w
Dan's circular
pool has a
circumference of
18.84 meters.
What is the
diameter of the
pool?
(use
13.14)
IS

The equation of the following graph in vertex form is y = (x + 1)².  This equation represents a parabola with its vertex at the point (-1, 0) and opening upwards.

The equation of a quadratic function in vertex form. The vertex form of a quadratic function is given by the equation:

y = a(x - h)² + k

In this equation, (h, k) represents the vertex of the parabola, and 'a' determines the direction and shape of the parabola. The points given are (0, 1), (-1, 0), and the term (x + 1)² is also mentioned.

Using these details, the vertex of the parabola can be identified as (-1, 0), since the term (x + 1)² is present, which corresponds to h = -1. The point (0, 1) can be used to determine the value of 'a'. Plugging in the coordinates (0, 1) into the vertex form equation:

1 = a(0 - (-1))² + 0

1 = a(1²)

a = 1

With these values, the equation of the graph in vertex form is:

y = (x + 1)²

This equation represents a parabola with its vertex at the point (-1, 0) and opening upwards.

To learn more about quadratic function click here

brainly.com/question/18958913

#SPJ11

The height of the flagpole, found using the ratio of the sides of similar triangles is 12.975 meters

Similar triangles are triangles  in which two angles of one triangle  are congruent to two angles in the other triangle, such that they have the same shape.

The parameters that can be used to find the height of the flagpole are;

Distance of the mirror from the flagpole = 8.65 meters

Distance of Feng on the other side of the flagpole = 1.1 meters

The height from Feng's eyes to the ground = 1.65 meters

According to the law of reflection, the angle of incident and the angle of reflection are the same

The angle made by Feng and the ground = Angle made by the flagpole and the ground = 90°

The triangle formed by the Feng and the flagpole are therefore similar by AA similarity postulate

The ratio of corresponding sides of similar triangles are the same, therefore;

\(\dfrac{1.65}{Height\, of \, the \, flagpole} = \dfrac{1.1}{8.65}\)

\(Height\, of \, the \, flagpole = \dfrac{1.65}{1.1} \times 8.65 = 12.975\)

Height of the flagpole = 12.975  meters

Learn more about similar triangles here:

https://brainly.com/question/14285697

#SPJ1

Answer:

5 and 6

Step-by-step explanation:

The corresponding speed of pulleys B, C and D are 300rpm, 1200rpm and 240 rpm

The speed of the pulleys can be determined by using the formula that relates the speed and diameters of the pulleys

N1/N2 = D2/D1

Where: D1 is the diameter of the driven pulley, D2 is the diameter of the drive pulley, N1 is the speed of the driven pulley and N2 is the speed of the drive pulley

Given: Da = 2'', Db =4''  Dc = 1'', Dd =5'' and Na = 600rpm

Na/Nb = Db/Da

600/Nb = 4/2

2Nb = 600

Nb = 600/2 = 300 rpm

Nb/Nc = Dc/Db

300/Nc = 1/4

Nc = 300 x 4 = 1200rpm

Nc/Nd = Dd/Dc

1200/Nd = 5/1

5Nd = 1200

Nd = 1200/5 = 240 rpm

Therefore, the speed of pulleys B, C and D are 300rpm, 1200rpm and 240 rpm respectively

Learn more speed of pulleys on:

https://brainly.com/question/9405220

#SPJ1

Answer:

x=4

Step-by-step explanation:

56/14=4

Answer:

4

Step-by-step explanation:

56÷14

there you go got that

Looking at the graph, we can see that it's always crescent, that means when x increases, y also increases.

Also, we can see that when x approaches minus infinity, the graph approaches the x-axis, that means the value of y approaches 0.

Also, when x approaches infinity, the values of y increases towards infinity as well.

Finally, when x approaches 0, the value of y approaches 2 units (where the graph intersects the y-axis).

Therefore, the correct sequence of answers is:

No, Yes, No.

Answer:

$ 100

Step-by-step explanation:

$ 200 = 200 %

x$ = 100%

The Rule of Three

x = (100%) ($200) / 200%

x = $ 100

Answer:

A

Step-by-step explanation:

Looking at the slope, it goes upward and it meets with the y-axis

Answer:

64% male

36% female

Step-by-step explanation:

We know

A class has 50 students, 18 female, and 32 male.

If a representative is chosen in their class, what is the probability of having a male?

32 divided by 50, times 100 = 64%

So, 64% that the representative is male.

