Given:
[tex]x^4-16[/tex]Required:
To factor the given expression.
Explanation:
Consider the given expression
[tex]x^4-16[/tex]Now
[tex]\begin{gathered} x^4-16=(x^2)^2-(4^)^2 \\ \\ =(x^2-4)(x^2+4) \\ \\ =(x^2-2^2)(x^2+4) \\ \\ =(x-2)(x+2)(x^2+4) \end{gathered}[/tex]Final Answer:
[tex]x^4-16=(x-2)(x+2)(x^2+4)[/tex]Find a degree 3 polynomial with real coefficients having zeros 3 and 4 − 3 i and a lead coefficient of 1. Write P in expanded form.
[tex]x^{3}[/tex]-2[tex]x^{2}[/tex]+9x-18 This is a degree 3 polynomial with real coefficients having zeros 3 and 4 − 3 i and a lead coefficient of 1
What is polynomial ?Algebraic expressions called polynomials include constants and indeterminates. Polynomials can be thought of as a type of mathematics. Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.
complex zeros always occur in pairs.
zeros are 2,3i,-3i
f(x)=(x-2)(x-3i)(x+3i)=(x-2)([tex]x^{2}[/tex]-[tex]3i^{2}[/tex])
=(x-2)([tex]x^{2}[/tex]-[tex]9i^{2}[/tex])
=(x-2)([tex]x^{2}[/tex]+9)
=[tex]x^{3}[/tex]-2[tex]x^{2}[/tex]+9x-18
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What is the domain of the inverse function of f(x) =x³?
values equivalent to -12/5
-12/5
This is a improper fraction, so lect's corvert it into a mixed fraction
2
5 12
2
Written as a mixed fraction -2 2/5
It's negative
The possible answers are -2 2/5
12/-5
-12/5
group the labels according to the type of interest they describe
There aren't any SARS-CoV-2 variations listed as Variant Of Interest right now.
A genetic variant with certain genetic markers linked to altered receptor binding, decreased ability of antibodies to neutralise an infection or immunisation, decreased therapy effectiveness, potential impact on diagnosis, or anticipated rise in disease severity.
Potential characteristics of an interesting variant:
Certain genetic markers that are believed to influence immune evasion, diagnosis, or treatment.Evidence indicates it is the source of unusual outbreak clusters or a higher percentage of cases.Limited occurrence or spread in the US or other nations.To know more about SARS-CoV-2 refer to the given link :
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The complete question is-
Labels for SARS-CoV-2 Variants of Interest and Concern.
Ben needs to buy so he can buy a package of three bars of soap for $3.75 or a package of eight bars of soap for $12. If he buys the cheapest soap how much will he save per bar
When he buys the cheapest soap, the amount he save per bar is $0.25.
What is money?Money is anything that's used as a medium of exchange.
In this case, three bars of soap cost $3.75. Each bar will bre:
= $3.75 / 3
= $1.25
Also, a package of eight bars of soap for $12. Each bar will be:
= $12 / 8
= $1.5
The amount that will be saved will be the difference between the values above. This'll be:
= $1.5 - $1.25
= $0.25
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In the xy-plane, line l is parallel to the line with equation 4x-y=1. If line l contains the point (0,2), which of the following is an equation of line l? A) 4x-y = -2 B) 4x-y = 2C) 4x+y= -2 D) 4x+y =2
The equation for the second line is:
[tex]4x\text{ - y = 1}[/tex][tex]\text{The general equation of a line is y = mx + c}[/tex]Where m = slope and c = Intercept
Let us rewrite the given equation in that form :
[tex]\text{ y = 4x - 1}[/tex]Comparing y = 4x - 1 with y = mx + c:
m = 4 and c = -1
Since line I is parallel to the given line, it means their slopes are equal. Therefore, the slope for line I is also m = 4
Line I contains the Point:
[tex](x_1,y_{1)\text{ = }}(0,\text{ 2)}[/tex]The equation of a line can also be written in the form:
[tex]y-y_1=m(x-x_{1\text{ }})[/tex][tex]y\text{ - 2 = 4 (x - 0)}[/tex][tex]y\text{ - 2 = 4x}[/tex]By rearranging the above equation:
[tex]4x\text{ - y = -2}[/tex]The above is the equation for line I
1. Mark bought a pen for $0.49, a box of pencils for $1.29, and a pad of paper for $0.98. How much did he spend in all? 2 The coach honght 10 ice cream cones for $0 35 each How much did he spend?
