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3 years ago

Rewrite the equation y-3=2(x+4) into slope form

Mathematics

1 answer:

soldi70 [24.7K]3 years ago

4 0

Answer:

Step-by-step explanation:

So we have y-3=2(x+4)

So the first thing we want to do is distribute the 2 in front of the (x+4)

2(x+4) = 2x+8

Which means we have:

y-3=2x+8

Remember we need to get it into the form y=mx+b

As you can see here the 3 is preventing our equation from being in that form to we need to add it to both sides. This leaves us with:

y - 3 + 3 = 2x+8+3

Which gives: y = 2x+11

Therefore the slope form of this equation is y = 2x+11

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Exponential function f is represented by the table. x -2 -1 0 1 2 f(x) -46 -22 -10 -4 -1 Function g is represented by the equati

Scrat [10]

The statement that describes better about function is "Both functions are increasing, but function g increases at a faster average rate." since option (c) is correct.

Given the table

x f(x)

-2 -46

-1 -22

0 -10

1 -4

2 -1

We have to choose which statement describes better about function

Let us assume $f(x)=ab^x+c$

at x=0, f(0)=-10

So, -10 =a+c

Similarly, by satisfying the above table in the f(x)

$f(x)=\frac{33}{5} (\frac{1}{11})^x-\frac{17}{5}$

$f'(x) > 0$

So we can say that f(x) is an increasing function.

$g(x) = - 18 (\frac{1}{3} )^ x + 2$

$g^ \prime (x) = - 18 (\frac{1}{3} )^ x ln(1/3)$

ln(1/3) < 0

So, g^ \prime (x) > 0

So, g(x) is an increasing function.

For any x∈f(x) and x∈g(x) $g'(x) > f'(x)$

So, g increases at a faster average rate

Thus, Both functions are increasing, but function g increases at a faster average rate.

Learn more about increasing functions here: brainly.com/question/12940982

#SPJ10

7 0

2 years ago

PQR is a right angled triangle calculate the size of angle marked x

romanna [79]

Answer:

$\displaystyle x \approx 37.4^\circ$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Trigonometry

[Right Triangles Only] SOHCAHTOA
[Right Triangles Only] cosθ = adjacent over hypotenuse

Step-by-step explanation:

Step 1: Define

Angle θ = x

Adjacent Leg = 5.8

Hypotenuse = 7.3

Step 2: Solve for x

Substitute in variables [Cosine]: $\displaystyle cosx^\circ = \frac{5.8}{7.3}$
[Fraction] Divide: $\displaystyle cosx^\circ = 0.794521$
[Equality Property] Trig inverse: $\displaystyle x^\circ = cos^{-1}(0.794521)$
Evaluate trig inverse: $\displaystyle x = 37.39^\circ$
Round: $\displaystyle x \approx 37.4^\circ$

8 0

3 years ago

Suppose you choose a marble from a bag containing 5 red marbles, 3 white marbles, and 6 blue marbles. You return the first marbl

Aneli [31]

$|\Omega|=14^2=196\\
|A|=5\cdot6\cdot2=60\\\\
P(A)=\dfrac{60}{196}=\dfrac{15}{49}$

5 0

3 years ago

What is one and one fourth times 30

n200080 [17]

1 1/4*30=37.5 because, first to make this easier to work with I like to turn the fraction into a decimal like so, 1/4=.25 because 1/4=.25 so 1/4=.25, so now we have 1.25*30=? What this is pretty much saying is that 30+(25% of 30)=? Which to solve this we just need to find how much 25% is of 30 which is .25*30=7.5 because 7.5*4=30 making it true that this is 25% of 30. Now what we have to do is take 30+7.5 (because we have a 1 infront of the 25% we add this instead of subtract it, if we had no whole number infront of the 30 and where solving this that way we would have to subtract instead of add) which adds up to be are end answer of 37.5.

Hope that this helps and makes sense, Enjoy!=)

6 0

3 years ago

25 apples to 10 oranges. What is the rate of the fruit

Klio2033 [76]

Answer:

The rate of the fruit is 5 apples to 2 oranges.

Step-by-step explanation:

The rate of the fruit is the ratio of apples to oranges. That is, the number of apples divided by the number of oranges into its simplest fraction form:

$x = \frac{25\,apples}{10\,oranges}$

$x = \frac{5\,apples}{2\,oranges}$

The rate of the fruit is 5 apples to 2 oranges.

6 0

3 years ago