One winter day the temperature ranged from a high of 20 F to a low of -25F . By how many degrees did the temperature change?

The equations for the transformed function in vertex form and in standard form are as follows: Vertex form: [tex]\( y = -(x - 3)^2 + 2 \)[/tex], Standard form: [tex]\( y = -x^2 + 6x - 7 \)[/tex]

To arrive at these equations, let's go through the transformation steps:

1. The original function is [tex]\( y = x^2 \)[/tex].

2. Reflecting the graph in the x-axis changes the sign of the function, resulting in [tex]\( y = -x^2 \)[/tex].

3. Translating the graph 3 units right means replacing [tex]\( x \)[/tex] with [tex]\( x - 3 \)[/tex], giving us [tex]\( y = -(x - 3)^2 \)[/tex].

4. Finally, translating the graph 2 units up means adding 2 to the function, yielding the vertex form [tex]\( y = -(x - 3)^2 + 2 \)[/tex].

To convert this vertex form into standard form, we expand the vertex form and simplify:

[tex]\( y = -(x - 3)^2 + 2 \)\\ \( y = -(x^2 - 6x + 9) + 2 \)\\ \( y = -x^2 + 6x - 9 + 2 \)\\ \( y = -x^2 + 6x - 7 \)[/tex]

This is the standard form of the transformed quadratic function.

The equation that describes the relationship between the number of leaves and the length of the vine in inches is y = x + 1. This is derived by calculating the slope of the line that fits the data points and the y-intercept.

The subject of this question is mathematics, specifically with a focus on linear relationships. To find an equation modeling the number of leaves y along x inches of vine, we can use the data given. Two points can be derived from this data: (2,3) and (14,15).

A line can be described by the equation y = mx + b, where m is the slope and b is the y-intercept. The slope of the line can be calculated as rise over run, or the change of y divided by the change of x. This gives us (14-2)/(15-3) = 12/12 = 1, so m = 1.

The y-intercept is the 'y' when 'x' equates to zero. By rearranging the equation to b = y - mx, and by substituting any given point and the slope, we can find b. For instance, using the point (2,3), b = 3 - (1*2) = 1. Therefore, the equation that models the number of leaves y along x inches of vine is y = x + 1.

https://brainly.com/question/32634451

#SPJ2

The coordinates of the mid-point is 5 if the XY has endpoints at -13 and 23 after using the segment bisector formula.

A segment bisector is a line, ray, line segment, or point that divides a line segment into two equal halves at its center.

It is given that:

XY has endpoints at -13 and 23.

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

The coordinate of the mid-point = (-13 + 23)/2

The coordinate of the mid-point = (10)/2

The coordinate of the mid-point = 5

Thus, the coordinate of the mid-point is 5 if the XY has endpoints at -13 and 23 after using the segment bisector formula.

Learn more about the segment bisector here:

brainly.com/question/4137998

#SPJ5

Answer:

Step-by-step explanation:

its 12 D

The pizza bot travels an average of 4 miles per hour. If he gets sent on a delivery to a house 1.5 miles away. The scientific notation is A. 401,570,000 miles.

We have this below shown relation between them

[tex]\text{Average speed} = \dfrac{\text{Distance traveled}}{\text{Total time taken to travel that distance}}\\\\or\\\\\text{Total time taken to travel that distance}= \dfrac{\text{Distance traveled}}{\text{Average speed} }[/tex]

The pizza bot travels an average of 4 miles per hour. If he gets sent on a delivery to a house 1.5 miles away.

The pizza bot is doing delivery which means it will go to the destination and return back.

So, the total distance traveled should be 2x of distance to the delivery target. Then the time needed for the bot to back to the restaurant would be:

Time needed = distance traveled / average velocity

                       = 2 x 1.5mi / 4mph

                        = 0.75 hour

                        = 45 minutes

For A, we have to write it in <number>.<numbers>*10^<number>.

Since 4 is the first number, we write it as 4.01570000 x 10^<number>. Since there are 8 numbers after 4, we have 4.01570000 x 10^8.

Learn more about Time ;

https://brainly.com/question/5021637

#SPJ2

A function assigns the value of each element of one set to the other specific element of another set. The total cost of the sand for this court is $2,324.

