a tiling of the plane occurs when we fill the entire infinite playing with a repeated pattern . the image to the right shows a portion of one such tiling. The pattern extends forever in all directions. A give all angles of rotational symmetry between 0 and 360 degrees about the two marked points. point A: Point B:

First, let's find the measure of the third side, using the law of cosine:

Now, let's use Heron's formula to calculate the area:

If the volume of a rectangular prism with a height of 8 inches is 200 cubic inches and the base of the prism is a square, then the width of the rectangular prism is 5  inches

The volume of the rectangular prism = 200 cubic inches

The height of the rectangular prism = 8 inches

We know the volume of the rectangular prism = l×w×h

Where ls if the length of the base

w is the width of the base

h is the height of the rectangular prism

Given that the base of the prism is a square, then the length of the base is equal to width of the base

Consider

l = w = x

Substitute the values in the equation of volume

x × x × 8 = 200

[tex]x^{2}[/tex] × 8 = 200

[tex]x^{2}[/tex]  = 25

x = 5 inches

Hence, if the volume of a rectangular prism with a height of 8 inches is 200 cubic inches and the base of the prism is a square, then the width of the rectangular prism is 5 inches

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Te solutions to the linear equation given as y = 12x + 24 are (0, 24), (1, 36) and (2, 48)

From the question, the linear equation is given as

y = 12x + 24

To determine the solutions, we assume values for the variable x and then calculate the y values

Having said that, we have

y = 12x + 24

Set x = 0

So, we have

y = 12 x 0 + 24 = 24

Set x = 1

So, we have

y = 12 x 1 + 24 = 36

Set x = 2

So, we have

y = 12 x 2 + 24 = 48

So, the ordered pairs of the solutions are (0, 24), (1, 36) and (2, 48)

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Given:

The expression given is,

Required:

To find the coefficient of the third term.

Explanation:

Let us expand the expression to find the coefficient.

Hence, the coefficient of the third term is 40.

Final Answer:

The coefficient of the third term is 40.

Option A is correct.

From the question we were given the following:

Area of the square is 19 square units

Area of the circle is 30 square units

Area of intersection is 3 square units.

We are asked to find the area in square units of the entire coloured region.

So,

Are of Square = 19 square units

Are of Circle = 30 square units

Area of Intersection = 3 square units

Area of coloured region = Area of Square + Area of Circle - Area of Intersection

Therefore, Area of coloured region = 19 + 30 - 3

= 46 saqure units.

Answer:

x=7, DF = 174

Step-by-step explanation:

18x-39=9x+24

9x=63

x=7

:]

In order to solve this problem, first let's draw the corresponding image to the problem:

Then, to calculate the distance x, we can use the sine relation of the angle of 18°.

The sine relation is the length of the opposite side to the angle over the length of the hypotenuse.

So we have:

So the distance wanted is 7.42 ft.

Lengths of similar triangles and similar polygons are proportional to each other so, answer to the question in image are-

a. ZY=20

b. X=20.8

c. 9miles

What are similar polygons?

similar polygons are the polygons in which all the corresponding angles are same. Hence, they have same shape. The ratio of sides in any two similar polygons are same. This concept of constant ratio of sides is useful in evaluating the length of sides.

a.    A/a=B/b=C/c = D/d

       WX/HI=ZY/JK

   ZY=20

b.  X=(2.4×39)/4.5

                  X= 20.8

c. If 5cm represents 2miles it implies 1cm represents

1cm=2/5

So, 22.5cm will represent

22.5cm=2/5×22.5

22.5cm=9miles

This means that 22.5cm track represents the distance of 9 miles on map

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Answer:

She can run 3/5 miles in 1 hour

Explanation:

Given that Ava can run 4/5 of a mile in 4/3 of an hour, we want to find how far she can run in 1 hour.

Let x represent the number of miles she can run in one hour.

The statement can be represented in the pair of equations:

Using these equations, we have:

That is, she can run 3/5 miles in 1 hour

[tex] \sqrt{25} [/tex] ()

what's the square root ​?

√25 = 5

because 5*5= 25

________________________

Answer

√25 = 5

Given:

To Determine: The standard form equation of an ellipse

Solution

Let's begin by listing out the information given to us:

To know which is greater between 0.123 To know which i3& 0.68, let's express it in tenth, hundredth & thousandth

0.123 has 3 decimal places, which means it is 123/1000

0.68 has 2 decimal places, which means it is 68/100

When you multiply by 100, we have:

0.123 * 100 = 12.3

0.68 * 100 = 68

It becomes very evident that 0.68 is greater than 0.123

The solution to the given inequality would be n ≤ 1/35 which is the correct answer would be an option (C).

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We have to determine the solution of the inequality n minus three-fifths is less than or equal to negative four sevenths for n.

As per the given condition, translate the phrase into an algebraic inequality as :

⇒ n - 3/5 ≤ - (4/7)

⇒ n ≤ 3/5 - (4/7)

⇒ n ≤ (21 - 20)/35

⇒ n ≤ 1/35

Therefore, the solution to the given inequality would be n ≤ 1/35.

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The given system of equations : 6x - y = 2 and 4x - y = -8.

6x - y = 2 ( 1 )

4x - y = -8 ( 2 )

for the value of y, use substitution method:

Solve the equation (1) for y :

6x - y = 2

y = 6x - 2

Susbtitute the value of y in the equation ( 2 )

4x - y = - 8

4x - (6x - 2) = - 8

4x - 6x + 2 = - 8

4x -6x = - 8 - 2

-2x = -10

Divide both side by ( -2)

-2x/(-2) = -10/(-2)

x = 5

Substitute x = 5 in the equation ( 1 )

6x - y = 2

6( 5 ) - y = 2

30 - y = 2

y = 30 - 2

y = 28

So, the value of y is 28

Answer : y = 28

The answers of the given questions are:

Given: There are 6 teaspoons of garlic powder and 15 teaspoons of salt in a triple batch of spice mix.

Let x be the teaspoons of salt.

Salt used with 8 teaspoons of garlic powder:

6/15 = 8/x

x = 20

Therefore, 20 teaspoons of salt is used with 8 teaspoons of garlic powder.

6 + 15 = 21 teaspoons of  spice mix

Salt used in 14 teaspoons of spice mix:

21/15 = 14/x

x = 10 teaspoons of salt.

Therefore, if there are 14 teaspoons of spice mix, 10 teaspoons of salt is there in it.

If 6 teaspoons of garlic powder are used then,

21-6 = 15 teaspoons of more salt is used

Therefore, 15 teaspoons of more salt is there than garlic powder if 6 teaspoons of garlic powder are used.

The answers of the given questions are:

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Given:

The length of the marathon is L= 46,145 yards.

The length covered by terrence is d = 23,561 yrads.

The objective is to find the remaining distance need to cover by terrence.

To calculate the remaining distance, we will use the relation,

On plugging the values in the above relation, we get,

Hence, Terrence needs to run about 23000 yards.

To create the abbreviated expression, combine similar terms by adding them all together. If the expression be [tex]$\sqrt{112 x^{10} y^{13}}$[/tex] then expression exists [tex]$4 \sqrt{7} x^5 y^6 \sqrt{y}$[/tex].

Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. In the conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.

Start by recognizing the like terms, or terms with the same variables and exponents, in algebraic formulas. Then, to create the abbreviated expression, combine similar terms by adding them all together.

Let the expression be [tex]$\sqrt{112 x^{10} y^{13}}$[/tex]

separating the roots of the expression, we get

[tex]$\sqrt{112 x^{10} y^{13}}=\sqrt{112} \sqrt{x^{10}} \sqrt{y^{13}}$[/tex]

simplifying the above equation, we get

[tex]$=\sqrt{112} \sqrt{x^{10}} \sqrt{y^{13}}$[/tex]

Simplify [tex]$\sqrt{x^{10}}= x^5$[/tex]

[tex]$=\sqrt{112} x^5 \sqrt{y^{13}}$[/tex]

Simplify [tex]$\sqrt{y^{13}}=y^6 \sqrt{y}$[/tex]

[tex]$=\sqrt{112} x^5 y^6 \sqrt{y}$[/tex]

[tex]$=\sqrt{112}=4 \sqrt{7}$[/tex]

[tex]$=4 \sqrt{7} x^5 y^6 \sqrt{y}$[/tex]

Therefore, the correct answer is [tex]$4 \sqrt{7} x^5 y^6 \sqrt{y}$[/tex].

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We have the function:

And we have to find the inverse function.

We can write this as:

We can solve this as:

The inverse function is:

The domain of H is all the real numbers, as the domain of H^-1.

sin theta = -0.5 degrees

cos theta=-0.86 degrees

hope it helped

Answer: Maximum height reached is 804.88 m

Step-by-step explanation:

At maximum height velocity is zero

We have equation of motion v² = u² + 2as

    Initial velocity, u = 320 ft/s = 97.536 m/s

    Final velocity, v = 0 m/s    

    Acceleration, a = -9.81 m/s²

    Substituting

                     v² = u² + 2as

                     0² = 97.536² + 2 x  -9.81 x s

                     s = 484.88 m

   So the arrow further a height of 484.88 m

Total height = 320 + 484.88 = 804.88 m

Answer: She needs approximately 142.5 pounds

Explanation:

From the information given,

A pound of fertilizer covers 39 square feet of lawn.

