Answers
Complementary means they add to make 90 degrees.
This means 2x+4x=90
2x+4x=90
combine like terms
6x=90
divide 6 from both sides
x=15
Related Questions
What is the common ratio for this geometric sequence?
Answers
Answer: The correct option is (C) [tex]\dfrac{1}{4}.[/tex]
Step-by-step explanation: We are given to find the common ratio for the following geometric sequence :
64, 16, 4, 1, . . .
We know that
if a(n) represents the n-th term of a geometric series, then the common ratio is given by
[tex]r=\dfrac{a(n+1)}{a(n)},~~~n=0,~1,~2,~~.~~.~~.[/tex]
For the given geometric sequence, we have
a(1) = 64, a(2) = 16, a(3) = 4, a(4) = 1, . . .
So, the common ratio r will be given by
[tex]r=\dfrac{a(2)}{a(1)}=\dfrac{a(3)}{a(2)}=\dfrac{a(4)}{a(3)}=~~.~~.~~.[/tex]
We have
[tex]\dfrac{a(2)}{a(1)}=\dfrac{16}{64}=\dfrac{1}{4},\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{4}{16}=\dfrac{1}{4},\\\\\\\dfrac{a(4)}{a(3)}=\dfrac{1}{4},~~\cdots[/tex]
Thus, the required common ratio for the given geometric sequence is [tex]\dfrac{1}{4}.[/tex]
Option (C) is CORRECT.
Chris has 5 1/2 cups of water in a pitcher. He pours 3/8 cup of water into a glass. How many cups of water is left in the pitcher? Enter your answer in the box as a mixed number in simplest form.
The Answer is 5 1/8
Answers
Answer:
The Answer is 5 1/8
Step-by-step explanation:
The formula d = rt gives the distance traveled in time t at rate r. A bicyclist rides for 1.5 hours and travels 25 miles.
What was her average speed?
Answers
Answer:
16 2/3
Step-by-step explanation:
The bicyclist's average speed was 16.67 miles per hour
The student asks about the average speed of a bicyclist who traveled for 1.5 hours and covered 25 miles. The average speed can be found using the formula v = d/t, which suggests speed (v) equals distance (d) divided by time (t). To solve for the bicyclist's average speed, we'll insert the given values into the formula.
Here's the step-by-step calculation:
Identify the given variables: d = 25 miles and t = 1.5 hours.
Substitute the values into the formula: v = 25 miles / 1.5 hours.
Calculate the quotient to find the average speed: v = 16.67 miles per hour (rounded to two decimal places).
Therefore, to find the bicyclist's average speed, divide the distance traveled, 25 miles, by the time spent, 1.5 hours, which yields an average speed of 16.67 miles per hour.
Nissan Appliances bought two dozen camcorders at a total cost of $3,864. The markup on the camcorders is 30% of the selling price. What was the original selling price of each camcorder?
Answers
now, we know that those 322 are including a 30% markup, so, the orignal price have been bumped up by 30%, now, if we take say "x" to be the original price, or 100%, then 322 is he 100% + 30%, or 130%, what's "x" anyway?
[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ x&100\\ 322&130 \end{array}\implies \cfrac{x}{322}=\cfrac{100}{130}\implies x=\cfrac{322\cdot 100}{130}[/tex]
The Long family spent $38.62 for school supplies and $215.78 for new school clothes. They paid % sales tax on their
Answers
Final answer:
The Long family spent $38.62 for school supplies and $215.78 for new school clothes. To find the total amount spent, add the cost of school supplies and new school clothes. To calculate the sales tax, multiply the total amount spent by the sales tax rate.
Explanation:
To find the total amount spent, we need to add the cost of school supplies and new school clothes. The Long family spent $38.62 on school supplies and $215.78 on new school clothes, so the total amount spent is $38.62 + $215.78 = $254.40. Now, to calculate the sales tax, we need to find the percentage of the total amount spent. Let's assume the sales tax rate is 8%. To find the sales tax amount, we multiply the total amount spent by the sales tax rate as a decimal: $254.40 x 0.08 = $20.35.
what is a natural number
Answers
The set of counting numbers {1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ...} is called the set of natural numbers. The natural numbers begin at 1 and go on indefinitely.
