THEIR AGES
If you add the square of Tom's age to the age of Mary the sum is 62; but if you
add the square of Mary's age to age of Tom, the result is 176. Can you say
what are the ages of Tom and Mary?

Answers

Answer 1

Answer:

Tom’s age is 7 years

Mary’s age is 13 years

Step-by-step explanation:

Since we do not know the ages, let’s represent the ages by variables at first.

Let m represent mary’s age will t represent Tom’s age.

Now, let’s proceed to have equations.

Adding square of Tom’s age (t^2) to mary’s age give 62

t^2 + m = 62 •••••••(i)

Adding square of mary’s age (m^2) to Tom’s age give 176

m^2 + t = 176 •••••••(ii)

Now, to get the individual ages, we will need to solve both equations simultaneously.

Solving both equations simultaneously without mathematical softwares can be a little hard.

By the use of mathematical software ( wolfram alpha to be specific), we can input both equations and allow the software to solve.

By inputing these equations, we have the values of t to be 7 and m to be 13

And if we try to check by inspection, we can see that these values are actually correct.

7^2 + 13 = 62

13^2 + 7 = 176


Related Questions

If p, q and r were three statements such that p → q and q → r then p → r, this is called

Answers

Answer:  Law of syllogism

Step-by-step explanation:

Law of Syllogism is described as

a logical reasoning by using  transitivity.a valid argument that applies deductive reasoning to get the final statement. it is similar to transitive property that if a=b and b=c then a=c.

So if p, q and r were three statements such that p → q and q → r then p → r, this is called law of syllogism.

For example: When Rita gets internet Shamy gets internet. When Shamy gets internet Raj gets internet.

By law of syllogism : When Rita gets internet Raj gets internet.

Solve the equation x/2-6=y for x

Answers

answer: x=2y+12

x/2-6=y
multiply both sides by 2
2(x/2-6)=2(y)
2x/2-12=2y
x-12=2y
add 12 to the both sides
x=2y+12

hope this helps <3

Answer:

            x = 2y + 12

Step-by-step explanation:

x/2 - 6 = y

     +6     +6

  x/2 = y + 6

    ×2     ×2

   x = 2(y + 6)    x = 2y + 12

If 225 is the dividend and 15 is the divisor, then what is the quotient?

Answers

Answer:

The answer is 15.

Step-by-step explanation:

When dividing 225 by 15 you can multiply 15 by 15 and you will get 225.

The answer is 15, 15 times 15 is 225

help me with this plzzzzz

Answers

Answer:

C

Step-by-step:

The answer is c because 7.6 & 8.2 are both rational numbers and it goes onto natural numbers. They are also ordered in the from least to greatest like on a number line, 7.6, 8.2, 50, 65, 78. Plus, I'm kinda on the same unit.

Please solve #5 and show your work! Will give BRAINLIST!!

Answers

Answer:

damita

Step-by-step explanation:

erin: 2/12 = 0.1666667

damita: 4/16 = 0.25

jayden: 3/15 = 0.2

0.25 is the highest concentration

Make x the subject of the formula a(x-b)=a^2+bx

Answers

Answer:

x = [tex]\frac{a(a + b)}{a-b}[/tex]

Step-by-step explanation:

Step 1: Write out formula

a(x - b) = a² + bx

Step 2: Distribute

ax - ab = a² + bx

Step 3: Add ab to both sides

ax = a² + bx + ab

Step 4: Subtract bx on both sides

ax - bx = a² + ab

Step 5: Factor

x(a - b) = a² + ab

Step 6: Divide (a - b) on both sides

x = [tex]\frac{a^{2} + ab}{a-b}[/tex]

Step 7: Factor

x = [tex]\frac{a(a + b)}{a-b}[/tex]

And we have our final answer!

This year,a farm planted 400,000corn stalks.Last year,the farm planted 275,650cornstalks. How many more cornstalks did the farm plants this year than last year?

Answers

Answer:

The farm planted 124,350 more cornstalks

Step-by-step explanation:

Here in this question, we want to know how much more corn stalks did a farm plant this year compared to last year.

Let’s picture it this way;

Possibly due to expansion purposes, the farm planted more cornstalks this year than last year. So to find the difference in the cornstalks planter between the two years, what needs to be done is simply to subtract the number of corn stalks planted last year from the number of corn stalks planted this year.

