Given the equation of the line:
[tex]y+2=\frac{1}{2}(x+20)[/tex]The slope-intercept form is: y = m * x + b
Where (m) is the slope
So, we will solve the given equation for (y)
[tex]\begin{gathered} y+2=\frac{1}{2}\cdot x+\frac{1}{2}\cdot20 \\ y+2=\frac{1}{2}x+10 \\ y=\frac{1}{2}x+10-2 \\ \\ y=\frac{1}{2}x+8 \end{gathered}[/tex]so, the answer will be the slope-intercept form:
[tex]y=\frac{1}{2}x+8[/tex]I need some help finding slope from an equation6x-5y=20
Okay, here we have this:
Considering that the slope of a line with the form Ax+By=C is equal to -A/B, we obtain the following:
m=-6/-5
m=6/5=1.2
Finally we obtain that the slope is 6/5 or 1.2.
Let's solve the exercise in another way, solving for "y", and the coefficient that we obtain from x will be our slope:
6x-5y=20
-5y=-6x+20
y=(-6x+20)/-5
y=-6x/-5-4
y=6/5x-4
Here we can see that the slope is 6/5.
In the figure, KM is perpendicular to JL Point Pis the midpoint of JL.KMGiven AJPKALPK and AJPM - ALPM, which criterion can be directly applied to show that AKIM AKLM?CAGReview progres
In this problem we have that
JK=KL
JM=LM
and
KM is a common side
therefore
triangle KJM and triangle KLM are congruent by SSS
Excuse the quality of my picture. I am trying to find which piecewise functions are represented by this graph.
Let's begin with the line that goes from minus infinity to zero
the equation of this line is
[tex]y=x+2[/tex]because of the filled circle we know that this interval touch the zero
[tex](-\infty,0\rbrack[/tex]in inequality, this will be
[tex]x\le0[/tex]then for the line that is between 0 and 2, we have a filled circle in the number two therefore we can touch this number
the interval will be
[tex](0,2\rbrack[/tex]in inequality notation
[tex]0 for the line that starts in 2 we have an emptythe interval
[tex](2,\infty)[/tex]in inequality notation
[tex]x>2[/tex]Therefore the piecewise function i
[tex]f(x)=f(x)=\begin{cases}x+2,ifx\le0 \\ \frac{x}{3}+1,if02\end{cases}[/tex]the correct option is the second one
solve equations by factoring:4x^2-81=0
We have the equation:
[tex]4x^2-81=0[/tex]We can see that there is a differnce of squares:
[tex]4x^2-81=(2x)^2-9^2[/tex]And then we can rewite the difference of squares as:
[tex](2x)^2-9^2=(2x-9)(2x+9)[/tex]And this is equal to 0:
[tex](2x-9)(2x+9)=0[/tex]Now, there are two possibilities:
[tex]\begin{gathered} 2x-9=0 \\ Or_{\colon} \\ 2x+9=0 \end{gathered}[/tex]Then, we need to solve this two equatiions:
[tex]\begin{gathered} 2x-9=0 \\ x=\frac{9}{2} \end{gathered}[/tex][tex]\begin{gathered} 2x+9=0 \\ x=-\frac{9}{2} \end{gathered}[/tex]The two solutions for the equation are:
[tex]\frac{9}{2}\text{ and}-\frac{9}{2}[/tex]Draw ALMN with vertices L(3,-1), M(7,-3), and N(6,3). Find the coordinates of the vertices after a 90° rotation about the origin and about each of the points L, M, and N. what are the coordinates of the points after a 90° rotation about the origin? L=? M=? N=?
