If 5 + 20 times 2^2 minus 3x = 10 times 2^- 2x + 5, what is the value of x?

The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel:

Stels [109]

Answer:

SAS postulate

Step-by-step explanation:

In the figure attached, quadrilateral ABCD is shown.

The Side Angle Side (SAS) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

AB is congruent to DC, and DB is the side common to triangles ABD and BCD. The included angle between sides AB and DB is angle ABD which is congruent with angle BDC, the angle included between sides DB and DC.

7 0

3 years ago

A used-car dealer sold one car at a profit of 25 percent of the dealer's purchase price for that car and sold another car at a l

Daniel [21]

Answer:

C. 1000 loss.

Step-by-step explanation:

Let x represent purchase price of each car.

We have been given that a used-car dealer sold one car at a profit of 25 percent of the dealer's purchase price for that car and sold another car at a loss of 20 percent of the dealer's purchase price for that car.

We can represent the car that dealer sold with 25% profit to find purchase price as:

$x+0.25x=20,000$

$1.25x=20,000$

$\frac{1.25x}{1.25}=\frac{20,000}{1.25}$

$x=16,000$

Therefore, the purchase price of 1st car was $16,000.

We can represent the car that dealer sold with 20% loss to find purchase price as:

$x-0.20x=20,000$

$0.80x=20,000$

$\frac{0.80x}{0.80}=\frac{20,000}{0.80}$

$x=25,000$

Therefore, the purchase price of 2nd car was $25,000.

The total purchase price of both cars would be $16,000+25,000=41,000$

The total sale price of both cars $20,000+20,000=40,000$ .

We can see that the sale price of both car is less than purchase price by $1000, so the dealer got a loss of $1000.

Therefore, the dealer's total loss, in dollars, for the two transactions combined was 1000 and option C is the correct choice.

4 0

3 years ago

Which cannot be used in a proof?

Gwar [14]

Hello,

you may not used what you are going to prove in a proof (la thèse)

4 0

3 years ago

Read 2 more answers

All rhombuses are parallelograms, but not all parallelograms are rhombuses. What attribute does a rhombus have that a parallelog

spin [16.1K]

C. 2 sets of opposite congruent angles

3 0

3 years ago

Read 2 more answers

The rate of transmission in a telegraph cable is observed to be proportional to x2ln(1/x) where x is the ratio of the radius of

sergij07 [2.7K]

Answer:

The value of x that gives the maximum transmission is 1/√e ≅0.607

Step-by-step explanation:

Lets call f the rate function f. Note that f(x) = k * x^2ln(1/x), where k is a positive constant (this is because f is proportional to the other expression). In order to compute the maximum of f in (0,1), we derivate f, using the product rule.

$f'(x) = k*((x^2)'*ln(1/x) + x^2*(ln(1/x)')) = k*(2x\,ln(1/x)+x^2*(\frac{1}{1/x}*(-\frac{1}{x^2})))\\= k * (2x \, ln(1/x)-x)$

We need to equalize f' to 0

k*(2x ln(1/x) - x) = 0 -------- We send k dividing to the other side
2x ln(1/x) - x = 0 -------- Now we take the x and move it to the other side
2x ln(1/x) = x -- Now, we send 2x dividing (note that x>0, so we can divide)
ln(1/x) = x/2x = 1/2 ------- we send the natural logarithm as exp
1/x = e^(1/2)
x = 1/e^(1/2) = 1/√e ≅ 0.607

Thus, the value of x that gives the maximum transmission is 1/√e.

7 0

4 years ago