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2 years ago

What is the solution set of the equation

Mathematics

1 answer:

cupoosta [38]2 years ago

5 0

Answer:

Step-by-step explanation:

Given

x² + 3x - 4 = 6 ( subtract 6 from both sides )

x² + 3x - 10 = 0 ← in standard form

Consider the factors of the constant term (- 10) which sum to give the coefficient of the x- term (+ 3)

The factors are + 5 and - 2, since

5 × - 2 = - 10 and 5 - 2 = + 3, thus

(x + 5)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 2 = 0 ⇒ x = 2

solution set is { - 5, 2 } → A

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( 2 x -6 ) +4 ( x - 3 )

OLga [1]

(2x-6) + 4(x-3) {distribute 4 out and expand problem}
2x+6+4x-12 {combine like terms}
6x-6 {your answer}

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2 years ago

If the temperature after 4.4 degree drop was -2.5 degrees Celsius what was the temperature at noon

Lostsunrise [7]

Answer:

1.9°C

Step-by-step explanation:

Let X be the temperature at noon and -2.5°C be the current temperature after the drop.

-We calculate temperature at noon as:

$\bigtriangleup =t_o-t_n\\4.4=X--2.5\\\\X=4.4-2.5\\\\=1.5\textdegree C$

Hence, the temperature at noon was 1.9°C

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3 years ago

Cory, Josh and Dan went shopping for Halloween treats. Cory bought 3 chocolate pumpkins, 4 masks and 8 candy witches. He spent $

bija089 [108]

Answer:

The cost of chocolate pumpkins is $1.89, masks cost $5.75 and candy witches cost $1.62

Step-by-step explanation:

Let x represent the cost of chocolate pumpkins, y the cost of masks and z the cost of candy witches.

Cory shopping can be represented as:

3x + 4y + 8z = 41.63 (1)

Josh shopping can be represented as:

6x + 2y + 14z = 45.52 (2)

Dan shopping can be represented as:

8x + 3y + 25z = 72.87 (3)

The equations in matrix form is:

$\left[\begin{array}{ccc}3&4&8\\6&2&14\\8&3&25\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}41.63\\45.52\\72.87\end{array}\right] \\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}3&4&8\\6&2&14\\8&3&25\end{array}\right] ^{-1}\left[\begin{array}{c}41.63\\45.52\\72.87\end{array}\right] \\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}1.89\\5.75\\1.62\end{array}\right]$

The cost of chocolate pumpkins is $1.89, masks cost $5.75 and candy witches cost $1.62

7 0

2 years ago

The Director of Admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall sem

VMariaS [17]

Answer:

Variance = 24900

Standard Deviation = 157.7973

Step-by-step explanation:

We are given the following in the question:

Number of admissions: 1000 1200 1500

Admissions Probability: 0.6 0.3 0.1

Formula:

$E(x) = \displaystyle\sum x_iP(x_i)\\E(x) = 1000(0.6) + 1200(0.3) + 1500(0.1)\\E(x) = 1110\\E(x^2) = \displaystyle\sum x_i^2P(x_i)\\E(x^2) = (1000)^2(0.6) + (1200)^2(0.3) + (1500)^2(0.1)\\E(x^2) = 1257000$