Answer:
The coordinates of the image are;
[tex]\begin{gathered} L^{\prime}=(-1,-3) \\ M^{\prime}=(-3,-7) \\ N^{\prime}=(3,-6) \end{gathered}[/tex]Explanation:
Given the coordinates of L,M and N as;
[tex]\begin{gathered} L=(3,-1) \\ M=(7,-3) \\ N=(6,3) \end{gathered}[/tex]A 90 degree clockwise rotation can be represented as;
[tex](x,y)\rightarrow(y,-x)[/tex]Applying this rule to the given coordinates we have;
[tex]\begin{gathered} L(3,-1)\rightarrow L^{\prime}(-1,-3) \\ M(7,-3)\rightarrow M^{\prime}(-3,-7) \\ N(6,3)\rightarrow N^{\prime}(3,-6) \end{gathered}[/tex]Therefore, the coordinates of the image are;
[tex]\begin{gathered} L^{\prime}=(-1,-3) \\ M^{\prime}=(-3,-7) \\ N^{\prime}=(3,-6) \end{gathered}[/tex]YOU HAVE TO FIND THE PRODUCT AND THEN SIMPLIFY IT THANK YOU :)
To find the product of 6 x 3 2/3
First change the mixed number to an improper fraction
That is;
6 x 11/3
we can now proceed to multiply
= 66/3
=22
A survey was conducted to find the possible relationship between age groups and the most favored of three book genres. The data is representedin the frequency table.MotivationalDo-It-YourselfTotalBiographies1101134026321-30 years31-40 years804421995· 10741-50 years9269268Total285153312750To the nearest tenth, what percentage of people were in the 41 – 50 age group and favored the Do-It-Yourself books?
The Solution.
The total number of people surveyed = 750.
The number of age group 41 - 50 that favored the Do-It-Yourself books = 69
The percentage of the people in age group 41 - 50, and favored the Do-It-Yourself books is calculated as below:
[tex]\frac{69}{750}\times100=9.2\approx9\text{ \%}[/tex]Hence, the correct answer is 9 percent.
A plant is 6.2cm tall.
The height of the plant increases by 11% each week
Find how tall the plant will be after 2 weeks
If A plant is 6.2cm tall. The height of the plant increases by 11% each week. Then 7.564 cm is the height of plant after two weeks.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
A plant is 6.2cm tall
The height of the plant increases by 11% each week
Let us convert 11% to the decimal value by dividing 11 with 100.
11/100=0.11
Now we have to find height plant will be after 2 weeks.
The increase of plant length in 1 week will be
0.11×6.2=0.682 inches
For 2 weeks it is 2×0.682
=1.364
Now add the initial length with increment of height to find the height after 2 weeks.
6.2cm+1.364m=7.564cm
Hence 7.564 cm tall the plant will be after 2 weeks
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Graph 2x+y<1Y>1/2x+2
We need to graph the next given inequalities:
[tex]\begin{gathered} 2x+y<1 \\ \text{and} \\ y>1/2x+2 \end{gathered}[/tex]For 2x+y<1.
We need to find the x-intercept and y-intercept
To find the y-intercept, set x=0
[tex]\begin{gathered} 2(0)+y<1 \\ \text{Then} \\ y<1 \\ \text{The y-intercept is the point (0,1)} \end{gathered}[/tex]To find the x-intercept, set y=0
[tex]\begin{gathered} 2x+0<1 \\ \text{solve for x} \\ x<\frac{1}{2} \end{gathered}[/tex]The symbol "<" means less than, so we get the next graph:
For the second inequality y>1/2x+2
To find the y-intercept, set x=0
describe the transformation.
[tex]y = x {}^{2} \: to \: y = 2(x - 3) {}^{2} + 4[/tex]
Answer:
A translation of 3 units to the right, followed by a vertical stretch by a factor of 2, followed by a translation of 4 units up.
Step-by-step explanation:
Transformations
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]
[tex]\begin{aligned} y =a\:f(x) \implies & \textsf{$f(x)$ stretched/compressed vertically by a factor of $a$}.\\& \textsf{If $a > 1$ it is stretched by a factor of $a$}.\\& \textsf{If $0 < a < 1$ it is compressed by a factor of $a$}.\end{aligned}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]
Therefore, the series of transformations of:
[tex]y=x^2 \quad \textsf{to} \quad y=2(x-3)^2+4\quad \textsf{is}:[/tex]
Translated 3 units to the right:
[tex]f(x-3)\implies y=(x-3)^2[/tex]
Stretched vertically by a factor of 2:
[tex]2f(x-3)\implies y=2(x-3)^2[/tex]
Translated 4 units up:
[tex]2f(x-3)+4\implies y=2(x-3)^2+4[/tex]
Therefore, the series of transformations is:
A translation of 3 units to the right, followed by a vertical stretch by a factor of 2, followed by a translation of 4 units up.
