Answer:
52.56 square inches.
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.
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
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
Please solve with explanation (high points)
Real life scenarios of acute angles are:
Sighting a bird on a tree at an angle of 55 degrees.The angle between a ladder and the horizontal groundWhat are acute angles?Acute angles are angles that have a measure less than 90 degrees.
How to create the real life scenario?To create a real life scenario to illustrate acute angles, the following must be put in place:
The scenario must involve an angleThe angle must be less than 90 degrees.Real life scenarios that satisfy the above highlights are:
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To make 1 batch of green paint, Ethan mixes 2 3/8 (Fraction) just so you know
ounces of blue paint and the same amount of yellow paint. How many ounces of blue paint is needed to make 5 batches of green paint?
Select the correct values to give your answer as a mixed number:
Answer:
[tex]11\frac{7}{8}[/tex] ounces
Step-by-step explanation:
Since Ethan needs [tex]2 \frac{3}{8}[/tex] ounces of blue paint to make 1 batch of green paint, we can multiply the amount of blue paint needed by 5 to see how much blue paint he'll need for 5 batches of green paint.
[tex](2 \frac{3}{8})5 = 10 \frac{15}{8} \rightarrow \boxed{11\frac{7}{8}}[/tex]
This means he will need [tex]11\frac{7}{8}[/tex] ounces of blue paint to make 5 batches of green paint.
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.
area of sector................................
Answer:
A ≈ 25.1 cm²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{\frac{4\pi }{9} }{2\pi }[/tex]
= π × 6² × [tex]\frac{\frac{4\pi }{9} }{2\pi }[/tex]
= 36π × [tex]\frac{\frac{4\pi }{9} }{2\pi }[/tex]
= 18 × [tex]\frac{4\pi }{9}[/tex]
= 2 × 4π
= 8π
≈ 25.1 cm² ( to the nearest tenth )
15 ( y - 4 ) - 2 (y - 9 ) + 5 (y + 6) = 0
Answer:
y = 2/3
Step-by-step explanation:
Assuming you are looking for "y":
15 * ( y - 4 ) - 2 * (y - 9 ) + 5 * (y + 6) = 0
15y - 60 - 2y + 18 + 5y + 30 = 0
15y - 2y + 5y -60 + 18 + 30 = 0
18y = 60 - 18 - 30
18y = 12
y = 12/18
y = 2/3
Find the volume of the sphere. Round your answer to the nearest tenth.
Answer:
Step-by-step expiation : 5575.3
A toy rocket is shot vertically into the air from a launching pad 6 feet above the ground with an initial velocity of 88 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=−16t2+88t+6. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ? second(s) after launch.
(simplify your answer.)
a) The time taken by the rocket to reach the maximum height is 2.75 seconds.
b) The maximum height of the rocket will be 127 feet.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
Given that:-
A toy rocket is shot vertically into the air from a launching pad 6 feet above the ground with an initial velocity of 88 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=−16t²+88t+6.a) The time taken by the rocket will be calculated as:-
We have a function h(t)=−16t²+88t+6. Now by taking the derivative of the function with respect to time and equating it to zero we will get the maximum time in which the rocket will reach the maximum height.
h(t) = -16t² + 88t + 6
h'(t) = 0
-32t + 88 = 0
32t = 88
t = 88 / 32 = 2.75 seconds
So the maximum time is 2.75 seconds.
b) Maximum height will be calculated as:-
Put the value of maximum time in the function h(t) = -16t² + 88t + 6 we will get the maximum height.
h(t) = -16t² + 88t + 6
h(2.75) = -16(2.75)² + ( 88 x 2.75 ) + 6
h(2.75) = 127 feet
Therefore the time taken by the rocket to reach the maximum height is 2.75 seconds and the maximum height of the rocket will be 127 feet.
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Evaluate:
6-(2/3)^2
A. 17/3
B. 52/3
C. 49/9
D. 50/9
Answer:
The correct answer is: "Option [D]".
Step-by-step explanation:
Hi student, let me help you out!
....................................................................................................................................
