Answer:
Step by step solution:
The
Find the complex zeros of the following polynomial function and write F in factored form.
Answer:
The complex zeros are:
[tex]\begin{gathered} x_1=-2i \\ x_2=2i \end{gathered}[/tex]The factored polynomial is:
[tex]f(x)=(x-1)(x-3)(x^{2}+4)[/tex]Step-by-step explanation:
Factoring the polynomial, we'll have:
[tex]f(x)=(x-1)(x-3)(x^2+4)[/tex]To find the complex zeroes, let's solve for the quadratic term as following:
[tex]\begin{gathered} x^2+4=0 \\ \rightarrow x^2=-4 \\ \rightarrow x=\pm2i \end{gathered}[/tex]Multiple Questions: Evaluate the Expressions:[tex]( - 4)^{2} [/tex][tex] - 8^{2} [/tex][tex] - 5^{2} \times 4[/tex]
Answer:
(a)16 (b)-64 (c)-100
Explanation
Part A
[tex]\begin{gathered} (-4)^2=(-1\times4)^2 \\ =(-1)^2\times4^2 \\ =1\times16 \\ =16 \end{gathered}[/tex]Part B
[tex]\begin{gathered} -8^2=-1\times8^2 \\ =-1\times64 \\ =-64 \end{gathered}[/tex]Part C
[tex]\begin{gathered} -5^2\times4 \\ =-1\times5^2\times4 \\ =-1\times25\times4 \\ =-100 \end{gathered}[/tex]Please help me i gotta finish this or else I fail
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(a)(i)
To evaluate f(4), we take the functional value at x = 4.
Looking at the graph, it is:
At x = 4, y = 2 [counting units]
Thus,
[tex]f(4)=2[/tex](a)(ii)To evaluate f(-3), we take the functional value at x = -3.
Looking at the graph, it is:
At x = -3, y = -5 [counting units]
Thus,
[tex]f(-3)=-5[/tex](b)The zeros are the x-intercepts of a graph. Looking at the graph, the x-axis cutting points are:
Zeros
[tex]x=2,x=-5[/tex](c)The function f(x) is increasing where the slope of the graph is positive.
Looking at the graph, the increasing part is from x = -3 to x = 5.
That is
- 3 < x < 5
The correct choice is (2).
(d)The relative minimum is the lowest point of the graph shown and the relative maximum is the highest point of the graph.
Looking at the graph,
The lowest point occurs at --- (-3, -5)
The highest point occurs at --- (-7, 5)
So,
Relative Maximum: (-7, 5)
Relative Minimum: (-3, -5)
(e)We want the interval in which f(x) < 0.
This means where the function is less than zero, or below the x-axis.
Looking at the graph,
from x = -5 to x = 2, the graph of f(x) is below the x-axis.
That is -5 < x < 2.
The correct choice is (3).
(f)A new function --
[tex]g(x)=2f(x)+5[/tex]Let's evaluate g(0) by using the formula:
[tex]g(0)=2f(0)+5[/tex]From the graph, f(0) = -2, thus,
g(0) = 2(-2) + 5
g(0) = -4 + 5
g(0) = 1
This means that the functional value of 'g' is 1 at x = 0.
(g)
A new function --
[tex]h(x)=x^3-3[/tex]We need to find g(h(2)). Let's boil it down to the function f(x).
[tex]\begin{gathered} h(x)=x^3-3 \\ h(2)=2^3-3 \\ \therefore h(2)=5 \\ \text{Now, we need g(5).} \\ g(x)=2f(x)+5 \\ g(5)=2f(5)+5 \\ g(5)=2(3)+5 \\ g(5)=6+5 \\ g(5)=11 \\ \text{ Final answer:} \\ g(h(2))=11 \end{gathered}[/tex]Thus, the answer is:
[tex]g(h(2))=11[/tex]2015 > Chapter 1: Chapter 1 Review Exercises > Section Exercises 1 > Exercise 23
23
The formula F =
(K-273.15) +32 converts a temperature from kelvin K to degrees Fahrenheit F.
a. Solve the formula for K.
