)
From the above, we can say the point which will fall in the line will follow that trend:
When we check the options, the only point with that trend is (14, 7).
This because (2(7), 7) = (2y, y)
Hence, the point which will fall in the line is (14, 7)
n a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer.
Answers
We can use the sine rule to find the hole angle, and then find the golfer angle:
[tex]\frac{200}{\sin(115)}=\frac{140}{\sin (Hole)}[/tex][tex]\text{Hole Angle = }\sin ^{-1}(\frac{140\times\sin (115)}{200})[/tex][tex]\text{Hole Angle = }39.37664303\text{ degre}es[/tex]Now we can find the golfer angle:
[tex]\text{Golfer = 180 - 115 - 39.38 }\cong25.6\text{ degre}es[/tex]Answer: 25.6 degrees.
Graph the image of the figure on the right under the given translation.T(3, -1) (x,y)
Answers
Answer:
The only image with edges at the given coordinates is;
Given the figure in the attached image.
we want to identify the image after a translation;
[tex]T(3,-1)(x,y)[/tex]Using one of the edges of the figure;
[tex](x,y)=(-4,0)[/tex]Applying the above translation we have;
[tex](-4,0)\rightarrow(-4+3,0-1)=(-1,-1)[/tex]The edge of the image would be at;
[tex](-1,-1)[/tex]Therefore, the only image with edges at the given coordinates is;
Find the ordered pair $(x,y)$ if
\begin{align*}
x+y&=(3-x)+(3-y),\\
x-y &=(x-2)+(y-2).
\end{align*}
Thanks
Answers
In accordance with the system of linear equations, the ordered pair is (x, y) = (1, 2).
How to find the values associated to an ordered pair
Ordered pairs are constructions characterized by two components, typically real numbers. The most common form of notation is (x, y). In this problem we need to resolve a system of linear equations to obtain the needed values. We find a system of two equations and two variables:
x + y = (3 - x) + (3 - y)
x - y = (x - 2) + (y - 2)
First, simplify each expression of the system:
First equation:
x + y = 6 - x - y
2 · x + 2 · y = 6
x + y = 3
Second equation:
x - y = (x - 2) + (y - 2)
x - y = x + y - 4
- 2 · y = - 4
y = 2
Second, substitute in the first equation:
x + 2 = 3
x = 1
The ordered pair is (x, y) = (1, 2).
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Find the sum of the following infinite series.1/3−2/21+4/147−8/1029+···
Answers
Given:
The series is 1/3−2/21+4/147−8/1029+··
Explanation:
For the given series, the first term is,
[tex]a=\frac{1}{3}[/tex]The common ratio is,
[tex]\begin{gathered} r=\frac{-\frac{2}{21}}{\frac{1}{3}} \\ =-\frac{2}{21}\cdot\frac{3}{1} \\ =-\frac{2}{7} \end{gathered}[/tex]The formula for the sum of infinite series is,
[tex]S_{\infty}=\frac{a}{1-r}[/tex]Substitute the values in the formula to determine the sum of infinite series.
[tex]\begin{gathered} S_{\infty}=\frac{\frac{1}{3}}{1-(-\frac{2}{7})} \\ =\frac{\frac{1}{3}}{\frac{9}{7}} \\ =\frac{1}{3}\times\frac{7}{9} \\ =\frac{7}{27} \end{gathered}[/tex]Answer: 7/27
Complete the steps to find the value of x
Answers
Answer:
2x=128⁰ x=64⁰
Step-by-step explanation:
since they are corresponding angles, the other side (2x) will also be 128⁰. This means that x=64⁰
and 2x=128⁰
A computer retail store has 10 personal computers in stock. A buyer wants to purchase 4of them. Unkown to either the retail store or the buyer, 4 of the computers in stock have defective hard drives. Assume that the computers are selected at random.A. In how many different ways can the 4 computers be chosen?Answer: 210B. What is the probability that exactly one of the computers will be defective?Answer:
Answers
A.
The number of different ways the computers can be chosen is given by a combination of 10 choose 4.
A combination of n choose p is given by the formula below:
[tex]C(n,p)=\frac{n!}{p!(n-p)!}[/tex]So we have:
[tex]C(10,4)=\frac{10!}{4!(10-4)!}=\frac{10\cdot9\cdot8\cdot7\cdot6!}{4\cdot3\cdot2\cdot6!}=210[/tex]B.
If the first computer chosen is the one defective, the probability of the first PC being defective is 4/10, the probability of the second one not being defective will be 6/9, for the third not being defective is 5/8 and for the fourth not being defective is 4/7.
Since the defective PC can be any of the 4 bought, we need to multiply the probability above by 4. So the final probability is:
[tex]P=4\cdot\frac{4}{10}\cdot\frac{6}{9}\cdot\frac{5}{8}\cdot\frac{4}{7}=0.3809[/tex]¡¡¡Help with this!!!
Answers
The value of sin 2x=0.8304 ,cos 2x=0.557,tan 2x=1.498 when the value of tan x is 8/15 and using the trigonometry identities as tan x as the formula in sin 2x, cos 2x, tan 2x.
