x [tex]\geq[/tex] -9; x [tex]\leq[/tex] 6 or in interval notation [-9,6]
To find out what are the steps in solving the below inequality:
Given equation is 2x - 3 > 15
The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.
−15≤2x-3≤15
First, subtract 3 from each segment of the system of equations to isolate the x term while keeping the system balanced:
−15−3≤2x-3−3≤15−3
−18≤2x-6≤12
−18≤2x-6≤12
Now, divide each segment of the system by 2 to solve for x while keeping the system balanced:
[tex]-\frac{18}{2}\leq \frac{2x}{2} \leq \frac{12}{2}[/tex]
-9 [tex]\leq[/tex] x [tex]\leq[/tex] 6
or
x [tex]\geq[/tex] -9; x [tex]\leq[/tex] 6
or in interval notation [-9,6]
on the horizontal axis.
The lines will be a solid line because the inequality operators contain "or equal to" clauses.
We will shade between the lines to show the interval:
Hence the steps to solve an inequality has been show
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7.78, 7.8, 6.969, 7.7081 order these numbers from least to greatest
Find the amount (future value) of ordinary annuity $1000 a year for 10 years at 10%/year compounded annually.
a.
$15,500
b.
$15,937
c.
$16,456
d.
$16,845
The future value of ordinary annuity $1000 a year for 10 years at 10% year compounded annually is $15937.
The value of a sum of money that will be paid on a specified date in the future is known as its future value. Since each payment is made at the end of a period, the formula for the future value of an ordinary annuity refers to the value on a specified future date of a series of periodic payments.
Given,
R=$1000, n=10, i=10%=10/100=0.1
The formula to calculate the future value is
FV=R[(1+i)^n-1]/i
[tex]FV=R(\frac{(1+i)^{n} -1}{i})[/tex]
[tex]FV=1000(\frac{(1+0.1)^{10} -1}{0.1})[/tex]
[tex]FV=1000(\frac{(1.1)^{10} -1}{0.1})[/tex]
[tex]FV=1000(\frac{1.593742}{0.1})[/tex]
[tex]FV=1000\times15.9374[/tex]
[tex]FV=15937.4[/tex]
Future Value approximately equal to $15937.
Therefore, the future value of the ordinary annuity $100 a year for 10 years at 10% compounded annually is $15937, Option c is the correct answer.
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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
Convert to vertex form. State the vertex. f(x)=-3x^2+12x-7
The vertex form of the quadratic equation is f(x) = -3(x - 2)² + 5. The coordinates of the vertex are (2, 5).
We are given a quadratic function. The equation of the quadratic function is f(x) = -3x² + 12x - 7. We need to convert the equation to vertex form. We can convert a quadratic equation to its standard vertex form by "completing the square" method. The calculations are done below.
f(x) = -3x² + 12x - 7
f(x) = -3(x² - 4x) - 7
f(x) = -3(x² - 4x + 2² - 2²) - 7
f(x) = -3(x² - 4x + 2²) - 7 + 3*2²
f(x) = -3(x - 2)² - 7 + 12
f(x) = -3(x - 2)² + 5
The coordinates of the vertex are (2, 5).
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Make A the subject of the formula
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]
11. Choose the correct answer.
Which theorem or postulate could be used to prove the congruence of the triangles
log((4x)/(8))=log(x-5)
The given logarithmic equation solved for x is x = 10
Solving Logarithmic equationsFrom the question, we are to solve the given logarithmic equation.
The given logarithmic equation is
log((4x)/(8)) = log(x - 5)
To solve the given logarithmic equation, we will determine the value of the unknown variable.
The unknown variable in the equation is x.
From one of the rules of logarithm, we have that
If logₓY = logₓZ
Then,
Y = Z
Thus,
From log((4x)/(8)) = log(x - 5)
We can write that
(4x)/(8) = (x - 5)
Now, solve for x
(4x)/(8) = (x - 5)
Multiply both sides by 8
8 × (4x)/(8) = (x - 5) × 8
4x = 8x - 40
Subtract 8x from both sides of the equation
4x - 8x = 8x - 8x - 40
-4x = -40
Multiply both sides by -1
-1 × -4x = -1 × -40
4x =40
Divide both sides by 4
4x/4 = 40/4
x = 10
Hence, the solution of the equation is x = 10
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Can someone pleaseeee solve this for me?
Answer:26
Step-by-step explanation:
Given (x – 1)^2 = 50, select the values of x.
x = –49
x = 51
x = 1+5√2
x = 1-5√2
Answer:
[tex]x=1+5\sqrt{2}, 1-5\sqrt{2}[/tex]
Step-by-step explanation:
[tex](x-1)^2=50 \\ \\ x-1=\pm 5\sqrt{2} \\ \\ x=1 \pm 5\sqrt{2}[/tex]
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.
(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
Emma recorded the weight of her kitten in ounces on certain days for 24 days. The data are shown in the scatter plot
Answer:
what are the instructions
Step-by-step explanation:
please repost with instructions
1024,-256,64,-16, 3rd term
The next term of the given geometric series is the fifth term which is; a₅ = 4
What is the nth term of the geometric series?We are given the geometric series as;
1024, -256, 64, -16,.....
The formula to find the nth term of a geometric series is;
aₙ = ar^(n - 1)
where;
a is first term
r is common ratio
n is position of term
Thus, from the given series, we have that;
a = 1024
r = -256/1024
r = -1/4
Thus, the formula for the nth term of the series is;
aₙ = 1024(-¹/₄)^(n - 1)
Next term is the fifth term and so we have;
a₅ = 1024(-¹/₄)^(5 - 1)
a₅ = 1024(-¹/₄)^(4)
a₅ = 4
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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
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I hope this was helpful!
