Answer:
woman is 37, girl is 7
Step-by-step explanation:
7(x-2) = y-2
4(x+3) = y+3
7x - 14 = y - 2
7x - 12 = y
4x + 9 = y
3x - 21 = 0
x = 7
y = 37
HELP PLEASE FOR 35 POINTS!!!! Solve the rational equation 3 divided by x equals quantity 4 times x plus 3 divided by x squared, and check for extraneous solutions.
Answer:
[tex]x=-3[/tex]
Step-by-step explanation:
So, we are given:
[tex]\frac{3}{x}=\frac{4x+3}{x^2}[/tex]
First, we should immediately rule out 0 as an answer. This is because the if [tex]x=0[/tex], the equation would be undefined.
[tex]x\neq 0[/tex]
Now, cross multiply.
[tex]3(x^2)=x(4x+3)[/tex]
[tex]3x^2=4x^2+3x[/tex]
Divide everything by x (and we can do this safely because we already know x cannot be equal to zero).
[tex]3x=4x+3[/tex]
[tex]-x=3[/tex]
[tex]x=-3[/tex]
We didn't run into any possibilities for extraneous solutions.
Ava is buying paint from Amazon. Ava needs 3⁄4 cup of blue paint for every 1 cup of white paint. Ava has 28 ounces of white paint. How much blue paint does he need?
Answer:
Blue paint=21 ounces
Step-by-step explanation:
3/4 cup=6 ounces
1 cup=8 ounces
3/4 cup of blue paint=6 ounces of blue paint
1 cup of white paint= 8 ounces of white paint
Ava has 28 ounces of white paint
Find the required blue paint
Let the required blue paint=x
Blue paint ratio white paint
6:8=x:28
6/8=x/28
Cross product
6(28)=x(8)
168=8x
x=168/8
x=21 ounces
Which of the binomials below is a factor of this trinomial?
5x2-18x+9
O A. 5x-3
O B. X-1
O c. X+1
O D. 5x+3
Answer:
The answer is option A.
Step-by-step explanation:
here, 5x^2-18x+9
=5x^2-(15+3)x+9
=5x^2-15x-3x+9
=5x(x-3)-3(x-3)
=(5x-3)(x-3)
so, the answer from the above options is (5x-3).
hope it helps..
3/25 as a percentage
Answer:
12%
Step-by-step explanation:
3/25 = .12
.12 x 100 = 12%
Answer:
12%
Step-by-step explanation:
All you have to do is divide this on a calculator and multiply it by 100. 3/25 = 0.12; 0.12 x 100 = 12%.
Solve the oblique triangle where side a has length 10 cm, side c has length 12 cm, and angle beta has measure thirty degrees. Round all answers using one decimal place.
Answer:
The missing side is [tex]B = 6.0\ cm[/tex]
The missing angles are [tex]\alpha = 56.2[/tex] and [tex]\theta = 93.8[/tex]
Step-by-step explanation:
Given
[tex]A = 10\ cm[/tex]
[tex]C = 12\ cm[/tex]
[tex]\beta = 30[/tex]
The implication of this question is to solve for the missing side and the two missing angles
Represent
Angle A with [tex]\alpha[/tex]
Angle B with [tex]\beta[/tex]
Angle C with [tex]\theta[/tex]
Calculating B
This will be calculated using cosine formula as thus;
[tex]B^2 = A^2 + C^2 - 2ACCos\beta[/tex]
Substitute values for A, C and [tex]\beta[/tex]
[tex]B^2 = 10^2 + 12^2 - 2 * 10 * 12 * Cos30[/tex]
[tex]B^2 = 100 + 144 - 240 * 0.8660[/tex]
[tex]B^2 = 100 + 144 - 207.8[/tex]
[tex]B^2 = 36.2[/tex]
Take Square root of both sides
[tex]B = \sqrt{36.2}[/tex]
[tex]B = 6.0[/tex] (Approximated)
Calculating [tex]\alpha[/tex]
This will be calculated using cosine formula as thus;
[tex]A^2 = B^2 + C^2 - 2BCCos\alpha[/tex]
Substitute values for A, B and C
[tex]A^2 = B^2 + C^2 - 2BCCos\alpha[/tex]
[tex]10^2 = 6^2 + 12^2 - 2 * 6 * 12 * Cos\alpha[/tex]
[tex]100 = 36 + 144 - 144Cos\alpha[/tex]
Collect Like Terms
[tex]100 - 36 - 144 = -144Cos\alpha[/tex]
[tex]-80 = -144Cos\alpha[/tex]
Divide both sides by -144
[tex]\frac{-80}{-144} = Cos\alpha[/tex]
[tex]0.5556 = Cos\alpha[/tex]
