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3 years ago

What is the value of x in the equation 1.5(x + 4) - 3 = 4.5(x - 2)?

Mathematics

2 answers:

Romashka [77]3 years ago

7 0

Answer:

Step-by-step explanation:

Isolate x on one side of the equation.

1.5(x+4)-3=4.5(x-2)

1.5(x+4)*10-3*10=4.5(x-2)*10 (First, multiply 10 from both sides.)

15(x+4)-30=45(x-2) (Refine.)

15(x+4) (Expand by using distributive property.)

DISTRIBUTIVE PROPERTY:

A(B+C)=AB+AC

A(B-C)=AB-AC

15*x=15x

15*4=30

15x+30

45(x-2)

45*x=45

45*2=90

45x-90

15x+30=45x-90

15x+30-30=45x-90-30 (Subtract by 30 from both sides.)

90-30 (Solve.)

90+30=120

15x=45x-120

15x-45x=45x-120-45x (Subtract 45x from both sides.)

15x-45x (Solve.)

15x-45x=-30x

-30x=-120

-30x/-30=-120/-30 (Then, divide by -30 from both sides.)

-120/-30 (Solve.)

-120/-30=4

x=4

Therefore, the correct answer is x=4.

padilas [110]3 years ago

5 0

Answer:4

Step-by-step explanation:

First distributive 1.5 to x+4 and 4.5 to x-2. You get 1.5x+6-3 = 4.5x-9. Next you need to move all the variable terms to one side. You can do either, it doesn't matter, but I subtracted 1.5 x to each side of the equation. You get left with 6-3 = 3x-9. Solve 6-3 and you get 3=3x-9. You 9 to both sides of the equation. You get 12=3x. You divide by 3 on both sides and get 4=x/x=4.

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3 years ago

What is 6x3/7 as a mixed number?

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3 years ago

Janeel has a 10-inch by 12-inch photograph. She wants to scan the photograph, then reduce the result

Vaselesa [24]

Complete Question:

Janeel has a 10 inch by 12 inch photograph. She wants to scan the photograph, then reduce the results by the same amount in each dimension to post on her Web site. Janeel wants the area of the image to be one eight of the original photograph. Write an equation to represent the area of the reduced image. Find the dimensions of the reduced image.

Correct Answer:

A) $(10-x)(12-x)=15$

B) Dimensions are : Length = 10-x = 3 inch , Breadth = 12-x = 5 inch

Step-by-step explanation:

a. Write an equation to represent the area of the reduced image.

Let the reduced dimensions is by x , So the new dimensions are

$length=10-x\\breadth=12-x$

According to question , Area of new image is :

⇒ $Area = \frac{1}{8}Length(breadth)$

⇒ $Area = \frac{1}{8}(10)(12)$

⇒ $Area = 15$

So the equation will be :

⇒ $(10-x)(12-x)=15$

b. Find the dimensions of the reduced image

Let's solve : $(10-x)(12-x)=15$

⇒ $120-10x-12x+x^2=15$

⇒ $120-22x+x^2=15$

⇒ $x^2-22x+105=0$

By Quadratic formula :

⇒ $x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

⇒ $x = \frac{22 \pm8 }{2}$

⇒ $x = \frac{22 +8 }{2} , x = \frac{22 -8 }{2}$

⇒ $x = 15 , x =7$

x = 15 is rejected ! as 15 > 10 ! Side can't be negative

⇒ $x =7$

Therefore, Dimensions are : Length = 10-x = 3 inch , Breadth = 12-x = 5 inch

5 0

3 years ago

Can someone please teach me how to do this? You can please do like 2 questions and please explain exactly how you got the answer

spayn [35]

All of these questions require one thing: trigonometric functions.

There are 3 main trigonometric functions, which can only be used on right triangles: sine, cosine, and tangent.

Sine = opposite / hypotenuse

Cosine = adjacent / hypotenuse

Tangent = opposite / adjacent

When trying to figure out what function to use, we always start by looking from the angle. Take problem a, for example. Looking from angle E, of which the value is not given, we have the side opposite and the side adjacent. Therefore, we should use the tangent function.

---The hypotenuse is always the longest side of the triangle. It is never considered the opposite or adjacent side.

Let's set up our function with the given information from problem a.

tan(x) = 9.7 / 5.2

---The tangent of an unknown angle is equal to the quotient of the opposite side and the adjacent side.

Now, solving for the value of x will require a calculator. We'll need to use what's called an inverse trigonometric function. Most calculators have these directly above the regular trigonometric functions, and the inverse functions are accessed using a "second" key.

---Ensure that your calculator is in degrees, not radians!

x = tan^-1(9.7 / 5.2)

x = 61.805 = 62 degrees

Next, let's take a look at problem b. This time, we're solving for a side length instead of an angle. But, we're still going to start by looking from our angle.

Looking from the 38 degree angle, we are given the adjacent side and an unknown hypotenuse. Therefore, we should use the cosine function.

cosine(38) = 53.1 / r

---The cosine of a 38 degree angle is equal to the quotient of 53.1 and an unknown hypotenuse, r.

Use your algebra skills to isolate the variable r.

r * cosine(38) = 53.1

r = 53.1 / cosine(38)

---From here, all you need to do is plug this into your calculator. Since we are solving for a side length (and given an angle), we are just using the regular trigonometric function buttons on the calculator.

r = 67.385 = 67.4 units

Hope this helps!

4 0

2 years ago