If Mark bought a pen for $0.49, a box of pencils for $1.29, and a pad of paper for $0.98, then he had spend a total of $ 2.76, and if 10 ice cream cones were brought for $0.35 each, then the total amount paid is $3.5
As per the question statement, Mark bought a pen for $0.49, a box of pencils for $1.29, and a pad of paper for $0.98,
And the coach bought 10 ice cream cones for $0.35 each.
We are required to calculate the following:
(a) The total amount Mark had to pay
(b) The total amount the coach had to pay
Starting with part (a),
If Mark bought a pen for $0.49, a box of pencils for $1.29, and a pad of paper for $0.98, then the total amount he will have to pay will simply be the summation of the individual costs, that is, $[0.49 + 1.29 + 0.98] = $ 2.76.
Now solving part (b),
If the coach bought 10 ice cream cones for $0.35 each, then the total amount he/she will have to pay, will be a simple multiplication of the price of one ice cream, with the number of ice creams bought, that is,
$[0.35 * 10] =$3.5
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y= -2/3x - 2 2x + y = 2 Find the solution of the systems of linear equation by graphing
x = 3, y = -4
Explanations:The given system of linear equations is:
[tex]\begin{gathered} y\text{ = }\frac{-2}{3}x\text{ - 2}\ldots\ldots\ldots\ldots.(1) \\ 2x\text{ + y = 2}\ldots\ldots\ldots\ldots\text{.}\mathrm{}(2) \end{gathered}[/tex]The graph representing the equations is plotted below:
[tex]\begin{gathered} \text{The red line represents y = }\frac{-2}{3}x\text{ -2} \\ \text{The blue line represents 2x + y = 2} \end{gathered}[/tex]The point where both lines intersect is the solution to the system of equations.
The lines intersect at the point (3, -4), therefore, (3, -4) is the solution to the system of equations
Steps for graphing a quadratic equation from vortex form
Graphing a Quadratic Equation
Let's take as an example the function:
[tex]y=-2\mleft(x-3\mright)^2+5[/tex]The vertex form of a quadratic function is:
[tex]y=a\mleft(x-h\mright)^2+k[/tex]Where a is the leading coefficient and (h,k) is the vertex.
If a is positive, the function is concave up, if negative the function is concave down.
The first step is to obtain the parameters by comparing the given equation with the general equation.
Thus, we have: a = -2. Vertex = (3,5)
Now we locate the vertex in the coordinate plane and draw the parabola opening down.
For more precision, we can substitute some points around the vertex, like for example:
x={1,2,4,5}
We get the y-coordinates:
y={-3,3,3,-3}
Then we plot the graph as follows:
Write an equation of the line passing through the points (3,2) and (-2,- 18).
To answer this question, we can use the two-point form of the line equation:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}\cdot(x-x_1)[/tex]Then, we have the points:
(3, 2) --->x1 = 3, y1 = 2
(-2, -18)---> x2 =-2, y2 = -18
Then, we have:
[tex]y-2=\frac{-18-2}{-2-3}\cdot(x-3)\Rightarrow y-2=\frac{-20}{-5}\cdot(x-3)\Rightarrow y-2=4(x-3)[/tex]The question in the slope-intercept form is:
[tex]y=4x-10[/tex]A coastline is lost to erosion at a constant rate. The graph shows the amount of coastline lost overtime . How many years will it take to lose 48 feet of the coastline
48 years falls between 40 to 50 on the graph
If you trace from a point close to 50 on the y -axis to meet the slope line
the point of intersection between the trace and the slope line, trace it down to x-axis
The value falls in between 6years and 9 years
Ann Marie has a gross annual income of $98,000. According to Housing Recommendation #1, how much can she devote to monthly housing expenses?
