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Studentka2010 [4]

2 years ago

11

In the process of proving that opposite sides of a parallelogram are congruent, Ross drew a diagonal of the parallelogram and de

termined that the two triangles formed are congruent. He then concluded that opposite sides must be congruent, because corresponding parts of congruent triangles are congruent.
Using his markings in the diagram, which postulate allowed him to determine that the two triangles formed are congruent?

A) AAS
B) ASA
C) SAS
D) SSS

1 answer:

ioda2 years ago

7 0

Answer:

(B) ASA

Step-by-step explanation:

we will verify each options

option-A:

we can see that there is no consecutive two angles

so, this postulates can not be true

so, this is FALSE

option-B:

We can see that

one angle and then side and another angle are equivalents

so, this is TRUE

option-C:

We can see that

one side and two angles are equivalents

so, this is FALSE

option-D:

we can see that

one side and two angles are equivalents

so, this is FALSE

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Due tomorrow Please help!!

anastassius [24]

Answer:

A

$\frac{1}{8}$ = $\frac{b}{4^{2} }$

b = $\frac{1}{8}$ × $4^{2}$

b = $\frac{4^{2} }{8}$

then b = $\frac{c^{2} }{a}$ that is ORANGE

B

-2 - v = -7

v = -7 +2

then v = k + m that is BROWN

C

$\frac{14}{q}$ = $\frac{-7}{-4}$

q = $\frac{14 * -4 }{-7}$

then q = $\frac{ps}{r}$ that is YELLOW

D

4m + 2(n) = 5 (n)

4m = 5 (n) - 2n

4m = 3n

m = $\frac{3n}{4}$

then m = $\frac{3n}{4}$ that is RED

E

-8 = $\frac{x}{-5}$ - 6

$\frac{x}{-5}$ = -8 + 6

x = -5 (-8 + 6)

then x = y( w + z ) that is LIGHT GREEN

7 0

2 years ago

A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int

Wittaler [7]

Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}$

By expanding the previous equation:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)$

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

$V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0$

Since there is no accumulation within the tank, expression is simplified to this:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}$

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

$V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}$ , where $c(0) = 0 \frac{pounds}{gallon}$ .

$\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}$

The solution of this equation is:

$c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})$

The salt concentration after 8 minutes is:

$c(8) = 0.166 \frac{pounds}{gallon}$

The instantaneous amount of salt in the tank is:

$m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds$

3 0

3 years ago

Find f(-4) if f(x) = 3x - 6.<br><br> A 6<br> B -6<br> C 18<br> D -18

brilliants [131]

Answer:

f(-4) = -18

Step-by-step explanation:

f(-4) means x = - 4

So Plug in x = - 4 into f(x) = 3x - 6

f(-4) = 3(-4) - 6

= -12 - 6

= -18

So

f(-4) = -18

8 0

2 years ago

Read 2 more answers

Rewrite the following expression.

faust18 [17]

We have been given the expression

$x^{\frac{9}{7}}$

We have the exponent rule

$x^{\frac{a}{b}}= x^{a^{(\frac{1}{b})}}$

Using this rule, we have

$x^{\frac{9}{7}}= x^{9^{(\frac{1}{7})}}$

Now, using the fact that $x^{\frac{1}{n}}=\sqrt[n]{x}$ , we get

$x^{\frac{9}{7}}= \sqrt[7]{x^9}\\
\\
x^{\frac{9}{7}}=\sqrt[7]{x^7\times x^2}\\
\\
x^{\frac{9}{7}}=x\sqrt[7]{x^2}$

D is the correct option.

6 0

2 years ago

Read 2 more answers

What are the zeros of the function f(x) = x2 + 8x +4, expressed in simplest radical form?

Elanso [62]

Answer:

x = - 4 ± 2 $\sqrt{3}$

Step-by-step explanation:

Given

f(x) = x² + 8x + 4

To find the zeros let f(x) = 0, that is

x² + 8x + 4 = 0 ( subtract 4 from both sides )

x² + 8x = - 4

To solve using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(4)x + 16 = - 4 + 16

(x + 4)² = 12 ( take the square root of both sides )

x + 4 = ± $\sqrt{12}$ = ± 2 $\sqrt{3}$ ( subtract 4 from both sides )

x = - 4 ± 2 $\sqrt{3}$

Thus the zeros are

x = - 4 - 2 $\sqrt{3}$ and x = - 4 + 2 $\sqrt{3}$

5 0

3 years ago