Factor completely and then place the factors in the proper location on the grid.

4y2 + 25y + 6

Length of the rectangle= 42 feet

Width of the rectangle =14 feet

A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.

Given,

Ratio of length to width of rectangle = 3:1

Let width be x then length will be 3x

Perimeter of the rectangle = 112 feet

2(Length + Width) = 112

2(3x + x) = 112

2(4x) = 112

8x = 112

x = 112/8

Width x = 14 feet

length = 3x = 3×14 = 42feet

Hence, 42 feet is length and 14 feet is width of the rectangle.

Learn more about rectangle here:

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Answer:

The arc's length is 1.8 ft

Step-by-step explanation:

For calcaulate the arc length S we used the formula below:

[tex] S=\frac{\pi.\alpha(\º)}{180}*R[/tex]

Here alpha is the arc angle in degrees and R is the circle radius. Thus, if alpha is equal to 26 and R equals to 4 ft:

[tex] S=\frac{\pi.26}{180}\ *\ 4ft[/tex]

[tex] S=0.45\ *\ 4ft[/tex]

[tex] S=1.8\ ft[/tex]

Domain:{−2,7,2}

Range:{7,2}

Answer:

Option d is correct

[tex]Csc \ \theta =\frac{1}{y}[/tex]

Step-by-step explanation:

Here P(x,y) is the point on unit circle  ( unit circle has radius 1 and center (0,0))

Now in a diagram we can see that

OA= x

AP= y

radius OP =1

∠POA =θ

Now in ΔAOP

[tex]Csc\ \theta =\frac{hypotenuse }{opposite \ side} \\Csc\ \theta =\frac{OP}{AP}[/tex]

[tex]Csc \ \theta =\frac{1}{y}[/tex] ( since OP =1 and AP =y)

Answer:

1/y

Step-by-step explanation:

apex

Answer:  D. [tex]\pi=\dfrac{C}{2r}[/tex]

Step-by-step explanation:

Given : The formula to find the circumference is given by :-

[tex]C=2\pi r[/tex], where r is the radius of the circle.

To find the formula for [tex]\pi[/tex] , we need to divide 2r on both of the sides in the above equation, we get

[tex]\pi=\dfrac{C}{2r}[/tex] , where  r is the radius of the circle.

Hence, the correct formula for [tex]\pi[/tex] : Option D [tex]\pi=\dfrac{C}{2r}[/tex]

Final answer:

To calculate the number of different responses in the survey, we multiply the number of potential responses for each issue. With 5 options for each of the 3 issues, there are 5 x 5 x 5 = 125 different possible combinations.

Explanation:

To determine the number of different responses to the survey conducted by a union, we need to calculate the total possible combinations that can occur when members are asked to rate the importance of three issues: (1) job security, (2) increased fringe benefits, and (3) improved working conditions. Since there are five different responses allowed for each issue, we would use a combination formula.

Each member can choose from 5 different responses for each of the 3 issues. This is a situation where we use the 'fundamental counting principle' where you multiply the number of options for each independent choice to get the total number of possibilities:

The total number of different responses to the survey is 5 x 5 x 5, which equals 125.

So, members have 125 different ways to respond to the survey based on how they rate the importance of each issue.

The equivalent equation is: -100k + 3 + 101k = -245 - 181k

Finding the Equivalent Equation

We need to find the equation equivalent to:

-k + 0.03 + 1.01k = -2.45 - 1.81k

To eliminate decimals, we can multiply the entire equation by 100:

100*(-k + 0.03 + 1.01k) = 100*(-2.45 - 1.81k)

This simplifies to: -100k + 3 + 101k = -245 - 181k

Therefore, the equivalent equation is: -100k + 3 + 101k = -245 - 181k

Complete question:

Which equation is equivalent to –k + 0.03 + 1.01k = –2.45 – 1.81k?

–100k + 3 + 101k = –245 – 181k

–100k + 300 + 101k = –245 – 181k

–k + 3 + 101k = –245 – 181k

–k + 300 + 101k = –245 – 181k

To factor the expression x³ - 2x² - 9x + 18, use the grouping method to factor out a common binomial factor.

To factor the expression x³ - 2x² - 9x + 18, we can first look for any common factors. Since there are no common factors among all the terms, we will use the grouping method to factor the expression.

Step 1: Group the terms in pairs.
(x³ - 2x²) - (9x - 18)
Step 2: Factor out the greatest common factor from each pair.
x²(x - 2) - 9(x - 2)
Step 3: Notice that we now have a common binomial factor of (x - 2).
(x² - 9)(x - 2)

Therefore, the factored form of the expression x³ - 2x² - 9x + 18 is (x² - 9)(x - 2).

