Answer:
$31.95
Step-by-step explanation:
The total cost is the initial fee plus the cost of the boxes.
12 + 5×3.99 = 31.95
2354 bdxbdbdbht55675443t35222222222222222222222222
You are choosing 3 of your 7 trophies and arranging them in a row on a shelf.
In how many different ways can you choose and arrange the trophies?
Answer:
21
Step-by-step explanation:
you can arrange 7×3 ways
Answer with explanation:
Number of trophies possessed by me= 7
Number of trophies that is to be selected from 7 trophies =3
⇒⇒So, Chosing 3 out of 7 trophies and arranging them on a shelf requires Concept of Permutation, as order of arrangement is also taken into consideration
[tex]=_{3}^{7}\textrm{P}\\\\=\frac{7!}{(7-3)!}\\\\=\frac{7!}{4!}\\\\=\frac{4!*5*6*7}{4!}\\\\=5*6*7\\\\=210\text{Ways}[/tex]
Or
⇒First place can be filled in 7 ways,second place can be filled in 6 ways and third place can be filled in 5 ways.
So total number of ways of selecting 3 trophies from 7 trophies
=7 *6 *5
=210 ways
⇒Now, 3 trophies can be arranged in a shelf in 3! =3 *2*1=6 ways.
Expected Value (50 points)
Game: Roll two dice. Win a prize based on the sum of the dice.
Cost of playing the game: $1
Prizes:
Win $10 if your sum is odd.
Win $5 if you roll a sum of 4 or 8.
Win $50 if you roll a sum of 2 or 12.
Answer both question. Will give brainly.
Explain HOW to find the expected value of playing this game. What is the expected value of playing this game? Show your work. (30 points)
Interpret the meaning of the expected value in the context of this game. Why should someone play or not play this game. Answer in complete sentences. (20 points)
Let [tex]W[/tex] be the random variable representing the winnings you get for playing the game. Then
[tex]W=\begin{cases}9&\text{if the sum is odd}\\4&\text{if the sum is 4 or 8}\\49&\text{if the sum is 2 or 12}\\-1&\text{otherwise}\end{cases}[/tex]
First thing to do is determine the probability of each of the above events. You roll two dice, which offers 6 * 6 = 36 possible outcomes. You find the probability of the above events by dividing the number of ways those events can occur by 36.
The sum is odd if one die is even and the other is odd. This can happen 2 * 3 * 3 = 18 ways. (3 ways to roll even with the first die, 3 ways to roll odd for the die, then multiply by 2 to count odd/even rolls)The sum is 4 if you roll (1, 3), (2, 2), or (3, 1), and the sum is 8 if you roll (2, 6), (3, 5), (4, 4), (5, 3), or (6, 2). 8 ways.The sum is 2 if you roll (1, 1), and the sum is 12 if you roll (6, 6). 2 ways.There are 36 total possible rolls, from which you subtract the 18 that yield a sum that is odd and the other 10 listed above, leaving 8 ways to win nothing.So the probability mass function for this game is
[tex]P(W=w)=\begin{cases}\frac12&\text{for }w=9\\\frac29&\text{for }w=4\text{ or }w=-1\\\frac1{18}&\text{for }w=49\\0&\text{otherwise}\end{cases}[/tex]
The expected value of playing the game is then
[tex]E[W]=\displaystyle\sum_ww\,P(W=w)=\frac{71}9[/tex]
or about $7.89.
The expected value is positive, so a player can expect to earn money in the long run, and so should play the game.
Please help me.. What is the length of side x?
3.25
12
14.5
16
Answer:
x = 16
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{RS}{MN}[/tex] = [tex]\frac{RT}{MO}[/tex], that is
[tex]\frac{8}{x}[/tex] = [tex]\frac{6.5}{13}[/tex] ( cross- multiply )
6.5x = 104 ( divide both sides by 6.5 )
x = 16
finding whole number equal to fraction 8/1
Answer: 8
Step-by-step explanation: 8 divided by 1 is 8
8 is the whole number equal to fraction 8/1.
What is Number system?A number system is defined as a system of writing to express numbers.
The given fraction is 8/1
Eight divided by one.
A fraction represents a part of a whole or, more generally, any number of equal parts.
8 is the numerator and 1 is the denominator.
The complete set of natural numbers along with '0' are called whole numbers.
If a number is divided by another number then the result will be the numerator which is whole number.
