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3 years ago

Is 1 +4(3x-10)-12x equivalent to -9

Mathematics

1 answer:

STALIN [3.7K]3 years ago

6 0

Answer:

This expression is not equivalent to -9.

Step-by-step explanation:

Given the expression

$1+4(3x-10)-12x$

Use distributive property to eliminate the brackets:

$1+4\cdot 3x-4\cdot 10-12x\\ \\=1+12x-40-12x$

Use commutative property to rearrange the terms:

$1+12x-40-12x\\ \\=(12x-12x)+(1-40)\\ \\=0+(-39)\\ \\=-39$

Hence, this expression is not equivalent to -9.

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7.Find the lengths of the missing sides in the triangle. If your answer is not an integer, leave it in simplest radical form. Th

Fed [463]

Here a right angled triangle given. one angle with measure $45^o$ given. The three sides of the triangle given 4, x, y.

We have to find, the sides which is opposite, adjacent and hypotenuse here.

We know that the side opposite to right angle is always hypotenuse. So, hypotenuyse = y.

The side adjacent to the given angle $45^o$ is x. So, here adjacent = x.

The opposite side is opposite to the given angle. So, opposite = 4.

Now we will use SOHCAHTOA that is $sin(x) =\frac{Opposite}{Hypotenuse} , cos(x) =\frac{Adjacent}{Hypotenuse} , tan(x) =\frac{Opposite}{Adjacent}$ , where x is the angle given.

To get x, we will use tan. So we will get,

$tan(45^o) = \frac{4}{x}$

We know the value of $tan(45^o) = 1$ . By substituting the value we will get,

$1 =\frac{4}{x}$

To find x, we have to move x here to the left side by multiplying it to both sides. We will get,

$(1)(x) = (\frac{4}{x}) (x)$

$x = 4$

So we have got the value of x here.

Now to find y, we will use the trigonometric function sine.

$sin(45^o) =\frac{4}{y}$

we know the value of $sin(45^o) =\frac{\sqrt{2}}{2}$

By substituting the value we will get,

$\frac{\sqrt{2}}{2} = \frac{4}{y}$

By cross multiplying we will get,

$(\sqrt{2}) (y) = (4)(2)$

$\sqrt{2}y = 8$

We will get y by dividing both sides by $\sqrt{2}$ , we will get,

$\frac{\sqrt{2}y}{\sqrt{2}} =\frac{8}{\sqrt{2} }$

$y =\frac{8}{\sqrt{2} }$

Now we will rationalize the denominator by multiplying $\sqrt{2}$ to the top and bottom.

$y =\frac{8\sqrt{2}}{(\sqrt{2})(\sqrt{2})}$

$y =\frac{8\sqrt{2}}{2}$

$y = 4\sqrt{2}$

So we have got the required values of x and y.

8 0

3 years ago

Read 2 more answers

The fee to check luggage with anew arline is based on the weightof each bag. Brett paid $7.14 tocheck a 42-pound bag. Howmuch wi

rodikova [14]

$10.71

Explanation

Step 1

you can easily solve this by using a rule of three.

Let

x represents the money Eileen will pay if her bag weighs 63 pounds

the proportion is the same

then

$\frac{7.14}{42}=\frac{x}{63}$

Step 2

solve for x

$\begin{gathered} \frac{7.14}{42}=\frac{x}{63} \\ 63\cdot7.14=42x \\ x=\frac{63\cdot7.14}{42} \\ x=\frac{449.82}{42} \\ x=10.71 \\ \end{gathered}$

I hope this helps you

5 0

1 year ago

Deepak wrote out the steps to his solution of the equation StartFraction 5 Over 2 minus 3 x minus 5 plus 4 x equals negative Sta

Anna35 [415]

Answer:

Step 1 is incorrect.

Step-by-step explanation:

The given expression is :

$\dfrac{5}{2}-3x-5+4x=\dfrac{-7}{4}$

In step 1, Deepak rearranged the terms in order to simplify like terms together that is followed in step 2.

o, rearranging of the terms of an expression is commutative property and not distributive property. The distributive property is generally applicable to multiplication and is given as:

$x(y+z)=xy+yz$