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3 years ago

What are the solutions to the quadratic equation x2 – 16 = 0?

Mathematics

2 answers:

Naily [24]3 years ago

5 0

X^2-16=0
x^2=16
x=+-4
so the answer is x=4 and x=-4

Ket [755]3 years ago

4 0

Answer: The correct option is (B) x = 4 and x = -4.

Step-by-step explanation: We are given to find the solutions to the following quadratic equation :

$x^2-16=0~~~~~~~~~~~~~~~~~~~~~(i)$

Since the coefficient of x is zero in the given equation, so we will be using the method of square root to solve the equation.

From equation (i), we have

$x^2-16=0\\\\\Rightarrow x^2=16\\\\\Rightarrow x=\pm\sqrt{16}~~~~~~~\textup{[taking square root on both sides]}\\\\\Rightarrow x=\pm4\\\\\Rightarrow x=4,~-4.$

Thus, the required solution is x = 4 and x = -4.

Option (B) is correct.

You might be interested in

(5.2x + 36.4x + 52)/ (2.6x +13)

g100num [7]

Combine like terms in the first set and get
41.6x +52/2.6x + 13

I got 16x + 4

4 0

3 years ago

If y = 5x – 4, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs?

lidiya [134]

Answer:

Step-by-step explanation:

Substitute the x value into the right side of the function and if the value obtained is equal to the y value of the point then it is a solution.

(0, - 4) → y = 5(0) - 4 = 0 - 4 = -4 ← True

(2, 6) → y = 5(2) - 4 = 10 - 4 = 6 ← True

(4, 20) → 5(4) - 4 = 20 - 4 = 16 ← False

(4, 16) → 5(4) - 4 = 20 - 4 = 16 ← True

(0, - 4), (2, 6), (4, 16) ← possible inputs and outputs

8 0

3 years ago

A ski lift is designed with a total load limit of 20,000 pounds. It claims a capacity of 100 persons. An expert in ski lifts thi

Yanka [14]

Answer:

0.5 = 50% probability that a random sample of 100 independent persons will cause an overload

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the sum of n values of a distribution, the mean is $\mu \times n$ and the standard deviation is $\sigma\sqrt{n}$

An expert in ski lifts thinks that the weights of individuals using the lift have expected weight of 200 pounds and standard deviation of 30 pounds. 100 individuals.

This means that $\mu = 200*100 = 20000, \sigma = 30\sqrt{100} = 300$

If the expert is right, what is the probability that a random sample of 100 independent persons will cause an overload

Total load of more than 20,000 pounds, which is 1 subtracted by the pvalue of Z when X = 20000. So

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

$Z = \frac{20000 - 20000}{300}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5

1 - 0.5 = 0.5

0.5 = 50% probability that a random sample of 100 independent persons will cause an overload

5 0

3 years ago

What value of x makes the equation true? 3(4x-5)-4x+1=-6 Please show work

V125BC [204]

Answer:

x = 1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

3(4x - 5) - 4x + 1 = -6

Step 2: Solve for x

Distribute 3: 12x - 15 - 4x + 1 = -6
Combine like terms: 8x - 14 = -6
Isolate x term: 8x = 8
Isolate x: x = 1

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x: 3(4(1) - 5) - 4(1) + 1 = -6
Multiply: 3(4 - 5) - 4 + 1 = -6
Subtract: 3(-1) - 4 + 1 = -6
Multiply: -3 - 4 + 1 = -6
Subtract: -7 + 1 = -6
Add: -6 = -6

Here we see that -6 does indeed equal -6.

∴ x = 1 is the solution to the equation.

3 0

3 years ago

Whats greater .007 or .07

Karolina [17]

.07 is greater than .007

5 0

3 years ago