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:
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
The graph of a sinusoidal function has a minimum point at (0,2)(0,2)left parenthesis, 0, comma, 2, right parenthesis and then has a maximum point at (3\pi,6)(3π,6)left parenthesis, 3, pi, comma, 6, right parenthesis.
Write the formula of the function, where xxx is entered in radians.
The (0, 2) and (3•π, 6) minimum and maximum points on the graph of the sinusoidal function indicates that the function is as follows
[tex]y = 2\cdot sin\left(\dfrac{1}{3} \times \left(x - \dfrac{3\times \pi}{2} \right)\right) + 4[/tex]
What is a sinusoidal function?A sinusoidal function is a function based on the trigonometric function of sine.
The points on the graph of the sinusoidal function are;
Minimum point of the function; (3•π, 6)
Maximum point of the function; (0, 2)
The general form of the equation of a sinusoidal function is presented as follows;
The sinusoidal function equation is; y = a×sin(b×(x - h)) + k
The amplitude, a, is half the distance between the maximum and minimum points, therefore;
a = (6 - 2)÷2 = 2
a = 2
From the information in the question, when x = 0, y = 2
Plugging in the values of x = 0, y = 2in the equation, y = a×sin(b×(x - h)) + k, produces;
2 = 2×sin(b×(0 - h)) + k
The point (0, 2) is a minimum point, therefore; sin(b×(0 - h)) = -1
2 = 2×sin(b×(0 - h)) + k = 2×(-1) + k = -2 + k
k = 2 + 2 = 4
At the minimum point the value of sine is -1, which indicates that the value of the argument, (b•(0 - h)) = -π/2
Therefore; -b•h = -π/2
h = π/(2·b)
At the maximum point, (b×(x - h)) = π/2
Therefore; (b×(3×π - π/(2×b))) = π/2
b = 1/3
Therefore;
h = π/(2×b) = 3×π/2
y = 2×sin((1/3)×(x - 3×π/2)) + 4
The function is; y = 2×sin((1/3)×(x - 3×π/2)) + 4
The formula of the function for the graph is therefore; y = 2×sin((1/3)×(x - 3×π/2)) + 4
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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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3³× (3⁴} ⁰.⁵ simplified
Thank you
Step-by-step explanation:
so, it is
3³ × (3⁴)^(0.5) ?
remember, when multiplying exponents of the same base, we add the exponents : e.g.
a⁵ × a³ = a⁸
when we have exponents in exponents we multiply the exponents : e.g.
(a³)⁴ = a¹²
now, also remember the priorities of mathematical operations :
1. brackets
2. exponents
3. multiplications and divisions
4. additions and subtractions
now, let's look at our expression again :
3³ × (3⁴)^(0.5)
since we only want to simplify and not to calculate, we leave (3⁴) alone, because the only thing we could do would be to actually calculate 3⁴.
so,
(3⁴)^(0.5) = 3^(4×0.5) = 3²
and then,
3³ × 3² = 3^(3+2) = 3⁵
so, the simplified expression is 3⁵.
which is 243 ...
Multiply. 3√2 ⋅ 2√8 ⋅ 3√. 6√ Enter your answer, in simplest radical form, in the box.
Answer:
the answer i think it is 432
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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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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These marbles are placed in a bag and two
of them are randomly drawn.
What is the probability of drawing two
yellow marbles if the first one is placed back
in the bag before the second draw?
Give your answer as a ratio, reduced to
simplest terms.
?
Hint: Multiply the probability of the 1st Event by the
probability of the 2nd Event to get your answer
Answer:
There are 10 marbles, 2 are yellow
The probability would be 2:10 but in simplest form 1:5
The probability of picking both the same = 1:5 x 1:5 = 1:25
Step-by-step explanation:
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)
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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i need help with my math work
Answer: I believe y=1x+0 (or y=x)
Step-by-step explanation: if you copy the slope and make the line go through (2,2), you get this line.
what are the factors of 28?
Answer:
1, 2, 4, 7, 14 and 28
Step-by-step explanation:
1 x 28 = 28
2 x 14 = 28
4 x 7 = 28
Answer:
1, 2, 4, 7, 14 and 28
Step-by-step explanation:
9 A rectangle and a square have the same area. The length
of the rectangle is 70 feet more than two times its width. The
length of a side of the square is 30 feet. Set up an equation to
find the dimensions of the rectangle. What are the dimensions
of the rectangle? Include units of measurement.
Answer:
Step-by-step explanation: If the square is 30 ft on one side the other side must be too. So 30x30 = 900. Now, we know the rectangle must also be 900 in area. So, the width must be 10feet and the length must be 90ft because 10x90 is also 900. How I got the length? I did 10x2+70.
Grace and her dad are planning to attend the state fair. An adult ticket is $15. The price of an adult ticket is one half the price of a student ticket plus $8. Write an equation to determine how much grace will pay for a student ticket.
1/2 x + 8 = 15 Grace will pay for a student ticket
the question requests the cost of a "student ticket." Because we don't know, let's assume the student ticket price is "x" dollars.
Because we know from the question that "the price of an adult ticket is half the price of a student ticket plus $8.00," we can represent the adult ticket price as follows:
1/2 x + 8
If we also get "An adult ticket costs $15.00" from the question, we can write the equation as:
1/2 x + 8 = 15
Grace will pay for a student ticket
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