The general term for the sequence [tex]a_{n}=(-1)^{n} 3 n[/tex]
Solution:Given sequence is -3, 6, -9, 12, -15
We have to find the general term of sequence
The terms in the sequence are found out by using the recursive definition:
[tex]a_{n}=(-1)^{n} 3 n[/tex]
Let us use this definition to find out the terms and check if it matches our given sequence
[tex]\begin{array}{l}{\text { For } n=1:-(-1)^{n} 3 n=(-1)^{1} \times 3 \times 1=-3} \\\\ {\text { For } n=2:-(-1)^{n} 3 n=(-1)^{2} \times 3 \times 2=1 \times 6=6} \\\\ {\text { For } n=3:-(-1)^{n} 3 n=(-1)^{3} \times 3 \times 3=-1 \times 9=-9} \\\\ {\text { For } n=4:-(-1)^{n} 3 n=(-1)^{4} \times 3 \times 4=1 \times 12=12} \\\\ {\text { For } n=5:-(-1)^{n} 3 n=(-1)^{5} \times 3 \times 5=-1 \times 15=-15}\end{array}[/tex]
Thus the general term is given by [tex]a_{n}=(-1)^{n} 3 n[/tex]
Simplify.
-6/7.415
-2.35
-24. 35
24 35
Answer:
-24*sqrt(35)
Step-by-step explanation:
while hiking paco ate 3/4 of a cup of nuts. levi ate 1/2 of a cup of nuts. how much more did paco eat than levi
This answer explains how to calculate the difference in the amount of nuts eaten by Paco and Levi.
To find out how much more Paco ate than Levi:
Calculate how much each person ate: Paco ate 3/4 cup, Levi ate 1/2 cup.
Subtract Levi's amount from Paco's: 3/4 - 1/2 = 1/4 cup.
Therefore, Paco ate 1/4 cup more than Levi.
If 1/2 is subtracted from four times the reciprocal of a number, the result is 0. Find the number.
Answer:
The Number is 8.
Step-by-step explanation:
Let the number be x.
Given:
1/2 is subtracted from four times the reciprocal of a number, the result is 0.
Hence the equation will become like;
[tex]4\times \frac{1}{x} - \frac{1}{2}=0[/tex]
Now Solving the equation we get.
[tex]\frac{4}{x} -\frac{1}{2}=0\\\\\frac{4}{x} = \frac{1}{2}\\\\x= 4\times 2\\x=8[/tex]
Now the we can see the number is 8, when 1/2 is subtracted from 4 times the reciprocal of number means 4/8 which becomes 1/2 and hence when 1/2 is subtracted from 1/2 it equals to 0.
Hence the number is 8.
What is the genotype of the offspring missing on the first row of the Punnett square?
A. IBIB
B. IAIB
C. IBiO
D. none of the above
Answer:
Option B
Step-by-step explanation:
On the first row of the Punnett square, the offspring inherits IA from one parent and IB from another parent hence the resulting genotype is IAIB.
Translate the sentence into an equation
Five times the sum of m and t is as much as four times r
Answer:
Step-by-step explanation:
5*m+t=4
Answer:
[tex]5(m+t)=4r[/tex]
Step-by-step explanation:
The given statement is
"Five times the sum of m and t is as much as four times r".
To find the equivalent expression to the given sentence, we just need to transform each part in mathematical expressions. Just remember, times is product, "as much as" indicates equality.
So, the part five times the sum of m and t, represents the product between the number five and the binomial expression, as follows
[tex]5(m+t)[/tex]
As much as four times r, expresses that the first part is equivalent to the product between 4 and r,
[tex]5(m+t)=4r[/tex]
Therefore, the expression is [tex]5(m+t)=4r[/tex]
a rectangular field is 13 feet longer than it is wide. the perimeter is 68 feet. how wide is the field
Answer:
21 feet
Step-by-step explanation:
multiple 13 by two which should give you 26 subtract 26 from 68 which them gives you 42.
then divide 42 by 2 which gives you 21 for your final answer.
