A line has the given slope m and passes through the first point listed in the table. Complete the table so that each point on the table lies on the line.
Answers
A line can be written as an equation in the slope-intercept form:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
We know the slope:
[tex]m=3[/tex]The y-intercept is the y value of the graph where it intercepts the y-axis, which happens when x = 0.
We know that the point x = 0 and y = 3 is on the line and, since the value of x is 0. the y value is the y-interceot, so:
[tex]b=3[/tex]Thus, we have the equation:
[tex]y=3x+3[/tex]To calculate the other points, we just need to substitute their x values and get their y values:
x = 1:
[tex]y=3\cdot1+3=3+3=6[/tex]So, when x = 1, y = 6
x = 2:
[tex]y=3\cdot2+3=6+3=9[/tex]So, when x = 2, y = 9.
x = 3:
[tex]y=3\cdot3+3=9+3=12[/tex]So, when x = 3, y = 12;
So, the complete table is:
x | 0 | 1 | 2 | 3
y | 3 | 6 | 9 | 12
Related Questions
Draw the angle 0=-pi/2 in standard position find the sin and cos
Answers
An angle in standard position has the vertex at the origin and the initial side is on the positive x-axis.
Thus, the initial side of the angle is:
Now, half the circumference measures pi, thus, pi/2 is a quarte of the circumference. As we want to find the angle -pi/2, then we need to rotate the terminal side clockwise:
Find the sine and the cosine.
The sine and the cosine in the unit circle are given by the coordinates as follows:
[tex](\cos\theta,\sin\theta)[/tex]As can be seen in the given unit circle, the terminal side is located at:
[tex](0,-1)[/tex]Thus, the values of cosine and sine are:
[tex]\begin{gathered} \cos\theta=0 \\ \sin\theta=-1 \end{gathered}[/tex]The table shows a function. Is the function linear or nonlinear?x y0 1918 1200
Answers
By plotting the points, we get a non-linear function
Give the following numberin Base 2.7710 = [ ? ] 2Enter the number that belongs in the green box.
Answers
To convert a number on base 10 to binary(base 2), we use the following steps
1 - Divide the number by 2.
2 - Get the integer quotient for the next iteration.
3 - Get the remainder for the binary digit.
4 - Repeat the steps until the quotient is equal to 0.
Using this process in our number, we have
Then, we have our result
[tex]77_{10}=1001101_2[/tex]A car is traveling at a speed of 70 kilometers per hour. What is the car's speed in miles per hour? How many miles will the car travel in 5 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
Answers
What is the car's speed in miles per hour?
Let's make a conversion:
[tex]\frac{70\operatorname{km}}{h}\times\frac{1mi}{1.6\operatorname{km}}=\frac{43.75mi}{h}[/tex]How many miles will the car travel in 5 hours?
1h---------------------->43.75mi
5h---------------------> x mi
[tex]\begin{gathered} \frac{1}{5}=\frac{43.75}{x} \\ x=5\times43.75 \\ x=218.75mi \end{gathered}[/tex](statistics) solve part A, B, and C in the question on the picture provide, in 1-3 complete sentences each.
Answers
(a.) First let's define the terms;
Population - it is the pool of individual in which a statistical sample is drawn.
Parameter - it is a measure of quantity that summarizes or describes a Population.
Sample - is a smaller and more managable version of a group or population.
Statistics - same with parameter but rather than the population, it summarizes or describes
the sample.
Now that we know the definitions we can now answe the letter a;
Population: Students
Parameter: the population portion of the new students that like the new healthy choices (p)
Sample: 150 students
Statistics: estimated propotion of the students that like the new healthy choices (p-hat)
(b) P-hat = 0.6267 simply means that 62.67% of the 150 sample students like the new healthy choices.
(c) The answer for that is NO, because the simulated propotion which is shown by the graph seems to be equally distributed below and above 0.7. To support the claim of the manager most of the dots should be below 0.7 to show support to his claim that 70% of the new students like the new healthy choices.
