Function for which x -intercepts is at 4 and -6 is given by
y = k (x - 4)( x + 6).
As given in the question,
Let us consider f(x) be the required function.
y = f(x)
Standard form of a function whose x- intercepts is defined as x = a and
x = b is given by ;
f(x) = k (x - a ) ( x -b)
⇒ y = k (x - a ) ( x -b)
Where 'k' is constant which can be evaluate when quadratic function passes through point ( x₁ , y₁).
Here x - intercept is at 4 and -6
a = 4 and b = -6
Function for which x -intercepts is at 4 and -6 is given by :
y = k (x - 4) ( x -(-6))
⇒ y = k ( x - 4 ) ( x+ 6 )
Therefore, function for which x -intercepts is at 4 and -6 is given by
y = k (x - 4)( x + 6).
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The Florida Fish and Wildlife Conservation Commission is conducting a study on wildlife patterns and behaviors in a specific area of the Florida Everglades. A stationary camera is placed where the area being observed can be filmed and recorded for 96 hours. Researchers found that the footage revealed that the Cape Sable Seaside Sparrows were observed in the area once every 6 hours and the Florida Leafwing Butterfly was observed in the area once every 9 hours.
How many hours of footage would the observers need to review to see the Cape Sable seaside sparrow and the Florida leafwing butterfly in the area at the same time?
Number of Hours:
Answer:
18 hours of footage.
Step-by-step explanation:
This is a LCM problem. The least common multiple of 6 and 9 is 18. The minimum amount of hours needed to see the sparrow and butterfly at the same time is 18.
find the missing side of the right triangle.
Answer:
8
Step-by-step explanation:
a^2 + b^2 = c^2
4^2 + (4√3)^2 = c^2
16 + 48 = c^2
64 = c^2
√64 = c
8 = c
Determine whether f(x) = 1 − x is linear. If so, give the slope and y-intercept.
A. yes
slope = −1
y-intercept = 1
B. false
C. yes
slope = 1
y-intercept = −1
D. yes
slope = 1
y-intercept = 1
Answer:
a
Step-by-step explanation:
f(x) = y, so y=1-x. the slope is always infront of the x, so if there is nothing infront of x then it'll be a 1. so in this cas slope is a -1 and the y intercept is 1.
there is a line that includes the point (2,10) and has a slope of 8. what is its equation in slope intercept form?
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{10})\hspace{10em} \stackrel{slope}{m} ~=~ 8 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ 8}(x-\stackrel{x_1}{2}) \\\\\\ y-10=8x-16\implies {\Large \begin{array}{llll} y=8x-6 \end{array}}[/tex]
Use point-slope form to write the equation of a line that passes through the point (-7,-8) with slope -3/11
Answer:
y + 8 = -3/11(x+7)
Step-by-step explanation:
What is the point-slope form formula?
y-y1=m(x-x1) -------> y+8=-3/11(x+7)
The circumference of a circle is 47 cm. Find its radius, in centimeters.
Answer:
The radius (in centimeters) is 18.9999, or roughly 19 centimeters.
Step-by-step explanation:
If you need a step-by-step explanation, please let me know and I will help you. Thanks!
A worker ha 23 % of her weekly pay withheld for taxe, inurance, and a penion plan. If her weekly gro pay i 740 $, find her total withholding and net pay
Answer:
569.80
Step-by-step explanation:
Write an equation for the line in the slope-intercept form.
slope= 8/9, y-intercept=-4
A) f(x) = 9/8x +9/2
B) f(x) = -8/9x - 4
C) f(x) = 8/9x - 4
D) f(x) = -8/9x + 4
Answer:
C
Step-by-step explanation:
the equation of a line in slope- intercept form is
f(x) = mx + c ( m is the slope and c the y- intercept )
here m = [tex]\frac{8}{9}[/tex] and c = - 4 , then
f(x) = [tex]\frac{8}{9}[/tex] x - 4 ← equation of line
In a two-digit number, the units digit is 5 more than the tens digit. The number itself is three times the sum of its digits. What is this number?
Answer:
The number is 27.
Step-by-step explanation:
Since the units digit has to be 5 more than the tens digit, there are only four possible two-digit numbers which satisfy this condition. They are 16, 27, 38, and 49.
Next, the digits can be added and multiplied by three to check that the answer is the same two-digit number.
3 (1 + 6) = 21 does not work because 16 isn't the same as 21.
3 (2 + 7) = 27 does work because 3 * 9 is 27.
3 (3 + 8) = 33
3 (4 + 9) = 39
POPULATION The projected population in thousands for a city over the next several years can be estimated by the
function P(x)=x³ + 2x² - 8x + 520, where x is the number of years since 2005. Use synthetic substitution to estimate
the population for 2015.
O 1,640,000
O 1,320,000
O 590,000
O 36,240,000
The population for 2015 is 1,640,000 ,so option A is correct.
