Given the following absolute value function sketch the graph of the function and find the domain and range.
ƒ(x) = |x + 3| - 1
pls show how did u solve it
Answers
In order to sketch the graph we need to find the vertex and two more points to connect with the vertex.
To do so set the inside of absolute value to zero:
x + 3 = 0x = - 3The y-coordinate of same is:
f(-3) = 0 - 1 = - 1.So the vertex is (- 3, - 1).
Since the coefficient of the absolute value is positive, the graph opens up, and the vertex is below the x-axis as we found above.
Find the x-intercepts by setting the function equal to zero:
|x + 3| - 1 = 0x + 3 - 1 = 0 or - x - 3 - 1 = 0x + 2 = 0 or - x - 4 = 0x = - 2 or x = - 4We have two x-intercepts (-4, 0) and (-2, 0).
Now plot all three points and connect the vertex with both x-intercepts.
Now, from the graph we see there is no domain restrictions but the range is restricted to y-coordinate of the vertex.
It can be shown as:
Domain: x ∈ ( - ∞, + ∞),Range: y ∈ [ - 1, + ∞)
Answer:
Vertex = (-3, -1).y-intercept = (0, 2).x-intercepts = (-2, 0) and (-4, 0).Domain = (-∞, ∞).Range = [-1, ∞).Step-by-step explanation:
Given absolute value function:
[tex]f(x)=|x+3|-1[/tex]
The parent function of the given function is:
[tex]f(x)=|x|[/tex]
Graph of the parent absolute function:
Line |y| = -x where x ≤ 0Line |y| = x where x ≥ 0Vertex at (0, 0)Translations
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]
Therefore, the given function is the parent function translated 3 units left and 1 unit down.
If the vertex of the parent function is (0, 0) then the vertex of the given function is:
⇒ Vertex = (0 - 3, 0 - 1) = (-3, -1)
To find the y-intercept, substitute x = 0 into the given function:
[tex]\implies \textsf{$y$-intercept}=|0+3|-1=2[/tex]
To find the x-intercepts, set the function to zero and solve for x:
[tex]\implies |x+3|-1=0[/tex]
[tex]\implies |x+3|=1[/tex]
Therefore:
[tex]\implies x+3=1 \implies x=-2[/tex]
[tex]\implies x+3=-1 \implies x=-4[/tex]
Therefore, the x-intercepts are (-2, 0) and (-4, 0).
To sketch the graph:
Plot the found vertex, y-intercept and x-intercepts.Draw a straight line from the vertex through (-2, 0) and the y-intercept.Draw a straight line from the vertex through (-4, 0).Ensure the graph is symmetrical about x = -3.Note: When sketching a graph, be sure to label all points where the line crosses the axes.
The domain of a function is the set of all possible input values (x-values).
The domain of the given function is unrestricted and therefore (-∞, ∞).
The range of a function is the set of all possible output values (y-values).
The minimum of the function is the y-value of the vertex: y = -1.
Therefore, the range of the given function is: [-1, ∞).
Related Questions
59.25 ÷ 0.75 = 1.06 × 7.3 =on chart. will send image
Answers
For the division, notice that we can multiply both numbers by 100, to get the following:
[tex]\begin{gathered} 59.25\cdot100=5925 \\ 0.75\cdot100=75 \end{gathered}[/tex]then, we can make the long division:
therefore, the result of 59.25 ÷ 0.75 is 79
For the multiplication, we can write the following:
notice that since both factors have 2 digits and 1 digit each after the decimal point, the final result will have 3 digits after the decimal point,
Therefore, the result of 1.06 × 7.3 is 7.738
Consider the line y= 3/5x-3Find the equation of the line that is parallel to this line and passes through the point (3, 4).Find the equation of the line that is perpendicular to this line and passes through the point (3, 4).