8/1=8
Hence, 8 is the whole number equal to fraction 8/1.
To learn more on Number system click:
https://brainly.com/question/22046046
#SPJ2
25. Tom and Jerry must stuff and mail 1000
envelopes for a new marketing campaign. Jerry
can do the job alone in 6 hours. If Tom helps,
they can get the job done in 4 hours. How long
would it take Tom to do the job by himself?
A. 4 hours
B. 5 hours
C. 8 hours
D. 12 hours
Answer:
12
Step-by-step explanation:
The general formula for this is
Formula
1/t1 + 1/t2 = 1/t_tot
givens
t1 = 6 hours
t2 = x
t_tot = 4 hours
Solution
1/6 + 1/x = 1/4 Subtract 1/6 from both sides.
1/6-1/6 + 1/x = 1/4 - 1/6 Change to 12 as your common denominator
1/x = 3/12 - 2/12 subtract
1/x = 1/12 Cross multiply
x = 12
Tom would need 12 hours to do the job alone.
Answer:
Option D. 12 hours
Step-by-step explanation:
Let the work done by Tom to do the job alone = x hours
So per hour work done by Tom = [tex]\frac{1}{x}[/tex]
Jerry can do the job alone in the time = 6 hours
Per hour work done by Jerry = [tex]\frac{1}{6}[/tex]
Similarly job done by both together in the time = 4 hours
Per hour work done by both together = [tex]\frac{1}{4}[/tex]
Now we know,
Per hour work done by both together = per hour work done by Tom + Per hour work don by Jerry
[tex]\frac{1}{4}=\frac{1}{x}+\frac{1}{6}[/tex]
[tex]\frac{1}{x}=\frac{1}{4}-\frac{1}{6}[/tex]
[tex]\frac{1}{x}=\frac{3-2}{12}[/tex]
[tex]\frac{1}{x}=\frac{1}{12}[/tex]
x = 12 hours
Option D. will be the answer.
PLEASE ANSWER FIRST GETS BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Let Bikes = B and cars = c
a bike has 2 wheels and a car has 4 wheels.
Equation 1: add bikes and cars to get total students:
b + c = 80
Equation 2: multiply the number of wheels by each type and add to equal the total wheels.
2b +4c = 270
Rewrite the first equation as b = 80- c
Now substitute that for b in the second equation:
2(80-c) + 4c = 270
Simplify:
160 - 2c + 4c = 270
160 +2c = 270
Subtract 160 from both sides:
2c = 110
Divide both sides by 2
c = 110/2
c = 55
Replace c with 55 in the first equation and solve for b:
b + 55 = 80
b = 80-55
b = 25
b = 25, c = 55
The function F(c) = 9/5 c + 32 allows you to
Answer:
convert from Celsius to Fahrenheit
Step-by-step explanation:
i work with thermometers i know
For this case we have that by definition, to convert degrees Celsius to Fahrenheit we use the following formula:
[tex]F = \frac {9} {5} C + 32[/tex]
Where:
C: Represents the degrees Celsius
So, we can write a function:
[tex]F (C) = \frac {9} {5} C + 32[/tex]
Answer:
The function allows to convert degrees Celsius to Fahrenheit
Give the equation for a circle with the given center and radius.
Center at (4, 1), radius = 6
Answer:
(x-4)^2 + (y-1)^2 = 6^2
or
(x-4)^2 + (y-1)^2 = 36
Step-by-step explanation:
The equation for a circle is given by
(x-h)^2 + (y-k)^2 = r^2
where (h,k) is the center and r is the radius
(x-4)^2 + (y-1)^2 = 6^2
or
(x-4)^2 + (y-1)^2 = 36
Answer:
(x - 4)^2 + (y - 1)^2 = 6^2
Step-by-step explanation:
Adapt the standard equation of a circle with center at (h, k) and radius r:
(x-h)^2 + (y-k)^2 = r^2
Here we have:
(x - 4)^2 + (y - 1)^2 = 6^2
1/8 x3-1/27y3 please help ...factor ths expression completely, then place the factors in the proper location on the grid
Answer:
factored form is: [tex](\frac{x}{2}-\frac{y}{3})(\frac{x^2}{4}+\frac{xy}{6}+\frac{y^2}{9})[/tex]
Step-by-step explanation:
The given expression is:
[tex]\frac{1}{8}x^3 - \frac{1}{27}y^3[/tex]
The expression can be written as:
[tex](\frac{1}{2}x)^3-(\frac{1}{3}y)^3[/tex]
We know, a^3-b^3 = (a-b)(a^2+ab+b^2)
a= x/2 and b = y/3
Putting values in the formula given:
[tex](\frac{x}{2}-\frac{y}{3})((\frac{x}{2})^2+(\frac{x}{2})(\frac{y}{3})+(\frac{y}{3})^2)\\(\frac{x}{2}-\frac{y}{3})(\frac{x^2}{4}+\frac{xy}{6}+\frac{y^2}{9})[/tex]
So, factored form is: [tex](\frac{x}{2}-\frac{y}{3})(\frac{x^2}{4}+\frac{xy}{6}+\frac{y^2}{9})[/tex]
What are the sides of PQR?
