Select the TABLE tab. What do all the points on this line have in common?

1) In this question, we can see that a point has been given. So let's plot that point that belongs to the function:

We can tell that this point is part of the function by plugging it into the given function:

2) So let's plot the graph:

Now, we can find another point by moving one unit down and three to the right.

3) Thus, the answer is:

Part a:  Average rate of change = 7.2 m/sec(going downward)

part b: Instantaneous rate of change = -7.6 m/sec

For the given question;

The height of ball kicked is given by equation;

h(t) = -4.9t^2 + 12t + 0.5

Where,  h(t) = -4.9t^2 + 12t + 0.5

Part a: Average rate of change of the height of the ball from 1s to 3s.

For t = 1 sec

h(1) =  -4.9(1)^2 + 12(1) + 0.5

h(1) = 7.6 m

For t = 3 sec

h(3) =  -4.9(3)^2 + 12(3) + 0.5

h(3) = -7.6

Average rate of change = -7.6 - 7.6 m/3 - 1

Average rate of change = - 15.2/2

Average rate of change = 7.2 m/sec(going downward)

Part b : instantaneous rate of change at 3s.

h(3) =  -4.9(3)^2 + 12(3) + 0.5

h(3) = -7.6

instantaneous rate of change = -7.6 m/sec

Thus, the instantaneous rate of change of the ball at 3s -7.6 m/sec.

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Correct graph: C

We have to approximate the area under the curve using the given rectangles.

Each rectangle will have an area that is equal to the width (the interval Δx) times the height (that is f(xi)).

We can express the formula for the approximation as:

We will have to calculate f(x) for x = 0, 4, 8 and 12, which are the left endpoints of the interval for each rectangle.

Given that f(x) is defined as:

we can calculate each value as:

We can now calculate the approximation as:

Answer: the approximation is equal to 1360 square units [Fourth option].

answer 1=-7

2=17

3=8

4=-45

Let the north and east with a positive sign, so, the south and west are negative signs

Because of one-way streets, they go 3.1 km north, turn right and go 1.7 km east, turn left and go 2.3 km north, turn right and go 0.9 km east, turn left and go 1.2 km north, turn left and go 4.1 km west, and finally turn left and go 0.4 km south.

So, the resultant horizontal distance = 1.7 + 0.9 - 4.1 = -1.5 km

The resultant vertical distance = 3.1 + 2.3 + 1.2 - 0.4 = 6.2 km

So, the direct distance will be calculated using Pythagorean theorem :

So, the distance d =

Rounding the answer to the nearest tenth

so, the answer is : 6.4 km

In linear equation, 432 milliliters of water does he use .

What are a definition and an example of a linear equation?

Nick bakes 3 dozen cookies for the bake sale.

1 cookie  requires 12 milliliters of water.

water does he use = 3 × 12 × 12

                                = 432 milliliters of water

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In a dice, obtain odd number

Its A CERTAIN probability, because can be calculated

P = (1,3,5) /(1,2,3,4,5,6) = 3/6 = 1/2

Then ANSWER IS OPTION A)

Step 1

Given;

Step 2

Multiply

Simplify

Answer;

Answer:

85

Explanation:

First, recall the formula for Z-Score.

Substitute the given values:

A z-score of -1.5 represents ​an IQ score of 85.

Given:

There are four shapes square, parallelogram, isosceles trapezoid and rectangle.

To find:

The shape is the most general of the quadrilaterals.

Explanation:

As we know,

If the quadrilateral has equal opposite sides and equal opposite angles, then it is a parallelogram.

So,

All squares are parallelograms.

All rectangles are parallelograms.

All rhombus is a parallelogram.

Therefore, the most general of the quadrilaterals is a parallelogram.

Final answer:

A parallelogram is the most general of the quadrilaterals.

Using simple interest, we know that the principal (p) is $6000.

OR

Using simple interest formula, we have:

To find a principal we have

Hence the value of the principal or p is $6000.

Therefore, using simple interest, we know that the principal (p) is $6000.

