the ages of three friends are represented by 3 consecutive odd integers. the sum of their ages is 63. if the youngest of the three is represented by x , what equation could be used to find x?
Answers
x + (x + 2) + (x + 4) = 63
Step by step
We know x is the youngest
We know our next number is 2 more than x because we are skipping the even number to go to the next odd number so
(x + 2)
We know the 3rd number is 2 more than the previous number because again, we are skipping the even number to go to the next odd number so
(x + 4)
And the 3 numbers added together = 63
x + (x + 2) + (x + 4) = 63
Is your answer
To solve we would have
3x + 6 = 63
Subtract 6 from both sides to combine constants
3x +6 -6 = 63 - 6
Combine
3x = 57
Divide both sides by 3 to solve for x
3/3 x = 57/3
x = 19
x + 2 = 21
x + 4 = 23
Added together = 63
Problem solved!
Related Questions
Determine the domain of the function f(x) = 1/√x-1 + 1/√2-x
Answers
The domain of the function is 1 ≤ x < 2.
What is domain ?The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.
The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates).
We have f : [tex]\frac{1}{\sqrt{x-1} } + \frac{1}{\sqrt{2-x} }[/tex]
[tex]\sqrt{x-1}[/tex] ≥ 0
x- 1 ≥ 0
x ≥ 1
Similarly , [tex]\sqrt{2-x}[/tex] > 0
2 - x > 0
2 > x
So our domain is 1 ≤ x < 2.
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PLEASE QUICK HELP MEE
Answers
Answer: 130 degrees
Step-by-step explanation:
The interior angle where line c intersects line b is equal to 50 (given). therefore, its supplementary angle is 130 degrees. the opposite angle is therefore equal to 130 degrees, which makes angel x equal to 130 degrees.
https://www.mathplanet.com/education/pre-algebra/introducing-geometry/angles-and-parallel-lines
Pls help me with this due tomorrow!
Answers
Answer: y = 3x +1
Step-by-step explanation:
y =mx +b
m(slope) = 3
b(y-int) = ?
y = 3x+b
substitute in values
4 = 3(1) +b
4 = 3+b
b = 1
y= 3x+1
what is the slope of a line that runs through the points (10,10) and (5,10)
Answers
The slope of the line that passes through the points (10,10) and (5,10) is 0
How to determine slope of a line?Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1 ( 10,10 )
x₁ = 10y₁ = 10Point 2 ( 5,10 )
x₂ = 5y₂ = 10To determine the slope, plug these coordinates into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 10 - 10 )/( 5 - 10 )
Slope m = ( 0 )/( 5 - 10 )
Slope m = ( 0 )/( -5 )
Slope m = 0
Therefore, the slope of the line is 0.
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Jenna had a collection of 206 quarters, nickels, and dimes. She has twice as many nickels as
she does dimes. All of her coins together are worth $31.70. How many of each coin does she
have?
With equational proof
Answers
In linear equation, $56.65are the value of the coins in dollars .
What is a linear equation example?
Ax+By=C is the usual form for two-variable linear equations.As an illustration, the conventional form of the linear equation 2x+3y=5 When an equation is given in this format, finding both intercepts is rather simple (x and y).A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.We need to find how many of the 206 coins are nickels, dimes, or quarters.
We know the quantities of each coin in relation to one another.
From that relationship we can set up a ratio.
Let Q = number of quarters
Let D = number of dimes
Let N = number of nickels
Then Q:D:N = 1:1:2
this tells us if the girl had 4 coins, she would have 1 quarter, 1 dime, and 2 nickels.
We want to keep this same ratio but we want the total number of coins to be 206.
If we divide 206 by 4, we get the number that we use to multiply our ratio.
206/4 = 51.5
So she has 51.5 quarters, 51.5 dimes, and 103 nickels.
the value of the coins in dollars = 51.5(0.10) + 51.5(0.05) + 103(.25) = $56.65
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Write a word to match the equation. 3+( 4 x 12 )
Answers
Answer:
The sum of 3 and the product of 4 times 12.
Step-by-step explanation:
The equal sign would mean the words "the sum", which also corresponds with "3+". The 4 x 12 would be referred to by "the product" and "times".
Determine the length of the missing side in the triangle shown.
right triangle with one leg labeled 11 and hypotenuse labeled 15
square root of 346
square root of 104
square root of 26
square root of 4
aspa pls thanks!
