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3 years ago

Freddy poured 1.4 liters of soda pop from a full 2-liter container. How much soda pop was left in the container?

Mathematics

2 answers:

eduard3 years ago

7 0

0.6 liters because 2-1.4 is 0.6

german3 years ago

6 0

Answer:

0.6 liters left

Step-by-step explanation:

So we know that the container is filled with 2 liters.

We also know that he poured 1.4 liters out of the container.

This leads to the conclusion

2 - 1.4 = 0.6

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Triangle DEF has vertices D(0,0), E(7,0), and F(3,7).

Leni [432]

Answer:

(3, 1.7)

Step-by-step explanation:

The point at which the vertices of a triangle meet is known as the orthocenter of the triangle. The orthocenter passes through the vertex of the triangle and is perpendicular to the opposite sides.

Two lines are perpendicular if the product of their slopes is -1.

The slope of the line joining D(0,0), F(3,7) is:

$m_1=\frac{7-0}{3-0}=\frac{7}{3}$

The slope of the line perpendicular to the line joining D and F is -3/7. The orthocenter is perpendicular to the line joining D and F and passes through vertex E(7, 0). The equation is hence:

$y-y_1=m(x-x_1)\\\\y-0=-\frac{3}{7} (x-7)\\\\y=-\frac{3}{7}x+3 \ .\ .\ .\ (1)$

The slope of the line joining E(7,0), and F(3,7). is:

$m_1=\frac{7-0}{3-7}=-\frac{7}{4}$

The slope of the line perpendicular to the line joining E and F is 4/7. The orthocenter is perpendicular to the line joining E and F and passes through vertex D(0, 0). The equation is hence:

$y-y_1=m(x-x_1)\\\\y-0=\frac{4}{7} (x-0)\\\\y=\frac{4}{7} x\ .\ .\ .\ (2)$

The point of intersection of equation 1 and equation 2 is the orthocenter. Solving equation 1 and 2 simultaneously gives:

x = 3, y = 1.7

4 0

3 years ago

HELPㅔPLS! BOTS STAY AWAY!! The mean amount of money withdrawn from

FromTheMoon [43]

The answer is $45 it wasn’t that hard

6 0

3 years ago

Read 2 more answers

Find a solution x = x(t) of the equation x′ + 2x = t2 + 4t + 7 in the form of a quadratic function of t, that is, of the form x(

Temka [501]

The particular quadratic solution to the ODE is found as follows:

$x=at^2+bt+c$
$x'=2at+b$

$(2at+b)+2(at^2+bt+c)=t^2+4t+7$
$2at^2+(2a+2b)t+(b+2c)=t^2+4t+7$

$\begin{cases}2a=1\\2(a+b)=4\\b+2c=7\end{cases}\implies a=\dfrac12,b=\dfrac32,c=\dfrac{11}4$

Note that there's also the fundamental solution to account for, which is obtained from the characteristic equation for the ODE:

$x'+2x=0\implies r+2=0\implies r=-2$

so that $x_c=Ce^{-2t}$ is a characteristic solution to the ODE, and the general solution would be

$x=Ce^{-2t}+\dfrac{t^2}2+\dfrac{3t}2+\dfrac{11}4$

4 0

4 years ago

At their family's pizzeria, Dave makes 6 pizzas in the first hour it is open and 3 pizzas each hour after that. Lauren makes 11

Nady [450]

Answer:

47 pizzas

Step-by-step explanation:

Dave makes 6 pizzas in the first hour it is open and 3 pizzas each hour after that.

If the number of hours after the first hour is represented as x, then the number of pizzas he makes after x hours is:

6 + 3x

Lauren makes 11 pizzas in the first hour and 3 pizzas each hour after that. Then:

11 + 3x

The pizzeria is open for 6 hours in all, that is, 5 hours after the first hour.

This means that:

x = 5

The total amount of pizzas that Dave and Lauren make is:

6 + 3x + 11 + 3x

=> 17 + 6x

Therefore, the total amount of pizza they make 5 hours after the first hour is:

17 + 6(5) = 17 + 30 = 47 pizzas

3 0

3 years ago

5.b) If z^(1/2)=x^(1/2)+y^(1/2) , show that (x+y-z)^2=4xy

Rudik [331]

Answer:

Step-by-step explanation:

(x+y-z)²= 4xy
(x+y-z)²- 4xy = 0
(x+y-z)²-(2√x√y)² = 0
(x+y-z-2√x√y)(x+y-z+2√x√y) =0
[(√x-√y)²-z]*[(√x+√y)²-z]=0
(√x-√y)²-z = 0 or (√x+√y)²-z = 0

We have : z^(1/2)= x^(1/2)+y^(1/2) ⇒ √z = √x + √y ⇒ z = (√x + √y)²

so (√x+√y)²-z = 0

so (x+y-z)²= 4xy

3 0

3 years ago