What is the next ordered pair in the table?

The drop down menu is used to match each situation as below.

1. The rocket reached its maximum  the x-value of the vertex

height in 5 s.

2. ground level                                    the y-intercept

3. The rocket launcher was                the y-value of the point containing

on the ground.                                     the x-intercept on the right

4. The rocket was in the air 10           the x-intercept on the right                                                                                    

5. The maximum height of the           the y-value of the vertex

rocket is 50 ft.

6. the time the rocket was                the x-value of the point containing the

launched                                          y-intercept

The key features of the curve such as the x intercept is the point the launcher and the rocket were on ground.

The vertex is the point the rocket had the maximum and height.

Generally, the curve traces a parabolic path

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The interest for Part 1 is approximately $385.10.

The interest for Part 2 is approximately $709.31.

The formula is as follows:

Interest is calculated as follows: Principal * Rate * Time

Where

Part 1:

$132,000 is the principal.

(Decimal) Rate = 12% = 0.12

Time = 8 days/365 days.

How much interest is there in Part 1?

Interest is calculated as follows : $132,000 * 0.12 * (8/365) = $385.10

Therefore, the interest for Part 1 is approximately $385.10.

Part 2:

$106,750 as the principal

(Decimal) Rate = 12% = 0.12

Time = 20 days / 365 days.

How much interest will there be in Part 2

Interest is calculated as follows : $106,750 * 0.12 * (20/365) = $709.31

Therefore, the interest for Part 2 is approximately $709.31.

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Answer:

x = - 1

Step-by-step explanation:

the equation of a vertical line is

x = c

where c is the value of the x- coordinates the line passes through

the line passes through the x- intercept of - 1 , then

x = - 1 ← equation of vertical line

Answer: 36/12 = 3

Step-by-step explanation:

Answer:

The expression should be something like: 36/12

Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

Answer:

4

Step-by-step explanation:

Find the number in the whole number place  

3

and look one place to the right for the rounding digit on the right side of the decimal point  

9

Round up if this number is greater than or equal to  

5

and round down if it is less than  

5

(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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Answer:

Total weight of the three fishes is 7.8125 lb

Step-by-step explanation:

To solve this type of problem we must be aware about lb to ounce conversion. we know that

1 lb = 16 ounce(oz)

So, 2lb 10oz= (2×16+10)oz = 42 oz

Similarly for, 2lb 8oz = (2×16+8)oz = 40oz

and for, 2lb and 11oz = (2×16+11)oz = 43oz

now adding all 3, we can say total weight = (42+40+43)oz = 125oz

To convert oz to lb again we will divide it with 16 so we get

Total weight in lb= \(\frac{125}{16}\) = 7.8125 lb

Therefore total weight of three fishes in ounce is 125oz or 7.8125lbs

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Answer:

B is the correct answer

Step-by-step explanation:

You have to do 6b- 1b 5b

-2a+5a= 3a

9

Answer:

13.01d − 2.65

The liked terms are "3.26d + 9.75d". Just add them accordingly.

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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Answer:

53$

Step-by-step explanation:

7X5=35

35+18=53

Answer:

14.

Step-by-step explanation:

3x + 7y = 12

x - y = 1           Multiply this by -3:

-3x + 3y = -3     Add this to equation 1:

0 + 10y = 9

so y = 9/10 = 0.9.

x - 0.9 = 1

x = 1.9.

So 5x + 5y = 5*1.9 + 5*0.9

= 14.

Daniella: Were you thinking of perpendicular lines?

Ori: It seems like you've got the basic idea, but your definition could be more precise.

Kaori: Yes! Well done. Here, have a cookie. You've earned it.

No, the relationship on the table is not proportional

From the question, we have the following parameters that can be used in our computation:

x   y

____ ____

6 -2

7 -1

8 0

9  1

On the table of values, we can see that:

Using the above as a guide, we have the following:

The relationship is not a proportional relationship

This is so because it does not have a constant rate (addition of 1 to x and y does not represent proportional relationship)

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The classification of the ordered pairs as functions and not functions are as follows;

{(2, 2), (4, 4), (6, 6), (8, 8)} is a function

{(0, 3), (3, 5), (5, 6), (8, 4)} is a function

{(1, 2), (3, 3), (4, 8), (6, 3)} is a function

{(3, 4), (5, 2), (5, 6), (7, 3)} is not a function

A function is a rule, law or definition that maps the elements of a set of values known as the input, to the elements of a set of values known as the output, such that each element of the input element is mapped to exactly one output element.