Given:
The projected population in thousands for a city over the next several years can be estimated by the function P(x)=x³ + 2x² - 8x + 520.
where x is the number of years since 2005.
x = 2015 - 2005
x = 10
P(x) = x³ + 2x² - 8x + 520.
= [tex]10^{3} +2(10^{2} )-8*10+520[/tex]
= 1000 + 2*100 - 80 + 520
= 1520 + 200 - 80
= 1720 - 80
= 1640.
Given the projected population in thousands so = 1640 * 1000
= 1640000.
Therefore The population for 2015 is 1,640,000 ,so option A is correct.
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Evaluate The Triple Integral. Triple Integral 7x2 DV, Where T Is The Solid Tetrahedron With Verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), And (0, 0, 1)
By evaluating The Triple Integral. Triple Integral 7x2 DV, Where T Is The Solid Tetrahedron With Verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), And (0, 0, 1) the value calculated is 7/60.
Given:
= ∫∫∫7[tex]x^{2}[/tex] dV
T(x,y,z) : 0≤x≤1; 0≤y≤1-x; 0≤z≤1-x-y]
apply limits and solving we get:
= 7/2([tex](x^{3} /3+x^{5} /5-x^{4}/2)[/tex]
= 7/2(1/3+1/5-1/2)
= 7/2(1*5+1*3/15 - 1/2)
= 7/2(8/15 - 1/2)
= 7/2(16 - 15/30)
= 7/2*1/30
= 7/60
Therefore after evaluating the value of triple integral is 7/60.
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1 What is the cost to get into a Green Cab?
2 How much does it cost per mile for a Green Cab?
3 What is the equation, in slope-intercept form, that relates the cost compared to the miles traveled for a Green Cab?
Answer:
1. $5
2. $1 per mile
3.y=x+5
Step-by-step explanation:
1. If you look at the graph you can see that the cost for 0 miles with the Green Cab is $5
2.If you look at the graph, for each mile traveled, the cost is $1
3. Since for each increase 1 increase in x, y increases by the same amount, the slope is 1
y=mx+b is the slope intercept form
m=slope
b=y intercept
since we know the slope is 1 we can put it in
y=1x+b
=y=x+b
to find the y intercept we can look at the graph and see what y equals when x is 0.
the y intercept is (0,5)
we can put that in so the equation in slope intercept form is
y=x+5
(r, 3), (5, 9), m=2 what is the answer
The value of the unknown variable in the ordered pair is 8
How to determine the value of the unknown variable in the ordered pair?From the question, we have the following ordered pairs that can be used in our computation:
(r, 3), (5, 9)
Also, we have
m = 2
The meaning of the above notations are
Ordered pairs (x, y) = (r, 3), (5, 9)
Slope, m = 2
The slope of points is calculated using the following slope equation
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (r, 3), (5, 9) and m = 2
Substitute the known values in the above equation, so, we have the following representation
(9 - 3)/(r - 5) = 2
Evaluate the difference
This gives
6/(r - 5) = 2
Divide both sides by 2
So, we have
3/(r - 5) = 1
Cross multiply
r - 5 = 3
So, we have
r = 3 + 5
Evaluate the sum
r = 8
Hence, the value of r is 8
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Possible question
What is the value of r using the following points and slope
(r, 3), (5, 9), m=2
Vickie Ewing deposits her savings of $2800 in an investment paying 6% ompounded quarterly and she leaves it there for 5 years. Find (a) the compound amount nd (b) the interest.
The compound amount with the compound quarterly will be $3771.19 and the equivalent annual interest rate will be 6.1363%.
What is compound interest?Compound interest is applicable when there will be a change in the principle amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
As per the given,
Principle amount P = $2800
Rate of interest = 6% = 0.06
Compound quarterly n = 4
Time period T = 5 yeras
a)
Total amount = P(1 + R/n)^(nT)
Total amount = 2800(1 + 0.06/4)^(4 x 5)
Total amount = 2800(1.015)^20
Total amount = $3771.19
b)
Let's say the equivalent annual interest rate is r.
n = 1
3771.19 = 2800(1 + r/1)^(1 x 5)
3771.19 = 2800(1 + r)^5
1.061 = 1 + r
r = 0.06136 = 6.136%
Hence"The compound amount with the compound quarterly will be $3771.19 and the equivalent annual interest rate will be 6.1363%".
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7.78, 7.8, 6.969, 7.7081 order these numbers from least to greatest
Make A the subject of the formula
One of the legs of a right triangle measures 3 cm and its hypotenuse measures 16 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
According to the Pythagoras theorem, the value of the other leg is, 15.7 cm
Pythagoras theorem:
Pythagoras theorem defines that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Given,
One of the legs of a right triangle measures 3 cm and its hypotenuse measures 16 cm.
