Why is the ratio of two integers always a rational number?

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Explanation:

T = tens digit of original number

U = units digit of original number

"units digit" is the same as "ones digit"

The original number is in the form 10T+U. For example, let's say that T = 3 is the tens digit and U = 1 is the units digit. This means 10T+U = 10*3+1 = 31 is the original number. Though in this example, the digits don't add to 12.

To make the digits add to 12, we have the equation T+U = 12. This solves to U = 12-T which we'll use later.

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The digits are reversed to get the new number 10U+T and this is 15 times the original tens digit, so

new number = 15*(original tens digit)

10U+T = 15T

from here we plug in U = 12-T which we found earlier. This effectively eliminates or gets rid of the U variable to leave us with T only

10U+T = 15T

10(12-T)+T = 15T ..... replace U with 12-T

which we can now solve for T

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10(12-T)+T = 15T

120-10T+T = 15T

-9T+120 = 15T

120 = 15T+9T ... adding 9T to both sides

120 = 24T

24T = 120

T = 120/24 .... divide both sides by 24

T = 5

The original tens digit is T = 5

The original units digit is U = 12-T = 12-5 = 7

So the original number is 10T+U = 10*5+7 = 57

Flipping the digits gets us 75 which is 15 times that of the original tens digit of 5. The original number has its digits add to 5+7 = 12. The answer has been confirmed.

Answer:

y = 4x + 7

Step-by-step explanation:

parallel = same slope

y = 4x + b

plug in (-4, -9)

-9 = 4(-4) + b

-9 = -16 + b

b = 7

y = 4x + 7

Answer:

7=4x+7

Step-by-step explanation:

To do this you would just plug in (-4,-9) into the equation y=mx+b so we would get -9=4(-4)+b when you simplify you will get -9=-16+b so we would add 16 to both sides and we would get 7=b so we would know that the y intercept is 7 and we know that if a line is parallel to another line is just has a different b so for our equation we would get 7=4x+7

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Answer:

4x² + 4x + 1

Step-by-step explanation:

We know that (a + b)² = a² + 2ab + b², therefore, (2x + 1)² = 4x² + 4x + 1.

Answer:

(2x)^2  + 2(2x)(1) + (1)^2

4x^2 + 4x + 1

Step-by-step explanation:

Answer: can you please post the expression

Step-by-step explanation:

Answer:

70 + 2 + 0.3 + (-30) + (-9) + (-0.1) = 70 + (-30) + 2 + (-9) + 0.3 + (-0.1)

Step-by-step explanation:

just took it

Answer:

  55 m²

Step-by-step explanation:

The arc length of a half-circle is πr, so the area of the curved surface is ...

  A = πrl = π(2.5 m)(7 m) = 17.5π m² ≈ 55 m²

Answer:

55m^2

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Answer:

87

Step-by-step explanation:

8+7=15

reverse the digits to get 78.

8x6=48

48+30=78

(There are only 4 two-digit numbers that equal 15.  78, 87, 69, and 96. Only 87 fits these qualifications.)

Answer:

6

Step-by-step explanation:

Answer: 16

Step-by-step explanation:

1. Add the numbers in the parenthesis (answer is 4).

2. Divide 8 by 2 (answer is 4).

3. Multiply 4 and 4.

Your answer is 16. Hope this helps. :)

Answer:

[tex] \boxed{ \boxed{ \bold{ \sf{16}}}}[/tex]

Step-by-step explanation:

[tex] \sf{8 \div 2(2 + 2)}[/tex]

Add the numbers

⇒[tex] \sf{8 \div 2 \times 4}[/tex]

Divide 8 by 2

⇒[tex] \sf{4 \times 4}[/tex]

Multiply the numbers

⇒[tex] \sf{16}[/tex]

Hope I helped!

Best regards!!

Answer: Hi!

Each 3 is in a different place value. That's why they have different values.

Hope this helps!

Answer:

the three before the decimal is a whole number that equals 3.0, while the three after the decimal is a decimal equaling 0.003.

