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ANEK [815]
3 years ago
12

Which of the following statements is not correct? A every square is a parallelogram B every parallelogram is a rectangle C every

rhombus is a parallelogram D every rectangle is a parallelogram
Mathematics
1 answer:
n200080 [17]3 years ago
7 0
A. A square is a special type of parallelogram, so every square is a parallelogram. A. is true.

B. Every parallelogram has two sets of opposite sides parallel, but not all angles are right angles. Only some parallelograms are rectangles, not all. B. is false.

C. A parallelogram with 4 congruent sides is a rhombus. A rhombus is a special type of parallelogram, so every rhombus is a parallelogram. C. is true.

D. A rectangle is a special type of parallelogram, so every rectangle is a parallelogram. D. is true.
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A tank initially contains 50 gallons of brine, with 30 pounds of salt in solution. Water runs into the tank at 6 gallons per min
balandron [24]

Answer:

1.857 minutes

Step-by-step explanation:

From the given information:

Consider the amount of salt present in the tank as x(t) at a given time (t); &

The volume of the solution = V(t)

At t = 0 i.e. (at initial conditions)  x(0) = 30; and V(0) = 50

However, the overall increase taken place for 1 gallon per minute is:

V(t) = 50 + t

The amount of salt x(t) at any given point for time (t) is;

\dfrac{x(t)}{V(t)}= \dfrac{x(t)}{50+t}

After 5 gallons of solution exit per minute; the concentration of the salt solution changes at:

\dfrac{dx(t)}{dt}= -\dfrac{5x(t)}{50+t}

Taking the integral of what we have above, we get:

In x(t) = - 5 In(t + 50) + In (C)

In x(t) = In (t+ 50)⁻⁵ + In (C)

In x(t) = In C ( t + 50)⁻⁵

x(t) = C(t + 50)⁻⁵      (General solution)

To estimate the required solution; we apply the initial conditions x(0) = 30;

Thus;

x(0) = C(50)⁻⁵ = 30

⇒ C = 30 × 50⁵

Hence; x(t) =  30 × 50⁵ × (t + 50)⁻⁵

The above expression can be re-written as:

x(t) = 25 \implies 30 \times \bigg ( \dfrac{50}{t+50} \bigg ) ^5= 25

i.e.

\bigg ( \dfrac{50}{t+50} \bigg ) ^5= \dfrac{25}{30}

\dfrac{50}{t+50}= \bigg ( \dfrac{25}{30}\bigg) ^{\dfrac{1}{5}}

\dfrac{50}{t+50}= 0.964192504

{50}= 0.964192504(t+50)

50 = 0.964192504t + 48.2096252

50 - 48.2096252 = 0.964192504t

1.7903748 =  0.964192504t

t = 1.7903748 / 0.964192504

t ≅ 1.857 minutes

We can thereby conclude that the estimated time it will require until there are 25 pounds of salt in the tank is 1.857 minutes.

7 0
2 years ago
What is the reflection image of P(0, 0) after two reflections, first across x = 4 and then across y = -3?
jek_recluse [69]

Answer:

The reflection image of P(0, 0) after two reflections is (8,-6)

Step-by-step explanation:

step 1

Find the coordinates of point P after reflection across x=4

we know that

The distance from point P to the line x=4 is equal to 4 units

so

(0,0) -----> (4+4,0) ----> (8,0)

The reflection image of P is (8,0)

step 2

Find the coordinates of point (8,0) after reflection across y=-3

The distance from point (8,0) to the line y=-3 is equal to 3 units

so

(8,0) -----> (8,-3-3) ----> (8,-6)

3 0
3 years ago
Hassan has 183/4 yard of fabric it takes 31
Karo-lina-s [1.5K]
Your question seems incomplete :-(
5 0
3 years ago
Which equation results from adding the equations in this system?
Diano4ka-milaya [45]

Answer:

  • D. - 5x = - 10

Step-by-step explanation:

<u>Given equations:</u>

  • -8x+8y = 8
  • 3x-8y=-18

<u>Add together:</u>

  • -8x + 8y + 3x - 8y = 8 - 18
  • - 5x = - 10

Correct option is D

7 0
3 years ago
Mike bought 2 3/4 pounds of riceHe wants to distribute it among bins that each hold 1/3 pound of rice. How many bins can he comp
KATRIN_1 [288]

Answer:

8 bins filled completely; remaining rice fills ⅓ bin.

Step-by-step explanation:

7 0
3 years ago
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