What is trigonometry?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations (csc).
What is trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.
sin 2x=2 tan x/(1+(tan x)²)
cos 2x=(1-(tan x)²)/(1+(tan x)²)
tan 2x=sin 2x/cos 2x=2 tan x/(1-(tan x)²)
Here,
tan x=8/15
sin 2x=2 tan x/(1+(tan x)²)
= 2*8/15/(1+(8/15)²)
=(16/15)/(289/225)
=(16*15)/(289)
≈0.8304
cos 2x=(1-(tan x)²)/(1+(tan x)²)
=(1-(8/15)²)/(1+(8/15)²)
=(225-64)/(225+64)
≈0.557
tan 2x=sin 2x/cos 2x
tan 2x= 0.8304/0.557
=1.498
≈1.5
When the value of tan x is 8/15, the values of sin 2x=0.8304, cos 2x=0.557, and tan 2x=1.498 using the trigonometry identities as tan x as the formula in sin 2x, cos 2x, tan 2x.
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In the translation shown the image is
moved
A up 5
B down 5
C left 5
D right 5
Answers
explanation: it’s down 5 because it’s minus (-)
PLEASE ANSWER QUICK THIS IS DUE TODAY!!
-6+7m = 6m - m
Answers
Answer:
m = 3
Step-by-step explanation:
Hello!
We can solve for m by isolating the variable.
Solve for m-6 + 7m = 6m - m-6 + 7m = 5m => Simplify7m = 5m + 6 => Add 6 to both sides2m = 6 => Simplifym = 3 => Divide by 2The value of m is 3.
Please assist Math with 50 points!
Answers
Answer:
A. (1/2) bucket
Step-by-step explanation:
6 11
4 ------ - 3 ------- = ?
14 12
14 × 4 = 56
56 + 6 = 62
12 × -3 = -36
-36 - 11 = -47
62 47
------- - -------
14 12
62(12) 47(14)
------- - -------
14(12) 12(14)
744 658 86
------- - ------- = --------
168 168 168
86 ÷ 2
-------
168 ÷ 2
43
----- = 0.511
84
0.511 ≈ (1/2)
I hope this helps!
Answer:
1/2 bucket
Step-by-step explanation:
What is the solution of -8/2y-8 = 5/y+4 - 7y+8/y^2-16?
y = -4
y = -2
y = 4
y = 6
Answers
The correct option for the fraction with polynomials is y=6.
Fractions with polynomials.Expressions of more than two algebraic terms that contain different powers of the same variable is a polynomial.
The polynomial fraction is an expression of polynomial divided by another polynomial.
We can solve the fraction to get the value of y as follows;
[-8/(2y-8)]= [5/(y+4)]-[(7y+8)/(y²-16)]
[-8/(2y-8)]= [5/(y+4)]-[(7y+8)/(y+4)(y-4)]
[-8/(2y-8)]= [5(y+4)-(7y+8)]/(y+4)(y-4)] (L.C.M) of the fraction
[-8/(2y-8)]= (5y-20-7y-8)/(y+4)(y-4)
[-8/(2y-8)]= (-2y-28)/(y+4)(y-4)
[-8/2(y-4)]= (-2y-28)/(y+4)(y-4)
[-8/2(y-4)]= [-2(y-14)]/(y+4)(y-4)
[-4/(y-4)]= [-2(y-14)]/(y+4)(y-4)
Multiply both sides of the equation by -(y-4)
4= 2(y-14)/(y+4)
Cross multiply
4(y+4)=2(y+14)
Divide through by 2
2(y+4)=y+14
2y+8=y+14
collect like terms
2y-y=14-8
y=6.
Hence, we can state that the value of y for the polynomial with fraction is 6.
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4.(06.07 HC)A teacher is assessing the correlation between the number of hours spent studying and the average score on a science test. The table below shows the data:Number of hours spent studying 0 0.5 1(x)1.5 2 2.5 33.54Score on science test(y)57 62 67727782 879297Part A: Is there any correlation between the number of hours students spent studying and the score on the science test? Justify your answer. (4 points)Part B: Write a function which best fits the data. (3 points)Part C: What does the slope and y-intercept of the plot indicate? (3 points)(10 points)
Answers
For part A. One way to know if there is a correlation between the data is to graph the data set, like this
Then, as can you see the data presents a positive linear correlation.
For part B. You can take the coordinates of two points and find the slope of the line using the formula
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex]If you take
[tex]\begin{gathered} (x_1,y_1)=(1,67) \\ (x_2,y_2)=(3,87) \\ \text{ You have} \\ m=\frac{87-67}{3-1} \\ m=\frac{20}{2} \\ m=10 \end{gathered}[/tex]Now, using the slope formula, you can find the equation of the line in its slope-intercept form
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-67=10(x-1) \\ y-67=10x-10 \\ \text{ Add 67 on both sides of the equation} \\ y-67+67=10x-10+67 \\ y=10x+57 \end{gathered}[/tex]Therefore, the function that best fits the data is
[tex]y=10x+57[/tex]For part C. The slope of the plot is 10 and indicates that for every hour students spend time studying, they get 10 more points on the science test.