The values in each of the set of ordered pairs can be arranged into an input and output set as follows;

{(2, 2), (4, 4), (6, 6), (8, 8)}

Input   \({}\) Output

2  \({}\)     ⇒    2

4      \({}\) ⇒    4

6 \({}\)      ⇒    6

8 \({}\)      ⇒    8

In the above mapping, each input is mapped to exactly (only) one value of the output, such that the relationship is a function.

{(0, 3), (3, 5), (5, 6), (8, 4)}

Input   \({}\) Output

0  \({}\)     ⇒    3

3      \({}\) ⇒    5

5 \({}\)      ⇒    6

8 \({}\)      ⇒    4

In the above mapping, each input is mapped to exactly (only) one value of the output, such that the relationship is a function.

{(1, 2), (3, 3), (4, 8), (6, 3)}

Input   \({}\) Output

1  \({}\)     ⇒    2

3      \({}\) ⇒    3

4 \({}\)      ⇒    8

6 \({}\)      ⇒    3

In the above mapping, each input is mapped to exactly (only) one value of the output, such that the relationship is a function.

{(3, 4), (5, 2), (5, 6), (7, 3)}

Input   \({}\) Output

3  \({}\)     ⇒    4

5      \({}\) ⇒    2

5 \({}\)      ⇒    6

7 \({}\)      ⇒    3

In the above mapping, the input value of 5 has two output values of 2 and 6, therefore, the input, 5 maps to two values of the output, 2 and 6, which indicates that the relationship is not a function

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Answer:

280lbs

Step-by-step explanation:

168/12=14

14×20=280

Patterns are used to represent sequence of numbers.

The shape at the 50th position is a triangle

The pattern rule is given as: square, triangle, circle, oval.

The number of shapes (n) is given as:

\(n =4\)

So, the 50th shape is calculated using the following absolute operator

\(Shape = 50\%4\)

i.e. divide 50 by 4, and take note of the remainder.

When 50 is divided by 4, the remainder is 2

So, we have:

\(Shape =2\)

This means that, the shape at the 50th position is the same shape at the 2nd position.

Hence, the shape is triangle

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Based on the definition of congruent triangles, the measures are:

4. m<R = 75°

5. XY = 6

6. m<X = 55°

7. m<S = 50°

Congruent triangles are two triangles that have the same size and shape. This means that all corresponding sides and angles of the two triangles are equal in measure.

Since triangles QRS are congruent to each other, therefore, their corresponding parts will be equal. Thus:

4. m<R = 180 - 55 - 50

m<R = 75°

5. XY = QR = 6

6. m<X = m<Q

m<X = 55°

7. m<S = m<Z

m<S = 50°

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1 year = 12 months and 52 weeks.

Divide the yearly salary to find both:

Monthly = 57300/12 = $4,775

Weekly: 57300 / 52 = $1,101.92

cos(tan^(-1)(-2/3)) simplifies to 3√13 / 13.

To evaluate the expression cos(tan^(-1)(-2/3)), we can use the trigonometric identity:

cos(tan^(-1)(x)) = 1 / √(1 + x^2)

In this case, x is -2/3. Substituting the value into the identity:

cos(tan^(-1)(-2/3)) = 1 / √(1 + (-2/3)^2)

Now, let's calculate the value:

cos(tan^(-1)(-2/3)) = 1 / √(1 + 4/9)

                   = 1 / √(13/9)

                   = 1 / (√13/3)

                   = 3 / √13

                   = 3√13 / 13

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The values are given below,

Left Hand Limit i.e.  \(\lim_{x \to 1^-} f(x)\) = 3 ,

Right Hand Limit i.e.  \(\lim_{x \to 1^+} f(x)\) = 1 ,

Function value at x = 1  \(f(1)\) = 1 ,

Left Hand Derivative \(\lim_{x \to 1^-} f'(x)\) = -6 and

Right Hand Derivative \(\lim_{x \to 1^+} f'(x)\) = -6.

So, the function f(x) is neither continuous nor differentiable at x = 1.

Given, a piecewise function

              3㏑(3 - 2x) + 3                for x < 1

f(x) =

                    -3x² + 4                     for x ≥ 1

Now, for  \(\lim_{x \to 1^-} f(x)\) we will consider the function  3㏑(3 - 2x) + 3, as we have to find the Left Hand Limit of the function, at x = 1.

\(\lim_{x \to 1}\) 3㏑(3 - 2x) + 3 = 3㏑(3 - 2(1)) + 3

= 3 ㏑(1) + 3

= 0 + 3

= 3

Now, for \(\lim_{x \to 1^+} f(x)\) we will consider the function -3x² + 4, as we have to find the Right Hand Limit of the function, at x = 1.

