MATHEMATICS HIGH SCHOOL

What is the solution to the system of linear equations?4x + 6y = 20
-5x + 7y = 62

Fill in the blanks with your x and y coordinates

( , _)

Answers

Answer 1

Answer:

To find the solution to the system of linear equations:

4x + 6y = 20

-5x + 7y = 62

We can use the method of substitution or elimination to solve for x and y. Let's use the elimination method:

1. Multiply the first equation by 5 and the second equation by 4 to eliminate the x variable:

20x + 30y = 100

-20x + 28y = 248

2. Add the two equations together:

(20x - 20x) + (30y + 28y) = 100 + 248

58y = 348

3. Divide both sides of the equation by 58:

y = 6

4. Substitute the value of y back into either of the original equations. Let's use the first equation:

4x + 6(6) = 20

4x + 36 = 20

4x = 20 - 36

4x = -16

x = -4

Therefore, the solution to the system of linear equations is:

(x, y) = (-4, 6)

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In a certain county, the number of charter schools is 6 less than twice the number of alternative schools. We know that there are 52 charter schools in the county. How many alternative schools are in the county?

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

So, 52 charter schools and the number is 6 less than the alternative schools doubled. In order to find the number of alternative schools, we need to reverse the equation. 52+6=58. That means 58 is twice the amount of alternative schools. 58/2 equals 29, therefore the answer is 29

Is knowing the coordinates of the vertex of a parabola enough to determine the domain and range?a.No: we would have no information about the domain.
b.Yes: if the vertex is at (m,n), then the domain is all reals and the range is y ≤ n.
c.No: we would need to know if the vertex is a minimum or a maximum.
d.Yes: if the vertex is at (m,n), then the domain is all reals and the range is y ≥ n.

Use a graphing calculator to approximate the vertex of the graph of the parabola defined by the following equation.

y=2x-x+6

A)( 0.25, 6.125)
B)(-0.25, 5.875)
C)( 0.25, 5.875)
D)( 0.25, 6)

Answers

The correct answers are:

C) No: we would need to know if the vertex is a minimum or a maximum; and

C)( 0.25, 5.875).

Explanation:

The domain of any quadratic function is all real numbers.

The range, however, would depend on whether the quadratic was open upward or downward. If the vertex is a maximum, then the quadratic opens down and the range is all values of y less than or equal to the y-coordinate of the vertex.

If the vertex is a minimum, then the quadratic opens up and the range is all values of y greater than or equal to the y-coordinate of the vertex.

There is no way to identify from the coordinates of the vertex whether it is a maximum or a minimum, so we cannot tell what the range is.

The graph of the quadratic function is shown in the attachment. Tracing it, the vertex is at approximately (0.25, 0.5875).

Steven wants to buy a $495 bicycle. Steven has no money saved, but will be able to deposit $40 into a savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he must give his sister $65 that he owes her. For how many weeks will Steven need to deposit money into his savings account before he can pay back his sister and buy the bike?

Answers

$495 + $65 = $560

$560 / 40 = 14

He must save for 14 paychecks.

Answer:

He must save for 14 paychecks.

Step-by-step explanation:

$495 + $65 = $560

$560 / 40 = 14

He must save for 14 paychecks.

Simplify 3x times 1/x to the -4 power times x to the -3 power

Answers

Answer:

3x²

Step-by-step explanation:

$3x\cdot(1)/(x^(-4))\cdot x^(-3)=3x^((1-(-4)-3))=3x^2$

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The applicable rules of exponents are ...

$x^ax^b=x^(a+b)\n\n(1)/(x^(-a))=x^a$

Answer:

3x^2.

Step-by-step explanation:

3x * (1/x)^-4 * x^-3

= 3x * x^4 * x^-3

= 3x * x

= 3x^2.

Solve the following expression when b = 12 10 + b/6 + b

Answers

Answer:

Step-by-step explanation:

Given that b = 12,

10 + 12/6 + 12

= 10 + 2 + 12

= 24

Answer:

Step-by-step explanation:

10+(12/6)+12 = 24 use brackets and divide first before adding

Wat is the common denominator of 1 and 6/4 and 1

Answers

Answer:

Step-by-step explanation:

4 is the common denominator.

1 and $(6)/(4)$ can be converted into $(4)/(4)$ + $(6)/(4)$ = $(10)/(4)$ we can divide both the numerator and denominator by 2 in order to simplify this fraction to get a fraction of $(5)/(2)$