If a representative is chosen for their class, what is the probability of having a female?

18 divided by 50, times 100 = 36%

So, 36% that the representative is female.

Answer:

37/45

Step-by-step explanation:

YEPPP THAT'S ITT DJJSJZJZK

Answer: The answer is 44/50 and the percentage is 88

Step-by-step explanation: Hope my answer helped you! Plz, mark my answer and Thank you!

The approximate population of the Latinos in the united states, growing at a growth rate of 2.5% per year in 2020 is 64,004,227

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the population of the latinos x years after 2010.

There were 50,000,000 latinos in the united states. at a growth rate of 2.5% per year, hence:

y = 50000000(1.025)ˣ

In 2020 (x = 10):

y = 50000000(1.025)¹⁰ = 64,004,227

The approximate population of the Latinos in the united states, growing at a growth rate of 2.5% per year in 2020 is 64,004,227

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

If Tony Stark could somehow add a 10% increase in his wealth to his current worth each year then the number of years will be 84 to reach T'Challa.

Exponential notation is a type of mathematical shorthand that allows us to express complex statements in a more concise manner. The basis of an exponent is a quantity or letter. It denotes that the base will rise to a specific level of strength. The base is X, and the power is n.

In Marvel comics, T'Challa (aka The Black Panther) as the king of Wakanda is estimated to be worth 90 trillion dollars.

Tony Stark (aka Iron Man) is only worth about 30 billion dollars.

If Tony Stark could somehow add a 10% increase in his wealth to his current worth each year.

Let t be a number of the years.

Then the equation is given as

\(\rm 9 \times 10^{13} = 3 \times 10^{10} \times (1.10)^t\)

Then the value of t will be

\(\rm 3000= (1.10)^t\\\)

Taking log both sides, we have

t (ln 1.1) = ln 3000

         t = 84

More about the exponent link is given below.

https://brainly.com/question/5497425

#SPJ1

The slope of the line from the table above is equal to -3.

The y-intercept for the line represented by the table is equal to 7.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope, m = (2 - 11)/(1 - (-2))

Slope, m = (-9)/3

Slope, m = -3.

In Mathematics, the y-intercept is also referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In this context, the y-intercept of the linear function for the second table is 7.

Read more on y-intercept here: brainly.com/question/6240745

#SPJ1

Answer:

t = 4

Step-by-step explanation:

In step two, instead of multiplying by -6 on both sides, you need to divide by -6 to isolate t.

-6t = -24

÷-6    ÷-6

t = 4

When you multiply by -6 on both sides, the equation would be 36t = 144, which is not what we want. The opposite of multiplication is division, and in order to get the answer, you divide by the number multiplied.

Answer:

5)x=25/3

6)x=2

7)x=3

8)x=10

9)x=5

10)x=10

11)x=21

12)x=-25/3(negative 25 over 3)

3 (hight) × 8 (base) = 24

24 ÷ 2 = 12 (area of triangle)

12 × 2 = 24 (because there are 2 triangles)

5 × 7 = 35 (because length times width)

35 × 2 = 70 (because there are 2 rectangles)

8 × 7 = 56 (because of the base)

24 + 12 + 24 + 35 + 70 + 56 = 221

The notation used for a vector pointing into the point is X.

A quantity with a magnitude and direction is called a vector. A vector quantity will be identified in these annotations by a bold letter (such as the electric field vector E). Vectors appear graphically as straight arrows. The magnitude of the vector is commonly represented by the length of the arrow, and both the arrow and the vector point in the same general direction.

Arrows are drawn on the page to represent vectors in the page's plane. Typically, circles with an X engraved on them are used to represent vectors that enter the screen's plane. A vector that deviates from the screen's plane is often represented by circles with dots in the center.

To learn more about vector, you can visit:

https://brainly.com/question/13322477?

#SPJ4

Each term of the sequence is obtained by multiplying the previous term by 2/3.

To find the sequence represented by a generating function, we can expand the function as a power series and read off the coefficients. In this case, we can write:

1/(1-7z+10z²) = (1/[(1-2z)(1-5z)]) = (A/(1-2z)) + (B/(1-5z))

where A and B are constants we need to determine. We can use partial fraction decomposition to find A and B, which gives:

A = 1/3 and B = -1/3

Now we can express the generating function as:

1/(1-7z+10z²) = (1/3)/(1-2z) - (1/3)/(1-5z)

Next, we use the geometric series formula to expand each term as a power series:

(1/3)/(1-2z) = 1/3 + 2z/9 + 4z²/27 + 8z³/81 + ...