Answers
Answer: square root of 104
Step-by-step explanation:
The length of the missing side in the right triangle is approximately √104.
Given is a right triangle with one leg labeled 11 and hypotenuse labeled 15.
We need to find length of the missing side.
To determine the length of the missing side in the right triangle, we can use the Pythagorean theorem.
It states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's denote the missing side as "x".
According to the given information:
One leg (one of the shorter sides) is labeled as 11.
The hypotenuse (the longest side) is labeled as 15.
Using the Pythagorean theorem, we can set up the equation:
11² + x² = 15²
Simplifying this equation:
121 + x² = 225
Subtracting 121 from both sides:
x² = 225 - 121
x² = 104
To find the value of "x," we can take the square root of both sides of the equation:
x = √104
Therefore, the length of the missing side in the right triangle is approximately √104.
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Geometry lvl 1 stuff but im dum
Answers
Answer:
A
Step-by-step explanation:
Point A
:] its ok we all dum sometimes lol
Fill in the missing number.
80% of 95 =
Answers
Answer: The answer is 76
Step-by-step explanation:
A circular swimming pool has a radius of 4
metres and a depth all over of 3 metres. Find the
volume of water in cubic metres, to the nearest
cubic metre. __m³.
Help please
Answers
= pie (4)(4) x (3)
= 48 pie
= 150.72 cubic metres
Answer: The volume of the circular swimming pool to the nearest cubic meter is 151 [tex]m^{3}[/tex].
Step-by-step explanation: According to the question the swimming pool is in the shape of a cylinder, and the top is circular having a radius and depth.
To calculate the volume of a cylinder(pool) we will use the formula for the volume of a cylinder:
The radius of the cylinder = 4 m
height h=3
The volume of the cylinder (V) = [tex]\pi r^{2} h[/tex]
=[tex]\pi (4)^{2} *3[/tex]
Plugging π =3.142
= 3.14*16*3
=150.72 [tex]m^{3}[/tex]
rounding off to the nearest cubic meter
=151 [tex]m^{3}[/tex]
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Can you please help me , last one like this
Answers
Answer:
-5
Step-by-step explanation:
m = (11 - 6) / (13 - 14) = 5/(-1) = -5
Answer:
-5
Step-by-step explanation:
1-6/15-14=-5/1=-5
I’m 2020 summer camp registration was $15 more than it was in 2021 in 2020 registration was $285 by what percentage did the summer camp registration decrease in 2021
Answers
The summer camp registration decreased in 2021 by 5.26 percent.
The summer camp registration fee in 2020 was $285.We are given that the summer camp registration fee in 2020 was $15 more than it was in 2021.From the above data, we can find the summer camp registration fee in 2021.The summer camp registration fee in 2021 was $285-$15.The summer camp registration fee in 2021 was $270.We need to find the percentage decrease in the summer camp registration fee.The percentage decrease is (decrease/initial value)*100.The percentage decrease is (15/285)*100.The percentage decrease in the summer camp registration fee is 5.26 percent.To learn more about percentage, visit :
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Find the value of the variable.
Answers
Answer:
x = 22
Step-by-step explanation:
(88 - x)° = 3x°
-x - 3x = -88
-4x = -88
[tex]x = \frac{-88}{-4} \\\\ x = 22[/tex]
Factor each quadratic expressionx^2-2x-15
Answers
When we are factoring a quadratic function, we are trying to reverse the following equation
[tex](x+a)(x+b)=x^2+(a+b)x+ab[/tex]Now, comparing the right-hand side of the above equation and the one given in the problem we see that
[tex]\begin{gathered} a+b=-2 \\ ab=-15 \end{gathered}[/tex]This means the question simplifies to "what are the two numbers that if I add them I get -2 and if I multiply them I get -15? "
Well, If we set a = -5 and b = 3, then
[tex]\begin{gathered} -5+3=-2 \\ -5\cdot3=-15 \end{gathered}[/tex]Hence, our expression factors to
[tex](x-5)(x+3)[/tex]A bag contains five white balls and four black balls. Your goal is to draw two black balls.
You draw two balls at random. What is the probability that they are both black?
Answers
Answer:
The probability that you draw two balls that are both black is [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
To find probability, take the number of desirable outcomes over the total number of possible outcomes.
