Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form.

The value of the digit 4 in the number 943,268 is 40,000 because it is in the ten thousand place.

The value of the digit 4 in the number 943,268 depends on its place value in the number.

In 943,268:

- The digit 4 is in the ten-thousands place.

So, the value of the digit 4 in 943,268 is:

4 × 10,000 = 40,000

Therefore, the value of the digit 4 in 943,268 is 40,000.

3/3 would be 1 hour

3/18 of the lawn would be done in 1 hour

18/3=6

6*1 = 6

 it would take 6 hours to do the whole lawn

It will take 360 minutes to water the entire lawn

Cross multiply can be defined as the process of multiplying the numerator of the first fraction on one side of the equals to symbol, with the denominator of the second fraction on the other side of the equals to symbol.

1/18 lawn is watered in 1/3 of hour = 20 min

Whole lawn will be watered in 20 × 18 = 360 min

To learn more about cross multiplication: https://brainly.com/question/26281051?referrer=searchResults

#FPJ2

Answer:

The value of bc is 5.9 units.

Step-by-step explanation:

Given information: b is between a and c, ac=15.8 and ab=9.9.

We need to find the measure of bc.

Since b is between a and c, therefore the segment ac is the sum of two segments ab and bc.

[tex]ac=ab+bc[/tex]

Substitute ac=15.8 and ab=9.9 in the above equation.

[tex]15.8=9.9+bc[/tex]

Subtract 9.9 from both sides.

[tex]15.8-9.9=9.9+bc-9.9[/tex]

[tex]5.9=bc[/tex]

Therefore the value of bc is 5.9 units.

If assumption of Collinearity is not for granted, then the length of Segment BC is defined by [tex]BC = \sqrt{347.65 -312.84\cdot \cos \beta}[/tex], for [tex]\beta \in [0^{\circ}, 180^{\circ}][/tex].

Reminder - Given that statement seems to be incomplete, we assume that we are talking about Line Segments and that Segments AC and BC may be Collinear.

By Geometry and, being more specific, by definition of Triangles, if we assume that all segment are not necessarily Collinear, then a Triangle may exist and can be modelled by the Law of Cosine:

[tex]BC = \sqrt{AC^{2}+AB^{2}-2\cdot AC\cdot AB\cdot \cos \beta}[/tex] (2)

Where [tex]\beta[/tex] is the angle at point B, in sexagesimal degrees and is between 0° and 180°.

If we know that [tex]AC = 15.8[/tex] and [tex]AB = 9.9[/tex], then the expression for the length of BC is:

[tex]BC = \sqrt{347.65 -312.84\cdot \cos \beta}[/tex]

If assumption of Collinearity is not for granted, then the length of Segment BC is defined by [tex]BC = \sqrt{347.65 -312.84\cdot \cos \beta}[/tex], for [tex]\beta \in [0^{\circ}, 180^{\circ}][/tex].

Please see this question related to Triangles: https://brainly.com/question/24160832

Solution: The average rate of change of [tex]\frac{-14}{3}[/tex] represents that the second variable is decrease by 14 if the first variable increase by 3. In terms of water slide the vertical height of slide is decreased at the rate of 4.66 per unit. The vertical height of the slide decrease 70 units from x = 0 to x = 15.

Explanation:

The rate of change shows the change in first variable with respect to change in second variable.

If the rate of chang is given by [tex]\frac{-14}{3}[/tex] it means second variable is decrease by 14 if the first variable increase by 3.

In the context of water slide it shows that the vertical height of slide is decreased by 14 units as we cover the distance of 3 units.

If we cover the distance from x = 0 to x = 15, it means we cover the distance of 15 units.

Let the vertical height of the slide covered from x = 0 to x =15 be y.

It means when distance increased by 15 units the height of slide decreased by y units.

So rate of change = [tex]\frac{-y}{15}[/tex].

It is given that the rate of change is [tex]\frac{-14}{3}[/tex].

Equate both equations.

[tex]\frac{-y}{15}=\frac{-14}{3}[/tex]

[tex]y=15(\frac{14}{3} )[/tex]

[tex]y=5(14)[/tex]

[tex]y=70[/tex]

Therefore, the average rate of change of [tex]\frac{-14}{3}[/tex] represents that the second variable is decrease by 14 if the first variable increase by 3. In terms of water slide the vertical height of slide is decreased at the rate of 4.66 per unit. The vertical height of the slide decrease 70 units from x = 0 to x = 15.

What this mean in terms of the waterslide, from x = 0 to x = 15 is:

This refers to how fast or slow a thing is required before it changes form from one form to another.

