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4 years ago

Decide whether each equation has one solution, no solutions, or infinitely many solutions. . 1. 2(x - 3) = 2x .

1 answer:

6 0

(1)
2(x - 3) = 2x -- distribute through the parenthesis
2x - 6 = 2x -- add 6 to both sides
2x = 2x + 6 -- subtract 2x from both sides
2x - 2x = 6 0 = 6 (incorrect)

If you answer comes out not equal, then there is no solution

(2)
3(y - 3) = 2y - 9 + y -- distribute and combine
3y - 9 = 3y - 9 -- subtract 3y
3y - 3y - 9 = - 9 -- add 9
3y - 3y = -9 + 9
0 = 0 (correct)

If you answer comes out equal, then there is infinite solutions 
(3)
10x - 2 - 6x = 3x - 2 + x -- combine like terms 4x - 2 = 4x - 2
same thing here...it is gonna come out to 0 = 0 making it have infinite solutions

(4)
4(x + 3) + 2x = x - 8
4x + 12 + 2x = x - 8
6x + 12 = x - 8
6x - x = -8 - 12
5x = - 20
x = -4

ONE SOLUTION

Read more about real numbers here:

brainly.com/question/17020343

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5 0

2 years ago

5-3x =-10 what is x?

Delvig [45]

Answer:

x = 5

Please tell me if im incorrect and hope this helped ^^

3 0

3 years ago

Read 2 more answers

Simplify: sec(θ) sin(θ) cot(θ)

krek1111 [17]

We have to simplify

sec(θ) sin(θ) cot(θ)

Now first of all let's simplify these separately , using reciprocal identities.

Sec(θ) = 1/cos(θ)

Sin(θ) is already simplified

Cot(θ)= cos(θ) / sin(θ) ,

Let's plug these values in the expression

sec(θ) sin(θ) cot(θ)

= ( 1/cos(θ) ) * ( sin(θ) ) * ( cos(θ) / sin(θ) )

= ( sin(θ) /cos(θ) ) * ( cos(θ) /sin(θ) )

sin cancels out with sin and cos cancels out with cos

So , answer comes out to be

=( sin(θ) /cos(θ) ) * ( cos(θ) /sin(θ) )

= 1

4 0

3 years ago

Read 2 more answers

13 POINTS- please help me

allsm [11]

Answer:

See explanation

Step-by-step explanation:

16. Two parallel lines are cut by transversal. Angles with measures $(6x+20)^{\circ}$ and $(x+100)^{\circ}$ are alternate exterior angles. By alternate exterior angles, the measures of alternate exterior angles are the same:

$6x+20=x+100\\ \\6x-x=100-20\\ \\5x=80\\ \\x=16$

Then

$(6x+20)^{\circ}=(6\cdot 16+20)^{\circ}=116^{\circ}\\ \\(x+100)^{\circ}=(16+100)^{\circ}=116^{\circ}$

17. Two parallel lines are cut by transversal. Angles with measures $(2x+12)^{\circ}$ and $(3x-22)^{\circ}$ are alternate interior angles. By alternate interior angles, the measures of alternate interior angles are the same:

$2x+12=3x-22\\ \\2x-3x=-22-12\\ \\-x=-34\\ \\x=34$

Then

$(2x+12)^{\circ}=(2\cdot 34+12)^{\circ}=80^{\circ}\\ \\(3x-22)^{\circ}=(3\cdot 34-22)^{\circ}=80^{\circ}$

18. Two parallel lines are cut by transversal. Angles with measures $(6x-7)^{\circ}$ and $(5x+10)^{\circ}$ are alternate exterior angles. By alternate interior angles, the measures of alternate exterior angles are the same:

$6x-7=5x+10\\ \\6x-5x=10+7\\ \\x=17$

Then

$(6x-7)^{\circ}=(6\cdot 17-7)^{\circ}=95^{\circ}\\ \\(5x+10)^{\circ}=(5\cdot 17+10)^{\circ}=95^{\circ}$

19. The diagram shows two complementary angles with measures $2x^{\circ}$ and $56^{\circ}$ . The measures of complementary angles add up to $90^{\circ},$ then

$2x+56=90\\ \\2x=90-56\\ \\2x=34\\ \\x=17$

Hence,

$2x^{\circ}=2\cdot 17^{\circ}=34^{\circ}$

Check:

$34^{\circ}+56^{\circ}=90^{\circ}$

20. Angles $\angle 1$ and $\angle 2$ are vertical angles. By vertical angles theorem, vertical angles are congruent, so

$m\angle 1=m\angle 2\\ \\5x+7=3x+15\\ \\5x-3x=15-7\\ \\2x=8\\ \\x=4$

Hence,

$m\angle 1=(5x+7)^{\circ}=(5\cdot 4+7)^{\circ}=27^{\circ}\\ \\m\angle 2=(3x+15)^{\circ}=(3\cdot 4+15)^{\circ}=27^{\circ}$

21. $\angle 5$ and $\angle 8$ are supplementary. The measures of supplementary angles add up to $180^{\circ},$ so

$m\angle 5+m\angle 8=180^{\circ}\\ \\3x-40+7x-120=180\\ \\10x-160=180\\ \\10x=180+160\\ \\10x=340\\ \\x=34$

Therefore,

$m\angle 5=(3x-40)^{\circ}=(3\cdot 34-40)^{\circ}=62^{\circ}\\ \\m\angle 8=(7x-120)^{\circ}=(7\cdot 34-120)^{\circ}=118^{\circ}\\ \\62^{\circ}+118^{\circ}=180^{\circ}$

7 0

3 years ago

If 1 is added to a number and the sum is tripled, the result is 17 more than the number. Find the number

bearhunter [10]

Form an equation. Start by representing the number you want to find as X. Now add 1.
X + 1
Now we need to triple it. That basically means multiply X+1 by 3. You can write that as:
3 (X + 1)
Now we write out that the result is 17 more than the number we want to find. So set an equals sign up
3 (X + 1) =
And now write X + 17
3 (X + 1) = X + 17

Now we solve for X.
Firstly, let's get rid of the X on the right.
Remember, if we want to get rid of a number of variable on one side, we need to use opposites, and do the same to the other side of the equation.
In this case, we have a positive X on the right. To get rid of that, we subtract X from both sides. This will leave us with:
2x + 3 = 17
Now let's get rid of the +3 on the left. To do this, we subtract 3 from both sides of the equation.
2x = 17 - 3
2x = 14
Now we just need to get X by itself. The 2 in front of the X multiplies X by 2. Therefore, to get X on its own, we need to divide 2x by 2, which just gives us 2.
We also need to divide the other side by 2, because if we do something on one side, we need to do something on the other too. So divide 14 by 2, and we get 7.
X = 7

But before we celebrate, let's double check the answer. Add 1 to 7. This gives us 8. Triple 8. This is 24. This should be 17 more than 7. So go, 24 - 17. And whaddya know - it's 7!

4 0

3 years ago