In this case, the black balls are desirable. There are four of them.
this means the numerator of the first fraction is 4. The denominator is the total possible outcomes or in this case the total number of black and white balls. This number is 9. The first probability fraction is [tex]\frac{4}{9}[/tex]
Lets say that the first one was black. Now we need to find the probability of drawing another one. Now there are black balls left in the bag. This means that the number of desirable outcomes is 3. There are also 8 balls total. This means the number of total possible outcomes is 8. The second probability is [tex]\frac{3}{8}[/tex]
To get the total probability you multiply both of the individual probabilities together.
[tex]\frac{4}{9} *\frac{3}{8} =\frac{1}{6}[/tex]
What is a line that passes through (3,1) and (0,-3)
Graph slope
Answers
Answer:
y=4/3x-3
Step-by-step explanation:
(y2-y1)/ (x2-x1)
Simplify the expression using the Distributive Property and explain each step.
70[2.50+(−0.60)]+25[3.75+(−0.70)]
Answers
The new expression by using distributive property is: 209.25
What is distributive property?
In mathematics, the distributive property tell the solution method for the expression who are in the form of a(b + c). In this, first add the expression which are in the parenthesis and later multiply it.
According to the question, the given expression is as follows:
70[2.50+(−0.60)]+25[3.75+(−0.70)]
Using distributive property, whose list contains parenthesis, exponents, multiplication/division, addition/subtraction. This is the list in which the given expression need to simplify.
First parenthesis calculation,
2.5 + - 0.6 = 1.9 and 3.75 + - 0.7 = 3.05
Now, substitute the values:
70(1.9) + 25(3.05)
Multiply it: 133 + 76.25;
Add it: 209.25
Hence, the new expression by using distributive property is: 209.25
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Rashon has a dimes and y nickels. He has no less than 12 coins worth at most $0.95
combined. Solve this system of inequalities graphically and determine one possible
solution.
Answers
A possible solution of the system of inequalities is 5 dimes and, 8 nickels
How to determine a possible solution?From the question, the given parameters are:
Number of coins = Not less than 12
Worth = At most $0.95
Represent dime with x and nickels with y
So, we have the following inequalities
x + y >= 12
0.1x +0.05y <= 0.95
Next, we plot the graph of the inequalities (see attachment)
From the graph, we have a possible solution to be (5, 8)
This is so because this point is in the shaded region
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an article suggests the uniform distribution on the interval (6.5, 21) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. (a) what are the mean and variance of depth? (round your variance to two decimal places.)
Answers
The meand and variance are 13.75 cm and 17.52 respectively.
Each possible outcome is equally likely when there is a uniform probability.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The mean of the uniform distribution is:
M = ( a + b ) / 2
The variance of the uniform distribution is given by:
V = ( b - a )² / 12
Uniform distribution on the interval ( 6.5, 21 )
Therefore, a = 6.5 and b = 21
Hence, the mean will be:
M = ( 6.5 + 21 )/ 2
M = 27.5 / 2
M = 13.75
The mean of depth is 13.75 cm.
The variance will be:
V = ( b - a )² / 12
V = ( 21 - 6.5 )² / 12
V = 210.25 / 12
V = 17.52
The variance of depth is of 17.52 cm².
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In Exercises 76, find an equation of the tagent line to
the graph of the function f through the point (xo, yo not on the
graph. To find the point of tangency (x, y) on the graph of f
solve the equation
76.
f(x) = 2/x
(xo, Yo) = (5,0)
Answers
The most appropriate choice for tangent to a curve will be given by- 2x + 25y = 10 is the required equation of tangent.
What is tangent to a curve?
In geometry, a tangent line is a straight line that most closely resembles (or "clings to") a curve at a particular point. It could be thought of as the limiting role of straight lines that pass through the specified point and a nearby curve point as the second point gets closer to the first. If two curves share the same tangent at a given point, they are said to be tangent. Similar definitions apply to the tangent plane to an exterior at a point and two surfaces that are tangent at a point.
Equation of tangent to a curve at a point [tex](x_1, y_1)[/tex] is given by
[tex]y-y_1 = \frac{dy}{dx}|_{(x_1, y_1)}(x - x_1)[/tex]
Here,
f(x) = [tex]\frac{2}{x}[/tex]
f'(x) = [tex]\frac{d}{dx} (\frac{2}{x})[/tex]
= [tex]2(-1)x^{-1-1}\\-2x^{-2}[/tex]
[tex]f'(x)|_{(5, 0)} = -\frac{2}{5^2}[/tex]
[tex]= -\frac{2}{25}[/tex]
Equation of tangent
[tex]y - 0 = -\frac{2}{25}(x - 5)\\\\25y = -2x +10\\2x + 25y = 10[/tex]
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I need this answer in detail as soon as possible.
