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3 years ago

5

Write: 4.9x10^-2 as an ordinary number

1 answer:

svet-max [94.6K]3 years ago

6 0

$4.9\cdot10^{-2}=4.9\cdot\frac{1}{100}=4.9:100=0.049$

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A dog trainer has 96 ft of fencing that will be used to create a rectangular work area. Encloses area of 320 ft^2. What will be

Anastaziya [24]

Answer:

<em>The dimensions of the area will be 8 ft x 40 ft</em>

Step-by-step explanation:

<u>Area and Perimeter</u>

The perimeter can be understood as the distance measured around a shape. The area gives us the idea of the space occupied by the shape. Being w and l the width and length of a rectangle, the perimeter and areas can be computed as follows

$A=wl$

$P=2w+2l$

The dog trainer has 96 ft of fencing to cover a $320 ft^2$ rectangular area. This means that

$wl=320$

$2w+2l=96$

A system of equations is formed

$\left\{\begin{matrix}wl=320\\ 2w+2l=96\end{matrix}\right$

We divide the last equation by 2

$w+l=48$

solve for w

$w=48-l$

Replacing in the first equation

$(48-l)l=320$

Operating and arranging

$l^2-48l+320=0$

$(l-8)(l-40)=0$

We have two possible answers

$l=8,\ l=40$

Which gives us

$w=40,\ w=8$

In any case, the dimensions of the area will be 8 ft x 40 ft

6 0

3 years ago

Calling all mathemeticians

MAVERICK [17]

Wouldn’t be a,or d. I would honestly say B..

4 0

3 years ago

Read 2 more answers

NEED HELP WITH PART B

Sergeu [11.5K]

Answer:

y = -20x + 100

Step-by-step explanation:

As per your requirement For Part B, the solution is

The equation in slope-intercept form to model the relations is below:-

To reach 2 points on the graph the line passes through

lets use p1(0, 100), p2(1, 80)

now we will compute the slope:

$m = \frac{(y2 - y1)}{(x2 - x1)}$

$m = \frac{(80 - 100)}{(1 - 0)}$

= -20

and now use line equation in form point-slope:

y - y1 = m(x - x1)

y - 100 = -20(x - 0)

y = -20x + 100

6 0

3 years ago

Which function has an inverse function?

daser333 [38]

Answer: Option B

Step-by-step explanation:

By definition, only those functions that are one to one have an inverse function.

A function is one by one if there are not two different input values, $x_1$ and $x_2$ , that have the same output value y

Note that the function $f(x)= \frac{|x+3|}{5}$ is not a one-to-one function

When x=2 $f(x)= \frac{|2+3|}{5}=1\ ,\ \ y=1$

When x=8 $f(x)= \frac{|-8+3|}{5}=1\ \ ,\ y=1$

Note that the function $f(x)= \frac{x^4}{7}+ 27$ is not a one-to-one function

When x=1 $f(x)= \frac{(1)^4}{7}+27\ ,\ \ y=\frac{190}{7}$

When x=-1 $f(x)= \frac{(-1)^4}{7}+27\ ,\ \ y=\frac{190}{7}$

Note that the function $f(x)= \frac{1}{x^2}$ is not a one-to-one function

When x=1 $f(x)= \frac{1}{(1)^2}\ ,\ \ y=1$

When x=-1 $f(x)= \frac{1}{(-1)^2}\ ,\ \ y=1$

Then the answer is the option B.

You can verify that The function $f (x) = x ^ 5-3$ is a one-to-one function and therefore its inverse is a function

5 0

3 years ago

Bianca and Meredith are sisters. Meredith's height is 23 of Bianca's height plus 32 inches. Meredith is 60 inches tall. A girl i

jarptica [38.1K]

Answer:

Bianca's height = 42 inches

Step-by-step explanation:

Let x be the Bianca height.

Given:

Meredith height = 60 inches

We need to find the Bianca height.

Solution:

From the given statement the Meredith's height is $\frac{2}{3}$ of Bianca's height plus 32 inches, so the equation is.

Meredith's height = $\frac{2}{3}(Bianca\ height)+32$

Substitute Meredith's height in above equation.

$60=\frac{2}{3}x+32$

Now we solve the above equation for x.

$\frac{2}{3}x=60-32$

$\frac{2}{3}x=28$

By cross multiplication.

$x=\frac{3\times 28}{2}$

28 divided by 2.

$x= 3\times 14$

$x=42\ in$

Therefore, the height of the Bianca is 42 inches.

7 0

3 years ago