Sandy has $5000 invested in three accounts. One account bears 2% annual interest, another 3%, and the other 5%, and she earned $202.50 for the year. Write and solve a system of equations to find out how much money Sandy has in each account.

The correct answer is easy 1x=12y

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

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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Final answer:

The next number in the arithmetic sequence 10, 23, 36, ? is 49.

Explanation:

The given sequence is an arithmetic sequence, where each number is obtained by adding a fixed value (the common difference) to the previous number. To find the next number in the sequence, we need to determine the common difference and add it to the last number in the sequence.

Looking at the given sequence: 10, 23, 36, ?, we can see that the common difference is 13, as each subsequent term is obtained by adding 13 to the previous term.

Therefore, to find the next term in the sequence, we add 13 to the last term, which is 36. So, the next number in the sequence is 49.

24/-30 would be the answer

Answer:

-270

Step-by-step explanation:

The value closest to zero on the number line is greatest because all of the values are negative which is less than zero. -270 is closer to 0 than the other values.

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

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]

The fraction that is equivalent to 2/-6 would be -2/6 because they both equal -.03333 or -1/3.

27.5 number of games Archie and kel will finish nonstop from 9:00 am to 2:30 pm.

What is mathematic expression?

A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Here, it is given that :

Archie and kel takes an average of 12 minutes to finish one game.

now calculating the total time being between 9:00 am to 2:30 pm = 330 minutes

Now, the number of games Archie and kel will finish in this 330 minutes will be calculated by dividing 330 minutes by 12 minutes :

330/12 = 27.5 games

Therefore,  27.5 number of games Archie and kel will finish nonstop from 9:00 am to 2:30 pm.

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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.

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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 phrase that completes the paragraph proof for the Vertical Angles Theorem is 'Angle 1 is congruent to angle 3 by the Vertical Angles Theorem'.

The phrase that completes the proof is Angle 1 is congruent to angle 3 by the Vertical Angles Theorem.

Here's how the proof can be completed:

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The missing phrase in Mackenzie's proof of the Vertical Angles Theorem is 'because they are both equal to 180 degrees'. This establishes that the sums of the angles are equal (since they are both supplementary), and allows her to then utilize the Subtraction Property of Equality to show that angle 1 is congruent to angle 3.

Mackenzie's paragraph proof for the Vertical Angles Theorem is almost complete. She has correctly identified that angle 1 and angle 4 are supplementary, as are angle 3 and angle 4, due to the fact that they each add up to 180 degrees. This establishes the equation: (angle 1 + angle 4) = (angle 3 + angle 4). The blank spot in Mackenzie's proof would need to be filled with the phrase 'because they are both equal to 180 degrees'. Mackenzie then correctly utilizes the Subtraction Property of Equality to state that, since the sums are equal, if you subtract angle 4 from both sides, you arrive at angle 1 = angle 3. Thus, completing the proof of the Vertical Angles Theorem: when two lines intersect, opposite or vertical angles are congruent, i.e., they have the same measure.

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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

Answer:

Given equation of the line,

[tex]y=\frac{4}{7}x-2[/tex]

If x = 0,

[tex]y=\frac{4}{7}(0) - 2=0-2=-2[/tex]

Thus, the line intercepts y-axis at (0,-2)

If y = 0,

[tex]0=\frac{4}{7}x-2\implies 2=\frac{4}{7}x\implies x=\frac{14}{4}=3.5[/tex]

Thus, the line intercepts x-axis at (3.5,0)

By joining these two points in the graph,

We will get the graph of the given line ( shown below )

The graph of the function y = 4/7x - 2 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 4/7x - 2

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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the square root of 31 is a irrational number

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:

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

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

3x+5x = 8x

-6-2 = -8

8x-8

Here's some work!

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. :)

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.

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.

If 4 - 3 + 5 = -6 + 8 + 4 is a mathematically correct statement, then both sides should end up with the same number:

4 - 3 + 5 = -6 + 8 + 4     Original statement.

1 + 5 = -6 + 8 + 4     You can do this in any order, but I start by doing the 4 - 3.

6 = -6 + 8 + 4     Finish simplifying the left side.

6 = 2 + 4     Combine the -6 and 8.

6 = 6     Finish simplifying the right side.

Because both sides are equal to each other, the sentence must be true.

Therefore, the sentence is true because when simplified, the statement is 6 = 6.

Hope this helps! :)

EDIT: Just incase anyone is curious, both this way and the way the other guy used both work, as they both prove that both sides are equal.

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:

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.