The pair of limits that would verify the existence of a vertical asymptote at x = –1 is:
[tex]\lim_{x \rightarrow -1^-} = \infty, \lim_{x \rightarrow -1^+} = \infty[/tex]
What are the vertical asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
For a vertical asymptote at x = -1, the denominator is zero at -1, hence both lateral limits at x = -1 go to infinity, that is:
[tex]\lim_{x \rightarrow -1^-} = \infty, \lim_{x \rightarrow -1^+} = \infty[/tex]
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Which expression is the simplest form of 2x^3 - x^2 + 3 (x^3 - 4x^2)
The simplest form of the given expression is 5x^3-5x^2.
We have given that
[tex]2x^3 - x^2 + 3 (x^3 - 4x^2)[/tex]
We have to determine the simplest form of the given expression.
What is the distributive property?
The distributive property of binary operations generalizes the distributive law, which asserts that equality is always true in algebra. elementary.
Use the distributive property we get,
[tex]2x^3 - x^2 + 3 (x^3 - 4x^2)\\=2x^3 - x^2 +3x^3-12x^2\\[/tex]
Add like terms we get,
Therefore we get,
[tex]=5x^3-5x^2[/tex]
Therefore the simplest form of the given expression is 5x^3-5x^2.
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$Need help with this pls (quickest answer gets brainliest)
Answer:
-1/2
Step-by-step explanation:
IK
Ahman has a lawn care business. he charges $25 per lawn to mow the grass. if his monthly expenses are $100, how many lawns must he mow in order to make a profit of at least $250 per month?
Answer:
14
Step-by-step explanation:
you can write an equation to represent the situation:
let x represent the number of lawns he has to mow
then, the monthly profit would be 25x - 100.
in order to make $250, this equation has to be equal to 250:
[tex]25x-100=250[/tex]
now, solve this:
add 100 to both sides
[tex]25x = 350[/tex]
divide both sides by 25
[tex]x = 14[/tex]
he must mow 14 lawns
Round 508.0219 to the nearest hundredth
Answer:
508.02
HOPE THIS HELPS
Todo <3
Step-by-step explanation:
CAN SOMEONE HELP ME PLS?????
You are correct, P(red) = P(green) = 0.25.
Find the slope of every line that is parallel to line on the graph (0,-3) (5,-4)
The slope of the line parallel to the line on the graph (0,-3) (5,-4) is - 1 / 5
How to find the slope of a parallel lines?Parallel lines have the same slope.
Therefore,
slope = m = y₂ - y₁ / x₂ - x₁
Therefore,
x₁ = 0
x₂ = 5
y₁ = -3
y₂ = -4
Therefore,
slope = -4 - (-3) / 5 - 0
slope = -4 + 3 / 5
slope = - 1 / 5
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A passenger jet plane cruises at 550 knots. It enters a jet stream with
a tailwind speed of 120 knots. If the speed of sound is 661 knots,
will the jet travel faster or slower than sound during its journey?
Considering the direction of the wind, it is found that the jet travels faster than the sound during it's journey.
What is the ground speed?The jet's speed, considering that there is a tailwind, is given by:
J = Plane speed + Wind speed.
In this problem, we have that the speeds are given as follows:
Plane: 550 knots.Wind: 120 knots.Hence the jet's speed is given by:
J = 550 + 120 = 670 knots.
670 knots > 661 knots, hence the jet travels faster than the sound during it's journey.
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sum of numbers 975,983,923,913 and 985 rounded upto hundredth place is
Answer:
4800
Step-by-step explanation:
If a question is asking for the "sum" of numbers, this just means we have to add them altogether.
975+983+923+913+985 = 4779
To find the hundredth place, we use our place value. 4 is in the thousands column, and 7 is in the hundreds. Once we find the hundreds, we need the number to the right of it (7).
7 > 5 so we round up. 7 becomes 8.
4800.
pls help
Enter the equation for the graph.