A submarine is sitting still along the surface of the ocean as a part of a drill it does at a constant speed to a certain number of feet below the surface of the ocean
The intervals in which the submarine is diving with a constant velocity is the intervals in which the graph is linear.
Velocity and positionThe velocity is given by the change in the position divided by the change in time, as follows:
Velocity = change position/change time.
It means that the velocity is the derivative of the position. Hence, if the velocity is constant, the position is represented by a linear graph, as the derivative of a line is a constant.
Hence, the submarine has a constant speed when the graph is linear, either constant, increasing or decreasing.
This problem is incomplete, hence I cannot give the exact intervals, as I can't see the graph, however you need to just check the graph and verify where it has linear behavior.
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Please help I will mark branlist
Answer:
False. It has no solutions.
Step-by-step explanation:
Hope it helps! =D
Answer:If a graph of a quadratic,
f
(
x
)
, does not have an x-intercept
then
f
(
x
)
=
0
has no Real solutions.
Explanation:
The x-axis is composed of all points for which
f
(
x
)
(or, if you prefer,
y
) is equal to
0
If the graph of
f
(
x
)
does not have an x-intercept
then it has no (Real) points for which
f
(
x
)
=
0
Step-by-step explanation:
No x-intercept means that it does not cross the x-axis. Thus two solutions is definitely ruled out.
However, if you DO NOT INCLUDE a point of coincidence (Vertex coincides with the x-axis) in the phrase "does not have an x-intercept". Then there could be a single value solution if you equate the quadratic to 0. Some people say that it still has two in such a case but they are both the same value. I do not like this way of thinking!
On the other hand, if you DO INCLUDE a point of coincidence in the phrase, then the plot does not cross the x-axis nor does any point on the curve coincide with it. In such an interpretation there is NO SOLUTION THAT IS REAL. hopes this helps
g(n)=-2n-2
h (n)=4n-2
Find (goh) (-3)
Answer:
[tex](g \circ h)(-3)[/tex] = 26
Step-by-step explanation:
We are told that:
• [tex]g(n) = -2n - 2[/tex]
• [tex]h(n) = 4n - 2[/tex]
In order to calculate the value of [tex](g \circ h)(-3)[/tex], we need to first define [tex](g \circ h)[/tex].
[tex](g \circ h)[/tex] means that the input for the function [tex]g(n)[/tex] is the function [tex]h(n)[/tex]. Therefore, we have to replace the [tex]n[/tex] in the definition of [tex]g(n)[/tex] with the definition of [tex]h(n)[/tex]:
[tex](g \circ h)[/tex] = [tex]-2(4n - 2) - 2[/tex]
= [tex]-8n + 4 - 2[/tex]
= [tex]-8n + 2[/tex]
Now that we know the definition of [tex](g \circ h)[/tex], we can find the value of [tex](g \circ h)(-3)[/tex] by substituting -3 into the definition:
[tex](g \circ h)(-3)[/tex] = [tex]-8(-3) + 2[/tex]
= [tex]24 + 2[/tex]
= [tex]26[/tex]
Let M be the event that a randomly chosen person has a master's degree. Let B be the event that a randomly chosen person was a business major. Place the correct event in each response box below to show:
Given that the person has a master's degree, the probability that a randomly chosen person was a business major.
The probability that the person has a business major is going to be represented by: p(B | M)
What is probability?This is the concept that is used in statistical and mathematical analysis to refer to the likelihood and the chances of something happening. That is the likelihood of an event occurring.
We have to define M as the event that the person that has been chosen randomly has a masters degree.
We have to define B as the event that the person that has being chosen randomly has a business major.
Given that the person has a master's degree, the probability that a randomly chosen person was a business major is given as p(B|M)
This would be the conditional probability that is written in the form of
p(B|M) = P(B and M) / P(M)
Where probability P(M) is the probability of having a masters degree, while the prbability P(B) is the probability of having a business degree.
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The cost of living last year went up 13%. fortunately, Alice Swanson got a 13% raise in her salary from last year. this year she is owning $22,570. How much did she make last year? Round to the nearest hundredth.
According to the information given in the problem, you know that Alice got got a 13% raise in her salary from last year, therefore, this year she is owning $22,570.