With this in mind, we can see that with the water slide, there exists the decrease of the vertical height by 14 units over a distance of 3 units.

Therefore, the rate of change is -y/15

Read more about rate of change here:

https://brainly.com/question/8728504

Answer:

Step-by-step explanation:

Givens:

So, the problem is asking how many more bears than cougars were in the given region. From the table, we know that there where 790 cougar when the study started.

Now, we have to calculate the initial condition of the function, because it's modelling bear population. Initial condition means when the study started, which is when [tex]x=0[/tex].

So, we have:

[tex]f(0)=830(0.8)^{0}=830(1)=830[/tex]

So, there were 830 bears when the study started.

If we compare, we find that there were 40 more bears than cougars when the study started, because 830-790 = 40.

Answer:

A graph of a hyperbola have 2 foci.

Step-by-step explanation:

Foci of a Hyperbola-

The foci of a hyperbola are two fixed points located inside each curve of a hyperbola.

The foci is a plural of the word focus i.e. two focus of a hyperbola are combinely called foci.

Hence, a graph of a hyperbola have 2 foci.

The probability that 3 randomly selected people all have the same birthday is 1 in 48,627,125.

In order to find the probability that 3 randomly selected people all have the same birthday, we need to consider the total number of possible outcomes and the number of favorable outcomes. There are 365 days in a year (excluding leap years) and each person's birthday is independent of the others. Therefore, the probability of each person having the same birthday as the previous person is 1/365. To calculate the probability that all 3 people have the same birthday, we multiply the probabilities together:

P(3 people have the same birthday) = (1/365) * (1/365) * (1/365) = 1/48,627,125

Thus, the probability that 3 randomly selected people all have the same birthday is approximately 0.0000000206, rounded to eight decimal places.

https://brainly.com/question/22962752

#SPJ11

Answer:

i think answer 1

Step-by-step explanation:

tell me i i am wrong

The solution of the expression will be;

⇒ x = 126

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ √(2x + 4) = 16

Now,

Solve the expression as;

The expression is,

⇒ √(2x + 4) = 16

Square both side, we get;

⇒ 2x + 4 = 16²

⇒ 2x + 4 = 256

⇒ 2x = 256 - 4

⇒ 2x = 252

⇒ x = 126

Thus, The solution of the expression will be;

⇒ x = 126

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ6

The value of the function f(x)= 1/x²-3 when x is 3, denoted as f(3), is -8/9.

To solve for f(3) in the function "f(x)= 1/x²-3", you should substitute x = 3 into the function. By doing so, we have:

f(3) = 1/(3²) - 3 = 1/9 - 3 = -8/9

Therefore, f(3) for this function is -8/9.

https://brainly.com/question/35064274

#SPJ11

2 feet 9 inches + 1 foot 6 inches = 3 feet 15 inches

15 inches = 1 foot 3 inches

3 feet + 1 foot = 4 feet

2 ft 9 inches + 1 ft 6 inches = 4 ft 3 inches

1 yard = 3 feet

4feet 3 inches = 1 yard, 1 foot 3 inches

140+170 = 310 yards

310 + 1 = 311

 so it traveled 311 yards 1 foot and 3 inches

Answer:

311 yards and 1 feet and 3 inches

Step-by-step explanation:

The first thing to do is to find the roots.

The sum of the roots, x1 + x2 = -b / a

x1 + x2 = 3 / 2

The product of the roots, x1 * x2 = c / a

x1 * x2 = 5 / 2

The AM means arithmetic mean and is calculated using the formula:

AM = (x1 + x2) / 2

AM = (3 / 2) / 2

AM = 3 / 4 = y1

The HM means harmonic mean and is calculated using the formula:

2 / HM = 1 / x1 + 1 / x2

or

2 / HM = (x1 + x2) / x1 * x2

Rewriting in terms of HM alone on the left side:

HM = 2 x1*x2 / (x1 + x2)

HM = 2 (5 / 2) / (3 / 2)

HM = 10 / 3 = y2

Creating an equation from y1 and y2:

(y – ¾) (y – 10/3) = 0

y^2 – 10/3 y – ¾ y + 30/12 = 0

y^2 - 49/12 y + 30/12 = 0       (ANSWER)

or

y^2 – 4.083y + 2.5 = 0

Answer:

Step-by-step explanation:

Remember that if two figures have corresponding angles congruent, but proportional sides, then those figures are similar.

However, if those figures have corresponding angles and sides congruent, then they are congruent.

Therefore, to determine if two polygons are congruent, that is, in size and shape, we need to prove that their corresponsing sides are all congruents, that way, we'll be able to demonstrate their absolute congruence.