The student is looking to factor the polynomial expression x^3 - 2x^2 - 9x + 18. This process typically involves finding whether factors like binomials divide the polynomial without a remainder, using methods like grouping, trial and error, or the Rational Root Theorem, followed by long or synthetic division.

The student has asked to factor the expression x^3 - 2x^2 - 9x + 18.

To factor this expression, we can follow a systematic approach, which often starts with looking for common factors or applying techniques such as grouping, trial and error, or the use of the Rational Root Theorem. In this case, we may not see an immediate common factor, so we might try to group terms or apply synthetic division or the Rational Root Theorem to identify potential roots of the polynomial.

A factor of a polynomial is a binomial (or another polynomial) that divides the original polynomial without leaving a remainder. If we find such a factor, we can then divide the original polynomial by this factor to simplify the expression further. For example, if we discover that (x - 3) is a factor, then we can divide the polynomial by (x - 3) to find the other factors.

Unfortunately, without performing the actual factoring process or having additional information, we cannot factor this specific expression purely based on the question provided. If we had one root or factor given, we could use long division or synthetic division to further factor the expression, and then possibly factorize it completely into the product of binomials or another polynomial.

To write a fraction as a percent, first remember that a percent is a ratio of a number to 100. If we want to convert [tex]\frac{3}{20}[/tex] to a percent, we need to find a fraction equivalent to [tex]\frac{3}{20}[/tex] that has a 100 in the denominator. We can do this by setting up a proportion.

[tex]\frac{3}{20}[/tex] = [tex]\frac{n}{100}[/tex]

Now, we can use cross products to find the missing value.

3 × 100 = 300

20 × n = 20n

300 = 20n ← Divide both sides by 20.

15 = n

Therefore, [tex]\frac{3}{20}[/tex] as a percent would be 15%.

Answer: So, the possible number of additional senators who must vote in favor of the treaty in order to radify it is given by

[tex]19\leq x\leq 52[/tex]

Step-by-step explanation:

Since we have given that

Number of states = 50

Number of senators from each of the 50 states = 2

Total number of senators would be

[tex]50\times 2\\\\=100[/tex]

Since [tex]\dfrac{2}{3}[/tex] of the senators present must approve the treaty.

[tex]\dfrac{2}{3}\times 100\\\\=66.67[/tex]

Number of senators have voted in favor of a treaty = 48

So, remaining senators would be

[tex]67-48\\\\=19[/tex]

Let x be the number of senators needed.

So, Inequality would be

[tex]x\geq 19[/tex]

Now, [tex]100-48=52[/tex]

[tex]x\leq 52[/tex]

So, the possible number of additional senators who must vote in favor of the treaty in order to radify it is given by

[tex]19\leq x\leq 52[/tex]

Answer:

LM= 4

Step-by-step explanation:

In the triangle KLM, ON is the mid segment of KLM

WE use triangle Mid segment theorem

MN= twice of ON

MN= 2 times of ON

4x= 2(x+1)

distribute 2 inside the parenthesis

4x= 2x+2

Subtract 2x on both sides

4x-2x= 2x+2-2x

2x= 2

divide by 2 on both sides

x= 1

To find length of MN, we plug in 1 for x

MN= 4x= 4(1)= 4

Answer:

t = 11

Step-by-step explanation:

From the equation that gives, the number of games you can get the number t of players who participated in the ronund-robin tormeo, is:

[tex]N = \frac{t ^ 2-t}{2}[/tex]

[tex]55 = \frac{t ^ 2-t}{2}[/tex]

[tex]110 = t ^ 2-t[/tex]

[tex]t ^ 2-t -110 = 0[/tex]

[tex](t-11) (t + 10) = 0[/tex].  Then

[tex]t - 11 = 0\\t = 11\\t + 10 = 0\\t = -10[/tex]

Since t cannot take negative values, then t = 11.

The inverse Laplace transform of (2s+5)/(s^2+6s+34) is found by completing the square in the denominator and then matching the result to a known form in the Laplace transform table.

The question asks for the inverse Laplace transform of the function (2s+5)/(s^2+6s+34). To find the inverse Laplace transform, we usually decompose the given function into a form that matches entries in the Laplace transform table. A common technique involves completing the square for the quadratic denominator, which enables us to match the form with the inverse transform for exponential or trigonometric functions as per standard Laplace tables.

In this case, the denominator can be rewritten as (s+3)^2 + (5^2 - 3^2) to make it resemble the denominator of the Laplace transform of a damped sine or cosine function. Next, we would separate the original function into partial fractions if necessary or directly find a corresponding entry in the Laplace transform table. Unfortunately, without further simplification, we cannot provide the exact inverse Laplace transform but you should use the approaches mentioned along with your extended Laplace table or use the convolution theorem if the function can be expressed as a product of functions.