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3 years ago

Write a quadratic equation in standard form with 1 over 2 and 3 as its roots

Mathematics

1 answer:

olasank [31]3 years ago

7 0

Answer:

f(x) = 2x² - 7x + 3

Step-by-step explanation:

Given the roots are x = $\frac{1}{2}$ and x = 3, then the corresponding factors are

(x - $\frac{1}{2}$ ) and (x - 3), that is

(2x - 1) and (x - 3)

The equation is then the product of the roots, that is

f(x) = (2x - 1)(x - 3) ← expand factors using FOIL

f(x) = 2x² - 7x + 3 ← in standard form

You might be interested in

You want to get from a point A on the straight shore of the beach to a buoy which is 54 meters out in the water from a point B o

anyanavicka [17]

Answer:

$x =\dfrac{45 \sqrt{6}}{ 2}$

Step-by-step explanation:

From the given information:

The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.

Now, let V(x) be the time needed for the runner to reach the buoy;

∴ We can say that,

$\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}$

In order to estimate the point along the shore, x meters from B, the runner should stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.

i.e

The differential of V(x) = V'(x) =0

= $\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0$

$-\dfrac{1}{7}+ \dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}=0$

$\dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}$

$\dfrac{5x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}$

$\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{\dfrac{7}{5}}$

$\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{5}{7}$

squaring both sides; we get

$\dfrac{x^2}{54^2+x^2}= \dfrac{5^2}{7^2}$

$\dfrac{x^2}{54^2+x^2}= \dfrac{25}{49}$

By cross multiplying; we get

$49x^2 = 25(54^2+x^2)$

$49x^2 = 25 \times 54^2+ 25x^2$

$49x^2-25x^2 = 25 \times 54^2$

$24x^2 = 25 \times 54^2$

$x^2 = \dfrac{25 \times 54^2}{24}$

$x =\sqrt{ \dfrac{25 \times 54^2}{24}}$

$x =\dfrac{5 \times 54}{\sqrt{24}}$

$x =\dfrac{270}{\sqrt{4 \times 6}}$

$x =\dfrac{45 \times 6}{ 2 \sqrt{ 6}}$

$x =\dfrac{45 \sqrt{6}}{ 2}$

8 0

3 years ago

A Mercedes can go 78 miles on 3 gallons of gas. How far can it go with a full tank of 16 gallons?

Alex787 [66]

Answer:

416 miles

Step-by-step explanation:

78 divided by 3 = 26

26 x 16 = 416

5 0

3 years ago

The weight, in pounds, of a newborn baby tt months after birth can be modeled by the function W(t)=1.25t+6.W(t)=1.25t+6. What is

ollegr [7]

Answer:

$6$

Step-by-step explanation:

GIVEN: The weight, in pounds, of a newborn baby $t$ months after birth can be modeled by the function $W(t)=1.25t+6$ .

TO FIND: What is the y-intercept of the function and what is its interpretation in the context of the problem.

SOLUTION:

in $W(t)=1.25t+6$

if $t=0$

$W(0)=6$

Hence y-intercept is $6$

the y-intercept in this represents the weight of baby just after he is born.

8 0

3 years ago

Please help and first right answer will be marked branliest

lakkis [162]

Answer:

a) 320 students

b) 25 students

Step-by-step explanation:

Number of 18-years old in the survey:

(We add all frequency points for each line)

0 + 30 + 20 + 60 + 70 + 40 + 60 + 40 + 0 = 320 students

Number of 18 year old spending between 25 and 35 minutes: 40 + 65 = 105

Number of 12 year old spending between 25 and 35 minutes: 30 + 50 = 80

105 - 80 = 25 students

5 0

4 years ago

Which ordered pairs are solutions to the inequality 2x + y > 8 ? Choose all answers that are correct.

gtnhenbr [62]

Hi again!

2x + y > 8

The correct answer is option D
-------------------------------------------

Honestly I don't think we can solve the equation to find the answer. What we can do is to find the boundary line. (I think you know what that is) After that, shading the appropriate area.

y > -2x + 8

Again, credit to my beautiful graphing calculator. Here is how it looks like.

6 0

3 years ago