[tex]\alpha = cos^{-1}(0.5556)[/tex]
[tex]\alpha = 56.2[/tex] (Approximated)
Calculating [tex]\theta[/tex]
This will be calculated using cosine formula as thus;
[tex]C^2 = B^2 + A^2 - 2BACos\theta[/tex]
Substitute values for A, B and C
[tex]12^2 = 6^2 + 10^2 - 2 * 6 * 10Cos\theta[/tex]
[tex]144 = 36 + 100 - 120Cos\theta[/tex]
Collect Like Terms
[tex]144 - 36 - 100 = -120Cos\theta[/tex]
[tex]8 = -120Cos\theta[/tex]
Divide both sides by -120
[tex]\frac{8}{-120} = Cos\theta[/tex]
[tex]-0.0667= Cos\theta[/tex]
[tex]\theta = cos^{-1}(-0.0667)[/tex]
[tex]\theta = 93.8[/tex] (Approximated)
He claims that the measures of the three sides of triangle ABX are all equal to AX, making AABX equilateral. Since this makes central angle AXB
measure 60°,mAB = 60°. Dylan also claims that by repeatedly applying the same argument, he can prove that the inscribed hexagon is regular.
Which statement is true?
Statement A " Dylan's reasoning about arc AB is correct, and the hexagon is regular. option (A) is correct.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
Three sides of the triangle ABX are all equal to AX, making ΔABX equilateral. Since this makes central angle AXB measure 60°,
m(arc)AB = 60°
AX = BX = AB
The measure of AXB = 60 degrees
m(arc)AB = 60 degrees
On applying the same argument, the inscribed hexagon is regular.
Statement A is correct.
Thus, statement A " Dylan's reasoning about arc AB is correct, and the hexagon is regular. option (A) is correct.
Learn more about the regular polygon here:
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Just trying to finish this so I can get my stanceboy racecar back
Answer:
x ≥ 4 AND x + y ≤ 10
Step-by-step explanation:
If you need up to 10 volunteers, then you can take 10 or less. If we add y and x, we'll get the total amount of people, therefore making the inequality:
x + y ≤ 10.
Now, he needs no fewer than 4 females, so he can take 4 or greater. This means that x should be greater than or equal to 4.
x ≥ 4.
Nothing was mentioned about how many males he needed (y) so these two inequalities match the situation.
Hope this helped!
WHY CAN'T ANYONE HELP ME PLEASE? THANKS! A student at a university makes money by buying and selling used cars. Charles bought a used car and later sold it for a 15% profit. If he sold it for $4669, how much did Charles pay for the car?
Step-by-step explanation:
Given,
a student (Charles) bought a car and sold it in 15 % profit for $4669.
we have the formula,
[tex]cp = \frac{sp \times 100}{100 + p\%} [/tex]
so,
[tex]cp = \frac{4669 \times 100}{100 + 15} [/tex]
by simplifying it we get,
CP is $4060.
Therefore, the cp was $4060.
Hope it helps...
Find the value of Xº if
Question: Find the value of Xº if <ADC = 71°
Answer:
15
Step-by-step explanation:
Given:
<ADC = 71°
<ADB = (x + 7)°
<BDC = (2x + 19)°
Required:
Value of x
Solution:
<ADB + <BDC = <ADC
(x + 7)° + (2x + 19)° = 71°
x + 7 + 2x + 19 = 71
x + 2x + 7 + 19 = 71
3x + 26 = 71
Subtract 26 from both sides
3x + 26 - 26 = 71 - 26
3x = 45
Divide both sides by 3 to make x the subject of formula
[tex] \frac{3x}{3} = \frac{45}{3} [/tex]
[tex] x = 15 [/tex]
The value of x is 15.
The product of 6 and a number (n) is 48 . Which equation shows this relationship? ANSWER CHOICES: 6n=48 n+6=48 48n=6 n-6=48
Answer:
6n=48
Step-by-step explanation:
product means multiplication
6×n=48
6n=48
An equation that shows this relationship is: A. 6n = 48.
