Answers
ANSWER:
-4.1201
SOLUTION
[tex]\log _b\frac{1}{4}=\log _b1-\log _b4[/tex]this is also equivalent to
[tex]\log _b\frac{1\times7}{4\times7}=\log _b\frac{7}{28}=\log _b7-\log _b28=5.7833-9.9034=-4.1201[/tex]Related Questions
I wonder what I’m doing wrong ?
P^2-10p+16=1+6p
Answer is (15,1)
But I can’t seem to figure it out.
Answers
Steps to Solve:
1. Collect like terms
2. Factor quadratic
3. solve for p
Factoring a Quadratic where a = 1
1. find two numbers that are the product of ac and the sum of b
2. set up the two linear terms with the variable associated with a
2. insert the values found in step 1 into parentheses
1. collect like terms
[tex]p^2-10p-6p+15-1=0[/tex]
[tex]p^2-16p+15 = 0[/tex]
2. Factor quadratic
ac = 15 and b =-16, two numbers that multply to ac and are the sum of b are -15 and 1[tex](p-15)(p-1)=0[/tex]
2 solutions can be found[tex]p-15=0[/tex] OR [tex]p-1=0[/tex]
[tex]p= 15[/tex] [tex]p=1[/tex]
A long distance runner runs 2⁵ miles one week and 2⁷ miles the next week. How many times farther did he run in the second week than the first week?
Answers
Answer:
he ran 96 miles farther in the second week.
Explanation:
Given that A long distance runner runs 2⁵ miles one week;
[tex]2^5miles=2\times2\times2\times2\times2=32miles[/tex]And 2⁷ miles the next week;
[tex]2^7miles=2\times2\times2\times2\times2\times2\times2=128\text{ miles}[/tex]The amount of miles farther he run in the second week than the first week is;
[tex]\begin{gathered} 128-32 \\ =96\text{ miles} \end{gathered}[/tex]Therefore, he ran 96 miles farther in the second week.
What is the unknown angle b?
Answers
Answer:
48°
Explanation:
A line always equals 180°. The angle on the right is a 90° angle (we know this because or the little red box shown) and the angle in the middle is 42°. We would add 42° and 90° to get the combination of both which is 132°
42+90=132
Then subtract 132° from 180° to find unknown angle b.
180-132=48
Unknown angle b= 48°
In may 2020, there were 2,119,800 people in the available labor force in oregon. the unemployment rate in oregon for may 2020 was 14.2%. determine the number of people who were unemployed in oregon during may 2020. round your answer to the nearest whole number.
Answers
301,012
1) Considering the data, we can write out the following equivalence:
[tex]\begin{gathered} 2,119,800---100\% \\ x--------14.2\% \end{gathered}[/tex]2) Notice that we need to rewrite those figures as 100% =1, and 14.2% as 0.142.
Now we can calculate how many people are equivalent to that rate of unemployment:
[tex]\begin{gathered} \frac{2119800}{x}=\frac{1}{0.142} \\ x=2119800\cdot0.142 \\ x=301,011.6\approx301,012 \end{gathered}[/tex]Notice that we rounded off to the nearest whole number.
3) So, there were approximately 301,012 Oregonians unemployed at that time
The diagram shows two similar polygonsN51P224048MR3016.5SFigures not drawn to scale.What is the length of CS?
Answers
Notice the correspondence between the vertices of the polygons:
[tex]VQRGX\approx CNPMS[/tex]Corresponding segments of similar polygons are proportional. Then:
[tex]\frac{CS}{VX}=\frac{PM}{RG}[/tex]Substitute VX=48, PM=22 and RG=16.5 and solve for CS:
[tex]\begin{gathered} \Rightarrow\frac{CS}{48}=\frac{22}{16.5} \\ \Rightarrow CS=\frac{22}{16.5}\times48 \\ \Rightarrow CS=64 \end{gathered}[/tex]Therefore, the length of CS is 64.
Pls help ASAP!!! Ill give you 5.0
Answers
The equivalent equation of 6x + 9 = 12 is 2x + 3 = 4.
