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Tom Q.

Glendora, CA (91740)

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how many liters of 40% antifreeze solution must be mixed with 8 liters 70% antifreeze solution to get a 50% antifreeze?

I know that the answer is 16, I just dont know how that answer is found

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Asked by Jonathon from Whittier, CA
30

Let x equal the number of liters of 40% solution, because that is the unknown value we want to find.

We can write the equation as follows (I'm writing the percentages as decimal values - e.g. 40% = 0.4)

(x)(0.4) + (8)(0.7) = (x+8)(0.5)

The total number of liters of solution (x+8) is the sum of the two individual amounts (x liters of 40% and 8 liters of 70%)

Multiply the values together and distribute the 0.5 into the parentheses on the right:

0.4x + 5.6 = 0.5x + 4.0

Subtract 0.4x from both sides to get all the terms with an x on the right side:

0.4x - 0.4x + 5.6 = 0.5x - 0.4x + 4.0

5.6 = 0.1x + 4.0

Subtract 4.0 from both sides to get all the constant terms on the left side:

5.6 - 4.0 = 0.1x + 4.0 - 4.0

1.6 = 0.1x

Divide both sides by 0.1 to get x by itself:

1.6/0.1 = (0.1x)/0.1

16 = x

So you need 16 liters of the 40% solution.

if 5-3(-4-6)^2= -295 how did it equal to -295?

i need help solving it bc im not sure what im doing wrong n why i keep getting the wrong number

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Asked by Amy from San Antonio, TX
20

This question is all about order of operations.

The mnemonic device to help you remember order of operations is PEMDAS.  This stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.  You must perform the operations according to this order to get the correct answer.  Some math books teach students to remember these six letters by remembering the phrase "Please Excuse My Dear Aunt Sally".

We start with 5-3(-4-6)^2.  Parentheses have the highest precedence, so we do what's in the parentheses first (-4-6).  This gives us -10:

5-3(-10)^2.  Next we have to take care of the exponent.  Raising -10 to the 2 power gives 100:

5-3(100).  Next we perform the multiplication, 3 * 100 = 300:

5-300.  Finally we do the subtraction, 5 minus 300 gives us -295.

Does a straight angle have a vertex?

I don't think it does.  The angle is labled K N X.

I also don't think it has any sides.  Am I correct?

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Asked by Debra from Englishtown, NJ
20

Even though it is a straight angle, it can be named with three letters just like any other angle. In your example of straight angle KNX, point N would be the vertex and the sides would be NK and NX. All three points just happen to lie on line KX.

properties of parallelogram

properties of parallelogram

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10

The key properties of a parallelogram are:

• Opposite sides are parallel
• Opposite sides are congruent
• Opposite angles are congruent
• Any two consecutive angles are supplementary (add up to 180 degrees)
• The two diagonals bisect each other

To find the perimeter of a parallelogram, add up the four side lengths.

To find the area of a parallelogram, multiply base * height.  Note that the height must be measured perpendicular to the base.

A rectangle and a square are special cases of parallelograms, where all four angles are right angles. A rhombus and a square are special cases of parallelograms, where all four side lengths are the same.

(+11) (-1)=

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Asked by Mikeal from Opp, AL
10

Multiplying a positive number by a negative number always gives you a negative number as the result.  So, +11 multiplied by -1 gives you -11.  (In contrast, if both numbers had been negative, then multiplying a negative number by another negative number would give you a positive number.)

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