MATHEMATICS HIGH SCHOOL

Which statement is true for the equation 3x − 3x − 2 = −2?It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.

Answers

Answer 1
Answer:

Answer:

D. It has infinitely many solutions.

Step-by-step explanation:

We have been given an equation 3x-3x-2=-2. We are asked to find the number of solutions for our given equation.

We know that an equation has infinitely many solutions, when both sides of the equation are equal.

Let us add 3x on both sides of our given equation.

3x-3x+3x-2=-2+3x

3x-2=3x-2

Since both sides of our given equation are equal, therefore, our given equation has infinitely many solutions and option D is the correct choice.
Answer 2
Answer: It would come out to 3x = 3x so it would be infinitely many solutions

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Which values from the given replacement set make up the solution set of the inequality?m+7<18 ; {8, 9, 10, 11}




{8, 9}

{10, 11}

{8, 9, 10}

{9, 10, 11}

Answers

Answer:

8,9 10

Step-by-step explanation:

when u add them they are all less than 18

What is the solution of the system of equations c+3d=8 and c=4d-6?
Show work plz.

Answers

\left\{\begin{array}{ccc}c+3d=8\nc=4d-6\end{array}\right\n\nsubstitute:\n\n(4d-6)+3d=8\n4d+3d-6=8\ \ \ \ /+6\n7d=14\ \ \ \ /:7\nd=2\n\nc=4\cdot2-6=8-6=2\n\n\left\{\begin{array}{ccc}c=2\nd=2\end{array}\right

At the soup to nuts cafeteria, larry orders two pieces of toast and a bagel, which comes out to $\$1.30$. Curly orders a bagel and a muffin, which comes out to $\$2.50$. Moe orders a piece of toast, two bagels, and three muffins, which comes out to $\$6.95$. How many cents does one bagel cost

Answers

Let us take costs of a piece of toast = $t, , one bagel cost=$b and a muffin cost=$m.

Larry

Two pieces of toast and a bagel cost  = $1.30

2t+b=1.30   -------------equation(1)

Let us solve the equation(1) for t in terms of b, because we need to find one bagel cost.

Subtracting b from both sides we get

2t+b-b=1.30-b

2t= 1.30-b

Dividing by 2 on both sides.

2t/2= (1.30-b)/2

t= (1.30-b)/2

Curly

A bagel and a muffin cost = $2.50.

b + m = 2.50 -------------equation(2)

Solving equation for m in terms of b, we get

m= 2.50-b.

Moe

A piece of toast, two bagels, and three muffins cost = $6.95

t + 2b + 3m = 6.95    ......................equation(3).

Substituting t= (1.30-b)/2 and m= 2.50-b in equation (3)

(1.30-b)/2 + 2b + 3(2.50-b) = 6.95 .

Multiplying each term by 2 to get rid 2 from denominator of (1.30-b).

2*(1.30-b)/2+ 2*2b + 2*3(2.50-b) = 2*6.95

1.30-b + 4b + 6(2.50-b) = 13.90.

1.30 - b + 4b  +15 - 6b = 13.90

Combining like terms

-3b +16.30 = 13.90

Subtracting 16.30 from both sides.

-3b +16.30-16.30 = 13.90-16.30.

-3b= -2.4

Dividing both sides by -3.

-3b/-3 = -2.4/-3

b = 0.8

Therefore, cost of one bagel = $0.80.

Which statement about 4x2 + 19x – 5 is true? One of the factors is (x – 4). One of the factors is (4x + 1). One of the factors is (4x – 5). One of the factors is (x + 5).

Answers

Answer:

Only "One of the factors is (x + 5)." is TRUE.


Step-by-step explanation:

  • What makes (x-4) equal to 0?

x-4=0\nx=4

  • What makes (4x+1) equal to 0?

4x+1=0\n4x=-1\nx=-(1)/(4)

  • What makes (4x-5) equal to 0?

4x-5=0\n4x=5\nx=(5)/(4)

  • What makes (x+5) equal to 0?

x+5=0\nx=-5


Note: Putting all those 4 values into the function 4x^(2)+19x-5, whichever value makes the function equal to 0, the corresponding expression would be considered a factor of the function4x^2+19x-5.

  • Putting x=4 into 4x^(2)+19x-5 gives us:

4(4)^(2)+19(4)-5\n=135

  • Putting x=-(1)/(4) into 4x^(2)+19x-5 gives us:

4(-(1)/(4))^(2)+19(-(1)/(4))-5\n=-(19)/(2)

  • Putting x=(5)/(4) into 4x^(2)+19x-5 gives us:

4((5)/(4))^(2)+19((5)/(4))-5\n=25

  • Putting x=-5 into 4x^(2)+19x-5 gives us:

4(-5)^(2)+19(-5)-5\n=0


As we can see, only putting x=-5 in the function gives us a value of 0. So the corresponding expression (x+5) is a factor of the function.
4 x^(2) + 19x - 5 \n \n 4 x^(2) + 20x - x - 5 \n \n 4x(x + 5)-(x + 5) \n \n (x + 5)(4x - 1)

The answer is D) one of the factors of (x + 5). Why? 

(x - 4) is not one of the factors. 
(4x + 1) is not one of the factors.
(4x - 5) is not one of the factors.
(x + 5) IS one of the factors.

You are going to mix a gallon bucket of window cleaner. The

You are going to mix a gallon bucket of window cleaner. The instructions

direct you to mix 1 part cleaner to 3 parts water. How much cleaning 
solution will you need to use?*

Answers

x-amount of cleaning soulution
1Gal=x+3x
1Gal=4x
x=1/4 Gal

The amount of solution needed will be 0.25 Gal.
Hope it helped!

Allison has a poster that is 15 in by 18 in. What will the dimensions of the poster be if she scales it down by a factor of 1/3 ?

Answers

Answer:

Answer 4 : 5in by 6in

Step-by-step explanation:

15 times 1/3 is 5.

18 times 1/3 is 6.

Hope I helped!!
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