Btw the biggest garden is the rectangular garden

Answer:

5 > \(\sqrt{18\)

Step-by-step explanation:

The square root of 18 is approximately 4.24.

5 is greater than 4.24, so we can use the inequality sign >.

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\(\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}\)

             Solve x²-5x+6

\(\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}\)

(x-2)(x-3)

\(\blue{\textsf{\textbf{\underline{\underline{How\:to\:Solve:-}}}}\)

                      First, we think of two numbers such that

     If we multiply them, we'll get 6

      If we add them, we'll get -5

These numbers are -2 and -3.

Write them here:

(x-2)(x-3)

Now, how do we get (x-2)(x-3) from x(x-2)-3(x-2)?

Notice that (x-2) is the common term, so we factor it out:

(x-2)

And now, we write the other two terms that are left in the parentheses:

(And the terms left are x and -3)

(x-2)(x-3)

Notice that we ended up with the same answer.

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A cone with a diameter of 16 centimeters has a volume of 320π cubic centimeters, the height of the cone is 15 cm.

A cone should be emptied at a time after being filled with water. The cylinder is filled to a third with each cone. Since there are three of them, the cylinder will be filled. As a result, the volume of a cone is equal to one-third of the volume of a cylinder.

Cone volume is calculated using the method V=1/3πhr².

Given that,

diameter(d) = 16 cm

radius (r) = d/2 = 8 cm

volume = 320π cubic centimeters

πr²h/3 = 320π

or, [π × (8)² × h]/3 = 320π

or,  h = (3 × 320)/(8)²

or, h = 15 cm

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Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

Answer:

True,  it is Known as a neutral integer Because it is neither negative or positive whole number

Step-by-step explanation:

Answer:

true. zero is an integer number

Step-by-step explanation:

Answer:

Step-by-step explanation:

The length of the third side is ( x - 2 )

Step-by-step explanation:

Volume of a box is the product of its length, width and height.

Volume of box = length × width × height.

One side is (x - 4) and another side is (2x + 1).

These given sides can be either length, height or width.

The volume of a box is given by V = 2x3-11x2 +10x +8. This means each of the sides are factors of the volume. To get the third side, we divide the volume by the product of the two given sides.

Product of the two given sides =

( x-4 ) (2x + 1) = 2x^2 + x - 8x + 4

= 2x^2 - 7x - 4

The long division is shown on the attached photo

The length of the third side is ( x - 2 )

Answer:

its x-4 ig

Step-by-step explanation:

If one side of the square is x-4 then the missing side has to be x-4 also.

Answer:

(0.0147, 4.0147) and (-4.04, 0.04)

Step-by-step explanation:

Let the smaller number be x

Let the larger number be y

If a positive integer is 4 less than another, then;

x = y - 4 ...1

If 3 times the reciprocal of the smaller integer is subtracted from the reciprocal of the larger integer and result is -67, then;

1/y - 3(1/x) = -67

1/y   -3/x = -67 ...2

Substitute 1 into 2

1/y - 3/y-4 = -67

y-4-3y/y(y-4) = -67

-4-2y = -67(y^2-4y)

- 4-2y = -67y^2 +268y

-67y^2 +268y+2y + 4  = 0

-67y^2 +270y +  4 =0

67y^2 -270y - 4 = 0

Factorize

-270±√270² - 4(-4)(67)/2(67)

= -270±√72,900+1072/134

= -270±271.97/134

= -270 -271.97/134 and  -270 +271.97/134

= -541.97/134 and 1.97/134

x = 0.0147 and -4.04

y = x+4

y = 0.0147+4

y = 4.0147

If x = -4.04

y = -4.04 + 4

y = 0.04

Hence the pair of values are (0.0147, 4.0147) and (-4.04, 0.04)

Solution.

The problem is an exponential growth problem (Because The number of cells in the tumor doubles every 2.5 months)

The formula for exponential growth is

In the problem given,

a = 1

r = 2

(i) After 2 years, that is ( 2 x 12 months = 24 months)

t = 24/2.5 = 9.6

The number of cell that will be after 2 years = 38,050 cells (nearest whole number)

(ii) After 5 years

5 years = 5 x 12 months = 60 months

t = 60/2.5 = 24

Answer: 36 combinations

Step-by-step explanation:

Since you have 4 toppings, 3 bases and 3 sauces, you can just multiply them to get the different combos.

4 * 3 * 3

= 36

Answer:

Hey there!

This is an obtuse isosceles, because two sides are congruent, and one angle is greater than 90 degrees.

Let me know if this helps :)

Answer:

\(\Large \boxed{\mathrm{C. \ obtuse \ isosceles }}\)

Step-by-step explanation:

An isosceles triangle has two equal angles. This triangle has two base angles equal.