Answer:
[tex]y=[1]cos([\frac{2\pi }{3}]x)[/tex]
Step-by-step explanation:
Looking at the graph, we can see the domain to be from (0 , 2π).
Now we have to find one period that corresponds to cos(x).
The half-period of cos(x) for this graph appears to be pi/3 and adding another pi/3 gets us 2pi/3 to be our cosine period.
b = 2pi/3
a is the same range as cos(x). Range: (0,0)
y = [a] * cos ([b]*x)
y = [1] * cos([2pi/3]x)
Select the statement below that correctly describes the relationship between the number of workers and the hours that they work.
Less workers = more hours
OR the answer might be worded as
More workers = less hours
If the triangles above are reflections of each other, then BC = to
Answer:
DF
Step-by-step explanation:
Paint a picture in your head reflecting the triangle. Just hold A and flip it so A = E , D = B
The temperature fell at a rate of 0.65 °C/h. The temperature was recorded at 37 °C
at 6 p.m. Which function can be used to represent this situation?
Of(x) = 37 -0.65x
Of(x) = 0.65x - 37
Of(x) = 37x + 0.65
Of(x) = 0.65x+37
The linear function that can be used to represent the temperature in x hours after 6 pm is given by:
f(x) = 37 - 0.65x.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem:
The y-intercept is the initial temperature of 37ºC.The slope is the rate of change of -0.65ºC/h.Hence the function is:
f(x) = 37 - 0.65x.
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[tex]\{ \frac { ( \sqrt { 3 } ) \times 3 ^ { - 2 } } { ( \sqrt { 5 } ) ^ { 2 } } \} ^ { \frac { 1 } { 2 } }[/tex]solve this equation
Answer:
Step-by-step explanation:
Exponent law:
[tex]\sf \bf a^m * a^n = a^{m+n}\\\\ (a^m)^n = a^{m*n}[/tex]
[tex]\sf a^{-m}=\dfrac{1}{a^m}[/tex]
First convert radical form to exponent form and then apply exponent law.
[tex]\sf \sqrt{3}=3^{\frac{1}{2}}\\\\\sqrt{5}=5^{\frac{1}{2}}[/tex]
[tex]\sf \left(\dfrac{(\sqrt{3}*3^{-2}}{(\sqrt{5})^2}\right)^{\frac{1}{2}}= \left(\dfrac{3^{\frac{1}{2}}*3^{-2}}{(5^{\frac{1}{2}})^2} \right )^{\frac{1}{2}}[/tex]
[tex]= \left(\dfrac{3^{\frac{1}{2}-2}}{5^{\frac{1}{2}*2}}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{1-4}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{-3}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\dfrac{3^{\frac{-3}{2}*{\frac{1}{2}}}}{5^{\frac{1}{2}}}\\\\ =\dfrac{3^{{\frac{-3}{4}}}}{5^{\frac{1}{2}}}[/tex]
The lowest point in the United States is the Death Valley in California. Its altitude is 282 feet below sea level. Identify the integer representing the lowest point (Death Valley).
Answer:
-282
Step-by-step explanation:
Any altitude below sea level would have a negative sign in front of it.
PLEASE HELP 15 POINTS
Answer:
B
Step-by-step explanation:
Used elimination method.
first plugged in (0,0)which remove A,D
than saw the line is not solid so chose B
8. Complete the table below by drawing an example of each shape.
Answer:
Please see attachment.
The first one is a quadrilateral that is not a parallelogram.
The second one is a triangle with a right angle.
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
answer?.............
Answer:
-21
Step-by-step explanation:
4
Find the measure of x.
X
12°
X = = [?]
Round to the nearest hundredth.
The measure of x will be 18.81 units.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
The given information are;
Perpendicular = 4
Base = x
Then, Tan ∅ = Perpendicular /Base
Tan 12 = 4/x
x = 4 /0.212
x = 18.818
Hence, the measure of x will be 18.81 units.