Here we need to find the measure of the other leg and round off it to nearest tenth.
Though the given question, we know that the value of
Hypotenuse = 16 cm
one leg = 3cm,
Then let us consider the length of the other leg as x.
So, according to the Pythagoras theorem,
It can be calculated as,
=> hypotenuse² = one leg² + other leg²
=> 16² = 3² + x²
=> 256 = 9 + x²
Here we need the value of x, so it can be rewritten as,
=> 247 = x²
=> x = √247
When we take square root for 247, then we get the value of x as,
=> x = 15.716
When we round off it to the nearest tenth then we get the value of another leg as 15.7 cm.
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In the given figure, the reflex angle DOB measures 3.5y and AOD measures Y. Find the measures of the non reflex DOB in degrees.
The measure of non reflex angle DOB in degrees is 140°
Calculating the measure of an angleFrom the given information, we are to determine the measure of the non reflex angle DOB
From the given information,
m reflex ∠ DOB = 3.5y
and
m ∠ AOD = y
First, we will determine the value of y
From Linear pair theorem, we can write that
3.5y + y = 180°
4.5y = 180°
y = 180°/4.5
y = 40°
Also,
y + m ∠ DOB = 180° (Linear pair theorem)
Thus,
40° + m ∠ DOB = 180°
m ∠ DOB = 180° - 40°
m ∠ DOB = 140°
Hence, the measure of ∠ DOB is 140°
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Last year, Dan opened an investment account with $7800. At the end of the year, the amount in the account had increased by 29.5%. How much is this increase
In dollars? How much money was in his account at the end of last year?
Answer:
10,101
Step-by-step explanation:
Percent (%) means 'out of one hundred'
29.5%= 29.5/100 'out of one hundred'
----------------------------------------------------------------------
How to increase the number 7,800
by 29.5% of it's value?
1.) Calculate the new value of the number increased by the percentage of it's initial value
The new value=
7,800+ The value of the percentage increase=
7,800 + (29.5% x 7,800) =
7,800 + 29.5% x 7,800=
(1 + 29.5%) x 7,800=
(100% + 29.5%) x 7,800=
129.5% x 7,800
129.5 ÷ 100 x 7,800=
129.5 x 7,800 ÷ 100=
1,010,100 ÷ 100=
10,101
-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-
I hope this was helpful!
Cross multiply the numbers
Answer:
2m/4m = 9m/xm
2m(xm) = 4m(9m)
2xm = 36m
A parabola can be drawn given a focus of
(-8, 1) and a directrix of y=-1. What
can be said about the parabola?
The parabola has a vertex at
( , ) has a p-value of ( )
and it
We can say about the parabola given a focus of (-8, 1) and a directrix of y = -1 is as:
The parabola is a vertical parabola and facing up.The vertex of the parabola is v(-8, 0).p value of the parabola is 1.A parabola refers to the shape that traces the equation of the form ax² + bx + c.
A parabola's directrix is a vertical or horizontal line that never contacts the parabola and is located at p distance from the vertex and 2p distance from the focus.
The parabola created when the directrix is on the y coordinate called a vertical parabola.
If the directrix value is greater than the corresponding focus or vertex, there will be a negative p and the parabola will face downhill.
If the directrix value is less than the corresponding focus or vertex, there will be positive p and the parabola will face up.
From the given definition of the directrix, we can find the value of p;
2p = y coordinate of focus - equation of the directrix
2p = 1 - (-1)
2p = 2
p = 1
Vertex, v(h, k) compared with f(h, k + p), we will get;
k + p = 1
k = 0
Therefore, the vertex is (-8, 0).
Thus, we can say about the parabola given a focus of (-8, 1) and a directrix of y = -1 is as:
The parabola is a vertical parabola and facing down.The vertex of the parabola is v(-8, 0).p value of the parabola is 1.To learn more about directrix of a parabola visit:
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Can someone pleaseeee solve this for me?
Answer:26
Step-by-step explanation:
Open-Ended Write an equation for the line in slope-intercept form. Use pencil and paper. Which part of writing
the equation is the most difficult? The easiest? Explain.
(Use integers or fractions for any numbers in the equation.)
The equation of the line in slope-intercept form is y = -5x
How to determine the equation of a line into slope-intercept form?From the question, we have the graph that can be used in our computation
On the graph, we have the following points
(0, 0) and (-1, -5)
Start by calculating the slope using
Slope = (y₂ - y₁)/(x₂ - x₁)
Where,
(x, y) = (0, 0) and (1, -5)
So, we have
Slope = (-5 - 0)/(1 - 0)
This gives
Slope = -5
The equation of the line is then calculated as
y= Slope * (x - X) + Y
So, we have
y = -5 * (x - 0) + 0
Evaluate
y = -5x
Hence, the equation is y = -5x
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Write the standard form of the line that passes through the given points using the steps below. Include your work for each step in your final answer. Type your answer in the box provided to submit your solution.