An obtuse triangle has an angle measuring greater than 90 degrees. This triangle has an angle measuring 136 degrees.

This triangle is an obtuse isosceles triangle.

Answer:

m= -5/9

Step-by-step explanation:

m= y2-y1/ x2-x1

m= -3-2/ 5-(-4)

m= -3-2/ 5+4

m= -5/9

y= mx + b

(-4,2)

2= -5/9(-4) + b

2= 2.2+ b

-2.2 +2= b

-0.2= b

Answer: 57.14 km/hr

Step-by-step explanation:  if an hour is divided into quarters it will be in increments of 15 minutes, since  one hour is 60 minutes.  60 minutes divided by 5 is 15 minutes.  

So 1 hour and 38 minutes is rounded off to 1 hour and 45 minutes.

this is 1 hour + 3/4 hour = 1 3/4 hour.  This is same as 1.75 hour

3/4 is .75

speed divided by the time will give the average speed.

100km/1.75hours  = 57.14 km/per hour

Answer:

(a)  1 hour 45 min

(b)  57.1 km/h (nearest tenth)

Step-by-step explanation:

Given information:

\(\large\boxed{\sf Speed=\dfrac{Distance}{Time}}\)

\(\begin{aligned}\sf \dfrac{1}{4}\;hour &= \sf 1 \; hour \div 4 \\& = \sf 60 \;mins \div 4\\& = \sf 15 \; mins\end{aligned}\)

Therefore, the nearest ¹/₄ hours either side of the given time is:

1 h 38 min 45 sec is 8 min 45 sec more than 1 hour 30 min.

1 h 38 min 45 sec is 6 min 15 sec less than 1 hour 45 min.

Therefore, the nearest ¹/₄ hour to the given time is:  

1 hour 45 min = 1.75 min (in decimal form)

Substitute the given distance and the rounded time (in decimal form) into the formula and solve for speed:

\(\begin{aligned} \implies \sf Speed & =\sf \dfrac{Distance}{Time}\\\\& = \sf \dfrac{100}{1.75}\\\\& = \sf 57.1\;km/h\;(nearest\;tenth)\end{aligned}\)

Step-by-step explanation:

In a circle

Diameter (d) = 22 cm

radius (r) = d / 2 = 22 /2 = 11 cm

Hope it will help :)

The area of the triangle MNO to the nearest tenth of an inch is 14.2 inches².

Given a triangle MNO.

It is given two sides and the included angle of the triangle.

The area of a SAS triangle can be found using the formula,

Area = \(\frac{1}{2}\) × ab × sin (C)

where a and b are the given sides and C is the included angle.

Here the given sides are,

n = 7.3 inches and o = 4.4 inches

Included angle is,

∠M = 118°

Using the formula,

Area = \(\frac{1}{2}\) × no × sin (M)

        =  \(\frac{1}{2}\) × (7.3)(4.4) × sin (118°)

        =  \(\frac{1}{2}\) × (7.3)(4.4) × 0.883

        = 14.18 ≈ 14.2 inches²

Hence the required area is 14.2 inches².

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Missing information:

How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point

\(P = (\frac{1}{2}, \frac{\sqrt 3}{2})\)

Answer:

\(Rate = 0.935042^\circ /cm\)

Step-by-step explanation:

Given

\(P = (\frac{1}{2}, \frac{\sqrt 3}{2})\)

\(T(x,y) =x\sin2y\)

\(r = 1m\)

\(v = 2m/s\)

Express the given point P as a unit tangent vector:

\(P = (\frac{1}{2}, \frac{\sqrt 3}{2})\)

\(u = \frac{\sqrt 3}{2}i - \frac{1}{2}j\)

Next, find the gradient of P and T using: \(\triangle T = \nabla T * u\)

Where

\(\nabla T|_{(\frac{1}{2}, \frac{\sqrt 3}{2})} = (sin \sqrt 3)i + (cos \sqrt 3)j\)

So: the gradient becomes:

\(\triangle T = \nabla T * u\)

\(\triangle T = [(sin \sqrt 3)i + (cos \sqrt 3)j] * [\frac{\sqrt 3}{2}i - \frac{1}{2}j]\)

By vector multiplication, we have:

\(\triangle T = (sin \sqrt 3)* \frac{\sqrt 3}{2} - (cos \sqrt 3) \frac{1}{2}\)

\(\triangle T = 0.9870 * 0.8660 - (-0.1606 * 0.5)\)

\(\triangle T = 0.9870 * 0.8660 +0.1606 * 0.5\)

\(\triangle T = 0.935042\)

Hence, the rate is:

\(Rate = \triangle T = 0.935042^\circ /cm\)

The congruent reason for the triangles is (b) HL theorem

From the question, we have the following parameters that can be used in our computation:

Triangles = FGH and JHK

The SSS similarity theorem implies that the corresponding sides of the two triangles in question are not just similar, but they are also congruent

From the question, we can see that the following corresponding sides on the triangles:

Sides GH and HK

Sides FH and JK

These parameters are given in reasons (2) and (3) and it implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following sides must also be congruent

GH must be congruent to HK

The above statement is true because point H is the midpoint of line GK

This is indicated in reason (2)

Hence, the congruent statement is SSS.