For the quadratic function, identify any horizontal or vertical translations. Enter "0" and "none" if there is none.f(x) = (x + 5)² - 4Horizontal:__ units to the (Select an answer (right, left, none)Vertical:__ units to the (Select an answer ( up, down, none)
Answers
Given:
[tex]f(x)=(x+5)^2-4[/tex]The parent function of the given function (x²)
We will find the horizontal or vertical translations to get the given function.
the general form of the translation will be as follows:
[tex]f(x\pm a)\pm b[/tex]Where (a) is the horizontal translation and (b) is the vertical translation
Comparing the given equation to the formula:
[tex]a=5,b=-4[/tex]So, the answer will be:
Horizontal: 5 units to the left
Vertical: 4 units down
Find the zero for the polynomial function and give the multiplicity for each zero. State whether the graph crosses to x axis or touch the x axis and turn around, at each zero.
Answers
we have the function
f(x)=2(x-6)(x-7)^2
REmember that the zeros of the function are the values of x when the value of the function is equal to zero
In this problem
the zeros of the function are
x=6 -------> multiplicity 1 (the graph crosses to x axis)
x=7 ----- multiplicity 2 (touch the x axis and turn around)
see the attached figure to better understand the problem
Sam goes to a fast food restaurant and orders some tacos and burritos. He sees on the nutrition menu that tacos are 250 calories and burritos are 330 calories. If he ordered 4 items and consumed a total of 1080 calories, how many tacos, and how many burritos did Sam order and eat?
Answers
Let x represent the number of tacos that Sam ordered and ate.
Let y represent the number of burritos that Sam ordered and ate.
From the information given, If he ordered 4 items, it means that
x + y = 4
If tacos are 250 calories, it means that the number of calories in x tacos is 250 * x = 250x
If burritos are 330 calories, it means that the number of calories in y burritos is 330 * y = 330y
If he consumed a total of 1080 calories, it means that
250x + 330y = 1080
From the first equation, x = 4 - y
By substituting x = 4 - y into the second equation, we have
250(4 - y) + 330y = 1080
1000 - 250y + 330y = 1080
- 250y + 330y = 1080 - 1000
80y = 80
y = 80/80
y = 1
x = 4 - y = 4 - 1
x = 3
Thus, Sam ordered and ate 3 tacos and 1 burritos
help meeeeeeeeee pleaseee !!!!!
Answers
The values of the functions are;
a. (f + g)(x) = x( 2 + 3x)
b. (f - g)(x) = 2x - 3x²
c. (f. g) (x) = 6x²
d. (f/g)(x) = 2/ 3x
What is a function?A function can be defined as an expression, rule, law or theorem that explains the relationship between two variables in a given expression
These variables are called;
The independent variablesThe dependent variablesFrom the information given, we have;
f(x) = 2xg(x) = 3x²To determine the composite functions, we have;
a. (f + g)(x)
Add the functions
(f + g)(x) = 2x + 3x²
Factorize the functions
(f + g)(x) = x( 2 + 3x)
b. (f - g) (x)
Subtract the functions
(f - g)(x) = 2x - 3x²
c. (f. g) (x)
Substitute the values of x as g(x) in f(x)
(f. g) (x) = 2(3x²)
(f. g) (x) = 6x²
d. (f/g)(x) = 2x/ 3x²
(f/g)(x) = 2/ 3x
Hence, the functions are determined by substituting the values of the dependent variables.
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if Maria collected R rocks and Javy collected twice as many rocks as Maria and Pablo collected 5 less than Javy. What is the sum of rocks collected by Pablo and Maria?
Answers
This problem deals with the numbers expressed in a more general way: letters or variables
That belongs to Algebra
We know Maria collected R rocks. Let's put this in a separate line:
M = R
Where M is meant to be the number of rocks collected by Maria
Now we also know Javy collected twice as many rocks as Maria did. Thus, if J is that variable, we know that
J = 2R
Pablo collected 5 less rocks than Javy. This is expressed as
P = J - 5
or equivalently:
P = 2R - 5
since J = 2R, as we already stated
We are now required to calculate the sum of rocks collected by Pablo and Maria.