Answer:
Hi there!
The answer to this question is: B
Answer choice B is correct because the dash above the two letter represents a line segment or side of a triangle
-------------------------------------------------------------------------------------------
Answer choice A: incorrect
Explanation: The little carrot in front of each letter shows that it is an angle not a side
Answer C: incorrect
Explanation: It tells you points of the triangle
Answer:
B.Step-by-step explanation:
[tex]A.\ \angle P,\ \angle Q,\ and\ \angle R-\bold{angles}\\\\B.\ \overline{PQ},\ \overline{QR},\ and\ \overline{PR}-\bold{sides}\\\\C.\ P,\ Q,\ and\ R-\bold{vertexs}[/tex]
La suma de las edades de unos gemelos y unos trillizos es 150 años si se intercambian las edades la nueva suma es 120 años ¿ cual es la edad de los trillizos?
Answer:
The age of triplets is 42 years old
Step-by-step explanation:
The question in English is
The sum of the ages of twins and triplets is 150 years if the ages are exchanged the new sum is 120 years. What is the age of triplets?
Let
x -----> twins age
y ----> triplets age
we know that
2x+3y=150 ------> equation A
2y+3x=120 -----> equation B
Solve the system by graphing
The intersection point both graphs is the solution of the system
The solution is the point (12,42)
see the attached figure
therefore
The age of triplets is 42 years old
y varies inversely with x. When y = 3.6, x = 1.2. What is the value of k, the constant of inverse variation? Round to the nearest hundredth, if necessary.
Answer:
The constant, k, is 4.32.
Step-by-step explanation:
y varies inversely with x means y=k/x.
y varies directly with x means y=kx.
Anyways we have the first relation: y=k/x where k is a constant.
We divided by x because it said inversely.
We are given (x,y)=(1.2,3.6) is on this curve.
This gives us enough information to find the constant, k.
[tex]y=\frac{k}{x}[/tex] with [tex](x,y)=(1.2,3.6)[/tex].
[tex]3.6=\frac{k}{1.2}[/tex]
Multiply both sides by 1.2:
[tex]3.6(1.2)=k[/tex]
[tex]4.32=k[/tex]
The constant, k, is 4.32.
what is an inequality? where would u use them in the real world
An inequality is comparing the relation of two equations that are not equal.
Depending on a persons cell phone plan, if they can only talk for so many minutes per month or send so many texts per month, this is an inequality written as number of minutes/ texts per month needs to be less than or equal to the allowable amount.
Find x to the nearest tenth.
Please answer
Using the Pythagorean theorem:
x = √(11.7^2 - 8.6^2)
x = √(136.89 - 73.96)
x = √62.93
x = 7.9
The answer is D.
the point (3,0) lies on the graph of P(x)=x^3-7x^2+15x-9. True or False
Answer:
True
Step-by-step explanation:
We can plug in and see.
If (3,0) is on the graph of P, then P(3) will evaluate to 0.
Let's try it:
P(3)=(3)^3-7(3)^2+15(3)-9
P(3)=27-7(9)+45-9
P(3)=27-63+45-9
P(3)=-36+45-9
P(3)=9-9
P(3)=0
Since P(3)=0, then (3,0) is an ordered pair of P.
Yes it is true that the point (3,0) lies on the graph of
P(x) = [tex]x^{3}-7x^{2} +15x-9[/tex].
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Given equation
P(x) = [tex]x^{3}-7x^{2} +15x-9[/tex]
If (3,0) is on the graph of P, then P(3) will evaluate to 0.
