What is the value of z in the equation 3z − 7 = 14? (4 points)

What is the product?(4y − 3)(2y2 + 3y − 5)8y3 + 3y + 158y3 − 23y + 158y3 − 6y2 − 17y + 158y3 + 6y2 − 29y + 15

motikmotik

We need to find the product of :

$\mleft(4y-3\mright)\mleft(2y2+3y-5\mright)$

So, the result as following:

$\begin{gathered} \mleft(4y-3\mright)\mleft(2y^2+3y-5\mright) \\ =4y\cdot(2y^2+3y-5)-3\cdot(2y^2+3y-5) \\ =8y^3+12y^2-20y-(6y^2+9y-15) \\ =8y^3+12y^2-20y-6y^2-9y+15 \\ \\ =8y^3+6y^2-29y+15 \end{gathered}$

So, the answer is the option 4. 8y3 + 6y2 − 29y + 15

5 0

1 year ago

It takes Jack Frost 5 minutes to fly 35 minutes with the wind. It takes him 7 minutes to go 35 minutes against the wind. Determi

dezoksy [38]

Answer:his speed in still air is 6 miles per minute.

the speed of the wind is 1 mile per minute.

Step-by-step explanation:

Let x represent his speed in still air.

Let y represent the speed of the wind.

It takes Jack Frost 5 minutes to fly 35 miles with the wind. This means that his total speed would be x + y

Distance = speed × time

It means that

35 = 5(x + y)

35 = 5x + 5y - - - - - - - - - - -1

It takes him 7 minutes to go 35 miles against the wind. This means that his total speed would be x - y

It means that

35 = 7(x - y)

35 = 7x - 7y - - - - - - - - - - -2

Multiplying equation 1 by 7 and equation 2 by 5, it becomes

245 = 35x + 35y

175 = 35x - 35y

Adding both equations, it becomes

420 = 70x

x = 420/70 = 6

Substituting x = 6 into equation 1, it becomes

35 = 5 × 6 + 5y

35 = 30 + 5y

5y = 35 - 30 = 5

y = 5/5 = 1

5 0

3 years ago

The function v(r) 4/3 pie r to the 3rd = can be used to find the volume of air inside a basketball given its radius. What does V

umka21 [38]

Answer:

the volume of the basketball when the radius is r

Step-by-step explanation:

V(r) is a function name V and argument list (r). Often the letter of the function name is a reminder of what the function computes. Here, V is chosen as the name because it computes Volume. The function uses r (for radius) as its independent variable. That is why r is listed in parentheses next to the function name.

So, V(r) represents a function that computes the volume of a sphere with radius r.

6 0

3 years ago

#20

yKpoI14uk [10]

0.48 miles

Step-by-step explanation:

Step 1

It is given that the grade(slope) is 4%. This means that for every 100 miles traveled, the elevation changes by 4 miles.

Step 2

Hence for a distance of 12 miles , the elevation changes by 12*4/100 = 48/100 = 0.48 miles. [Using direct proportion]

6 0

3 years ago

Show that ( 2xy4 + 1/ (x + y2) ) dx + ( 4x2 y3 + 2y/ (x + y2) ) dy = 0 is exact, and find the solution. Find c if y(1) = 2.

fredd [130]

$\dfrac{\partial\left(2xy^4+\frac1{x+y^2}\right)}{\partial y}=8xy^3-\dfrac{2y}{(x+y^2)^2}$

$\dfrac{\partial\left(4x^2y^3+\frac{2y}{x+y^2}\right)}{\partial x}=8xy^3-\dfrac{2y}{(x+y^2)^2}$

so the ODE is indeed exact and there is a solution of the form $F(x,y)=C$ . We have

$\dfrac{\partial F}{\partial x}=2xy^4+\dfrac1{x+y^2}\implies F(x,y)=x^2y^4+\ln(x+y^2)+f(y)$

$\dfrac{\partial F}{\partial y}=4x^2y^3+\dfrac{2y}{x+y^2}=4x^2y^3+\dfrac{2y}{x+y^2}+f'(y)$

$f'(y)=0\implies f(y)=C$

$\implies F(x,y)=x^2y^3+\ln(x+y^2)=C$

With $y(1)=2$ , we have

$8+\ln9=C$

so

$\boxed{x^2y^3+\ln(x+y^2)=8+\ln9}$

8 0

3 years ago