20 / 10 to the first power

Miguel can buy the notebook, pencils, and erasers. This combination ensures he spends his entire $12 budget while acquiring essential school supplies for note-taking, writing, and correction needs.

Miguel's budget is $12. Among the available items, the notebook costs $5, pencils cost $3, and erasers cost $2 each. Considering Miguel's budget, he can afford the notebook, pencils, and erasers with a total cost of $5 + $3 + ($2 x 2) = $12. This exhausts his budget entirely.

Firstly, Miguel can buy the notebook, which is essential for note-taking and organization. Secondly, he can purchase the pencils, providing him with the necessary writing tools. Finally, Miguel can acquire two erasers, offering him the convenience of correcting mistakes. This selection ensures he spends exactly $12 without exceeding his budget.

In essence, Miguel makes a balanced and practical choice, covering both writing and correction needs within the constraints of his budget. This strategic allocation of funds allows him to maximize the utility of his $12 while obtaining a variety of essential school supplies.

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. :)

Hello!

The approximate volume of the cylinder is the second option: 59.3 [tex]ft^{3}[/tex]

V = [tex]\pi r^{2} h[/tex]

V = 3.14 * 3^2 * 2.1

V = 3.14 * 9 * 2.1

V = 59.346 [tex]ft^{3}[/tex]

Final answer:

Explanation of calculating the volume of a cylinder with given radius and height using the formula V = πr²h.

Explanation:

The volume of a cylinder can be calculated using the formula V = πr²h. Given a radius of 3 feet and a height of 2.1 feet, when plugged into the formula with π = 3.14, the volume is approximately 19.74 cubic feet.

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.

Jocelyn answered 76% of the questions correctly on her test. To find the percentage of questions Jocelyn answered correctly, we can use the following formula: Percentage = (Number of Correct Answers / Total Number of Questions) × 100

Given that Jocelyn got 19 out of 25 questions correct, we can plug these values into the formula:

Percentage = (19 / 25) × 100

Now, let's calculate the percentage:

Percentage = 0.76 × 100

Percentage = 76

Jocelyn answered 76% of the questions correctly on her test.

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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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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:

n= -4

Step-by-step explanation:

First we have to find the equation of line which passes through (6,3) and (8,4).

Then we have to pass this line through the point (n , -2).

we know, equation of line passing through (x1,y1) and (x2,y2) is

[tex]\frac{x-x1}{x1-x2}=\frac{y-y1}{y1-y2}[/tex]

So, the equation of line passing through (6,3) and (8,4) is

[tex]\frac{x-6}{6-8}=\frac{y-3}{3-4}[/tex]

or, [tex]\frac{x-6}{-2} =\frac{y-3}{-1}[/tex]

multiplying both sides by  -2

x-6=2(y-3)

or, x-6=2y-6

or, x-2y=6-6

or, x-2y=0

Now, we have to pass this line through  (n,-2)

So, using the point in the line, that is using  x=n  , y=-2

we get

n-2(-2)=0

or, n+4=0

or, n=-4

Answer:

Step-by-step explanation:

Given that the line passes through

(6,3), (8,4), and (n,-2).

We have to find the value of n.

Let us name the points as A, B and C in that order

Slope of AB = slope of BC since all 3 points lie in the same line

To find slope of AB:

Slope = (y2-y1)/(x2-x1) = (4-3)/(8-6) = 1/2

To find slope of BC:

Using the same formula slope = (-2-4)/(n-8) = -6/(n-8)

The two slopes are equal.

Hence 1/2 = -6/(n-8)

n-8 = -12

n = -4

Answer:

It is A the first quadrant

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

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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Ohhh your in K12, here i got you let me do the equation and i promise ill be right with you.

Answer:

20 cm

Step-by-step explanation:

ik its looks like a different question your is just a shorter question but its the same

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

3x+5x = 8x

-6-2 = -8

8x-8

Here's some work!

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

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.

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:

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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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.

Hey there!!

Given equation :

... c(x) = 29x + 54.5

In this equation $54.50 is installation fee and this would remain as a constant. ( This value wouldn't change ).

'x' is represented as the number of months.

The total cost or c(x) is given as $344.50

Getting this into equations :

... 344.50 = 29x + 54.5

Subtracting 54.5 on both sides :

... 29x = 290

Dividing by 29 on both sides :

... x = 10

Hence, the number of months is 10.

Hope my answer helps!!

By manipulating the provided cost function, we find that with $344.50, you can afford 10 months of cable service.

To determine the number of months of cable service you can have for $344.50, you simply need to solve the equation C(x) = 29x + 54.5 = 344.5, where C(x) represents the cost of the service and x is the number of months you are paying for. We can start by subtracting the installation fee (54.5) from both sides of the equation, which gives us 29x = 290. Then, dividing through by 29, we arrive at x=10.

Therefore, you can have cable service for 10 months if you have $344.50.

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24/-30 would be the answer

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:

The correct answer is easy 1x=12y

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.

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

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