This is done by adding P + M:
P + M = (2R - 5) + (R)
We have used parentheses to indicate we are replacing variables for their equivalent expressions
Now, simplify the expression:
P + M = 2R - 5 + R
We collect the same letters by adding their coefficients:
P + M = 3R - 5
Answer: Pablo and Maria collected 3R - 5 rocks together
Find the minimum or maximum value of the function f(x)=8x2+x−5. Give your answer as a fraction.
Answers
Answer
Minimum value of the function = (-41/8)
Explanation
The minimum or maximum of a function occurs at the turning point of the graph of the function.
At this turning point, the first derivative of the function is 0.
The second derivative of the function is positive when the function is at minimum and it is negative when the function is at maximum.
f(x) = 8x² + 2x - 5
(df/dx) = 16x + 2
At minimum or maximum point,
16x + 2 = 0
16x = -2
Divide both sides by 16
(16x/16) = (-2/16)
x = (-1/8)
Second derivative
f(x) = 8x² + 2x - 5
(df/dx) = 16x + 2
(df²/d²x) = 16 > 0, that is, positive.
So, this point is a minimum point.
f(x) = 8x² + 2x - 5
f(-1/8) = 8(-1/8)² + 2(-1/8) - 5
= 8 (1/64) - (1/4) - 5
= (1/8) - (1/4) - 5
= (1/8) - (2/8) - (40/8)
= (1 - 2 - 40)/8
= (-41/8)
Hope this Helps!!!
The revenue function R in terms of the number of units sold, a, is given as R = 300x - 0.4x^2where R is the total revenue in dollars. Find the number of units sold a that produces a maximum revenue?Your answer is x =What is the maximum revenue?
Answers
1) Considering the Revenue function in the standard form:
[tex]R(x)=-0.4x^2+300x[/tex]2) Since this is a quadratic function, we can write out the Vertex of this function:
[tex]\begin{gathered} x=h=-\frac{b}{2a}=\frac{-300}{2(-0.4)}=375 \\ k=f(375)=-0.4(375)^2+300(375)\Rightarrow k=56250 \end{gathered}[/tex]3) So, we can answer this way:
[tex]x=375\:units\:yield\:\$56,250[/tex]Write an equation that represents a reflection in the y-axis of the graph of g(x)=|x|.
h(x)= ?
Answers
the reflection of the function g(x)=|x| in the y-axis will be h(x) = |x|
What is reflection in coordinate geometry ?
this represents the flip or mirror image of transformation about the given axis.
For every point in the plane (x, y), a 90° rotation can be described by the transformation P(x, y) → P'(-y, x). We can achieve this same transformation by performing two reflections.
Here, the given function is :
g(x)=|x|
Now, the reflection in the y-axis will be same that is :
h(x)= g(x)
h(x) = |x|
Therefore, the reflection of the function g(x)=|x| in the y-axis will be h(x) = |x|
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TWENTY POINTS//WILL MARK BRAINLIEST
Marty graphs the hyperbola (y+2)236−(x+5)264=1 .
How does he proceed?
Drag a value, phrase, equation, or coordinates in the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Marty first identifies the center of the hyperbola as Response area, and that the hyperbola opens Response area. Since a = Response area, the coordinates of the vertices are Response area.
The slopes of the asymptotes of this parabola are ± Response area, and the asymptotes pass through the center of the hyperbola. The equations of the asymptotes are Response area.
Once this information is gathered, the asymptotes are graphed as dashed lines, and the hyperbola is drawn through the vertices, approaching the asymptotes.
Answers
The procedure to construct the graph of the hyperbola is described as follows:
Marty first identifies the center of the hyperbola as (-5,2), and that the hyperbola opens up and down. Since a = 6, the coordinates of the vertices are (-5, -4) and (-5, 8).The slopes of the asymptotes of this parabola are a = ± 3/4, and the asymptotes pass through the center of the hyperbola. The equations of the asymptotes are y - 2 = ± 3/4(x + 5).Hyperbola equation and graphThe equation of a vertical hyperbola with center (x*, y*) is given according to the equation presented as follows:
(y - y*)²/a² - (x - x*)²/b² = 1.
