The area of a square ice rink is 400 yd.². What is the perimeter of the rink in yards

Answer:

state whether this function is quadratic? why or why not?

f(x) = - 3(x - 2)(x + 3)(x + 5)

The

The distance travelled by the snail in 1 hour = 2 feet

Let the distance travelled in 1 hour be represented by d₁

d₁ = 2 feet

The snail travelled two-thirds the distance it travelled in the previous hour

This means that the common ratio of the distance travelled is 2/3

Let the common ratio be represented as r

r = 2/3

Since the distance travelled by the snail in subsequent hours has a common ratio, r, this scenario can be modelled by the sum of n terms in a Geometric Progression.

The distance travelled by the snail in n hours will be given as:

The distance travelled by the snail in 8 hours will be calculated by substituting n = 8 into the equation above:

The distance travelled in 8 hours is 5.8 feet

Answer:

\(\tan \theta = \dfrac{8}{15}\)

Step by step explanation:

\(\text{Given that,}\\\\~~~~~~~\sin \theta = \dfrac{8}{17}\\\\\implies \sin^2 \theta = \dfrac{64}{289}\\\\\implies 1-\cos^2 \theta = \dfrac{64}{289}\\\\\implies \cos^2 \theta = 1-\dfrac{64}{289}\\\\\implies \cos^2 \theta = \dfrac{225}{289}\\\\\implies \cos \theta =\pm\sqrt{\dfrac{225}{289}}\\\\\implies \cos \theta = \pm\dfrac{15}{17}\)

\(\text{In quadrant I, all ratios are positive, so,}~ \cos \theta = \dfrac{15}{17}\\\\\text{Now,}\\\\\tan \theta = \dfrac{\sin \theta }{\cos \theta}\\\\\\~~~~~~~~=\dfrac{\tfrac{8}{17}}{\tfrac{15}{17}}\\\\\\~~~~~~~~=\dfrac{8}{17} \times \dfrac{17}{15}\\\\\\~~~~~~~=\dfrac{8}{15}\)

Answer:

5 units

Step-by-step explanation:

Step one:

Given data

Le the first number be x

and the second number be y

So

x*y= 10-----------------1

and

x+y= 7-----------------2

from eqn 1

x= 10/y

put x= 10/y in eqn 2

\(10/y+y= 7\\\\10/y= 7-y\)

cross multiply we have

\(10=y(7-y)\\\\10=7y-y^2\)

rearrange

\(y^2-7y+10=0\)

the factors of the quadratic expression are

-5 and -2

\(y^2-5y-2y+10= 0\\\\y(y-5)-2(y-5) =0\\\\y-2=0\\\\y= 2\\\\y-5= 0\\\\y=5\\\\\)

The longest side is 5 units

Answer:

cos ( 390 )

  sin ( 330 )

− 4  cot  ( − 45 )

Step-by-step explanation:

Answer:

(0.5, 4 )

Step-by-step explanation:

2x + 3y = 13 → (1)

4x - y = - 2 → (2)

Multiplying (2) by 3 and adding to (1) will eliminate the y- term

12x - 3y = - 6 → (3)

Add (1) and (3) term by term to eliminate y

14x + 0 = 7

14x = 7 ( divide both sides by 14 )

x = \(\frac{7}{14}\) = \(\frac{1}{2}\) = 0.5

Substitute x = 0.5 into either of the 2 equations and solve for y

Substituting into (1)

2(0.5) + 3y = 13

1 + 3y = 13 ( subtract 1 from both sides )

3y = 12 ( divide both sides by 3 )

y = 4

solution is (0.5, 4 )

One factor that affects the slope of the aggregate demand curve is the multiplier effect is a "true" statement.

Aggregate demand would be a macroeconomic term which refers to the total consumption of goods and services in a given period at any price level.

Some key features regarding the aggregate demand curve?

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To determine the equation that represents the inverse function b(a), which returns the length of the other base when the trapezoid's area is given, we need to analyze the given information.Option b is correct.

The equation provided, a(b) - 10.5 + 7, represents the area of the trapezoid as a function of the length of the other base. To find the inverse function, we need to solve this equation for b.

a(b) - 10.5 + 7 = A

a(b) - 3.5 = A

a(b) = A + 3.5

Now, we need to swap the roles of a and b to find the inverse function:

b(a) = A + 3.5

Comparing this with the options provided, we can see that the correct equation is:

B. b(a) = A + 3.5

Therefore, option B represents the inverse function that returns the length of the other base when the trapezoid's area is given.

