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san4es73 [151]
3 years ago
5

|3n – 6| = 6 absolute value equation

Mathematics
1 answer:
ZanzabumX [31]3 years ago
3 0

Answer:

n=\{0,\: 4\}

Step-by-step explanation:

|3n-6| = 6\\\therefore 3n - 6 = \pm 6\\\therefore 3n = 6 \pm 6\\\therefore 3n =6+6\:\: or\:\: 3n = 6-6\\\therefore 3n =12\:\: or \:\:3n = 0\\\\\therefore n =\frac{12}{3}\:\: or\:\: n =\frac{0}{3}\\\\\therefore n = 4 \:\: or\:\: n = 0\\\\\therefore n=\{0,\: 4\}\\

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Which choice gives the solution of this inequality?<br> 3t + 7 &lt; 28
Butoxors [25]

Answer:7

Step-by-step explanation:

5 0
2 years ago
The following uses a 4-step proof, starting with the given statement. Complete the following proof
AlladinOne [14]

1) \overline{JK} \perp \overline{MN}

2) \angle JKM is a right angle (perpendicular lines form right angles)

3) \triangle JKM is a right triangle (definition of a right triangle)

4) \angle 1 and \angle 2 are complementary (the acute angles of a right triangle are complementary)

8 0
2 years ago
Help please hurry need help
Misha Larkins [42]

Answer:

1: D

2: B

3: y=-4x+22

4: y=-8x+26

Step-by-step explanation:

1: Parallel lines have the same slope, and the only one with a slope of 3x is D

2: Perpendicular lines have an opposite slope, so a line with a slope of -1/2 would be 2, so you just flip the number and add or take away a negative sign, depending on the original slope

3: Like I said before, perpendicular lines have an opposite slope, so the slope would be -4. After you've figured that out, you just plug in the numbers given to you (and remember, x is first, y is last)

Plug in: 6=-4(4)+b

You would then solve for b.

6=-16+b

22=b

Then plug that into y=mx+b, with m being the slope (-4) and b being the y intercept (22)

4: The process for finding parallel and perpendicular lines is very similar, except you don't have to change the slope.

Plug in: 10=-8(2)-b

10=-16+b

26=b

Again, plug that into the equation y=mx+b

Hope I could be of help! Sorry if it doesn't make sense, this is my first time on this website.

5 0
3 years ago
Worldwide, the proportion of babies who are boys is about 0.51 . Let the random variable X represent the number of boys in five
solmaris [256]

Answer:

mean = 2.55

Standard deviation = 1.118

Step-by-step explanation:

Probability of babies who are boys

P = 0.51

Then we have q = 1-p

= 1-0.51

= 0.49

We have n = 5

We calculate the mean as:

np

= 0.51x5

= 2.55

Therefore mean = 2.55

The standard deviation

= √variance

= √npq

= √0.51x5x0.49

=√1.2495

= 1.118

6 0
2 years ago
Help please!!
Pavel [41]

Answer:

1. Left side = 3 inches, Bottom side = 4 inches, Right side = 2 inches, Top side = 5 inches

2.  A = 6 inches²

3.  A = 8 inches²

4.  A = 10 inches²

5.  A = 12 inches²

6.  A = 36 inches²

7. Left side = 5 cm, Bottom side = 12 cm, Right side = 4 cm, Top side = 13 cm

8. A = 180 cm²

Step-by-step explanation:

1. Label the dimensions of the prism:

Left side = 3 inches

Bottom side = 4 inches

Right side = 2 inches

Top side = 5 inches

2. Area of the red rectangle:

Formula:

LH = A (Length x Height = Area)

A = 3 x 2

A = 6 inches²

3. Area of the blue rectangle:

Formula:

LH = A (Length x Height = Area)

A = 4 x 2

A = 8 inches²

4. Area of the green rectangle:

Formula:

LH = A (Length x Height = Area)

A = 5 x 2

A = 10 inches²

5. (They gave the formula of the two triangles, but the question said green rectangle?  They must've meant yellow triangles)

Area of the yellow triangles:

Formula:

2 (1/2 Bh) (2 (half of base x height))

A = 2(1/2 3 x 4)

A = 2(1/2 12)

A = 2(6)

A = 12 inches²

6. Total surface area of the triangular prism:

Formula:

LH + LH + LH + 2 (1/2 Bh) = Surface Area of the triangular prism (Area of the red rectangle + Area of the blue rectangle + Area of the green rectangle + Area of the yellow triangles = Total surface area of the triangular prism)

A = 6 inches² + 8 inches² + 10 inches² + 12 inches²

A = 36 inches²

7. Label the dimensions of the prism:

Left side = 5 cm

Bottom side = 12 cm

Right side = 4 cm

Top side = 13 cm

8. Total surface area of the triangular prism:

First, we can find the area of each shape, as we had previously to find the total area of the net and the surface area of the triangular prism.

Area of the red rectangle:

Formula:

LH = A (Length x Height = Area)

A = 5 x 4

A = 20 cm²

Area of the blue rectangle:

Formula:

LH = A (Length x Height = Area)

A = 12 x 4

A = 48 cm²

Area of the green rectangle:

Formula:

LH = A (Length x Height = Area)

A = 13 x 4

A = 52 cm²

Area of the yellow triangles:

Formula:

2 (1/2 Bh) (2 (half of base x height))

A = 2(1/2 5 x 12)

A = 2(1/2 60)

A = 2(30)

A = 60 cm²

Total surface area of the triangular prism:

LH + LH + LH + 2 (1/2 Bh) = Surface Area of the triangular prism (Area of the red rectangle + Area of the blue rectangle + Area of the green rectangle + Area of the yellow triangles = Total surface area of the triangular prism)

A = 20 cm² + 48 cm² + 52 cm² + 60 cm²

A = 180 cm²

5 0
2 years ago
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