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Andrea has 3 tiles. One is a regular octagon, one is a regular pentagon and one is a regular hexagon. Andrea thinks the 3 tiles will fit together perfectly, as shown in the diagram. Show calculations to prove that she is wrong.
From calculations, we can say that the given tiles will not fit together perfectly.
How to find the sum of interior angles of a Polygon?If the tiles join perfectly at a point, sum of all angles around the joining point should be 360°.
Expression for the measure of the interior angle of a polygon,
Interior angle of a polygon = [(n - 2) * 180]/n
Interior angle of a pentagon = [(5 - 2) * 180]/5 = 108°
Interior angle of a hexagon = [(6 - 2) * 180]/6 = 120°
Interior angle of an octagon = [(8 - 2) * 180]/8 = 135°
To prove that the given tiles fit together perfectly → Sum of all the angles around the common point should be 360°
Sum of all interior angles = 108° + 120° + 135° = 363°
Therefore, given tiles will not fit together perfectly.
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Find all solutions of the equation in the interval .
Write your answer in radians in terms of .
If there is more than one solution, separate them with commas.
The solutions to the trigonometric equation in the desired interval are given as follows:
[tex]\theta = \frac{\pi}{3}, \theta = \frac{5\pi}{3}[/tex]
What is the solution to the trigonometric equation?The trigonometric equation is given by:
[tex]\sqrt{3}\cot{\theta} - 1 = 0[/tex]
Solving it similarly to an equation, we have that:
[tex]\sqrt{3}\cot{\theta} = 1[/tex]
[tex]\cot{\theta} = \frac{1}{\sqrt{3}}[/tex]
Since [tex]\cot{\theta} = \frac{1}{\tan{\theta}}[/tex], we have that the equation is equivalent to:
[tex]\tan{\theta} = \sqrt{3}[/tex]
The tangent is positive in the first and in the fourth quadrant. In the first quadrant, the angle [tex]\theta[/tex] with [tex]\tan{\theta} = \sqrt{3}[/tex] is:
[tex]\theta = \frac{\pi}{3}[/tex]
In the fourth quadrant, the equivalent angle is:
[tex]\theta = 2\pi - \frac{\pi}{3} = \frac{5\pi}{3}[/tex]
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8 1/2 - 3/8=?
pls answer fast
Answer:
65/8
Step-by-step explanation:
1) Turn all numbers into improper fractions: 17/2 - 3/8 = ?
2) Make all denominators the same number by finding the least common factor, which is 8. Multiply the denominator in 17/2, which is 2, by 4 to match the other denominator. And then multiply the numerator (17) by 4 as well so that the fraction still has the same value: 68/8 - 3/8 = 65/8
3) Can not simplify since there are no common factors between 65 and 8.
Need Help Fast!!!!!! The graph of the piecewise function f(x) is shown. f(x) What is the range of f(x)?
Answer:
The second option
Step-by-step explanation:
If you look at the graph, it appears that from negative infinity to 0, the line is just constant, so the range of that would simply be the constant value or in this case 4. from 0 to infinity it appears the line is decreasing at a constant rate and should go towards negative infinity as x goes towards infinity. So the range would be -infinity < f(x) <= 4
Which expression is equivalent to startfraction (4 p superscript negative 4 baseline q) superscript negative 2 baseline over 10 p q superscript negative 3 baseline endfraction? assume p not-equals 0, q not-equals 0.
The given expression is equivalent to [tex]\frac{p^{7}q}{160}[/tex]
What are indices?
An index is a small number that tells us how many times a term has been multiplied by itself.
The plural of index is indices.
Below is an example of a term written in index form :[tex]4^{3}[/tex]
4 is the base and 3 is the index.
We can read this as ‘4 to the power 3’
Another way of expressing [tex]4^{3}[/tex] is
4 x 4 x 4 = 64
Indices can be positive or negative numbers.
