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4 years ago

△MNP≅△QST. What is m∠S?

Mathematics

2 answers:

Cerrena [4.2K]4 years ago

4 0

Answer:

78°

Step-by-step explanation:

Corresponding parts of congruent triangles are congruent, so m∠S = m∠N, which is 78°.

LiRa [457]4 years ago

3 0

Answer:

$m\angle S=78^{\circ}$

Step-by-step explanation:

We have been given that △MNP≅△QST. We are asked to find the measure of angle S.

Since both angles are congruent, so measure of their corresponding angles would be equal.

$m\angle M=m\angle Q$

$m\angle N=m\angle S$

$m\angle P=m\angle T$

Since angle S corresponds to angle N and measure of angle N is 78 degrees, therefore, measure of angle S is 78 degrees as well.

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What are the potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2?

Dmitry_Shevchenko [17]

The potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)

<h3>How to determine the potential zeros of the function f(x)?</h3>

The function is given as:

f(x)=6x^4+ 2x^3 - 4x^2 +2

For a function P(x) such that

P(x) = ax^n +...... + b

The rational roots of the function p(x) are

Rational roots = ± Possible factors of b/Possible factors of a

In the function f(x), we have:

a = 6

b = 2

The factors of 6 and 2 are

a = 1, 2, 3 and 6

b = 1 and 2

So, we have:

Rational roots = ±(1, 2)/(1, 2, 3, 6)

Split the expression

Rational roots = ±1/(1, 2, 3, 6)/ and ±2/(1, 2, 3, 6)

Evaluate the quotient

Rational roots = ±(1, 1/2, 1/3, 1/6, 2, 1, 2/3, 1/3)

Remove the repetition

Rational roots = ±(1, 1/2, 1/3, 1/6, 2, 2/3)

Hence, the potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)

The complete parameters are:

The function is given as:

f(x) = 3x^3 + 2x^2 + 3x + 6

The potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)

Read more about rational roots at

brainly.com/question/17754398

#SPJ1

4 0

2 years ago

A tank is filled with 1000 liters of pure water. Brine containing 0.04 kg of salt per liter enters the tank at 9 liters per minu

klemol [59]

Answer:

The differential equation which describes the mixing process is $\frac{dc_{salt,out}}{dt} + \frac{2}{125}\cdot c_{salt,out} = \frac{71}{100000}$ .

Step-by-step explanation:

The mixing process within the tank is modelled after the Principle of Mass Conservation, which states that:

$\dot m_{salt,in} - \dot m_{salt,out} = \frac{dm_{tank}}{dt}$

Physically speaking, mass flow of salt is equal to the product of volume flow of water and salt concentration. Then:

$\dot V_{water, in, 1}\cdot c_{salt, in,1} + \dot V_{water, in, 2} \cdot c_{salt,in, 2} - \dot V_{water, out}\cdot c_{salt, out} = V_{tank}\cdot \frac{dc_{salt,out}}{dt}$

Given that $\dot V_{water, in, 1} = 9\,\frac{L}{min}$ , $\dot V_{water, in, 2} = 7\,\frac{L}{min}$ , $c_{salt,in,1} = 0.04\,\frac{kg}{L}$ , $c_{salt, in, 2} = 0.05\,\frac{kg}{L}$ , $\dot V_{water, out} = 16\,\frac{L}{min}$ and $V_{tank} = 1000\,L$ , the differential equation that describes the system is:

$0.71 - 16\cdot c_{salt,out} = 1000\cdot \frac{dc_{salt,out}}{dt}$

$1000\cdot \frac{dc_{salt, out}}{dt} + 16\cdot c_{salt, out} = 0.71$

$\frac{dc_{salt,out}}{dt} + \frac{2}{125}\cdot c_{salt,out} = \frac{71}{100000}$

3 0

3 years ago

What is the area of triangle ABC?

Stella [2.4K]

9514 1404 393

Answer:

C. 36√3 square units

Step-by-step explanation:

Your knowledge of special triangles tells you that height CD is ...

CD = 6√3

so the area is ...

A = 1/2bh

A = 1/2(12)(6√3) = 36√3 . . . . square units

_____

<em>Additional comment</em>

The 30°-60°-90° right triangle that is half an equilateral triangle has a short side equal to half the length of the long side. The Pythagorean theorem tells you that the middle-length side is √(2²-1²) = √3 times the shortest side. That is, the side length ratios in this "special" triangle are ...

1 : √3 : 2

This means the length DB is 12/2 = 6, and the length CD is 6√3.

7 0

3 years ago

12/15 divided by -1 1/6

alekssr [168]

Answer:-11/30

Step-by-step explanation:i think not 100% sure

4 0

2 years ago

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Simplify the radical expression.<br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B40%7D%20" id="TexFormula1" title=" \sqrt{40}

Elden [556K]

Answer:

√40 = √ ( 2× 2 ×2 ×5) = 2√10

.........

6 0

3 years ago