Mathematics College

Jason's age is 1 2 of his brother's age. His brother's age can be represented by the expression 12a - 9. Write an expression that can be used to represent the sum of their ages. A) 12a - 5.5 B) 18a - 13.5 C) 18a + 21 Eliminate D) (12a-9) 2

Answers

Answer 1
B. 18a-13.5   The expression 6a-4.5 can represent Jason's age. (Because this is half of the given expression for his brother.) When 6a-4.5 is added to the age of his bother, 12a-9, the result is the function 18a-13.5.
Answer 2

Answer:

[tex]18a - 13.5[/tex]

Step-by-step explanation:

Jason's age is [tex]\frac{1}{2}[/tex] of his brother's age.

Brother age is [tex]12a-9[/tex]

Sum of their ages = Age of Jonson + age of his brother

Jonson's age = half of his brother age

[tex]Jonson's \ age=\frac{12a-9}{2}[/tex]

Sum of their ages =[tex]\frac{12a-9}{2}+12a-9[/tex]  

Take common denominator 2

[tex]\frac{12a-9}{2}+\frac{24a-18}{2}[/tex]  

[tex]\frac{36a-27}{2} [/tex]  

[tex]18a - 13.5[/tex]

Related Questions

The 1998 team payroll of the Baltimore orioles was $68,988,134

Answers

what is the rest of the question

Matlab the equation of a circle with its center at x=3 and y=2 is given by , where r is the radius of the circle. first derive the equation(symbolically) of the tangent line to the circle at the point on the upper part of the circle ( and ). then for specific values of r, , , make a plot of the circle and the tangent line. (r=9, )

Answers

the equation of a circle with center at (h,k) and radius r is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
we are given
center is at (3,2)
[tex](x-3)^2+(y-2)^2=r^2[/tex]
solving for y
[tex](y-2)^2=-1(x-3)^2+r^2[/tex]
[tex]y-2=\sqrt{-1(x-3)^2+r^2}[/tex]
[tex]y=2+\sqrt{-1(x-3)^2+r^2}[/tex]
take the derivitive to find the slope at any point
[tex]\frac{dy}{dx}=((-1)(x-3)^2+r^2))(-x+3)[/tex]


we can use point slope form
for apoint (h,k) and slope m, the equation is
y-k=m(x-h)
not sure if you want in terms of what
I'll just say for a point (h,k)
so we get
[tex]y-k=((-1)(x-3)^2+r^2))(-x+3)(x-h)[/tex]
where [tex]k=2+\sqrt{-1(h-3)^2+r^2}[/tex]
that's the equation of the tangent line at (h,k) for arbitrary values of r

do the plots and other stuff yourself
Final answer:

To derive the equation of the tangent line to the circle, differentiate the circle equation implicitly and substitute the coordinates of a point on the circle to find the specific equation. For r = 9 and x = 3, the specific equation of the tangent line is y = 9 + 3x. Use software like Matlab or a graphing calculator to plot the circle and the tangent line.

Explanation:

To derive the equation of the tangent line to the circle at the upper part, we need to find the slope of the tangent line and the coordinates of a point on the circle. The slope of a tangent line to a circle at a given point is the negative reciprocal of the slope of the radius from the center to that point. In this case, the center of the circle is (3, 2) and the radius is 9, so the equation of the circle is (x-3)^2 + (y-2)^2 = 9^2. By differentiating this equation implicitly, we can find the slope of the tangent line.

The equation of the circle is (x-3)^2 + (y-2)^2 = 81.

Differentiating implicitly with respect to x:
2(x-3) + 2(y-2) dy/dx = 0
Simplifying:
(x-3) + (y-2) dy/dx = 0
(y-2) dy/dx = 3-x
dy/dx = (3-x) / (y-2)

To find the slope of the tangent line at the upper part of the circle, we substitute y = 2 + sqrt(81 - (x-3)^2) into the derived equation of dy/dx. After simplifying, we can substitute the coordinates of a point on the circle to find the specific equation of the tangent line.

