The width of a rectangle measures (2h-6) centimeters, and its length measures (7h+8) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

Recall the definition of absolute value:

• |x| = x if x ≥ 0

• |x| = -x if x < 0

So you need to consider 4 different cases (2 absolute value expressions with 2 possible cases each).

(i) Suppose 2x + 3 < 0 and x - 2 < 0. The first inequality says x < -3/2 and the second says x < 2, so ultimately x < -3/2. Then

|2x + 3| + |x - 2| = 6x

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

-2x - 3 - x + 2 = 6x

-3x - 1 = 6x

9x = -1

x = -1/9

But -1/9 is not smaller than -3/2, so this case provides no valid solution.

(ii) Suppose 2x + 3 ≥ 0 and x - 2 < 0. Then x ≥ -3/2 and x < 2, or -3/2 ≤ x < 2. Under this condition,

|2x + 3| + |x - 2| = 6x

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

2x + 3 - x + 2 = 6x

x + 5 = 6x

5x = 5

x = 1

This solution is valid because it does fall in the interval -3/2 ≤ x < 2.

(iii) Suppose 2x + 3 < 0 and x - 2 ≥ 0. Then x < -3/2 or x ≥ 2. So

|2x + 3| + |x - 2| = 6x

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

-2x - 3 + x - 2 = 6x

-x - 5 = 6x

7x = -5

x = -5/7

This isn't a valid solution, because neither -5/7 < -3/2 nor -5/7 ≥ 2 are true.

(iv) Suppose 2x + 3 ≥ 0 and x - 2 ≥ 0. Then x ≥ -3/2 and x ≥ 2, or simply x ≥ 2.

|2x + 3| + |x - 2| = 6x

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

2x + 3 + x - 2 = 6x

3x + 1 = 6x

3x = 1

x = 1/3

This is yet another invalid solution since 1/3 is smaller than 2.

So there is one solution at x = 1.

9514 1404 393

Answer:

  (c) 288π m²

Step-by-step explanation:

The area of a sphere is found using the formula ...

  A = 4πr²

Then the area of a half-sphere with radius 12 m will be ...

  A = (1/2)(4π)(12 m)² = 288π m²

Answer:

4 Flaps per second

Step-by-step explanation:

M = 120/30

Answer:

4 times per second

Step-by-step explanation:

120 ÷ 30 = 4

30 ÷ 30 = 1

4 flaps per 1 second

so basically 4

Answer:

When

when x = - 3 then y=. -10

when y = 2 then x =. -1

Step-by-step explanation:

here's the answer to your question

Answer:

Answer is 0.002

Step-by-step explanation:

15÷7500 = 0.002

Answer:

ampota ma,pakyu

Step-by-step explanation:

what is the answer dapalon taka karun

Answer:

oooooooooooooooooooo

Answer:

[tex]{ \tt{ = \frac{ {9}^{5} }{ {3}^{6} } }} \\ \\ = { \sf{ \frac{( {3}^{2}) {}^{5} }{ {3}^{6} } }} \\ \\ { \sf{ = \frac{ {3}^{10} }{ {3}^{6} } }} \\ \\ = { \tt{ {3}^{(10 - 6)} }} \\ = { \sf{ {3}^{4} }}[/tex]

Answer:

B

Step-by-step explanation:

A student correctly evaluated an expression where p = -2 and q = 3 and acquired 3 as the result.

And we want to determine which expression could the student have been evaluating.

Thus, we simply need to check each expression by letting p = -2 and q = 3 and see which one equals 3.

Checking the first one:

[tex]\displaystyle \begin{aligned} 3p^2 +2pq - 6q +2 &= 3(-2)^2+2(-2)(3)-6(3) + 2\\ &= (12)+(-12) +(-18) + 2 \\ &=-16\end{aligned}[/tex]

The result is not 3. Hence, A is not correct.

The second expression:

[tex]\displaystyle \begin{aligned} p^3 + 2p^2q-p^2+2pq+q &= (-2)^3+2(-2)^2(3)-(-2)^2+2(-2)(3)+(3)\\ &= (-8)+(24)-(4)+(-12)+(3) \\ &= 3\stackrel{\checkmark}{=}3\end{aligned}[/tex]

Therefore, we can conclude that our answer is B.

We can check the other two regardless.

The third expression:

[tex]\begin{aligned} p^2+q-4q^2 &= (-2)^2 + (3) - 4(3)^2 \\ &= (4) + (3) -(36) \\ &= -29\end{aligned}[/tex]

And the fourth:

[tex]\displaystyle \begin{aligned} p^2+3q^2-q^2+p &= (-2)^2+3(3)^2-(3)^2+(-2) \\ &= (4) + (27) - (9) + (-2) \\ &= 20\end{aligned}[/tex]

Thus, neither the third expression nor the fourth is also correct.

In conclusion, our answer is B.

