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2 years ago

2xsquared +3x+1=0 solve using quadratic formula

Mathematics

1 answer:

vlada-n [284]2 years ago

5 0

Answer:

x = $\frac{1}{2}$ , -1

Step-by-step explanation:

The quadratic formula is: -b±√b²-4ac

The discriminant (Δ) is b²-4ac. Evaluating this expression after substituting for a, b and c helps you identify the number of real solutions to the quadratic equation.

a = 2, b = 3, c = 1

Δ = -3²- 4 x 2 x 1;

Δ = 1

-3±1

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Write the equation of the function whose graph is shown. y = (x + )2 +

Deffense [45]

Quadratic form is given in the form
$y= ax^{2}+bx+c$ , where a, b, and c are constants

We substitute the value (8, 12) and (5,3) in turn

$12= a(8)^{2}+b(8)+c$
$12=64a+8b+c$ ... Equation 1

$3=a(5)^{2}+b(5)+c$
$3=25a+5b+c$ ... Equation 2

Equation 1 - Equation 2 gives
$39a+3b=9$ , we call this Equation 3

We also know that (5, 3) is the turning point of the curve, where the value of $x$ is given by $x=- \frac{b}{2a}$
Substitute $x=5$
$5=- \frac{b}{2a}$
$10a=-b$
$b=-10a$ ... Equation 4

Substitute Equation 4 into Equation 3
$39a+3b=9$
$39a+3(-10a)=9$
$39a-30a=9$
$9a=9$
$a=1$

Now we need to work out the value of $b$ and $c$

Substitute $a=1$ back into equation 4
$-10a=b$
$-10(1)=b$
$b=-10$

Substitute $a=1$ and $b=-10$ into either equation 1 or equation 2

$64a+8b+c=12$
$64(1)+8(-10)+c=12$
$64-80+c=12$
$c=12+80-64$
$c=28$

Hence the equation of the quadratic curve is
$y= x^{2} 10x+28$

8 0

2 years ago

Read 2 more answers

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate

KonstantinChe [14]

Answer:

It will take 47 hours

Step-by-step explanation:

We can have the exponential function as follows;

P = I( 1 + r)^n

if the initial value was x , the final will be 2x

The change rate is 1.5% , which is r, this is same as;

1.5/100 = 0.015

So what we want to calculate is the n attached

This will be;

2x = x ( 1 + 0.015)^n

2 = 1.015^n

ln 2 = n ln 1.015

n = ln 2/ln 1.015

n = 46.55

This is approximately 47 hours

7 0

2 years ago

The function f(x) is given by the set of ordered pairs.

NISA [10]

The true equation will be f(6) = 0. Then the correct option is C.

<h3>What is a function?</h3>

A statement, principle, or policy that creates the link between two variables is known as a function.

The function f(x) is given by the set of ordered pairs.

{(1,0), (–10,2), (0,6), (3,17), (–2,–1)}

Then the function can be written as

f(abscissa) = ordinate

Then the function will be

f(0) = 6

Then the correct option is C.

More about the function link is given below.

brainly.com/question/5245372

#SPJ1

6 0

1 year ago

30 points if correct. Select all the are true.

ivann1987 [24]

Answer:

Options B,C and E are correct choices.

Step-by-step explanation:

We are asked to find correct answers for the given box and whisker plots.

Let us our options one by one.

A. This option is false as lowest value for children's cereals is 30 and highest value for adults is 35.

B. This option is correct. We can see our upper value for combined range will be 60 and lower value will be 5 and range is upper value- lower value.

$60-5=55$

C. Since we know that we can find spread of data by its range.

$\text{Range for children's cereals}=60-30=30$

$\text{Range for adult's cereals}=60-30=30$

So option C is correct indeed.

D. This options is false because for adults mean and median are different while for children mean and median are same.

E. We can see that median for children's cereals is 45 and it is about 12 for adults.

We can see that $12*3$ . So median amount of sugar in children's cereals is 3 times as much as the median amount of sugar in adult's cereals.

Therefore, options B,C and E are correct choices.

4 0

2 years ago

If four times the sum of a number and 5 is divided by 3 , the result is 16

Black_prince [1.1K]

If four times the sum of a number and 5 is divided by 3, the result is 16. Step 1. Let x be the number.

Step 2. Four times the number and 5 is divided by 3

Step 3. The result is 16

Step 4. Multiply by 3 to both sides of equation to get rid of denominator

Step 5. Subtract 20 from both sides of equation

Step 6. Divide by 4 to both sides of equation

Step 7 ANSWER is x=7.

I hope the above steps were helpful.

6 0

3 years ago

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