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3 years ago

Please Show/Explain Your Work! Thank You!

Mathematics

2 answers:

RSB [31]3 years ago

7 0

In order to solve for the width (which in turn will help us solve for the area), we need to find a scale.

Since the actual floor is 36 feet in length and the diagram has 9, we know the scale is 36/9, which can be simplified to 4/1.

Since we know that the width, is 32, we just have to divide by 4 to find the scaled down drawing, which will be 8 feet.

8*9 = 72 ft^2

mote1985 [20]3 years ago

3 0

Answer:

72 square inches

Step-by-step explanation:

the length of the floor is 36 feet, the scale drawing length is 9 inches

put that into a ratio (fraction) and simplify to get the scale factor

$\frac{9 inches}{36 feet}$ which simplifies to $\frac{1 inch}{4 feet}$

so every inch on the drawing equals 4 feet in real life.

that would make the width of the floor in the drawing 8 inches

the area of the drawing would be 9 inches x 8 inches = 72 square inches

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arsen [322]

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3 years ago

Solving systems by substitution

Kipish [7]

9514 1404 393

Answer:

(x, y) = (0, -2)

Step-by-step explanation:

When solving by substitution, you usually want to find an expression for one of the variables in terms of the other. So, the first thing you look for is an equation that has a coefficient of 1 or -1 on one of the variables. Recognizing that the second equation's terms all have a common factor of 3, you basically have two choices.

<h3>Substitute for y</h3>

Using equation 1, you can write an expression for y:

y = 5x -2 . . . . . . add 5x to both sides

Then substituting this into the original equation 2, you have ...

-3x +6(5x -2) = -12

27x -12 = -12 . . . . . . . simplify

27x = 0 . . . . . . . . . add 12

x = 0 . . . . . . . . . divide by 27

y = 5(0) -2 = -2 . . . . find y using the expression for substitution

The solution is (x, y) = (0, -2).

<h3>Substitute for x</h3>

If you decide you'd rather substitute for x, you can solve the second equation easily for x.

-3x +6y = -12

x -2y = 4 . . . . . . divide by -3

x = 2y +4 . . . . . . add 2y

Substituting for x in the first equation gives ...

-5(2y +4) +y = -2 . . . . substitute for x

-9y -20 = -2 . . . . . . . simplify

-9y = 18 . . . . . . . . . add 20

y = -2 . . . . . . . . . . . divide by -9

x = 2(-2) +4 = 0 . . . . find x using the expression for substitution

The solution is (x, y) = (0, -2).

_____

<em>Additional comment</em>

In some cases, there are no variables that have a coefficient of ±1, so you just need to "bite the bullet" and deal with the resulting fractions.

<u>Example</u>:

solve for y: -5x +2y = -2

2y = 5x -2

y = 5/2x -1 . . . . expression used to substitute for y

Of course, you can multiply the equation after substitution by 2 to eliminate fractions, or just work the problem as is. The point of looking for coefficients of ±1 is to avoid having to do arithmetic with fractions. It can help avoid errors to work with integers, but ultimately the method is the same regardless of the form of the numbers.

You don't always have to substitute for the "bare" variable. Sometimes it can save steps to substitute for expressions instead of variables. If our system of equations were ...

-5x +2y = -2
-3x +6y = -12

You can substitute into the second equation for (2y). In that case, the second equation becomes ...

-3x +3(2y) = -12

-3x +3(5x-2) = -12 . . . . . . where 2y = 5x -2

8 0

3 years ago

Rewrite y=5(14)t/6 in the form y=a(1+r)t or y=a(1−r)t. Round the value of r to the nearest ten thousandth. Then tell whether the

Sveta_85 [38]

Answer:

$y=5(1+0.5525)^t$ where r=0.5525 which is in the form of $y=a(1+r)^t$ or $y=a(1-r)^t$ ..

The expression represents an exponential growth function.

Step-by-step explanation:

Given that $y=5(14)^{\frac{t}{6}$

To rewrite the given equation in the form $y=a(1+r)^t$ or $y=a(1-r)^t$ ..

$y=5(14)^{\frac{t}{6}$

$=5((14)^{\frac{1}{6}})^t$

$=5[1.5525]^t$

$y=5(1+0.5525)^t$ where r=0.5525 which is in the form of $y=a(1+r)^t$ or $y=a(1-r)^t$ ..

Since 1.5525 > 1, we have that the expression represents an exponential growth function.

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3 years ago

Explain how the difference of a fraction or a rational number and its additive inverse is equal to zero.

FromTheMoon [43]

The additive inverse property states that when you add a number and its opposite (rational numbers), the result is zero. The reason is that the inverse of a number is the opposite, so if you have a number and when do the opposite with it (add the opposite), the result will be zero. This applies to adding!!!

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4 years ago

If 2x + 6 =4x-4 then x=

Rina8888 [55]

The correct answer would be x = 4

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3 years ago