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3 years ago

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Let y be the difference of two numbers such that one number varies directly as x while the other number varies inversely as x. I

f y = -7 when x = -2, and y = 5 when x = 1. Express y in terms of x.

1 answer:

Ostrovityanka [42]3 years ago

3 0

Answer:

y is 5 units greater than x

Step-by-step explanation:

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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 <em>x</em> to the left side and factor out <em>x</em> :

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

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

Solve for <em>x</em> 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

3 years ago

Below is a pair of vectors. add them and insert your answer here: ab+bc=(-3-1)+(-4 2)=<br>

jarptica [38.1K]

Answer:

(-7, 1)

Step-by-step explanation:

Add the x and y values separately which is across from your screen to get the function which is (-7, 1).

8 0

2 years ago

Shanice's car is traveling 10 miles per hour slower than twice the speed of Brandon's car. She covers 93 miles in 1 hour 30 minu

joja [24]

Shanice's rate: 93 / 1.5 = 62 miles per hour

she is 10 miles slower than twice the speed of Brandon

62 +10 = 72

72/2 = 36

Brandon is driving 36 miles per hour

3 0

3 years ago

Divide 33 photos into two groups so the ratio is 4 to 7

Artist 52 [7]

33 photos in a 4x to 7x ratio

4x + 7x = 33
11x = 33
x = 3

33 photos can be put in a 4(3) to 7(3) ratio

which is a 12 to 21 ratio

so 12 photos on one side, and 21 on the other side to get the ratio of 4 to 7

Note:
<span>a(b) = ab = a x b = a times b</span>

5 0

3 years ago

Find the domain of the equation

goblinko [34]

The domain is all real numbers, since x can be any number and create a y value

This can be written in a few ways, including:

X:X

X: R

-(infinity sign) is less than or equal to X is less than or equal to (infinity sign)

8 0

3 years ago