At the bank, Derek made 7 withdrawals, each in the same amount. His brother, John, made 5 withdrawals, each in the same amount. Each of John’s withdrawals was $5 more than each withdrawal that Derek made. Both Derek and John withdrew the same amount of money in the end. How much did each brother withdraw?
A) Write an equation. Let x represent the amount of one of Derek’s withdrawals. B) Solve the equation. Show your work.
C) Check your solution. Show your work. D) State the solution in complete sentences

The correct answer is easy 1x=12y

If you combine the like terms it will be 8x-8

3x+5x = 8x

-6-2 = -8

8x-8

Here's some work!

24/-30 would be the answer

(12x-14)-(3x+9)-(-4-1)

= 9x-18

12x-3x=9x

-14-9+4+1=-18

*Subtracting a group of numbers in parenthesis is the same as -1 times what every is in the parenthesis.

So it would be (12x-14)+(-3x-9)+(4+1)... which makes the equation alot easier to simplify.

Answer:

Equation of the line that it is perpendicular to y=7x-3 and passes through the origin is given by 7y + x = 0

Explanation:

  We have equation of line , y =7x -3, comparing it with y = mx +c

  So slope of line , m = 7

 We know that the product of slopes of perpendicular lines = -1

 So   m*Slope of perpendicular line = -1

        7* slope of perpendicular line = -1

        slope of perpendicular line = -1/7

 Given that the perpendicular line passes through origin (0,)0)

 We also know that equation of a line passing though origin is given by the expression, y = mx

 Here m = -1/7

 So equation of perpendicular line, y = -x/7

                   or      7y + x = 0

 Equation of the line that it is perpendicular to y=7x-3 and passes through the origin is given by 7y + x = 0

30 C is equal to 86F

So Rome had the higher temperature

The temperature in Rome was higher.

To compare these temperatures directly, we can convert the

temperature in Rome from Celsius to Fahrenheit using the formula:

[tex]F = \left( C \times \frac{9}{5} \right) + 32[/tex]
Where:  

Substituting the value for Rome's temperature:

[tex]F = \left( 30 \times \frac{9}{5} \right) + 32[/tex]

[tex]F = (54) + 32 = 86 ^{\circ} F[/tex]
So, the temperature in Rome is approximately 86 °F.  

Now we can compare the two temperatures:

Chemical changes in mixtures can be identified by the creation of a new substance, a change in color or odor, production of gas, or formation of a precipitate. When two clear liquids change color or form a new solid upon mixing, as happens with silver nitrate solution and copper wire, or potassium iodide and lead nitrate, a chemical change has occurred.

In order to identify which of the four mixtures has undergone a chemical change, we need to look for indications of that change. There are several telltale signs of a chemical reaction. Such signs include the creation of a new substance, a change in color or odor, the production of gas (bubbles), or the formation of a precipitate (a solid that forms from a liquid mixture).

If two clear liquids mix and then change color, as seen when copper wire is immersed in an aqueous solution of silver nitrate and the solution turns blue, a chemical change has likely occurred. The copper wire also becomes covered with a gray solid, demonstrating the creation of a new substance. Another example is when two solutions, potassium iodide and lead nitrate, mix and form a solid, or precipitate, of lead iodide. This is another clear indication of a chemical change.

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The mixture demonstrating a chemical change would exhibit characteristics such as a change in color, gas evolution, precipitate formation, or temperature change, indicating the formation of new substances.

In order to identify which mixture demonstrates a chemical change, it's essential to understand the characteristics of physical and chemical changes. Physical changes involve alterations in the state or appearance of a substance without forming new substances. On the other hand, chemical changes result in the formation of new substances with distinct properties.

If one of the mixtures exhibits a change in color, the evolution of gas, the formation of a precipitate, or a change in temperature, it suggests a chemical change. These are indicative of chemical reactions where bonds between atoms are broken and new ones are formed.

For instance, if a mixture produces a gas with effervescence, it implies the release of a new substance. Similarly, if a color change occurs, indicating the formation of a new compound, or if a solid precipitate forms, these are strong indicators of a chemical change.

Observing these characteristics in a mixture would signify a chemical reaction between the clear liquids, indicating the occurrence of a chemical change. It's crucial to analyze the physical and chemical properties of each mixture to pinpoint the one that demonstrates such transformative chemical processes.

