If we know the area of this base, we'll know how many cubes can fill the bottom layer. We can find the area of the rectangle

Help me solve these 4 plssss ASAP

Arisa [49]

Step-by-step explanation:

$1) \\ - 2 \leqslant x \leqslant 1 \\ 2) \\ - 3 > x \geqslant 2 \\ 3) \\ x> 0$

$4) \\ x \leqslant - 3 \\ 5) \\ - 4 \leqslant x \geqslant 1$

$6) \\ - 2< x \leqslant 0$

7 0

2 years ago

How to solve this problem

lozanna [386]

Answer:

x = 2

Step-by-step explanation:

We are given the equation 3 - 4x - 2 = 2x - 11;

$3 - 4x - 2 = 2x - 11,\\3 - 2 = 6x - 11,\\1 = 6x - 11,\\12 = 6x,\\\\x = 2\\Conclusion, x = 2$

If you want this explanation in a " statement reasoning " format refer to the attachment below;

8 0

3 years ago

Question 1

12345 [234]

Answer:

A). Surface area = 222 cm²

Volume = 180 cm³

B). Surface area = 375 cm²

Volume = 360 cm³

C). % increase in surface area = 67.57%

% increase in volume = 100%

Step-by-step explanation:

In the figure attached base of a prism has been given.

A). Surface area of the prism = (Perimeter of the base of the prism) × height + 2(area of the base)

Perimeter of the base = 5 + 3 + 2 + 2 + 2 + 3 + 5 + 8

= 30

Area of the base = 8×5 - 2×2 = 36 cm²

Surface area of the prism = 30×5 + 2×(36)= 222 cm²

Volume of the prism = volume of the bigger prism - volume of the smaller prism cut off

= 8×5×5 - 2×2×5

= 200 - 20

= 180 cm³

B). Surface area of the prism if it's height is 10 cm,

Surface area = 30×10 + 2×(36) = 372 cm²

Volume of the prism = 8×5×10 - 2×2×10

= 400 - 40

= 360 cm³

C). Increase in surface area = 372 - 222 = 150 cm²

% increase in the surface area = $\frac{150}{222}\times 100$ = 67.57%

Increase in volume = 360 - 180 = 180 cm³

% increase in volume = $\frac{180}{180}\times 100$ = 100%

4 0

2 years ago

Simplify 5^2 • 5^4 O A. 5^8 O B. 5^6 O C. 5•8 O D. 5^2

amid [387]

Answer:

Option B

Step-by-step explanation:

Given the following question:

$5^2\times5^4$

In order to find the answer, we simply apply the exponent rule and add the exponents.

$5^2\times5^4$
$2+4=6$
$=5^6$

The answer is option B or "5^6."

Hope this helps.

6 0

2 years ago

Jim wants to build a rectangular parking lot along a busy street but only has 2400 feet of fencing available. if no fencing is r

PSYCHO15rus [73]

Length = 1200, width = 600
First, let's create an equation for the area based upon the length. Since we have a total of 2400 feet of fence and only need to fence three sides of the region, we can define the width based upon the length as: W = (2400 - L)/2
And area is: A = LW
Substitute the equation for width, giving: A = LW A = L(2400 - L)/2
And expand: A = (2400L - L^2)/2 A = 1200L - (1/2)L^2
Now the easiest way of solving for the maximum area is to calculate the first derivative of the expression above, and solve for where it's value is 0. But since this is supposedly a high school problem, and the expression we have is a simple quadratic equation, we can solve it without using any calculus. Let's first use the quadratic formula with A=-1/2, B=1200, and C=0 and get the 2 roots which are 0 and 2400. Then we'll pick a point midway between those two which is (0 + 2400)/2 = 1200. And that should be your answer. But let's verify that by using the value (1200+e) and expand the equation to see what happens:
A = 1200L - (1/2)L^2
A = 1200(1200+e) - (1/2)(1200+e)^2
A = 1440000+1200e - (1/2)(1440000 + 2400e + e^2)
A = 1440000+1200e - (720000 + 1200e + (1/2)e^2)
A = 1440000+1200e - 720000 - 1200e - (1/2)e^2
A = 720000 - (1/2)e^2
And notice that the only e terms is -(1/2)e^2. ANY non-zero value of e will cause this term to be non-zero and negative meaning that the total area will be reduced. Therefore the value of 1200 for the length is the best possible length that will get the maximum possible area.

7 0

3 years ago