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2 years ago

Solve for x. x2 + 4x - 21 = 0 A. -3, -7 B. -3, 7 C. 3, -7 D. 3, 7

Mathematics

2 answers:

julia-pushkina [17]2 years ago

6 0

Please, use " ^ " to denote exponentiation: x^2 + 4x - 21 = 0

Factor: (x+7)(x-3)=0

Solve for the 2 roots: x= -7 and x= 3: {3, -7} Note how this is in set notation.

WINSTONCH [101]2 years ago

6 0

Answer: the correct option is

(C) 3, -7.

Step-by-step explanation: We are given to solve the following equation for x :

$x^2+4x-21=0~~~~~~~~~~~~~~~~~~~~~~~```(i)$

We will be solving the given quadratic equation by factorization.

The solution of equation (i) is as follows :

$x^2+4x-21=0\\\\\Rightarrow x^2+7x-3x-21=0\\\\\Rightarrow x(x+7)-3(x+7)=0\\\\\Rightarrow (x-3)(x+7)=0\\\\\Rightarrow x-3=0,~~~x+7=0\\\\\Rightarrow x=3,~-7.$

Thus, the required values of x are

x = 3, -7.

Option (C) is CORRECT.

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2 years ago

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a = $\sqrt{7}$

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.:

<em>Suppose ABC is a right triangle with sides a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the values of the six trigonometric functions for angle B. when b=3 and c=4</em>.

My answer:

We will Pythagoras theorem, which states that the sum of squares of two legs of a right triangle is equal to the square of the hypotenuse of right triangle. Because the question says that ABC is a right triangle.

$a^2+b^2=c^2$

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$a^2+3^2=4^2a^2+9=16a^2+9-9=16-9a^2=7$

so a = $\sqrt{7}$

We know that tangent relates opposite side of a right triangle with adjacent side.

$\text{tan}(B)=\frac{a}{b}\\\text{tan}(B)=\frac{\sqrt{7}}{3}$

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3 years ago

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ValentinkaMS [17]

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Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

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 p-value, we get the probability that the value of the measure is greater than X.

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