From the question, the number of cornstalks planted last year was 275,650 while the number of cornstalks planted this year was 400,000; So the difference between the two will be ;

400,000 - 275,650 = 124,350 cornstalks

Solve for x: the quantity of x plus 20 over 2 = 3x

Answers

Answer:

x = 4

Step-by-step explanation:

For this problem, we simply need to convert the words into the left hand side of the equation and solve for x:

The quantity of implies a grouping

x plus 20 is the quantity

And we want the quantity over 2 all equal to 3x:

( x + 20 ) / 2  = 3x

( x + 20 )  = 6x

20 = 5x

4 = x

And now we can check to see if x is correct by plugging back into the equation:

( x + 20 ) / 2 = 3x

( (4) + 20 ) / 2 ?= 3(4)

( 24 ) / 2 ?= 12

12 == 12

Therefore, we have shown the value of x to be equal to 4.

Cheers.

Answer:

x+20/2=3x.

6x=x+20.

6x-x=20.

5x=20.

x=4.

There are 7 pens in a bag. Four of the pens are blue and the other 3 are red. What's the probability of pulling out a red
pen? Write your answer as a fraction.

Answers

Answer:

3/7

Step-by-step explanation:

P(red) = number of red pens / total number of pens

         = 3/7

Answer:

3/7

Step-by-step explanation:

Total pens = 7

Blue pens = 4

Red pens = 3

probability of pulling out a red pen

= No of red pens / Total pens

= 3/7

On Monday the temperature was 32° On Tuesday the temperature was -5°. What was
the change in temperature?

Answers

The temperature decreased by 37 degrees.

Answer:

37°

Step-by-step explanation:

Think of 0° as a reference point.  Then 32° is above this reference by 32 degrees, and -5° is below it by 5 degrees.  Summing up 32 and 5, we get 37.  The change in temperature was 37°

If (1,-1) is a point on the line 2x-(2a+5)y=5 then find the value of a​

Answers

Answer:

a = - 1

Step-by-step explanation:

Since ( 1 , -1) is a point on the line 2x-(2a+5)y=5 we can substitute it into the equation to find a

We have

2(1) - (-1)(2a + 5) = 5

Multiplying two negatives make a positive

That's

2 + 2a + 5 = 5

2a + 7 = 5

Group like terms

Send the constants to the right side of the equation

That's

2a = 5 - 7

2a = - 2

Divide both sides by 2

That's

[tex] \frac{2a}{2} = \frac{ - 2}{2} [/tex]

We have the final answer as

a = - 1

Hope this helps you

Find the slope of the line containing the points (-5,-4) and (-3,-6)

Answers

Use the slope formula y2 - y1/x2 - x1
-6 - (-4)/-3 - (-5)
You get -2/2, which is -1.

evaluate the expression m + p for m = 9 and p =7

Answers

Answer:

16

Step-by-step explanation:

Step 1: Write out expression

m + p

Step 2: Define variables

m = 9

p = 7

Step 3: Plug in variables

9 + 7

Step 4: Evaluate

16

A local dog show features 8 Portuguese water dogs. The weights of the dogs are 38, 40, 42, 46,
45, 39, 42, 40. What are the mean and median weights of the Portuguese water dogs in the dog
show?

Answers

Answer:

[tex] \boxed{ \bold{ \sf{Mean \: = 41.5}}}[/tex]

[tex] \boxed{ \bold{ \sf{Median = \: 41}}}[/tex]

Step-by-step explanation:

Given weights of the dogs :

38 , 40 , 42 , 46 , 45 , 39 , 42 , 40

Find the sum of the whole data:

sum of all items ( Σx ) = 38 + 40 + 42 + 46 + 45 + 39 + 42 + 40 = 332

Number of items ( n ) = 8

To find mean, divide the sum by the total number of data.

Finding the mean weights:

[tex] \boxed{ \sf{Mean = \: \frac{ Σx}{n}}} [/tex]

⇒[tex] \sf{ \frac{332}{8} }[/tex]

⇒[tex] \sf{41.5}[/tex]

Mean weights = 41.5

-----------------------------------------------------------------------

Finding the median

To find the median, arrange the given data in ascending order.

Given data : 38, 40 , 42 , 46 , 45 , 39 , 42 , 40

Arranging the data in ascending order :

38 , 39 , 40 , 40 , 42 , 42 , 45 , 46

Total number of observation ( n ) = 8

Finding the position of median

[tex] \boxed{ \sf{Position \: of \: median = ( \frac{n + 1}{2} ) ^{th} item}}[/tex]

⇒[tex] \sf{( \frac{8 + 1}{2} ) ^{th} item}[/tex]

⇒[tex] \sf{( \frac{9}{2} ) ^{th} item}[/tex]

⇒[tex] \sf{ {4.5}^{th} item}[/tex]

4.5 th item is the average of 4 th and 5th items .