Step-by-step explanation:

$650

90% .............. $585

100% ............ $ x

x = 100×585/90

= 58500/90

= $650

Answer:527.5

Step-by-step explanation:

585-585×10%

585-58.5

527.5

Answer:

c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

0.05203*10 to the power 2

Step-by-step explanation:

To get the standard form you divide a number in order to multiply it by a power of 10 to get the same number. So 5.203 in standard form is o.o5203 * 10 to the power 2. The 10 to the power 2 comes from the number of palces you move the comma/ decimal point to the left

HOPE IT HELPED

Answer:

5.203

*I wrote the answer in decimal form*

When it says *and* that means u are adding a decimal point to ur number. Like this ( four and thirty-two hundredth = 4.32)

Answer:

1

Step-by-step explanation:

let the number=x

x-4=-3x

x+3x=4

4x=4

x=4/4=1

The number that is four greater than three times its additive inverse

is - 3n + 4.

A number's additive inverse is a number that is added to it until the result is zero.

A number multiplied by another such that the result is 1 is the multiplicative inverse of that number.

Let the unknown number be 'n' so its additive inverse is '-n'.

So,  the number that is four greater than three times its additive inverse is,

Three times of additive inverse is -3n.

Now the number is 4 greater than 3 times its additive inverse which is

= - 3n + 4.

learn more about additive inverse here :

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Answer:

15<13

Step-by-step explanation:

Answer:

25 dollars (B)

Step-by-step explanation:

$5 * 5 weeks is $25 in total

Answer:

A. -25

Step-by-step explanation:

if you buy something you are spending money therefore lossing money.

Answer:

-7.5

Step-by-step explanation:

3.5z-2.7z is .8z

.8x=-6

.8 is 4/5

5/4 times .8z=5/4 times -6

-7.5

The required solution of the given function is z = -7.5.

Given that,
To determine the simplified solution, of the given expression 3.5z - 2.7z = -6 and determine the value of z.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
3.5z - 2.7z = -6
Simplifying,
0.8z = -6
z = -6 / 0.8
z = -7.5

Thus, the required solution of the given function is z = -7.5.

Learn more about simplification here: https://brainly.com/question/12501526

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Answer:

D)4

Step-by-step explanation:

rise over run

rise=8 run=2

8/2

=4/1

=4

Answer:

4

Step-by-step explanation:

For every 1 you go over you go up 4

Answer:

20,000

+

8,000

+

300

+

40

+

9

Step-by-step explanation:

Answer:

12 is the answer

Step-by-step explanation:

Answer:

x= 10

Step-by-step explanation:

[tex]\frac{-2-2x}{3} =-8\\-2-2x=-24\\-2x= -24+2\\-2x=-20\\x=10[/tex]

Answer:

198

Step-by-step explanation:

198

Answer: 66°

Step-by-step explanation: Triangle TVU is a mirror reflection of triangle QRS, so angle V is 56, angle T is 58, and angle U is 66

Answer:

66 becase all it is is its reflected or mirrored acrossed

Step-by-step explanation:

Answer:

x = 13,

Step-by-step explanation:

they are diagonal angles so they are equal, so basically all you have to do is solve 8x+14=118, x = 13

Answer:

x = 13,

Step-by-step explanation:

Answer:168

Step-by-step explanation:   First you do 82 times 3.75 which is 307.50. Then you do 2071.5 - 307.5 = 1764 Then you do 1764 divided by 10.50 which is 168

Answer:

168 adult tickets

Step-by-step explanation:

just checked it and got 100 on edge

Answer:10

Step-by-step explanation: this is a middle school question? lool

Answer:

[tex]\frac{15}{2}[/tex] or 7.5 (they're the same)

Step-by-step explanation:

Answer:

[tex]7\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]-3:-\frac{2}{5}= \\=-\frac{3}{1}*-\frac{5}{2}\\\\=\frac{-3*-5}{2}\\ \\=\frac{15}{2}\\ \\=7\frac{1}{2}[/tex]

Answer:

Elsa earned the most

Ben earned the least

Step-by-step explanation:

E = Elsa's speed

B = Ben's speed

C = Cal's speed

The combined speeds are:

E + B = 1/11

E + C = 1/9

B + C = 1/9.9

If we add up all three equations:

2B + 2C + 2E = 10/33

B + C + E = 5/33

If we subtract each of the first three equations from the total equation, we can find the individual speeds.