A track coach is standing in the center of a circular track whose diameter is 70 meters and she has to rotate 280 degrees to watch her runner. how far has the runner traveled?
Diameter is 70m
Thus radius = half of diameter= 70/2 = 35meters
Angle of rotation (teta) = 280 degrees
The distance covered will be
[tex]\begin{gathered} \text{Distance = }\frac{\theta}{360^0}\times2\times\pi\times r \\ =\text{ }\frac{280}{360}\times2\times3.142\times35 \\ =\frac{61583.2}{360} \\ =171.06\text{ meters} \end{gathered}[/tex]The runner has traveled 171.06 meters
If c(x) = 4x-2 and d(x) = x2 + 5x, what is (c.d)(x)?
O 4x³ + 18x² - 10x
O x² +9x-2
O 16x² + 4x - 6
O4x² + 20x - 2
In a case whereby c(x) = 4x-2 and d(x) = x2 + 5x, is two different equation, then the value of c(d(x)) is 4x2 + 20x - 2.
How can the value of the expression c(d(x)) be calculated?the first equation is been given as c(x) = 4x-2
And the second equation is been given as d(x) = x2 + 5x
Then to know the value of c(d(x)) then we will need to find the multiplication of the values that is been associated with c and d and this can be done as:
c(d(x)) = [c(x2 + 5x)]
And this will give us
=[ 4(x2 + 5x) - 2]
then after expansion we will have 4x2 + 20x - 2, going through the solution, we can see that the function that is given is been followed and the values for each of the function is been substituted so that the the value of c(d(x)) can be gotten.
Therefore, option D is correct.
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The graph of the function f(x) = –(x + 3)(x – 1) is shown below. On a coordinate plane, a parabola opens down. It goes through (negative 3, 0), has a vertex at (negative 1, 4), and goes through (1, 0).Which statement about the function is true?The function is positive for all real values of x wherex < –1.The function is negative for all real values of x wherex < –3 and where x > 1.The function is positive for all real values of x wherex > 0.The function is negative for all real values of x wherex < –3 or x > –1.
The graph of the function is shown below:
From it we notice that the function is positive in the interval (-3,1) and negative otherwise. With this in mind we conclude that the true statement is:
The function is negative for all real values of x where x < –3 and where x > 1.
A scatter plot could have a positive and negative relationship.O TrueO False
Remember that
We often see patterns or relationships in scatterplots. When the y variable tends to increase as the x variable increases, we say there is a positive correlation between the variables. When the y variable tends to decrease as the x variable increases, we say there is a negative correlation between the variables
therefore
The answer is True2. Which statement best describes the relationship based on the graph?
Sandsher, this is the solution to the exercise:
As you can see in the image, when the outside temperature increases, there is also an increase in the number of cars sold. However, we are not sure if the outside temperature is the only cause to explain such trend, and the increase is not constant and steady.
In consequence, the correct answer to this exercise is:
C. An increase in temperature is related to an increase in cars sold.
Accurately sketch or graph: f(x) = x^4/4 - 2x^3/3 -x^2/2 + 2xon the interval [ -2.5, 2.3] using the graph paper provided.
