Ask question

Ask question

All categories

4 years ago

5

The variable z is directly proportional to x, and inversely proportional to y. When x is 16 and y is 5, z has the value 16. What

is the value of z when x= 21, and y= 14 Round to at least the thousandths place if needed.

1 answer:

uysha [10]4 years ago

5 0

Answer:

z = 7.5

Step-by-step explanation:

Given that z is directly proportional to x and inversely proportional to y then the equation relating them is

z = $\frac{kx}{y}$ ← k is the constant of proportionality

To find k use the condition when x = 16, y = 5, z = 16, then

k = $\frac{zy}{x}$ = $\frac{16(5)}{16}$ = 5

z = $\frac{5x}{y}$ ← equation of proportionality

When x = 21, y = 14, then

z = $\frac{5(21)}{14}$ = 7.5

You might be interested in

Find the midpoint of the segment connecting (4,7) to (-2,3).

Vadim26 [7]

Answer:

<h2>Midpoint (1 , 5)</h2>

Step-by-step explanation:

Let (x , y) be the coordinates of the midpoint then:

$x=\frac{4+(-2)}{2} = 1\\\\y=\frac{7+3}{2} =5$

6 0

3 years ago

Solve x2 + 14x + 17 = –96 for x

jarptica [38.1K]

For this case we have to:

Given the quadratic equation of the form:

$ax ^ 2 + bx + c = 0$

The roots are given by:

$x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}$

If we have: $x ^ 2 + 14x + 17 = -96$

We can rewrite it in the following way:

$x ^ 2 + 14x + 17 + 96 = 0\\x ^ 2 + 14x + 113 = 0$

Where:

$a = 1\\b = 14\\c = 113$

Where we have:

$x = \frac {-14 \pm \sqrt {(14) ^ 2-4 (1) (113)}} {2 (1)}$

$x = \frac {-14 \pm \sqrt {(196-452)}} {2}$

$x = \frac {-14 \pm \sqrt {-256}} {2}$

By definition: $\sqrt {-1} = i$

$x = \frac {-14 \pm \sqrt {256} i} {2}$

$x = \frac {-14 \pm16i} {2}$

$x = \frac {-14} {2} \pm \frac {16i} {2}$

$x = -7 \pm8i$

Thus, the roots are given by imaginary numbers:

$x_ {1} = - 7 + 8i\\x_ {2} = - 7-8i$

Answer:

$x_ {1} = - 7 + 8i\\x_ {2} = - 7-8i$

5 0

3 years ago

Read 2 more answers

What is the smallest solution to this equation?

Lapatulllka [165]

Answer:

x = - 6

Step-by-step explanation:

Given

$\frac{2}{3}$ x² = 24 ( multiply both sides by 3 )

2x² = 72 ( divide both sides by 2 )

x² = 36 ( take the square root of both sides )

x = ± $\sqrt{36}$ ← note plus or minus

x = ± 6

solutions are x = - 6, x = + 6

The smallest solution is x = - 6

8 0

3 years ago

PLEASE AND THANK YOU CONFUSED ON THIS

ICE Princess25 [194]

After staring at this for a few seconds, I think the equation

$-5\sqrt{10}\cdot\sqrt{15}=[1]\sqrt{[2]}$

is asking you to simplify the left hand side so that it has a form matching the right hand side, and [1] and [2] are placeholders. My guess is that they're supposed to be integers.

Notice that

$\sqrt{10}=\sqrt{5\cdot2}=\sqrt5\cdot\sqrt2$

$\sqrt{15}=\sqrt{5\cdot3}=\sqrt5\cdot\sqrt3$

$\implies\sqrt{10}\cdot\sqrt{15}=(\sqrt5)^2\cdot\sqrt2\cdot\sqrt3=5\sqrt{2\cdot3}=5\sqrt6$

Then multiplying by -5, we have

$-5\sqrt{10}\cdot\sqrt{15}=-25\sqrt6$

so I believe [1] = -25, and [2] = 6.

5 0

3 years ago

Help me with this one

vaieri [72.5K]

Plant (A) have a higher median at 6 and the IQR is low at 3, however, Plant (B) has a lower median of 5 but High IQR of 4 so the Plant (B) is growth is high.
hopes loves.

3 0

3 years ago