Given expression can be written as [tex]\frac{({4p^{-4}q})^{-2}}{10pq^{-3}}[/tex]
Now to simplify the given fractional expression :[tex]\frac{({4p^{-4}q})^{-2}}{10pq^{-3}}[/tex]
= [tex]\frac{4^{-2}p^{8}q^{-2}}{10pq^{-3}}[/tex] By using the property of exponents is given by:
[tex](a^{m})^{n}=a^{m n}[/tex]
=[tex]\frac{p^{7}q}{10 .16}[/tex] By using the property of exponents given by
[tex]a^{m}a^{n}=a^{m + n}[/tex] and [tex]a^{-m}= \frac{1}{a^{m}}[/tex]
= [tex]\frac{p^{7}q}{160}[/tex]
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its math help me out?
Its the first one
--------------------
Answer:
$24 = $0.40(60)
Step-by-step explanation:
Match the input value and its location in the equation.
__
$24 = $0.40(60)
_____
Additional comment
When input is liters and output is dollars, the constant of proportionality must have units of "dollars per liter." The dollar sign of these units is not shown in the left panel, but is shown on the answer choices. If you understand units conversion, this should not be a mystery. (The mystery is why the curriculum materials are inconsistent.)
what does 5r-r-9=15 look like after combining like terms ?
and whats the answer for r?
The value of r from the expression is 6
Simplifying expressionGiven the expression below;
5r-r-9=15
Add 9 to both sides
5r - r - 9 + 9 = 15 + 9
4r = 15 + 9
4r = 24
After combining the like terms the expression will be 4r = 24
4r/4 = 24/4
r = 6
Hence the value of r from the expression is 6
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Each of 36 students at a school play bought either a cup of orange juice or a sandwich. A cup of orange juice costs $1 and a sandwich costs $3. The total amount collected was $76. How many students bought orange juice, and how many bought a sandwich?
Let represent the number of students who bought a cup of orange juice and represent the number of students who bought a sandwich. Then the problem can be represented by this system of equations:
+ 3 = 76
+ = 36
Answer the questions to solve the problem.
1. Explain what you should do with the two equations to eliminate one of the variables.
In order to eliminate one of the variables, subtract one of the equation from the other equation.
How to eliminate one of the variables?Given these equations:
o + 3s = 76 equation 1
o + s = 36 equation 2
Where:
o = number of orange juice bought
s = number of sandwiches bought
In order to eliminate one of the variables, subtract equation 2 from equation 1. The result is :
2s = 40
s = 20
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. If we start with one bacterium and it doubles in
number every 15 minutes, HOW LONG WILL IT
TAKE for one bacterium to become one million??
Answer:
298.97 minutes
Step-by-step explanation:
2^x = 1 000 000 where 'x' is the number of 15 minute periods
x = 19.931 15 minute periods = 298.97 minutes
Mr. Lopez fruit salad recipe requires 3/4 of a cup of fresh peaches for 1 serving. He uses 9 cups of fresh peaches to prepare the salad. How many servings of the fruit salad did he prepare?
Answer:
6.75 servings
Step-by-step explanation:
[tex] \frac{3}{4} \times 9 = \frac{27}{4} = 6 \frac{3}{4} = 6.75[/tex]
Answer:
9 servings
Step-by-step explanation:
feel free to ask where you don't understand.
Gene has a gasoline budget of $300 per month. He uses an average of $6 of gasoline each day he drives. Which of the following equations represents how much money is left in his gasoline budget after x days of driving?
Answer:
300-6x
Step-by-step explanation:
Trust me
The nature of a graph, which has an even degree and a positive leading coefficient will be
The nature of a graph, which has an even degree and a positive leading coefficient will be up left, up right position
What is the nature of the graph of a quadratic equation?The nature of the graphical representation of a quadratic equation with an even degree and a positive leading coefficient will give a parabola curve.
Given that we have a function f(x) = an even degree and a positive leading coefficient. i.e.
y = f(x) = 2x²+ 4The domain of this function varies from -∞ < x < ∞ and the parabolic curve will be positioned on the upward left and upward right x-axis.
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