Answers
a) y = 3/5x + 11/5
b) y = -5/3x + 9
Explanation:[tex]\begin{gathered} a)\text{ }y\text{ = }\frac{3}{5}x\text{ - 3} \\ \text{compare with equation of line:} \\ y\text{ = mx + b} \\ m\text{ =slope, b = y-intercept} \\ m\text{ =slope = 3/5} \\ b\text{ = -3} \end{gathered}[/tex]For a line to be parallel to another line. the slope of the 1st line will be equalt to the slope of the 2nd line:
slope of 1st line = 3/5
So, the slope of the 2nd line = 3/5
Given point: (3, 4) = (x, y)
To get the y-intercept of the second line, we would insert the slope and the point into the equation of line
[tex]\begin{gathered} y\text{ = mx + b} \\ 4\text{ = }\frac{3}{5}(3)\text{ + b} \\ 4\text{ = 9/5 + b} \\ 4\text{ - }\frac{\text{9}}{5}\text{ = b} \\ \frac{20-9}{5}\text{ = b} \\ b\text{ = 11/5} \end{gathered}[/tex]The equation of line parallel to y = 3/5x - 3:
[tex]\begin{gathered} y\text{ = mx + b} \\ y\text{ = }\frac{3}{5}x\text{ + }\frac{11}{5} \end{gathered}[/tex][tex]b)\text{ line perpendicular to y = 3/5x - 3}[/tex]For a line to be perpendicular to another line, the slope of one will be the negative reciprocal of the second line
Slope of the 1st line = 3/5
reciprocal of 3/5 = 5/3
negative reciprocal = -5/3
slope of the 2nd line (perpendicular) = -5/3
We need to get the y-intercept of the perpendicular line:
[tex]\begin{gathered} \text{given point: (3,4) = (x, y)} \\ y\text{ = mx + b} \\ m\text{ of the perpendicular = -5/3} \\ 4\text{ = }\frac{-5}{3}(3)\text{ + b} \\ 4\text{ = -5 + b} \\ 4\text{ + 5 = b} \\ b\text{ = 9} \end{gathered}[/tex]The equation of line perpendicular to y = 3/5x - 3:
[tex]\begin{gathered} y\text{ = mx + b} \\ y\text{ = }\frac{-5}{3}x\text{ + 9} \end{gathered}[/tex]I didn't really get it when my teacher tried to explain this
Answers
The formula for determining the volume of a cylinder is expressed as
V = pi * r^2h
Where
V represents volume of cylinder
pi is a constant whose value is 3.142
r represents radius of cylinder
h represents height of cylinder
From the information given,
h = 10
r = 3
V = 3.142 * 3^2 * 10
V = 282.78 in^3
The closest measurement is option A
The function P(x) is mapped to I(x) by a dilation in the following graph. Line p of x passes through (negative 2, 4) & (2, negative 2). Line I of X passes through (negative 4, 4) & (4, negative 2).© 2018 StrongMind. Created using GeoGebra. Which answer gives the correct transformation of P(x) to get to I(x)?
Answers
When we're dilating a line, we can either multiply the function value by a constant
[tex]f(x)\to kf(x)[/tex]or the argument of the function
[tex]f(x)\to f(kx)[/tex]Since the y-intercept of both functions is the same, then the multiplied quantity was the argument of the function.
We want to know the constant associated to the transformation
[tex]I(x)\to I(kx)=P(x)[/tex]We have the following values for both functions
[tex]\begin{gathered} I(-4)=4,\:I(4)=-2 \\ P(-2)=4,\:P(2)=-2 \end{gathered}[/tex]For the same y-value, we have the following correlations
[tex]\begin{gathered} I(-4)=P(-2)=P(\frac{1}{2}\cdot-4) \\ I(4)=P(2)=P(\frac{1}{2}\cdot4) \\ \implies I(x)=P(\frac{1}{2}x) \end{gathered}[/tex]and this is our answer.