Answer:

Three hundreds equals $300 which is equivilant to 300 1's you get that because there is 100 cents in 1 dollar. And there are 100 ones in $100. Therefore your answer would be 300. Hope this helps

Step-by-step explanation:

the first option is the correct one

13/18 = 0.72

11/14 = 0.78

So 13/18 < (less than) 11/14.

Hope this Helps!!

The lists he would add would be C because 74.05 rounds to 74, 9.72 rounds to 10 and 45.49 rounds to 45 because it is closer to 45 than 46.

The Answer Is C) because 74.05 rounds to 74, 9.72 rounds to 10 and 45.49 rounds to 45 because it is closer to 45 than 46.

There are 5 fewer trucks, that means there are 5 more cars than trucks  

So no. of cars = 8+5 = 13

Answer:

A (Wrong)

B (Correct)

C (Wrong)

D (Wrong)

Step-by-step explanation:

The y-intercept is [tex]-2[/tex] because the line intercepts are touch the y-intercept at [tex]-2[/tex]. Further more find two point on the line that has whole number in the order pair. Which is [tex]-\frac{3}{2}[/tex] meaning that it takes the point to move [tex]3[/tex] units down and to [tex]2[/tex] right.

Hey there!!

Equations given :

y = x² - x - 20 -------- ( 1 )

y = 3x - 15 ------------ ( 2 )

Now, lets first solve for the 1st equation ...

... x² - x - 20

We can write -x as -5x + 4x

... x² + 4x - 5x - 20

... x ( x + 4 ) - 5 ( x + 4 )

... ( x - 5 ) ( x + 4 )

y = ( x - 5 ) ( x - 4 )

Now, let's solve the second equation ...

y = 3x - 15

... y = 3 ( x - 5 )

We have two equations, now getting them together..

3 ( x - 5 ) = ( x - 5 ) ( x - 4 )

Divide by x-5 on both sides

3 = x - 4

Add 4 on both sides

x = 7

The value of x is 7

Now substituting this, we get the value of y

We have,

y = 3x - 15

... y = 3(7 ) - 15

... y = 21 - 15

... y = 6

Hence, the ordered pair is ( 7 , 6 )

Hope my answer helps!

The ordered pair that serves as a solution to the given system of equations is found by setting the equations equal to each other, coupling the x-values with their corresponding y-values after calculation. The solutions are (5,0) and (-1,-18).

To find the ordered pair that is a solution to the system of equations y = x^2 - x - 20 and y = 3x - 15, we can set the two equations equal to each other and solve for the variable x.

So, the solutions to the system are (5,0) and (-1,-18).

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Solution

Here the first term = -2

5th term = -1/8

Now we have to find the common ratio (r)

Fifth term A5 = -1/8

-1/8 = [tex]a_{1} r^{4}[/tex]

Here [tex]a_{1} = -2[/tex]

Plug in [tex]a_{1} = -2[/tex]  in the fifth term and find the value of r.

-1/8 = -2[tex]r^{4}[/tex]

r^4 = 1/16

Taking 4th root, we get

r = 1/2

Now let's find the second term.

first term *r = -2 *1/2 = -1

2nd term = first term * 1/2 = -1

3rd term = second term * 1/2 = -1 * 1/2 = -1/2

4th term = 3rd term *r = -1/2 *1/2 = -1/4

Thank you :)

To find the answer, multiply the decimal by 10. 0.05 X 10 = 0.5, and since 0.05 goes into 0.5 10 times, it is equivalent to 1/10th of 0.5.

0.05 is 1/10 the value of 0.5.

In this question, we are given that 0.05 is 1/10 the value of something, and we need to find out what that something is. To solve this, we can set up an equation:

0.05 = 1/10 * x

To isolate x, we can multiply both sides of the equation by 10:

0.05 * 10 = 1/10 * 10 * x

0.5 = x

Therefore, 0.05 is 1/10 the value of 0.5.

Learn more about Proportions here:

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all you have to do is add 64 + 45 which equals 109 then subtract from fifty which is b 47

Answer:

x= 47

Step-by-step explanation:

They are biking 3 days

64+45+x  where x is the distance on the third day

The total is 156

64+45+x = 156

Combine like terms

109 +x = 156

subtract 109 from each side

109+x-109 = 156-109

x =47

Really none of the above.  