The y-intercept of the plot is 57 and indicates that if students study 0 hours for the science test, they will obtain 57 points as a grade.
Part A Write the multiplication expression shown by the model. Do not solve the problem. Part B
Explain the expression written in Part A. Include the final product and how it is shown with the model.
active attachment
Answers
The multiplication expression is L×w
The expression is written as N= r+ g + w + b
The final product = 200 boxes
How to determine the expressionIt is important to note that the formula for calculating the area of a rectangle is expressed as;
Area = lw
Where;
l is the length of the rectanglew is the width of the rectangleThe area can be determined by multiplying the length and the width and also by then adding the boxes.
Mathematically, we have;
10( 4 + 5 + 4 + 7)
Also
L × w = r + g + w + b
Hence, we have that L×w is a multiplication expression.
Total number of boxes for the length = 20
Total number of boxes for the width = 10
Total area = L×w = 20×10=200
Number of red boxes = 46Number of green boxes = 46Number of blue boxes = 46Number of white boxes = 62We then have;
N= r+ g + w + b
but r = g = b
Also,
L×B = 3r + w
Hence, a multiplication expression is an expression in which variables or numbers are being multiplied.
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1)bowl a contains 2 red chips; bowl b contains two white chips; and bowl c contains 1 red chip and 1 white chip. a bowl is selected at random, and one chip is taken at random from that bowl. what is the probability of selecting a white chip? if the selected chip is white, what is the probability that the other chip in the bowl is red?
Answers
Probability that selected chip is white: 1/2
Probability that the other chip in the bowl is red given if the selected chip is white: 1/3
Let A be the event that bowl A is randomly selected; let B be the event that bowl B is randomly selected; and let C be the event that bowl C is randomly selected. All these three bowls are equally likely to be selected:
P(A) = P(B) = P(C) = 1/3
The probability of selecting a white chip from a bowl depends on from which bowl the chip is selected.
Let W be the event that a white chip is randomly selected.
Attached is the picture solution.
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(1,-3),y=-4x-1 in slope intercept form
Answers
Lisa is putting money into a savings account, she starts with $350 in the savings account, and each week she adds $60
Answers
The total amount of money in the savings account after 11 weeks is $1010.
What is the total amount in the savings account?The from of the equation that can be used to determine the total amount of money in the savings account is a linear equation. A linear equation is an equation that has one variable that is raised to the power of one. When a linear equation is drawn on a coordinate graph, it is usually a straight line.
The form of the linear equation is:
Total amount = amount she starts with + (number of weeks x amount of money she adds each week)
S = $350 + ($60 x W)
S = $350 + $60W
Amount she would have in 11 weeks : $350 + ( 11 x $60)
$350 + 660 = $1010
Here is the complete question:
Lisa is putting money into a savings account. She starts with $350 in the savings account, and each week she adds $60. Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Jenny has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 11 weeks.
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please help with this geometry question i attempted it but dont understand it
Answers
You have the following vertices of a triangle:
A(1,1)
B(4,1)
C(4,5)
For the translation four untis to the right, consider this kind of translation means that it is necessary to sum 4 units to the x-coordinate:
A(1,1) => A'(1+4,1) = A'(5,1)
B(4,1) => B'(8,1)
C(4,5) => C'(8,5)
Next, a translation three units up is done by adding 3 units to the y-coordinate of points A', B' and C':
A'(5,1) => A''(5,1+3) = A''(5,4)
B'(8,1) => B''(8,4)
C'(8,5) => C''(8,8)
Next, a reflection around y=-1 consists in subtracting to the y-coordinate units equivalent to the vertical distance to the line y =-1, just as follow:
for the point A''(5,4) you can notice that the vertical distance of the y-coordinate, which is 4, to the line y=-1 is 5 units, then, it is necessary to subtract 5 units to such line:
A''(5,4) => A'''(5,-1-5)=A'''(5,-6)
for the point B''(8,4), the distance is again 5 units, then, you have:
B''(8,4) => B'''(8,-1-5) = B'''(8,-6)
for the point C''(8,8) the distance from y-coordinate y=8 to the line y=-1 is 9 units, then, yu subtract 9 units to -1:
C''(8,8) => C'''(8,-1-9) = C'''(8,-10)
Hence, the final points are:
A'''(5,6)
B'''(8,-6)
C'''(8,-10)
solve the systems using equal values.y= 2xy= -3x + 5
Answers
a) Write 98 as the product of prime factors. Write the prime factors in ascending order.
Answers
Step-by-step explanation:
Write 98 as the product of prime factors. Write the prime factors in ascending order.
2 × 7 × 7
2 × 7 × 7 = 98
Answer: 2×7×7
Step-by-step explanation: 98= 2×7×7
Lets first know about what is prime factor :- A factor which is a Prime number and not a composite number.
prime factor in ascending order = 2,7
hence the required product of prime factor is 2×7×7 or 2×[tex]7^{2}[/tex]