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3 years ago

Find the number of real number solutions for the equation. x2 + 5x + 7 = 0 0 cannot be determined 1 2

Mathematics

2 answers:

alisha [4.7K]3 years ago

5 0

$\Delta=5^2-4\cdot1\cdot7=25-28=-3$

$\Delta$ so 0 solutions.

DaniilM [7]3 years ago

4 0

Answer:

No Real roots to this Quadratic Equation

Step-by-step explanation:

Our Quadratic equation is given as

$x^2+5x+7=0$

In order to find that do we have the real roots of a quadratic equation , the Discriminant must be greater or equal to 0. The Discriminant is denoted by D and given by the formula

$D= b^2-4ac$

Where b is the coefficient of the middle term containing x, a is the coefficient of the term containing $x^{2}$ and the c is the constant term.

Hence we have

a = 1 , b = 5 and c = 7

Calculate D

$D=b^2-4ac\\D=5^2-4*1*7\\D=25-28\\D=-3$

Hence we see that the Discriminant (D) is less than 0, our answer is no real roots to this quadratic equation.

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Kelly has a rectangular fish aquarium that measures 18 inches long, 8 inches wide, and 12 inches tall.

BigorU [14]

Answer:

a) The maximum amount of water the aquarium can hold is 1728 in³.

b) The cover has to be 624 in² big.

Step-by-step explanation:

a) The maximum volume of water that the aquarium can have is the same as the volume of the aquarium:

V=L×W×H=18 in × 8 in × 12 in= 1728 in³

b) The protective covering is used on the four walls of the aquarium. We have to find the areas of the four walls:

One of them is given by the multiplication of the width and the height:

A₁= W×H= 8 in × 12 in=96 in²

The other area is given by the multiplication of the length and the height:

A₂= L×H= 18 in × 12 in= 216 in²

As the fish aquarium is rectangular the area of the walls is given by:

$A_T=2A_1+2A_2$ =2×96 in²+2×216 in²=624 in²

8 0

3 years ago

Solve the linear system using substitution

levacccp [35]

Hello there!

3x - y = 3
-x + y = 3

We need to solve 3x - y = 3 for y

Let start by adding -3x to both sides

3x - y = 3

3x - 3x - y = 3 - 3x

-y = 3 - 3x
We cannot leave the variable with a negative sign. We must multiply both sides by -1

-y * -1= (3 - 3x)-1

y = 3x - 3

Substitute 3x -3 for y in -x+y=3

-x + y = 3

-x + 3x - 3 = 3

2x - 3 = 3

2x = 3 + 3

2x = 6

x = 6/2

x = 3

Now substitute 3 for x in y=3x -3

y = 3x - 3

y = 3(3) - 3

y= 9 - 3

y= 6

Thus,

The answer is x=3 and y=6

It is always my pleasure to help students like you :)

As always, I am here to help!

7 0

3 years ago

Verify that -5, 1/2, and 3/4 are the zeroes of the cubic polynomial 4x^3+20x^2+2x-3. Also verify the relationship between the ze

Finger [1]

Solution:

we have been asked to verify that -5, 1/2, and 3/4 are the zeroes of the cubic polynomial $4x^3+20x^2+2x-3$

To verify that whether the given values are zeros or not we will substitute the values in the given Polynomial, if it will returns zero, it mean that value is Zero of the polynomial. But if it return any thing other than zeros it mean that value is not the zero of the polynomial.

Let $f(x)=4x^3+20x^2+2x-3\\\\\text{when x=-5}\\\\f(-5)=4(-5)^3+20(-5)^2+2(-5)-3=-13\\\\\text{when x=}\frac{1}{2}\\$

$f( \frac{1}{2} ) = 4 ( \frac{1}{2} )^3+20(\frac{1}{2})^2+2(\frac{1}{2})-3=\frac{7}{2}\\\\$

$\text{when x=}\frac{3}{4}\\\\$

$f( \frac{3}{4} ) = 4 ( \frac{3}{4} )^3+20(\frac{3}{4})^2+2(\frac{3}{4})-3=\frac{183}{16}\\$

Hence -5, 1/2, and 3/4 are not the zeroes of the given Polynomial.

Since sum of roots $=\frac{-b}{a}= \frac{-20}{4}=-5\\$

But $-5+\frac{1}{2}+\frac{3}{4}= \frac{-15}{4}\neq-5$

Hence we do not find any relation between the coefficients and zeros.

Anyway if the given values doesn't represents the zeros then those given values will not have any relation with the coefficients of the p[polynomial.

6 0

3 years ago

Which function is the inverse of f(x) = 2x + 3?

Gnesinka [82]

Answer:

f(x inv)=-1/2x-3

Step-by-step explanation:

You pretty much just have to flip all the numbers to fractions and all the positives to negatives.

6 0

2 years ago

1. if √16 = x, then x^2

vivado [14]

1. A squares and square root cancels

2. CE square root of a perfect square is rational square root of non perfect squares are irrational

4. ✓16=4 ✓9 =3 therefore ✓10 will be between 4 and 3 which is 3.1 answer is C

4 0

3 years ago