The width of rectangular field is x metres.

The length of the field is 30m longer than the width.

The perimeter of the field is less than 500m.

The area of the field is greater than 4000m^2


By writing suitable inequalities, find the possible values of x

Answer:

y = x - 6.

Step-by-step explanation:

Do the division:

x + 2 ) x^2 - 4x + 8 (  x - 6 <------- Quotient.

          x^2 + 2x

                    -6x + 8

                    -6x - 12

                     ----------

                              20

Answer: 88 inches

Step-by-step explanation:

Given : A bicycle tire is 28 inches in diameter. approximately.

To find the distance traveled by the bicycle each time the wheel goes around we need to find the circumference of the tire.

The circumference of a circle : [tex]\pi d[/tex], where d is the diameter of the circle.

Now, the circumference of tire : [tex]\dfrac{22}{7} \times(28)=88[/tex]

Hence, the distance traveled by the bicycle each time the wheel goes around  =88 inches.

The wheel moves forward each time, in a single round it will cover distance of 88 inches.

Given information:

The diameter of the tire is 28 inches.

Now, if we need to find the distance covered by the tire in one round, we need to understand that the tire will cover exactly same distance as it's circumference in one round.

So, the distance will be equal to its circumference :

[tex]D=\pi\times d[/tex]

Hence, distance covered (D)

[tex]D=3.14\times 28\\D=88[/tex]

Hence, when the wheel move forward each time the in a single round it will cover 88 inches.

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Answer:

100 Degrees

Step-by-step explanation:

It's correct for Acellus! :-)

Answer:

The first number is 8

Step-by-step explanation:

Let

x -----> the first number

y ----> the second number

x=3y-4 ----> equation A

3+2x-2y=11 ----> equation B

Substitute equation A in equation B and solve for y

3+2(3y-4)-2y=11

3+6y-8-2y=11

4y=11+5

y=16/4=4

Find the value of x

x=3(4)-4=8

Answer:

I’m not sure, but I think it’s C

Answer:

V≈4.19ft³

Step-by-step explanation:

The volume of a sphere with a radius of 1 foot is 4.19ft³.

In order to find this:

V=4

3πr3=4

3·π·13≈4.18879ft³

[tex]V=\dfrac{4}{3}\pi r^3\\\\V=\dfrac{4}{3}\cdot3.14\cdot 1^3\approx4.19\text { ft}^3[/tex]

Answer:

no solutions

Step-by-step explanation:

-4x-4=-4(x+2)​

Distribute the negative

-4x-4 = -4x-8

Add 4x to each side

-4x+4x-4 = -4x+4x-8

-4 = -8

Since this is not true there are no solutions

Answer:

(x+2)^{2} +5(x+2)-6=0

Let

u=(x+2)

Substitute in the expression

(u)^{2} +5(u)-6=0

therefore

the answer is

(u)^{2} +5(u)-6=0 is equivalent to (x+2)^{2} +5(x+2)-6=0

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Answer:

6

Step-by-step explanation:

For both to be chosen the other spot can be taken by any of the other 6 people in the row. So six possibilities

Answer:

A. [tex]^6C_1=6[/tex]

Step-by-step explanation:

Given,

The total number of people = 8,

The number of people have to chosen = 3,

Since, me and my friend both have to be chosen,

So, the remaining number of people = 8 - 2 = 6,

And, the number of remaining number of people have to be chosen = 3 - 2 = 1

Also, the order does not matter,

Hence, the total way of choosing = Total combination of me and my friend × total combination of choosing 1 person out of 6 people

[tex]=^2C_2\times ^6C_1[/tex]

[tex]=1\times ^6C_1[/tex]

[tex]=6[/tex]

Option A is correct.

Answer:  Point, Point, Line

Step-by-step explanation:

A plane and a line intersect at a point .  Think of a piece of paper as a plane and a pen as a line.  What happens when you push the pen through the paper?  It creates a point!

Two lines intersect at a point .

Two planes intersect at a line . Think of a piece of paper laid horizontally on a table and another piece of paper standing on it vertically.  What can you draw at the places of intersection? A line!

Given the provided conditions, we set up an equation to determine the width and length of the indoor football field. After simplifying the appropriate mathematical expressions, we find that length of the football field is 66 yards.

In this problem, we're solving for the length of an indoor football field. We know that the perimeter of a rectangle is given by [tex]2L + 2W[/tex] (twice the length plus twice the width) and the length is said to be 45 yards longer than the width. Therefore, we would describe the length as 'W + 45'

Let's represent the width as W and thus the length as W + 45. Substituting these into our perimeter equation we get [tex]2(W) + 2(W +45) = 174.[/tex] Simplifying gives [tex]4W + 90 = 174[/tex]

Subtracting 90 from both sides gives 4W = 84. Thus, W = 21. Substituting this value back into our equation for the length gives us L = 21 + 45 which equals 66 yards. Therefore, the length of the indoor football field is 66 yards.

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Answer:

m = [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 4x + 7 is in this form with slope m = - 4

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex]

Hence the value of m = [tex]\frac{1}{4}[/tex]

Answer:

10r(d - 6).

Step-by-step explanation:

The GCF is 10r.

So the answer is:

10r(d - 6).

Answer:

The true statements are,

x ∈ B

x ∉ C

x ∈ A ⋃ B

x ∈ A ⋂ B

x ∈ A ⋃ C

Step-by-step explanation:

From the figure we can see three sets A, B, C

Check all options

1)  x ∉ A

From the figure we get, x is an element of A

x ∉ A is False

2)  x ∈ B

From the figure we get, x is an element of B

x ∉ B is True

3)  x ∉ C

From the figure we get, x is not an element of C

x ∉ C is True

4). x ∈ A ⋃ B

From the figure we get, x is an element of A ⋃ B

x ∈ A ⋃ B  is True

5). x ∈ A ⋃ C

From the figure we get, x is an element of A ⋃ C

x ∈ A ⋃ C  is True

6).x ∈ A ⋂ B

From the figure we get, x is an element of A ⋃ B

x ∈  A ⋂ B   is True

Answer:

Everything is true expect for the first answer choice .

Step-by-step explanation:

let's convert the 0.05 to a fraction first, so we have two decimals, so our fraction will have two zeros then.

[tex]\bf 0.\underline{05}\implies \cfrac{005}{1\underline{00}}\implies \cfrac{1}{20} \\\\[-0.35em] ~\dotfill\\\\ 10\div 0.05\implies \cfrac{10}{1}\div \cfrac{1}{20}\implies \cfrac{10}{1}\cdot \cfrac{20}{1}\implies 200[/tex]

Answer:

28 deg

Step-by-step explanation:

Reference angle is the smallest angle formed by the terminal ray, x-axis, and origin. So at 180 you are on the x-axis so just for this question you have to do 180-152=28.

The reference angle should be a positive between 0 and 90 degrees.

Answer:

-2

Step-by-step explanation:

The only domain problems are going to come from the square root you have there. You only want to square root 0 or positive numbers,. In other words, you want x+2 to be greater than 0 or equal to 0.

x+2>=0

x>=-2

So x has to be greater than ot equal to 0

Answer:

[tex]x^3+1[/tex]

Step-by-step explanation:

[tex] 26(x^3+1)^2-22(x^3+1)-3=0 [/tex]

Comparing to

[tex] A(u)^2+B(u)+C =0 [/tex]

Where A,B,C are constants

You should see that we need to substitute the [tex]x^3+1[/tex] with u.

Answer:

7

Step-by-step explanation:

Blue is 7 and the Red is 7

Answer:

7

Step-by-step explanation:

Answer:

Practical probability:  9 / 20 = 45%

Theoretical probability: 3 / 6 = 50%

Step-by-step explanation:

So, we have 20 rolls:

1 5 3 2 3 6 5 6 3 3 4 4 1 3 6 5 3 2 2 6

Out of which we have 9 even numbers: 2 6 6 4 4 6 2 2 6

So, the practical probability is 9 / 20 or 45%

The theoretical probability is:

Possible outcomes (6): 1 2 3 4 5 6

Even numbers possible (3): 2 4 6

P = 3 / 6 = 50%

The practical probability is a bit lower (45%) than the theoretical probability (50%) but that's most probably due to the low number of rolls, it's just one roll away from being on target.  With a greater number of rolls, the student would get closer to the theoretical probability.

Answer:

unlikley

Step-by-step explanation:

Step-by-step explanation:

a = x^2 - 1

b = 2x

c = x^2 + 1

The Pythagorean theorem states

a^2 + b^2 = c^2

Let's find a^2 and b^2 and add them to get a^2 + b^2:

a^2 = (x^2 - 1)^2 = x^4 - 2x^2 + 1

b^2 = (2x)^2 = 4x^2

a^2 + b^2 = x^4 - 2x^2 + 1 + 4x^2 = x^4 + 2x^2 + 1

Now let's find c^2:

c = x^2 + 1

c^2 = (x^2 + 1)^2 = x^4 + 2x^2 + 1

We see that both a^2 + b^2 and c^2 equal x^4 + 2x^2 + 1, so we have shown that the triangle is a right triangle.

We can see that a² + b² = c² = x⁴ + 2x² + 1, indicating that the triangle is a right triangle.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometric function.

According to Pythagoras, the sum of the squares of two sides equals the square of the longest side.

Given data;

a = x² - 1

b = 2x

c = x² + 1

According to the Pythagorean theorem;

[tex]\rm a^2 + b^2 = c^2[/tex]

Let's find a^2 and b^2 and add them to get a^2 + b^2:

[tex]\rm a^2 = (x^2 - 1)^2 \\\\ a^2 = x^4 - 2x^2 + 1 \\\\ b^2 = (2x)^2 \\\\ b^2 = 4x^2\\\\[/tex]

Left hand side:

[tex]\rm a^2 + b^2 = x^4 - 2x^2 + 1 + 4x^2 \\\\ a^2 + b^2 =x^4 + 2x^2 + 1[/tex]

Right hand side:

[tex]\rm c^2 = (x^2 + 1)^2 \\\\ c^2 = x^4 + 2x^2 + 1[/tex]

L.HS.=R.H.S

Hence,the given triangle is a right angled triangle.

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Answer:

13.9 containers or 14 rounded

Step-by-step explanation:

2/7 of a pound is 0.28571429 in decimal form. To solve you have to know how many 2/7 of a pound will go into 4 pounds. So you divide 2/7 of a pound by 4 pounds, and the answer is 14.

Answer:

14

Step-by-step explanation:

He will need 14 containers. 4 times 7/2 is 28/2. You then have to simplify it and will get 14.

we can take a peek at two of those lines  hmmm say y = 5x + 3 and y = 5x + 7.

let's notice, those two equations for those lines are in slope-intercept form, so let's solve the system.

since y = y then

5x + 3 = 5x + 7

3  = 7    what the?

well, notice, both lines have the same slope of 5, but different y-intercept, one has it at y = 3 and the other at y = 7, what does that mean?

it means that both lines are parallel to each other, one may well be above the other, but both are parallel, and since a solution to the system is where their graphs intersect, well, parallel lines never touch, so a system with two parallel lines has no solutions.

The two lines are parallel.

We have a girl Deedra who has the equations for lines A and B. When she solved for the point where these two lines intersect, she ended up with the equation 3 = 7.

We have to investigate what it tells about the nature of lines.

The slope intercept form of an equation of line is -

y = mx + c

Let's assume we have two lines with their equations be -

[tex]y_{1} = m_{1} x_{1} + c\\y_{2} = m_{2} x_{2} + d[/tex]

To find the intersecting points of these two lines, then -

[tex]y_{1} =y_{2} \\x_{1} =x_{2}[/tex]

Therefore -

[tex]m_{1} x_{1} +c =m_{2} x_{2} +d\\[/tex]

Now, in the question she found out that 3 =7 which is same c = d. To fulfill this condition, the slope of these two lines should be equal. Hence, we can conclude that the two lines are parallel.

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The volume of the space outside the pyramid but inside the prism is 250 cubic centimeters.

To find the volume of the space outside the pyramid but inside the prism, we first need to determine the volumes of both the prism and the pyramid.

The prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. The volume of a rectangular prism is calculated by multiplying the base area by the height. In this case, the base area is 5 cm * 5 cm = 25 square centimeters. Therefore, the volume of the prism is 25 cm² * 12 cm = 300 cubic centimeters.

The pyramid has the same square base as the prism, with sides measuring 5 centimeters. However, its height is half that of the prism, which is 12 cm / 2 = 6 centimeters. The volume of a pyramid is calculated by multiplying the base area by one-third of the height. In this case, the base area is 25 cm², and one-third of the height is 6 cm / 3 = 2 centimeters. Therefore, the volume of the pyramid is 25 cm² * 2 cm = 50 cubic centimeters.

To find the volume of the space outside the pyramid but inside the prism, we subtract the volume of the pyramid from the volume of the prism: 300 cubic centimeters - 50 cubic centimeters = 250 cubic centimeters.

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Answer:

Step-by-step explanation:

Let x - y = A

A^4 - A^2

A^2 ( A^2 - 1)

A^2 (A + 1)(A - 1)

(x - y)^2 (x - y + 1)(x - y - 1)

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Hello there!

X = 67°

Answer and work are provided in the image attached.

Answer:

x = - 8, x = 8

Step-by-step explanation:

Given

x² - 64 = 0 ( add 64 to both sides )

x² = 64 ( take the square root of both sides )

x = ± [tex]\sqrt{64}[/tex] = ± 8

Answer:

12) 154   squared meters

13) 307  cm^2

Step-by-step explanation:

12) A circle has area pi*r^2

r is half the diameter so half of 14 is 7

pi in this case is 22/7

A=22/7 * (7)^2

A=22/7  * 49

A=22     *49/7

A=22     *7

A=154 squared meters

13)  Area of rectangle is 10(18)=180

      Area of half a circle is .5*pi*r^2=.5*pi*9^2  

       Adding the two areas together would result in a total area of 307.2 squared centimeters