[tex]I(x)=P(\frac{1}{2}x)[/tex]The sum of 4 times a number and 5 is the same as the difference of the number and 7
Answers
Answer:
4nx5=n-7
-7/19
Step-by-step explanation:
Let's Write this equation step by step.
The sum of 4 times a number and 5
That means: 4nx5
The difference of the number and 7
That means: n-7
Now, combine:
4nx5=n-7
-7/19
need help with part a with a summary and all work shown to help me understand better
Answers
ANSWER:
[tex]\left(16u^{\frac{1}{3}}\right)^{\frac{3}{4}}=8\sqrt[4]{u}[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]\left(16u^{\frac{1}{3}}\right)^{\frac{3}{4}}[/tex]When you raise an exponent to another exponent, multiply therefore:
A local band was interested in the average song time for rock bands in the 1990s. They sampled eight different rock bands and found that the average time was 3.19 minutes with a standard deviation of 0.77 minutes.
Calculate the 95% confidence interval (in minutes) for the population mean.
Answers
The 95% confidence interval (in minutes) for the population mean is of:
(2.55, 3.83).
What is a t-distribution confidence interval?The bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the parameters are described as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The distribution is used when the standard deviation of the population is not known, only for the sample.
In the context of this problem, the values of the parameters are given as follows:
[tex]\overline{x} = 3.19, s = 0.77, n = 8[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 8 - 1 = 63 df, is t = 2.3646.
Then the lower bound of the confidence interval is calculated as follows:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 3.19 - 2.3646\frac{0.77}{\sqrt{8}} = 2.55[/tex]
The upper bound is calculated as follows:
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 3.19 + 2.3646\frac{0.77}{\sqrt{8}} = 3.83[/tex]
More can be learned about the t-distribution at https://brainly.com/question/16162795
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Rewrite each equation in slope intercept form . Then determine whether the lines are perpendicular . Explain your answer .. y - 6 = - 5/2 (x + 4) 5y = 2x + 6
Answers
y - 6 = - 5/2 (x + 4)
To write in slope-intercept form means to write in the form;
y= mx + b
where m is the slope and b is the intercept
y - 6 = - 5/2 (x + 4)
open the parenthesis
y - 6 = -5/2 x - 10
add 6 to both-side of the equation
y = - 5/2 x - 10 + 6
y = -5/2 x - 4
[tex]y=-\frac{5}{2}x\text{ - 4}[/tex]Next is to check whether 5y = 2x + 6 is perpendicular to the above
To do that, we have to make the equation to be in the form y=mx+ b
5y = 2x + 6
Divid through by 5
y = 2/5 x + 6/5
[tex]y\text{ = }\frac{2}{5}x\text{ + }\frac{6}{5}[/tex]The slope of perpendicular equation, when multiply gives minus one (-1)
The slope of the first equation = -5/2
The slope of the second equation is 2/5
Multiplying the two slopes;
(-5/2) (2/5) = -1
Hence the lines are perpendicular
Conner plans to plow a field in one day. Before lunch he plows 15 acres, which is 30% of the field. Howmany acres will he have to plow after lunch in order to finish the field?
Answers
Solution:
Let the total field to plow be 100 %
According to the question,
The field plowed before lunch is shown below:
15 acres field = 30%
30 % field = 15 acres
1 % field = 15/30 acres
The field plow after lunch is 70%.
[tex]\begin{gathered} 70\text{ \% of field = }\frac{15}{30}\times70 \\ =35\text{ acres} \end{gathered}[/tex]Final Answer:
Therefore, the field to plow after lunch in order to finish the field is 35 acres.
Use one or more transformations to transform the pre-image (purple) onto the image (white). helppp
Answers
The transformation required to transform the preimage in purple to the image in white is
Rotation 180 degreesTranslation to the right 14 unitsTranslation down 4 unitsWhat is transformation?Transformation is the term used to describe when a body is repositioned or makes some movement.