Here, 4 th item = 40

5 th item = 42

Finding the median

[tex] \boxed{ \sf{Median = ( \frac{{4}^{th} \: item + {5}^{th} item}{2}) }}[/tex]

⇒[tex] \sf{ \frac{40 + 42}{2} }[/tex]

⇒[tex] \sf{ \frac{82}{2} }[/tex]

⇒[tex] \sf{41 }[/tex]

Hope I helped!

Best regards!!

Answer:

A local dog show features 8 Portuguese water dogs. The weights of the dogs are 38, 40, 42, 46,

45, 39, 42, 40. What are the mean and median weights of the Portuguese water dogs in the dog

show?

Step-by-step explanation:

what number set 1/2 belongs to? rational, irrational, integer, or natural​

Answers

Answer:

Rational

Step-by-step explanation:

1/2 would be 0.5 and 0.5 goes into the Rational catagory.

I need help! I can’t understand!

Answers

What’s the chapter and page I got you

7(6+5n) + 5(7 + n) = 37
I need help please

Answers

Answer:

or, 42+35n+35+5n=37

or, 77+40n=37

or, 40n=40

so, n=1

Step-by-step explanation:

hope it helps you

n=-1. as the other person said, but you’re supposed to subtract and not combine like terms from the last step

Hailey divided 92 ÷ 5. Her work is shown below.


92 divided by 5. 5 goes into 9 1 time. 9 minus 5 = 4. 5 goes into 42 8 times. 42 minus 40 = 2. The answer is 18 R 2. There are 5 groups of 1 ten plus 8 ones.
Which statements are true about Hailey’s work? Check all that apply.

Hailey found the correct quotient.
The “1” in the quotient represents the number of tens in each of the 5 groups.
Hailey placed the dividend and divisor in the wrong places in the problem.
The “R2” represents the number of ones in each of the 5 groups.
Since only 5 tens could be divided evenly among the groups, Hailey subtracted 5 from 9 to find out how many tens were left over.

Answers

Answer:

The “1” in the quotient represents the number of tens in each of the 5 groups.

Since only 5 tens could be divided evenly among the groups, Hailey subtracted 5 from 9 to find out how many tens were left over.

Step-by-step explanation:

Given:

92÷5

Hailey's workings:

92 divided by 5.

5 goes into 9 1 time.

9 minus 5 = 4.

5 goes into 42 8 times.

42 minus 40 = 2.

The answer is 18 R 2.

The true statements about Hailey's work are:

The “1” in the quotient represents the number of tens in each of the 5 groups.

Since only 5 tens could be divided evenly among the groups, Hailey subtracted 5 from 9 to find out how many tens were left over.

4. Bill Watson is the Swanton Village computer technician. He earns $22.22 per hour. What is his straight-time pay for a 36-hour week?​

Answers

Answer:

$799.92

Step-by-step explanation:

To find his pay, multiply the number of hours he worked by his pay per hour:

22.22(36)

= 799.92

So, his pay was $799.92

At a height of 3,281 feet, Angel Falls in Venezuela is the tallest waterfall in the world. Niagara Falls in the United States is only 190 feet tall. About how much taller is Angel Fall

Answers

Answer:

Angel Fall is 3091 ft taller.

Step-by-step explanation:

Height of Angel fall = 3281 ft

Height of Niagara falls in the United States = 190 ft

Angel fall is taller than Niagara Fall by

==> 3281 - 190 = 3091 ft


What value of x will make each equation below true? 4x-1=4x+7

Answers

Answer:

4X-1=4X+7

4x - 4x = 1 + 7

0 = 8

Step-by-step explanation:

Since there is no value of x that will make this true,

this has no solution and x is the empty set.

Answer:

Step-by-step explanation:

4x-1=4x+7

4x-1-4x=4x+7-4x

-1=7

Need help Only 5 questions

Answers

Answer:

for question no 5

answer is 1/10

Convert the angle to degrees, minutes, and seconds. 292.41°

Answers

Answer:

292° 24' 36"

Step-by-step explanation:

d = int(292.41°) = 292°

m = int((292.41° - 292°) × 60) = 24'

s = (292.41° - 292° - 24'/60) × 3600 = 36"

292.41°

= 292° 24' 36"

Answer:

292 degrees 24 minutes and 36 seconds:

292° 24' 36"

Step-by-step explanation:

There are 60 minutes in a degree and 60 seconds in a minute.

so 0.41 degrees = 0.41 * 60 = 24.6 minutes

and 0.6 of a minute = 0.6 * 60 = 36 seconds.

