A rectangular Corn Hole area at the recreation center has a width of 5 feet and a length of 10 feet. If a uniform amount is added to each side, the area is increased to 84 square feet. What is the amount added to each

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The correct answer is option B. -1.5.

To calculate the z-score for a wide receiver who dropped 13 footballs over the course of a season, we use the z-score formula:

z = (X - μ) / σ

where:

Substitute the values into the formula:

z = (13 - 16) / 2

This simplifies to:

z = -3 / 2 = -1.5

Therefore, the z-score for a wide receiver who dropped 13 footballs is B. -1.5.

To solve binomials, one can use the binomial theorem, which involves the use of binomial coefficients calculated via factorials. For large numbers, Stirling's formula can help manage calculations by using approximations of factorials through logarithms.

Understanding Binomials and the Binomial Theorem

To solve binomials and expand binomial expressions, we often use the binomial theorem. This theorem expresses the expansion of the power of a binomial as a sum of terms in the form of coefficients multiplied by powers of the two parts of the binomial. A binomial coefficient, represented by (n), counts the number of ways to choose r objects from n without regard to order and is computed using factorials.

When dealing with large binomial coefficients, calculators may return overflow errors. To handle this, one might use Stirling's formula, an approximation for logarithms of factorials. This approach makes it more feasible to work with large numbers.

Using the example of expanding (1 + x)³, we get 1 + 3x + 3x² + x³, where the coefficients 1, 3, 3, and 1 represent the binomial coefficients for each term. This pattern applies generally when using the binomial theorem for expansion.

Answer:

[tex]x_1=1\\x_2=\frac{1}{2} =0.5[/tex]

Step-by-step explanation:

Given a equation of the form:

[tex]ax^2+bx+c=0[/tex]

The roots of this equation can be found using the quadratic formula which is given by:

[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]

In this case we have this equation:

[tex]2x^2-3x+1=0[/tex]

So:

[tex]a=2\\b=-3\\c=1[/tex]

Using the the quadratic equation :

[tex]x= \frac{-(-3)\pm\sqrt{(-3)^{2}-4(2)(1) } }{2(2)} = \frac{3\pm\sqrt{9-8 } }{4}=\frac{3\pm 1}{4}[/tex]

Therefore the two roots would be:

[tex]x_1=\frac{3+ 1}{4}=\frac{4}{4}= 1\\x_2=\frac{3- 1}{4}=\frac{2}{4}=\frac{1}{2}=0.5[/tex]

The equation of a line that is perpendicular to the given line is                 y = -4/3x + c.

The equation of a line means an equation in x and y whose solution set is a line in the (x,y) plane. The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term.

For the given situation,

The equation of a line is y = 3/4x - 1/2 ------ (1)

The general form of equation of line in slope intercept form is

[tex]y=mx+c[/tex]

On comparing the equation 1 with general form,

Slope of the line, [tex]m=\frac{3}{4}[/tex]

Then, the slope of the line perpendicular to the given line is [tex]\frac{-1}{m}[/tex]

⇒ [tex]\frac{-1}{m}=\frac{-1}{\frac{3}{4} }[/tex]

⇒ [tex]\frac{-1}{m}=\frac{-4}{3}[/tex]

No points were defined that this 'normal' should pass through, so its intercepts are indeterminate.

Thus the equation of line in slope intercept form is

[tex]y=\frac{-4}{3}x+c[/tex]

Hence we can conclude that the equation of a line that is perpendicular to the given line is y = -4/3x + c.

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To represent an earthquake that is 100 times more intense than a standard earthquake, an increase of 2 on the Richter scale is required due to the logarithmic nature of the scale.

The magnitude of an earthquake that is 100 times more intense than a standard earthquake would be represented by an increase of 2 on the Richter scale. This scale is logarithmic, meaning that each whole number increase on the Richter scale represents a tenfold increase in amplitude. To be 100 times more intense, we need a tenfold increase for each magnitude, so an increase from, for example, magnitude 3 to 5 would represent an earthquake that is 100 times more intense.

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A polynomial of one-variable is given by following expression :-

[tex] Ax^n + Bx^{n-1} +Cx^{n-2}+Dx^{n-3}+Ex^{n-4}+..... [/tex]

where A, B, C, D, E are the coefficients of terms in the polynomial and x is variable of the equation.

A is the leading coefficient and it can not be zero i.e. A≠0.

n is the degree of the polynomial.

It says to write a trinomial in one variable of degree 5.

Trinomial means only three terms with non-zero coefficients, and degree 5 means n = 5.

There could be many answers, but an example of "trinomial of degree 5" would be :-

[tex] Ax^5 + Bx^4 + Cx^3 [/tex]

[tex] 3x^5 + 5x^4 + 2x^3 [/tex]

A trinomial in one variable of degree 5 in standard form is [tex]\( ax^5 + bx^3 + cx \),[/tex] where [tex]\( a \), \( b \), and \( c \)[/tex] are non-zero coefficients and [tex]\( a \neq 1 \)[/tex].

A trinomial is a polynomial with three terms. The degree of a polynomial is the highest power of the variable that appears in the polynomial with a non-zero coefficient. Since we are asked to write a trinomial of degree 5, the highest power of the variable x must be 5.

The standard form of a polynomial lists its terms in descending order of their degrees. Therefore, the first term of our trinomial must be [tex]\( ax^5 \),[/tex] where a is a non-zero coefficient, and [tex]\( a \neq 1 \)[/tex] to ensure that the coefficient is explicit.