K=
b. Convert 180°F to kelvin K. Round your answer to the nearest hundredth.
The solution is about K.
The most appropriate choice for subject of a formula will be given by -
180° F has been converted to 355.35 K
What is subject of a formula?
Subject of a formula is the variable which is expressed in terms of other variables present in the formula.
Here,
[tex]F = \frac{9}{5}(K - 273.15) + 32\\F - 32 = \frac{9}{5}(K - 273.15)\\K = \frac{5}{9}(F - 32)+273.15[/tex]
Putting F = 180
[tex]k = \frac{5}{9}(180 - 32) + 273.15\\K=\frac{5}{9}\times 148+273.15\\K=82.2 + 273.15\\K=355.35[/tex]
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A red die is tossed and then a green dieis tossed. What is the probability thatthe red die shows an even number orthe green die shows an even number?Make sure your answer is reduced.3[?]Hint: The two events are not mutually exclusive. Soto the find the probability of the union, use:P(A or B) = P(A) + P(B) - P(A and B)L
Given:
A red die is tossed and then a green die is tossed.
Required:
We have to find the probability that the red die shows an even number or the green die shows an even number.
Explanation:
Let A denotes the event that the red die shows an even number and B denote the event that the green die shows an even number.
Here the total number of outcomes is 6(1-6) and the number of favorable outcomes are 3(2, 4, 6).
Then we have
[tex]\begin{gathered} P(A)=\frac{3}{6}=\frac{1}{2} \\ \\ P(B)=\frac{3}{6}=\frac{1}{2} \end{gathered}[/tex]Therefore,
[tex]P(A\text{ and }B)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}[/tex]Hence the probability that the red die shows an even number or the green die shows an even number is
[tex]\begin{gathered} P(A\text{ or }B)=P(A)+P(B)+PA(A\text{ and }B) \\ \\ =\frac{1}{2}+\frac{1}{2}-\frac{1}{4} \end{gathered}[/tex][tex]\begin{gathered} =1-\frac{1}{4} \\ =\frac{3}{4} \end{gathered}[/tex]Final answer:
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O LINES
Finding the slopes of horizontal and vertical lines
Fill in the blanks below.
Find the slope of the line passing through the points (-4, 7) and (-4, -8).
slope:
Find the slope of the line passing through the points (-7, -3) and (8, -3).
slope:
Round 1436.1406616345 to one decimal place as needed
We want to round up to one decimal place;
The number after the decimal should be rounded up to the nea
[tex]1436.1406616345\approx1436.1[/tex]Write the equation of line in slope-intercept form, which is parallel to y=−2x+5 and passing through the point (1, −4).
Answer: y= -2x -2
Step-by-step explanation:
1) Create an equation going through (1,-4)
Replace 5 with b otherwise, we can't find an equation that goes through it.
y = -2x + b
2) Substitute y and x with the point. Solve.
-4 = -2(1) + b
-4 = -2 + b
-2 = b
3) Reput in the equation
y= -2x -2
Note: It is parallel because they have the same slope!
a right triangle has an angle measure of 18.4 what is the value of x the missing angle
The value of x is 71.6 degrees
How to find third angle :The sum of a triangle's interior angles equals 180o. When the other two angles of a triangle are known, subtract the number of degrees in the other two angles from 180 degrees to find the third angle. A triangle has three parallel straight sides. The lengths of the sides can vary, but the largest side's length cannot be equal to or greater than the sum of the other two sides. Furthermore, a triangle has three interior angles, the sum of which is always 180 degrees.
We have a Right angle triangle and a value of an angle 18.4.
That is one angle is 18.4° and other is 90°.
To find third angle just add two angles and subtract that with 180.