Graphing the function f(x) over the interval [-2.5, 2.3], we have the following
x-intercepts
Judging on the graph, the x-intercept of the function f(x) are the following
[tex]x=-1.619\text{ and }x=0[/tex]critical points
Finding the first derivative and setting it to zero and solve for x to get the critical points in the interval [-2.5,2.3] we have
[tex]\begin{gathered} f\mleft(x\mright)=\frac{x^4}{4}-\frac{2x^3}{3}-\frac{x^2}{2}+2x \\ f^{\prime}\left(x\right)=x^3-2x^2-x+2 \\ \\ x^3-2x^2-x+2=0 \\ \left(x−2\right)\left(x+1\right)\left(x−1\right)=0 \end{gathered}[/tex]Therefore, the critical points are x = 2, x = 1, x = -1.
relative minimums
Basing on the graph our relative minimum is at x = -1, and x = 2
asymptotes
Since the given function is a polynomial function, the function has no asymptotes
critical numbers
same as critical points with x = 2, x = 1, and x = -1.
relative maximum
observing the graph, the relative maximum of the function is at x = 1.
inflection points
get the second derivative of the function and set it to zero
[tex]\begin{gathered} f^{\prime}\left(x\right)=x^3-2x^2-x+2 \\ f^{\prime}^{\prime}\left(x\right)=3x^2-4x-1 \\ 3x^2-4x-1=0 \end{gathered}[/tex]Using the quadratic formula we have the values at
[tex]x=\frac{2}{3}\pm\sqrt{\frac{7}{3}}[/tex]end behavior
Since the function is a polynomial with a degree of 4, and a positive leading coefficient, the end behavior of the function is increasing in both approaching to -2.5, and 2.3.
Which expression will produce an answer with the fewest significant figures?A. 15.4 - 8.1B. 4350 - 2210C. 18.8 - 6.5D. 54.5 * 30.7
we have following:
[tex]\begin{gathered} 15.4-8.1=7.3\cong7\rightarrow2sf \\ 4350-2210=2140\rightarrow3sf \\ 18.8-6.5=12.3\cong12\rightarrow3sf \\ 54.5\cdot30.7=1673.15\cong1670\rightarrow3sf \end{gathered}[/tex]therfore, the answer is the option A.
If 1/2 cup of water fills 2/3 of a plastic container, how many containers will 1 cup full?
1 cup will fills double than 1/2 cup, so:
[tex]\frac{2}{3}\cdot2=\frac{4}{3}[/tex]With 1 cup you will be able to fills 4/3, in other words 1 full container and 1/3 of another.
Find the distance between the pair of points,(9, 3), (9,7)Set up the problem here:
We are given the following two points.
[tex]\mleft(9,3\mright)\: and\: (9,7)[/tex]Let us find the distance between these two points.
Recall that the distance formula is given by
[tex]undefined[/tex]I don’t know how to solve for eI already solved everything else, I just need to know how to write an equation for f(x)=___ using my answers from questions c & d
e)
1) Since we know the slope, and the y-intercept from the previous items we can tell the function's rule is:
[tex]f(x)=\frac{1}{2}x+13[/tex]Note that the slope tells us how steep is the line, and the b-coefficient is 13.
2) And that is the answer.
someone help i’m stuck on this :c
Answer:
40 m × 7 m28 m × 10 mStep-by-step explanation:
You want possible dimensions of a field that is 280 square meters in area and has a 3-sided perimeter of 54 meters or less.
DefinitionsFor the purpose here, we can define the length of the field as the distance parallel to the river. Then the width is the distance out from the river.
DimensionsPossible whole-number dimensions of the field can be found by considering factor pairs of 280. Listing length first, we could have ...
280 = (280)(1) = (140)(2) = (70)(4) = (56)(5) = (40)(7) = (35)(8) = (28)(10) = (20)(14) . . . and the reverse of these
Perimeter fenceThe length of the fence required will be the length plus 2 times the width. For the factor pairs shown, the fence lengths, respectively, are ...
282, 144, 78, 66, 54, 51, 48, 48, 54, 66, 78, 87, 117, 144, 282, 561 . . . meters
The highlighted values are 54 meters or less, corresponding to dimensions ...
40 m × 7 m35 m × 8 m28 m × 10 m20 m × 14 m14 m × 20 mPossible dimensions are 40 m by 7 m, and 28 m by 10 m.
