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3 years ago

Solve x^2 +14x=15 by completing the square

Mathematics

2 answers:

ivanzaharov [21]3 years ago

6 0

Answer:

x = -15 and x = 1

Step-by-step explanation:

Since we have to use the complete the square method, we first need to <u>rewrite the equation</u> in the form $x^{2}+2ax+a^{2}=(x+a)^{2}$ .

This results in $x^{2} + 14x + 7^{2} = 15 + 7^{2}$ .

Next, we <u>simplify the equation</u> to get $x^{2} +14x+7^{2} = 64$ .

<u>Factoring </u>the left side gives us $(x+7)^{2} = 64$ .

Finally we <u>solve the equations</u>: $x+7=\sqrt{64}$ and $x+7=-\sqrt{64}$ .

This gives us x=1, and x=-15

jeyben [28]3 years ago

4 0

X=-15. X=1…..............

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Suppose that the useful life of a car battery, measured in months, decays with parameter 0.03 . We are interested in the life of

scZoUnD [109]

Answer:

a) X ~ $e(0.03)$

b) μ = 100/3

c) $\sigma = 100/3$

d) A battery is expected to last 100/3 months (33 months and 10 days approximately).

e) For seven batteries, i would expect them to last 700/3 months (approximately 19 years, 5 months and 10 days).

Step-by-step explanation:

a) The life of a battery is usually modeled with an exponential distribution X ~ $e(0.03)$

b) The mean of X is μ = 1/0.03 = 100/3

c) The standard deviation is $\sigma = 1/0.03 = 100/3$

d) The expected value of the bateery life is equal to its mean, hence it is 100/3 months.

e) The expected value of 7 (independent) batteries is the sum of the expected values of each one, hence it is 7*100/3 = 700/3 months.

4 0

3 years ago

On the grid draw the graph of y = 3x + 2 for values of x + 2 for values of x from -2 to 2

sladkih [1.3K]

Answer:

The required graph is shown below.

Step-by-step explanation:

Consider the provided equation $y=3x+2$

We need to draw the graph of the equation.

Put x=0 in the above equation.

$y=3(0)+2$

$y=2$

The coordinate is (0,2).

Put y=0 in the given equation.

$0=3x+2$

$-2=3x$

$x=\frac{-2}{3}$

The coordinate is ( $\frac{-2}{3}$ ,0).

Now draw the graph by using the above coordinates.

The required graph is shown below.

6 0

3 years ago

Help me pleaseeeeeee

morpeh [17]

Answer:

Step-by-step explanation:

u move the decimal place left 2 spaces and u would get 0.024

3 0

3 years ago

Is the following relation linear, quadratic, or cubic? If it is linear, find the equation. Explain your reasoning and include al

Sergio [31]

The given relation is linear. Equation of the linear function; (Y-y1)/(x-x1)= m Or Y= 1/2x +2.

<h3>What is a linear equation?</h3>

A linear equation is an equation that has the variable of the highest power of 1.

The standard form of a linear equation is of the form Ax + B = 0.

Where m is the slope and c is the y intercept.

WE have given R = {(x, y) : (2,3), (4,4), (6,5), (8,6), ...}

Let's use these two points to determine both the slope and the equation;

(2, 3), (4,4)

Slope= (y2-y1)/(x2-x1)

Slope= (4-3)/(4-2)

Slope= 1/2

Then Equation of the linear function;

(Y-y1)/(x-x1)= m

(Y-3)/(x-2)= 1/2

2(y-3) = x-2

2y -6 = x-2

2y= x-2+6

2y= x+4

Y= 1/2x +2

Hence, the given relation is linear. Equation of the linear function; (Y-y1)/(x-x1)= m Or Y= 1/2x +2.

Learn more about linear equations;

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8 0

2 years ago

In how many ways can 4 boys and 4 girls be arranged in a row such that no two boys and no two girls are next to each other?(A) 1

nirvana33 [79]

Answer:

1152

Step-by-step explanation:

4 boys and 4 girls be arranged in a row such that no two boys and no two girls are next to each other.

Two boys and two girls are not next to each other. so one boy and one girl are next to each other in two ways.

BGBGBGBG, GBGBGBGB

4 boys are arranged in 4! ways and 4 girls are arranged in 4! ways

So number of ways = $2 \cdot 4! \cdot 4!=2 \cdot 24 \cdot 24=1152$

4 0

3 years ago