-(1/3)/(1-5z) = -1/3 - 5z/9 - 25z²/27 - 125z³/81 - ...

Finally, we can combine the coefficients of each power of z to obtain the sequence represented by the generating function. We have:

1/3, 2/9, 4/27, 8/81, ...

This is a geometric sequence with first term 1/3 and common ratio 2/3. Therefore, the nth term of the sequence is given by the closed-form expression:

aₙ = (1/3) * (2/3)ⁿ⁻¹

We can also express the sequence recursively by noting that:

a₁ = 1/3 aₙ = (2/3) * aₙ₋₁

To know more about expression here

https://brainly.com/question/14083225

#SPJ4

Answer:

Step-by-step explanation:

\(8c-4-2c+5\\\\\mathrm{Group\:like\:terms}\\=8c-2c-4+5\\\\\mathrm{Add\:similar\:elements:}\:8c-2c=6c\\=6c-4+5\\\\\mathrm{Add/Subtract\:the\:numbers:}\:-4+5=1\\=6c+1\)

The measures of angles 4 and 5 are:

∠5 = 104°

∠4 =76°

On the image we can see that angles 1 and 2 are next to eachother, that means that the sum of their measures must be a plane angle, that is an angle of 180°.

Then we can write the sum:

∠1 + ∠2 = 180°

(3x + 5) + (2x + 10) = 180

5x + 15 = 180

5x = 180 - 15

x = 165/5 = 33

the measure of angle 5 is the same one of angle 1 then:

∠5 = (3*33 + 5)° = 104°

And angle 4 is supplementary of angle 1, then:

∠4 + 104° = 180°

∠4 = 180 - 104= 76°

These are the measures

Learn more about angles at:

https://brainly.com/question/25716982

#SPJ1

Answer:

20 : 100% = x : 115%

Step-by-step explanation:

Do 115 x 20

divide the answer by 100

and that is your answer

The solution to the inequality are the region in the shaded area and the graph is attached

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

y ≥3(0.8)^x

y ≥ x² - 5

Represent properly

y ≥ 3(0.8)^x

y ≥ x² - 5

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (0, 5)

None of the options represent the shaded area (see attachment)

Read more about inequality at

brainly.com/question/25275758

#SPJ1

Answer:

3

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(f(x)=(x-\sqrt5)(x+\sqrt5)(x+7)\\\\f(x)=(x^2+x\sqrt5-x\sqrt5-(\sqrt5)^2)(x+7)\\\\f(x)=(x^2-5)(x+7)\\\\f(x)=x^3+7x^2-5x-35\)

Answer:

Step-by-step explanation:

Given zeros of cubic function:

The cubic function has standard form:

Without multiplying lets find the value of a, b, c and d:

Sum of the roots

Sum of the products of the roots (taken two at a time)

Product of the roots

So the cubic function is:

Correct option is C

Answer:If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles

Answer:

8x + 80

Step-by-step explanation:

positive side

Answer:

Step-by-step explanation:

Cost of 1 kg of Potatoes = $ 2

Cost of 1 kg of Carrots = $ 2.40

Let the cost of 1 kg of Potatoes = x

Let the cost of 1 kg of Carrots = y

ATQ , 8x + 5y = 28 - 1)

2x + 3y = 11.20 - 2)

Multiplying 2) by 4

8x + 12y = 44.80 - 3)

Applying Elimination method in 1) and 3)

8x + 5y = 28.00

8x + 12y = 44.80

0 + -7y = - 16.80

y = 16.8/7

y = 2.4

Putting the value of "y" in 1)

8x + 5(2.4) = 28

8x + 12 = 28

8x = 16

x = 16/8

x = 2

Answer:

Step-by-Expressions 1 and 2 are equal and right and 3rd is not correct .

What is expression in math?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

An example of expression is a term or phrase that is regularly used or a means of expressing your thoughts, feelings, or emotions.

The idiom "a penny saved is a penny earned" is a prime example. A smile is an illustration of an expression.

2x(x+3)  = 2x² + 6x is correct Distribution of expressions .

expressions 1 and 2 are equal and right .

Lear more about expressions

brainly.com/question/14083225

step explanation:

Answer:

The answer is C - 2.77 km

Answer: C=2.77

Step-by-step explanation: because it is lol