Answer:

Rate of plane 735 km/hr

Rate of wind 65 km/hr

Step-by-step explanation:

Calculation to determine the rate of the plane in still air

Let Va represent the velocity of the airplane

Let Vw represent the velocity of the wind

When flying with the wind:

(Va+Vw)*(6 hours) = 4800

6Va + 6Vw = 4800

6Vw = 4800 - 6Va

Vw=4800/6-Va

Vw = 800 - Va

When flying against the wind:

(Va-Vw)*(6 hours) = 4020 km

6Va - 6Vw = 4020

Substitute 800-Va for Vw and solve for Va:

6Va - 6(800-Va) = 4020

6Va -4800 + 6Va = 4020

12Va = 8820

Va=8820/12

Va = 735 km/hr

Therefore the rate of the plane in still air is 735 km/hr

Calculation to determine the rate of the wind

Rate of wind:

Vw = 800 - Va

Vw= 800 -735

Vw= 65 km/hr

Therefore the rate of the wind is 65 km/hr

Positive parabola that has a minimum.

It’s positive if it opens upward, negative if it opens downward. It has a minimum if it opens upward, and maximum when it opens downward.

Step-by-step explanation:

Slope = rise/run = 1/2

You need to plot these two points = (1,0) and (3,1) and make a line paas through

Answer by Gauthmath

Answer:

Binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" (one). The base-2 numeral system is a positional notation with a radix of 2.

Answer:

[tex] \frac{9}{7} = 1.2857 = 1 \frac{2}{7} [/tex]

Answer:

Step-by-step explanation:

[tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\displaystyle\ \Large \boldsymbol {\frac{9}{7}=1\frac{2}{7} \ \ or \ \ 1.(28571)}[/tex]

Answer:

3 three point baskets

9 two point baskets

4 one point baskets

Step-by-step explanation:

Since you cannot have a 1/3 or 2/3 of a three point basket, finding multiples of threes for the initial two point baskets is the easiest way to start.

Answer:

use Pisagor teorem

Step-by-step explanation:

The line which start on the edge and divided other side 64 and 36 be Y and we use Pisagor teorem so Y²=64*36...... y=8*6=48 .................(1)

use other triangle to find hipotenus 48²+36²=x² .... x= 60

Answer:

Step-by-step explanation:

Degrees   Radians   tangent

60°      π/3         √3

45°            π/4                     1

30°           π/6                 1/√3

0°            0                   0

yfd sat fltfurjbhviccyvihkjobkb 47 I have

Step-by-step explanation:

i Will help wit Shape A and Next Try to figure out Shape B

shape A Looks the Shape XY coordinate, which Horizontal & Vertical Line

Shape A Coordinate

X = 7, 8.5, 7,5, 7.5,

Y = 7, 7, 6.5 , 5

if you wanna to understand this coordinate between X & Y try plotting with Horizontal or Vertical Line at your Shape And you Would be Understanding about these coordinate meaning

Answer:

42.94$ is the answer.....

Answer:

the answer is -299.808 well that's what I think it's

Answer:

-299.808

Step-by-step explanation:

= 10700/100 + 5192/100 - 412

= 107 + 5.192 - 412

= -299.808

Answer:

A = 96 inches ^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 ( b1+b2)h  where b1 and b2 are the bases and h is the height

A = 1/2( 14+10)*8

A = 1/2(24)*8

A = 12*8

A = 96 inches ^2

The area of trapezoid is given

A = 1/2 (b1+b2)h where b1 and b2 is base and h is height

A = 1/2 (14+10)*8

A = 1/2 (24)*8

A = 12 * 8

Answer:

The length = The width = The height  ≈ 5.8 cm

Step-by-step explanation:

The volume of a rectangular pyramid, V = l × w × h

The surface area of the pyramid = 2 × l × h + 2 × w × h + 2 × l × w = 200

∴  l × h + w × h + l × w = 200/2 = 100

We have that the maximum volume is given when the length, width, and height are equal and one length is not a fraction of the other. Therefore, we get;

At maximum volume, l = w = h

∴ l × h + w × h + l × w = 3·l² = 100

l² = 100/3

l = 10/√3

Therefore, the volume, v = l³ = (10/√3)³

The length = The width = The height = 10/√3 cm ≈ 5.8 cm

For the equal distribution each child can take either 1 or 3 or 7 or 9 or 21 or 27 or 63 or 189 apple.

What is equal distribution?

The distribution of a something in a way that each will get same amount.

How 189 can be divided equally?

If the distribution is equally then each child should take, either 1 or 2 or 3 an so on means same amount.

For this we will check that 189 is divisible by which numbers.

Now we can see that 189 is divisible by 1, 3, 7, 9, 21, 27, 63, 189. It is clear that each child can take either 1 or 3 or 7 or 9 or 21 or 27 or 63 or 189 apple then the distribution will be equal means every child will have same amount of apple.

Therefore, the correct answer is 1, 3, 7, 9, 21, 27, 63, 189.

Learn more: https://brainly.ph/question/4734029

#SPJ2

Answer:

abc is a triangle so ,

a is ( 9,6 )

b is ( 9,3 )

and c is ( 3,3 )

Answer:

(8x3)x4+(3x3)x2=114

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

(3+5)^2/8=(8)^2/8=64/8=8

Answer: 8

Step-by-step explanation:

(3+5)^2/8=

(8)^2/8=

64/8=

8

Step-by-step explanation:

Slope is [tex]\frac{rise}{run}[/tex], so the slope is [tex]\frac{y}{x}[/tex], which also equals [tex]-\frac{37}{4}[/tex].