Let be "x" the amount of money in dollars Alice made last year.
Set up the following equation:
[tex]x+0.13x=22,570[/tex]So, to solve this equation, you must solve for the variable "x". The procedure for this is shown below:
[tex]\begin{gathered} 1.13x=22,570 \\ x=\frac{22,570}{1.13} \\ x=19,973.451 \end{gathered}[/tex]Rounded to the nearest hundredth:
- Look at the digit in the hundreths place. In this case it is 5.
- Look at the digitt to the right of the digit 5 (In this case is the digit 1, which is located in the thousandths place).
- Since the number in the thousandths place is less than 5, you must round down and just remove all the digits located after the digit 5.
Then:
[tex]x\approx19,973.45[/tex]She made about $19,973.45 last year.
Need help with part C. I have the first integral but cannot seem to get the second.
Answer:6_7
Step-by-step explanation:
A company has recently been hiring new employees. Today the company has 26% more employees than it did a year ago. If there are currently 44,100 employees, how many employees did the company have a year ago?
the current amount of employees today represents an increase of 26% from the previous year, this can be written as:
[tex]\begin{gathered} 1+26\% \\ 1+0.26 \\ 1.26 \end{gathered}[/tex]then,
[tex]44100=1.26x[/tex]where x is the number of employees the previous year, then, solve for x
[tex]\begin{gathered} x=\frac{44100}{1.26} \\ x=35000 \end{gathered}[/tex]Answer:
there were 35000 employees one year ago.
PLEASE HELP HELP HELP HELP HELP
Answer:
WHAT IS THATT??
Step-by-step explanation:
OSKSKQKANSNSNSNSZKNSNSNSN
Rewrite the function by completing the square. g(x) = x^2 + 15x +54
g(x) = _ ( x + _ )^2 + _
PLEASEEE HELP I"LL GIVE LOTS OF POINTSS
and don't scam me
Answer:
The difference in the depths is equal to 5ft
Step-by-step explanation:
A) snapper (-10 ft) : (b) redfish (-3ft): (c) clam (0 ft) : (d) Hermit Crab (2 ft)
B The comparison of the depth of hermit crab and redfish,
D = hermit crab - redfish = 2 - (-3) = 5 ft
In order would be 1 snapper) 2 red fish) 3 clam)4 hermit
Answer:
a) Flounder, Bluefish, Clam, Hermit Crab
b) The bluefish is deeper than the hermit crab.
The picture is attached. I have to solve each one and then choose the graph. Well I have to graph it.
Graphing the function:
[tex]\begin{gathered} x=-8 \\ f(-8)=\frac{1}{4}(-8)=-2 \end{gathered}[/tex][tex]\begin{gathered} x=1 \\ f(1)_{\text{ }}does_{\text{ }}not_{\text{ }}exist \end{gathered}[/tex][tex]undefined[/tex]Question 3 Below are hvo parallel lines with a third line intersecting them. Find the value of x
In this case, we are given the value of one angle and told to find the value of angle x. To do so, we will try to relate them based on the position they have in the diagram.
Notice that the two parallel lines split the space into two. One space is in between the lines, and the other space is outside the lines. We can see that both angles are located outside of the parallel lines.
Now, see that the third line splits the space into two. One space is on the left of the third line, and the other one is on the right of the third line. From the diagram, we can tell that each angle is on an opposite side of the third line.
This two relations between these angles (being outside the parallel lines and on opposite sides of third line) gives them the name of alternate outer angles. This angles have the property that they have the same measure.
So, we have the following
[tex]x=56[/tex]so the measure of x, in degrees, is 56°.
a=1/2h(b1+b2) is the formula for the area of a trapezoid. Rewrite the formula for b1. Then find the unknown base of the trapezoid that has an area of 78 in2, a height of 12 inches, and one base length of 8 inches.
The formula rewritten for b1 is b1 = 2a/h - b2
The unknown base of the trapezoid is 5 inches
What is subject of formula?A subject of formula is simply described as the variable that is made to stand alone on one side of the equality sign.
It is the variable expressed in terms of other variables in an expression.
