All categories

3 years ago

3) Solve each equation using the quadratic formula. Show a. x2 – 3x – 10 = 0

Mathematics

1 answer:

Naya [18.7K]3 years ago

5 0

Answer:

Step-by-step explanation:

The quadratic formula of a quadratic equation

$ax^2+bx+c=0\\\\\text{If}\ b^2-4ac>0\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$\text{If}\ b^2-4ac=0\ \text{then the equation has one solution}\ x=\dfrac{-b}{2a}$

$\text{If}\ b^2-4ac$

We have:

$x^2-3x-10=0\to a=1,\ b=-3,\ c=-10\\\\b^2-4ac=(-3)^2-4(1)(-10)=9+40=49>0\\\\x=\dfrac{-(-3)\pm\sqrt{49}}{2(1)}=\dfrac{3\pm7}{2}\\\\x=\dfrac{3-7}{2}=\dfrac{-4}{2}=-2\\or\\x=\dfrac{3+7}{2}=\dfrac{10}{2}=5$

You might be interested in

Translate this sentence into an equation.

Andrew [12]

Step-by-step explanation:

"product" means multiplication. the same as "times".

so,

135 = r×9

3 0

3 years ago

How many gallons of a 20% acid solution should be mixed with 30 gallons of a 40% solution, to obtain a mixture of 30% acid solut

Alexeev081 [22]

Answer:

30 gallons of 20% acid solution should be mixed.

Step-by-step explanation:

Let x gallons of a 20% acid solution was mixed with 30 gallons of a 40% solution, to obtain a mixture of 30% acid solution.

Therefore, final volume of the solution will be (x + 30) gallons.

Now concept to solve this question is

20%.(x) + 40%.(30) = 30%.(x + 30)

0.20(x) + 0.40(30) = 0.30(x + 30)

0.20x + 12 = 0.30x + 9

0.30x - 0.20x = 12 - 9

.10x = 3

x = $\frac{3}{0.1}$

x = 30 gallons

Therefore, 30 gallons of the 20% acid solution should be mixed.

4 0

3 years ago

Marisa is baking cakes for a bake sell. She plans on making 21 cakes. Each cake calls for 200 grams of all purpose flour. She ha

True [87]

1,700 grams

or

1.7 kilograms

8 0

3 years ago

If the original function () = 22 − 1 is shifted to the left 3 units to make the

Rom4ik [11]

A horizontal translation is expressed by transforming

$f(x)\mapsto f(x+k)$

If $k$ is positive, the function is translated to the left. If $k$ is negative, the function is translated to the right.

So, a 3-units left shift is given by $k=3$ . So you have

$f(x)=2x^2-1 \implies f(x+3)=2(x+3)^2-1$

4 0

3 years ago

Suppose that one-way commute times in a particular city are normally distributed with a mean of 15.43 minutes and a standard dev

vovikov84 [41]

Answer:

Yes, a commute time between 10 and 11.8 minutes would be unusual.

Step-by-step explanation:

A probability is said to be unusual if it is lower than 5% of higher than 95%.

We use the normal probability distribution to solve this question.

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 15.43, \sigma = 2.142$

Would it be unusual for a commute time to be between 10 and 11.8 minutes?

The first step to solve this problem is finding the probability that the commute time is between 10 and 11.8 minutes. This is the pvalue of Z when $X = 11.8$ subtracted by the pvalue of Z when X = 10. So