A principal square root of a real number is a positive real number (or a positive real number times i, if you're up to complex numbers, but let's assume not.)  It's not necessarily a positive integer, √2 being the obvious example.

Is √2 a positive fraction?   We can write it as √2 / 1 so I suppose it is.  It's certainly not a rational number.  Even if we grant irrationals as fractions surely √0=0 isn't a positive fraction.  So "always" isn't correct.

I'd go with none of the above, but if I had to choose I'd choose D.

In order to simplify the expression (b+11)2b, we need to use the concept of distributive property.

Distributive property:

The distributive property of multiplication over addition can be used when you multiply a number by a sum.

[tex]a(b+c)=a*b+a*c[/tex]

Our expression is:

2b(b+11)

Applying distributive property here :

[tex]2b(b+11)=2b*b+2b*11[/tex]

[tex]=2b^{2}+22b[/tex]

Answer: [tex]2b^{2}+22b[/tex]

calculate the paychecks of the following people. select the total hours and paycheck?

TimeKeep

Time cards employee time record

#0000 Tim Doe Art Dept.

DAY     in          out          ANSWER

Mon    8:00     3:10         7 1/6

Tue     8:05      3:25        7 1/3

Wed    8:00      2:30       6 1/2

Thur    7:55      2:45       6 5/6

Fri        7:58     3:38        7 2/3

the square root of 31 is a irrational number

The additive inverse of the number is the same number but with the opposite sign.

The number you are given is negative, so the additive inverse would be positive.

The answer is 10 1/4

The additive inverse of -10 1/4 is 10 1/4, as it is the number that results in zero when added to the original.

The additive inverse of a number is the number that, when added to the original, will result in zero. For the number -10 1/4, its additive inverse would be the opposite sign of that number. Therefore, the additive inverse of -10 1/4 would be 10 1/4.

Answer:

58.33 lbs.

Step-by-step explanation:

There are already 25 lbs of alloy of copper

Of this 25 lbs, 20% is pure i.e. copper content = 25(0.5) = 5lbs.

Now available is

Copper      Other metals

5 lbs                20 lbs

Let x lb of 30% copper is added.

Then new alloy will have 5+0.3x lb copper in total of 25+x lbs

Percentage pure = [tex]\frac{5+0.3x}{25+x} =27%[/tex]

Simplify to get

[tex]\frac{5+0.3x}{25+x} =\frac{27}{100} \\\\Cross multiply:\\27(25+x) =100(5+0.3x)\\500+30x =675 +27x\\3x = 175\\x = 175/3 = 58.33 lbs[/tex]

Hence answer is 58.33 lbs should be added.

The answer should be B or the second option. :)

First, you need to convert the minutes into hours, to do this you divide the minutes by 60 (the amount of minutes in an hour). Once you've gotten the value (which is 2.5), you divide that by the amount of miles drove, then you get the unit rate, or in other words       the kilometers per hour, which equals 49.6 km/h

First, we must subtract

57

-

26

______

31

Second, we isolate the variable!

X + 0 = 31 - 5

X+0 = 26

X=26

Finally,Plug it in

26 + 5 = 57 - 26

26 + 5 = 31

31 = 31

Check

Hope I helped!

Good Luck!

x + 5 = 57 - 26

x = 57 - 26 - 5

x = 26

Out of 50 students, 11 are taking neither English nor Chemistry.

To find the number of students taking neither English nor Chemistry, we need to subtract the number of students taking English, the number of students taking Chemistry, and the number of students taking both from the total number of students. So, the number of students taking neither is:

Total number of students - Number of students taking English - Number of students taking Chemistry + Number of students taking both = 50 - 15 - 30 + 6 = 11.

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The answer is 122.5 using long division

720/6=120

15/6=2.5

735 divided by 6, or in standard form, [tex]735/6[/tex], is a division problem.

In order to divide 735 by 6, you must first:

See how many times 6 goes into 7: 1 time

6*1=6

Then subtract 6 from 7 (which comes from the 7 in the hundreds place): Which gives you 1

Then bring down the 3 and combine it with 1: Which gives you 13

Once you do that, see how many times 6 goes into 13: 2 times

6*2=12

Subtract 12 from 13: You get 1

Then bring down the 5 and combine it with the 1: Which gives you 15

Finally, see how many time 6 goes into 15: 2 times

6*2=12

Subtract 12 from 15: You get 3

This means that the answer is: 122 with a remainder of 3

This is the process: