Last month David and Mary saved some money in a ratio of 3:5. This month they saved an additional $154 together, and David now has three times as much money as he had last month and Mary has two times as much as she had last month. How much money did they save last month?
Answer:
David: $42Mary: $70Step-by-step explanation:
The two relations can be translated to a system of linear equations in two variables. These can be solved in any of the usual ways.
__
setupLet d and m represent the amounts David and Mary saved last month, respectively.
The first relation tells us
d/m = 3/5 ⇒ 5d = 3m ⇒ 5d -3m = 0
The second relation tells us that adding 3 times what David had last month to 2 times what Mary had last month will give a total that is 154 greater than the sum of their funds last month.
d +m + 154 = 3d +2m ⇒ 2d +m = 154
__
solutionWe can add 3 times the second equation to the first to eliminate m.
(5d -3m) +3(2d +m) = (0) +3(154)
11d = 462 . . . . . . . . simplify
d = 42 . . . . . . . . . divide by 11
Using the second equation, we can find Mary's savings:
m = 154 -2d
m = 154 -2(420 = 70
David saved $42 last month; Mary saved $70.
A Pythagorean triple is a set of three positive integers a, b, and c that satisfy the equation a² + b² = c².
The numbers 3, 4, and 5 are a Pythagorean triple because 3² + 4² = 5². Pythagorean triples are usually written in parentheses, such as (3, 4, 5) .
You can determine other Pythagorean triples by multiplying every number in (3, 4, 5) by the same positive integer. This creates similar triangles where the number you multiplied every triple by is the scale factor.
To create Pythagorean triples that are not similar to a triangle with side lengths of 3, 4, and 5, follow these steps.
Choose two positive integers, m and n, where m>n .
Determine a using a=m2−n2 .
Determine b using b=2mn .
Determine c using c=m2+n2
.
Write the triple (a, b, c) .
a. What Pythagorean triple results when m = 3 and n = 2? Explain.
b. Determine two other Pythagorean triples by multiplying every triple in part a by the same number.
c. Choose your own values for m and n. What Pythagorean triple results? Explain.
Answer:
Step-by-step explanation:
(3k,4k,5k)
sea k=2
la terna es:
(6,8,10)
sea k=5
la terna sería:
(15,20,25)
What is the value of n?
A. 69
B. 20
C. 29
D. 49
Answer:
[tex] \pink{\boxed{{\colorbox{white}{Answer}}}}[/tex]
C. 29
Step-by-step explanation:
[tex] \pink{\boxed{{\colorbox{white}{- MsTiyana}}}}[/tex]
i need helppp with this question
Answer:
2
Step-by-step explanation:
g/5 - h is equal to 20/5 - 2
equal to 20 divided by 5 is equal to 4(20÷5=4)
then 4minus h which is 4- 2 =2
therefore the answer is 2
I hope this helps you
Instructions: Given the figure, what is the
angle of rotational
symmetry?
Rotation:
o
Answer:
The angle of rotational symmetry is 4
Lamar is considering two loans
Which loan will have the lowest total payback?
Answer:
Loan A will have the lowest total paycheck because the total of the principal than the same total for loan B
In a recent season in a basketball league, a certain player made 746 field goals, which was 48.9% of the shots he tried. How many shots did he try?
Answer:
I don't no ok ok ok ok ok ok ok ok ok
Find the area of a regular polygon with 6 sides that has a side length of 6 inches and an apothem of 4 inches.
Area = [?]in2
Answer:
see the attachment photo!
Answer the question below please
The correct answer is : of those planning to not to go on vacation, more of them are women.
The correct answer is (C)
What is probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event
Given: total people asked =145
The first option is not correct because plan to go on vacation women are more than men.
The second option is also incorrect because more women were asked than men.
The third option is correct because out of planning who were not going any vacation, women are more than of men.
The fourth option is incorrect because More men plan to go on vacation.
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nate spent 3/8 of his money on clothes .he spent £510 on clothes.calculate how much money he had left over?
Answer:
£850
Step-by-step explanation:
We can compute the left-over amount by comparing that to the amount spent.
