Chris is building a large deck for the community center. The deck is shaped as a rectangle. The width of the deck is 29 ft. The perimeter of the deck is to be at least 134 ft. (please answer both questions)

1) Write an inequality that represents all possible values for the length of the deck.

2) Solve algebraically to find all possible values for the length of the deck.

The square root of the given algebraic expression [tex]64y^{16}[/tex] is [tex]\bold{8y^8}[/tex]

"It is a mathematical statement which consists of numbers, variables and mathematical operations."

For given question,

We have been given an algebraic expression [tex]64y^{16}[/tex]

We need to find the square root of given algebraic expression.

[tex]\Rightarrow \sqrt{ 64y^{16}}\\\\= \sqrt{ 64\times y^{16}} \\\\=\sqrt{64} \times \sqrt{y^{16}} \\\\=8\times (y^{16})^{\frac{1}{2} }\\\\=8\times y^{\frac{16}{2} }\\\\= 8\times y^8[/tex]

Therefore, the square root of the given algebraic expression [tex]64y^{16}[/tex] is [tex]\bold{8y^8}[/tex]

Learn more about the algebraic expression here:

https://brainly.com/question/19245500

#SPJ2

The length of the rectangle whose area is (10r² − 11r − 6) and the width is (2r−3) is (5r+2).

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but reverse statement may or may not be true.

Area of rectangel = Length × Width

Given that the area of a rectangle is 10r² − 11r − 6, while the width is 2r − 3. Therefore, it can be writen as,

[tex]\text{Area = Length}\times\text{Width}\\\\10r^2 - 11r - 6 = \text{Length} \times (2r - 3)\\\\\text{Length} = \dfrac{10r^2 - 11r - 6}{2r-3}\\\\\text{Length} = 5r+2[/tex]

Hence, the length of the rectangle is (5r+2).

Learn more about Rectangle:

https://brainly.com/question/15019502

#SPJ3

Answer: the answer is FALSE. Just took this on a p e x

Step-by-step explanation:

1. The equation 5x^2+9x=4, can be rewritten as 5x^2+9x-4=0, where a=5 (the coefficient of the quadratic term), b = 9 (the coefficient of the linear term) and c = -4 (the independent term).

2. No attachment is shown.

3. To use the quadratic formula, the coefficients are: a = 2, b = -1 and c = 10. However, the discriminant, i. e., b^2 -4(a)(c) is negative, therefore, there is no real solution.  

4. You have to use the quadratic formula, with a = 4, b = 3 and c = -10, as follows:

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

[tex]x = \frac{-3 \pm \sqrt{3^2 - 4(4)(-10)}}{2(4)} [/tex]

[tex]x = \frac{-3 \pm \sqrt{169}}{8} [/tex]

[tex]x_1 = \frac{-3 + 13}{8} [/tex]

[tex]x_1 = \frac{5}{4} [/tex]

[tex]x_2 = \frac{-3 - 13}{8} [/tex]

[tex]x_2 = -2 [/tex]

5. Rewriting the formula, so that all the terms are on one side and ordering the polynomial expression, gives: -x2-6x+27=0. Here a = -1, b = -6 and c = 27.  Using the quadratic formula gives

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

[tex]x = \frac{6 \pm \sqrt{6^2 - 4(-1)(27)}}{2(-1)} [/tex]

[tex]x = \frac{6 \pm \sqrt{144}}{-2} [/tex]

[tex]x_1 = \frac{6 + 12}{-2} [/tex]

[tex]x_1 = -9 [/tex]

[tex]x_2 = \frac{6 - 12}{-2} [/tex]

[tex]x_2 = 3 [/tex]

6. When the second grade polynomial has all of its coefficients (a, b and c) different than zero, like this case, the best method for solving the equation is the quadratic formula  .

7. When the discriminant is greater than zero, there are two different solutions and when it is equal to zero, it has one double solution.

The discriminant for this case is 7^2 - 4(5)(-4) = 129. So, there are two different solutions .