Substitute x = 3 in the given equation
P(3) = [tex](3)^3-7(3)^2+15(3)-9[/tex]
P(3) = [tex]27-7(9)+45-9[/tex]
P(3) = [tex]27-63+45-9[/tex]
P(3) = 9-9
P(3) = 0
Since P(3)=0, then (3,0) is an ordered pair of P.
Yes it is true that the point (3,0) lies on the graph of
P(x) = [tex]x^{3}-7x^{2} +15x-9[/tex].
Find out more information about equation here
brainly.com/question/2263981
#SPJ2
Find the center and radius of the circle (x+3)^2+(y-1)^2=81
The equation of a circle is written as ( x-h)^2 + (y-k)^2 = r^2
h and k is the center point of the circle and r is the radius.
In the given equation (x+3)^2 + (y-1)^2 = 81
h = -3
k = 1
r^2 = 81
Take the square root of both sides:
r = 9
The center is (-3,1) and the radius is 9
What is the vertex of the graph of y = 5(x + 4)2 + 3? (1 point)
Answer:
[-4, 3]
Step-by-step explanation:
That -h gives you the OPPOSITE terms of what they really are, and k gives you the EXACT terms of what they really are. So, your vertex is [-4, 3].
If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.
Solve the system of equation and choose the correct ordered pair.!2x-6y=8 5x-4y=31
Answer:
The correct ordered pair is (7,1)
Step-by-step explanation:
The given system has equations:
[tex]2x - 6y = 8....(1)[/tex]
[tex]5x- 4y = 31....(2)[/tex]
We make x the subject in the first equation to get:
[tex]x = 4 + 3y...(3)[/tex]
Put equation 3 into equation 2 to get:
[tex]5(4 + 3y) - 4y = 31[/tex]
Expand:
[tex]20 + 15y - 4y = 31[/tex]
[tex]15y - 4y = 31 - 20[/tex]
[tex]11y = 11[/tex]
[tex]y = 1[/tex]
Put y=1 into equation 3 and solve for x.
[tex]x = 4 + 3( 1) = 7[/tex]
The correct ordered pair is (7,1)
Everyday there are 4 times more like on an internet video of a horse which is modeled by the function c(n)=(4)^n-1 where n is the number of day since the video posted on the first day there were 100 likes what is the function that shows the number of likes each day
Answer:
Step-by-step explanation:
A better way to write the first function would be:
c(n) = 4*c(n-1), meaning that the number of likes is equal to four times the number of likes from the previous day.
On the first day, c(n)=c(0) = 100
Therefore:
C(n) = 100 * 4^n
Let's plug in a view values to test our function:
When n= 0 (first day)
C(0) = 100 * 4 ^0 = 100*1 = 100 likes
C(1) = 100 * 4^1 = 100 * 4 = 400 likes, four times the previous day
C(2) = 100 * 4^2 = 100 * 16 = 1600 likes, four times the previous day
And so on. Our function is an accurate descriptor of the model.
Select the equation of the line parallel to the equation 2x + 4y = -5 that passes through the point (-4, -8).
a). x + 2y = 16
b). 2x + y = -16
c). 2x + 4y = -9
d). x + 2y = -20
Answer:
D.
Step-by-step explanation:
First, put your original equation in slope-intercept form to find your slope.
[tex]y=mx+b\\2x+4y=-5\\4y=-2x-5\\y=-\frac{1}{2} x-\frac{5}{4}[/tex]
Now that you have your slope ([tex]-\frac{1}{2}[/tex]) and a point, you can use point-slope form to find your y-intercept.
[tex]y-y1=m(x-x1)\\y-(-8)=-\frac{1}{2} (x-(-4))\\y+8=-\frac{1}{2} (x+4)\\y+8=-\frac{1}{2} x-2\\y=-\frac{1}{2} x-10[/tex]
Your answer choices are all in [tex]Ax+By=C[/tex] form, so lets convert our equation into that form.
[tex]y=-\frac{1}{2} x-10\\1/2x+y=-10\\x+2y=-20[/tex]
If we multiply all of our terms by 2, we can get answer choice D.
find an explicit formula for the arithmetic sequence -45,-30,-15,0...
Answer:
15(n-1)-45
Step-by-step explanation:
Increases by 15, so sequence is arithmetic, and goes to positive.
1st term is -45
so 15(n-1) gives us first term.