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The question said we should find the possible outcome of each of the following:

(1) Flipping a coin three times.

Recall, when flipping a coin, there are two possible outcomes (heads or tails).

So flipping a coin three times means:

2³ = 8

Therefore, the possible outcomes of flipping a coin three times is 8.

(2) Rolling a 6-sided die twice.

recall, there are 6 outcomes for a first roll and 6 for the second so, the total number of possible outcome is:

6 * 6 = 36

Therefore, the possible outcomes of rolling a 6-sided die twice is 36.

(3) Rolling a 6-sided die and flipping a coin.

When you flip a coin there are two possible outcomes (heads or tails) and when you roll a die there are six outcomes(1 to 6).

So, putting these together, we will have:

2 * 6 = 12.

Therefore, the possible outcomes of rolling a 6-sided die and flipping a coin 12.

The final answer is (1 + 21√2)/(21√2). The process of rationalization involves changing the form of an expression to eliminate radicals from its Denominator, or to eliminate denominators from a radical expression.

To rationalize the denominator 1/7 + 3√2,

A rational number is a number that can be expressed as a ratio of two integers, with the denominator not equal to zero. The fraction 4/5, for example, is a rational number since it can be expressed as 4 divided by 5.

Step-by-Step SolutionTo rationalizes the denominator 1/7 + 3√2, we'll need to follow these steps.

Step 1: First, we need to create a common denominator for the two terms. The common denominator is 7. Thus, we can convert the expression to the following form:(1/7) + (3√2 × 7)/(7 × 3√2).

Step 2: Simplify the denominator to 7. (1/7) + (21√2)/(21 × 3√2).

Step 3: The numerator and denominator can now be simplified. (1 + 21√2)/(7 × 3√2).Step 4: Simplify further. (1 + 21√2)/(21√2).We have successfully rationalized the denominator!

The final answer is (1 + 21√2)/(21√2).

The final answer is (1 + 21√2)/(21√2). The process of rationalization involves changing the form of an expression to eliminate radicals from its denominator, or to eliminate denominators from a radical expression.

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The solution to the system of equations is x = −7 and y = −1.

To solve the given system of equations using an inverse matrix, we can represent the system in matrix form, Ax=B, then find the inverse of matrix A to solve for 'x'.

Given matrix:

\(\left\{\begin{array}{ccc}x-6y=-1\\-2x+9y=5\end{array}\right\)

\(\hrulefill\)

First, we rewrite the system of equations in matrix for, Ax=B:

\(A = \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right], \ x = \left[\begin{array}{cc}x\\y\\\end{array}\right], \ B = \left[\begin{array}{cc}-1\\5\\\end{array}\right]\)

So, Ax=B can be written as:

\(\Longrightarrow \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right] \left[\begin{array}{cc}x\\y\\\end{array}\right] = \left[\begin{array}{cc}-1\\5\\\end{array}\right]\)

\(\hrulefill\)

\(\boxed{\left\begin{array}{ccc}\text{The inverse of a 2x2 matrix,} \ \left(\begin{array}{ccc}a&b\\c&d\end{array}\right), \ \text{is given by:}\\\\\\A^{-1}= \dfrac{1}{ad-bc}\left(\begin{array}{ccc}d&-b\\-c&a\end{array}\right)\end{array}\right}\)

Here,

\(\Longrightarrow A = \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right]\)

The determinant ∣A∣ is:

\(\Longrightarrow |A|=(1)(9)-(-6)(-2)=9-12\\\\\\\\\therefore |A|=-3\)

Since the determinant is not zero, A has an inverse, which can be calculated as:

\(\Longrightarrow A^{-1}= \dfrac{1}{-3}\left(\begin{array}{ccc}9&6\\2&1\end{array}\right)\\\\\\\\\therefore A^{-1}=\left(\begin{array}{ccc}-3&-2\\-2/3&-1/3\end{array}\right)\)

\(\hrulefill\)

We can solve for 'x' using x=A⁻¹B:

\(\Longrightarrow x = \left(\begin{array}{ccc}-3&-2\\-2/3&-1/3\end{array}\right)\left(\begin{array}{cc}-1\\5\\\end{array}\right)\)

Upon multiplication, we get:

\(\Longrightarrow x = \left(\begin{array}{cc}(-3)(-1)+(-2)(5)\\(-2/3)(-1)+(-1/3)(5)\\\end{array}\right)\\\\\\\\\Longrightarrow x = \left(\begin{array}{cc}3-10\\2/3-5/3\\\end{array}\right)\\\\\\\\\Longrightarrow x = \left(\begin{array}{cc}-7\\-3/3\\\end{array}\right)\\\\\\\\\therefore \boxed{\boxed{x=\left(\begin{array}{cc}-7\\-1\\\end{array}\right)}}\)

Thus, the solution to the system of equations is x = −7 and y = −1.

p = 76 a = 330 so your answer is D

The perimeter of the polygon is 76ft and Area is 338 sq.ft, the correct option is A.