What is the value of m < a + m < b
34°
56°
90°
180°
Answer:
Angle a+ Angle b= 90 degrees
Step-by-step explanation:
a=180-124
a=56
b=180-90-56
b=34
a+b
34+56= 90
The solution is, the value is, Angle a+ Angle b= 90 degrees.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
from the given figure we get,
we have,
a=180-124
a=56
and,
b=180-90-56
b=34
now,
a+b
putting the values , we get,
34+56= 90
Hence, The solution is, the value is, Angle a+ Angle b= 90 degrees.
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What is the answer???
The conclusion about the relationship between the number of cars sold and the high temperature is "The high temperature and the number of cars sold may have a negative correlation, but one may not cause the other". Option D.
What can you conclude about the relationship between the number of cars sold and the high temperature?
Correlation in scatter plot indicates the strength and direction of a relationship between two variables. A positive correlation means that as one variable increases, the other also increases, while a negative correlation means that as one variable increases, the other decreases.
Therefore, from the scatter plot, it can be concluded that high temperature and the number of cars sold may have a negative correlation, but one may not cause the other.
Complete question:
A salesperson uses a scatter plot to compare the number of cars sold on a particular day to the high temperature that day. What can you conclude about the relationship between the number of cars sold and the high temperature?
A) Lower temperatures mean more cars are sold.
B) There is no correlation between the number of cars sold and the high temperature.
C) The more cars are sold, the more the temperature drops.
D) The high temperature and the number of cars sold may have a negative correlation, but one may not cause the other.
5. 4x2 - 31x + 21
Factoring
Answer:
x=7 and x=(3/4)
Step-by-step explanation:
can anyone help with pre- alerba
Answer:
[tex] \sqrt{x^2} = |x| [/tex]
Step-by-step explanation:
[tex] \sqrt{x^2} = |x| [/tex]
The radical symbol when used for a square root means the non-negative square root. You cannot state that sqrt(x^2) = x because x may be negative. That is why you need use the absolute value symbol.
Annabelle has math and reading homework tonight. Annabelle can solve each math problem in 3 minutes and she can read each page in 2 minutes. The number of pages Annabelle read is 4 times the number of math problems she solved. and it took her 55 minutes to complete all of her homework. Determine the number of math problems Annabelle solved and the number of pages she read.
Answer:
The number of math problems Annabelle solved = 5 problems
The number of pages Annabelle read= 20 pages
Step-by-step explanation:
Given:
Time taken for Annabelle to solve one problem =3 minutes
Time taken for Annabelle to read one page =2 minutes
Total time taken by Annabelle to complete her homework= 55 minutes
To find:
Total Number of problems solved by Annabelle=?
Total Number of pages read by Annabelle=?
Solution:
Let the number of problem solved be x
Let the number of pages read be y
It is given that the number pages read is 4 times the number of problem solved
So number of pages read y= 4x
Now time taken to solve x problems = time taken to solve one problem X total number of problem
=>[tex]3\times x[/tex]
=>[tex]3x[/tex]
Similarly,
Time taken to read 4x pages= total number of pages read X time taken to read one problem
=>[tex](4x)\times 2[/tex]
=>[tex]2(4x)[/tex]
Now we know that
Time taken to solve x problems + Time taken to read 4x pages= 55 minutes
3x + (4x)2=55
3x+8x=55
