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3 years ago

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Mathematics

1 answer:

Troyanec [42]3 years ago

3 0

The graph has a y-intercept of 2 and is shifted to the right 6 from the parent function.

The parent function, y=√x, looks like a parabola laid on its side. We generally only consider the positive square root unless told otherwise. Since we have √(x-6) instead of just √x, the graph is shifted to the right 6 units. The +2 at the end of the equation shifts the graph up 2.

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I NEED HELP!! please show all work

PtichkaEL [24]

Take the logarithm of both sides. The base of the logarithm doesn't matter.

$4^{5x} = 3^{x-2}$

$\implies \log 4^{5x} = \log 3^{x-2}$

Drop the exponents:

$\implies 5x \log 4 = (x-2) \log 3$

Expand the right side:

$\implies 5x \log 4 = x \log 3 - 2 \log 3$

Move the terms containing x to the left side and factor out x :

$\implies 5x \log 4 - x \log 3 = - 2 \log 3$

$\implies x (5 \log 4 - \log 3) = - 2 \log 3$

Solve for x by dividing boths ides by 5 log(4) - log(3) :

$\implies \boxed{x = -\dfrac{ 2 \log 3 }{ 5 \log 4 - \log 3 }}$

You can stop there, or continue simplifying the solution by using properties of logarithms:

$\implies x = -\dfrac{ \log 3^2 }{ \log 4^5 - \log 3 }$

$\implies x = -\dfrac{ \log 9 }{ \log 1024 - \log 3 }$

$\implies \boxed{x = -\dfrac{ \log 9 }{ \log \frac{1024}3 }}$

You can condense the solution further using the change-of-base identity,

$\implies \boxed{x = -\log_{\frac{1024}3}9}$

5 0

2 years ago

What is 4(x-7)=2(x+3)?

hram777 [196]

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

4(x−7)=2(x+3)

Simplify both sides of the equation.

4(x−7)=2(x+3)

4x+−28=2x+6

4x−28=2x+6

Subtract 2x from both sides.

4x−28−2x=2x+6−2x

x−28=6

Add 28 to both sides.

2x−28+28=6+28

2x=34

Divide both sides by 2.

2x/2 = 34/2

x = 17

5 0

3 years ago

Read 2 more answers

Well when you do a problem and it's multiplication and you have to us your math skills and then when you get it wrong don't that

masha68 [24]

Not necessarily. You could have done your multiplication wrong. Or in some cases, yes, you could have to use another skill. For example, you can't solve an optimization problem with addition, you need some calculus skills under your belt.

8 0

3 years ago

What is A number divided by 82

lara [203]

Answer:

Hey there, Lets solve this step by step.

A number t divided by 82

Let the number be represented by y.

t divided by 82 = t / 8

Therefore-

In algebraic expressions, "y" is normally used as the dependent variable and "x" is normally used as the independent variable, instead of other variables. So that is why i used the variable y in the equation.

Step-by-step explanation:

6 0

3 years ago

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for every 5 pounds of pasta served , 15 people can be fed. how many people can be fed with 4 pounds of pasta?

Sidana [21]

Answer:

Step-by-step explanation:

its direct proportion. 15 divided by 5 is 3 so you must multiply 3 by 4 to get the amount of people, which is 12

7 0

3 years ago