__
setupWritten as ratios, we have ...
spent : left-over = 3/8 : 1 -3/8 = 3/8 : 5/8 = 3 : 5
Writing this using fractions, we have ...
left-over / spent = 5 / 3
solutionSolving for left-over gives ...
left-over = spent × (5/3) = £510×5/3 = £850
Nate had £850 left over.
_____
Additional comment
Nate's money totaled £510 +850 = £1360.
The fraction spent is £510/£1360 = 3/8, as required.
help me with this please
Answer:
1/12 more red rice then white rice
Step-by-step explanation:
3/4 = 0.75
2/3 = 0.666666....
Clearly Red rice is more but it will be difficult to state how much more in decimal form so we must use fraction form :
3/4 = 9/12
2/3 = 8/12
So there is 1/12 more red rice then white rice
Hope this helped and have a good day
If (1, 0) is an ordered pair of the function F(x), which of the following is an
ordered pair of the inverse of F(x)?
If the ordered pair (1, 0) represents the function F(x), then the ordered pair (0, 1) represents the inverse of F(x). Option A is correct.
What is a function?A connection between independent variables and the dependent variable.is defined by the function.
The complete question is
"If (1,0) is an ordered pair of the function f(x), which of the following is an ordered pair of the inverse of f(x)?
A. (0,1)
B. (0,0)
C. (1,0)
D. (1,1)"
Functions help to represent graphs and equations. A function is represented by the two variables one is dependent and another one is an independent function.
The relation between them is shown as y if dependent and x is the independent variable.
If the ordered pair (1, 0) represents the function F(x), then the ordered pair (0, 1) represents the inverse of F(x).
F(x)∈ (1, 0)
F⁻¹(x)∈(0, 1)
Hence, option A is correct.
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3. The diagonal of a rectangular field is 169 m. Ifthe ratio of the length to the width is 12:5, find the: (a) (b) dimensions; perimeter of the field.
The dimensions of the rectangle are length 156 m and a width of 65m, and a perimeter P = 442m
How to find the dimensions of the rectangle?For a rectangle of length L and width W, the diagonal is:
[tex]D = \sqrt{L^2 + W^2}[/tex]
Here we know that the diagonal is 169m.
And the ratio of the length to the width is 12:5
This means that:
W = (5/12)*L
Replacing all that in the diagonal equation:
[tex]169 = \sqrt{((5/12)^2*L^2 + L^2} \\\\169^2 = (25/144)*L^2 + L^2 = ( 25/144 + 1)*L^2\\\\\frac{169}{\sqrt{25/144 + 1} } = L = 156[/tex]
So the length is 156 meters, and the width is:
W = (5/12)*156 m = 65m
Finally, the perimeter is:
P = 2*(L + W) = 2*(156 m + 65m) = 442m
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Suppose you make $1500 at your summer job and you decide to invest this money in a savings account that
pays interest at an annual rate of 5.5% compounded continuously. How many dollars will be in the account
after 5 years?
Answer:
$1912.50
Step-by-step explanation:
5.5% of $1500 is 82.50
so 82.50×5(years)
=412.5 + 1500
=1912.50
Answer:
You will need this formula
Total = Principal * e ^ (rate * years)
where 'e' equals 2.718281828459
Total = 1,500 * 2.718281828459 ^ (.055 * 5)
Total = 1,500 * 2.718281828459 ^ (.275)
Total = 1500 * 1.31653067486762
Total = 1,974.80
formula www.1728.org/rate2.htm
Calculator located here: https://www.1728.org/compint.htm
Step-by-step explanation:
WILL MARK AS BRAINLINEST!!
Answer:
Step-by-step explanation:
1. 54 Students
2. 4 Students
3.) 33 Students
4.) 10 Students
Just justify the answer for 5 and 6 you can do it<<33
What is the area of the hexagon?
5m
4 m
4 m
12 m
5m
60 m ²
120 m 2
106 m ²
68 m 2
Answer:
68 square meters
Step-by-step explanation:
The hexagon is made up of two trapezoids. Use the formula to find the area of each trapezoid then add those two areas together.