Add two angle we have 18.4 + 90 = 108.4Subtract 108.4 with 180 = 180 -108.4 = 71.6°The third angle is 71.6°
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the sum of a number and six is less than the sum of three times the number and ten. Write an inequality
The correct answer or an inequality is x+6 < 3x + 10.
What is an inequality equation in mathematics?
An inequality in mathematics is said to be a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is said to size-compare two numbers on a number line.
Many straightforward inequalities can be resolved by adding, taking away, multiplying, or dividing both sides until the variable is all that remains.
However, these factors will shift the direction of inequality:
1. By using a negative number to multiply or divide both sides
2. Reversing the left and right sides.
Let the number be x. It is given in the question that the sum of a number and six is less than the sum of three times the number and ten.
According to the question,
x+6 < 3x + 10
Hence, the correct answer is x+6 < 3x + 10.
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The store clerk put b bottles of milk in the cooler, and 11 of the bottles are chocolate milk.
Choose the expression that shows the number of milk bottles that are not chocolate.
11
b- 11
b + 11
11b
Answer: b-11
Step-by-step explanation:
b= total number of milk
11= total number of chocolate milk
b - 11 = number of milks that aren't chocolate
Lakita’s dad was teaching her about the stock He has 100 shares of Company A stock valued at $45 a share and 250 shares of Company B stock valued at $22 a share. How much is his stock worth?
Having trouble finding an explanation to put into the boxes.
Given:
A regular hexagon inside a circle with a radius of 2 inches.
1)
Two radii are drawn to two consecutive vertices of the regular hexagon to form a central angle whose measure can be found based on the rotational symmetry of the figure.
Yes, Agree, because the rotational symmetry of the hexagon is 6. To find the measure of each central angle, divide 360° by 6. The central angle is 60 degrees.
2)
The hexagon can be decomposed by 6 congruent isosceles triangles.
Agree, because the angles of each of the triangles are 60 degrees.
Each of the 6 triangles is an isosceles because the sides are the radii of the same circle.
3).
The length of the altitude of each of these 6 congruent triangles can be found using trigonometry.
Agree, because an attitude split the triangle into two equals 30-60-90 triangles. The side of the original equilateral triangle is the hypotenuse of the 30-60-90 triangle.
The adjacent side is attitude and the hypotenuse is 2 inches with an angle is 30 degrees.
Use the cosine formula.
[tex]Cos\theta\text{ =}\frac{Adjacent\text{ side}}{Hypotenuse}[/tex][tex]cos30^o=\frac{Altitude}{2}[/tex][tex]2cos30^o=Altitude[/tex][tex]2\times\frac{\sqrt{3}}{2}=Altitude[/tex][tex]\text{ The length of altitude}=\sqrt{3}\text{ inches.}[/tex]The length of the altitude of each of these 6 congruent triangles is a sqaure root of 3 inches.
Can I get a in depth explanation to simplifying non perfect roots with quotients? Ex: image
To get the answer, we will attempt to simplify the first expression into its simplest format.
[tex]\sqrt[]{\frac{126xy^5}{32x^3}}[/tex]We begin by dividing both the numerator and the denominator by 2:
[tex]\sqrt[]{\frac{63xy^5}{16x^3}}[/tex]Since x appears in both the numerator and the denominator, we can simplify such that
[tex]\frac{x}{x^3}=\frac{1}{x^2}[/tex]Hence, we have the expression to be
[tex]\sqrt[]{\frac{63y^5}{16x^2}}[/tex]Let us compare the both expressions to each other now:
[tex]\sqrt[]{\frac{63y^5}{16x^2}}=\sqrt[]{\frac{63y^5}{ax^b}}[/tex]Therefore,
[tex]\begin{gathered} a=16 \\ b=2 \end{gathered}[/tex]
the square of a number y subtracted by 1
translate english phrase to mathematical expression
Answer: y^2 - 1 or y^2 - 2y + 1
Step-by-step explanation:
I assume you mean do the square of y and not (y - 1).