For r = 9 and x = 3, the specific equation of the tangent line is y = 9 + 3x.

To make a plot of the circle and the tangent line, we graph both the circle equation and the tangent line equation using a software like Matlab or a graphing calculator.

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The outside diameter of a pipe is 5 and 7/32 inches. The walls of the pipe are 5/32 inches thick. What is the inside diameter?

Answers

check the picture below

thus

[tex]\bf 5\frac{7}{32}-\cfrac{5}{32}\implies \cfrac{5\cdot 32+7}{32}-\cfrac{5}{32}\implies \cfrac{167}{32}-\cfrac{5}{32}\implies \cfrac{162}{32} \\\\\\ \cfrac{81}{16}\implies 5\frac{1}{16}''[/tex]

Which of the following expressions represents the total earnings of a commissioned employee earning 9.5% commission with sales of $8,540?

Answers

$145. Hope my answer helped you out bro.

If a1=2, b2=3, and c3=10, the resulting value of =a1-b2+c3/10 is ____. 4 1 0 11/10

Answers

A1=2 b2=3 c3=10
2-3+10÷10
2-3+1
-1+1=0

Find the dimensions of a rectangle with a perimeter of 148 feet that has the maximum area

Answers

Final answer:

The dimensions of the rectangle with a perimeter of 148 feet that has the maximum area would be 37 feet by 37 feet, forming a square. The maximum area of the rectangle is 1369 square feet.

Explanation:

To find the dimensions of a rectangle with a known perimeter and the maximum area, first understand that the rectangle with the maximum area is a square. In this case, the perimeter is 148 feet.

To calculate the side length of the square, divide the perimeter by 4. Thus, the side of the square would be 148 feet / 4 = 37 feet. Therefore, the maximum area will be achieved when each side of the rectangle is 37 feet long, making it a square with these dimensions.

The maximum area of such a rectangle, which in this case is a square, is obtained by squaring the side length: Area = side × side = 37 feet × 37 feet = 1369 square feet.

3a/(a+1)^2
Give the equivalent numerator if the denominator is (a + 1)³.

Answers

Given 3a/(a+1)^2
To make the denominator a cube, you would have to multiply by 1 or (a+1)/(a+1)
yielding 3a(a+1)/(a+1)^3
(3a^2 + 3a) is the equivalent numerator

Answer:

3a(a+1)

Step-by-step explanation: for those who were confused on the other asnwer he gave a different veriation of this answer. however it is correct.



Brainliest plsss


A segment has endpoints ar (-2,3) and (7,9) how long is the segment

Answers

[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -2}}\quad ,&{{ 3}})\quad % (c,d) &({{ 7}}\quad ,&{{ 9}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ d=\sqrt{[7-(2)]^2+[9-3]^2}\implies d=\sqrt{(7+2)^2+(9-3)^2} \\\\\\ d=\sqrt{9^2+6^2}\implies d=\sqrt{81+36}\implies d=\sqrt{117} \\\\\\ \boxed{117=3^2\cdot 13}\qquad \qquad d=\sqrt{3^2\cdot 13}\implies d=3\sqrt{13}[/tex]

Solve ( x + 4 ) / 2 = ( x - 3 ) / 3


Answers

simplify x - 3/3 to -1 + x/3

regroup terms

multiply both sides by 6 (The LCM of 2,3)

expand

subtract 2x from both sides

simplify 3x + 12 - 2x to x + 12

subtract 12 from both sides

simplify -6 - 12 to -18

Answer: x = -18.

Factor:
7s(x−2y)+2t(x−2y)+2(x−2y)=

Answers

=7sx−14sy+2tx−4ty+2x−4y
(X-2y)(7s+2t+2)

Hope this helps.

