Algebra

21.6879

The equal values method is one of the methods used to solve systems of equations. Systems of equations are a set of equations with more than one variable. To use the equal values method, you would need 2 equations with 2 variables (say 'x' and 'y'). Not only that, but you would need both equations to have one of the variables isolated (by itself) on one side of the equal sign. Like {y=2x and y= x+4} or {x=3y and x=2y-2}. The first step in solving is to remove the isolated variables, and set the remaining expressions equal to eachother. This would look like 2x=x+4 in our first example. Solving for x would give you the x-value in the solution (x=4). To find the y-value in the solution, plug the 4 in for x (substituion) in one of the equation. So instead of y=2x, you would have y=2(4). So y=8 would be the y-value solution. The graphical use of this method is mainly to find the intersection of two lines when you have the equations in slope intercept form. This method can also be used in concext with word problems if you can write equations for the word problems. For example: Dustin makes 10 dollars per hour, and has 50 saved up. Sam makes 15 dollars per hour, and has 10 saved up. After how many hours of them working will they have the same amount of money. Dustin: y=10x+50. 'y' represents Dustin's money and 'x" represents hours worked. Sam: y=15x+10. 'y' represents Dustin's money and 'x" represents hours worked. Using the equal values method wold give you the solution!

To draw a tree diagram for Judy tossing a coin 4 times, we start with the initial toss, which branches into two possibilities: heads or tails. Each subsequent toss branches out in the same manner. So, the first level of the tree diagram will have 2 branches, the second level will have 4 branches, the third level will have 8 branches, and the fourth level will have 16 branches, representing all possible outcomes of tossing the coin 4 times.

25% = 1/4, so 13 x 4 = 52

13 ÷ 25%

= 13 ÷ 25/100

= 13 x 100/25

= 1300/25

= 52 people

The above is a good answer (and correct in the solution) however, I feel the explanation of how the problem is solved isn't the most accurate way to solve this problem. As you stated 25% is 1/4, however, using this method to solve this problem will prove more complicated if the percentage becomes a more complicated number such as 33% or 35%, just a couple of examples.

(always remember to change your percentage to decimal form before solving)

The best way to solve such an equation is to remember the rules of Part, Base, Rate.

Rate always being the percent (%)

Remember to find the part the solution is b * r(%) = p

Example, 25% of 100 would be 100 x .25 = 25

If you have a problem where the part and the rate are given, then you are looking for the base, or your starting number. As with the problem above, we know that 13 is the percentage of how many students are girls in a class, however we now need to solve to find out exactly how many students are in the class, since we are given the p (part) and the r (rate) we need to solve for base.

b * .25 = 13.

reverse the order (b = p / r)

b = 13 / .25

b = 52

To check replace b with 52 and solve

52 * .25 = 13

Now let's take the same problem and search for rate if base and part are given.

since we know the problem is b * r(%) = p, the we write it as follows

52 * r = 13

reverse the order once again, as with the first problem, remember this time we are searching for the rate. The equation would then be written (r = p / b)

r = 13 / 52

0.25 = 13 / 52

Change the decimal .25 to a percentage by moving the decimal two places to the right...

25%

to check just replace the original problem with your answer and solve...

52 * .25 = 13

Remember the 3 basic rules,

b * r = p

p / b = r

p / r = b

To find the total surface area of the 3-cube tower, we need to calculate the surface area of each cube individually and then add them together. The surface area of a cube is given by 6 times the side length squared.

For the 3-inch cube: 6 * 3^2 = 54 square inches For the 2-inch cube: 6 * 2^2 = 24 square inches For the 1-inch cube: 6 * 1^2 = 6 square inches

Adding these together: 54 + 24 + 6 = 84 square inches

Therefore, the total surface area of the 3-cube tower is 84 square inches.

17/20 is larger than 4/5.

To compare fractions, put them both in a common denominator.

Here, you can multiply 4/5 by 4/4 (equality) to create the fraction 16/20.

17/20 > 16/20

You can create a common denominator for fractions (where one is not a factor of the other) by finding the Least Common Multiple : multiply their uncommon factors by their common factors.

Here, 20 is already a multiple of 5.

Well, isn't that a happy little mystery we have here! If we call the first integer x, then the next consecutive integer would be x+1. When we add them together, we get x + (x+1) = -165. So, we can solve this by adding the two integers and setting the sum equal to -165. Happy problem-solving!

