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3 years ago

What is the solution to 2x2+8x=x2-16?

Mathematics

2 answers:

natita [175]3 years ago

6 0

Answer:

x = -4

Step-by-step explanation:

=> 2x²+8x = x²-16

=> 2x²- x² + 8x + 16 = 0

=> x² + 8x + 16 = 0

Using mid-term break formula

=> x² + 4x + 4x + 16 = 0

=> x(x+4)+4(x+4) = 0

=> (x+4)(x+4) = 0

=> (x+4)² = 0

Taking square root on both sides

=> x+4 = 0

=> x = -4

Semmy [17]3 years ago

3 0

Answer:

x = -4

Step-by-step explanation:

1. (2x2 + 8x) - (x2 - 16) = 0

2. Factoring x2+8x+16

The first term is, x2 its coefficient is 1 .

The middle term is, +8x its coefficient is 8 .

The last term, "the constant", is +16

Step-1 : Multiply the coefficient of the first term by the constant 1 • 16 = 16

Step-2 : Find two factors of 16 whose sum equals the coefficient of the middle term, which is 8 .

-16 + -1 = -17

-8 + -2 = -10

-4 + -4 = -8

-2 + -8 = -10

-1 + -16 = -17

1 + 16 = 17

2 + 8 = 10

4 + 4 = 8 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 4

x2 + 4x + 4x + 16

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x+4)

Add up the last 2 terms, pulling out common factors :

4 • (x+4)

Step-5 : Add up the four terms of step 4 :

(x+4) • (x+4)

Which is the desired factorization

Multiply (x+4) by (x+4)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (x+4) and the exponents are :

1 , as (x+4) is the same number as (x+4)1

and 1 , as (x+4) is the same number as (x+4)1

The product is therefore, (x+4)(1+1) = (x+4)2

(x + 4)2 = 0

Solve : (x+4)2 = 0

(x+4) 2 represents, in effect, a product of 2 terms which is equal to zero

For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : x+4 = 0

Subtract 4 from both sides of the equation :

x = -4

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A gas is said to be compressed adiabatically if there is no gain or loss of heat. When such a gas is diatomic (has two atoms per

Tems11 [23]

Answer:

The pressure is changing at $\frac{dP}{dt}=3.68$

Step-by-step explanation:

Suppose we have two quantities, which are connected to each other and both changing with time. A related rate problem is a problem in which we know the rate of change of one of the quantities and want to find the rate of change of the other quantity.

We know that the volume is decreasing at the rate of $\frac{dV}{dt}=-4 \:{\frac{cm^3}{min}}$ and we want to find at what rate is the pressure changing.

The equation that model this situation is

$PV^{1.4}=k$

Differentiate both sides with respect to time t.

$\frac{d}{dt}(PV^{1.4})= \frac{d}{dt}k\\$

The Product rule tells us how to differentiate expressions that are the product of two other, more basic, expressions:

$\frac{d}{{dx}}\left( {f\left( x \right)g\left( x \right)} \right) = f\left( x \right)\frac{d}{{dx}}g\left( x \right) + \frac{d}{{dx}}f\left( x \right)g\left( x \right)$

Apply this rule to our expression we get

$V^{1.4}\cdot \frac{dP}{dt}+1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}=0$

Solve for $\frac{dP}{dt}$

$V^{1.4}\cdot \frac{dP}{dt}=-1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}\\\\\frac{dP}{dt}=\frac{-1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}}{V^{1.4}} \\\\\frac{dP}{dt}=\frac{-1.4\cdot P \cdot \frac{dV}{dt}}{V}}$

when P = 23 kg/cm2, V = 35 cm3, and $\frac{dV}{dt}=-4 \:{\frac{cm^3}{min}}$ this becomes

$\frac{dP}{dt}=\frac{-1.4\cdot P \cdot \frac{dV}{dt}}{V}}\\\\\frac{dP}{dt}=\frac{-1.4\cdot 23 \cdot -4}{35}}\\\\\frac{dP}{dt}=3.68$

The pressure is changing at $\frac{dP}{dt}=3.68$ .

7 0

4 years ago

Which sentence is correct? A. -4 > 3 B. -4< -6 C. -4 > -7 D. -5 > -4

prisoha [69]

Answer:

C. -4 > -7

Step-by-step explanation:

answer= option C

3 0

3 years ago

Read 2 more answers

Complete the solution table from left to right for the quadratic function. (I did not select an answer, that was a mistake) Than

Karo-lina-s [1.5K]

Answer: OPTION D

Step-by-step explanation:

To complete the table, you need to substitute the values of "x" given in the table into the quadratic equation $y=x^{2}-x-6$ to obtain the corresponding value of "y".

Then:

When $x=-5$ :

$y=(-5)^{2}-(-5)-6$

$y=24$

When $x=-3$ :

$y=(-3)^{2}-(-3)-6$

$y=6$

When $x=-1$ :

$y=(-1)^{2}-(-1)-6$

$y=-4$

When $x=2$ :

$y=(2)^{2}-(2)-6$

$y=-4$

8 0

4 years ago

Please help I wanna get an a :(

kramer

Answer:

Graph C

Step-by-step explanation:

Point T is located on Graph C at T(1, 7). To help, (x, y) = count over however many spaces horizontally, then count however many spaces vertically.

It will always be this way.

4 0

3 years ago

Share £747 in the ratio 2:7 between tom and Ben. Tom will get Ben will get

Olenka [21]

Add the ratio:
2+7=9
747 divided by 9 = 83

Tom -
2x83 = £166

Ben -
7x83= £581

7 0

3 years ago