12 tenths plus 9 tenths =21 tenths = ____ ones _____ tenths

Answers

2100 ones if I am thinking about this right. hope it helps

If you drive for 2 hours, at 60 miles per hour, you will have traveled 120 miles. this is a very common type of calculation, involving three quantities: distance, rate and time. if you know just two of these three quantities, you can always calculate the third. thus, if you want to know how much time it is going to take you to get somewhere, and you know that the distance is 120 miles and you will drive at a rate of 60 miles per hour, you can divide the 120 miles by the 60 miles per hour and obtain a time of 2 hours.

Answers

do u still need the answer

Using only definition 2.2.3, prove that if (x

Answers

you can use Google or a calculated but to check it but it's : 6

Is 0.5 greater than or less than 6/10

Answers

6/10 is equal to 0.6 and 0.6 is greater than 0.5
0.5 has a 5 in the tenths place, which means it's the same as [tex]\frac{5}{10}[/tex]. Which is bigger, [tex]\frac{5}{10}[/tex] or [tex]\frac{6}{10}[/tex]?

50 POINTS!!! DO NOT ANSWER JUST FOR THE POINTS!!! IF YOU DO, ALL OF YOUR EARNED POINTS WILL BE TAKEN~~~~~~~~~~~~~~~

Refer to the graph.

The function is increasing on the interval(s):

The function is decreasing on the interval(s):

The function is constant on the interval(s):

Please explain the steps you used.

Answers

A) [-7,-4] U [4,7]; B) [-4,-1]; C) [1,4]


A) [-7,-4] U [4,7]; B) [-4,-1]; C) [1,4]

what does 3.35 equal to

Answers

The answer is 45.2 by my calculations!!! I hope that helps
3.35 as a fraction is 67/20 but as a mixed number, it's 3 7/20.

Hope this helps. 
Have a blessed day.


The distance that light travels in 1 second is 186,000 miles. How far will light travel in 1 year? (There are approximately 31,500,00 seconds in 1 year. ) change the numbers to scientific notation and then perform the appropriate operations.

Answers

light travels 186,000 miles per second.....1.86 x 10^5
31,500,000 seconds per yr....3.15 x 10^7

how far will light travel in 1 yr...
(1.86 x 10^5)(3.15 x 10^7) =
(1.86 * 3.15)(10^5 * 10^7) =
5.859 x 10^12 miles in 1 yr <===
(5,859,000,000,000 miles)....whoa....a lot of traveling...thats like 5 trillion + miles

Which of the following is the inverse of the statement "If I like math, then I like science"? A. If I do not like science, then I do not like math. B. If I do not like math, then I like science. C. If I do not like math, then I do not like science. D. If I like science, then I like math

Answers

Original Conditional: If P, then Q

Inverse: If not P, then not Q

Using that template, the inverse would be "If I do not like math, then I do not like science" (simply insert those two "not" words keeping the order the same)

so the answer is choice C

Answer:

Option C If I do not like math, then I do not like science

Step-by-step explanation:

we know that

To find the inverse of a conditional, negating both the hypothesis and conclusion of a conditional statement

In this problem we have

"If I like math, then I like science"

therefore

the inverse is

If I do not like math, then I do not like science

Lydia makes 10 pancakes she tops each pancake with for blueberries how many blueberries does Lydia use in all use the break apart and distribute strategy and draw a number bond to solve

Answers

she uses forty blueberries

Prove that if an converges to a nonzero constant then 1/an is bounded

Answers

Assume [tex]\dfrac1{a_n}[/tex] is not bounded, i.e. there are no [tex]u,\ell[/tex] for which [tex]\ell\le\dfrac1{a_n}\le u[/tex] for all [tex]n[/tex].

Now, [tex]a_n\to k\neq0[/tex] is to say that for any [tex]\varepsilon>0[/tex], we can find a large enough [tex]N[/tex] such that [tex]|a_n-k|<\varepsilon[/tex] whenever [tex]n\ge N[/tex]. Simultaneously, this means that [tex]a_n[/tex] is bounded.

Let's suppose without loss of generality that [tex]a_n\neq0[/tex] for any [tex]n[/tex]. (Note that if [tex]a_n=0[/tex] for some finite number of values of [tex]n[/tex], we can simply remove them from consideration.)