11x=55 [tex]x=\frac{55}{11}[/tex]
x=5
So number of problem solved is x=5
Number of pages read y=4(x)=4(5)=20
How to solve the problems
Answer:
1. 79°
2. 54°
3. 107.5°
4. 44°, 35 cm
5. 76°, 3.5 cm
6. m∠U=36°, m∠M=m∠D=72°, MD=8.6 cm
7. 78°, 93 cm
8. 81°, 75 cm
Step-by-step explanation:
1. The diagram shows an isosceles triangle because TH = OT. Angles adjacent to the base OH of isosceles triangle are congruent, so
[tex]m\angle H=m\angle O[/tex]
The sum of the measures of all interior angles is always 180°, thus
[tex]m\angle H+m\angle O+m\angle T=180^{\circ}\\ \\2m\angle H+22^{\circ}=180^{\circ}\\ \\2m\angle H=180^{\circ}-22^{\circ}\\ \\2m\angle H=158^{\circ}\\ \\m\angle H=79^{\circ}[/tex]
2. The diagram shows an isosceles triangle DGO because DG = GO. Angles adjacent to the base DO of isosceles triangle are congruent, so
[tex]m\angle D=m\angle O=63^{\circ}[/tex]
The sum of the measures of all interior angles is always 180°, thus
[tex]m\angle D+m\angle O+m\angle G=180^{\circ}\\ \\63^{\circ}+63^{\circ}+m\angle G=180^{\circ}\\ \\m\angle G=180^{\circ}-63^{\circ}-63^{\circ}\\ \\m\angle G=54^{\circ}[/tex]
3. The diagram shows an isosceles triangle SLO because LO = SO. Angles adjacent to the base SL of isosceles triangle are congruent, so
[tex]m\angle S=m\angle L[/tex]
The sum of the measures of all interior angles is always 180°, thus
[tex]m\angle S+m\angle L+m\angle O=180^{\circ}\\ \\2m\angle L+35^{\circ}=180^{\circ}\\ \\2m\angle L=180^{\circ}-35^{\circ}\\ \\2m\angle L=145^{\circ}\\ \\m\angle L=72.5^{\circ}[/tex]
Angles OLE and L (SLO) are supplementary (add up to 180°), so
[tex]m\angle OLE=180^{\circ}-m\angle L\\ \\m\angle OLE=180^{\circ}-72.5^{\circ}\\ \\m\angle OLE=107.5^{\circ}[/tex]
4. The diagram shows an isosceles triangle AMR because [tex]m\angle A=m\angle M=68^{\circ}[/tex] (angles adjacent to the side AM are congruent, so triangle AMR is isoseceles).
The sum of the measures of all interior angles is always 180°, thus
[tex]m\angle A+m\angle M+m\angle R=180^{\circ}\\ \\m\angle R+2\cdot 68^{\circ}=180^{\circ}\\ \\m\angle R=180^{\circ}-2\cdot 68^{\circ}\\ \\m\angle R=44^{\circ}[/tex]
To legs in isosceles triangle are always congruent, so
[tex]RM=AR=35\ cm[/tex]
5. The diagram shows isosceles triangle RYD because YD = RD. Angles adjacent to the base RY are congruent, so
[tex]m\angle R=m\angle Y[/tex]
The sum of the measures of all interior angles is always 180°, thus
[tex]m\angle R+m\angle Y+m\angle D=180^{\circ}\\ \\2m\angle Y+28^{\circ}=180^{\circ}\\ \\2m\angle Y=180^{\circ}-28^{\circ}\\ \\2m\angle Y=152^{\circ}\\ \\m\angle Y=76^{\circ}[/tex]
To legs in isosceles triangle are always congruent, so
[tex]YD=RD=3.5\ cm[/tex]
6. The diagram shows an isosceles triangle UMD because UM = UD. Angles adjacent to the base MD of isosceles triangle are congruent, so
[tex]m\angle D=m\angle M=72^{\circ}[/tex]
The sum of the measures of all interior angles is always 180°, thus
[tex]m\angle D+m\angle M+m\angle U=180^{\circ}\\ \\72^{\circ}+72^{\circ}+m\angle U=180^{\circ}\\ \\m\angle U=180^{\circ}-72^{\circ}-72^{\circ}\\ \\m\angle U=36^{\circ}[/tex]
To legs in isosceles triangle are always congruent, so
[tex]UM=UD=14\ cm[/tex]
The perimeter of isosceles triangle MUD is 36.6 cm, so
[tex]UM+MD+UD=36.6\\ \\MD=36.6-14-14\\ \\MD=8.6\ cm[/tex]
7. The sum of the measures of all interior angles is always 180°, thus
[tex]m\angle T+m\angle S+m\angle B=180^{\circ}\\ \\m\angle T+78^{\circ}+24^{\circ}=180^{\circ}\\ \\m\angle T=180^{\circ}-78^{\circ}-24^{\circ}\\ \\m\angle T=78^{\circ}[/tex]
Triangle STB is isosceles triangle because [tex]m\angle S=m\angle T=78^{\circ}[/tex] (angles adjacent to the side ST are congruent, so triangle STB is isoseceles).