A function assigns the value of each element of one set to the other specific element of another set.

The function for the total cost can be written as in the form as shown below,

Total cost = Cost of sand + Cost of delivery

The total cost for x tons of sand can be written as,

Total cost(x) = $11(x) + $3(x)

Since the volleyball court needs 166 tons of sand, therefore, the total cost for 166 tons of sand can be written as,

Total cost(x) = $11(x) + $3(x)

Total cost(166) = $11(166) + $3(166)

Total cost = $1826 + $498

Total cost = $2,324

Hence, the total cost of the sand for this court is $2,324.

Learn more about Function here:

https://brainly.com/question/5245372

#SPJ2

Answer:

4.2

Step-by-step explanation:

Answer:

6:1 = 12:2

Step-by-step explanation:

In the second statement, we see that 12 is double the amount of the original, meaning it had been multiplied by 2.  

Apply the same rule to the second part of the ratio.

Equation: 1 x 2 = 2

Conclusion: 6:1 = 12:2

The distance between 3/4 and 7/8 is 11/8

The absolute value of a number is the distance value from zero without considering the sign of a number. It is also represented as |x|, where x is any number.

Given:

The expressions are 3/4 and 7/8.

To find the distance:

Subtract the number with another number.

And take the absolute value of the number.

So,

distance = 7/8 - 3/4

Distance = (14 - 3)/8

Distance = 11/8

Therefore, 11/8 is the required distance.

To learn more about the absolute value;

https://brainly.com/question/1301718

#SPJ2

Answer: 5.3oz/0.33 lbs

Step-by-step explanation:

Since a lb is 16 oz divide by 3 (number of apples) and get 5.3 oz each then convert into lbs which is 0.33lbs

Final answer:

The commutative property of addition is a mathematical principle that states the sum of two numbers remains the same regardless of the order in which they are added; for example, 2 + 3 is the same as 3 + 2. It applies to both ordinary numbers and vector addition.

Explanation:

The commutative property of addition states that when two numbers are added, the sum is the same regardless of the order of the addends. In other words, if you have two numbers A and B, then A + B will equal B + A. This property is true for the addition of ordinary numbers, as well as for more complex structures like vectors.

For example, with ordinary numbers, adding 2 + 3 yields the same result as 3 + 2, which is 5 in both cases. The same property applies to vector addition, where the resultant vector from combining A + B is the same as B + A, confirming the commutative nature of this operation.

The commutative property is fundamental in mathematics as it provides flexibility in calculation, making it easier to solve problems and understand the underlying structure of mathematical systems.

The requested ratios of the width to length and length to width of the magazine photograph are 2:3 and 3:2 respectively.

The question is asking for the ratios relating to the dimensions of the magazine photograph. In this case, the photo is 24 cm long and 16 cm wide. Therefore, you can derive various ratios from this.

The first is the ratio of width to length, which is 16 : 24. This can be simplified by finding the highest common factor of 16 and 24, which is 8. So divide both sides of the ratio by 8 to get 2 : 3.

Another ratio is the ratio of length to width, which is 24 : 16. Similarly, this can be simplified to a ratio of 3 : 2 by dividing both sides by 8.

https://brainly.com/question/32531170

#SPJ2

The total area of the field is 280 sq. ft.

"A process of finding the value of a single unit, and based on that value we can find the required value."

"[tex]A=l\times w[/tex], where l is the length and w is the width."

For given question,

We have been given the dimension of a plot which is 10 x 7 ft

From the dimension we can say that, a plot must be rectangular in shape.

Here, length (l) = 10 ft

and width = 7 ft

Using the formula for the area of the rectangle,

[tex]\Rightarrow A=l\times w\\\Rightarrow A=10\times 7\\\Rightarrow A=70~ft^2[/tex]

This means, the area of each plot is 70 sq. ft.

Four workers are hired to weed a field by hand.

Using unitary method the total area of the field would be,

[tex]70\times 4= 280~sq.ft.[/tex]

Therefore, the total area of the field is 280 sq. ft.

Learn more about the unitary method here:

https://brainly.com/question/22056199

#SPJ2