So we have

[tex]|a_n-k|=\left|a_n\left(1-\dfrac k{a_n}\right)\right|=|a_n|\left|1-\dfrac k{a_n}\right|<\varepsilon[/tex]

Because [tex]a_n[/tex] is bounded, we know there is some [tex]\alpha[/tex] such that [tex]|a_n|\le\alpha[/tex] for all [tex]n[/tex]. Now,

[tex]|a_n|\left|1-\dfrac k{a_n}\right|\le\alpha\left|1-\dfrac k{a_n}\right|<\varepsilon[/tex]
[tex]\left|1-\dfrac k{a_n}\right|<\dfrac\varepsilon\alpha[/tex]
[tex]-\dfrac\varepsilon\alpha<1-\dfrac k{a_n}<\dfrac\varepsilon\alpha[/tex]
[tex]-1-\dfrac\varepsilon\alpha<-\dfrac k{a_n}<-1+\dfrac\varepsilon\alpha[/tex]
[tex]1-\dfrac\varepsilon\alpha<\dfrac k{a_n}<1+\dfrac\varepsilon\alpha[/tex]
[tex]\dfrac1k-\dfrac\varepsilon{\alpha k}<\dfrac 1{a_n}<\dfrac1k+\dfrac\varepsilon{\alpha k}[/tex]

But we initially assumed that [tex]\dfrac1{a_n}[/tex] is unbounded, so the above is impossible. Thus [tex]\dfrac1{a_n}[/tex] must be bounded.

Shelia mixed 3 ounces of blue paint with 2 ounces of yellow paint. She decided to create 20 ounces of the same mixture. How many ounces of yellow paint does Sheila need for the new mixture?

Please explain!!

Answers

Yellow:blue is a ratio of 2:3, meaning that 2/5 of the desired mixture is yellow. From this, you need to find how much yellow is necessary for 20 ounces. Well, 2/5 of the 20 ounces will be yellow paint, while the other 3/5 will be blue. So she will need 8 ounces of yellow paint to get 20 ounces of the desired mixture. Hope this helps! :)
3 ounces of blue paint added with 2 ounces of yellow you would get 5 onces

Then you divide 20 by 5 you get 4
Then multiply 4 by 2 ounces you get 8

Sheila will need 8 ounces of of yellow paint for the new mixture.

An important part of customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first 5 troubles reported on a given day, what is the probability that fewer than 2 troubles will be repaired on the same day?

Answers

The answer to your question is
D.  .2373


Hope this helps

Answer:

The probability that fewer than 2 troubles will be repaired on the same day is:

0.015576

Step-by-step explanation:

We have to use the Binomial function is n=order to calculate the probability of r successes out of the n-events.

We know that the probability of r success out of the n-events is given by:

[tex]P(X=r\ successes)=n_C_r\cdot p^r\cdot (1-p)^{n-r}[/tex]

where p is the probability of an success.

Here we have:

n=5 and r=0,1.

since we are asked to find the probability that fewer than 2 troubles will be repaired on the same day.

i.e we have to find:

[tex]P(X<2)=P(X=0)+P(X=1)[/tex]

Also p=0.75 ( since, likelihood is 0.75 that troubles in a residential service can be repaired on the same day )

Hence,

[tex]P(X=0)=5_C_0\cdot (0.75)^{0}\cdot (1-0.75)^{5-0}\\\\P(X=0)=1\cdot 1\cdot (0.25)^5\\\\P(X=0)=0.000976[/tex]

and

[tex]P(X=1)=5_C_1\cdot (0.75)^{1}\cdot (0.25)^{5-1}\\\\P(X=1)=5\cdot (0.75)\cdot (0.25)^4\\\\P(X=1)=0.0146[/tex]

Hence,

[tex]P(X<2)=0.000976+0.0146\\\\P(X<2)=0.015576[/tex]