If the lawn measures 5557.4 square feet, then

the number of pounds of fertilizer that she needs to buy = 5557.4/39 = 142.4975

Rounding to the nearest tenth,

She needs approximately 142.5 pounds

Based on the fact that the submarine's depth was descended to at a constant rate, the submarine's depth relative to sea level with the passing of the first minute was -6⁴/₅ miles

The submarine descended at a constant rate to the current depth of -34 miles in 5 minutes. This means that the rate can be found by the formula:
= Current depth / Time

= -34 / 5

= -6.8 miles per minute

After the first minute, the depth is:

= -6.8 x 1

= -6.8 miles

This number in fractions is:

= -6 + 8/10

= -6 + 4 / 5

= -6⁴/₅ miles

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In order to add these two numbers, we need to add the algarisms that are in the same position.

Since the first number has 7 zeros and the second one has 8 zeros, the numbers 2 and 3 will not be added, since they are in different positions (the number 3 has more "value", since it's in a higher position).

So, adding these two numbers, we have:

Therefore the result of this sum is 320,000,000 (three hundred and twenty million).

The required sample size, using the z-distribution, is given as follows:

n = 253.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The equation for the margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 95%, hence the critical value z has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The estimate and the margin of error are given as follows:

[tex]\pi = 0.22, M = 0.015[/tex]

Hence the required sample size is calculated as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.015 = 1.96\sqrt{\frac{0.015(0.985)}{n}}[/tex]

[tex]0.015\sqrt{n} = 1.96\sqrt{0.015(0.985)}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.015(0.985)}}{0.015}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.015(0.985)}}{0.015}\right)^2[/tex]

n = 253. (rounding up, as a sample size of 252 would result in a margin of error slightly above 1.5%).

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Answer:

Step-by-step explanation:

Soh Cah Toa

S stand for sine, C stand for Cosine and the T stand for Tangent

'o' is the opposite, 'a' stand for adjacent (next to) and h stand for hypotenuse (the longest length of the triangle)

[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]

[tex]cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]

[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]

We care about angle A and we want sine. So we will use the first equation.

The opposite from A is 3 and the hypotenuse is 5.

[tex]sin(A)=\frac{3}{5}[/tex]

Supplementary angles add 180 degrees.

One of the two angles is 8 degrees more than 3 times the other.

If one of the angles is A and the other is B, then:

As they are supplementary, they add 180 degrees:

We replace the information of the second equation in the first one and solve:

Now we can solve for the other angle:

The measure of the angles is 34.4 degrees and 111.2 degrees.

Solution

We have the following info given:

x: 75,76, 91, 65,48,75,85,62,51,80,94,43

y: 69, 88, 101, 63, 59, 82, 86, 67, 56, 84, 105, 44

After apply OLS (Ordinary LEast Squares) we got the following regression line:

y= 1.0607x + 0.6442

We want to find the best prediction for a student who scored 52 in the first test so we have this:

y= 1.0607* 52 + 0.6442 = 55.80

Then the best prediction for this case is 55.80

The expression given as [x²+ 5x + 4]/[x² + 8x + 16] - [x² - 3x - 4]/[x²-16] simplifies to 0

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

[x²+ 5x + 4]/[x² + 8x + 16] - [x² - 3x - 4]/[x²-16]

Factorize the expression

So, we have

[x²+ 5x + 4]/[x² + 8x + 16] - [x² - 3x - 4]/[x²-16] = [(x + 4)(x + 1)]/[(x + 4)(x + 4)] - [(x - 4)(x + 1)]/[(x + 4)(x - 4)]

Simplify the common factors

So, we have

[x²+ 5x + 4]/[x² + 8x + 16] - [x² - 3x - 4]/[x²-16] = [(x + 1)]/[(x + 4)] - [(x + 1)]/[(x + 4)]

The terms of the above equation are the same

So, the result of subtracting one from the other is 0

This gives

[x²+ 5x + 4]/[x² + 8x + 16] - [x² - 3x - 4]/[x²-16] = 0

Hence, the value of the expression is 0

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Answer:

Step-by-step explanation:

Number of yellow marbles =13

Number of teal marbles  = 13

Two marbles are drawn randomly

Probability that both marbles are teal

Hence the probability that both marbles are teal is 0.026