MATHEMATICS HIGH SCHOOL

True or false, there is no solution to the systems of inequalities shown belowy<3x+5
y>-x+4

Answers

Answer 1
Answer: False 
Because if you plot a graph to both the equation as i have attached the image.. you can see there can be multiple solution to the above system of inequalities. 
Answer 2
Answer: false.
there are solutions to this system of inequalities.
-> For a quick check you can take random x, e.g. consider x=0, and substitute it       in the inequality, which gives 
    y<5  and  y>4 . 
    there are infinite number of y satisfying these conditions.
-> You can solve it graphically to get exact solution. draw the line y=3x+5 and          y = -x+4. The common region, below y=3x+5 and above y=-x+4 , is  the solution for the system of inequalities.

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Which property of equality justifies the following statement?"If 5x = 60, then x = 12.. "

Symmetric Property

Transitive Property of Equality

Division Property of Equality

Algebra Properties

Answers

5x=60
x=60/5

C division property
You divide five from both sides

If Tom had a base pay of $6.35 and worked 28 hours, what would be his pay for the week

Answers

$6.35 per hour ×28 hours =$177.80

five dice are thrown simultaneously. find the number of outcomes in which at most one of the dice shows 5?

Answers

P(obtaining 5 in one die) = 1/6
P (obtaining 5 in five dice) = (1/6) x 5
= 5/6

(09.02 HC)The function f(x) = −x2 + 50x − 264 models the profit, in dollars, a yoga studio makes for selling monthly memberships, where x is the number of memberships sold and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)

Part B: Determine the x-intercepts. What do these values mean in the context of the problem?

Answers

We factor the equation to get:

-(x-25)^2+361

In the form a(x-h)^2+k, the vertex is (h, k), so the vertex is (25, 361).  This means that the studio makes the most profit from selling 25 memberships, and thus makes 361 dollars.

B.  The x-intercepts are the values of x for which f(x) is 0.  This equation can be factored as (-a+6)(a-44)=0, with solutions 6 and 44.  Therefore, by selling either 6 memberships or 44 memberships, the studio breaks even, neither making nor losing money.

Answer:

x = 6, x = 44; The zeros represent the number of monthly memberships when no profit is made.

Step-by-step explanation:

I took the quiz and got it right.

The sum of two numbers is 50. the greater number is four less than five times the lesser number. Find the numbers

Answers

The required two numbers are 9 and 41.

What is the equation?

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

Let x be the lesser number, and y be the greater number.

From the question, we know that:

x + y = 50 (Equation 1: The sum of the two numbers is 50)

y = 5x - 4 (Equation 2: The greater number is four less than five times the lesser number.)

The equation is to solve for one of the variables, and then substitute that value into the other equation to find the other variable.

Then, two numbers are x = 9 and y = 41.

Learn more about the equations here:

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X=greater number
Y=lesser number
x+y=50
x=5y-4

5y-4+y=50
+4 +4
5y+y=54
V
6y=54
/6 /6
y=9

X=5(9)-4
X=45-4
X=41

41+9=50 ✔️

Greater number=41
Lesser number=9

The sum of two numbers is twenty. Three times the smaller is equal to twotimes the larger. Find the two numbers.

Answers

the smaller number is 8, and the larger number is 12, and they indeed add up to 20, and three times the smaller number (3 * 8) is equal to two times the larger number (2 * 12).

Let's call the two numbers x and y, with x being the smaller number and y being the larger number.

We have two pieces of information from the problem:

1. The sum of the two numbers is twenty:

  x + y = 20

2. Three times the smaller number is equal to two times the larger number:

  3x = 2y

Now, we can solve this system of linear equations.

First, we can solve equation (1) for x:

x = 20 - y

Now, substitute this expression for x into equation (2):

3(20 - y) = 2y

Now, distribute the 3 on the left side:

60 - 3y = 2y

Now, isolate the variables on one side of the equation and constants on the other side:

60 = 2y + 3y

Combine like terms:

60 = 5y

Now, divide by 5 to solve for y:

y = 60 / 5

y = 12

Now that we have found the value of y, we can substitute it back into equation (1) to find x:

x + 12 = 20

Subtract 12 from both sides:

x = 20 - 12

x = 8

So, the two numbers are:

x = 8 (smaller number)

y = 12 (larger number)

Therefore, the smaller number is 8, and the larger number is 12, and they indeed add up to 20, and three times the smaller number (3 * 8) is equal to two times the larger number (2 * 12).

To know more about number:

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Answer:

The smaller number is 8

The larger number is 12

Step-by-step explanation:

Let the smaller number be x

Let the larger number be y

Translate the question and solve ;

x +y = 20\n3(x) =2(y) \n\n\begin{bmatrix}x+y=20\n 3x=2y\end{bmatrix}\n\n\mathrm{Isolate}\:x\:\mathrm{for}\:x+y=20:\quad x=20-y\n\n\mathrm{Subsititute\:}x=20-y\n\n\begin{bmatrix}3\left(20-y\right)=2y\end{bmatrix}\n\n\mathrm{Isolate}\:y\:\mathrm{for}\:3\left(20-y\right)=2y:\quad y=12\n\n\mathrm{For\:}x=20-y\n\n\mathrm{Subsititute\:}y=12\n\nx=20-12\n\nSimplify\n\nx =8\n\nx=8,\:y=12
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