Another equivalent equation of 6x + 9 = 12 is 3x + 4.5 = 6
What are equivalent equations?Equivalent equations are algebraic equations that have identical solutions or roots. In other words, equivalent equations are equations that have the same answer or solution.
Therefore, the equivalent equation of 6x + 9 = 12 can be calculated as follows:
6x + 9 = 12
Divide through by 3
6x / 3 + 9 / 3 = 12 / 3
2x + 3 = 4
Therefore, the equivalent equation of 6x + 9 = 12 is 2x + 3 = 4
Another equation that is equivalent to 6x + 9 = 12 is 3x + 4.5 = 6
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A right triangle is shown in the figure what is the value of x
Answers
So,
We could use the pythagorean theorem as follows:
[tex](3x)^2+x^2=(\sqrt[]{40})^2[/tex]And then solve for x:
[tex]\begin{gathered} 10x^2=40 \\ x^2=\frac{40}{10} \\ x^2=4 \\ x=2 \end{gathered}[/tex]Therefore, x=2.
Expand the polynomial. 1. (m^2-n)(m^2+2n^2)2. (a-2)(4a^3-3a^2)
Answers
1)
The given polynomial is
[tex](m^2-n)(m^2+2n^2)[/tex]Multiply as follows:
[tex](m^2-n)(m^2+2n^2)=m^2(m^2+2n^2)-n(m^2+2n^2)[/tex][tex]=m^2\times m^2+m^2\times2n^2-n\times m^2-n\times2n^2[/tex][tex]=m^4+2m^2n^2-m^2n-2n^3[/tex]Hence the required expansion is
[tex](m^2-n)(m^2+2n^2)=m^4+2m^2n^2-m^2n-2n^3[/tex]2)
The given polynomial is
[tex](a-2)(4a^3-3a^2)[/tex]Multiply as follows:
[tex](a-2)(4a^3-3a^2)=a(4a^3-3a^2)-2(4a^3-3a^2)[/tex][tex]=a\times4a^3-a\times3a^2-2\times4a^3-(-2)\times3a^2[/tex][tex]=4a^4-3a^3-8a^3+6a^2[/tex][tex]=4a^4-11a^3+6a^2[/tex]Hence the required expansion is
[tex](a-2)(4a^3-3a^2)=4a^4-11a^3+6a^2[/tex]TRIGONOMETRY Find the length of the longer diagonal of this parallelogram round to the nearest tenth
Answers
Given the parallelogram ABCD
As shown: AB = 4 ft
m∠BAC = 30
m∠BDC = 104
We will find the length of the longer diagonal which will be AC
See the following figure:
The point of intersection of the diagonals = O
The opposite sides are parallel
AB || CD
m∠ABD = m∠BDC because the alternate angles are congruent
So, in the triangle AOB, the sum of the angles = 180
m∠AOB = 180 - (30+104) = 46
We will find the length of OA using the sine rule as follows:
[tex]\begin{gathered} \frac{OA}{\sin104}=\frac{AB}{\sin 46} \\ \\ OA=AB\cdot\frac{\sin104}{\sin46}=4\cdot\frac{\sin104}{\sin46}\approx5.3955 \end{gathered}[/tex]The diagonals bisect each other
So,
[tex]AC=2\cdot OA=10.79[/tex]The longer diagonal is AC
Rounding to the nearest tenth
So, the answer will be AC = 10.8 ft
An object was dropped off the top of a building. The function f(x) = -16x2 + 36represents the height of the object above the ground, in feet, X seconds after beingdropped. Find and interpret the given function values and determine an appropriatedomain for the function.
Answers
f(x) = -16x^2 + 36
Where:
f(x) = height of the object
x = seconds after being dropped.
f(-1) = -16 (-1)^2 + 36
f(-1) = -16 (1) + 36
f(-1) = 20
-1 seconds after the object was dropped, the object was 20 ft above the ground.