Some of the movements involved in transformation are:
Rotation Translation and so onHow to transform the pre- image to the imageThe movement can start in several ways however we stick to this as described
The first movement is rotation by 180 degrees about the topmost edge at the left side.The next step is translation 14 units to the right. This gets the preimage exactly on top of the imageFinally, translation 4 units downLearn more about translation at: https://brainly.com/question/29042273
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End Behavior Graphically
Answers
We will investigate how to determine the end behaviours of polynomial functions.
The function given to us is:
[tex]f(x)=123x^3+9x^4-786x-3x^{5^{}}-189x^2\text{ + 1260}[/tex]Whenever we try to determine the end-behaviour of any function. We are usually looking for value of f ( x ) for the following two cases:
[tex]x\to\infty\text{ and x}\to-\infty[/tex]The most important thing to note when dealing with end-behaviour of polynomial functions is that the behaviour is pre-dominantly governed by the highest order term of a polynomial. The rest of the terms are considered small or negligible when considering end-behaviours of polynomials.
The highest order terms in the given function can be written as:
[tex]f(x)=-3x^5[/tex]Then the next step is to consider each case for the value of ( x ) and evaluate the value of f ( x ) respectively.
[tex]\begin{gathered} x\to\infty \\ f\text{ ( }\infty\text{ ) = -3}\cdot(\infty)^5 \\ f\text{ ( }\infty\text{ ) = -3}\cdot\infty \\ f\text{ ( }\infty\text{ ) = -}\infty \end{gathered}[/tex]Similarly repeat the process for the second case:
[tex]\begin{gathered} x\to-\infty \\ f\text{ ( -}\infty\text{ ) = -3}\cdot(-\infty)^5 \\ f\text{ ( -}\infty\text{ ) = 3}\cdot\infty \\ f\text{ ( -}\infty\text{ ) = }\infty \end{gathered}[/tex]Combining the result of two cases we get the following solution:
[tex]As\text{ x}\to\text{ }\infty\text{ , y}\to\text{ -}\infty\text{ and as x}\to-\infty\text{ , y}\to\text{ }\infty[/tex]Correct option is:
[tex]\text{Option C}[/tex]State whether the given set of lines are parallel, perpendicular or neither.3x-2y=56y-9x=6The lines are Answer
Answers
Two lines are parallel if:
[tex]m1=m2[/tex]Two lines are perpendicular if:
[tex]m1\cdot m2=-1[/tex]---------------------
Let's rewrite the given equations in the slope-intercept form:
[tex]\begin{gathered} 3x-2y=5 \\ y=\frac{3}{2}x-\frac{5}{2} \\ -------- \\ 6y-9x=6 \\ y=\frac{3}{2}x+1 \end{gathered}[/tex]Since:
[tex]\begin{gathered} m1=m2 \\ \frac{3}{2}=\frac{3}{2} \\ \end{gathered}[/tex]We can conclude that the lines are parallel.
Devon saw 19 adults wearing hats
Answers
Answer:
please add rest of question?
Step-by-step explanation:
What are the coefficient(s) in the following expression:
x² + 2x-5xy-y+3y¹
2,4
A
B
C
D
1, 2, 5, 1,3
2,-5, 3
1, 2, 5, 1, 3
Answers
Step-by-step explanation:
based on the expression you wrote here, the correct answer is
1, 2, -5, -1, 3
since none of your answer options show this, you must have made a mistake either with the expression itself or with the answer options.
please choose in your original the one matching my answer above.
Find the missing factor. x2 - 11x + 18 = (x - 2)( .) Enter the correct answer. 000 DONE Clear all DOO
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we have the second degree polynomial
[tex]x^2-11x+18[/tex]we must find two numbers a,b such that
[tex]\begin{gathered} x^2-11x+18=(x+a)(x+b)\text{ and} \\ a+b=11 \\ ab=18 \end{gathered}[/tex]We can see that, a=-2 and b=-9 fulfill the above conditions. Therefore, we have
[tex]x^2-11x+18=(x-2)(x-9)\text{ }[/tex]Over a set of 5 chess games, Yolanda's rating increased 10 points, increased 4 points,
decreased 21 points, increased 23 points and decreased 8 points.
