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2 years ago

Find the rate of change given the following solutions: (6, 2) and (1, 12).

Mathematics

1 answer:

blagie [28]2 years ago

7 0

Answer:

The rate of change is -2

Step-by-step explanation:

f(b)-f(a) 12-2 10

---------- = ------------ = -------- = -2

b-a 1-6 -5

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If the triangles in the diagram are congruent, what is the value of x?

Natalija [7]

If shapes are congruent, then they are mathematically equal (same dimensions, angles etc.). So just locate where the angle x is on both triangles, it should have a value on or a calculable value on the other. If you provide us with the actual sheet I could walk you through it.

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2 years ago

Read 2 more answers

Amanda earns £285 a week.This is due to increase by 10%.How much is the increase

Natali [406]

Answer:

28.5

Step-by-step explanation:

i think itś 28.5 because 285 is after an increase of 10% which would mean 28.5 was the increase

3 0

2 years ago

Please help! i dont understand

kvv77 [185]

QUESTION 1

The given inequality is

$y\leq x-3$ and $y\geq -x-2$ .

If (3,-2) is a solution; then it must satisfy both inequalities.

We put x=3 and y=-2 in to both inequalities.

$-2\leq 3-3$ and $-2\geq -3-2$ .

$-2\leq 0$ :True and $-2\geq -5$ :True

Both inequalities are satisfied, hence (3,-2) is a solution to the given system of inequality.

QUESTION 2

The given inequality is

$y\:>\:-3x+3$ and $y\:>\: x+2$ .

If (1,4) is a solution; then it must satisfy both inequalities.

We put x=1 and y=4 in to both inequalities.

$4\:>\:-3(1)+3$ and $4\:>\: 1+2$ .

$4\:>\:0$ :True and $4\:>\: 3$ :True

Both inequalities are satisfied, hence (1,4) is a solution to the given system of inequality.

Ans: True

QUESTION 3

The given inequality is

$y\leq 3x-6$ and $y\:>\: -4x+2$ .

If (0,-2) is a solution; then it must satisfy both inequalities.

We put x=0 and y=-2 in to both inequalities.

$-2\leq 3(0)-6$ and $-2\:>\: -4(0)+2$ .

$-2\leq -6$ :False and $-2\:>\:2$ :False

Both inequalities are not satisfied, hence (0,-2) is a solution to the given system of inequality.

Ans:False

QUESTION 4

The given inequality is

$2x-y\:$ and $x+y\:>\:-1$ .

If (0,3) is a solution; then it must satisfy both inequalities.

We put x=0 and y=3 in to both inequalities.

$2(0)-3\:$ and $0+3\:>\:-1$ .

$-3\:$ :True and $3\:>\:-1$ : True

Both inequalities are satisfied, hence (0,3) is a solution to the given system of inequality.

Ans:True

QUESTION 5

The given system of inequality is

$y\:>\:2x-3$ and $y\:$ .

If (-3,0) is a solution; then it must satisfy both inequalities.

We put x=-3 and y=0 in to both inequalities.

$0\:>\:2(-3)-3$ and $0\:$ .

$0\:>\:-9$ ;True and $0\:$ :True

Both inequalities are satisfied, hence (-3,0) is a solution to the given system of inequality.

Ans:True

3 0

2 years ago

URGENT ! HELP ! Question is in photo below.

kifflom [539]

$\frac{3(x+5)}{2} \cdot 2=21\cdot 2$

Above step we use "Multiplication property of equality"

$3(x+5)=42$

In the above step we "Simplify on both sides of equation"

$3x+15 = 42$

In the above step we use "Distribution property"

$3x+15-15=42-15$

The above step is the result of using "Subtraction property of equality"

$3x=27$

Above step is result of "Combining the like terms"

$\frac{3x}{3} =\frac{27}{3}$

Above step is the result of using "Division property of equality"

$x=9$

Above step is result of "Simplifying fractions on either side of equation"

4 0

3 years ago

The function of f(x) = 3x + 2 has a domain of -3 < x < 5. What is the domain of f-1(x)?

Flura [38]

<h3>Answer: -7 < x < 17</h3>

====================================================

Explanation:

Plug in the lower bound of the domain, which is x = -3

f(x) = 3x+2

f(-3) = 3(-3)+2

f(-3) = -9+2

f(-3) = -7

If x = -3, then the output is y = -7. Since f(x) is an increasing function (due to the positive slope), we know that y = -7 is the lower bound of the range.

If you plugged in x = 5, you should find that f(5) = 17 making this the upper bound of the range.

The range of f(x) is -7 < y < 17

Recall that the domain and range swap places when going from the original function f(x) to the inverse $f^{-1}(x)$

This swap happens because how x and y change places when determining the inverse itself. In other words, you go from y = 3x+2 to x = 3y+2. Solving for y gets us y = (x-2)/3 which is the inverse.

-----------------------

In short, we found the range of f(x) is -7 < y < 17.

That means the domain of the inverse is -7 < x < 17 since the domain and range swap roles when going from original to inverse.

6 0

2 years ago