This interpretation does not make sense, because seconds can't be negative.
f(0.5) = -16 (0.5)^2 + 36
f(0.5) = -16 (0.25) +36
f(0.5) = -4 + 36
f(0.5) = 32
0.5 seconds after the object was dropped, the object was 32 ft above the ground.
This interpretation makes sense in the context of the problem.
f(2) = -16 (2)^2 + 36
f(2) = -16 (4) +36
f(2) = -64+36
f(2) = -28
2 seconds after the object was dropped, the object was -28 ft above the ground.
This interpretation does not make sense in the context of the problem, because the height can't be negative.
Based on the observation, the domain of the function is real numbers in a <- x <-b , possible values of x where f(x) is true.
before the object is released x=0
next, calculate x when f(x)=0 ( after the object hits the ground)
0= -16x^2+36
16x^2 = 36
x^2 = 36/16
x^2 = 2.25
x = √2.25
x = 1.5
0 ≤ x ≤ 1.5
I need help understanding slope
Answers
we know that
the formula to calculate teh slope between two points is equal to
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]where
(x1,y1) is one point
and
(x2,y2) is the other point
substitute the values in the formula and solve for m
Example
you have the points
(1,4) and (3,2)
so
(x1,y1)=(1,4)
(x2,y2)=(3,2)
substitute in te formula
m=(2-4)/(3-1)
m=-2/2
m=-1
the slope is -1
i need help with my homework PLEASEMCHECK WORK WHEN FINISHED
Answers
Given:
The population of a town increases by 9 % annually.
The current population is 4,500.
Required:
We need to find the equation that gives the population of the town.
Explanation:
The population can be found by the following equation.
[tex]Th\text{e population =4500+9 \% of 4500}[/tex]Let now be the current population of the town =4500.
Let Next be the population of the town.
The population can be found by the following equation.
[tex]Next\text{ =Now+9\% of Now.}[/tex][tex]Next\text{ =Now+}\frac{9}{100}\times\text{Now.}[/tex]Take the common term now out.
[tex]Next\text{ =Now\lparen1+}\frac{9}{100})[/tex][tex]Use\text{ }\frac{9}{100}=0.09.[/tex][tex]Next\text{ =Now\lparen1+0.09})[/tex][tex]Next\text{ =Now\lparen1.09})[/tex][tex]Next\text{ =Now}\times\text{1.09}[/tex]Final answer:
[tex]Next\text{ =Now}\times\text{1.09}[/tex]Not a timed or graded assignment. Need a quick answer tho. Thank you
Answers
ANSWER:
Difference of squares
[tex]8x-7[/tex]STEP-BY-STEP EXPLANATION:
We have the following quotient:
[tex]\frac{64x^2-49}{8x+7}[/tex]We factor, knowing that the numerator is a difference of squares, therefore:
[tex]\begin{gathered} a^2-b^2=(a+b)(a-b) \\ \text{ in this case} \\ a=8x \\ b=7 \\ 64x^2-49=(8x+7)(8x-7) \\ \text{ Replacing:} \\ \frac{(8x+7)(8x-7)}{8x+7}=8x-7 \end{gathered}[/tex]i need help on number 7. Please use 4 points
Answers
In order to graph this equation, we need at least two points that are solution to the equation.
To find these points, we can choose values for x and then calculate the corresponding values of y.
Choosing the x-values of -2, -1, 0 and 1, we have:
[tex]\begin{gathered} x=-2\colon \\ y=-\frac{5}{2}\cdot(-2)-1 \\ y=5-1 \\ y=4 \\ \\ x=-1\colon \\ y=-\frac{5}{2}(-1)-1 \\ y=2.5-1 \\ y=1.5 \\ \\ x=0\colon \\ y=-\frac{5}{2}\cdot0-1 \\ y=-1 \\ \\ x=1\colon \\ y=-\frac{5}{2}\cdot1-1 \\ y=-2.5-1 \\ y=-3.5 \end{gathered}[/tex]So we have the points (-2, 4), (-1, 1.5), (0, -1) and (1, -3.5). Graphing these points and the line that passes through them, we have:
Factor completely. (3.2² - 12x)(x2 – 2x + 1) =
Answers
We will have the following:
Find the measures of the numbered angles in rhombus DEFG. I just need someone to shown me how to find each of the numbered angles
Answers
Step 1
Properties of a Rhombus
Below are some important facts about the rhombus angles:
Rhombus has four interior angles.
The sum of interior angles of a rhombus add up to 360 degrees.
The opposite angles of a rhombus are equal to each other.
The adjacent angles are supplementary.
In a rhombus, diagonals bisect each other at right angles.
The diagonals of a rhombus bisect these angles.
Step 2
From the figure
Angle DGF = Angle DEF = 118
Step 3
Since adjacent angles are supplementary, that is add to 180 degrees
[tex]\begin{gathered} \angle\text{DGF + }\angle GFE\text{ = 180} \\ 118\text{ + }\angle GFE\text{ = 180} \\ \angle GFE\text{ = 180 - 118} \\ \angle GFE\text{ = 62} \end{gathered}[/tex]Step 4
The diagonals of a rhombus bisect these angles
[tex]\begin{gathered} \angle3\text{ = }\angle4\text{ = }\frac{62}{2}\text{ = 31} \\ \angle3\text{ = }\angle4\text{ = 31} \end{gathered}[/tex]Step 5
The opposite angles of a rhombus are equal to each other.
[tex]\angle1\text{ = }\angle\text{ 2 = 31}[/tex]Final answer
[tex]\angle\text{1 = }\angle\text{ 2 = }\angle\text{ 3 = }\angle4\text{ = 31}[/tex]What is 4 1/10 equal to
Answers
We are given the following mixed fraction:
[tex]4\frac{1}{10}[/tex]This is a fraction of the form:
[tex]a\frac{b}{c}[/tex]Any mixed fraction can be rewritten using the following relationship:
[tex]a\frac{b}{c}=a+\frac{b}{c}[/tex]Applying the relationship we get:
[tex]4\frac{1}{10}=4+\frac{1}{10}[/tex]Now, we add the whole number and the fraction using the following relationship:
[tex]a+\frac{b}{c}=\frac{ac+b}{c}[/tex]Applying the relationship we get:
[tex]4+\frac{1}{10}=\frac{40+1}{10}=\frac{41}{10}=4.1[/tex]Therefore, the mixed fraction is equivalent to 4.1
The figure below is an iscoceles trapezoid. If m
Answers
..Given an isosceles trapezoid
The following are the properties of an isosceles trapezoid
The legs are congruent by definition (From the diagram, the legs are JM and KL)
The lower base angles are congruent. The lower base angles are
[tex]m\angle M\cong m\angle L[/tex]The upper base angles are congruent. The upper base angles are
[tex]m\angle J\cong m\angle K[/tex]Any lower base angle is supplementary to any upper base angle. This means that
[tex]\begin{gathered} m\angle J+m\angle M=180^0 \\ m\angle K+m\angle L=180^0 \end{gathered}[/tex][tex]\begin{gathered} \text{If} \\ m\angle K=61^0 \\ \text{Therefore} \\ m\angle J\cong m\angle K=61^0 \\ m\angle J=61^0 \end{gathered}[/tex]Also,
[tex]\begin{gathered} m\angle L+m\angle K=180^0 \\ m\angle L+61^0=180^0 \\ m\angle L=180^0-61^0 \\ m\angle L=119^0 \end{gathered}[/tex][tex]\begin{gathered} m\angle L\cong m\angle M,m\angle L=119^0 \\ Therefore\colon \\ m\angle M=119^0 \end{gathered}[/tex]Hence
m∠J = 61⁰
m∠L = 119⁰
m∠M = 119⁰
K
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in
the table.
Drive-thru Restaurant D
B C
D
280
245
122
60
32
12
A
Order Accurate
331
Order Not Accurate 38
If one order is selected, find the probability of getting an order that is not accurate or is from Restaurant C. Are the events of selecting an order that is not accurate and
selecting an order from Restaurant C disjoint events?