Let's use the acronym PEMDAS. With the help of this little acronym, we will not make mistakes in the Order of Operations! :)
[tex]\dag\textsf{Acronym \: PEMDAS}[/tex]
P=Parentheses,
E=Exponents,
M=Multiplication,
D=Division,
A=Addition,
S=Subtraction.
Now let's start evaluating our expression, which is [tex]\mathsf{6-(\cfrac{2}{3})^2}[/tex]
According to PEMDAS, the operation that we should perform is "E-Exponents".
Notice that we have a fraction raised to a power. When this happens, we raise both the numerator (2 in this case) and the denominator (3 in this case) to that power, which is 2. After this we obtain [tex]\mathsf{6-\cfrac{4}{9}}[/tex].
See, we raised both the numerator and the denominator to the power of 2.
Now what we should do is subtract fractions.
Note that 6 and -4/9 have unlike denominators. First, let's write 6 as a fraction: [tex]\mathrm{\cfrac{6}{1}-\cfrac{4}{9}}[/tex]. Now let's multiply the denominator and the numerator of the first fraction times 9: [tex]\mathrm{\cfrac{54}{9}-\cfrac{4}{9}}[/tex].
See, now the fractions have the same denominator. All we should do now is subtract the numerators: [tex]\mathrm{\cfrac{50}{9}}[/tex].
∴, the answer is Option D.
Hope this helped you out, ask in comments if any queries arise.
Best Wishes!
[tex]\star\bigstar\underline{\overline{\overline{\underline{\textsf{Reach \: far. Aim \: high. Dream \: big.}}}}}\bigstar\star[/tex]
[tex]\underline{\rule{300}{5}}[/tex]
Calculate 2/3, to the power of 3, therefore
[tex]\bf{\left(\dfrac{2}{3}\right)^{2}=\dfrac{2\times2}{3\times3}=\dfrac{4}{9} }[/tex]
[tex]\bf{6-\dfrac{4}{9} }[/tex]
Convert 6 to the fraction 54/9.
[tex]\bf{\dfrac{54}{9}-\dfrac{4}{9} }[/tex]
Since 54/9 and 4/9 have the same denominator, join their numerators to subtract them.
[tex]\bf{\dfrac{54-4}{9} \ \ \to \ \ \ Subtract }[/tex]
Subtract 4 from 54 to get 50.
[tex]\bf{\dfrac{50}{9} \ \ \to \ \ \ Answer }[/tex]
Therefore, the correct alternative is "D".
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
Pls I do not know how to rotate without tracing paper
Answer:
Point A:
(1, 3) ------> (3, -1)
Point B:
(3, 3) ------> (3, -3)
Point C:
(3, 2) ------> (2, -3)
Step-by-step explanation:
To find the coordinates of a 90° clockwise rotation, use the following:
[tex](x, y)[/tex] -----> [tex](y, -x)[/tex]
This means you will switch the x and y coordinates of the point and then take the opposite of the x coordinate (if it is positive make it negative and if it is negative make it positive).
Point A:
(1, 3) ------> (3, -1)
Point B:
(3, 3) ------> (3, -3)
Point C:
(3, 2) ------> (2, -3)
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
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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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.
URGENT HELP A contest allows anyone to enter as many times as they would like and at the end of the contest, a winner is randomly chosen from all the entries. Suppose 450 people enter the contest. If Sabine entered 3 times and Joe entered 5 times, then what is the probability Joe or Sabine will win the contest?
Answer:
4/225
Step-by-step explanation:
Formula :
Probability (Event) = No. of times event has occurred / Total possibilities
==============================================================
Solving :
⇒ P (Joe or Sabine) = No. of times Joe or Sabine has entered / Total number of people
⇒ P (Joe or Sabine) = 3 + 5 / 450
⇒ P (Joe or Sabine) = 8/450
⇒ P (Joe or Sabine) = 4/225
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
why does the equation 3x+7=-3x+2+6x has no solution?
Answer:
[tex]3x+7=-3x+2+6x[/tex]
Combine the like terms on the right side of the equation.
[tex]3x+7=3x+2[/tex]
Eliminate 3x from the equation.
[tex]7\neq 2[/tex]
Seven will never equal 2.