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Those are like terms because are constants

Those aren't like terms because 25 is a constant, x is a variable, and 3x² is a quadratic variable

Answer:

(6, 4)

Step-by-step explanation:

(x, y) = ((x1 + x2)/2, (y1 + y2)/2)

= ((10 + 2)/2, (7 + 1)/2)

= (12/2, 8/2)

= (6, 4)

Answer:8.5 and 2.5

Step-by-step explanation:7, 8, MD 9, 10        There are four numbers in this sequence and MD is the midpoint. To find MD we have to find what is in the middle of 8 and 9. The number between them is 8.5 or

8 1/2(which is also 8 and one half)

For 2 and 1 same thing, what is between 2 and 1?   To find that the number line goes 2, 2.9, 2.8, 2.7, 2.6, 2.5, 2.4, 2.3, 2.2, 2.1, and 1.

The y-intercept of the given line on the graph is -3.

So, the y-intercept of the given line:

Let's now follow the graph's value of y at x = 0.

Now, according to the given graph (Graph is attached below).

Therefore, the y-intercept of the given line on the graph is -3.

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In order to find the trade discount amount and the net price, you first calculate the 25% of $450. You proceed as follow:

(25/100) x 450 = 112.5

the percentage is divided by 100, an

Then, $112.5 is the 25% of $450. And $112.5 is the discount amount

Next, to calculate the net price, you simply calculate the difference between the intial price ($450) and the price after the discount ($112.5), just as follow:

net price = $450 - $112.5 = $337.5

Hence, the discount amount is $112.5 and the net price is $337.5

To solve the exercise you can use the point-slope formula, that is,

So, in this case, you have

Then,

Notice that the first number is 4, that would be the missing number.

The complete expression is

Remember that the associative property just groups the numbers differently.

total people(TOTAL) : 400

People that said that the outback was the best ( BEST) : 240

percent of people said Outback was the best steakhouse : BEST / TOTAL : 240/400 = 0.6

Percent = 0

Using the Factor Theorem, the equation of the quartic polynomial in standard form is given by:

y = 4(x^4 + x³ - 13x² - x + 12).

The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the rule given as follows:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).

From the given table, the roots are given by the values of x when y = 0, hence they are given by:

[tex]x_1 = -4, x_2 = -1, x_3 = 1, x_4 = 3[/tex]

Hence the function is given by:

f(x) = a(x + 4)(x + 1)(x - 1)(x - 3)

f(x) = a(x² + 5x + 4)(x² - 4x + 3)

f(x) = a(x^4 + x³ - 13x² - x + 12).

From the table, we also have that when x = 0, y = 48, hence the leading coefficient a can be found as follows:

12a = 48

a = 48/12

a = 4.

Hence the equation is:

y = 4(x^4 + x³ - 13x² - x + 12).

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Hence, the radius of the circle is 10, and the coordinates of its centre is (6,-2)

Answer:

Solution examples: (5,0) and (5,5)

Not a Solution (1,5) and (5, 10)

Explanation:

The graph and the points inside and outside the solution set are given below.

The grey-blue region is the solution to the system and the region outside it is not.

Therefore, the point (5, 0) is a solution and (1, 5) is not a solution.

The co-ordinates when reflected over the y-axis are (-2,1), (-5,1) and (-2,4).

The co-ordinates of the figure given are (2,1), (5,1), and (2,4). It is clear that the figure is a triangle as (2,1) and (2,4) has same x-co-ordinates and (2,1) and (5,1) has same y-co-ordinates.

So this figure is reflected over the y-axis and we need to find the co-ordinates of the new transformed figure.

The reflection over y-axis does not change the y-co-ordinates but the x-co-ordinates are changed into their corresponding opposite signs. That is,

x ----> -x.

So the reflection over y-axis can be represented as (x, y) ----> (-x, y)

Hence the co-ordinates of the reflected figure are:

(-2,1), (-5,1), and (-2,4).

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Solution

Step 1

Write an expression for the probability of an event

No of the required events can be found with the following table

The numbers(1,2,3,4,5,6) on the vertical are for one dice and the others on the horizontal are for the second dice

No of required of numbers on both dices less than 5 are : 1,1 1,2 1,3 1,4 2,1 2,2 2,3 2,4 3,1 3,2 3,3 3,3 3,4 4,1 4,2 4,3 4,4. The number of the events are therefore, = 16

No of total events = 36

Step 2

Substitute the values and find the required probability

Answer:

What is the relationship between altitude and boiling point of a liquid?