Mrs. Lawrie tried to write this number in standard form and made a mistake. What was Mrs. Lawrie's mistake? 600,000 + 8,000 + 500 + 70 + 3 = 68,573 what did she do wrong

Answers

Answer:

Mrs. Lawrie forgot the 600,000 in the equation. Answer = 608,573

Step-by-step explanation:

The equation was:

600,000 + 8,000 + 500 + 70 + 3 = 608,573

Mrs. Lawrie got 68,573, while the answer was 608,573

Pls halp due today >_<. Thank you

Answers

Answer:

-√(1/4) is smaller

Step-by-step explanation:

Step 1: Evaluate -√(1/4)

-√(1/4) = -(0.5) = -0.5

Step 2: Evaluate -1/5

-1/5 = -0.2

Step 3: Align

-0.5 < -0.2

1/3 + a + 5/4. what is A

Answers

Answer:

a = -1.58

Step-by-step explanation:

1/3 +a+5/4 =0

1/3+5/4= -a

4+15/12 = -a

19/12 = -a

1.58= -a

1.58/-1 = -a/-1

-1.58 = a

rose had $1000 in her bank account when she was 8 year old. each birthfay her grandma gave rose $20 until she turned 21

Answers

Answer:

1260

Step-by-step explanation:

Subtract 21 from 8,to get 13.Multiply 13 to the 20 dollars,when you do that you get 260.You add the 260 and the 1000 dollars together.

the hypothenus of a right angle triangle is 13cm. if one other side of the triangle is 1cm shorter than the hypothenus, calculate the third side of the triangle

Answers

Answer:

5 cm.

Step-by-step explanation:

Let the lengths of the other 2 sides be 13-1 = 12  and x cm.

Then by Pythagoras:

13^2 = 12^2 + x^2

x^2 = 13^2 - 12^2

x^2 = 169 - 144 = 25

x = √25

x = 5 cm.

Step-by-step explanation:

Hey, there!!

As per your question,

There is a Right angled triangle, whose hypotenuse is 13 cm, one side is (13-1)=12 cm.

another side = ?

Let ABC be a Right angled triangle, taking angle "theta" as a refrence angle.

Hypotenuse (h)= 13 cm.

base ( b) = x

perpendicular (p)= 12cm.

By Pythagoras relation we get,

[tex]b = \sqrt{ {h}^{2} - {p}^{2} } [/tex]

[tex]b = \sqrt{ {13}^{2} - {12}^{2} } [/tex]

[tex]b = \sqrt{169 - 144} [/tex]

Therefore, base is 5 cm. Or the third side is 5 cm.

Hope it helps...

Last one, use trigonometry to help you solve for y given that one side is 4 and there is an angle of 50 degrees.

Answers

Answer:

y = 6.22

You can solve this in two ways.

1.) Use SOH CAH TOA:

I typically start off by labeling the sides of the triangle with H (hypotenuse), O (opposite), and A (adjacent). Because I need to figure out what y is when given an angle and 4, I will use CAH, or cosine.

[tex] \cos(angle) = \frac{adjacent}{hypotenuse} [/tex]

[tex] \cos(50) = \frac{4}{y} [/tex]

[tex] \cos(50) \times y = 4[/tex]

[tex]y = \frac{4}{ \cos(50) } [/tex]

[tex]y = 6.22[/tex]

2.) Use Law of Sines:

Solve for the last angle inside the triangle first.

[tex]180 - (50 + 90) = 40[/tex]

Then use the angle you found (40°) in the equation.

[tex] \frac{4}{ \sin(40) } = \frac{y}{ \sin(90) } [/tex]

[tex] \frac{4}{ \sin(40) } \times \sin(90) = y[/tex]

[tex]y = 6.22[/tex]

Idk how to do this!!?!?

Answers

Answer:

∠ AED = 130°

Step-by-step explanation:

CD is a straight line, thus

∠ AEC + ∠ AED = 180° , that is

50° + ∠ AED = 180° ( subtract 50° from both sides )

∠ AED = 130°

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