Reply for any questions I got you
[tex]\bf -45~~,~~\stackrel{-45+15}{-30}~~,~~\stackrel{-30+15}{-15}~~,~~\stackrel{-15+15}{0}~\hspace{7em}\stackrel{\textit{common difference}}{d=15} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=-45\\ d=15 \end{cases} \\\\\\ a_n=-45+(n-1)15\implies a_n=-45+15n-15\implies a_n=15n-60[/tex]
The phosphate groups that are the polar of the phospholipid because they are A.charged B. Neutral C. Hydrophilic D. hydrophobic
Answer:
The phosphate groups that are the polar of the phospholipid because they are charged - A.
The phosphate groups that are the polar of the phospholipid because they are A. charged
What is phospholipid?It is group of polar lipids that consist of two fatty acids , a glycerol unit and a phosphate group .
A phosphate group has a negatively charged oxygen and a positively charged nitrogen to make this group ionic. A single phospholipid molecule has a phosphate group on one end and two chains of fatty acids . The phosphate group is negatively charged making the head polar and hydrophilic .
correct answer A) charged
learn more about phospholipid
https://brainly.com/app/ask?q=phospholipid
#SPJ2
If $125 is invested at an interest rate of 18% per year and is compounded continuously, how much will the investment be worth in 2 years? Use the continuous compound interest formula A=Pe^rt
Answer:
$179.17
Step-by-step explanation:
https://brainly.com/question/12714871
Answer: The investment be worth $ 174.05 in 2 years .
Step-by-step explanation:
Given : The principal amount invested : A= $125
Interest rate : r = 18% =0.18 [ Percent convert into decimal if we divide it by 100]
Time : t = 2 years
The formula to find the accumulated amount if compounded continuously :-
[tex]A=Pe^rt\\\\=(125)(1+0.18)^{2}\\\\= 125 (1.18)^2\\\\ = 125 (1.3924)\\\\=174.05[/tex]
Hence, the investment be worth $ 174.05 in 2 years .
please Answer fast .......
Answer:
Option 3 [tex]\frac{67}{441}[/tex]
Step-by-step explanation:
step 1
Find the roots of the quadratic equation
we have
[tex]3x^{2}+5x-7=0[/tex]
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]3x^{2}+5x-7=0[/tex]
so
[tex]a=3\\b=5\\c=-7[/tex]
substitute in the formula
[tex]x=\frac{-5(+/-)\sqrt{5^{2}-4(3)(-7)}} {2(3)}[/tex]
[tex]x=\frac{-5(+/-)\sqrt{109}} {6}[/tex]
[tex]x=\frac{-5+\sqrt{109}} {6}[/tex]
[tex]x=\frac{-5-\sqrt{109}} {6}[/tex]
step 2
Let
[tex]\alpha=\frac{-5+\sqrt{109}} {6}[/tex]
[tex]\beta=\frac{-5-\sqrt{109}} {6}[/tex]
we need to calculate
[tex]\frac{1}{(3\alpha+5)^{2}}+ \frac{1}{(3\beta+5)^{2}}[/tex]
step 3
Calculate [tex](3\alpha+5)^{2}[/tex]
[tex](3\alpha+5)^{2}=[3(\frac{-5+\sqrt{109}} {6})+5]^{2}[/tex]
[tex]=[(\frac{-5+\sqrt{109}} {2})+5]^{2}[/tex]
[tex]=[(\frac{-5+\sqrt{109}+10} {2})]^{2}[/tex]
[tex]=[(\frac{5+\sqrt{109}} {2})]^{2}[/tex]
[tex]=[(\frac{25+10\sqrt{109}+109} {4})][/tex]
[tex]=[(\frac{134+10\sqrt{109}} {4})][/tex]
[tex]=[(\frac{67+5\sqrt{109}} {2})][/tex]
step 4
Calculate [tex](3\beta+5)^{2}[/tex]
[tex](3\beta+5)^{2}=[3(\frac{-5-\sqrt{109}} {6})+5]^{2}[/tex]
[tex]=[(\frac{-5-\sqrt{109}} {2})+5]^{2}[/tex]
[tex]=[(\frac{-5-\sqrt{109}+10} {2})]^{2}[/tex]
[tex]=[(\frac{5-\sqrt{109}} {2})]^{2}[/tex]
[tex]=[(\frac{25-10\sqrt{109}+109} {4})][/tex]
[tex]=[(\frac{134-10\sqrt{109}} {4})][/tex]
[tex]=[(\frac{67-5\sqrt{109}} {2})][/tex]
step 5
substitute
[tex]\frac{1}{(3\alpha+5)^{2}}+ \frac{1}{(3\beta+5)^{2}}[/tex]
[tex]\frac{1}{[(\frac{67+5\sqrt{109}} {2})]}+ \frac{1}{[(\frac{67-5\sqrt{109}} {2})]}[/tex]
[tex]\frac{2}{67+5\sqrt{109}} +\frac{2}{67-5\sqrt{109}}\\ \\\frac{2(67-5\sqrt{109})+2(67+5\sqrt{109})}{(67+5\sqrt{109})(67-5\sqrt{109})} \\ \\\frac{268}{1764}[/tex]
Simplify
Divide by 4 both numerator and denominator
[tex]\frac{268}{1764}=\frac{67}{441}[/tex]
Answer:
3) 67/441
Step-by-step explanation:
Comparing the given equation to the expressions you need to evaluate, you find there might be a simplification.