Three examples of natural numbers are below.
642,000
440
81
A stack of one hundred fifty cards is placed next to a ruler, and the height of the stack is measured to be
3/4 inches.
How thick is one card?
Answers
Answer: One card is 0.005 inches thick.
Step-by-step explanation:
Since we have given that
Number of cards in a stack = 150
Thickness of the stack = [tex]\dfrac{3}{4}\ inches[/tex]
So, Thickness of each card is calculated by "Unitary method":
Thickness of 150 cards = [tex]\dfrac{3}{4}\ inches[/tex]
Thickness of 1 card is given by
[tex]\dfrac{3}{4\times 150}\\\\=\dfrac{1}{4\times 50}\\\\=\dfrac{1}{200}\\\\=0.005\ inches[/tex]
Hence, One card is 0.005 inches thick.
Divide and write the result in standard form: 3-i/1+5i
A. 1/13 +8/13i
B. -1/13+8/13i
C. 1/13-8/13i
D. -1/13-8/13i
Answers
Whenever we are dividing by a complex number by another complex number a+bi, to write the result in standard form, we multiply the expressions in the numerator and denominator by the conjugate of a+bi, that is a-bi:
[tex]\displaystyle{ \frac{3-i}{1+5i}= \frac{(3-i)(1-5i)}{(1+5i)(1-5i)} [/tex]
in the numerator we distribute (3-i) to 1 and -5i, in the denominator we use the difference of squares formula [tex](a-b)(a+b)=a^2-b^2[/tex], and [tex]i^2=-1[/tex]:
[tex]\displaystyle{ \frac{(3-i)(1-5i)}{(1+5i)(1-5i)}= \frac{(3-i)\cdot1+(3-i)\cdot(-5i)}{1^2-(5i)^2}= \frac{3-i-15i-5}{1-25i^2}[/tex]
[tex]\displaystyle{= \frac{-2-16i}{1+25}= \frac{-2-16i}{26}=-1/13-(8/13)i [/tex]
Answer: D
Final answer:
The division of the complex numbers (3 - i) by (1 + 5i) results in the standard form -1/13 - 8/13i, by multiplying both the numerator and denominator by the conjugate of the denominator. The correct answer is option D.
Explanation:
To divide the complex number 3 - i by 1 + 5i, we should multiply numerator and denominator by the conjugate of the denominator to get rid of the imaginary part in the denominator:
Multiply both top and bottom by the conjugate of the denominator, which is 1 - 5i.(3 - i) * (1 - 5i) = 3 - 15i - i + 5i2
Since i2 = -1, it simplifies to:
3 - 16i - 5 = -2 - 16i
(1 + 5i) * (1 - 5i) = 1 - 5i + 5i - 25i2
Similarly, it simplifies to:
1 + 25 = 26
Divide the top result by the bottom result:(-2 - 16i) / 26 = -2/26 - 16i/26
Simplify the fractions:
-1/13 - 8/13i
The standard form of the result is -1/13 - 8/13i, which corresponds to option D.
Lee King Earns $5 per hour. Lee's brother, Nosmo, starts working three hours after Lee and earns $7 per hour. Write an equation that says each earned the same amount. Solve to find out how long each brother worked.
Answers
5x=7(x-3)
Solving the equation, x=10.5
Therefore Leeking worked 10.5 hours and Nosmo worked 7.5 hours
An animal shelter that only cares for cats and dogs has 8 fewer dogs than cats. The animal shelter has 12 dogs.
Use the five-step problem-solving plan.
How many cats are at the animal shelter?
Answers
(c = number of cats)
8 fewer dogs than cats can be written: c - 8
since we know how many dogs there are: c - 8 = 12
Now, just solve for the variable: c = 20
Hope I helped :)
wire the place of the underlined digit. then write it's value. 5,342 the 3 is underlines
Answers
Find, correct to the nearest degree, the three angles of the triangle with the vertices d(0,1,1), e( 2, 4,3) − , and f(1, 2, 1)
Answers
For reference, let 'a' be the side opposite A (segment BC), 'b' be the side opposite B (segment AC) and 'c' be the side opposite C (segment AB).
