A pool cover tarp is 27 feet wide. What is the width of the pool cover in yards?

What two numbers multiply to -36 and add to -5

quester [9]

Answer:

9 and -4 is the answer it should be correct

5 0

3 years ago

How does the graph of g(x) = −(x + 3)^4 compare to the parent function of f(x) = x^4

kotykmax [81]

Answer: Option D

g(x) is shifted 3 units to the left and reflected over the x-axis.

Step-by-step explanation:

If we have a main function $f (x) = x ^ 4$

And we perform the transformation:

$g (x) = f (x + h) = (x + h) ^ 4$

Then it is fulfilled that:

If $h> 0$ the graph of f(x) moves horizontally h units to the left

If $h$ the graph of f(x) moves horizontally h units to the right

If we have a main function $f (x) = x ^ 4$

And we perform the transformation:

$g (x) = -f(x) = -x ^ 4$

Then it is fulfilled that:

The graph of g(x) is equal to the graph of f(x) reflected on the x axis

In this case we have to:

$g(x) = -(x + 3)^4$ and $f(x) = x^4$

Therefore $h=3>0$ and $g(x) = -f(x)$

This mean that: g(x) is shifted 3 units to the left and reflected over the x-axis.

6 0

3 years ago

A 500500-gallon tank initially contains 200200 gallons of brine containing 100100 pounds of dissolved salt. brine containing 11

mixer [17]

Let $A(t)$ denote the amount of salt in the tank at time $t$ . We're given that the tank initially holds $A(0)=100$ lbs of salt.

The rate at which salt flows in and out of the tank is given by the relation

$\dfrac{\mathrm dA}{\mathrm dt}=\underbrace{\dfrac{11\text{ lb}}{1\text{ gal}}\times\dfrac{44\text{ gal}}{1\text{ min}}}_{\text{rate in}}-\underbrace{\dfrac{A(t)}{200+(44-11)t}\times\dfrac{11\text{ gal}}{1\text{ min}}}_{\text{rate out}}$
$\implies A'(t)+\dfrac{11}{200+33t}A(t)=484$

Find the integrating factor:

$\mu(t)=\exp\left(\displaystyle\int\frac{11}{200+33t}\,\mathrm dt\right)=(200+33t)^{1/3}$

Distribute $\mu(t)$ along both sides of the ODE:

$(200+33t)^{1/3}A'(t)+11(200+33t)^{-2/3}A(t)=484(200+33t)^{-1/3}$
$\bigg((200+33t)^{1/3}A(t)\bigg)'=484(200+33t)^{-1/3}$
$A(t)=484\displaystyle\int(200+33t)^{-1/3}\,\mathrm dt$
$A(t)=22(200+33t)^{2/3}+C$

Since $A(0)=100$ , we get

$100=22(200)^{2/3}+C\implies C\approx-652.39$

so that the particular solution for $A(t)$ is

$A(t)=22(200+33t)^{2/3}-652.39$

The tank becomes full when the volume of solution in the tank at time $t$ is the same as the total volume of the tank:

$200+(44-11)t=500\implies 33t=300\implies t\approx9.09$

at which point the amount of salt in the solution would be

$A(9.09)\approx733.47\text{ lb}$

4 0

3 years ago

What is the area of this figure ?

PIT_PIT [208]

<span> Remember that what you must do for this case is to calculate the area of the parallelogram and add it to the area of the rectangle.
</span> Palelogram area:
Knowing the base and the height, the area of the parallelogram is calculated by its formula:
A1 = b * h
We have then
b = root ((- 4 - (- 10)) ^ 2+ (2-2) ^ 2) = 6
h = root ((- 7 - (- 7)) ^ 2+ (3-2) ^ 2) = 1
A1 = (6) * (1) = 6 units ^ 2
Rectangle area
A2 = L * W
We have then:
L = root ((1 - (- 2)) ^ 2 + (- 3 - (- 4)) ^ 2) = 3.16227766
W = root ((- 4 - (- 2)) ^ 2+ (2 - (- 4)) ^ 2) = 6.32455532
A2 = (3.16227766) * (6.32455532)
A2 = 20 units ^ 2
The total area is the sum of both ares:
A = A1 + A2
A = 6 + 20
A = 26 units ^ 2
Answer:
the area of this figure
A = 26 units ^ 2

5 0

4 years ago

Best answer gets the points!!!!

Anvisha [2.4K]

The inscribed angle theorem says that the measure of angle BDC is 2 times larger than the measure of angle BAC.

Angle CBD has measure 44 degrees, and we're told angles CBD and BCD are congruent. This means triangle BCD is isosceles.

The interior angle measures of any triangle add up to 180 degrees, so the measure of angle BDC must be

$m\angle BDC=180^\circ-2(44^\circ)=92^\circ$

Then $m\angle BAC=\dfrac{92^\circ}2=46^\circ$ .

6 0

3 years ago