(6, 1) and (5, 4)
a) Using variables, write out the formula for the standard form of the equation.
b) Determine the slope of the line.
c) Write the point-slope form of the line.
d) Using the properties of algebra, rearrange the equation into the standard form.
a) The general equation is:
y = m*(x - h) + k
b) The slope is -3
c) the point-slope form is: y = -3*(x - 6) + 1
d) The standard form is: y + 3x = 19
How to get the equation for the line?We will write a linear equation that relates two variables x and y, and the slope-point form is given by:
y = m*(x - h) + k
Where m is the slope, and (h, k) is a point on the line.
Particularly, if a line passes through two points (a, b) and (c, d), then the slope of that line is:
m = (d - b)/(c - a)
In this case, the line passes through (6, 1) and (5, 4), then the slope is:
m = (4 - 1)/(5 - 6) = 3/-1 = -3
Now we can use one of the given points to write the line in the point-slope form, I will use (6, 1) to get:
y = -3*(x - 6) + 1
Now we want to write this in standard form.
Expanding the right side we get:
y = -3x + 18 + 1
y = -3x + 19
Adding 3x in both sides we get:
y + 3x = 19
This is the standard form.
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graph the function f(x) = 1/3x + 1 and the function g(x) = f(6x)
PLEASE HELP!! (add picture of graph, or give formula
Graph of the given function f(x) = ( 1 / 3 )x + 1 and g ( x ) = f ( 6x ) is attached for the different values of x and y. Graph of both the function f(x) and g(x) intersect at point ( 0, 1 ).
As given in the question,
Given function are as follow:
f(x) = ( 1 / 3 )x + 1
g ( x ) = f ( 6x )
Calculate the function g(x) for f ( 6x ) is given by,
g ( x ) = f ( 6x )
⇒ g ( x ) = ( 1 / 3 )6x + 1
⇒ g ( x ) = 2x + 1
Substitute the value of x to get value of f ( x ) and g ( x ) and put it on graph.
After putting all the values of f(x) and g(x) .
Graph intersect at ( 0, 1 )
Graph is attached.
Therefore, graph of the given function f(x) = ( 1 / 3 )x + 1 and g ( x ) = f (6x ) is attached for the different values of x and y. Graph of both the function f(x) and g(x) intersect at point ( 0, 1 ).
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0.75(8+e)=2−1.25e slove for E
The value of 'E' in the algebraic equation is -2
What is algebraic equation?Algebraic equation is a mathematical statement in which two expressions are set equal to each other.
Therefore, let solve for 'E' in the equation 0.75(8+e)=2−1.25e
Use 0.75 to open the bracket
6 + 0.75e = 2 -1.25e
Collect the like terms
0.75e+1.25e = 2-6
2e = -4
Divide both sides by 2
2e/ 2 = -4/2
e =-2
Therefore, the value of 'E' in the equation is -2
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In a circle, an angle measuring 9.3 radians intercepts an arc of length 19.1. Find the
radius of the circle to the nearest 10th.
The radius of the circle to the nearest 10th is 2.0537.
Given:
In a circle, an angle measuring 9.3 radians intercepts an arc of length 19.1.
we know that,
radians = arc / radius
radius = arc/radians
= 19.1/9.3
= 191/10/93/10
= 191/93
≈ 2.0537
Therefore the radius of the circle to the nearest 10th is 2.0537.
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A flagpole casts a shadow 18m long when the athlete of the sun is 54°. What is the height of the flagpole.
If flagpole casts a shadow 18m long when the angle of elevation of the sun is 54° then the height of the flagpole will be 24.8 m .
In the question ,
it is given that ,
the length of the shadow of the flag pole = 18m
the angle of "elevation" of the sun = 54°
let the height of the flagpole be = "x" ,
The flagpole and the shadow form a right triangle ,
So , tan(54°) = (height of flag pole)/(shadow of flagpole)
Substituting the values from above ,
we get ,
tan(54°) = x/18
on cross multiplication ,
x = 18 × tan(54°)
x = 18 × 1.3763
x = 24.7734
x ≈ 24.8
Therefore , If flagpole casts a shadow 18m long when the angle of elevation of the sun is 54° then the height of the flagpole will be 24.8 m .
The given question is incomplete , the complete question is
A flagpole casts a shadow 18m long when the angle of elevation of the sun is 54°. What is the height of the flagpole ?
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You work a basic week of 40 hours and your basic rate is $19.50 per hour. What is your basic wage for the week and showing working for this question.
If you work $19.50 per hour and you work 40 hours a week, you need to multiply 19.50 by 40 to get your answer
19.50 x 40 = $ 780 a week.
I hope this helps!
what is 1/3 plus 4.1 in simplest form written as a mixed number