At a higher elevation, the lower atmospheric pressure means heated water reaches its boiling point more quickly—i.e., at a lower temperature. Water at sea level boils at 212 degrees Fahrenheit; at 5,000 feet above sea level, the boiling point is 203 degrees F. Up at 10,000 feet, water boils at 194 degrees F.

Step-by-step explanation:

Answer:

[tex]\textsf{Equation}: \quad b=-0.0019a+214[/tex]

209.44 °F

Step-by-step explanation:

Define the variables:

Given:

If the relationship between altitude (a) and boiling point (b) is linear, this can be modelled as:

[tex]\boxed{b=ma+c}[/tex]

where:

Find the slope of the linear equation by substituting the given ordered pairs into the slope formula:

[tex]\implies \textsf{slope}\:(m)=\dfrac{b_2-b_1}{a_2-a_1}=\dfrac{205.45-198.61}{4500-8100}=\dfrac{6.84}{-3600}=-0.0019[/tex]

Substitute the found slope and one of the ordered pairs into the point-slope formula:

[tex]\implies b-b_1=m(a-a_1)[/tex]

[tex]\implies b-205.45=-0.0019(a-4500)[/tex]

[tex]\implies b-205.45=-0.0019a+8.55[/tex]

[tex]\implies b=-0.0019a+214[/tex]

Therefore, an equation giving the boiling point (b) of the​ liquid in terms of altitude​ (a) is:

[tex]\boxed{b=-0.0019a+214}[/tex]

To find the boiling point of the liquid at 2400 ​ft, substitute a = 2400 into the found equation:

[tex]\implies b=-0.0019(2400)+214[/tex]

[tex]\implies b=-4.56+214[/tex]

[tex]\implies b=209.44[/tex]

Therefore, the boiling point of the liquid at 2400 ft is 209.44 °F.

After evaluating the limit we have came to find that the limit of   [tex]\lim_{x\rightarrow \left(1/2)^-} $$|2x-1| 2x-1[/tex]    as x approaches 1/2- is -1.

In mathematics, a limit is the value that a function, sequence, or index approaches as an input or as an index approaches a specific value. Limits, which are fundamental to calculus and mathematical analysis, are required for the definitions of continuity, derivatives, and integrals.

The concept of a limit of a sequence is further generalized to include the concept of a limit of a topological network, in addition to having a connection to the category theory concepts of limit and direct limit.

A function's limit is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L}[/tex]

We need to solve the given equation

⇒ [tex]\lim_{x\rightarrow \left(1/2)^-} $$|2x-1| 2x-1[/tex]

⇒ [tex]\lim_{x\rightarrow \left(1/2)^-} $$(2\times|2x-1| x) + \lim_{x\rightarrow \left(1/2)^-}}$$( -1)[/tex]

⇒ Evaluate for x

⇒ [tex]0+ \lim_{x\rightarrow \left(1/2)^-}}$$( -1)[/tex]

⇒ 0 - 1

⇒ -1

Thus, after evaluating the limit we have came to find that the limit of   [tex]\lim_{x\rightarrow \left(1/2)^-} $$|2x-1| 2x-1[/tex]    as x approaches 1/2- is -1

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When a point is reflected across the line, y = x, the x and y coordinates changes places. Given that the coordinates of the original point is (a, b), the coordinate of the new point would be (b, a)

Again, this new point was reflected across the x axis. Recall, if reflection is done across the x axis, the sign of the x coordinate remains the same while the sign of the y coordinate is reversed,

Therefore, the coordinates of its final image point in terms of a and b is (b, - a)

The correct option is number 3

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given points

STEP 2: Write the formula for finding the modulus

STEP 3: Substitute the values into the formula to get the answer

Hence, the required modulus is approximately 3.6 to the nearest tenth.

Answer:

Step-by-step explanation:

2(x-3) + 21 = -3

So:

My first step is to open the brackets

2x - 6 + 21 = -3

Then I plus two numbers in the equation:

2x + 15 = -3

Third step is: 2x = -3 - 15

2x = -18

The value of x that makes the equation true is:

x = -18/2

x = -9