How to determine the equation representing the product?In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:
Let the variable n represent the unknown number.
Based on the statement "The product of 6 and a number is 48," we can logically deduce the following algebraic equation;
6 × n = 48
6n = 48
n = 48/6
n = 8.
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Graph the equation y=−4x+3 by plotting points.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
y=4x+3
Price of an item is reduced by 40% of its original price. A week later it’s reduced 20% of the reduced price. What’s the actual % of the reduction from the original price
Answer: 52%
Step-by-step explanation:
Let the original price be 100.
After 40% reduction, price will be 100 - 40% = 60
After further 20% reduction, price will be 60 - 20% = 48
%age = (cur val - orig. val ) / orig val x 100
= (48 - 100) / 100 x 100%
= -52
The actual percentage of reduction is 52%
The first reduction is given as:
[tex]r_1 = 40\%[/tex]
The second reduction is given as:
[tex]r_2 = 20\%[/tex]
Assume that the original price of the item is x.
After the first reduction of 40%, the new price would be:
[tex]New = x\times (1 -r_1)[/tex]
So, we have:
[tex]New = x\times (1 -40\%)[/tex]
[tex]New = x\times 0.6[/tex]
[tex]New = 0.6x[/tex]
After the second reduction of 20% on the reduced price, the new price would be:
[tex]New = 0.6x\times (1 -r_2)[/tex]
So, we have:
[tex]New = 0.6x\times (1 -20\%)[/tex]
[tex]New = 0.6x\times 0.8[/tex]
[tex]New = 0.48x[/tex]
Recall that the original price is x.
So, the actual reduction is:
[tex]Actual = \frac{x - 0.48x}{x}[/tex]
[tex]Actual = \frac{0.52x}{x}[/tex]
Divide
[tex]Actual = 0.52[/tex]
Express as percentage
[tex]Actual = 52\%[/tex]
Hence, the actual percentage of reduction is 52%
Read more about percentage change at:
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an office supply company sells two types of printers. they charge $95 for one of the printers and $125 for the other. if the company sold 32 printers for a total of$3340 last month, how many of each type were sold
Answer:
22 of the 95$ ones and 10 of the 125
Step-by-step explanation:
22 times 95 = 2090
10 times 125 = 1250
2090+1250=3340
hope this helped
Need Assistance
Show Work
Answer:
-52, and the opposite of this is 52.
Step-by-step explanation:
If we are losing 52 pounds, then our number is -52 since we are losing 52 pounds (adding a negative number to a positive number is the same as subtracting that number).
The opposite of a number is when we negate the number, or multiply it by -1.
A negative number times a negative number is a positive number.
[tex]-52\cdot-1 = 52\cdot1 = 52[/tex]
Hope this helped!
Answer:
Hey there!
Loss of 52 pounds, -52
Opposite, 52
Hope this helps :)
(25 points) PLEASE HELP! Gotta get this done before my mom comes home
1. The owner of an organic fruit stand also sells nuts. She wants to mix cashews worth $5.50 per pound with peanuts worth $2.30 per pound to get a 1/2 pound mixture that is worth $2.80 per pound. How much of each kind of nut should she include in the mixed bag?
A. Cashews: 0.10 lb.; peanuts: 0.40 1b.
B. Cashews: 0.42 lb.; peanuts: 0.08 1b.
C. Cashews: 0.40 lb.; peanuts: 0.10 1b
D. Cashews: 0.27 lb.; peanuts: 0.23 1b.
E. Cashews: 0.23 lb.; peanuts: 0.27 1b.
F. Cashews: 0.08 lb.; peanuts: 0.42 1b
2. A nursery owner has 288 rose bushes. There are 36 fewer red roses than pink roses. How many of each type of roses are there?
A. Red roses: 162; pink roses: 252.
B. Red roses: 162; pink roses: 126.
C. Red roses: 99; pink roses: 126.
D. Red roses: 126; pink roses: 162
E. Red roses: 126; pink roses: 99
F. Red roses: 252; pink roses: 162
3. The sum of the ages of Stephanie and Heather is 46. Heather is two years younger than Stephanie. Write a system of equations to determine the ages of Stephanie and Heather.
