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3 years ago

8

Find n 5|6n+15|+2=-43

1 answer:

Ivenika [448]3 years ago

3 0

Answer:

<h2>No solution</h2>

Step-by-step explanation:

$5|6n+15|+2=-43\qquad\text{subtract 2 from both sides}\\\\5|6n+15|+2-2=-43-2\\\\5|6n+15|=-45\qquad\text{divide both sides by 5}\\\\\dfrac{5\!\!\!\!\diagup^1|6n+15|}{5\!\!\!\!\diagup_1}=\dfrac{-45\!\!\!\!\!\diagup^9}{5\!\!\!\!\diagup_1}\\\\|6n+15|=-9\qquad\bold{FALSE}\to\text{no solution}\\\\\text{because}\ |a|\geq0\ \text{for any real value of}\ a.$

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Page's front door measures 84 inches by 54 inches. What is the area of the door? (ONLY IF YOU KNOW)

jarptica [38.1K]

4536 inches² or 31.5 ft²

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4 years ago

5. A store sells bags of pecans for $3.00, bags of walnuts for $3.50, and bags of almonds for $4.00. One day, 15

kondaur [170]

Answer:

x = 4

y = 6

z = 5

Step-by-step explanation:

Let

bags of pecans = x

bags of walnuts = y

bags of almonds = z

x + y + z = 15

3x + 3.5y + 4z = 53

Two more bags of walnuts were sold than pecans.

Walnuts = x + 2

x + y + z = 15

3x + 3.5y + 4z = 53

x + x + 2 + z = 15

3x + 3.5(x+2) + 4z = 53

2x + z = 15 - 2

3x + 3.5x + 7 + 4z = 53

2x + z = 13 (1)

6.5x + 4z = 46 (2)

Multiply (1) by 4

8x + 4z = 52 (3)

6.5x + 4z = 46 (2)

Subtract (2) from (3)

8x - 6.5x = 52 - 46

1.5x = 6

Divide both sides by 1.5

x = 4 bags

y = x + 2

= 4 + 2

= 6

y = 6 bags

Substitute the value of x into (1)

2x + z = 13 (1)

2(4) + z = 13

8 + z = 13

z = 13 - 8

= 5

z = 5 bags

Check:

x + y + z = 15

4 + 6 + 5 = 15

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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3 years ago

Which is an x-intercept of the graph of the function y=cot(3x)

AveGali [126]

Answer:

x-intercept of the graph of the function $y = \cot(3x)$ is, $(\frac{\pi}{6} \pm \frac{n\pi}{3} , 0)$

Step-by-step explanation:

Given the function: $y = \cot(3x)$ ......[1]

x-intercept defined as the graph crosses the x-axis.

Substitute value of y = 0 in [1] and solve for x;

$0 = \cot(3x)$ or

$\cot(3x) = 0$

Take the inverse cotangent of both sides of the equation and solve for x;

3x = arccot (0)

We know the exact value of $arc\cot(0) = \frac{\pi}{2}$

then;

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

Divide both sides by 3 we get;

$x = \frac{\pi}{6}$

Since, the cotangent function is positive in the first and third quadrants.

The period of the function $\cot(3x)$ is $\frac{\pi}{3}$ so values will repeat every $\frac{\pi}{3}$ radians in both directions.

we have;

$x =\frac{\pi}{6} \pm \frac{n\pi}{3}$

Therefore, the x-intercept of the graph of the function $y = \cot(3x)$ is ;

$(\frac{\pi}{6} \pm \frac{n\pi}{3} , 0)$ for every integer n;

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3 years ago