To legs in isosceles triangle are always congruent, so
[tex]SB=TB\\ \\y+22.5=38.5\\ \\y=38.5-22.5\\ \\y=16[/tex]
Hence,
[tex]ST=16\ cm\\ \\TB=SB=38.5\ cm[/tex]
and the perimeter of triangle STB is
[tex]P_{STB}=16+38.5+38.5=93\ cm[/tex]
8. The diagram shows isosceles triangle CNB because CN = CB. Angles adjacent to the base RY are congruent, so
[tex]m\angle N=m\angle B[/tex]
The sum of the measures of all interior angles is always 180°, thus
[tex]m\angle N+m\angle B+m\angle C=180^{\circ}\\ \\2m\angle N+18^{\circ}=180^{\circ}\\ \\2m\angle N=180^{\circ}-18^{\circ}\\ \\2m\angle N=162^{\circ}\\ \\m\angle N=81^{\circ}[/tex]
To legs in isosceles triangle are always congruent, so
[tex]CB=CN=2x+90\ m[/tex]
The perimeter of the triangle CNB is
[tex]2x+90+2x+90+x=555\\ \\5x+180=555\\ \\x+36=111\\ \\x=111-36\\ \\x=75\ m[/tex]
So, [tex]NB=75 \ m[/tex]
joey earns $16 per hour as a telemarketer. he also earns a monthly bonus of $400 . joey earned $2000 last month. how many hours did he work
Answer:
100 hours
Step-by-step explanation:
Monthly salary = monthly bonus + total wage based on hours worked
Monthly salary = monthly bonus + (dollars per hour x number of hours worked)
Given, monthly salary = $2000
MOnthly bonus = $400
dollars per hour = $16/hr
let h = number of hours worked
hence, equation becomes
2000 = 400 + (16 x h)
2000 = 400 + 16h (subtract 400 from each side and rearrange)
16h = 2000 - 400
16h = 1600 (divide both sides by 16)
h = 1600 / 16 = 100 hours
There are 3 feet in 1 yard. This is equivalent to 12 feet in 4 yards. Which proportion can be used to represent this?
Proportion which can be used to represent equivalency of 3 feet in 1 yard and 12 feet in 4 yard is 3 : 1 : : 12 : 4
Solution:Given that
There are 3 feet in one yard
And there are 12 feet in 4 yard
Number of feet in one yard = 3 that is feet : yard = 3 : 1
Number of feet in 4 yards = 12 that is feet : yard = 12 : 4
And 3 feet in 1 yard is equivalent to 12 feet in 4 yards means
[tex]\frac{3}{1}=\frac{12}{4}[/tex]
That is 3 : 1 : : 12 : 4
A proportion is statement that two ratios are equal. It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a : b = c : d
Hence proportion which can be used to represent equivalency of 3 feet in 1 yard and 12 feet in 4 yard is 3 : 1 :: 12 : 4
Answer: Proportion which can be used to represent equivalency of 3 feet in 1 yard and 12 feet in 4 yard is 3 : 1 : : 12 : 4
Step-by-step explanation: D
Tell me please !!!!!!
Answer:
(1)
Donna = Pounds 180
Kyra = Pounds 240
(2)
Kelly = Pounds 225
Nelly = Pounds 175
Step-by-step explanation:
(1)
Donna = x
Kyra = x + 60
If Donna spends 1/3 of her money she is left with 2/3 of her money;
2/3 x
Kyra now has twice as much money as Donna can be represented as;
X + 60 = 2 * 2/3 x
X + 60 = 4/3 x
(x + 60)3 = 4x
3x + 180 = 4x
180 = 4x – 3x
180 = x
Donna = 180
Kyra = 180 + 60 = 240
(2)
Kelly = x
Ned = y
Kelly spends 40% of her money. Therefore he is left with 60%;
60/100 x
Nelly spends Euros 40 of his money. Therefore he is left with;
y- 40
If they now have the same amount of money;
60/100 x = y – 40
3/5 x = y – 40
3x = 5y – 200
3x – 5y = -200
Remember Kelly & Ned has Euros 400 in total;
x + y = 400
Now we can solve the simultaneous equation by substitution;
x + y= 400
3x – 5y = -200
3x + 3y = 1200
-
3x – 5y = - 200
=
8y = 1400
Y = 175
X = 225
Kelly = 225
Nelly = 175
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Answer:
3. £60
4. Ned had £175
Step-by-step explanation:
3. 3 segments of Donna plus £60 is the money that Kyra has. Ater Donna spend 1/3 of her money, Kyra has twice as much money as Danna. This means that 2 segments of Donna are equal to 1 segment plus £60, so 1 segment is equal to £60. Donna spend 1 segment of her money, that is, £60.