__
Additional comment
As you have noted, other values of dimensions are possible, for example, 22.4 m × 12.5 m, a size requiring a fence 47.4 m long.
Question 1 (1 point) page 6 #1 Match each spinner with its likelihood to land on black. Column A Column B 1. impossible a 2. unlikely 3. equally likely 4. likely 5. certain b. - o Type here to search
Answer:
1.......c
2.....a
3.....b
4......e
5.....d
Because of the size of the black section,
To install an outdoor swimming pool will cost you £800 in England. how much will it cost you to install a swimming pool of the same capacity in South African Rand?
Answer:
It would cost you approximately R15836.13
Expand: (m + 4) 0 m2 + 8m + 16 0 m2 + 4m + 16 O mp + m +- 8
we have the next squared binomial
[tex](m+4)^2[/tex]we have the next formula in order to expand a squared binomial
[tex](a+b)^2=a^2+2ab+b^2[/tex]So we can expand
[tex](m+4)^2=m^2+2(4)(m)+4^2=m^2+8m+16[/tex]so the correct answer is the first one
A textbook store sold a combined total of 260 chemistry and physics textbooks in a week. The number of chemistry books sold was three times the number of physics textbooks sold. How many textbooks of each type were sold?
Let:
x = Chemistry textbooks sold
y = Physics textbooks sold
The textbook store sold a combined total of 260, so:
[tex]x+y=260[/tex]The number of chemistry books sold was three times the number of physics textbooks sold, so:
[tex]x=3y[/tex]Let:
[tex]\begin{gathered} x+y=260_{\text{ }}(1) \\ x=3y_{\text{ }}(2) \end{gathered}[/tex]Replace (2) into (1):
[tex]\begin{gathered} 3y+y=260 \\ 4y=260 \\ y=\frac{260}{4} \\ y=65 \end{gathered}[/tex]Replace the value of y into (2):
[tex]\begin{gathered} x=3(65) \\ x=195 \end{gathered}[/tex]hi I need help with this question because my math teacher explains it very hardly for me to understand
The reflection image is as follows,
In an inverse variation, y = 2 when x = 8. Write an inverse variation equation that showsthe relationship between x and y
The general equation for the inverse variation is,
[tex]\begin{gathered} y\propto\frac{1}{x} \\ y=\frac{k}{x} \end{gathered}[/tex]Substitute the value of x and y in the equation to obtain the value of k.
[tex]\begin{gathered} 2=\frac{k}{8} \\ k=8\cdot2 \\ =16 \end{gathered}[/tex]Thus, relation between x and y is,
[tex]y=\frac{16}{x}[/tex]How much would $150 invested at 8% interest compounded continuously beworth after 17 years? Round your answer to the nearest cent.
Answer: A. $584.43
Explanation
Given
[tex]A(t)=P\cdot e^{rt}[/tex]where A(t) is the amount obtained, P is the initial amount, e is a mathematical constant, r is the rate, and t is the time.
Thus, we are also given that:
• P = $150
,• r = 8% = 0.08
,• t = 17
Therefore, replacing the values:
[tex]A(17)=150\cdot e^{0.08(17)}[/tex][tex]A(17)=150\cdot e^{1.36}[/tex][tex]A(17)\approx584.43[/tex]Transform each graph as specified below.(a) The graph of y=f(x) is shown. Draw the graph of y=2(x).(b) The graph of y=g(x) is shown. Draw the graph of y=ry=g(2x)
(a)
In order to graph y = 2f(x), we just need to use the values of y two times higher than the values of y = f(x), that is, a vertical stretch. So we have:
(In black: y = 2f(x), in red: y = f(x))
(b)
In order to graph y = g(2x), we just need to use half the values of x from y = g(x), that is, a horizontal compression. So we have:
(in green: y = g(2x), in blue: y = g(x))
PLEASE. HELP
The table shows the number of gallons of paint Mrs. Brown used to paint the of rooms in her house. Find the slope of the line
Answer: 2/3
Step-by-step explanation: