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3 years ago

Translate the verbal phrase into an inequality. All real numbers that are greater than or equal to -1.5 and less than 9.2

Mathematics

2 answers:

kari74 [83]3 years ago

8 0

4 is because it is greater and less than

Lina20 [59]3 years ago

6 0

Answer: -1.5 ≤ x < 9.2

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

"All real numbers": we will use the variable x to represent all the real numbers.

"All real numbers that are greater than or equal to -1.5". This means that x is greater or equal (≤) to the number 1.5.

"And less than 9.2": less is represented with the symbol <

Mathematically speaking :

-1.5 ≤ x < 9.2

Feel free to ask for more if needed or if you did not understand something.

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A square garden plot measures 180 square feet. A second square garden plot measures 320 square feet. How many more feet of fence

REY [17]

The second garden plot will require 8√5 feet more fence than the first garden plot.

Further explanation:

In order to find the fence, we have to find the perimeter of both squares

So,

Area of Square 1: A1=180 square feet

Area of Square 2: A2=320 Square feet

Let x be the side of square 1:

Then,

$A_1=x^2\\180=x^2\\Taking\ square\ root\ on\ both\ sides\\\sqrt{180}=\sqrt{x^2}\\x=\sqrt{2*2*3*3*5}\\x=\sqrt{2^2*3^2*5}\\x=2*3\sqrt{5}\\x=6\sqrt{5}$

For second square:

Let y be the side of second square

$A_2=y^2\\320=y^2\\Taking\ square\ root\ on\ both\ sides\\\sqrt{320}=\sqrt{y^2}\\y=\sqrt{2*2*2*2*2*2*5}\\y=\sqrt{2^2*2^2*2^2*5}\\y=2*2*2\sqrt{5}\\y=8\sqrt{5}$

Perimeter of First Square:

$P_1=4x\\=4(6\sqrt{5})\\=24\sqrt{5}\ feet$

Perimeter of Second Square:

$P_2=4y\\=4(8\sqrt{5})\\=32\sqrt{5}\ feet$

The smaller perimeter will be subtracted from larger perimeter to find that how much more fence will be needed.

$P_2-P_1=32\sqrt{5}-24\sqrt{5}\\=(32-24)\sqrt{5}\\=8\sqrt{5}\ feet$

The second garden plot will require 8√5 feet more fence than the first garden plot.

Keywords: Radicals, Operations on Radicals

Learn more about radicals at:

#LearnwithBrainly

6 0

3 years ago

Electric charge is distributed over the disk x2 + y2 ≤ 16 so that the charge density at (x, y) is rho(x, y) = 2x + 2y + 2x2 + 2y

professor190 [17]

Answer:

Required total charge is $256\pi$ coulombs per square meter.

Step-by-step explanation:

Given electric charge is dristributed over the disk,

$x^2=y^2\leq 16$ so that the charge density at (x,y) is,

$\rho (x,y)=2x+2y+2x^2+2y^2$

To find total charge on the disk let Q be the total charge and $x=r\cos\theta,y=r\sin\theta$ so that,

$Q={\int\int}_Q\rho(x,y) dA$ where A is the surface of disk.

$=\int_{0}^{2\pi}\int_{0}^{4}(2x+2y+2x^2+2y^2)dA$

$=\int_{0}^{2\pi}\int_{0}^{4}(2r\cos\theta+2r\sin\theta+2r^2 \cos^{2}\theta+2r^2\sin^2\theta)rdrd\theta$

$=2\int_{0}^{2\pi}\int_{0}^{4}r^2(\cos\theta+\sin\theta)drd\theta+2\int_{0}^{2\pi}\int_{0}^{4}r^3drd\theta$

$=\frac{2}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)\Big[r^3\Big]_{0}^{4}d\theta+2\int_{0}^{2\pi}\Big[\frac{r^4}{4}\Big]d\theta$

$=\frac{128}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)d\theta+128\int_{0}^{2\pi}d\theta$

$=\frac{128}{3}\Big[\sin\theta-\cos\theta\Big]_{0}^{2\pi}+128\times 2\pi$

$=\frac{128}{3}\Big[\sin 2\pi-\cos 2\pi-\sin 0+\cos 0\Big]+256\pi$

$=256\pi$

Hence total charge is $256\pi$ coulombs per square meter.

3 0

3 years ago

Help AB and CD are straight lines find z

chubhunter [2.5K]

Answer: z=16

Step-by-step explanation:

Angles on a straight line add up to 180.

As AB is a straight line we can use that to help us find z.

So you would do 68+85+11=164 (I got the 11 from the angle trapped between like C and F as opposite angles are the same).

Then you would do 180-164=16

So z=16

Hope this helps :)

3 0

3 years ago

What is 13 divied it by 2

MrMuchimi

Answer:

6.5

Step-by-step explanation:

4 0

2 years ago

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irga5000 [103]

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4 years ago