A) S + H = 46
H = S + 2
B) S - H = 46
H - 2 = S
C) S + H = 46
H = S - 2
D) S - H = 2
H = S - 46
E) S + H = 2
H = S - 46
F) 2S – H = 46
4. You want to borrow three rock CDs from your friend. She loves math puzzles and she always makes you solve one before you can borrow her stuff. Here’s the puzzle: Before you borrow three CDs, she will have 39 CDs. She will have half as many country CDs as rock CDs, and one-fourth as many soundtracks as country CDs. How many of each type of CD does she have after you borrow three rock CDs?
A. After borrowing 3 rock CDs, your friend will have 21 rock CDs, 12 country CDs, and 3 soundtracks.
B. After borrowing 3 rock CDs, your friend will have 24 rock CDs, 12 country CDs, and 3 soundtracks.
C. After borrowing 3 rock CDs, your friend will have 25 rock CDs, 10 country CDs, and 4 soundtracks.
D. After borrowing 3 rock CDs, your friend will have 21 rock CDs, 9 country CDs, and 3 soundtracks.
E. After borrowing 3 rock CDs, your friend will have 24 rock CDs, 12 country CDs, and no soundtracks.
F. After borrowing 3 rock CDs, your friend will have 18 rock CDs, 15 country CDs, and 3 soundtracks.
5. Three times the width of a certain rectangle exceeds twice its length by two inches. Four times its length is twelve more than its perimeter. Write a system of equations that could be used to solve this problem. (hint: P = 2L + 2W)
A) 3W = 2L + 2
2L = 2W + 12
B) 3W + 2 = 2L
4L = P – 12
C) 3W = 2L + 2
4L + 12 = P
D) 2W + 2 = 2L
4L = 12 + P
E) 3W + 2 = 2L
4L = 12 + P
F) 2L – 2 = 3W
P = 4L - 12
Thank you!!!!
A clinic treated 536 children over a 4month period how many children did the clinic treat in 1month
536 children = 4 months
536/4 children = 4/4 months ... divide both sides by 4
134 children = 1 month
The clinic treated 134 children in 1 month. This is assuming that every month was the same number of patients.
Answer: 134Step-by-step explanation:
Solution,
Number of children treated in 4 months = 536
Now, let's find the number of children treated in one month:
[tex] = \frac{total \: number \: of \: childrens \: }{total \: month} [/tex]
Plug the values
[tex] = \frac{536}{4} [/tex]
Calculate
[tex] = 134 \: [/tex] childrens
Therefore, A clinic treated 134 childrens in one month.
Hope this helps...
Best regards!!
Which of the following expressions could be used to find 80% of X (the lines are there to show the different expressions)
Answer:
80/100 times x => [tex] \frac{80}{100}*x [/tex]
(0.8) times x => [tex] (0.8)*x [/tex]
4/5 times x => [tex] \frac{4}{5}*x [/tex]
8/10 times x => [tex] \frac{8}{10}*x [/tex]
Step-by-step explanation:
80% of x means 80 ÷ 100 × x
that is: [tex] \frac{80}{100}*x = \frac{8}{10}*x = \frac{4}{5}*x = (0.8)*x [/tex]
Therefore, the expressions that can be used to find 80% of x are:
80/100 times x => [tex] \frac{80}{100}*x [/tex]
(0.8) times x => [tex] (0.8)*x [/tex]
4/5 times x => [tex] \frac{4}{5}*x [/tex]
8/10 times x => [tex] \frac{8}{10}*x [/tex]
find the standard deviation for the binomial distribution which has the stated values of n and p n=47 p= 0.4 round you answer to the nearest hundredth
Answer:
Option (3)
Step-by-step explanation:
Standard deviation for the binomial distribution is given by,
σ = [tex]\sqrt{n\times P(1-P)}[/tex]
where n = Number of trials
P = probability of success of an individual trail
If n = 47 and P = 0.4
σ = [tex]\sqrt{47\times 0.4(1-0.4)}[/tex]
= [tex]\sqrt{47\times 0.24}[/tex]
= [tex]\sqrt{11.28}[/tex]
= 3.3586
≈ 3.36
Therefore, standard deviation for the binomial distribution will be 3.36.
Option (3) will be the answer.