However, we can also make use of the HL theorem in (B)

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Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

Answer: 18

Step-by-step explanation:

\(\triangle HJK \cong \triangle HLK\) by HL. Therefore, \(JK=2\) by CPCTC.

Using the segment addition postulate, \(GK=9\).

Furthermore, \(\triangle HGK \cong \triangle HMK\) by HL. This means that \(MK=9\) by CPCTC.

Using the segment addition postulate again, \(GM=9+9=18\).

Answer:

1:4

Step-by-step explanation:

because the ratio go first

Answer:

See attachment and explanation

Step-by-step explanation:

The question requires us to plot a graph of width on the x axis and area on the y axis.

We know that in plotting a graph, the nature of the values determines the shape and nature of the graph. The values we have here will ultimately lead us to a smooth curve as we can see from the excel document attached to this answer.

well, since we know that there are 180° in π radians, how many degrees will it be in 345°?

\(\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ 345&x \end{array}\implies \cfrac{180}{345}~~ = ~~\cfrac{\pi }{x}\implies \cfrac{12}{23}~~ = ~~\cfrac{\pi }{x} \\\\\\ 12x=23\pi \implies x=\cfrac{23\pi }{12}\)

The new area would be 40 square inches. When a scale factor dilates a polygon, the area is multiplied by the square of the scale factor. If the original area is 10 square inches and the scale factor is 4, the new area would be 10 x 4^2 = 10 x 16 = 40 square inches.

With the Application of Integral calculus the volume of  solid generated is π.

what is integral calculus?

We study integrals and their characteristics in the calculus area known as integral calculus. A crucial idea is integration, which is the opposite of difference. The fundamental theorem of calculus establishes a connection between integral and differential calculus.

v = 2π∫0√π/2xcosx2dx

  = π·sinx20√π/2

v = π

Hence the volume of  solid generated when the region enclosed by the given curves is revolved about the y-axis is π

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\(w^2 - 6w + 4\) is a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.

The profit earned by selling w pear trees is 2w + 10

To find the difference in profit, we need to subtract the profit earned by selling w pear trees from the profit earned by selling w apple trees:

\((w^2 - 4w + 14) - (2w + 10)\)

Simplifying the expression:

\(w^2 - 6w + 4\)

Therefore, the polynomial that represents how much more profit is earned by selling w apple trees than w pear trees is \(w^2 - 6w + 4\).

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Answer:

A

Step-by-step explanation:

-3 + 2 = -1

1 = 9 - 8

Answer:

-3t-1

Step-by-step explanation:

Answer:

You will find the answer from my explanation.

Step-by-step explanation:

Let the cost of one small shirt be x

And that of a large shirt be y

From the expression above;

4x + 14y = 210; since the total cost of a small shirt by Wili is;

4 * x and the large shirts 14 * y

Similarly for Jordan we have:

12x + 11y = 110; since the total cost of a small shirt by Jordan is;

12 * x and the large shirts 11 * y

We now have two equations,

So you can solve both equations now using elimination method;

If you multiply all the variables of x and y in the first equation by 3 and then subtract the second equation from it, x would be eliminated remaining y;

Multiplying the first equation we have;

12x + 42y = 630

- 12x + 11y = 110

------------------------------

0. + 31y = 520

You can continue from there

On solving the provided question, we can say that -  95 confidence interval Z alpha 2 = 1.96, CI = (4.1 , 53.9)

The z critical value is 1.96 for a test with a 95% confidence level (e.g. = 0.05). The z critical value is 5.576 for a test with a 99% confidence level (for instance, with = 0.01).

The two red tails represent the alpha level split by two. Finding the z-score for an alpha level for a two-tailed test is what is meant when a question asks you to determine z alpha/2. The confidence interval may be subtracted from 100% to calculate alpha, which is connected to confidence levels.

for 95% confidence,

\(Z_{\frac{\alpha }{2} }\) = 1.96

CI = (5279 - 5250) ± 1.96\(\sqrt{\frac{140^2}{395} + \frac{210^2}{395} } \\\)

CI = (4.1 , 53.9)

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