The squared of y is, well, y^2
So, the answer is y^2 - 1.
However, if you meant (y - 1) ^2 you will end up with y^2 - 2y + 1
The following table represents a linear function. use the value in the tables to find the slope of the line.
7 x+2 1 3. Add/Subtract: + Simplify and state the domain. 2x + 2 4 x+1 4. Subtract: 4 x2-3x+2 Simplify and state the domain. 3x - 3 Ź 5. Add Subtract: 2 3x-5 x2-7x 2x – 14 Simplify and state the domain.
Answer:
Explanation:
Given the below;
[tex]\frac{1}{2}+\frac{15}{2x-14}-\frac{3x-5}{x^2-7x}[/tex]To simplify the above, we have to 1st find the LCM of 2, 2x - 14, and x^2 - 7x which is 2x(x - 7), so we'll have;
[tex]\frac{x(x-7)+15x-2(3x-5)}{2x(x-7)}[/tex]Let's go ahead and simplify;
[tex]undefined[/tex]true or false3. The expression 78 − 22 + − 4 is a polynomial of degree 8
The expression is:
[tex]7x^8-2x^2+x-4^{}[/tex]In general, a polynomial has the form:
[tex]a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0,a_n\ne0[/tex]And we say that the polynomial is the degree n.
In our expression. a_n=7 and that is not equal to zero. Then, the expression is of degree 8 since a_n=7=a_8. The answer is true.
3r^2+27[tex]3r { +}^{2} + 27 = 0[/tex]
Solution
For this case we have the following:
[tex]3r^2+27=0[/tex]We can subtract 27 in both sides and we got:
[tex]3r^2=-27[/tex]Then we can divide both sides by 3 and we got:
[tex]r^2=-9[/tex]Then the possible to solution are:
[tex]r=3i,r=-3i[/tex]Your younger brother just heard about the 50-20-30 savings rule of thumb and asks you what it is. What do you tell him?
The 50-20-30 savings rule is a simple plan that helps people on managing their money.
It states that over your total after-tax earnings, 50% should be spent on your needs and obligations. 20% should be spent on savings and debt payments, and 30% on whatever else you like.
Determine the constant of proportionality for the relationship.
p equals 2 over 150
p = 0.0133
p = 75
p = 150
The constant of proportionality is 0.0133
How to determine the constant of proportionality?From the question, the given parameters are
Relationship: p = 2 over 150 q
Rewrite the expression properly
So, we have
p = 2/150q
The above parameters can be represented as the following points
(p, q) = (150, 2)
The constant of proportionality of the points is then calculated as
k = q/p
Substitute the known values in the above equation
So, we have the following equation
k = 2/150
Evaluate the quotient in the above expression
So, we have
k = 0.0133
Hence, the relationship has a constant of proportionality of 0.0133
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what's the velocity of a sound wave traveling through Air at a temperature of 20 degrees Celsius
The velocity of a sound wave as a function of the temperature of the air is given by the equation
[tex]V=331+\text{0}.6\cdot T[/tex]Where T is the temperature in degrees celsius.
Using this equation, calculate the velocity of a sound wave at 20 degrees Celsius:
[tex]V=331+0.6\cdot20=331+12=343[/tex]Answer: the velocity is 343 m/s
Solve in simplest form
3x(9/8)
Answer:
27x/8
Step-by-step explanation:
3*9/8
3x*9/8
27x/8
Graph the line y= −5/2x + 2, then name the slope and y-intercept by looking at the graph.
ANSWER and EXPLANATION
We want to graph the given function:
[tex]y=-\frac{5}{2}x+2[/tex]To do that, we have to find two points that lie on the line.
Let us solve for y when x is 0 and 2.