Trigonometry Dilemma
Answer:
17.1
Step-by-step explanation:
The missing side is x
tan 25° = [tex]\frac{opposite }{adjacent }[/tex] tan 25° = [tex]\frac{8}{x}[/tex]switch tan 25° and x
x = [tex]\frac{8}{tan 25}[/tex] x= 17.15≈17.1What is the solution to the system that is created by the equation y = 2 x + 10 and the graph shown below? On a coordinate plane, a line goes through (negative 2, 0) and (0, 2). (–8, –6) (–4, –2) (0, 2) (2, 4)
Answer:
(–8, –6)
Step-by-step explanation:
The given points represent the x- and y- intercepts of the line, so we can write the equation in intercept form as ...
x/(x-intercept) +y/(y-intercept) = 1
x/(-2) +y/2 = 1 . . . use the given intercepts
x - y = -2 . . . . . multiply by -2
Then the system is ...
y = 2x +10x - y = -2Using the first to substitute into the second, we get ...
x - (2x +10) = -2
-8 = x . . . . . . . . . . . add x+2, simplify
y = 2(-8) +10 = -6
The solution is (x, y) = (-8, -6).
Answer:
(-8,-6)
Step-by-step explanation:
Got it right on edge soooo <3
The circumference of C is 72cm. What is the length of AB (the minor arc)
Answer:
Step-by-step explanation:
Can you please include a image?
Thanks!!!
Using this model, what would be the cost of a flight that travels 1375 miles?
Round your answer to the nearest dollar.
Answer:
C) $143.
Step-by-step explanation:
We are given an equation: y = 0.0714x + 44.8.
x is the number of miles, and y is the cost.
y = 0.0714 * 1,375 + 44.8
y = 98.175 + 44.8
y = 142.975
So, the cost is about C) $143.
Hope this helps!
The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set.
2, 10, 15, 4, 11, 10, 15, 10, 2, 10
Answer:
a
[tex]R =13[/tex]
b
[tex]\= x =8.9[/tex]
c
[tex]var(x) = 16.57[/tex]
d
[tex]\sigma = 4.1[/tex]
Step-by-step explanation:
From the question we are given a data set
2, 10, 15, 4, 11, 10, 15, 10, 2, 10
The sample size is n = 10
The range is
[tex]R = maxNum - MinNum[/tex]
Where maxNum is the maximum number on the data set which is 15
and MinNum is the minimum number on the data set which is 2
So
[tex]R = 15 - 2[/tex]
[tex]R =13[/tex]
The mean is mathematically represented as
[tex]\= x = \frac{\sum x_i}{N}[/tex]
substituting values
[tex]\= x = \frac{2 + 10 + 15 + 4 + 11 + 10 + 15 + 10 + 2 + 10 }{10}[/tex]
[tex]\= x =8.9[/tex]
The variance is mathematically evaluated as
[tex]var(x) = \frac{\sum (x - \= x)^2}{N}[/tex]
substituting values
[tex]var(x) = \frac{(2 - 8.9 )^2 + (10 - 8.9 )^2 + (15 - 8.9 )^2 +(4 - 8.9 )^2 +(11 - 8.9 )^2 +(10 - 8.9 )^2 +(15 - 8.9 )^2 +(10 - 8.9 )^2 +} {10}[/tex] [tex]\frac{(2 - 8.9 )^2 +(10 - 8.9 )^2 }{10}[/tex]
[tex]var(x) = 16.57[/tex]
The standard deviation is [tex]\sigma = \sqrt{var(x)}[/tex]
substituting values
[tex]\sigma = \sqrt{16.57}[/tex]
[tex]\sigma = 4.1[/tex]
Consider the statemen P. P.X=5 which of the following is an equivalent statement
Answer:
(D)R: x+2=7
Step-by-step explanation:
Given the statement P:x=5
An equivalent statement will be a statement whose result is exactly x=5.
From the given options:
R: x+2=7
R: x=7-2
R: x=5
Therefore, R is an equivalent statement.
The correct option is D.
The radius of circle is 11 miles. What is the area of a sector bounded by a
300° arc?
The area of a circle is pi x r^2
Area of full circle: 3.14 x 11^2
Area = 379.94 square miles.
To find the area of the bounded arc, multiply the full area by the fraction of a full circle the arc is:
379.94 x 300/360 = 316.62 square miles
Answer:
316.62 miles²
Step-by-step explanation:
Area of circle = 3.14 × r²
3.14 × 11²
= 379.94 (area of whole circle)
We need to find the area of the blue shaded sector.
