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Brilliant_brown [7]

3 years ago

15

If x

ss="latex-formula">
yz, and when y=-2, z=-3, x=30. when y=4, x=80. find z

1 answer:

Rom4ik [11]3 years ago

3 0

Answer: $z = 4$

Step-by-step explanation:

Given:

$x \alpha yz$

replacing the proportionality sign with a constant , we have :

$x = kyz$

substituting : $y = -2$ , $z = -3$ and $x = 30$ into the equation , we have :

$30 = k(-2)(-3)$

$30 = 6k$

divide through by 6

$k = 5$

substituting $k = 5$ into the equation , the equation becomes

$x = 5yz$

To find the value of z , when y = 4 , x = 80 , we will substitute the values into the formula , we have :

$80 = 5(4)(z)$

$80 = 20z$

dividing through by 20 , we have :

$z = 4$

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What is the value of x? Please show step by step.

3241004551 [841]

Start by using trig to find the length of the line LJ

The triangle KJL (big right angled triangle) has been given the following dimensions

Hypotenuse = $8 \sqrt{2}$
The adjacent angle is 30 degrees

Since we have the hypotenuse and the angle we must use the equation
opposite = Sin(angle) x Hypotenuse

Opposite= sin30 x $8 \sqrt{2}$

Opposite= $4 \sqrt{2}$

Therefore line LJ is $4 \sqrt{2}$

Now look at the smaller right angled triangle (LMJ)

Hypotenuse is the line LJ which is $4 \sqrt{2}$

The adjacent angle is 45

Since we have hypotenuse and angle we must use the equation opposite = sin(angle) * h

therefore
x= $4 \sqrt{2}$ * sin45= 4

3 0

3 years ago

F:[1/2,infinity)—>[3/4,infinity) <br> f(x)=x^2-x+1 <br> find the inverse of f(x);please explain

dexar [7]

Answer:

$f^{-1}(x)=\frac{1}{2}+\sqrt{x-\frac{3}{4}}$

Step-by-step explanation:

y=x^2-x+1

We want to solve for x.

I'm going to use completing the square.

Subtract 1 on both sides:

y-1=x^2-x

Add (-1/2)^2 on both sides:

y-1+(-1/2)^2=x^2-x+(-1/2)^2

This allows me to write the right hand side as a square.

y-1+1/4=(x-1/2)^2

y-3/4=(x-1/2)^2

Now remember we are solving for x so now we square root both sides:

$\pm \sqrt{y-3/4}=x-1/2$

The problem said the domain was 1/2 to infinity and the range was 3/4 to infinity.

This is only the right side of the parabola because of the domain restriction. We want x-1/2 to be positive.

That is we want:

$\sqrt{y-3/4}=x-1/2$

Add 1/2 on both sides:

$1/2+\sqrt{y-3/4}=x$

The last step is to switch x and y:

$1/2+\sqrt{x-3/4}=y$

$y=1/2+\sqrt{x-3/4}$

$f^{-1}(x)=1/2+\sqrt{x-3/4}$

8 0

3 years ago

What is 7/6 reduced to

evablogger [386]

7/6 is 1 and 1/6 (1 1/6) as a reduced fraction. 7/6 is an improper fraction. So, how many times does 6 go into 7, it goes into it one time and there is one remainder.

8 0

3 years ago

Read 2 more answers

In a group of dogs and their owners, there are exactly 20 heads and 64 legs. How many dogs are in the group

Juliette [100K]

Answer:

If we assume that everyone in the group is an owner, we would have

$20*2=40$ legs.

$64-40=24$ legs

Therefore, we need 24 more legs.

These 24 additional legs can be made from the difference of legs between the owners and dogs.

In this case, dogs have $4-2=2$ more legs than an owner.

24 ÷ 2 = 12.

There are 12 dogs in the group.

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%2072" id="TexFormula1" title="\sqrt{x} 72" alt="\sqrt{x} 72" align="absmiddle"

AveGali [126]

Answer:

Step-by-step explanation:

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4 0

3 years ago