Let P=(4,0) be the projection of B onto the x-axis.
Let Q=(-3,0) be the projection of C onto the x-axis.
Look at the angle QAC. It has tangent = 5/4 (do you see why?), so angle A is atan(5/4).
Likewise, angle PAB has tangent = 6/3 = 2, so angle PAB is atan(2).
Angle A, then, is 180 - atan(5/4) - atan(2) = 65.225. One down, two to go.
||b|| = sqrt(41) (use Pythagorian Theorum on triangle AQC)
||c|| = sqrt(45) (use Pythagorian Theorum on triangle APB)
Using the Law of Cosines...
||a||^2 = ||b||^2 + ||c||^2 - 2(||b||)(||c||)cos(A)
||a||^2 = 41 + 45 - 2(sqrt(41))(sqrt(45))(.4191)
||a||^2 = 86 - 36
||a||^2 = 50
||a|| = sqrt(50)
Now apply the Law of Sines to find the other two angles.
||b|| / sin(B) = ||a|| / sin(A)
sqrt(41) / sin(B) = sqrt(50) / .9080
(.9080)sqrt(41) / sqrt(50) = sin(B)
.8222 = sin(B)
asin(.8222) = B
55.305 = B
Two down, one to go...
||c|| / sin(C) = ||a|| / sin(A)
sqrt(45) / sin(C) = sqrt(50) / .9080
(.9080)sqrt(45) / sqrt(50) = sin(C)
.8614 = sin(C)
asin(.8614) = C
59.470 = C
So your three angles are:
A = 65.225
B = 55.305
C = 59.470
If A=4-3i, M=-4+i, S=i, and$P=2, find A-M+S-P.
Please help!
Answers
treat i as a variable
A-M+S-P=
(4-3i)-(-4+i)+(i)-(2)=
4-3i+4-i+i-2=
4+4-2-3i-i+i=
6-3i
The value of the A - M + S - P by using an arithmetic operation will be 6 + 3i.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
As per the given values,
A=4-3i, M= -4+i, S=i, and P=2
Put the above values into A - M + S - P as
4 - 3i - (-4 + i) + i - 2
⇒ 4 - 3i + 4 - i + i - 2
⇒ 4 - 2 + 4 - 3i
⇒ 6 + 3i
Hence "The value of the A - M + S - P by using an arithmetic operation will be 6 + 3i".
To learn more about the arithmetic operators,
brainly.com/question/25834626
#SPJ2
rearrange w=3(2a+b)-4 to make A the subject
Answers
To make A the subject in the equation w = 3(2a + b) - 4, the rearranged equation is: a = (w + 4 - 3b) / 6.
To rearrange the equation w = 3(2a + b) - 4 to make A the subject, we need to isolate A on one side of the equation. Here's how we can do it step by step:
Step 1: Distribute the 3 to the terms inside the parentheses:
w = 6a + 3b - 4.
Step 2: Move the 3b and -4 terms to the other side of the equation:
w + 4 = 6a + 3b.
Step 3: Rearrange the terms to isolate a:
6a = w + 4 - 3b.
Step 4: Divide both sides of the equation by 6 to solve for a:
a = (w + 4 - 3b) / 6.
Now, a is the subject of the equation. We have successfully rearranged the equation to express a in terms of w and b.
The probable question maybe:
rearrange w=3(2a+b)-4 to make A the subject in the equation.
The rearranged equation solving for [tex]\( a \)[/tex] is : [tex]\[ a = \frac{{w + 4}}{6} - \frac{{b}}{2} \][/tex]
This equation expresses [tex]\( a \)[/tex] as a function of [tex]\( w \)[/tex] and [tex]\( b \)[/tex], where [tex]\( w \)[/tex] is multiplied by [tex]\( \frac{1}{6} \) and \( b \)[/tex] is subtracted and then divided by [tex]\( 2 \)[/tex]. This equation can be used to calculate the value of [tex]\( a \)[/tex] given [tex]\( w \) and \( b \).[/tex]
To rearrange the equation [tex]\( w = 3(2a + b) - 4 \)[/tex] to solve for [tex]\( a \)[/tex], the first step is to isolate the term containing [tex]\( a \)[/tex] on one side of the equation.