This means that the hyperbola opens up vertically, up and down.
The equation of the hyperbola in this problem is given as follows:
(y + 2)²/36 - (x + 5)²/64 = 1.
Thus the coordinates of the center are given as follows:
(-5, 2).
The numeric value of coefficient a is calculated as follows:
a² = 36 -> a = 6.
Meaning that the coordinates of the vertices of the hyperbola are given as follows:
(-5, 2 - 6) = (-5,-4).(-5, 2 + 6) = (-5,8).The slopes of the asymptotes of the parabola are given according to the rule presented as follows:
±a/b.
The coefficient b is calculated as follows:
b² = 64 -> b = 8.
Hence:
a/b = 6/8 = 3/4.-a/b = -6/8 = -3/4.Since the asymptotes pass through the center, the equation is:
y - 2 = ± 3/4(x + 5).
The graph is given by the image at the end of the answer.
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How long will it take money to double if it is invested at the following rates?(A) 7.8% compounded weekly(B) 13% compounded weekly(A) years(Round to two decimal places as needed.)
Answers
Answer:
Explanation:
A) We'll use the below compound interest formula to solve the given problem;
[tex]A=P(1+r)^t[/tex]where P = principal (starting) amount
A = future amount = 2P
t = number of years
r = interest rate in decimal = 7.8% = 7.8/100 = 0.078
Since the interest is compounded weekly, then r = 0.078/52 = 0.0015
Let's go ahead and substitute the above values into the formula and solve for t;
[tex]\begin{gathered} 2P=P(1+0.0015)^t \\ \frac{2P}{P}=(1.0015)^t \\ 2=(1.0015)^t \end{gathered}[/tex]Let's now take the natural log of both sides;
[tex]\begin{gathered} \ln 2=\ln (1.0015)^t \\ \ln 2=t\cdot\ln (1.0015) \\ t=\frac{\ln 2}{\ln (1.0015)} \\ t=462.44\text{ w}eeks \\ t\approx\frac{462.55}{52}=8.89\text{ years} \end{gathered}[/tex]We can see that it will take 8.89 years for
B) when r = 13% = 13/100 = 0.13
Since the interest is compounded weekly, then r = 0.13/52 = 0.0025
Let's go ahead and substitute the values into the formula and solve for t;
[tex]\begin{gathered} 2P=P(1+0.0025)^t \\ \frac{2P}{P}=(1.0025)^t \\ 2=(1.0025)^t \end{gathered}[/tex]Let's now take the natural log of both sides;
[tex]\begin{gathered} \ln 2=\ln (1.0025)^t \\ \ln 2=t\cdot\ln (1.0025) \\ t=\frac{\ln 2}{\ln (1.0025)} \\ t=277.60\text{ w}eeks \\ t\approx\frac{2.77.60}{52}=5.34\text{ years} \end{gathered}[/tex]
A line passes through the points (7,9) and (10,1). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answers
Answer:
[tex](y - 9) = (-8/3)\, (x - 7)[/tex].
Step-by-step explanation:
If a line in a cartesian plane has slope [tex]m[/tex], and the point [tex](x_{0},\, y_{0})[/tex] is on this line, then the point-slope equation of this line will be [tex](y - y_{0}) = m\, (x - x_{0})[/tex].
The slope of a line measures the rate of change in [tex]y[/tex]-coordinates relative to the change in the [tex]x[/tex]-coordinates. If a line goes through two points [tex](x_{0},\, y_{0})[/tex] and [tex](x_{1},\, y_{1})[/tex], the slope of that line will be:
[tex]\begin{aligned}m &= \frac{y_{1} - y_{0}}{x_{1} - x_{0}}\end{aligned}[/tex].
In this question, the two points on this line are [tex](7,\, 9)[/tex] and [tex](10,\, 1)[/tex], such that [tex]x_{0} = 7[/tex], [tex]y_{0} = 9[/tex], [tex]x_{1} = 10[/tex], and [tex]y_{1} = 1[/tex]. Substitute these values into the equation to find the slope of this line:
[tex]\begin{aligned}m &= \frac{y_{1} - y_{0}}{x_{1} - x_{0}} \\ &= \frac{1 - 9}{10 - 7} \\ &= \left(-\frac{8}{3}\right)\end{aligned}[/tex].