The probability of getting an order from Restaurant C or an order that is not accurate is
(Round to three decimal places as needed.)
Are the events of selecting an order from Restaurant C and selecting an inaccurate order disjoint events?
disjoint because it
possible to
The events
Answers
The probability is 0.236 and the events are not disjoint events
Given,
The data;
A B C D
Order accurate ; 280 245 122 331
Order not accurate; 60 32 12 38
The probability of getting an order that is not accurate or is from Restaurant C
This is illustrative of
P(Not accurate or Restaurant C) (Not accurate or Restaurant C)
The calculation is
P(Not accurate or Restaurant C) is equal to [n(Not accurate) + (Not accurate and Restaurant C) - n(Restaurant C)] /Total
Thus, we have
P(Not accurate or Restaurant C) is calculated as follows: (60 + 32 + 12 + 38 + 122 + 12 - 12)/(280 + 245 + 122 + 331 + 60 + 32 + 12 + 38).
Analyze the difference and the total.
Restaurant C or P(Not accurate) = 264/1120
Assess the quotient.
P(Not accurate or Restaurant C) = 0.236
Last but not least, choosing an incorrect order and choosing an order from Restaurant C are not separate events.
This is because choosing an inaccurate order from restaurant C is a possibility.
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you get a student loan from the educational assistance Foundation to pay for your educational expenses as you earn your associate's degree you will be allowed 10 years to pay the loan back find the simple interest on the loan if you borrow $3,600 at 8 percent
Answers
Simple interest = PRT/100
where p = $3600
R=8
T=10
Substituting into the formula;
S.I = $3600 x 8 x 10 /100
=$36 x 8 x 10
=$2880
A certain marine engine has cylinders that are 5.25 cm in diameter and 5.64 cm deep.Find the total volume of 4 cylinders (to the nearest hundredth). Use 3.14 as the approximate value of
Answers
Given:
A cylinder is given with 5.64 cm deep and 5.25 cm diameter.
Required:
Total volume of 4 cylinders.
Explanation:
Diameter of cylinder d = 5.25 cm
Height of cylinder or deepness of cylinder h = 5.64 cm
Radius r of cylinder is
[tex]r=\frac{d}{2}=\frac{5.25}{2}=2.625\text{ cm}[/tex]volume of cylinder is
[tex]v=\pi r^2h=3.14*2.625^2*5.64=122.03\text{ cm}^3[/tex]here we need volume of 4 cylinder
for this we just multiply v with 4
[tex]V=4v=4*122.03=488.121\text{ cm}^3[/tex]Final Answer:
The volume of 4 cylinder is 488.121 cube cm
Hello I need help with this question as fast as possible please , I am on my last few questions and I have been studying all day for my final exam for math tomorrow. It is past my bed time and I am exhausted . Thank you so much for understanding:))
Answers
Notice that:
[tex]665.6=10.4\times64.[/tex]Therefore, if we divide the resulting equation of step 3 by 10.4 we get:
[tex]\begin{gathered} \frac{10.4x}{10.4}=\frac{665.6}{10.4}, \\ x=64. \end{gathered}[/tex]Then the missing step is:
Divide both sides of the equation by 10.4.
Answer: Last option.
The world's largest swimming pool is the Orthalieb pool in Casablanca, Morocco the length is 30 m longer then 6 times the width. If the perimeter of the pool is 1110 Meters what are the dimensions of the pool?
Answers
The length of the rectangular pool is 30m longer than 6 times the width.