Since we want a trinomial, we need two more terms. The next term should have a lower degree, and since we're dealing with a degree 5 polynomial, the next possible lower odd degree is 3 (we choose an odd degree to maintain the trinomial structure with distinct powers). This gives us the second term [tex]\( bx^3 \),[/tex] where b is also a non-zero coefficient.

The third and final term of our trinomial must have a degree lower than 3. The next possible lower odd degree is 1, which gives us the term [tex]\( cx \),[/tex] where c is again a non-zero coefficient.

Putting it all together, we have the trinomial [tex]\( ax^5 + bx^3 + cx \)[/tex] as the standard form of a degree 5 polynomial with three terms.

Answer:

x=22 degrees

Step-by-step explanation:

We are given a circle C

Centre is at C

A line passes through the centre makes angle x and 68 on either side

A triangle is formed with angles x, 68 and another angle at the circumference.

Since the line passing through the centre is diameter of the circle, we have

the third angle of the triangle = 90 degrees ( BY semi circle angle theorem)

In the triangle sum of three angles

=90+x+68 =180

x =22 degrees

Answer:

The correct answer is 81

Step-by-step explanation:

Here are all the perfect squares.

1 2 1 × 1 1

2 2 2 × 2 4

3 2 3 × 3 9

4 2 4 × 4 16

5 2 5 × 5 25

6 2 6 × 6 36

7 2 7 × 7 49

8 2 8 × 8 64

9 2 9 × 9 81    81 Is a perfect square!

10 2 10 × 10 100

11 2 11 × 11 121

12 2 12 × 12 144

Can I have brainliest please?

Answer:

(a) The relation is RT × ST = TU²

(b) TU = 6

Step-by-step explanation:

(a) There is a secant law for circles that says the following: "if two secants are drawn to a circle from one exterior point, then the product of the external segment and the total length of each secant are equal". Applying this for the mentioned question, we have that RT × ST = TU x TU = TU² (considering that for TU case, the tangent is also a secant).

Then RT × ST = TU²

(b) Let's apply the equation in (a). RT × ST = TU² means 9 × 4 = TU²

Solving that equation, we have TU = √36 = 6

Thus TU = 6

Final answer:

The surface area of a cylinder with a given radius of 3 cm and height of 18.2 cm is calculated using the formula 2πr(height + r), which results in approximately 400.1 square centimeters.

Explanation:

The question asks to find the surface area of a cylinder with a radius of 3 cm and a height of 18.2 cm, using 3.14 for pi. The formula for the surface area of a cylinder is 2πr(height + r), where r is the radius, and the height is the vertical dimension of the cylinder.

Plugging in the given values:

We get: Surface Area = 2 * 3.14 * 3 * (18.2 + 3) = 2 * 3.14 * 3 * 21.2 = 400.1 cm²

Therefore, the surface area of the cylinder, rounded to the nearest tenth, is 400.1 square cm.

Answer:

the answer is: (x-4y)(x-6y)

Step-by-step explanation:

Answer: The answer is (a) cos 30° = square root of three over two, because the cosine and sine are complements

Step-by-step explanation:  Given that -

[tex]\sin 60^\circ=\dfrac{\sqrt 3}{2}.[/tex]

we are to select the correct statement from the given four options.

We know that sine and cosine functions are supplement of each other. So, we have

[tex]\sin 60^\circ=\cos(90^\circ-60^\circ)=\cos 30^\circ=\dfrac{\sqrt 3}{2}.[/tex]

Thus, the correct option is (a) cos 30° = square root of three over two, because the cosine and sine are complements.

We need to find the area of the regular polygon as shown in the image.

Now in a regular hexagon the line joining the center and the vertex of a hexagon have the same length as the length of each side. (Refer the attached image)

[tex]10 \sqrt3cm=10 \times 1.732=17.32 cm[/tex]

A regular hexagon is made up of 6 equilateral triangles inside which means all the sides are of the same length.

Now, we know that the length of a side of an equilateral triangle is [tex]10 \sqrt 3[/tex] cm. So the area of one equilateral triangle is:

[tex]\frac{\sqrt 3}{4} \times (a)^2[/tex]

Where, 'a' is the side length of the equilateral triangle.

Therefore,  area [tex]= \frac{\sqrt 3}{4} \times (10 \sqrt3)^2= \frac{\sqrt 3}{4} \times 100 \times 3=75 \sqrt3[/tex] square centimeters.

Now that we have the area of one equilateral triangle and there are 6 of them in a regular hexagon we can find the area of hexagon.

So, the area of given regular polygon is [tex]=6 \times 75 \sqrt 3=450 \sqrt 3 cm^2[/tex].

When (x + 7) is a factor, f(-7) = 0. Thus, option C is correct: f(-7) = 0.

When the polynomial f(x) has (x + 7) as a factor, it implies that when x is replaced by -7, f(x) becomes zero.

This follows from the factor theorem which states that if (x - c) is a factor of a polynomial f(x), then f(c) = 0.

Therefore, to satisfy this condition, f(-7) = 0.

Consequently, option C, stating that f(-7) = 0, must be true when (x + 7) is a factor of f(x).

Thus, the correct answer is C) f(-7) = 0.

The value of sin x is sqrt(b^2 - 16)/16.

To find the value of sin x, we can use the trigonometric identity: sin^2(x) + cos^2(x) = 1.

Given that tan x = a/4 and cos x = 4/b, we can use the Pythagorean identity (1 + tan^2(x) = sec^2(x)) to find the value of sin x:

1 + (a/4)^2 = (4/b)^2

Substituting the value of a in the equation sin x = a/4, we get: sin x = sqrt(b^2 - 16)/16

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Answer:

Bottom Left.

Step-by-step explanation:

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