\(\lim_{x \to 1}\) -3x² + 4 = -3(1)² + 4

= -3 + 4

= 1

Now, for \(f(1)\) we will consider the function -3x² + 4,

\(f(1)\) = -3(1)² + 4

= -3 + 4

= 1

Now, for \(\lim_{x \to 1^-} f'(x)\) we will consider the derivative of the function

3㏑(3 - 2x) + 3,

\(\lim_{x \to 1}\) -6/(3 - 2x) = -6/(3 - 2(1))

= -6

Now, for \(\lim_{x \to 1^+} f'(x)\) we will consider the derivative of the function

-3x² + 4,

\(\lim_{x \to 1}\) -6x = -6(1)

= -6

So, the function f(x) is neither continuous nor differentiable at x = 1.

Hence,  \(\lim_{x \to 1^-} f(x)\) = 3 ,  \(\lim_{x \to 1^+} f(x)\) = 1 ,  \(f(1)\) = 1 ,  \(\lim_{x \to 1^-} f'(x)\) = -6 and  \(\lim_{x \to 1^+} f'(x)\) = -6

The function is neither continuous nor differentiable at x = 1.

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Check the picture below.

\(\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{24+x}\\ a=\stackrel{adjacent}{24}\\ b=\stackrel{opposite}{32}\\ \end{cases}\implies (24+x)^2~~ = ~~24^2+32^2 \\\\\\ (24+x)(24+x)~~ = ~~24^2+32^2\implies \stackrel{F~O~I~L}{24^2+48x+x^2}~~ = ~~24^2+32^2 \\\\\\ 48x+x^2=32^2\implies x^2+48x-32^2=0\implies x^2+48x-1024=0 \\\\\\ (x-16)(x+64)=0\implies x= \begin{cases} 16~~\textit{\Large \checkmark}\\\\ -64 \end{cases}\)

notice, we didn't use -64, since the value of "x" must be a positive value.

The equation of the line passing through y = 3x-1 and (3,2) is y = 3x-7.

According to the question,

We have the following information:

y = 3x-1 and the point through which line is passing is (3,2)

We know that the slope of the given line (denoted by m) is 3.

Now, the following formula is used to find the equation of the line passing through a point:

y-y' = m(x-x')

In this case, we have x' = 3 and y' = 2.

y-2 = 3(x-3)

y-2 = 3x-9

Moving 2 from the left hand side to the right hand side will result in the change of the sign from minus to plus:

y = 3x-9+2

y = 3x-7

Hence, the equation of the line passing through y = 3x-1 and (3,2) is y = 3x-7.

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Answer:

Its D

Step-by-step explanation:

There are 17 nonmetal elements, and all are located on the right side of the periodic table with the exception of hydrogen, which is on the top left side. Nonmetal elements have relatively low boiling points, are poor conductors of heat and electricity, and don't like to lose electrons.

Have a Great Day!!

Answer:20

Step-by-step explanation:this is wrong

Answer:

40

Step-by-step explanation:

subtract median of dogs and median of cats

Answer:

PQ = 4

Step-by-step explanation:

\(tan(30)=\frac{RQ}{8}\\RQ=8tan(30)\\RQ=\frac{8}{3}\\RQ=\frac{8}{3}/3\\HYPOTENUSE=8\\PQ = 4\\\)

Given:

In a right triangle,

The length of the adjacent side is P.

The length of the hypotenuse side is 12cm.

The angle is 60 degrees.

To find:

The value of P.

Explanation:

Using the formula of trigonometric ratio,

On substitution we get,

Final answer:

The value of P is 6cm.

To determine the area of the remaining piece of cardboard expressed in terms of x when a square of side length x inches is cut out from a rectangular piece of cardboard having a length of 6x+2 inches and a width of 2x-4 inches, use the following steps.

Draw and label a diagram of the problem. The rectangle should be labeled as 6x+2 inches by 2x-4 inches, and the square cut out should be labeled as x inches by x inches. This is how the diagram looks like: Determine the area of the rectangle, Arect.

The area of the rectangle is given by the product of its length and width. Thus, Arect = (6x + 2)(2x - 4) Determine the area of the square, Asq. The area of the square is given by the square of its side length. Thus, Asq = x²Step 4: Determine the area of the remaining cardboard after the square is cut out, Ar.

This is the difference between the area of the rectangle and the area of the square. Thus, Ar = Arect - Asq= (6x + 2)(2x - 4) - x²= 12x² - 20x - 16

Simplify the expression. The final answer is given in terms of x. Thus, Ar = 12x² - 20x - 16.The area of the remaining piece of cardboard is expressed in terms of x as 12x² - 20x - 16.

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