4. Let's define x the money of Kelly, and y the money of Ned.
Kelly and Ned have £400 in total:
x + y = 400 (eq. 1)
Kelly spends 40% of her money (so she conserves the other 60%), Ned spends £40, They now have the same amount of money:
0.6*y = x - 40 (eq. 2)
From equation 1:
y = 400 - x
Replacing into equation 2:
0.6*(400 - x) = x - 40
240 - 0.6*x = x - 40
- 0.6*x - x = - 40 - 240
-1.6*x = -280
x = -280/-1.6
x = £175
Which of these scatter plots has a trend line that would lie closest to y=x?
A. Scatter plot A
B. Scatter plot B
C. Scatter plot C
D. Scatter plot D
Correct Answer: A. Scatter plot A
Explanation: The line y=x slopes upward from the lower left corner of the graph to the upper right corner, at a 45-degree angle. The scatter plot whose points most closely match that trend is scatter plot A.
Answer:
A. Scatter plot A.Step-by-step explanation:
We need to find the scatter plot that is closest to y = x.
First of all, you must know the behaviour of y = x. That equation represents a straight line that passes through the origin of the coordinate system.
So, the right scatter plot must have the majority of points on this line that passes through the origin.
Notice that the Scatter plot A has this beahivour, if you draw a straight line through the origin and the points, you'll observe that the line best fits.
On the other hand, the other scatter plots are not following this linear behaviour.
Therefore, the right answer is A.
Evaluate the expression when m=6 and n= 7
8n+m
Answer:
62
Step-by-step explanation:
8 x n + m = ?
8 x 7 + 6
8 x 7 = 56
56 + 6 = 62
Answer: 62
Step-by-step explanation:
solution here m=6,n=7,and 8n+m=? now 8n+m =8×7+6 =56+6 =62
Decide whether the two equations are equivalent.
2a + 6 = 12
a+3 = 6
Answer:
Yes
Step-by-step explanation:
2a+6=12
2a=12-6
2a=6
a=6/2
a=3
--------------
a+3=6
a=6-3
a=3
----------
Yes, the two equations are equivalent.
What are the answers of these and if work is needed please explain? Thank you
50 pts! An event management company purchases a new van. The value of the van, x years after the purchase, is shown in the table.
Which statement is true?
Answer:
I believe the answer is A.
Step-by-step explanation:
Multiply each nunber by .10
Afterwards subtract what you get from the number (ex-20,000)
You get the next number after it.
Do the same for each number
The statement that is true about the given table is "The situation can be modelled by an exponential decay function with a percent change of -10%".
What is exponential growth or decay function?Consider the function:
y= a(1 ± r)ˣ
where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
If there is a plus sign, then there is exponential growth happening by r fraction or 100r %If there is a negative sign, then there is exponential decay happening by r fraction or 100r %Given that An event management company purchases a new van. The value of the van, x years after the purchase, is shown in the table.
Now, if the rate of decay and the initial price of the van can be found by substituting the value of x and y in the equation as shown below.
For the first column from the table, when the value of x and y is 0 and 20,000, respectively.
y= a(1 + r)ˣ
20,000 = a(1 + r)⁰
20,000 = a (1)
a = 20,000
For the second column from the table, when the value of x and y is 1 and 18,000, respectively. Also, the value of a=20,000.
y= a(1 + r)ˣ
18,000 = 20,000(1 + r)¹
18,000/ 20,000 = 1 + r
0.9 = 1 + r
0.9 - 1 = r
-0.1 = r
r = -0.1 = -10%
Hence, the statement that is true about the given table is "The situation can be modelled by an exponential decay function with a percent change of -10%".
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On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Everything to the right of the line is shaded. Which linear inequality is represented by the graph?
