Find the product of (x + 5)(x − 5).

12.15x19 Need this asap thanks yall have a blessed day :)

valentinak56 [21]

Answer:

The answer would be 230.85

5 0

2 years ago

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What decimal fraction is between 1.2 and 1.5

Readme [11.4K]

$1.2=1\frac{2}{10}=1\frac{2:2}{10:2}=1\frac{1}{5}\\\\1.5=1\frac{5}{10}=1\frac{5:5}{10:5}=1\frac{1}{2}\\\\1\frac{1}{5} < \boxed{1\frac{1}{4} < 1\frac{1}{3}}$

7 0

3 years ago

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Find all roots: x^3 + 7x^2 + 12x = 0 Show all work and check your answer.

Aliun [14]

The three roots of x^3 + 7x^2 + 12x = 0 is 0,-3 and -4

Solution:

We have been given a cubic polynomial.

$x^{3}+7 x^{2}+12 x=0$

We need to find the three roots of the given polynomial.

Since it is a cubic polynomial, we can start by taking ‘x’ common from the equation.

This gives us:

$x^{3}+7 x^{2}+12 x=0$

$x\left(x^{2}+7 x+12\right)=0$ ----- eqn 1

So, from the above eq1 we can find the first root of the polynomial, which will be:

x = 0

Now, we need to find the remaining two roots which are taken from the remaining part of the equation which is:

$x^{2}+7 x+12=0$

we have to use the quadratic equation to solve this polynomial. The quadratic formula is:

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Now, a = 1, b = 7 and c = 12

By substituting the values of a,b and c in the quadratic equation we get;

$\begin{array}{l}{x=\frac{-7 \pm \sqrt{7^{2}-4 \times 1 \times 12}}{2 \times 1}} \\\\{x=\frac{-7 \pm \sqrt{1}}{2}}\end{array}$

Therefore, the two roots are:

$\begin{array}{l}{x=\frac{-7+\sqrt{1}}{2}=\frac{-7+1}{2}=\frac{-6}{2}} \\\\ {x=-3}\end{array}$

And,

$\begin{array}{c}{x=\frac{-7-\sqrt{1}}{2}} \\\\ {x=-4}\end{array}$

Hence, the three roots of the given cubic polynomial is 0, -3 and -4

4 0

3 years ago

If p=(-3,-2) and q=(1,6) are the endpoints of the diameter of a circle find the equation of the circle

stira [4]

Answer:

The equation of the circle (x +1) )² +(y-(2))² = (2(√5))²

 or 

The equation of the circle x² + 2 x + y² - 4 y = 15

Step-by-step explanation:

Given points end Points are p(-3,-2) and q( 1,6)

The distance of two points formula

P Q = $\sqrt{x_{2} - x_{1})^{2} + ((y_{2} -y_{1})^{2} }$

P Q = $\sqrt{1 - (-3)^{2} + ((6 -(-2))^{2} }$

P Q = $\sqrt{16+64} = \sqrt{80}$

The diameter 'd' = 2 r

2 r = √80

= $\sqrt{16 X 5}$

= $4 \sqrt{5}$

r = 2√5

Mid-point of two end points

$(\frac{x_{1} + x_{2} }{2} , \frac{y_{1} +y_{2} }{2} ) = (\frac{-3+1}{2} ,\frac{-2 +6}{2} )$

= (-1 ,2)

Mid-point of two end points = center of the circle

(h,k) = (-1 , 2)

The equation of the circle

(x -h )² +(y-k)² = r²

(x -(-1) )² +(y-(2))² = (2(√5))²

x² + 2 x + 1 + y² - 4 y + 4 = 20

x² + 2 x + y² - 4 y = 20 -5

x² + 2 x + y² - 4 y = 15

Final answer:-

The equation of the circle (x +1) )² +(y-(2))² = (2(√5))²

 or 

The equation of the circle x² + 2 x + y² - 4 y = 15

6 0

3 years ago

A family has two cats named Gordo and Flaco. Gordo weighs 15 pounds and Flaco weighs 8 pounds. A cat’s weight is classified as u

Elena-2011 [213]

Answer:

Gordo's weight = 15 pounds

It is outside the healthy weight range and is in the top 5% of weights of cats.

Gordo's weight makes Gordo unhealthy.

Step-by-step explanation:

μ = mean weight = 9.5 pounds

σ = standard deviation = 1.5 pounds

This is a normal distribution problem

We first calculate the limit of the bottom 5% of weights

Let the z-score for this limit be z'

P(z < z') = 0.05

From the normal distribution table,

z' = -1.645

And the limit for the top 5% which is z" = 1.645.

The weight that corresponds to these scores are then calculated.

Standardized scores are given as

z = (x - μ)/σ

So,

z' = (limit for the bottom 5% - μ)/σ

-1.645 = (limit for the bottom 5% - 9.5)/1.5

limit of the bottom 5% = (-1.645)(1.5) + 9.5 = 7.033 pounds

z" = ( (limit for the top 5% - μ)/σ

1.645 = (limit for the top 5% - 9.5)/1.5

limit of the bottom 5% = (1.645)(1.5) + 9.5 = 11.968 pounds

Therefore the healthy weight range for cats is (7.033 < x < 9.968)

Gordo's weight = 15 pounds

It is outside the healthy weight range and is in the top 5% of weights of cats.

Gordo's weight makes the cat unhealthy.

Flaco's weight = 8 pounds

Flaco's weight lies in the healthy weight range for cats. Hence, Flaco is a healthy cat.

8 0

2 years ago