Area of a trapezoid (add the two bases together, multiply by the height then divide by 2):
[tex]A = \frac{1}{2} (b_{1}+b_{2})h[/tex]
Top trapezoid:
[tex]A = \frac{1}{2} (5 + 12)4\\A = \frac{1}{2} (17)4\\A= \frac{1}{2} (68)\\A = 34[/tex]
Bottom trapezoid (identical to the top trapezoid):
[tex]A = \frac{1}{2} (5 + 12)4\\A = \frac{1}{2} (17)4\\A= \frac{1}{2} (68)\\A = 34[/tex]
Add the areas together:
34 + 34 = 68
Can someone pls help me with this
The length has [tex]\frac{3.5}{0.5}=\boxed{7}[/tex]
The width has [tex]\frac{2.5}{0.5}=\boxed{5}[/tex]
The height has [tex]\frac{1.5}{0.5}=\boxed{3}[/tex]
Which expression is equivalent to -1/2 (1/4 x - 3/8). SHOW WORK
Hey there!
-1/2 (1/4 * - 3/8)
= -1/2(1/4)(-3/8)
= -1/2(-3/32)
= 3 / 64
Therefore, your answer should be:
3/64
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Which action will help increase a low FICO score?
A.
reducing credit card balances
B.
holding payment on bills
C.
applying for credit more frequently
im a senior trying to graduate my school has me in the wrong classes i have adhd and i was supposed to be in diffrent classes but anyways i need help bad its due tn at 12 and if i dont get them in i dont graduate
Step-by-step explanation:
hope you can send the questions again because your question is to long to answer everything. I answered 1,2,3,4
a 2 gallon container of window cleaner costs $11.52. what is the price per cup?
Answer:
$0.36
Step-by-step explanation:
To convert between gallons, quarts, pints, and cups it can be helpful to memorize this:
2 Cups in a Pint
2 Pints in a Quart
4 Quarts in a Gallon
We can work backwards using this, finding that there are 4 quarts in a gallon, 8 pints in a gallon, and 16 cups in a gallon.
Since we have 2 gallons, we must multiply the number of cups by 2 to get 32 cups in 2 gallons.
Now we can solve for the price per cup by dividing the cost of all 2 gallons by how many cups are in it (32.)
$11.52 / 32 = $0.36
That is the answer
- Kan Academy Advance
In a triangle ABC, if angle A = 53 degree and Angle C=45 degree then find the value of Angle B is:
Answer:
69
It wont always be easy, but always try to do what ' s right!
In a world of worriers, be the warrior!
When nothing goes right, go left.
What's the most effective method for controlling inventory ? a ) Electronically , by reviewing billing receipts b ) Electronically , by checking recent orders Oc ) Visually , by looking at discarded packaging d ) Visually , by looking at what's on the shelf
Answer:
a ) Electronically , by reviewing billing receipts
Step-by-step explanation:
The main purpose of controlling inventory is to make sure that the optimal amount of products are being kept.
Therefore, option A is correct.
PLEASE HELP ME. QUAD has coordinates Q(-4, 9), U(2, 3), A(-3, -2), and D(-9, 4). Prove that quadrilateral QUAD is a
rectangle.
Check the picture below.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ Q(\stackrel{x_1}{-4}~,~\stackrel{y_1}{9})\qquad U(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill QU=\sqrt{[ 2- (-4)]^2 + [ 3- 9]^2} \\\\\\ ~\hfill \boxed{QU=\sqrt{72}} \\\\\\ U(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad A(\stackrel{x_2}{-3}~,~\stackrel{y_2}{-2}) ~\hfill UA=\sqrt{[ -3- 2]^2 + [ -2- 3]^2} \\\\\\ ~\hfill \boxed{UA=\sqrt{50}}[/tex]
[tex]A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad D(\stackrel{x_2}{-9}~,~\stackrel{y_2}{4}) ~\hfill AD=\sqrt{[ -9- (-3)]^2 + [ 4- (-2)]^2} \\\\\\ ~\hfill \boxed{AD=\sqrt{72}} \\\\\\ D(\stackrel{x_1}{-9}~,~\stackrel{y_1}{4})\qquad Q(\stackrel{x_2}{-4}~,~\stackrel{y_2}{9}) ~\hfill DQ=\sqrt{[ -4- (-9)]^2 + [ 9- 4]^2} \\\\\\ ~\hfill \boxed{DQ=\sqrt{50}}[/tex]
now, let's take a peek at that above, DQ = UA and QU = AD, so opposite sides of the polygon are equal.
