Which alphabet is missing V S P W T P

Solve this equation by completing the square: x2 + 4x – 13 = –8

marishachu [46]

Answer:

x = 1 or x = -5

Step-by-step explanation:

We are given;

The quadratic equation, x² + 4x - 13 = -8

We are required to solve the equation using the completing square method.

To do this, we use the following steps;

Step 1: We make sure the coefficient of x² is one

x² + 4x - 13 = -8

Step 2: Combine the like terms (take the constant term to the other side)

x² + 4x - 13 = -8

x² + 4x = -8 + 13

we get

x² + 4x = 5

Step 3: We add the square of half the coefficient of x on both sides of the equation

Coefficient of x = 4

Half of coefficient of x = 2

Square of half the coefficient of x = 2² (4)

We get;

x² + 4x + (2²) = 5 + (2²)

Step 4: Put x and 2 under one square and the solve the other side of the equation.

We get

(x + 2)² = 5 + 4

(x + 2)² = 9

Step 5: Get the square root on both sides of the equation;

(x + 2)² = 9

√(x + 2)² = ±√9

(x + 2)= ±3

Therefore;

x+2 = + 3 or x + 2 = -3

Thus, x = 1 or -5

The solution of the equation is x = 1 or x = -5

6 0

2 years ago

One satellite is scheduled to be launched from Cape Canaveral in Florida, and another launching is scheduled for Vandenberg Air

Lisa [10]

Answer:

$P(A) = 0.45$

$P(B) = 0.32$

Step-by-step explanation:

Given

$P(A) > P(B)$

$P(A\ u\ B) = 0.626$

$P(A\ n\ B) = 0.144$

Required

Find P(A) and P(B)

We have that:

$P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)$ --- (1)

and

$P(A\ n\ B) = P(A) * P(B)$ --- (2)

The equations become:

$P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)$ --- (1)

$0.626 = P(A) + P(B) - 0.144$

Collect like terms

$P(A) + P(B) = 0.626 + 0.144$

$P(A) + P(B) = 0.770$

Make P(A) the subject

$P(A) = 0.770 - P(B)$

$P(A\ n\ B) = P(A) * P(B)$ --- (2)

$0.144 = P(A) * P(B)$

$P(A) * P(B) = 0.144$

Substitute: $P(A) = 0.770 - P(B)$

$[0.770 - P(B)] * P(B) = 0.144$

Open bracket

$0.770P(B) - P(B)^2 = 0.144$

Represent P(B) with x

$0.770x - x^2 = 0.144$

Rewrite as:

$x^2 - 0.770x + 0.144 = 0$

Expand

$x^2 - 0.45x - 0.32x + 0.144 = 0$

Factorize:

$x[x - 0.45] - 0.32[x - 0.45]= 0$

Factor out x - 0.45

$[x - 0.32][x - 0.45]= 0$

Split

$x - 0.32= 0 \ or\ x - 0.45= 0$

Solve for x

$x = 0.32\ or\ x = 0.45$

Recall that:

$P(B) = x$

So, we have:

$P(B) = 0.32 \ or \ P(B) = 0.45$

Recall that:

$P(A) = 0.770 - P(B)$

So, we have:

$P(A) = 0.770 - 0.32 \ or\ P(A) =0.770 - 0.45$

$P(A) = 0.45 \ or\ P(A) =0.32$

Since:

$P(A) > P(B)$

Then:

$P(A) = 0.45$

$P(B) = 0.32$

6 0

2 years ago

Suppose that 76% of americans prefer coke to pepsi. a sample of 80 was taken. what is the probability that at least seventy perc

vladimir2022 [97]

The standard deviation of the sample proportion is:
$\sqrt{ \frac{0.76(1-0.76)}{80}} =0.048$
The z-score for 0.7 is:
$z= \frac{0.7-0.76}{0.048} =-1.25$
Reference to a standard normal distribution table shows that the probability that at least 70% of the sample prefers coke to pepsi is 0.8944 or 89.44%.

6 0

3 years ago

Please help :// I need to finish this

Charra [1.4K]

The answers to the questions