Her rating is now 1647.
What was her rating before the 5 games?
A. 1639
B. 1649
C. 1655
D. 1661
Answers
Answer:
C. 1655
Step-by-step explanation:
+10, +4, -21, +23, -8
Adding all those terms together we get 8
1647 + 8 = 1655
Write problem as a single radical using the smallest possible root. 20
Answers
Answer::
[tex]\sqrt[30]{r^{29}}[/tex]Explanation:
Given the expression:
[tex]\sqrt[5]{r^4}\sqrt[6]{r}[/tex]First, rewrite the expression using the fractional index law:
[tex]\begin{gathered} \sqrt[n]{x}=x^{\frac{1}{n}} \\ \implies\sqrt[5]{r^4}=r^{\frac{4}{5}};\text{ and} \\ \sqrt[6]{r}=r^{\frac{1}{6}} \end{gathered}[/tex]Therefore:
[tex]\sqrt[5]{r^4}\times\sqrt[6]{r}=r^{\frac{4}{5}}\times r^{\frac{1}{6}}[/tex]Use the multiplication law of exponents:
[tex]\begin{gathered} a^x\times a^y=a^{x+y} \\ \implies r^{\frac{4}{5}}\times r^{\frac{1}{6}}=r^{\frac{4}{5}+\frac{1}{6}} \\ \frac{4}{5}+\frac{1}{6}=\frac{24+5}{30}=\frac{29}{30} \\ \operatorname{\implies}r^{\frac{4}{5}}\times r^{\frac{1}{6}}=r^{\frac{4}{5}+\frac{1}{6}}=r^{\frac{29}{30}} \end{gathered}[/tex]The resulting expression can be rewrittem further:
[tex]\begin{gathered} r^{\frac{29}{30}}=(r^{29})^{\frac{1}{30}} \\ =\sqrt[30]{r^{29}} \end{gathered}[/tex]The single radical is:
[tex]\sqrt[30]{r^{29}}[/tex]Find the equation of the line described. Write your answer in standard form. Vertical and containing (10,14)
Answers
We have here a special case where the line is vertical. In this case, the line has an "infinite" slope (or it is not defined). Therefore, since the line is vertical and contains the point (10, 14), the line is given by the equation:
[tex]x=10[/tex]The standard form of the line is given by the general equation:
[tex]Ax+By=C[/tex]Then, we can rewrite the equation as follows:
[tex]x+0y=10[/tex]We can see that this line contains the point (10,14):
We can see that the vertical line, x + 0y = 10 passes through the point (10, 14).
In summary, the line is given by x + 0y = 10 (A = 1, B = 0, C = 10).
I need help figuring out how to write out this problem correctly.
Answers
Answer
[tex]\frac{\sqrt{10}}{11}[/tex]Step-by-step explanation
Given the expression:
[tex]\sqrt{\frac{10}{121}}[/tex]Distributing the square root over the division and evaluating the square root at the denominator:
[tex]\begin{gathered} \frac{\sqrt{10}}{\sqrt{121}} \\ \frac{\sqrt{10}}{11} \end{gathered}[/tex]H is the circumcenter of triangle BCD, BC=18, and HD=14. Find CH.
Answers
Given that H is the circumcenter of the triangle.
It means, the length between each vertex point of the triangle and the point H is the radius of the circle.
Thus, the line DH=CH=BH are the radius of the circle.
It is given that DH=14.
Therefore CH=14.
Hence the value of CH is 14.