C = 5/33 − 1/11 = 2/33

B = 5/33 − 1/9 = 4/99

E = 5/33 − 1/9.9 = 5/99

Ben and Cal paint together for 1 hour.  The fraction of the wall they paint is:

(1/9.9) × 1 = 10/99

Elsa, Ben, and Cal all paint together for the next 4.5 hours.  The fraction of the wall they paint is:

(5/33) × 4.5 = 15/22

Ben and Elsa then finish the job.  The amount of wall left is 1 − 10/99 − 15/22 = 43/198.  So the time it takes is:

(43/198) / (1/11) = 43/18 hours

The fraction of the wall that Ben paints is:

(4/99) (1 + 4.5 + 43/18) = 284/891

The fraction of the wall that Cal paints is:

(2/33) (1 + 4.5) = 1/3 = 297/891

The fraction of the wall that Elsa paints is:

(5/99) (4.5 + 43/18) = 310/891

Answer:

Ben earned the most as 6 of 16.5 as a percentage = (6*100):16.5 =36.36%

We check with Elsa and she earned the least as (5*100):16.5 =30.31%

Cal earned the average as 5.5 of 16.5 as a percentage = (5.5*100):16.5 =33.33%

Step-by-step explanation:

E + B = 11hrs    

E + C = 9hrs

B+C = 9.9 hrs

Lets say the house was 100ft sq

if E took 5.5 hrs

B took 5.5hrs  we would have 11

C took  3.5 hrs  we would have 9hrs for E+C

B took 5.5 hrs + 3.5hrs we are 0.9hrs short and see that B would need to take 0.9 more which means E works 0.9hrs less and shares 0.4 less with C having 0.5 less which gives B an extra 0.4 instead of 0.9

This equates to B: 5.9  , C:  3.9 ,  E: 5.1  

We can change to B: 6  , C: 3.94  , E: 5.4  

= E+B =  11.4  = 11  

= E+C = 8.99 = 9  

= B+C = 9.94  = 9.9

Percentages of fixed net pay when B: 6  , C: 3.94  , E: 5.4 = 6+ 3.94+ 5.4 = 100

Time when 15.34 hrs = 100% if working same rate changes to 16.5hrs to account for the hours given 8am-1.30pm 8am-1.30+ 9am-1.30+ =  minimum 1hr more = 2pm

Cal worked 8 am till 1.30 pm = 5.5hrs = 1.66hr extra

Ben worked 8am till 2pm = 6 hrs = 0 hr extra  together worked 11.5hrs

Elsa worked 9am till 2pm = 5 hrs = -0.4hr less

11.5+ 5 = 16.5 This equals 16.5hrs = 100%

Ben earned the most as 6 of 16.5 as a percentage = (6*100):16.5 =36.36%

Cal earned the average as 5.5 of 16.5 as a percentage = (5.5*100):16.5 =33.33%

We check with Elsa and she earned the least as (5*100):16.5 =30.31%   is the same as 100-69.67%

Answer:

The third answer. ( John's boat was farther from the deck at the beginning but Roberta's boat traveled more quickly)

Step-by-step explanation:

You already know that in the beginning John's boat begins 20 miles  from the dock. Now you need to find Roberta! When each boat begins from the dock, it means when x=0. So lets insert that! y= 6(0)+15. You get 15. Now you know that its either the 3rd or 4th answer.  The second piece of info you have for John is that it is 45 miles from the dock after 5 hours. Again, in the beginning it started with 20 miles. 45-20= 25 miles TRAVELED in 5 hours.  For Roberta, we need to insert 5 in the equation for x. y=6(5)+15. You get: 45 again! But... Roberta started at 15 miles. So 45-15 is 30 miles. She traveled 30 miles in 5 hours. The only answer that is matching to our problem solving is the third answer. Hope this helps!

Answer:

Ten

Step-by-step explanation:

Answer

original speed X=10

Step-by-step explanation:

We know that Speed= distance/ time

Then

time =distance/speed

We were told the cyclist travels 40 km at a speed of x km/h.

Which means

Distance= 40km

speed =x km/h

Then time t =40/x

Again we we were told his speed was

reduced by 2 km/h

Then speed= (x-2)

But the Distance is still 40km

But we were told the difference in time is 1 hour

Time t=40/(x-2)

Then if we find the difference between the time t of the first condition and second condition we have

40/(x-2) - (40/x) =1

[40x-40(x-2)]/ x(x-2)= 1

80=x(x-2)

x^2-2x-80=0

This is a quadratic equation , if we solve using factorization we have

(x+8)(x-10)

x+8=0 or x-10= 0

X= -8 or 10

But we cannot have a negative value for speed then

X=10

Therefore, original speedX=10

Answer:

x=10

Step-by-step explanation: