Which multiplication problem is represented by the model

Find the positive solution of x when:<br><br> 25 = 4/x²

sladkih [1.3K]

1) Multiply both sides by x²

$25 {x}^{2} \: = \: 4$

2) Divide both sides by 25

${x}^{2} \: = \: \frac{4}{25}$

3) Square root both sides

$x \: = \: \frac{2}{5}$

Viola!

7 0

3 years ago

The parent function f(x) = x^2 is vertically stretched by a scale factor of 2, translated 14 units right, and 6 units up. Which

Elena-2011 [213]

Answer:

$(1)\; G(x)=2(x-14)^2+6$

Step-by-step explanation:

Assuming, right and up are positive directions.

The given parent function, $f(x)=x^2$

Let $f_1(x)$ be the function when the parent function is stretched by a scale factor of 2.

So, $f_1(x)=2f(x)$

$\Rightarrow f_1(x)=2x^2$

Let $f_2(x)$ be the function when $f_1(x)$ is translated $14$ units right.

So, $f_2(x)=f_1(x-14)$

$\Rightarrow f_2(x)=2(x-14)^2$

Again, let $f_3(x)$ be the function when $f_2(x)$ is translated 4 units up.

So, $f_3(x)=f_2(x)+6$

$\Rightarrow f_3(x)=2(x-14)^2+6$

So, the resulting function, $f_3(x)=G(x)=2(x-14)^2+6$ .

Hence, option (1) is correct.

4 0

3 years ago

The mean purchase total is $93.80 and the median purchase total is $75.80. The store

sleet_krkn [62]

Answer:

Both decrease, but the mean has a more significant change.

Step-by-step explanation:

The first thing is to know what happens to the mean and the median, removing a value, the normal thing is that both change. Now, how much they would change, what we know is that when removing or removing this value, it is normal for both to decrease.

Since $ 500 is a much larger value than the mean, removing this value from the dataset will significantly decrease the mean. The median, on the other hand, will move to the next smaller number, so the change will be small or even none.

Therefore, both change, but the mean has a more significant change.

4 0

4 years ago

Street C is perpendicular to Street A and passes through

earnstyle [38]

Given:

Street C is perpendicular to Street A and passes through (4, -6).

The equation of street A is:

$y=-2x+2$

To find:

The equation of street C.

Solution:

The equation of street A is:

$y=-2x+2$

On comparing this equation with slope intercept form $y=mx+b$ , we get

$m_2=-2$

Slope of this line is -2.

We know that, the product of slopes of two perpendicular lines is always -1.

$m_1\times m_2=-1$

$m_1\times (-2)=-1$

$m_1=\dfrac{-1}{-2}$

$m_1=\dfrac{1}{2}$

The slope of street C is $m_1=\dfrac{1}{2}$ and it passes through the point (4,-6). So, the equation of street C is

$y-y_1=m(x-x_1)$

$y-(-6)=\dfrac{1}{2}(x-4)$

$y+6=\dfrac{1}{2}(x-4)$

Therefore, the point slope form of the street C's equation is $y+6=\dfrac{1}{2}(x-4)$ .

4 0

3 years ago

Determine the equation for a line that passes through the point M(-7, 3) and

adell [148]

Answer:

y = 2x/7 + 5

Step-by-step explanation:

the first line is defined by

7x - 2y + 3 = 0

in the most common way to write this we need an equation like y = ...

so, we isolate the y-expression in the equation :

2y = 7x + 3

y = (7x + 3) / 2 = 7x/2 + 3/2

the factor of x is the slope of the line, which is expressed by the y/x ratio indicating how many units y will change, when x changes e.g. 1 unit.

7/2 means that y will change by 7 units for every change in x by 2 units.

the slope of a perpendicular line is inverse to the slope of the original line, which means x and y are simply trading places (original x / original y).

so, the perpendicular slope of 7/2 is 2/7 (when x changes by 7 units, then y changes by 2 units).

that means the equation for the perpendicular line is something like

y = 2x/7 + c

the c we determine by using the coordinates of the given point (x and y values).

3 = 2×(-7)/7 + c = 2×(-1) + c = -2 + c

c = 5

so, the complete equation of the perpendicular line is

y = 2x/7 + 5

8 0

3 years ago