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11 months ago

Factoring a quadratic with leading coefficient greater than 1 3n^2+5n+2=0

1 answer:

8 0

The algebraic factor is the multiplication term that can be common to the whole equation thus the factorization form of 3n²+5n+2=0 will be (n + 1)(3n + 2) = 0.

<h3>What is an algebraic factor?</h3>

An algebraic factor is the multiplication of two algebraic terms.

The root of the quadratic equation formed by the algebraic factor is always real.

That term could be in form of summation multiplication or in subtraction.

As per the given quadratic equation,

3n²+5n+2=0

Let's 5n = 2n + 3n

3n²+ (3n + 2n) + 2 = 0

3n² + 3n + 2n + 2 = 0

(3n² + 3n) + (2n + 2) = 0

3n(n + 1) + 2(n + 1) = 0

(n + 1 )(3n + 2) = 0

Hence "The algebraic factor is the multiplication term that can be common to the whole equation thus the factorization form of 3n²+5n+2=0 will be (n + 1)(3n + 2) = 0".

For more about the algebraic factor,

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Which transformation shows that the two given circles are similar?

gregori [183]

Circle A -- center(2, 0), radius 8 Circle A' -- center(-1, 5), radius 3

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3 years ago

A survey of 46 college athletes found that 24 played volleyball, while 22 played basketball. a) If we pick one athlete survey pa

PSYCHO15rus [73]

Answer:

A) $\dfrac{11}{23}$

B) $\dfrac{88}{345}$

Step-by-step explanation:

A survey of 46 college athletes found that

24 played volleyball,
22 played basketball.

A) If we pick one athlete survey participant at random, the probability they play basketball is

$P_1=\dfrac{22}{46}=\dfrac{11}{23}$

B) If we pick 2 athletes at random (without replacement),

the probability we get one volleyball player is $\dfrac{24}{46}=\dfrac{12}{23};$
the probability we get another basketball player is $\dfrac{22}{45}$ (only 45 athletes left).

Thus, the probability we get one volleyball player and one basketball player is

$P_2=\dfrac{12}{23}\cdot \dfrac{22}{45}=\dfrac{88}{345}$

5 0

3 years ago

BEST ANSWER GETS BRAINLYEST

denis23 [38]

0.024 is 2.4%
0.125 is 12.5%
0.05 is 5%

Showing the workMultiply 0.05 by 100 to convert to percent:

<span>0.05 × 100 = </span>5 %

0.5 is 50%
Showing the work - Multiply 0.5 by 100 to convert to percent:

0.5 × 100 = 50 %
Showing the work -multiply 0.024 by 100 to convert to percent:

0.024 × 100 = 2.4 %

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3 years ago

Read 2 more answers

Devin is buying 2 concert tickets. The concert tickets have a regular price of $40 each. Devin has a coupon that gives a 5% disc

Svetach [21]

Given :

Devin is buying 2 concert tickets. The concert tickets have a regular price of $40 each.

Devin has a coupon that gives a 5% discount off of the regular price of the tickets. He will then pay a 10% purchasing fee on the discounted price of the tickets.

To Find :

Devin's total cost of the two tickets after the discount and the fee.

Solution :

Discount on price, D = 40×0.05 = $2 .

Price of product after discount, P = $( 40 - 2 ) = $38 .

Now, total price after adding purchasing fee is :

T = P + (P×0.10)

T = 38 + (38×0.10)

T = 38 + 3.8

T = $41.8

Therefore, Devin's total cost of the two tickets after the discount and the fee is $41.8 .

Hence, this is the required solution.

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2 years ago

In a certain region of space, the potential is given by v=2x−5x2y 3yz2. How much is the magnitude of the electric field at point

Masja [62]

The magnitude of the electric field at the point (-2, 2, 0) is 46.52 V/m

<h3>How to calculate the electric field?</h3>

Since in a certain region of space, the potential is given by v = 2x − 5x²y 3yz²,

The electric field, E = -grad(V) where grad(V) = (dV/dx)i + (dV/dy)j + (dV/dz)k

Since V = 2x − 5x²y + 3yz²

dV/dx = d(2x − 5x²y + 3yz²)/dx

= d2x/dx - d5x²y/dx + d3yz²/dx

= 2 - 10xy + 0

= 2 - 10xy

dV/dy = d(2x − 5x²y + 3yz²)/dy

= d2x/dy - d5x²y/dy + d3yz²/dy

= 0 - 5x² + 3z²

= - 5x² + 3z²

dV/dz = d(2x − 5x²y + 3yz²)/dz

= d2x/dz - d5x²y/dz + d3yz²/dz

= 0 - 0 + 6z

= 6z

<h3>The electric field</h3>

So, E = -grad(V)

= -[(dV/dx)i + (dV/dy)j + (dV/dz)k]

= -[(2 - 10xy)i + (- 5x² + 3z²)j + (6z)k]

So, the electric field at (-2, 2, 0) is

E = -[(2 - 10xy)i + (- 5x² + 3z²)j + (6z)k]

E = -[(2 - 10(-2)(2))i + (- 5(2)² + 3(0)²)j + (6(0))k]

E = -[(2 + 40)i + (- 5(4) + 0)j + (0)k]

E = -[42i + (-20 + 0)j + (0)k]

E = -[42i - 20j + 0k]

E = -42i + 20j - 0k

<h3>The magnitude of the electric field</h3>

So, the magnitude of E at (-2, 2, 0) is

|E| = √[(-42)² + 20² + 0²]

= √[1764 + 400 + 0]

= √2164

= 46.52 V/m

So, the magnitude of the electric field at the point (-2, 2, 0) is 46.52 V/m

Learn more about electric field here:

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3 0

1 year ago