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3 years ago

What is the solution to the equation 1/2x+3 = 2/3+1?

Mathematics

1 answer:

Alex3 years ago

7 0

Answer:

x = -8/3

Step-by-step explanation:

1/2x+3 = 2/3+1

Combine like terms

1/2x+3 = 2/3 + 3/3

1/2x + 3 = 5/3

Subtract 3 from each side

1/2x + 3-3 = 5/3 - 3

1/2x = 5/3 - 9/3

1/2x = -4/3

Multiply each side by 2

1/2x *2 = -4/3*2

x = -8/3

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Question 1- explain how Sheldon immediately knew howard was incorrect?

Dmitrij [34]

Answer:

Part 1) In the procedure

Part 2) In the procedure

Step-by-step explanation:

Part 1) Observing the graph

The roots are x=-1/2 and x=4

Remember that, the roots are the x-values when the value of y is equal to zero (the x-intercepts)

That's why Sheldon immediately realizes Howard's solution is incorrect

Part 2) we have

$y=2x^{2}-7x-4$

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

equate the equation to zero

$2x^{2}-7x-4=0$

$a=2\\b=-7\\c=-4$

substitute

$x=\frac{-(-7)(+/-)\sqrt{-7^{2}-4(2)(-4)}} {2(2)}$

$x=\frac{7(+/-)\sqrt{49+32}} {4}$

Howard's error is in this step, is wrong with the sign of the number 7, is positive instead of negative

$x=\frac{7(+/-)\sqrt{81}}{4}$

$x=\frac{7(+/-)9}{4}$

$x=\frac{7(+)9}{4}=4$

$x=\frac{7(-)9}{4}=-1/2$

4 0

3 years ago

75,15,3 find the 6th term

Karolina [17]

Answer:

0.024

Step-by-step explanation:

75, 15, 3, ...

Now, let's take a look at thus pattern.

You'll notice how the numbers decrease.

Divide 75 by 5.

We get 15

Divide 15 by 5.

We get 3.

Then we have the pattern now.

3 ÷ 5 = 0.6 (4th term)

0.6 ÷ 5 = 0.12 (5th term)

0 12 ÷ 5 = 0.024 (6th term)

I hope it helps.

8 0

2 years ago

Which of the following statements is true?

laiz [17]

Answer:

D.All of these statements are true

5 0

3 years ago

Tell whether the angles are adjacent or vertical. Then find the value of $x$ .

boyakko [2]

Answer:

they are adjacent angles

Step-by-step explanation:

for adjacent angles

${(x + 3)}^{o} = {84}^{0} \\ x = 84 - 3 \\ x = 81$

7 0

2 years ago

Dr bell donated 2(3x+60) dollars to the salvation army, 5x dollars to the church and $100 to a sport shop. If he donated a total

Andreyy89

He donated $285 to the salvation army.
The first thing to do is solve for "x". The equation would be {2(3x+60)}+5x+100=550.
Then, you would multiply 2 with 3x and 60. Your new equation would be 5x+120+5x+100=550.
Next, you would combine like terms. This means to combine the terms that are similar. In this case, it would be the whole numbers and the numbers with the variable. Your new equation would be 10x+220=550.
After that, you subtract 220 on both sides of the equal sign. This makes the equation 10x=330.
Then, you divide ten on both sides of the equal sign, giving you x=33.
The second things to is replace the x with 33. The amount for the salvation army is 5x+120. Replacing 33 with x, your final equation will be 165+120=$285.

Have a great day!!! :)

5 0

3 years ago