The con 3720bertar What can be interpreted from the youtercept of the functionRachel must pay $37 per month to use the gymRachel must pay $20 per month to use the gymRachel must pay a $37 membership fee to join the gymRachel must pay a $20 membership fee to join the samMaria wants to rent a car. She learns that the total daily costcated using the formula C = 5x + 30. hereseS driven that day. What does the constanteseer
Answers
f(x) = 37x + 20
Answer:
Option D, $20 is the membership beause it is a fixed cost, it does not depend on the amount of months
complete the table of ordered pairs for the linear equation. 5x+8y=3
Answers
Given:
5x+8y=3
The objective is to fill the table using the given values of x otr y.
Let's take that, x=0 and substitute in the given equation.
[tex]\begin{gathered} 5x+8y=3 \\ 5(0)+8y=3 \\ 0+8y=3 \\ y=\frac{3}{8} \end{gathered}[/tex]Hence, the the required solution will be (0,3/8).
Let's take that, y=0 and substitute in the given equation.
[tex]\begin{gathered} 5x+8y=3 \\ 5x+8(0)=3 \\ 5x+0=3 \\ x=3-5 \\ x=-2 \end{gathered}[/tex]Hence, the the required solution will be (-2,0).
Let's take that, y=1 and substitute in the given equation.
[tex]\begin{gathered} 5x+8y=3 \\ 5x+8(1)=3 \\ 5x+8=3 \\ 5x=3-8 \\ 5x=-5 \\ x=-\frac{5}{5} \\ x=-1 \end{gathered}[/tex]Hence, the the required solution will be (-1,1).
What is 4x+10(2x) - 8x
Answers
4x+10(2x) - 8x
First, multiply to solve the parentheses:
4x+20x-8x
Add and subtract
16x
write 0.751 as a percentage
Answers
To convert decimal numbers to percentage, what we need to do is to multiply the decimal number by 100, and we will get the representation as a percentage.
In this case we have the decimal number:
[tex]0.751[/tex]We multiply that number by 100 to write is as a percentage:
[tex]0.751\times100=71.5[/tex]Answer: 75.1%
The endpoints are a side of a rectangle ABCD in the coordinate plane at A(3,4), B(6,1) Find the equation of the line the given segment The line segment is line Segment AB
Answers
The endpoints are a side of a rectangle ABCD in the coordinate plane at A(3,4), B(6,1) Find the equation of the line the given segment
The line segment is line Segment AB
step 1
Find the slope of segment AB
m=(1-4)/(6-3)
m=-3/3
m=-1
step 2
Find the equation of the line in slope intercept form
y=mx+b
we have
m=-1
point (3,4)
substitute
4=(-1)*(3)+b
4=-3+b
b=4+3
b=7
therefore
the equation of segment AB is
y=-x+7You are scuba diving at 120 feet below sea level. You begin to ascend at a rate of 4 feet per second.a. Where will you be 10 seconds after you begin your ascension? b. How long will it take to reach the surface?
Answers
The ascension can be modeled using the function:
[tex]d(t)=d_0-r\cdot t[/tex]Where d is the number of feet below the sea level at time t (in seconds), d₀ is the initial "depth", and r is the ascension rate.
From the problem, we identify:
[tex]\begin{gathered} r=4\text{ feet per second} \\ d_0=120\text{ feet} \end{gathered}[/tex]Then:
[tex]d(t)=120-4t[/tex]a)
After 10 seconds, we have t = 10:
[tex]\begin{gathered} d(10)=120-4\cdot10=120-40 \\ \\ \Rightarrow d(10)=80\text{ feet} \end{gathered}[/tex]After 10 seconds, we will be 80 feet below sea level.
b)
To find how long will it take to reach the surface, we need to solve the equation d(t) = 0.
[tex]\begin{gathered} d(t)=0 \\ 120-4t=0 \\ 4t=120 \\ \\ \therefore t=30\text{ seconds} \end{gathered}[/tex]We will reach the surface after 30 seconds.