Answer:
42 TOTAL
Step-by-step explanation:
How many x-intercepts appear on the graph of this polynomial function?
1 Rx)= x -x + x²-x
1 x-intercept
2 x-intercepts
3 x-intercepts
4 x-intercepts
Answer:
The given function[tex]R(x) = x - x + x^2 - x[/tex] has 2 x -intercepts.
Step-by-step explanation:
Here, the given polynomial function is :
[tex]R(x) = x - x + x^2 - x\\\implies R(x) = x^2 - x[/tex]
or, [tex]y = x^2 - x[/tex] ............ (1)
X- intercept is the point in the graph of R(x), where the coordinate y = 0.
Now, substituting the value of y = 0 in (1) find all x - intercepts:
[tex]y = 0 \implies x^2 - x = 0\\x(x-1) =0\\\implies(x-0)(x-1) = 0[/tex]
⇒ Either x = 0 , or x - 1 = 0 ⇒ x = 1
⇒The given function has two x intercepts at x = 0 and x = +1
Hence, the given function[tex]R(x) = x - x + x^2 - x[/tex] has 2 x -intercepts.
Answer:
2 x-intercepts on edge2020
Step-by-step explanation:
What is the value of n in this expression (9^3)^12 =9^n
Answer:
n = 36
Step-by-step explanation:
1. Let's find the value of n for the expression: (9^3)^12 =9^n
(9^3)^12 =9^n
(9³) ¹² = 9 ⁿ
Let's remember that the power rule tells us that to raise a power to a power, we multiply the exponents. Here you see that 9³ is raised to the 12th power is equal to 36 (3 * 12)
9 ³⁶ = 9 ⁿ
n = 36
Help please, I don’t understand it.
Answer:
[tex]K=-2J+28[/tex]
Step-by-step explanation:
For the given trend line, we need to find the y-intercept and slope of the line for determining its equation.
Equation of a line is of the form [tex]y=mx+b[/tex]
Where, 'm' is the slope and 'b' is the y-intercept.
Here, the variables are 'J' and 'K'.
The y-intercept is the point where the 'J' value is 0. From the graph, when 'J' is 0, then the 'K' value is 28. Therefore, the y-intercept is 28.
Slope is given as the ratio of change in 'K' and change in 'J'
The overall change in 'K' is 0 - 28 = -28.
The overall change in 'J' is 14 - 0 = 14
Therefore, the slope is given as:
[tex]m=\frac{\Delta K}{\Delta J}=\frac{-28}{14}=-2[/tex]
Therefore, the equation of trend line is given as:
[tex]K=-2J+28[/tex]
simplify the square root of -121?
Answer:
11i
Step-by-step explanation:
first you have to get a postive root.
[tex]\sqrt{-121} \\ \sqrt{-1} \sqrt{121} \\[/tex]
then you solve the square roots from there, keeping in mind the imaginary number answer to the square root of -1, i.
[tex]\sqrt{-1} = i\\ \sqrt{121} =11\\ 11i[/tex]
Two times the reciprocal of a number equals 32 times the reciprocal of 40. Find the number
Answer:
The number is x=2.5 x=5/2
Step-by-step explanation:
x = number
2(1/x) = 32/40
2/x = 32/40
cross multipli cation
2*40 = 32x
80=32x
2.5 = x or 5/2 or 2(1/2)
perform the indicated operation square root of 8 + square root of 50
Answer:
√8 + √50
= 2√2 + 5√2
=√2(2+5)
= 7√2
Hope this helps!
Please help! The question is in the picture!
Answer:
OPTION A and OPTION C
Step-by-step explanation:
OPTION A:
[tex]$ \frac{1}{5}x - 10 $[/tex] and [tex]$ \frac{1}{5}(x - 50) $[/tex]
Consider [tex]$ \frac{1}{5}(x - 50) = \frac{x}{5} - \frac{50}{5} $[/tex]
This is equal to [tex]$ \frac{1}{5}x - 10 $[/tex].
This is exactly the first expression. So, we say both expressions are equivalent.