Let "x" represent the length of the width, then you can express the dimensions of the pool as follows:
[tex]\begin{gathered} w=x \\ l=6x+30 \end{gathered}[/tex]The perimeter of the pool is 1110m, this perimeter was obtained using the formula:
[tex]P=2w+2l[/tex]Replace the formula with the expressions determined for the width and length:
[tex]1110=2(x)+2(6x+30)[/tex]From this expression, you can determine the value of x:
-First, distribute the multiplications on the right side of the equation:
[tex]\begin{gathered} 1110=2x+2\cdot6x+2\cdot30 \\ 1110=2x+12x+60 \\ 1110=14x+60 \end{gathered}[/tex]-Second, pass 60 to the left side of the equal sign by applying the opposite operation to both sides of it:
[tex]\begin{gathered} 1110-60=14x+60-60 \\ 1050=14x \end{gathered}[/tex]-Third, divide both sides of the equation by 14 to determine the value of x:
[tex]\begin{gathered} \frac{1050}{14}=\frac{14x}{14} \\ 75=x \end{gathered}[/tex]The width of the pool is w= 75 meters
Now you can determine the length of the pool:
[tex]\begin{gathered} l=6x+30 \\ l=6\cdot75+30 \\ l=480 \end{gathered}[/tex]The length of the pool is l=480 meters
The first five multiples for the numbers 4 and 6 are shown below.Multiples of 4: 4, 8, 12, 16, 20Multiples of 6: 6, 12, 18, 24, 30,What is the least common multiple of 4 and 6?241224
Answers
We have
Multiples of 4: 4, 8, 12, 16, 20
Multiples of 6: 6, 12, 18, 24, 30,
the least common multiple is the first number share between these numbers as we can see the first number share is 12
Tell whether the triangle with the given side lengths is a right triangle. 18, 80, 82 Write the pythagorean theorem Substitute the values from the triangle in the equation then solve If both side of the equation is the same then yes the triangle is right triangle. Il both sides are different then no the triangle is not a right triangle
Answers
Pythagorean theorem :
c^2 = a^2 + b^2
Where:
c = hypotenuse (the longest side ) = 82
A & b = the other 2 sides (18 and 80)
Replacing:
82^2 = 80^2 + 18^2
Solve:
6,724 = 6,400+ 324
6,724 = 6,724
Both sides of the equations are equal. IT is a right triangle
The formula to calculate the gravitational force between two objects is F_g=\frac{GM_1M_2}{r^2},F
g
=
r
2
GM
1
M
2
, where M_1M
1
and M_2M
2
are the masses of the objects, GG is the gravitational constant and rr is the distance between the objects. Solve for M_2M
2
in terms of F_g,F
g
, G,G, M_1M
1
and r.r.
Answers
The expression for M in terms of other variables is M = Fr^2/Gm
Subject of formulaThe variable being calculated is the formula's subject. On one side of the equals sign, it is identifiable as the letter on its own.
In order to make one of the the variables the subject of the formula, we place rewrite the expression in a different form.
Given the formula to calculate the gravitational force between two objects as;
Fg = GMm/r^2
We are to make M the subject of the formula in terms of other variables.
F = GMm/r^2
Cross multiply
Fr^2 = GMm
Divide both sides by Gm
Fr^2/Gm = GMm/Gm
Fr^2/Gm = M
Swap
M = Fr^2/Gm
This gives the expression for the variable M.
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Rewrite the following equation in slope-intercept form.
10x − 10y = –1 ?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer:
y = x + 1/10
Step-by-step explanation:
Rewrite the following equation in slope-intercept form: 10x − 10y = –1 ?
slope intercept form: y = mx + b so you are solving for y:
10x − 10y = –1
subtract 10x from both sides:
10x − 10y – 10x = –1 – 10x
-10y = –1 – 10x
divide all terms by -10:
-10y/(-10) = –1/(-10) – 10x/(-10)
y = 1/10 + x
rearrange for slope intercept form: y = mx + b
y = x + 1/10
Answer:
[tex]y=x+\dfrac{1}{10}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given equation:
[tex]10x-10y=-1[/tex]
To write the given equation in slope-intercept form, perform algebraic operations to isolate y.