With the point [tex](7,\, 9)[/tex] as the specific point [tex](x_{0},\, y_{0})[/tex] (such that [tex]x_{0} = 7[/tex] and [tex]y_{0} = 1[/tex]) as well as a slope of [tex]m = (-8 / 3)[/tex], the point-slope equation of this line will be:
[tex]y - y_{0} = m\, (x - x_{0})[/tex].
[tex]\displaystyle y - 9 = \left(-\frac{8}{3}\right)\, (x - 7)[/tex].
help meeeeeeeeee pleaseee !!!!!
Answers
The addition of the given functions f(x) and g(x) is equal to the expression x^2+ 3x + 5
Composite function.Function composition is an operation that takes two functions, f and g, and creates a function, h, that is equal to g and f, such that h(x) = g.
Given the following functions
f(x) = x^2 + 5
g(x) = 3x
We are to determine the sum of both functions as shown;
(f+g)(x) = f(x) + g(x)
Substitute the given functions into the formula
(f+g)(x) = x^2+5 + 3x
Write the expression in standard form;
(f+g)(x) = x^2+ 3x + 5
Hence the sum of the functions f(x) and g(x) is equivalent to x^2+ 3x + 5
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I need help with this
Answers
Express $20.35 as an equation of working h hours, when I equals income
Answers
Let
I ------> income in dollars
h -----> number of hours
$20.35 is the hourly pay
so
the linear equation that represent this situation is
I=20.35*hWrite the slope-intercept form of the equation of the line graphed on the coordinate plane.
Answers
The slope-intercept form is:
[tex]y\text{ = mx + b}[/tex]We have to find these coefficients. To do that we have to choose two points in the graph and apply the following formula. I will use (0,1) and (-1,-1). The formula is:
[tex]y-yo\text{ = m(x-xo)}[/tex]The formula of the coefficient 'm' is:
[tex]m\text{ = }\frac{y2-y1}{x2-x1}[/tex]Let's substitute the points into the formula above to find the value of m. Then we use one of the points to find the slope-intercept form of the equation:
[tex]m\text{ = }\frac{-1-1}{-1-0}=2[/tex]Applying it to the second equation using the point (0,1):
[tex]y-1=2(x-0)[/tex][tex]y=2x+1[/tex]Answer: The slope-intercept form of the equation will be 2x+1.
Which of the following points is in the solution set of y < x2 - 2x - 8? O 1-2. -1) O 10.-2) 0 (4.0)
Answers
Given the functon
[tex]yExplanation
To find the points that lie in the solution set we will lot the graph of the function and indicate the ordered pirs.
From the above, we can see that the right option is
Answer: Option 1
Write the equation for a parabola with a focus at (1,2) and a directrix at y=6
Answers
Solution:
Given:
[tex]\begin{gathered} focus=(1,2) \\ directrix,y=6 \end{gathered}[/tex]Step 1:
The equation of a parabola is given below as
[tex]\begin{gathered} y=\frac{1}{4(f-k)}(x-h)^2+k \\ (h,f)=focus \\ h=1,f=2 \end{gathered}[/tex]Step 2:
The distance from the focus to the vertex is equal to the distance from the vertex to the directrix:
[tex]\begin{gathered} f-k=k-6 \\ 2-k=k-6 \\ 2k=2+6 \\ 2k=8 \\ \frac{2k}{2}=\frac{8}{2} \\ k=4 \end{gathered}[/tex]Step 3:
Substitute the values in the general equation of a parabola, we will have
[tex]\begin{gathered} y=\frac{1}{4(f-k)}(x-h)^{2}+k \\ y=\frac{1}{4(2-4)}(x-1)^2+4 \\ y=-\frac{1}{8}(x-1)^2+4 \\ \end{gathered}[/tex]By expanding, we will have
[tex]\begin{gathered} y=-\frac{1}{8}(x-1)^{2}+4 \\ y=-\frac{1}{8}(x-1)(x-1)+4 \\ y=-\frac{1}{8}(x^2-x-x+1)+4 \\ y=-\frac{1}{8}(x^2-2x+1)+4 \\ y=-\frac{x^2}{8}+\frac{x}{4}-\frac{1}{8}+4 \\ y=-\frac{x^2}{8}+\frac{x}{4}-\frac{1+32}{8} \\ y=-\frac{x^2}{8}+\frac{x}{4}+\frac{31}{8} \end{gathered}[/tex]Hence,
The final answer is
[tex]\begin{gathered} \Rightarrow y=-\frac{x^{2}}{8}+\frac{x}{4}+\frac{31}{8}(standard\text{ }form) \\ \Rightarrow y=-\frac{1}{8}(x-1)^2+4(vertex\text{ }form) \end{gathered}[/tex]The Leaning Tower of Pisa
was completed in 1372 and
makes an 86* angle with
the ground. The tower is
about 57 meters tall, measured
vertically from the ground
to its highest point. If you
were to climb to the top and
then accidently drop your
keys, where would you
start looking for them?