Given the formula for the area of a trapezoid as;
a = 1/2h(b1+b2)
Where;
a is the area of the trapezoidh is the heightb1 and b2 are the basesLet's make b1 the subject of formula
cross multiply
(b1+b2)h = 2a
Now, divide both sides by h, we have!
b1 + b2 = 2a/h
Take b2 over the equality sign
b1 = 2a/h - b2
Now, substitute the values into the formula
b1 = 2(78)/12 - 8
Expand the bracket
b1 = 156/12 - 8
Find the quotient
b1 = 13 - 8
find the difference
b1 = 5 inches
Hence, the value is 5 inches
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The table shows the speeds s (in feet per second) of sound in water at various
temperatures t (in degrees Fahrenheit). Write a function that models the data. Use
the model to approximate the speed of sound when the water temperature is 100°F.
Temperature (°F), t: 32 50 90 120 180 212
Speed (ft/sec), s: 4603 4748 4960 5049 5095 5062
A function which models the data in the given table is y = 3848.2x^0.054. Also, an approximate speed of sound when the water temperature is 100°F is equal to 4935 ft/sec.
What is a line of best fit?A line of best fit can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.
In this scenario, the temperature of water would be plotted on the x-axis of the scatter plot while the speed of sound would be plotted on the y-axis of the scatter plot.
By critically observing the scatter plot (see attachment) which models the data in the given table, we can reasonably and logically deduce that a function for the line of best fit is given by:
y = 3848.2x^0.054
Next, we would determine the speed of sound when the water temperature is 100°F as follows:
y = 3848.2x^0.054
y = 3848.2 × (100)^0.054
y = 3848.2 × 1.2823
y = 4934.55 ≈ 4935 ft/sec.
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Terrell opened a savings account 10 years ago. The account earns 9% interest, compounded annually. If the current balance is $300.00, how much did he deposit initially? Round your answer to the nearest cent.
1) Gathering the data
Time: 10 yrs ago
Interest rate (r) : 9% (0.09)
Future Value: 300
Initial Deposit:?
2) Since the current balance is given, let's call it Future Value because the amount that made that $300 is what we need to find out. Let's go find the Future Value since it's been 10 yrs ago. Plugging into the formula we have:
[tex]\begin{gathered} F=P(1+r/n)^{nt} \\ 300=P(1+\frac{0.09}{1})^{1\cdot10} \\ 300=P(1.09)^{10} \\ 300=2.367363675P \\ P=\frac{300}{2.367363675} \\ P=126.723 \\ P\cong126.72 \end{gathered}[/tex]Notice that, since this investment was compounded yearly, so n=1.
3) So the initial deposit, 10 years ago was approximately $126.72
Which multiplication expression can you use to find
3/4 divided by 3/8
The given multiplication expression is 3/4÷3/8 or 3/4×8/3
What is multiplication expression?
Mathematical expressions that include multiplication are called multiplication expressions. We combine the integers and then the like variables to simplify the equation. We will therefore obtain x to the second power if we multiply two xs together.
An answer to a multiplication sentence is obtained by multiplying the various components. The multiplier (first number), multiplicand (second number), and product are the components of a multiplication phrase (third number).
The simplest form of an expression is one in which terms cannot be concatenated. In order to write 3 + (2 5) simply: Start by carrying out the procedure between parenthesis. The addition should then be done.
Given, 3/4÷3/8
3/4×8/3
=2
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Our rental car company turns $42 50% per day to run a car in 10 cents for every mile driven video want to run a car knowing next plans drive 225 miles and she has at the most $150 to spend
a rental car company charges $42.50 per day to rent a car intense sense for every mile driven Lydia wants to run a car knowing that she plans to drive 225 miles in she has at most $150 to spend
Let
x -------> the number of miles
y -----> the total charge
we have that
the linear equation that represent this problem is
y=0.10x+42.50
For x=225 miles
substitute teh value of x
y=0.10(225)+42.50
y=$65
Can somebody please help me right now??? i’m stuck and i need help with this bad
Answer:
B
Step-by-step explanation:
Using a minor key within a song is usually to make it more sad or negative in emotion, though with this question the fast tempo should already rule out A because it is quite the opposite to laziness.