Natural numbers are all numbers 1, 2, 3, 4… They are the numbers you usually count and they will continue on into infinity. This includes all numbers that can be written as a decimal.
Hence, 6.35 is a natural number. It is natural number, whole number, integer, and rational number.
May I please get help with describing each or the math problems
From the given traingles, let's select the correct statements.
(a) Select all that describe BD.
Here, the line BD divides angle B into 2 equal parts. It means BD bisects ∠D.
An angle bisector is a line that divides an angle into two equal angles.
Hence, we can say BD is an angle bisector of ∠B.
(b) Select all that describe HI.
Since m∠FIH is a right triangle, it means ∠HIG is also a right triangle.
Also, the line HI originates from the vertex.
Since. the it forms a right angle, we can say HJ is an altitude of the triangle FGH.
Hence, HJ is an altitude of ΔFGH.
(c) Select all that describe MN.
Here, we can see that line MN divides the line segment KL into two equal parts, it means that point M is the median of the line segment KM and the pperpendicular bisector of line segment KL.
A perpendicular bisector is a line segment that divides another line segement into two equal parts.
KM = LM
Hence, MN is the perpendicular bisector of KL.
ANSWER:
• (a) Angle bisector of ∠B.
,• (b) Altitude of ΔFGH.
,• (c) Perpendicular bisector of KL.
Write an equation that represents a reflection in the y-axis of the graph of g(x)=|x|.
h(x)= ?
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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I need help with this
Write the slope-intercept form of the equation of the line graphed on the coordinate plane.
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.
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.)
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]
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)
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
The table shows a function. Is the function linear or nonlinear?x y0 1918 1200
By plotting the points, we get a non-linear function
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?
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
(statistics) solve part A, B, and C in the question on the picture provide, in 1-3 complete sentences each.
(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.
45 + 54 = 99 times ( ) + ( )
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]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)
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).
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?
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
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
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
pleaseee help meeee For questions 9 - 10, answer the question about inverses. 9. The function m(d) below relates the miles Bob can drive his rental car and the numbers of dollars it will cost. 10. The function a(h) below relates the area of a triangle with a given base 7 and the height of the triangle. It takes as input the number of dollars spent and returns as output the number of miles. It takes as input the height of the triangle and returns as output the of the triangle. m(d) = 40(d- 35) ain= Write the equation that represents the inverse function, d(m), which takes the number of miles driven, m, as input and returns the number of dollars owed, d. Write the equation that represents inverse function, h(a), which takes triangle's area as input and returns height of the triangle.
First problem:
Find the inverse of the function
m = 40 (d - 35)
Recall that for the inverse function we need to solve for d in terms of m (reverse the dependence), so we proceed to isolate d on the right hand side of the equation:
divide both sides by 40
m/40 = d - 35
now add 35 to both sides:
m/40 + 35 = d
The inverse function (dollars in terms of miles) is given then by:
d(m) = 1/40 m + 35
Second problem:
a = 7 * h / 2
in order to find the inverse function (as h in terms of a) we solve for h on the right hand side of the equation as shown below:
multiply both sides by 2:
2 * a = 7 * h
now divide both sides by 7 in order to isolate h on the right
2 a / 7 = h
So our inverse function of height in terms of area is given by:
h(a) = (2 a) / 7
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
Explanation:
The table of values is given below as
Using a graphing tool, we will have the parabola represented below as
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.
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]Which is equal to 2 over 5? A. 2%B. 2.5%C. 20%D. 25%E. 40%
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.
help meeeeeeeeee pleaseee !!!!!
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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Draw the angle 0=-pi/2 in standard position find the sin and cos
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]Finding the area of unusual shapes
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]Express $20.35 as an equation of working h hours, when I equals income
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*hWhich of the following points is in the solution set of y < x2 - 2x - 8? O 1-2. -1) O 10.-2) 0 (4.0)
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
Give the following numberin Base 2.7710 = [ ? ] 2Enter the number that belongs in the green box.
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]Find the minimum or maximum value of the function f(x)=8x2+x−5. Give your answer as a fraction.
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 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?
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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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.
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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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.
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].
Write the equation for a parabola with a focus at (1,2) and a directrix at y=6
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 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?
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]help meeeeeeeeee pleaseee !!!!!
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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