300/360 × 379.94
= 316.62
(3x + 4y)^3
i am confused
pls help
ANSWER
(a+b)(a^2+ab+b^2)=(3x+4y) 9x^2+12xy+16y^2)
11) $ 8,000 is invested in an account that yields 6% interest per year. After how many years will the account be worth 13709.60$ if the interest is compounded monthly?
Answer:
[tex]\large \boxed{\sf \ \ 9\text{ years} \ \ }[/tex]
Step-by-step explanation:
Hello,
First of all, a few remarks:
>>> 1 year is 12 months, right?
>>> Monthly compounding means that each month we compute the interest and they will be included in the investment for the next month.
>>> 6% is an interest per year, it means that to compute the interest for 1 month we need to compute by 6% multiplied by [tex]\dfrac{1}{12}[/tex]
Let's do it !
At the beginning, we have:
$8,000
After 1 month, we will have:
[tex]8000 + 8000\cdot \dfrac{6\%}{12}=8000\cdot (1+ \dfrac{6}{1200})= 8000\cdot (1+ \dfrac{1}{200})[/tex]
After 2 months, we will have:
[tex]8000\cdot (1+ \dfrac{1}{200})\cdot (1+ \dfrac{1}{200})=8000\cdot \left(1+ \dfrac{1}{200}\right)^2[/tex]
After n months, we will have
[tex]8000\cdot \left(1+ \dfrac{1}{200}\right)^n=8000\cdot \left(1.005\right)^n[/tex]
We are looking for n such that
[tex]8000\cdot \left(1.005\right)^n=13709.60\\\\ln(8000)+ n\cdot ln(1.005)=ln(13709.60)\\\\\\n = \dfrac{ln(13709.60)-ln(8000)}{ln(1.005)}=108[/tex]
So, we need 108 months to reach this amount, which means 108/12=9 years.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The half-life of a radioactive isotope is the time it takes for a quantity of the Isotope to be reduced to half its initial mass. Starting with 210 grams of a
radioactive isotope, how much will be left after 6 half-lives?
Round your answer to the nearest gram
Answer:
after 6 half lives: 210(1/2)^6= 3.28125
Step-by-step explanation:
isotope to be reduced to half its initial mass at first:
210(1/2)=105 half it is original weight
after second life: 210(1/2)^2=105(1/2)=52.5
after third : 210(1/2)^3=52.5/2=26.25
after fourth : 26.25/2=12.125
after fifth : 13.125/2
after 6 half lives: 210(1/2)^6= 3.28125
The JUST-SAY-MOW lawn mowing company consists of two people: Marsha and Bob. If Marsha cuts the lawn by herself, she can do it in 3 hours. If Bob cuts the same lawn himself, it takes him an hour longer than Marsha. How long would it take them if they worked together? Round to the nearest hundredth of an hour.
Answer:
it will take them 1.71 hours to finish cutting the lawn if they work together.
Step-by-step explanation:
If Marsha cuts the lawn by herself it will take her 3 hours, this mean that in one hour she cuts 1/3 of the lawn.
On the other hand Bob needs one more hour to finish the lawn, this means it takes him 4 hours to cut it and therefore he cuts 1/4 of the lawn per hour.
Now, to know how much they cut by working together we need to sum up the amount of lawn they cut per hour:
Working together in one hour: Marsha's one hour + Bob's one hour
Working together in one hour: [tex]\frac{1}{3}+ \frac{1}{4}=\frac{4+3}{12}=\frac{7}{12}[/tex]
Therefore, working together they will cut 7/12 in one hour.
Now, to know how long will it take it to cut the entire lawn (which is equivalent to 12/12), we can write this in terms of proportions
Time Total amount of lawn
1 hour 7/12
x hours 12/12
Solving for x (to know the amount of hours it will take them) we have:
[tex]x=\frac{12}{12}[/tex]÷[tex]\frac{7}{12}[/tex]=[tex]1[/tex]×[tex]\frac{12}{7}=\frac{12}{7}=1.714[/tex]
Rounded to the nearest hundredth, we have that working together it will take them 1.71 hours to finish cutting the lawn.
Two angles are supplementary. Angle A is twice as large as angle B. What is the measure of each angle ?