3x² +5x -7 = 0 . . . . . given equation
3x² +5x = 7 . . . . . . . add 7
x(3x +5) = 7 . . . . . . . factor
3x +5 = 7/x . . . . . . . . divide by x
Now, we can substitute into the expression you are evaluating to get ...
1/(3α +5)² +1/(3β +5)² = 1/(7/α)² +1/(7/β)² = (α² +β²)/49
__
We know that when we divide the original quadratic by 3, we get
x² +(5/3)x -7/3 = 0
and that (α+β) = -5/3, the opposite of the x coefficient, and that α·β = -7/3, the constant term. The sum of squares is ...
α² +β² = (α+β)² -2αβ = (-5/3)² -2(-7/3) = 25/9 +14/3 = 67/9
Then the value of the desired expression is ...
(67/9)/49 = 67/441
4 times the sun q and p
Typo is probably in "sun" being really "sum".
Just write an equation.
[tex]4(q+p)=4q+4p[/tex]
Hope this helps.
r3t40
Solve for x.
A. 2
B. 4
C. 6
D. 8
The full length of one line times the length of the line outside the circle is equal the the other line.
(x-1) +5 x 5 = (2+x)+4 x 4
Simplify:
(x+4) x 5 = (x +6) x 4
5x +20 = 4x +24
Subtract 20 from each side:
5x = 4x +4
Subtract 4x from each side:
x = 4
The answer is B. 4
37. Two years ago, Bob flew 6 x 105 miles in an airplane. This was 15 times as many
miles as he flew last year.
How many miles did Bob fly last year?
A. 4* 104 miles
B. 4 x 106 miles
C. 9 x 104 miles
D. 9 * 106 miles
Answer:
A. 4·10⁴
Step-by-step explanation:
The problem statement tells you ...
6×10⁵ miles = 15 × (last year's mileage)
Dividing by 15 gives ...
(60×10⁴ miles)/15 = (last year's mileage) = 4×10⁴ miles
_____
Further explanation
An exponent is an indication of repeated multiplication.
10⁵ = 10·10·10·10·10 = 100,000
We can use the associative property of multiplication to rewrite the number of miles:
6×10⁵ = 6·(10·10·10·10·10) = 600,000 = (6·10)·(10·10·10·10) = 60×10⁴
4.4.45
For the following polynomial, one zero
is given. Find the remaining zeros.
The
(Sim
to se!
P(x) = x4 + 27x^2 - 324, 6i is a zero.
Answer:
[tex](x-6i)(x+6i)(x-3)(x+3)[/tex]
Step-by-step explanation:
If 6i is a zero then -6i is a zero.
In general, if a+bi is a zero then a-bi is a zero (if the polynomial has real coefficients which this one does: 1,27,-324).
Let's test it to see:
Check [tex]x=6i[/tex]
[tex]P(6i)=(6i)^4+27(6i)^2-324\\
P(6i)=6^4(i^4)+27(6)^2(i^2)-324\\
P(6i)=1296(1)+27(6^2)(-1)-324\\
P(6i)=1296-27(36)-324\\
P(6i)=1296-972-324\\
P(6i)=1296-1296\\
P(6i)=0\\[/tex]
Check [tex]x=-6i[/tex]
[tex]P(-6i)=(-6i)^4+27(-6i)^2-324\\
P(-6i)=(6i)^4+27(6i)^2-324\\
P(-6i)=P(6i)\\
P(-6i)=0\\[/tex]
So yep they both give us 0 when we plug it in.
If x=6i is a zero then x-6i is a factor by factor theorem.
