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3 years ago

A 140-meter rope is cut into two pieces. One piece is four times as long as the other. How long is each piece?

Mathematics

1 answer:

grandymaker [24]3 years ago

3 0

Answer:

28meters and 112meters

Step-by-step explanation:

one piece is x

the other is 4x

therefore; 4x+x=140

5x= 140

divide both sides by 5

x=28

4x=4(28)

=112

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Solve for substitution 8x+2y=13 and 4x+y=11

damaskus [11]

Solving for X:
1) y=-8x+6.5 y=-4x+11
2) -8x+6.5=-4x+11
3) -8x=-4x+11-6.5 (Subtract 6.5 from both sides)
4) -8x+4x=11-6.5 (Add 4x to both sides)
5)-4x=4.5
5)x=-1.125

Solving for Y:
y=-8(-1.125)+6.5
y=9+6.5
y=15.5

y=-4(-1.125)+11
y=4.5+11
y=15.5

x=-1.125
y=15.5
or
(-1.125,15.5)

7 0

3 years ago

The probability of getting a head when a biased coin is tossed is . The coin is tossed three times. Find the following probabili

S_A_V [24]

Answer:

a) P(three tails) = $\frac{1}{8}$

b) P(two tails followed by one head) = $\frac{1}{8}$

Step-by-step explanation:

coin is tossed three times so, outcome is

HHH, TTT, HTH, THH, HHT, THT, TTH, HTT.

Hence sample space will be

S = {HHH, TTT, HTH, THH, HHT, THT, TTH, HTT}

chance of getting three tails is '1' i.e. TTT

hence,

P(three tails) = $\frac{1}{8}$

two tails followed by one head is TTH

so, chance of getting that outcome is also '1'

hence,

P(two tails followed by one head) = $\frac{1}{8}$

6 0

3 years ago

Use the Chain Rule to find the indicated partial derivatives. z = x^4 + xy^3, x = uv^4 + w^3, y = u + ve^w Find : ∂z/∂u , ∂z/∂v

k0ka [10]

I'll use subscript notation for brevity, i.e. $\frac{\partial f}{\partial x}=f_x$ .

By the chain rule,

$z_u=z_xx_u+z_yy_u$

$z_v=z_xx_v+z_yy_v$

$z_w=z_xx_w+z_yy_w$

We have

$z=x^4+xy^3\implies\begin{cases}z_x=4x^3+y^3\\z_y=3xy^2\end{cases}$

and

$\begin{cases}x=uv^4+w^3\\y=u+ve^w\end{cases}\implies\begin{cases}x_u=v^4\\x_v=4uv^3\\x_w=3w^2\\y_u=1\\y_v=e^w\\y_w=ve^w\end{cases}$

When $u=1,v=1,w=0$ , we have

$\begin{cases}x(1,1,0)=1\\y(1,1,0)=2\end{cases}\implies\begin{cases}z_x(1,2)=12\\z_y(1,2)=12\end{cases}$

and the partial derivatives take on values of

$\begin{cases}x_u(1,1,0)=1\\x_v(1,1,0)=4\\x_w(1,1,0)=0\\y_u(1,1,0)=1\\y_v(1,1,0)=1\\y_w(1,1,0)=1\end{cases}$

So we end up with

$\boxed{\begin{cases}z_u(1,1,0)=24\\z_v(1,1,0)=60\\z_w(1,1,0)=12\end{cases}}$

3 0

3 years ago

Number 7 thanks ASAP ASAP

stellarik [79]

Answer:

Price is $1088 (agrees with answer B)

Step-by-step explanation:

Notice that the linear equation that represents this relationship can be estimated via finding the slope and y-intercept using a couple of the given points on the plane (for example (5, 140), and (10, 200), which results in;

Price = 12 x + 80

where "x" is the number of computers shipped.

Then, to ship 84 computers, we have the following price:

Price = 12 (84) + 80 = 1088

Then the price is $1088.

6 0

3 years ago

What is this functie<br> f(x) = 2x + 5

Aloiza [94]

Slope function
Hope this will help!

8 0

3 years ago

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