Hence,  the probability that fewer than 2 troubles will be repaired on the same day is:

0.015576

mathematical modeling results in formulas that give exact values of real world phenomena over time

Answers

Mathematical modeling is when you create a mathematical expression to model the behavior you're studying. This is usually formulated after doing research studies. An example would be the Langmuir isotherm model. This model describes an adsorption behavior. It tells you the maximum adsorption capacity of your adsorbent at a specific process condition. Although it may not give you the exact value of the real behavior, it can be an approximation.

jada gets 2 new packs of earses.each pack has 6 earsers in it. draw an array to show how many erasers Jada has together

Answers

jada has 12 erasers all together

A washer and a dryer cost $795 combined. The washer costs $55 less than the dryer. What is the cost of the dryer?

Answers

7 cause the amount you paid and it subtracts the amount of money you have
$740 since you subtract 795 by 55 which is 740

michael wittry has been investing inhis roth IRA retirement account for 20 years. Two years ago his account was worth $215,658. after losing 1/3 of its origional value, it then gained 1/2 of its new value back, what is the current value of his roth IRA?

Answers

let's say

a = 215,658

ok... so.. he first lost 1/3 of that

[tex]\bf \textit{\underline{lost} }\frac{1}{3}a\qquad \qquad a-\cfrac{1}{3}a\implies a-\cfrac{a}{3}\implies \cfrac{3a-a}{3}\implies \cfrac{2a}{3} \\\\\\ \textit{then he \underline{gained} }\frac{1}{2}\textit{ of }\frac{2a}{3}\qquad \qquad \cfrac{2a}{3}+\cfrac{\frac{2a}{3}}{2}\implies \cfrac{\frac{2a}{3}}{\frac{2}{1}} \\\\\\ \cfrac{2a}{3}+\cfrac{2a}{3}\cdot \cfrac{1}{2}\implies \cfrac{2a}{3}+\cfrac{2a}{6}\implies \cfrac{4a+2a}{6} \\\\\\ \cfrac{6a}{6}\implies \boxed{a}\implies 215,658[/tex]


so, his nickname might just be even steven, because, he ended up with the same original amount after the 1/2 bump.

His current value is 215658 dollars.

How to calculate a fraction of amount of a total amount ?

To calculate a fraction of amount of a total amount just multiply the given fraction to the total amount.

According to the given question

Michael  wittry has been investing in his roth IRA retirement account for 20 years.

Two years ago his account was worth $215,658.

1/3rd of it's original value is

= (1/3) × 215658

= 71886 dollars.

∴ Remaining value is

=(215658 - 71886)

=143772 dollars.

After some time it gained half of it's new value back

∴ Half of this new value is

(1/2) × 143772

= 71886 dollars.

So , the current value is

(143772 + 71886)

=215658 dollars.

Actually his currect value of roth IRA is same as it was two years ago.

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Harry estimates that the dinner will have 48 g of fat. if the recommended daily allowances is 70 g What percentage of her total daily allowance of fat will the dinner be

Answers

divide 48 by 70

48 / 70 = 0.6857 = 68.6%

The length of a rectangle is 11 m greater than the width. The area is 42 m^2. Find the length and width.

Answers

the answer is that the width is 3 m and the length will be 14 m because 3•14 = 42m² and 3+11=14
Hello friends my name is blank I'm sorry but I need to ask a question so buy

round 2,412 to the nearest thousands

Answers

2,000 since you're rounding to the nearest thousands.
The answer is 2,000 because 2,412 is closer to 2,000 than 3,000. Hope I helped!

solve (6-5x)/10-(2x+1)/5+x/3=2x/15

Answers

multiply2 * x/15 to 2x/15

multiply both sides by 30 which is the LCM of 10, 5, 3, and 15

expand it

simplify 18 - 15x - 12x - 6 + 10x to 12 - 17x

add 17x to both sides

add 4x + 17x to = 21x

divide both sides by 21

simplify 12/21 to 4/7

now simplify

Answer: x = 4/7.
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