Complete the proof that the point (-2, V5 ) does or does not lle on the circle centered at the origin and containing the point (0,3). Part 1 out of 4 The radius of the circle is
Answers
We will have the following:
*First: We have that the equation of the circle will be given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Here (h, k) is the coordinate of the center of the circle and r is the radius of the circle.
*Second: We will replace the center of the circle and determine the radius:
[tex]x^2+y^2=r^2[/tex]*Third: We determine the radius of the circle by using the point given:
[tex](0)^2+(3)^2=r^2\Rightarrow r^2=9\Rightarrow r=3[/tex]*Fourth: We have the following expression representing the circle:
[tex]x^2+y^2=9[/tex]So, we replace the point (-2, sqrt(5)) to determine whether or not it belongs to the circle, that is:
[tex](-2)^2+(\sqrt[]{5})^2=9\Rightarrow4+5=9\Rightarrow9=9[/tex]Thus proving that the point (-2, sqrt(5)) does lie in the circle.
i inserted a picture of the question can you please list the answers as well
Answers
Solution
We want to find the equation of the line given in the graph
We can see the four points on the graph where the line pass through
The points are
[tex](4,4),(2,3),(0,2),(-4,0)[/tex]We first obtain the slope (m)
The formula for finding the slope is given as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Using the points (0,2) and (-4,0) (indeed we can pick any two points, we will still obtain the same answer)
Here
[tex]\begin{gathered} x_1=0 \\ y_1=2 \\ x_2=-4 \\ y_2=0 \end{gathered}[/tex][tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0-2}{-4-0} \\ m=\frac{2}{4} \\ m=\frac{1}{2} \\ m=0.5 \end{gathered}[/tex]We can use any of the points above to find the equation
Equation of a line is given by
[tex]y-y_1=m(x-x_1)[/tex]Using (4,4)
[tex]y-4=0.5(x-4)[/tex]Option D is correct
Using (2,3)
What is a quadrilateral that has reflection symmetry, but not rotation symmetry?
Answers
The quadrilaterals, parallelogram,square, rectangle has rotational symmetry but no reflectional symmetry
A trapezoid has neither a rotational symmetry nor a reflectional symmetry
But for an isosceles with only one pair of parallel sides has a reflectional symmetry but no rotational symmetry
Thus, the correct answer is
an isosceles with only one pair of parallel sides
Given the function f(x)={4x+7 if x<0 6x+4 if x>0 _
Answers
Given:
[tex]f(x)=\begin{cases}4x+7ifx<0{} \\ 6x+4ifx\ge0{}\end{cases}[/tex]Required:
To find the value of f(-8), f(0), f(4), and f(-100)+f(100).
Explanation:
f(-8) :
Clearly -8<0,
So
[tex]\begin{gathered} f(x)=4x+7 \\ f(-8)=4(-8)+7 \\ =-32+7 \\ =-25 \end{gathered}[/tex]f(0) :
Clearly 0=0,
[tex]\begin{gathered} f(x)=6x+4 \\ =6(0)+4 \\ =4 \end{gathered}[/tex]f(4) :
Clearly 4>0,
[tex]\begin{gathered} f(x)=6x+4 \\ f(4)=6(4)+4 \\ =24+4 \\ =28 \end{gathered}[/tex]f(-100)+f(100) :
-100<0
[tex]\begin{gathered} f(x)=4x+7 \\ f(-100)=4(-100)+7 \\ =-400+7 \\ =-393 \end{gathered}[/tex]100>0
[tex]\begin{gathered} f(x)=6x+4 \\ f(100)=6(100)+4 \\ =600+4 \\ =604 \end{gathered}[/tex][tex]\begin{gathered} f(-100)+f(100)=-393+604 \\ \\ =211 \end{gathered}[/tex]Final Answer:
[tex]\begin{gathered} f(-8)=-25 \\ \\ f(0)=4 \\ \\ f(4)=28 \\ \\ f(-100)+f(100)=211 \end{gathered}[/tex]