8. Let's call  the sides of the rectangle a and b.

perimeter formula: 2a + 2b = 54 cm (eq. 1)

area formula: (a)(b) = 176 cm2 (eq. 2)

Isolating a in equation 1, gives (units are omitted):

2a + 2b = 54

2a = 54 - 2b

a = 27 - b (eq. 3)

Replacing equation 3 into equation 2, gives (units are omitted):

(a)(b) = 176

(27 - b)(b) = 176

-b^2 + 27b - 176 = 0

Using quadratic formula, we get

[tex]x = \frac{-27 \pm \sqrt{27^2 - 4(-1)(-176)}}{2(-1)} [/tex]

[tex]x = \frac{-27 \pm \sqrt{25}}{-2} [/tex]

[tex]x_1 = \frac{-27 + 5}{-2} [/tex]

[tex]x_1 = 11 [/tex]

[tex]x_2 = \frac{-27 - 5}{-2} [/tex]

[tex]x_2 = 16 [/tex]

Then, there are two possible values for b, 11 cm and 16 cm. Replacing these values into equation 3 gives:

a = 27 - 11 = 16 cm

a = 27 - 16 = 11 cm

Therefore, the two sides are 11 cm and 16 cm long, despite their names.

Answer: The missing term of the Geometric sequence can be 150.

Step-by-step explanation:

Let the missing number is x,

Hence, the G.P. will,

50, x, 450

Since, the consecutive element of G.P. are in same ratio,

[tex]\implies \frac{x}{50}= \frac{450}{x}[/tex]

[tex]\implies x^2 = 50\times 450 = 22500[/tex]

[tex]\implies x = 150[/tex]

Thus, the missing term of the Geometric sequence can be 150.

Jake has shifted the (B) social-psychological context by moving to a quieter, more private space in the stadium to ask Diane a serious question, which changes the norms and atmosphere to match the situation's gravity.

Jake has changed the social-psychological context by moving from the stands to a quiet lounge. The social-psychological dimension of context includes status relationships among participants, roles, norms of the society or group, and the overall atmosphere like friendliness, formality, or gravity of the situation. By choosing to ask Diane a serious question in a quieter, more private environment, Jake is altering the norms and atmosphere to better suit the gravity of the conversation he intends to have, thus changing the social-psychological context.

Answer:

No correlation.

Step-by-step explanation:

A Scatter (XY) Plot has points that show the relationship between two variables.

Scatter plots use a collection of points placed using Cartesian coordinates to show values of two variables. By showing a variable on each axis, it can be detected if there is a relationship or correlation between the two variables.

Several types of correlation can be interpreted through the patterns shown in the scatter diagrams. These are: positive (values increase together), negative (one value decreases as the other increases), null (no correlation).

In the case presented, it can be clearly seen that the variables have no correlation, because the trend is not that the points form a straight line, but that there is too much dispersion.

So, the answer is:

No correlation.

Hope this helps!

Answer:

the answer  60

Step-by-step explanation:

First I did 10x7 which equals 70, Second I did 5x7 which equals 35 and then subtracted 5 to get 30, Third I did 100-70 to get 30 and than I did 30+30 to get 60.

Answer:

2 solutions

Step-by-step explanation:

Given the equation sin(4x)=1/2, to know the total number of solutions that the equation has within the interval (0,2π), we will need to solve for x first.

sin(4x)=1/2

4x = arcsin1/2

4x = 30°

x = 30/4

x1 = 7.5° (This angle lies in the first quadrant)

Since sine is positive in the second quadrant as well and the angle in the second quadrant is (180°-theta) where theta is 7.5°, therefore;

x2 = 180-7.5°

x2 = 172.5°

Therefore 7.5° and 172.5° are the two solutions of x that falls within the range (0,2π)

Answer:   [tex]a.\ 129,400\ ft^3[/tex]

Step-by-step explanation:

The volume of a cylinder is given by:-

[tex]\text{Volume}=\pi r^2h[/tex]

Given: The diameter of cylinder = 203 ft.

Then the radius of the cylinder =[tex]\dfrac{203}{2}[/tex] ft.

The height of the cylinder = 4 ft.

Now, The volume of cylinder :will be -

[tex]\text{Volume}=(3.14)(\dfrac{203}{2})^2(4)=\\\\\Rightarrow\text{Volume}=129,396.26\approx129,400\ ft^3[/tex]