1. Start by distributing the [tex]\( 3 \)[/tex] on the right side:
[tex]\[ w = 6a + 3b - 4 \][/tex]
2. Next, move the constants to the other side of the equation by adding [tex]\( 4 \)[/tex] to both sides:
[tex]\[ w + 4 = 6a + 3b \][/tex]
3. Now, to isolate [tex]\( a \)[/tex], divide both sides by [tex]\( 6 \):[/tex]
[tex]\[ \frac{{w + 4}}{6} = a + \frac{{3b}}{6} \][/tex]
4. Simplify:
[tex]\[ \frac{{w + 4}}{6} = a + \frac{{b}}{2} \][/tex]
5. To solve for [tex]\( a \)[/tex], subtract [tex]\( \frac{{b}}{2} \)[/tex] from both sides:
[tex]\[ \frac{{w + 4}}{6} - \frac{{b}}{2} = a \][/tex]
So, the rearranged equation solving for [tex]\( a \)[/tex] is:
[tex]\[ a = \frac{{w + 4}}{6} - \frac{{b}}{2} \][/tex]
Simplify 2(x + y) + 3(x + y)
Answers
2x+2y+3x+3y
Combine like terms
5x+5y
Final answer: 5x+5y
ps Another way to do it is that know the two inner binomials are the same so you can write it as (2+3)(x+y) which simplifies to 5(x+y) and distributes to 5x+5y
You are given n = 5 measurements: 5, 3, 3, 8, 8. (a) calculate the sample mean, x. (enter your answer to one decimal place.)
Answers
= (5 + 3 + 3 + 8 + 8) / 5
= 27 / 5
= 5.4 Answer
41>6m-7 help please
Answers
So, I added 7 to both sides and got 48>6m and then divided both sides by 6 to get 8>m or m<8.
An equation that is not true for any values of the variable is called a(n
Answers
Answer:
I am pretty sure this is either a Linear Equation or called a Contradiction
An equation that is not true for any values of the variable is called a false or inconsistent equation.
Explanation:An equation that is not true for any values of the variable is called a false equation or an inconsistent equation. This means that the equation has no solution that satisfies the given equation. For example, if we have the equation x + 3 = x + 5, subtracting x from both sides gives us 3 = 5, which is not true for any value of x.
Learn more about false or inconsistent equation here:https://brainly.com/question/30868182
#SPJ2
Rewrite the equation so that y is a function of x 5y-2x=15
Answers
Pablo is a technical writer who works 7.5 hours per day. He spends twice as much time on writing tasks as he does on other work tasks. How much time per day does he spend on writing tasks?
Answers
answer: twice as much=2 times this number
then twice as much= 7.5 times 2
7.5 times 2= 15hrs
A rectangular box has length 14 inches, width 11 inches, and a height of 16 inches. find the angle between the diagonal of the box and the diagonal of its base. the angle should be measured in radians.
Answers
Which is the fraction 14/5 written as mixed number?
Answers
Answer: 2 and 4/5
Step-by-step explanation: To write an improper fraction as a mixed number, divide the denominator into the numerator.
[tex]\sqrt[5]{14}[/tex] = 2 with a remainder of 4
Therefore, 14/5 can be written as the mixed number 2 and 4/5.
The fraction 14/5 written as a mixed fraction is equivalent to 2 4/5
Writing improper fraction as mixed fractionGiven the expression below:
14/5
Since 5 can go in 14 twice, the whole number of the mixed fraction will be 2.
Given the remainder as 4, the numerator will be 4 and the denominator will be the same that is 5 as shown below:
14/5 = 2 4/5
Hence the fraction 14/5 written as a mixed fraction is equivalent to 2 4/5
Learn more mixed and improper fraction here: brainly.com/question/970872
#SPJ6
Suppose the cpi was 110 last year and is 121 this year. instructions: in part a, enter your answer as a whole number. in part b, round your answer to 1 decimal place. if you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers.
a. what is this year’s rate of inflation?
Answers
The rate of inflation from last year to this year is calculated by finding the 'change in CPI' which is then divided by the 'old CPI' and multiplied by 100 to convert it into percentage. The change in CPI is the new CPI minus the old CPI. By following the steps, we find that the rate of inflation is 10%.