If x=-6i is a zero then x+6i is a factor by factor theorem.
What is (x-6i)(x+6i)?
Let's use the multiply conjugates formula: [tex](u-v)(u+v)=u^2-v^2[/tex].
[tex](x-6i)(x+6i)=x^2-36i^2=x^2-36(-1)=x^2+36[/tex]
Now we know [tex](x^2+36)[/tex] is a factor of [tex]x^4+27x^2-324[/tex].
We can use long division or we could try to find two numbers that multiply to be -324 and add up to be 27 since this is a quadratic in terms of [tex]x^2[/tex] with leading coefficient of 1.
Well we already know we are looking for number times 36 that would give us -324.
So -324=-9(36) and 27=-9+36
So the factored form in terms of real numbers is:
[tex](x^2+36)(x^2-9)[/tex]
We already know the first factor can be factored as (x+6i)(x-6i).
The other can factored as (x-3)(x+3) since (-3)(3)=-9 and -3+3=0.
So the complete factored form is
[tex](x-6i)(x+6i)(x-3)(x+3)[/tex].
To find the remaining zeros of the polynomial, we use synthetic division and find a quadratic factor. The remaining zeros are the solutions to the quadratic equation x^2 + 9 = 0, which are 3i and -3i.
Explanation:To find the remaining zeros of the polynomial, we can use polynomial long division or synthetic division. Let's use synthetic division:
Since 6i is a zero of P(x), the conjugate -6i is also a zero. We can divide P(x) by (x - 6i)(x + 6i) to find the remaining quadratic factor.
Performing the synthetic division, we get a quadratic factor of x^2 + 9. Therefore, the remaining zeros of the polynomial are the solutions to the equation x^2 + 9 = 0.
Solving the quadratic equation x^2 + 9 = 0, we find that the remaining zeros are x = 3i and x = -3i.
Learn more about Polynomial zeros here:https://brainly.com/question/33963189
#SPJ11
Please help!!!
Estimate the value of \sqrt(14)+\sqrt(3) to the nearest hundredth.
A. 3.79
B. 5.47
C. 2.01
D. 4.12
Answer:
B.
Step-by-step explanation:
Let's figure out what two consecutive integers is 14 between.
We also need to do this for 3.
14 is between 9 and 16 which means [tex]\sqrt{14}[/tex] is between [tex]\sqrt{9}[/tex] and [tex]\sqrt{16}[/tex].
3 is between 1 and 4 which means [tex]\sqrt{3}[/tex] is between [tex]\sqrt{1}[/tex] and [tex]\sqrt{4}[/tex].
So 14 is closer to 16 which means [tex]\sqrt{14}[/tex] is closer to 4. Let's say [tex]\sqrt{14}\approx 3.7[/tex]
So 3 is closer to 4 which means [tex]\sqrt{3}[/tex] is closer to 2. Let's say [tex]\sqrt{3}\approx 1.8[/tex].
So now we do 3.7+1.8=5.5.
The answer that is closet to this is 5.47.
Now if we put [tex]\sqrt{14}+\sqrt{3}[/tex] in our calculator we get:
3.74+1.73=5.47
what is the equation of a line that contains the point (2,-5) and is parallel to the line y=3x-4
Answer:
y = 3x - 11
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x - 4 ← is in slope- intercept form
with slope m = 3
• Parallel lines have equal slopes, hence
y = 3x + c ← is the partial equation of the parallel line
To find c substitute (2, - 5) into the partial equation
- 5 = 6 + c ⇒ c = - 5 - 6 = - 11
y = 3x - 11 ← equation of parallel line
the equation of the line that is parallel to y = 3x - 4 and passes through the point (2, -5) is:
y = 3x - 11To find the equation of a line that is parallel to a given line and passes through a certain point, we need to use the concept that parallel lines have the same slope. The slope-intercept form of a line's equation is y = mx + b, where m is the slope and b is the y-intercept. Given that the line is parallel to y = 3x - 4, it will have the same slope, which is 3. Thus the slope of our new line is also 3.
We want our line to pass through the point (2, -5). Plugging these values into the slope-intercept form, we get:
-5 = 3(2) + bwhich simplifies to:
-5 = 6 + bThus, the y-intercept b of our new line is:
-5 - 6 = bTherefore, the equation of the line that is parallel to y = 3x - 4 and passes through the point (2, -5) is:
y = 3x - 11