Add 10y to both sides of the equation:
[tex]\implies 10x-10y+10y=10y-1[/tex]
[tex]\implies 10x=10y-1[/tex]
Add 1 to both sides of the equation:
[tex]\implies 10x+1=10y-1+1[/tex]
[tex]\implies 10x+1=10y[/tex]
[tex]\implies 10y=10x+1[/tex]
Divide both sides of the equation by 10:
[tex]\implies \dfrac{10y}{10}=\dfrac{10x+1}{10}[/tex]
[tex]\implies \dfrac{10y}{10}=\dfrac{10x}{10}+\dfrac{1}{10}[/tex]
[tex]\implies y=x+\dfrac{1}{10}[/tex]
Therefore, the given equation in slope-intercept form is:
[tex]\boxed{y=x+\dfrac{1}{10}}[/tex]
Find a polynomial f(x) of degree 4 with real coefficients and the following zeros.3 (multiplicity 2) , -i
Answers
We are told that we want a polynomial f(x) with the given zeros.
Recall that if we know the zeros oa polynomial, we can write the polynomial by writing the factors (x - zero of the polynomial) and multiply them all together.
For example, if we want a polynomial of degree 2 with zeros at 2 and 3, then the polynomial would be
[tex](x\text{ -2)}\cdot(x\text{ -3)}[/tex]In this case, we have a polynomial f(x) of degree 4. So far, we know that 3 is a zero and that -i is a zero. So we write the following
[tex]f(x)=(x\text{ -a)}\cdot(x\text{ -b)}\cdot(x\text{ -c) }\cdot\text{ (x -d)}[/tex]where a,b,c and d are the zeros of f(x). We know that 3 is a zero and that -i is a zero. So we have
[tex]f(x)=(x\text{ -3)}\cdot(x\text{ -b)}\cdot(x\text{ -( -i)) }\cdot(x\text{ -d)}[/tex]So to fully describe f(x) we need to find the values of b and d. We are told that 3 is a zero of multiplicity 2. This means that the factor (x -3) appears two times in the factorization of f(x). So we can say that b=3. So we have
[tex]f(x)=(x\text{ -3)}\cdot(x\text{ -3) }\cdot(x\text{ +i ) }\cdot(x-d)=(x-3)^2\cdot(x\text{ +i)}\cdot(x\text{ -d)}[/tex]Now, we need to find the value of d. Note that we are told that -i is a zero of the function. -i is a complex number, so one important property of polynomials is that if a complex number a+bi is a zero of the polynomial, then the number a-bi (which is called the complex conjugate) is also a zero. Note that the complex conjugate of a complex number is calculated by leaving the real part intact and multiplying the imaginary part by -1.
In our case we have the complex number -i. So we can write -i= 0 - 1i . Then, its complex conjugate is i.
So, we have that d=i.
Then our polynomial would look like this
[tex]f(x)=(x-3)^2\cdot(x+i)\cdot(x\text{ -i)}[/tex]Note that
[tex](x+i)\cdot(x-i)=x^2\text{ -i}\cdot x\text{ + i}\cdot x+1=x^2+1[/tex]So our polynomial ends up being
[tex]f(x)=(x-3)^2\cdot(x^2+1)[/tex]Solve for x: 3x + 2 = 11 A : 11/5 B: 3. C : 11/3. D : 13/3. E : 6
Answers
Explanation:
The equation is given as:
3x + 2 = 11
The first step is to collect like terms ( Note that if 2 crosses to the other side of the equality sign, it becomes -2)
3x = 11 - 2
3x = 9
The next step is to divide both sides by 3:
3x/3 = 9/3
x = 3
3
Drag each tile to the correct box.
Place the parallelograms in order from least area to greatest area.
3 cm
4 cm
6 cm
3 cm
4 cm
5 cm
4 cm
3 cm
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4 cm
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Answers
The least area of the parallelogram will be 12cm² and the greatest area will be 20cm².
What will be the area of the parallelogram?The area of a parallelogram is simply calculated thus:
= Base × Height
The least area will be:
= Base × Heights
= 3cm × 4cm
= 12cm²
The greatest area of the parallelogram will be:
= Base × Height
= 4cm × 5cm
= 20cm²
Note that the figures are gotten from the. information given.
Learn more about parallelogram on:
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