A polygon is a closed structure with 3 or more than 3 sides.

The given polygon has 4 sides, so it is a quadrilateral

To find the area of the polygon, it can be divided into a rectangle and a triangle as shown

Area of Rectangle = Length * Width

Area of Triangle = (1/2) * base * height

Area of Rectangle = 15 *18

Area of Rectangle = 270 sq.ft

Area of Triangle = (1/2) * 8 *17

Area of Triangle = 4 * 17

Area of Triangle = 68 sq.ft

Therefore, the total area = 68 +270 = 338 sq.ft.

Perimeter of a polygon is equal to sum of all the sides

= ( 15+18+17+18+8)

= 76 ft.

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Answer:

The answers is 369 and 577... good luck. ♥️♥️♥️

The numbers 31.3 sec, 41.05 sec, and 42.015 sec represent continuous data since time measurements can take on any value within a given range. Therefore, these numbers are not discrete but continuous.

The numbers, 31.3 sec, 41.05 sec, and 42.015 sec, represent the times taken by the runners to complete their runs. In this case, the numbers are continuous.

Continuous data refers to measurements that can take any value within a certain range or interval. In the context of measuring time, it is possible to have infinitely many possible values between any two given points. For example, between 31.3 sec and 31.31 sec, there can be an infinite number of additional decimal places.

Discrete data, on the other hand, consists of values that are separate and distinct with no intermediate values possible. Discrete data is typically based on counting or whole numbers, such as the number of runners or the number of wins in a competition.

In this scenario, the times of the runners are measured using a continuous scale, where the smallest unit of time can be divided further into smaller increments. Therefore, the times of the runners, 31.3 sec, 41.05 sec, and 42.015 sec, are considered continuous data.

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To find the probability of no successes in a binomial experiment with a probability of success of 30%, we need to use the binomial probability formula.

The formula for the probability of k successes in n trials with probability of success p is:

P(X = k) = (nCk) * (p^k) * ((1-p)^(n-k))

In this case, we want to find the probability of no successes (k = 0) in the binomial experiment. The probability of success is 30%, so p = 0.3.

P(X = 0) = (nC0) * (0.3^0) * ((1-0.3)^(n-0))

P(X = 0) = 1 * 1 * (0.7^n)

Since the probability of no successes is the complement of the probability of any successes (1 - P(X > 0)), we have:

P(X = 0) = 1 - P(X > 0)

Therefore,

P(X = 0) = 1 - (1 - 0.7^n)

To calculate the probability of no successes, we need to know the number of trials (n) in the binomial experiment. If you provide the value of n, I can calculate the probability for you.

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9514 1404 393

Answer:

  C.  4

Step-by-step explanation:

The slope formula is helpful:

  m = (y2 -y1)/(x2 -x1)

  m = (4 -(-4))/(3 -1) = 8/2 = 4

The slope of the line is 4.

Answer:

i belive it is the first one.

Step-by-step explanation:

Answer:

2.5 pounds of meat

Step-by-step explanation:

One pound of meat is equal to 16 OZ

Answer:

y= -6x+62

Step-by-step explanation:

y-y1=m(x-x1)

y-8=-6(x-9)

y-8=-6x+54

+8        +8

y= -6x+62

Answer:

6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

2×3=6

Have a nice day!

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Answer:

Step-by-step explanation:

To solve this problem, we need to find the Greatest Common Factor (GCF) which is the greater factor possible in common for all three numbers 5000, 2500 and 245 liters.

5,000 | 2

2,500 | 2

1,250  | 2

625    | 5

125     | 5

25      | 5

5        | 5

1

So, \(5,000 = 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 5\), \(2,500 = 2 \times 2 \times 5 \times 5 \times 5 \times 5\)

245 | 5

49   | 7

7     | 7

1

\(245 = 5 \times 7 \times 7\)

As you can observe, the greatest common factor is 5, because it's the greater number in common for all three numbers.

Therefore, the greatest recipient possible must be 5 liters capacity.