How far from the base of.
the tower would they land?
Answers
The distance where the keys would drop from the base is 3.5m
Calculation far from the base of tower?Height of the tower = 57m
Angle it makes to the ground = 86°
To solve this question, you have to understand that the tower isn't vertically upright and the height of the tower is different from the distance from the top of the tower to the ground.
The tower makes an angle 86° to the ground and that makes it not vertically straight because a vertically straight building is at 90° to the ground.
The distance from where the keys drop to the base of the tower can be calculated using
We have to use cosθ = adjacent / hypothenus
θ = 86°
Adjacent = ? = x
Hypothenus = 57m
Cos θ = x / hyp
Cos 86 = x / 57
X = 57 × cos 86
X = 57× 0.06976
X = 3.97 = 4m
The keys would fall from the tower's base at a distance of about 4 meters.
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Which is equal to 2 over 5? A. 2%B. 2.5%C. 20%D. 25%E. 40%
Answers
Calculating the value of 2 over 5 in percentage, we have:
[tex]\begin{gathered} \frac{2}{5}=\frac{20}{50}=\frac{40}{100}=40\text{\%} \\ or \\ \frac{2}{5}=0.4=40\text{\%} \end{gathered}[/tex]So the correct option is E.
Finding the area of unusual shapes
Answers
The shape in question is a composite shape.
It comprises two(2) shapes which are a triangle and a semi-circle.
The area of the shape is the sum of the area of the triangle and that of the semi-circle
The area of the triangle is:
[tex]A_{triangle}=\frac{1}{2}\times base\times height[/tex][tex]\begin{gathered} \text{Base of the triangle =}6\text{ yard} \\ Height\text{ of the triangle= 4 yard} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} A_{triangle}=\frac{1}{2}\times6\times4 \\ A_{triangle}=12\text{ yards} \end{gathered}[/tex]Area of the Semi-circle is:
[tex]A_{semi-circle}=\frac{\pi\times r^2}{2}[/tex][tex]\begin{gathered} \text{Diameter of the circle=6 yard} \\ \text{Radius}=\frac{Diameter}{2} \\ \text{Radius}=\frac{6}{2}=3\text{ yard} \end{gathered}[/tex][tex]\begin{gathered} A_{semi-circle}=\frac{3.14\times3^2}{2} \\ A_{semi-circle}=\frac{28.26}{2} \\ A_{semi-circle}=14.13\text{ yard} \end{gathered}[/tex]Hence, the area of the composite shape is:
[tex]\begin{gathered} \text{Area of the triangle + Area of the semi-circle} \\ 12+14.13=26.13\text{ yard} \end{gathered}[/tex]45 + 54 = 99 times ( ) + ( )
Answers
a) You have to find the greatest common factor for the values 45 and 54
To do so you have to determine the factors for each value and determine the highest value both numbers are divisible for.
