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8 days ago

7

The record high January temperature in Austin, Texas, is 90 degrees F The record low January temperature is -7 degrees F, Find t

he difference between the high and low temperatures.

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The mAngle6 = (11x + 8)° and mAngle7 = (12x – 4)° Parallel lines x and y are cut by transversal w. On line x where it intersects

Inessa [12570]

Answer:

It is a) 40°

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2 months ago

Read 2 more answers

Linda found that the cost to get a swimming pool installed in her backyard is a linear function of the pool's area. A swimming p

lawyer [12517]

Answer:

The equation for the line is $C = 30A + 9000$

Step-by-step explanation:

Let A denote Area and C stand for Cost, we can deduce that:

For an area of $A = 1500$ square feet, the cost amounts to $C = 54000$

If $A = 700$ , then, $C = 30000$

Since the cost equation represents a function of area, this establishes a linear connection, necessitating the formulation of the line's equation.

$C = mA + b$

Where:

m denotes the slope of the line

b indicates the intercept with the C axis..

We possess two coordinates:

(700, 30000)

(1500, 54000)

Using these points, we calculate the slope via the formula:

$m = \frac{y_2 -y_1}{x_2-x_1}\\\\m = \frac{54000-30000}{1500-700}\\\\m = 30$

Consequently, the equation concludes with:

$C = 30A +b$

To find b, we substitute the point (700, 30000) into the equation

$30000 = 30(700) + b\\\\30000 -21000=b$

$b = 9000$

Thus

$C = 30A + 9000$

The linear equation's graph is depicted in the provided image

3 0

2 months ago

What are the solutions of the equation x4 + 6x2 + 5 = 0? Use u substitution to solve.

tester [12383]

The solutions to the equation are $x=\pm i, x=\pm \sqrt{5}i$

Explanation:

Given the equation $x^{4}+6 x^{2}+5=0$

, we aim to find the solutions of the equation.

Let us use $x^{2} =u$ and $x^4=u^2$

Thus, the equation transforms into

$u^{2}+6 u+5=0$

Factoring the equation results in:

$(u+1)(u+5)=0$

$u=-1, u=-5$

Inserting back $x^{2} =u$ and allows us to solve for x.

Initially, we will substitute $u=-1$

Consequently, we find;

$x^{2} =-1$

$x=\sqrt{-1}$

$x=\pm i$

Similarly, by substituting $u=-5$ , we derive;

$x^{2} =-5$

$x=\sqrt{-5}$

$x=\pm \sqrt{5}i$

Thus, the solutions to the equation are $x=\pm i, x=\pm \sqrt{5}i$

6 0

1 month ago

Nandini makes 'halwa' one evening and divides it into four equal portions for her family of four. However, just as they are abou

zzz [12365]

Answer:

5%

Step-by-step explanation:

With four individuals, each receives 25% of the halwa. Yet, when a fifth individual joins, each share drops to 20%. Consequently, the original four individuals experience a 5% reduction in their servings due to the new arrival.

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3 months ago