Step-by-step explanation:
[tex]3x+7=-3x+2+6x[/tex]
Combine the like terms on the right side of the equation.
[tex]3x+7=3x+2[/tex]
Eliminate 3x from the equation.
[tex]7\neq 2[/tex]
Seven will never equal 2.
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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write the equation representing the number of children in your family
Answer:
0+4
Step-by-step explanation:
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.
solve it step by step
The solution for this expression is:[tex]9\sqrt{6}-15\sqrt{15}+6\sqrt{10}-50[/tex].
Properties of MultiplicationThe properties of multiplication are:
Distributive: a(b±c)= ab±acComutative: a . b = b. aAssociative: a(b+c)= c(a+b)Identity: b.1=bHere, you should apply the distributive property for solving this expression.
[tex](3\sqrt{3}+2\sqrt{5} )*(3\sqrt{2}-5\sqrt{5})\\ \\[/tex]
Applying the distributive property, you have:
[tex]9\sqrt{6}-15\sqrt{15}+6\sqrt{10}-10*\sqrt{25} \\ \\ 9\sqrt{6}-15\sqrt{15}+6\sqrt{10}-10*5\\ \\ 9\sqrt{6}-15\sqrt{15}+6\sqrt{10}-50[/tex]
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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.
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
Old MacDonals raises chickens and sheep on his farm. His livestock has a total of 55 heads and 142 legs among them (not counting the farmer). How many chickens and how many sheep does he have
The number of chickens and sheeps on the Old MacDonals farm is 39 and 16 respectively.
Simultaneous equationlet
x = number of chickeny = number of sheep'sx + y = 55
2x + 4y = 142
Multiply (1) by 2
2x + 2y = 110
2x + 4y = 142
subtract the equation4y - 2y = 142 - 110
2y = 32
y = 32/2
y = 16
substitute y = 16 into (1)
x + y = 55
x + 16 = 55
x = 55 - 16
x = 39
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Given the function f(x) = 2x, evaluate ƒ(3).
Answer:
f(3) = 6
Step-by-step explanation:
you substitute 3 for x.
So you have 2(3) which is 2 multiplied by 3 which is 6
In a certain board game, a 12-sided number cube
showing numbers 1 through 12 is rolled. In this game, a
number cube must be rolled until a number 9 or higher
appears.
What is the probability that the first such number is on
the 3rd roll?
Answer:
4/27 ezzzzzzzzzzzzzzzzzzzz
Solve Multi-Step Equations, Part 2 - Instruction
ceady
Solve the equation - 10(g - 6) = 65.
») What is the value of g?
g=
?
Answer:
g = -0.5
Step-by-step explanation:
Divide both sides by the numeric factor on the left side, then solve.
Answer:
g = -0.5 or -1/2
Step-by-step explanation:
-10(g – 6) = 65 : apply distributive property
(-10 • g) + (-10 • -6) = 65 : multiply
-10g + 60 = 65 : apply property of equal subtraction
-10g + 60 – 60 = 65 – 60 : subtract
-10g = 5 : apply property of equal division
-10g ÷ -10 = 5 ÷ -10 : divide
g = -0.5
6 liters of a gas has a pressure of 4 atmospheres. The gas's original pressure was 6 atmospheres.
What was the original volume in liters?
Enter your answer as a decimal to the 10th place, like this: 4.2 l
The original volume of the gas would be 4.00 liters
What is Boyle's law?Boyle's law is a gas law that states that the pressure of a gas is inversely proportional to it's volume with temperature kept constant.
It is represented thus;
P1V1 = P2V2
Where P1 = Original pressure = 6 atmospheres
V1 = Original volume =?
P2 = Final pressure =4 atmospheres
V2 = Final volume= 6 liters
How to calculate the original volumeMake the original volume V1, subject of formula
V1 = P2× V2 ÷ P1
V1 = 4× 6 ÷ 6 = 24 ÷ 6 = 4. 00 liters
Hence, the original volume of the gas is 4.00 liters
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Steve travels two times as fast as you. Traveling in opposite directions, they are 120 miles apart after 2.5 hours. Find the rate of travel