Answer:

what are the questions. for this

Answer:

D) This is a voluntary response sample. It will almost certainly overestimate the level of displeasure among the city's residents.

The sample is voluntary response because the residents themselves chose whether or not to respond to the announcement in the newspaper. This type of sampling is often biased because those who choose to respond may not be representative of the entire population. In this case, those who are particularly unhappy with the condition of the city's roads may be more likely to respond, while those who are satisfied with the roads may not feel the need to respond. Therefore, the sample is likely to overestimate the level of displeasure among the city's residents.

give thanks and rate5* po! your welcome!

Answer:

The third graph(left to right)

Step-by-step explanation:

the vertex would be (-1,-3) from the formula.

In the regression line y = a+ bx+ e, a is the slope of the regression line.

The above statement is False.

The correct Statement is :

The linear regression line has an equation of the form Y =a + bX

where, Y is called the dependent variable or response.

X means independent or predictor or explanatory variable.

a is the y-intercept and b is the slope of the line.

Regression Line:

A regression line is a statistical tool that shows the correlation between two variables. Specifically, it is used when the variation of one (the dependent variable) depends on changes in the value of the other (the independent variable).

Simple linear regression has two cases:

The formula for the least squares regression line (LSRL) from Y to X is:

                           Y=a + bX + ɛ

where,

Y is the dependent variable.

a is the Y intersection.

b is the slope of the regression line.

X is the independent variable.

ɛ is the residual (error).

and

b = (N∑XY-(∑X)(∑Y) / (N∑X2– (∑X)2) ;

and

a = (∑Y – b ∑X) / N

where, N is the total number of observations.

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Answer:

3

Step-by-step explanation:

Answer:The slope of the line would be 1/3 because if you put those two coordinates in the table then you can see the the difference between 5 and 1 is 4 and the difference between 9 and 21 is 12 then do 4 divided by 12 and you get 1/3 for your slope.

Step-by-step explanation:  I know math just trust me i am a sraight A student.

Answer:

in went down 6 floors.

Step-by-step explanation:

9-6=3 so that's how I found the answer.

The expression that represents the length, in inches, of the third side of the triangle is 5 + 2 = 7 a 3 inches.

A triangle is a three-sided geometric shape that has three angles and three sides. The three sides all join together at the vertices to form a closed shape. Triangles are one of the most basic shapes and can be found in many objects and structures in nature, such as mountains, trees, and the human body. Triangles can also be seen in architecture, artwork, and mathematics.

This can be calculated by subtracting the sum of the two given side lengths (8 a 6 inches) from the given perimeter (9 a 12 inches). The difference of 1 a 6 inches is equal to the third side length of the triangle (7 a 3 inches).

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Answer:

7mph and he stayed the same

Step-by-step explanation:

Larry's average speed from hour 2 to hour 4 and from hour 4 to hour 7 is the same, 7 mi/hr, he maintained a constant speed throughout this period.

Given that Larry recorded his time as he ran

Time elapsed(hr)         Distance run(mi)

     2                                       13.5

     4                                       27.5

     7                                       48.5

We need to calculate his average speed,

To calculate Larry's average speed, we need to divide the total distance he ran by the time elapsed.

Let's calculate his average speed from hour 2 to hour 4 and from hour 4 to hour 7:

Average speed from hour 2 to hour 4:

Distance covered = 27.5 mi - 13.5 mi = 14 mi

Time elapsed = 4 hr - 2 hr = 2 hr

Average speed = Distance covered / Time elapsed = 14 mi / 2 hr = 7 mi/hr

Therefore, Larry's average speed from hour 2 to hour 4 was 7 miles per hour.

Average speed from hour 4 to hour 7:

Distance covered = 48.5 mi - 27.5 mi = 21 mi

Time elapsed = 7 hr - 4 hr = 3 hr

Average speed = Distance covered / Time elapsed = 21 mi / 3 hr = 7 mi/hr

Therefore, Larry's average speed from hour 4 to hour 7 was also 7 miles per hour.

Since Larry's average speed from hour 2 to hour 4 and from hour 4 to hour 7 is the same (7 mi/hr), he maintained a constant speed throughout this period. He neither sped up nor slowed down.

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Complete question =

Larry recorded his time as he ran. What was his average speed from hour 2 to hour 4?

What was his average speed from hour 4 to hour 7?

Did he speed up or slow down?

time elapsed(hr)         distance run(mi)

2                                       13.5

4                                       27.5

7                                       48.5