Now, let's check the slopes of DQ and QU
[tex]D(\stackrel{x_1}{-9}~,~\stackrel{y_1}{4})\qquad Q(\stackrel{x_2}{-4}~,~\stackrel{y_2}{9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-9)}}} \implies \cfrac{9 -4}{-4 +9}\implies \cfrac{5}{5}\implies \cfrac{1}{1}\implies 1 \\\\[-0.35em] ~\dotfill[/tex]
[tex]Q(\stackrel{x_1}{-4}~,~\stackrel{y_1}{9})\qquad U(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{3 -9}{2 +4}\implies \cfrac{-6}{6}\implies \cfrac{-1}{1}\implies -1[/tex]
keeping in mind that perpendicular lines have negative reciprocal slopes, let's notice that the reciprocal of 1/1 is just 1/1 and the negative of that is just -1/1 or -1, so QU has a slope that is really just the negative reciprocal of DQ, those two lines are perpendicular, thus making a 90° angle, and their congruent opposite sides will also make a 90°, that makes QUAD hmmm yeap, you guessed it.
write the equation representing the number of children in your family
Answer:
0+4
Step-by-step explanation:
I really need help with this
Are these numbers rational or irrational? √10 (square root of 10) √16 (square root of 16) 52% 1.235 1. Rational 2. Irrational please answer fast this needs to be in before tomorrow
Step-by-step explanation:
any rational number can be expressed as a/b, with a and b being integer numbers, and b different to 0.
-7 = -7/1 rational
sqrt(10) irrational (because there is no rational number multiplied by itself that results in 10)
sqrt(16) = sqrt(4×4) = 4 = 4/1 rational
52% = 52/100 rational
1.235 = 1235/1000 rational
Follow the steps below for the following set of data. In your final answer include all of your calculations and all work in steps 1, 2, and 3.
8, 3, 5, 5, 4, 7
Find the median, lower quartile, and upper quartile of the set of data.
Use the median, lower quartile, upper quartile, lowest value, and highest value of the set to construct a box-and-whisker plot on your own sheet of paper.
Use the box-and-whisker plot to find the range and the interquartile range of the set of data.
The answers to the question are
Median = 5Lower quartile = 4Upper quartile = 7What is the median?The median of the data set is gotten by arranging the values in order
3, 4, 5, 5, 7, 8
The median can be gotten by
5 + 5 / 2
= 10/2
Median = 5
What is the lower quartile?This is the value under which 25 percent of the data are found in the group of data. The lower quartile is 4.
What is the upper quartile?This is the point from which 75 percent of the data is found when it is in ascending order. The upper quartile is 7.
What is the lowest valueThe lowest value in the data set is 3
What is the highest valueThe highest value in the data set is 8
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PLEASE HELP "What is the value of x in the triangle" (15 Points)
Answer:
The answer is B.) 3
Step-by-step explanation:
Answer:
jesse got right
Step-by-step explanation:
branliest.
All of the following are irrational except _____.
The number that is not irrational is [tex]1.\overline{45}[/tex]. The correct option is the second option [tex]1.\overline{45}[/tex]
Irrational numbersFrom the question, we are to determine which of the given options is not irrational
Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q, where p and q are integers.
[tex]1.\overline{45}[/tex] is a repeating decimal and it can be expressed as a fraction
[tex]1.\overline{45} = \frac{144}{99}[/tex]
∴ [tex]1.\overline{45}[/tex] is not an irrational number. It is a rational number
The other options cannot the expressed as a fraction.
Hence, the number that is not irrational is [tex]1.\overline{45}[/tex]. The correct option is the second option [tex]1.\overline{45}[/tex]
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