Explanation:To calculate the rate of inflation, we first need to determine the 'change in CPI', which will then be divided by the 'old CPI'. The formula is:
(New CPI - Old CPI) / Old CPI x 100%
The 'change in CPI' is the new CPI (this year's CPI) minus the old CPI (last year's CPI). This will be:
121 (this year's CPI) - 110 (last year's CPI) = 11
Now, we'll divide 'change in CPI' by old CPI, which is:
11 (change in CPI) / 110 (old CPI) = 0.1
To convert the value into percentage, we should multiply it by 100:
0.1 x 100 = 10
So, this year's rate of inflation is 10%.
Learn more about Inflation Rate Calculation here:https://brainly.com/question/30402084
#SPJ12
How to solve 5 x 198 with the distributive property that includes multiplication and subtraction
Answers
Then the answer is 5(200) - 5(2) = 1000 - 10 = 990.
Answer:
Value of 5×198 is:
990
Step-by-step explanation:
We have to find the value of 5 x 198 with the help of distributive property that includes multiplication and subtraction
Distributive property says that if a,band c are three numbers
then, a(b-c)= ab-ac
5 x 198= 5(200-2)
= 5×200 - 5×2
= 1000-10
= 990
Hence, Value of 5×198 is:
990
The planet Mars has two moons – Phobos and Deimos. Phobos has a mass of 10.8 × 1015 kilograms, and Deimos has a mass of 2.0 × 1015 kilograms. How much greater is the mass of Phobos than the mass of Deimos?
Answers
Answer:
mass of Phobos is 8.8 × 10¹⁵ Kilograms greater than mass of Deimos.
Step-by-step explanation:
The planet Mars has two moons Phobos and Deimos.
Mass of Phobos = 10.8 × 10¹⁵ Kilograms
Mass of Deimos = 2 × 10¹⁵ Kilograms
So the difference in the masses of the moons
= 10.8 × 10¹⁵ - 2 × 10¹⁵
= (10.8 - 2) × 10¹⁵
= 8.8 × 10¹⁵ Kilograms
Therefore, mass of Phobos is 8.8 × 10¹⁵ Kilograms greater than mass of Deimos.
0.059 seconds into milliseconds
Answers
0.059 seconds is equal to 59 milliseconds.
Explanation:Unit conversion is the process of changing the measurement units of a quantity from one system to another. It is essential for comparing and working with measurements expressed in different units. Common examples include converting between metric and imperial units for length (e.g., meters to feet) or weight (e.g., kilograms to pounds).
Accurate unit conversion is crucial in fields like science, engineering, and international trade.Thus for the given case, 0.059 seconds is equal to 59 milliseconds.
Learn more about Unit Conversion here:https://brainly.com/question/19420601
#SPJ12
elizabeth plans to hand out door prizes as the guest arives. every 6th guest will receive a mug and every 9th guess will receive a t shirt . Elizabeth believe that the 12th guess will both receive a t shirt and a mug . is she correct or incorrect. show your work and explain your reasoning
Answers
Every 9th guest: 9, 18, 27, 36, and so on.
18 appears in each of these lists; 12 does not. Elizabeth is wrong. The first person to receive both a t-shirt and a mug would be the 18th guest.
if i need 5 tomatoes to feed 7 people, how many tomatoes do i need to feed 100 leople
Answers
10 - 14
15 - 21
20 - 28
25 - 35
30 - 42
35 - 42
40 - 56
45 - 63
50 - 70
55 - 77
60 - 84
65 - 91
70 - 98
75 - 105
105 with a little extra c:
you have a secret that you to one person every hour each of the people that know the secret tells one person. The number of people who know when is N and T is the number of hours since you told the first person. Is an a linear function s of t?
Answers
Before you tell anybody, only one person knows the secret (that is you), therefore: N(0) = 1
When the first person know, now two people know, therefore: N(1) = 2
After an hour, each of you would have told another person. So now, four people know, therefore, N(2) = 4
This pattern continues with the same manner where it doubles every hour.
As you can see, this is NOT a linear function. It is an exponential function where N(t) = 2^t
Round 915 to the nearest ten