This is grade 6 maths
It will be better if you write in in a paper step by step answer and attach the picture.
Answers
The answer is 14metres 4m long 3m wide 2 x (4+3) = 14
Each length of bunting is 70 cm but a knot at each end will take 2 x 5 = 10 cm off
1400 / 60 = 23.333…
So she will need 24 lengths of bunting
HELP! I have a paper due and I have no idea how to do this problem! I attached a screenshot of the problem any help is appreciated.
Answers
Answer:
7.5
Step-by-step explanation:
750 is the volume, so divided by then is 75, then divided by 10 again is 7.5
Hope this helps!
Answer:
7.5
Step-by-step explanation:
10x10x7.5=750
10k²=50 quadratic equation
Answers
Answer:
see my photo. hope it can help
what is eighty nine divided by six
Answers
Answer:
about 14, (its not a whole number but its the closest i could get)
Step-by-step explanation:
Answer:
14.833333333
Step-by-step explanation:
I'm assuming you want a rounded answer (14.83), but if you didn't it's 14.83 into perpetuity (meaning that the 3's don't end!)
Hopefully, I helped!
Kareem went for a drive in his new car. He drove at a speed of 63 miles per hour for 157.5 miles. For how many hours did he drive?
Answers
Answer: He drove for 2 hours and 30 minutes. Hope you do great! :)
Answer:2.5 hours
Step-by-step explanation:
Question number 4, how do I do the equation for question 4?
Answers
100 ml of the first solution and 200 ml of the second are required.
The ratio of mystery books to fantasy books in the library is 7:9.
Fill in the missing values to show the possible number of
mystery and fantasy books.
Mystery Books Fantasy Books
21
Select Answer -
63
Select Answer -
27
54
Select Answer
117
Answers
Answer:
42
81
91
Step-by-step explanation:
m = mystery
f = fantasy
[tex]\frac{m}{f}[/tex] = [tex]\frac{m}{f}[/tex]
Compare the ratio with the actual numbers. Solve for the missing number
[tex]\frac{7}{9}[/tex] = [tex]\frac{m}{54}[/tex] you need to multiply 9 by 6 to get 54 so multiply 7 x 6 to get 42.
[tex]\frac{7}{9}[/tex] = [tex]\frac{63}{f}[/tex] Multiply 7 x 9 to get 63,so multiply 9 by 9 to get 81.
[tex]\frac{7}{9}[/tex] = [tex]\frac{m}{117}[/tex] 9 x 13 is 117, so multiply 7 by 13 to get 91.
I know it's easy but, I'm thinking of different ways of doing it.
Answers
Answer:
9 students
Explanation:
Every 8th person that entered the cinema received a free ticket.
The number of students who entered in the first hour = 76.
The first person given a ticket was the 8th person.
To calculate the number of persons who received a free ticket, we can view this problem as an arithmetic sequence in which:
• The first term = 8
,• The last term = 76.
,• The common difference (every 8th person) = 8.
Using the formula for the last term of an arithmetic sequence, we have:
[tex]\begin{gathered} l=a+(n-1)d_{} \\ 76=8+8(n-1) \end{gathered}[/tex]Our goal is to find n, the number of students.
[tex]\begin{gathered} 76=8+8n-8 \\ 76=8n \\ n=\frac{76}{8} \\ n=9.5 \end{gathered}[/tex]Since the number of students that entered in the first hour is not more than 76, we have that:
[tex]\begin{gathered} n\le9.5 \\ \implies n=9 \end{gathered}[/tex]9 students received a free ticket.
Which inequality represents the situation: "Macy has at least $75 to spend on her homecoming
dress including a 8.1% tax?"
a. 0.081d > 75
b. d + 0.081d ≥ 75
c. d + 0.081d < 75
d. d + 0.081d ≤ 75
Answers
One week, Claire earned $395.00 at her job when she worked for 25 hours. If she is paid the same hourly wage, how many hours would she have to work the next week to earn $126.40?
hurry, please<3
Answers
Answer:
8?
Step-by-step explanation:
so if 25 hours gets her to 395 dollars that you divide 395 by 25 to get how much money she makes per hour.
you get 15.8 then you have to see how many hours she has to work to make 126.40 which is 8 cuz 15.8 * 8 = 126.4
I THINK??