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2 years ago

What is the factored form of the following expression? 25x^2 + 70x+ 49

Mathematics

1 answer:

sertanlavr [38]2 years ago

6 0

Answer:

( 5x + 7 ) ²

Step-by-step explanation:

25 x ² + 70 x + 49

Identity Used

(a + b) ² = a ² + 2 ab + b ²

= 25 x ² + 35 x + 35 x + 49

= 5 x ( 5x + 7 ) + 7 ( 5 x + 7)

= ( 5x + 7 )

More to know about Algebraic Identities :-

➛ (a + b)² = a² + 2ab + b²
➛ (a - b)² = a² - 2ab + b²
➛ a² - b² = (a +b) (a-b)
➛ (x + a) (x + b) = x² + (a + b) x + ab
➛ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac
➛ (a + b)³ = a³ + b³ + 3ab (a + b)
➛ (a - b)³ = a³ - b³ - 3ab (a + b)
➛ a³ + b³ + c³ = 3abc (If a + b + c = 0)
➛ a² + b² + c² = (a + b + c)² - 2 (ab + bc + ca)

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LuckyWell [14K]

Slope is -1/2

You can get that by isolating the x by moving it to the other side then divide the y value by the other side.

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2 years ago

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Part A

Trava [24]

Answer:

The total water usage at the park this year, in gallons, U = 16,206 + 22.2·x

Step-by-step explanation:

The given parameters are;

The increase in water usage for both regular days and special event for the current year = 20%

The water usage for last year regular days = 13,505 gallons

The water usage per special event = 18.5 gallons

The total water usage = 13,616 gallons

Therefore, we have;

The water usage for regular days on the current year = 13,505 gallons + (20/100)×13,505 gallons = 16,206 gallons

The water usage per special event for the current year, x = 18.5 gallons + (20/100) × 18.5 gallons = 22.2 gallons

The total water usage, U, at the park this year in terms of 'x', the number of special events the park hosted is given by the sum of the amount of water used on regular days and the product of 'x', and the amount of water used per special event this year as follows;

U = 16,206 gallons + x × 22.2 gallons

∴ The total water usage at the park this year, U = 16,206 + 22.2·x

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2 years ago

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The table shows the functions representing the height and base of a triangle for different values of x

mars1129 [50]

ANSWER

B. A(x)=0.5 (f .g)(x)

EXPLANATION

The area of a triangle is calculated using the formula:

Area=0.5 Base × Height

The base is given by

g(x)=2x

and the height of the function is

$f(x)= {x}^{2} + 3$

This implies that:

A(x)=0.5f(x) × g(x)

A(x)=0.5 (f .g)(x)

3 0

3 years ago

65pts

r-ruslan [8.4K]

Answer:

Part 1)

$\sqrt{x+2}=x$ ......[1]

Equation 1 has an extraneous solution.

$\sqrt{3x+1}=4$ ......[2]

Equation 2 does not have extraneous solution.

Part 2)

$\sqrt{x+2}=x$ has an extraneous solution which is x = -1.
the equation $\sqrt{3x+1}=4$ does not have an extraneous solution.

Part 3)

The first equation $\sqrt{x+2}=x$ has an extraneous solution. The reason is that x = -1 does not satisfy the equation.
The second equation $\sqrt{3x+1}=4$ does not have an extraneous solution. The reason is that x = 5 satisfies the equation.

Step-by-step explanation:

Part 1)

Creating Two Radical Equations

Let us consider two radical equations

$\sqrt{x+2}=x$ ......[1]

Equation 1 has an extraneous solution.

$\sqrt{3x+1}=4$ ......[2]

Equation 2 does not have extraneous solution.

Part 2)

Solving Equation [1]

$\sqrt{x+2}=x$ ......[1]

$\mathrm{Square\:both\:sides}$

$\left(\sqrt{x+2}\right)^2=x^2$

$x+2=x^2$

$x^2-x-2=0$

$(x-2)(x+1)=0$

$x=2,\:x=-1$

$\mathrm{Check\:the\:solutions\:by\:plugging\:them\:into\:}\sqrt{x+2}=x$

Plugging x = 2

$\sqrt{2+2}=2$

$2 = 2$

2 is true.

Plugging x = -1

$\sqrt{\left(-1\right)+2}=-1$

$1 = -1$

-1 does not satisfy the solution. Therefore, -1 is an extraneous root.

Therefore, $\sqrt{x+2}=x$ has an extraneous solution which is x = -1.

Solving Equation [2]

$\sqrt{3x+1}=4$ ......[2]

$Square\:both\:sides$

$\left(\sqrt{3x+1}\right)^2=4^2$

$3x+1=16$

$3x=15$

$x=5$

$\mathrm{Check\:the\:solutions\:by\:plugging\:them\:into\:}\sqrt{3x+1}=4$

Plugging x = 5

$\sqrt{3\cdot \:5+1}=4$

$4=4$

As x = 5 satisfies the equation. So, the equation $\sqrt{3x+1}=4$ does not have an extraneous solution.

Hence, x = 5 is the solution of $\sqrt{3x+1}=4$ .

Part 3)

The first equation $\sqrt{x+2}=x$ has an extraneous solution. The reason is that x = -1 does not satisfy the equation.

Check this verification:

Plugging x = -1

$\sqrt{\left(-1\right)+2}=-1$

$1 = -1$

Hence, $\sqrt{x+2}=x$ has an extraneous solution which is x = -1.

The second equation $\sqrt{3x+1}=4$ does not have an extraneous. The reason is that x = 5 satisfies the equation.

Check this verification:

Plugging x = 5

$\sqrt{3\cdot \:5+1}=4$

$4=4$

Hence, $\sqrt{3x+1}=4$ does not have an extraneous solution.

Keywords: radical equation, extraneous solution

Learn more about radical equations from brainly.com/question/4532928

#learnwithBrainly

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3 years ago

Express 125 = 5x as a logarithmic equation.

Marizza181 [45]

Answer: x log[5] = log[125]

Explanation:

The original expression is 125 = 5^x

To express that as a logarithmic equation take logarithms on both sides:

log [125] = [log 5^x]

By the properties of the logartims of powers that is:

log [125] = x log[5]

And that is the equation required.

If you want to solve it, you can do 125 = 5^2, and apply the same property (logarithm of a power) to the left side, yielding to:

log [5^2 ]= x log[5]

=> 2 log[5] = x log[5]

=> 2 = x

3 0

2 years ago

What is the factored form of the following expression? 25x^2 + 70x+ 49​

What is the factored form of the following expression? 25x^2 + 70x+ 49