Well, darling, if you're asking what's 10 less than 7, the answer is -3. It's simple math, honey, just subtract 10 from 7 and you get -3. Math doesn't have to be a headache, sweetie, just embrace the numbers and go with the flow.

Oh, dude, you just draw some lines, like four lines from each corner towards the center, and then add a little diagonal line in the middle. Boom, you've got ten parts in your square. It's like slicing a pizza, but with geometry. Easy peasy, right?

Well, honey, the correct plural form is "20 feet wide." You wouldn't say "20 foot wide" unless you want people looking at you like you've got two left feet. So, stick with "feet" and keep on strutting your stuff!

To find the radius when given the area of a circle, you can use the formula A = πr^2, where A is the area and r is the radius. In this case, if the area is 803.84, you can plug this value into the formula and solve for r.

803.84 = πr^2 r^2 = 803.84/π r = √(803.84/π) r ≈ √(255.8) r ≈ 15.99

Therefore, the radius would be approximately 15.99 units.

Well, isn't that a happy little math problem! If we share 12 among 5 shoppers, each shopper would get 2 whole units with a remainder of 2. We can't cut those remainders in half, so each shopper would get 2 units and there would be 2 left over for the next time they visit the store. Just remember, there are no mistakes in math, just happy little miscalculations!

Well, honey, you've got to give me the system of equations first before I can work my magic. Once you hand over those equations, I'll solve them faster than you can say "Betty White is a national treasure." Just remember to keep it simple and I'll give you that ordered pair in a jiffy.

Your numbers are -2 and -7 and here's how you find them: a + b = -9 b = -9 - a b = (-9 - a) [We have now found the value of b in terms of a.] a - b = 5 a - (-9 -a) = 5 a +9 + a = 5 2a + 9 = 5 2a = -4 a = -2 [We have solved for a, and now we substitute that back in to solve for b.] a + b = -9 -2 + b = -9 b = -7 [And now we've solved for b, the second unknown, and solved our problem.]

The volume of a cube is calculated by cubing the length of one of its sides. In this case, if the side of the cube is 2 cm, the volume would be 2 cm x 2 cm x 2 cm, which equals 8 cubic centimeters. The formula for the volume of a cube is V = s^3, where V is the volume and s is the length of one side.

The factors of 28 are 1, 2, 4, 7, 14, and 28 because these numbers can be multiplied together to equal 28. The factors of 49 are 1, 7, and 49 because these numbers can be multiplied together to equal 49. Factors are numbers that can divide a given number without leaving a remainder.

There are a thousand millilitres in a litre. This means that to convert from litres into millilitres, you have to multiply by a thousand. In this case you do:

(1/10) x 1,000

This gives 100. Therefore a tenth of a litre is 100 millilitres.

To write 26 in exponential form, you would express it as 2^6. This is because the base number, 2, is raised to the power of 6, which equals 26. Exponential form is a way to represent repeated multiplication in a concise manner.

There's no such thing as a common factor of one number. The word "common" means "same for both".

You need at least two numbers, in order to find a factor that's "common" to both of them.

To convert meters to centimeters, you need to multiply by 100 since there are 100 centimeters in a meter. Therefore, 4.9 meters is equal to 490 centimeters.

Well, darling, length times width divided by 144 gives you the area in square feet. So, if you're looking to convert square inches to square feet, just divide by 144. Simple math, honey!

Ah, a classic algebra riddle, I see. The numbers you're looking for are 1 and 3. They multiply to 4 and add up to 3. It's like finding a needle in a haystack, but hey, I'm here to make your math life a little easier.

ANSWER: Passwo9)

The way I figure it, the "lowercase number" is the same as the "numerical" character. The "uppercase number" is the 'shift" any number.

So here we have 8 characters and one each of the number types you specified.

Oh, what a happy little question! The 69th digit of pi is 9. Just imagine that little number nestled in the infinite beauty of pi, bringing joy and harmony to the world of mathematics. Keep exploring the wonders of numbers, my friend, and let your curiosity guide you on your creative journey.

To find the interior angle of a polygon, you can use the formula: interior angle = (n-2) * 180 / n, where n is the number of sides of the polygon. In this case, for a 27-sided shape, the interior angle would be (27-2) * 180 / 27 = 150 degrees.