Factors of 45 are
1, 3, 5, 9, 15, 45
Factors of 54 are
1, 2, 3, 6, 9, 18, 27, 54
The greatest common factor is 9, this means that you can divide both numbers by 9 and the result will be an integer:
[tex]\frac{45}{9}=5[/tex][tex]\frac{54}{9}=6[/tex]b) Given the addition
[tex]45+54[/tex]You have to factorize the adition using the common factor.
That is to "take out" the 9 of the addition, i.e. divide 45 and 54 by 9 and you get the result (5+6) but for this result to be equvalent to the original calculation, you have to multiply it by 9
[tex]45+54=9(5+6)[/tex]For the bird, determine the following: The maximum height The axis of symmetry The total horizontal distance travelled A quadratic equation written in vertex form
Answers
Explanation:
The table of values is given below as
Using a graphing tool, we will have the parabola represented below as
Triangle LMN is drawn with vertices at L(−2, 1), M(2, 1), N(−2, 3). Determine the image vertices of L′M′N′ if the preimage is rotated 90° clockwise. L′(1, 2), M′(1, −2), N′(3, 2) L′(−1, 2), M′(−1, −2), N′(−3, 2) L′(−1, −2), M′(−1, 2), N′(−3, −2) L′(2, −1), M′(−2, −1), N′(2, −3)
Answers
ANSWER
L'(1, 2), M'(1, -2), N'(3, 2)
EXPLANATION
The rule for rotating a point (x, y) 90° clockwise is,
[tex](x,y)\rightarrow(y,-x)[/tex]So, the vertices of triangle LMN will be mapped to,
[tex]\begin{gathered} L(-2,1)\rightarrow L^{\prime}(1,2) \\ M(2,1)\rightarrow M^{\prime}(1,-2) \\ N(-2,3)\rightarrow N^{\prime}(3,2) \end{gathered}[/tex]Hence, the image has vertices L'(1, 2), M'(1, -2), N'(3, 2).
Question 11 5 pts Find the value of x. Round to the nearest tenth. х 329 12. Not drawn to scale a. 10.2 b. 14.3 C. 10.4 d. 14.2
Answers
Explanation
Step 1
Let
angle= 32
hypotenuse=x
adjacent side=12
so, we need a function that relates angel, hypotenuse and adjacent side
[tex]\text{cos}\emptyset=\frac{adjacent\text{ side}}{\text{hypotenuse}}[/tex]replace,
[tex]\begin{gathered} \text{cos}\emptyset=\frac{adjacent\text{ side}}{\text{hypotenuse}} \\ \text{cos32}=\frac{12}{\text{x}} \\ \text{Multiply both sides by x} \\ x\cdot\text{cos32}=\frac{12}{\text{x}}\cdot x \\ x\cdot\text{cos32}=12 \\ \text{divide both sides by cos 32} \\ \frac{x\cdot\text{cos32}}{\cos \text{ 32}}=\frac{12}{cos\text{ 32}} \\ x=14.15 \\ rounded \\ x=14.2 \end{gathered}[/tex]so, the answer is
[tex]d)x=14.2[/tex]I hope this helps you
Find the measurement of each side indicated and round to the nearest tenth for both triangles
Answers
a) We have a right triangle.
We have to find the value of x, which is the hypotenuse.
We can relate the angle B, the side AC and x with a trigonometric ratio as:
[tex]\begin{gathered} \sin (B)=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{AC}{AB} \\ \sin (57\degree)=\frac{10.8}{x} \\ x=\frac{10.8}{\sin (57\degree)} \\ x\approx\frac{10.8}{0.83867} \\ x\approx12.9 \end{gathered}[/tex]b) In this case, x is the adyacent side to angle A.
We can relate the sides and the angle as:
[tex]\begin{gathered} \cos (A)=\frac{\text{Adyacent}}{\text{Hypotenuse}}=\frac{AC}{AB} \\ \cos (47\degree)=\frac{x}{3} \\ x=3\cdot\cos (47\degree) \\ x\approx3\cdot0.682 \\ x\approx2.0 \end{gathered}[/tex]Answer:
a) x = 12.9
b) x = 2.0