OPTION B:
[tex]$ \frac{1}{3} x - 6 $[/tex] and [tex]$ - \frac{1}{3}(3x + 18) $[/tex]
Distributing [tex]$ -\frac{1}{3} $[/tex] to [tex]$ (3x + 18) $[/tex] we get:
[tex]$ \frac{-x}{3} + \frac{-18}{3} $[/tex]
⇒ [tex]$ -x - 6[/tex]
This is not equivalent to the first expression.
OPTION C:
[tex]$ \frac{1}{2}x + 8 $[/tex] and [tex]$ \frac{1}{2}(x + 16) $[/tex]
[tex]$ \frac{1}{2}(x + 16) = \frac{x}{2} + \frac{16}{2} $[/tex]
[tex]$ \implies \frac{1}{2}x + 8 $[/tex]
This is exactly the first expression. So, we say the expressions are equal.
We apply similar techniques to OPTION D and OPTION E. Note that the expressions are not equal in both the options.
Ivory makes $18 a day babysitting. Which expression would you use to find how much Ivory earns if she works 20 days in 6 months?
a) 20x20
b) 20x18
c) 20x 6
d) 18x18
Answer:
The answer is C.
Step-by-step explanation:
Very easy question.
Answer:
its a or c
Step-by-step explanation:
find all the solutions in there interval (0,2pi) for cos5x=-1/2
Answer:
[tex]\frac{2\pi}{15},\frac{4\pi}{15},\frac{8\pi}{15},\frac{2\pi}{3},\frac{14\pi}{15}, \frac{16\pi}{15}, \frac{4\pi}{3},\frac{22\pi}{15}, \frac{26\pi}{15}, \frac{28\pi}{15}[/tex]
Step-by-step explanation:
Solving trigonometric equations.
We are given a condition and we must find all angles who meet it in the provided interval. Our equation is
[tex]cos5x=-\frac{1}{2}[/tex]
Solving for 5x:
[tex]5x=\frac{2\pi}{3}+2n\pi[/tex]
[tex]5x=\frac{4\pi}{3}+2n\pi[/tex]
The values for x will be
[tex]x=\frac{\frac{2\pi}{3}+2n\pi}{5}[/tex]
[tex]x=\frac{\frac{4\pi}{3}+2n\pi}{5}[/tex]
To find all the solutions, we'll give n values of 0, 1, 2,... until x stops belonging to the interval [tex](0,2\pi)[/tex]
For n=0
[tex]x=\frac{\frac{2\pi}{3}}{5}=\frac{2\pi}{15}[/tex]
[tex]x=\frac{\frac{4\pi}{3}}{5}=\frac{4\pi}{15}[/tex]
For n=1
[tex]x=\frac{\frac{2\pi}{3}+2\pi}{5}=\frac{8\pi}{15}[/tex]
[tex]x=\frac{\frac{4\pi}{3}+2\pi}{5}=\frac{2\pi}{3}[/tex]
For n=2
[tex]x=\frac{\frac{2\pi}{3}+4\pi}{5}=\frac{14\pi}{15}[/tex]
[tex]x=\frac{\frac{4\pi}{3}+4\pi}{5}=\frac{16\pi}{15}[/tex]
For n=3
[tex]x=\frac{\frac{2\pi}{3}+6\pi}{5}=\frac{4\pi}{3}[/tex]
[tex]x=\frac{\frac{4\pi}{3}+6\pi}{5}=\frac{22\pi}{15}[/tex]
For n=4
[tex]x=\frac{\frac{2\pi}{3}+8\pi}{5}=\frac{26\pi}{15}[/tex]
[tex]x=\frac{\frac{4\pi}{3}+8\pi}{5}=\frac{28\pi}{15}[/tex]
For n=5 we would find values such as
[tex]x=\frac{\frac{2\pi}{3}+10\pi}{5}=\frac{32\pi}{15}[/tex]
[tex]x=\frac{\frac{4\pi}{3}+10\pi}{5}=\frac{34\pi}{15}[/tex]
which don't lie in the interval [tex](0,2\pi)[/tex]
The whole set of results is
[tex]\frac{2\pi}{15},\frac{4\pi}{15},\frac{8\pi}{15},\frac{2\pi}{3},\frac{14\pi}{15}, \frac{16\pi}{15}, \frac{4\pi}{3},\frac{22\pi}{15}, \frac{26\pi}{15}, \frac{28\pi}{15}[/tex]