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3 years ago

Find the solutions to the equation below check all that apply 4x2 -8x +3 =0

Mathematics

1 answer:

notka56 [123]3 years ago

4 0

Answer:

Hello :

4x² - 8x +3 = 0

4 ( x² - 2x +3/4 ) = 0

4 ( (x² -2x +1) -1 + 3/4) = 0

4 ((x-1)² - 1/4 ) =0

(x-1)² - 1/4 = 0

(x-1)² - ( 1/2 )²=0

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

( x - 3/2) ( x - 1/2) = 0

x - 3/2 = 0 or x - 1/2 = 0

two solutions : 3/2 ; 1/2

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Write an equation for a quadratic function that has x intercepts (-3, 0) and (5, 0)

Blizzard [7]

Answer:

One possible equation is $f(x) = (x + 3)\, (x - 5)$ , which is equivalent to $f(x) = x^{2} - 2\, x - 15$ .

Step-by-step explanation:

The factor theorem states that if $x = x_{0}$ (where $x_{0}$ is a constant) is a root of a function, $(x - x_{0})$ would be a factor of that function.

The question states that $(-3,\, 0)$ and $(5,\, 0)$ are $x$ -intercepts of this function. In other words, $x = -3$ and $x = 5$ would both set the value of this quadratic function to $0$ . Thus, $x = -3\!$ and $x = 5\!$ would be two roots of this function.

By the factor theorem, $(x - (-3))$ and $(x - 5)$ would be two factors of this function.

Because the function in this question is quadratic, $(x - (-3))$ and $(x - 5)$ would be the only two factors of this function. In other words, for some constant $a$ ( $a \ne 0$ ):

$f(x) = a\, (x - (-3))\, (x - 5)$ .

Simplify to obtain:

$f(x) = a\, (x + 3)\, (x - 5)$ .

Expand this expression to obtain:

$f(x) = a\, (x^{2} - 2\, x - 15)$ .

(Quadratic functions are polynomials of degree two. If this function has any factor other than $(x - (-3))$ and $(x - 5)$ , expanding the expression would give a polynomial of degree at least three- not quadratic.)

Every non-zero value of $a$ corresponds to a distinct quadratic function with $x$ -intercepts $(-3,\, 0)$ and $(5,\, 0)$ . For example, with $a = 1$ :

$f(x) = (x + 3)\, (x - 5)$ , or equivalently,

$f(x) = x^{2} - 2\, x - 15$ .

6 0

2 years ago

Sam and hector are gaining weight for football season. Sam weighs 205 lbs and is gaining 2 per week. Hector weighs 195 and is ga

Sauron [17]

It takes 10 weeks for them to be the same weight

7 0

3 years ago

Ryan is 23 years older than stacy. In 6 years he will be 2 times her age. how old is each person now?

Aloiza [94]

Answer:

Ryan 40

Stacy 17

Step-by-step explanation:

x -----> Stacy

x + 23 -----> Ryan

x + 6 Stacy

x + 23 + 6 Ryan

x + 29 Ryan

x + 29 = 2(x + 6)

x + 29 = 2x + 12

x - 2x = 12 - 29

-x = - 17

x = 17 Stacy

x + 23

17 + 23

40 Ryan

4 0

3 years ago

A rectangle is drawn so that the width is 3 feet shorter than the length. The area of the rectangle is 70 square feet. Find the

Vedmedyk [2.9K]

Answer:

The length of the rectangle (l) = 10 cm

The width of the rectangle (w) = 7 cm

Step-by-step explanation:

Step(i):-

Let 'x' be the length of the rectangle

Given that the width is 3 feet shorter than the length

The width of the rectangle = x -3

Area of the rectangle = length × width

Step(ii):-

Area of the rectangle = length × width

= x ( x-3)

Given that the area of the rectangle = 70 square feet

x ( x-3) = 70

⇒ x² - 3x - 70 =0

⇒ x² - 10 x + 7 x - 70 =0

⇒ x (x -10) +7( x-10) =0

⇒ ( x+7) ( x-10) = 0

⇒ x =-7 and x=10

Final answer:-

we choose x=10

The length of the rectangle (l) = 10 cm

The width of the rectangle (w) = 7 cm

8 0

3 years ago

Select all the expressions that are equal to 8 x104.

DedPeter [7]

Answer:

A. 8 x 100

D. 8 x 10 x 10 x 10

Step-by-step explanation:

When you do the original equation it is 912

these 2 are close but don't go over

5 0

3 years ago

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