When x = 0:
[tex]\begin{gathered} y=-\frac{5}{2}(0)+2 \\ y=0+2 \\ y=2 \end{gathered}[/tex]When x = 2:
[tex]\begin{gathered} y=-\frac{5}{2}(2)+2 \\ y=-5+2 \\ y=-3 \end{gathered}[/tex]Now, we have two points to plot the line: (0, 2) and (2, -3)
Let us plot the graph:
From the graph, we see that the slope of the graph is:
[tex]m=-\frac{5}{2}[/tex]and the y-intercept is:
[tex]b=2[/tex]If a shape is dilated by a scale factor of 3, what is the resulting perimeter? A.)The new perimeter is 9 times larger than the preimageB.)The same as theperimeter of thepreimageC.)The new perimeter is 4 times the originalD.)The new perimeteris 3 times largerthan the preimage
The perimeter of the figure is sum of the side of the figure. If figure is dilated by factor of 3, means that each side of the figure is dilated by 3.
The addition of dilated side to obtain the perimeter results in 3 times the original perimeter.
So new perimeter is 3 times larger than the preimage. Option D is correct.
Seven movie tickets to a movie cost $50.75. What constant of proportionality relates the number of tickets and total cost?
Group of answer choices
$7
$7.25
$7.75
$7.50
Use the table below. I don’t know how to do ordered pairs I forgot.
Solution
To write in ordered pairs is to arrange it in the form of x and y values
The ordered pairs are
[tex]\begin{gathered} (5.0,4.20) \\ (6.0,5.05) \\ (7.0,5.90) \\ (8.0,6.75) \end{gathered}[/tex]B725с24АFind sin(a) in the triangle.
The sine of an angle on a right triangle is the ratio of the side opposite to that angle divided by the hypotenuse of the triangle.
The side opposite to alpha, is BC, while the hypotenuse is BA. Then:
[tex]\sin (\alpha)=\frac{BC}{BA}[/tex]Substitute the values of BC and BA to find the sine of alpha:
[tex]\sin (\alpha)=\frac{7}{25}[/tex]all you need is on the photo please just give me the answer don't do step-by-step is so confusing is homework
You have the following function:
f(x) = x² - x
- In order to determine the vertex of the function, consider that for the general form of a quadratic function:
f(x) = ax² + bx + c
the value of x at the vertex is:
x = -b/2a
for the given function you have a = 1, b = -1, c =0:
x = -(-1)/2(1) = 1/2 = 0.5
next, replace the previous value of x into the function:
f(1/2) = (1/2)² - (1/2) = 1/4 - 1/2 = -1/4 = -0.25
Hence, the vertex is (0.5 , -0.25)
- The axis of symmetry is the value of x atthe vertex:
x = 0.5
- The x-intercepts are the zeros of the function:
x² - x = 0 by factorizing
x(x - 1) = 0
Then, the zeros are:
x =0
x = 1
Hence, the x-intercepts are x=0 and x=1
- Due to the coefficient a is positive and the term ax² is the dominant term, this curve has a minimum. This minimum is the vertex (0.5 , -0.25)
- The minimum value of the function is -0.25
- The y-intercept is the value of y when x=0:
f(0) = 0² - 0 = 0
What is the approximate slope of the curve with equation-atx=1.2?
a) -25
b) -1/25
c) 25
d) 1/25
The most appropriate choice of slope of a curve will be given by
Slope of the curve at x = 1.2 = -25
First option is correct
What is slope of a curve?
Slope of curve at a point is the tan of the angle that the tangent to the curve at that point makes with the positive direction of x axis.
Here,
f(x) = [tex]\frac{1}{x - 1}[/tex]
[tex]f^{'}(x) = \frac{d}{dx} (\frac{1}{x-1})[/tex]
= [tex]-(x -1)^{-2}[/tex]
= [tex]-\frac{1}{(x-1)^2}[/tex]
At x = 1.2,
Slope = [tex]f^{'}(1.2) = -\frac{1}{(1.2 - 1)^2}[/tex]
= -[tex]\frac{1}{0.04}[/tex]
= -25
First option is correct
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