The path of a diver is modeled by
f(x) = −
4
9
x2 +
24
9
x + 13
where f(x) is the height (in feet) and x is the horizontal distance (in feet) from the end of the diving board. What is the maximum height of the diver?

The remaining wire (W) is just the original wire (850') minus the cut wire on Monday, Tuesday...

There is merely 1' of wire in the reel.

It is important the order we write the vertices of a triangle in a congruent statement as

B. The order tells us what sides are congruent.

D. The order tells us what angles are congruent.

A vertex (plural vertices) in geometry is the intersection of two straight lines. Three line segments come together to form a triangle. The ends of a triangle's three sides meet at three separate points in a plane to form the triangle, which has three sides with two endpoints each. The vertices of a triangle are the three distinct intersecting points or corners.

Congruent triangles are triangles that are precisely the same size and shape. The word congruent has the sign. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent.

The vertices of a triangle in a congruent statement are important for the ordering. In conclusion, the correct options are B and D.

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The average consumption of the fruit juice would be 7.6 gallons for the year 2006.

Average consumption is derived by dividing the total measured consumption of that municipal service by that consumer during the three months before by three. It refers to the average consumption of a consumer of a municipal service during a certain time.

Utilizing the total of quantities consumed or dispersed over a period of time, typically 12 months, the average monthly consumption can be computed. The average number of units used each month is known as average monthly consumption, stock-outs corrected (CA).

Total consumption of the fruit juice in 2006=2.28x109 gallons.

Total population of the country in year 2006=3x108

Average Consumption=(2.28x109)/(3x108)

                = 7.6 gallons    

Hence the average consumption would be 7.6 gallons per person.

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The most appropriate choice for Arithmetic Progression will be given by-

The sum of the first sixteen terms of the Arithmetic Progression is 640

What is Arithmetic Progression?

A series of numbers are said to be in Arithmetic Progression if the difference between consecutive terms of the series are same.

If [tex]a_n[/tex] is the [tex]n^{th}[/tex] term of the series, a be the first term and d the common difference,

[tex]a_n = a+(n-1)d[/tex]

If [tex]S_n[/tex] is the sum of first n terms of the series,

[tex]S_n = \frac{n}{2}(2a+(n-1)d)[/tex]

Here,

Let the first term be a and the common difference be d

The sum of the fourth and thirteen terms of an arithmetic progression is 80.

[tex]a_4 + a_{13} = 80[/tex]

[tex]a + (4-1)d + a + (13-1)d = 80[/tex]

[tex]a + 3d +a +12d =80\\2a+15d =80[/tex]

[tex]S_{16} = \frac{16}{2}(2 \times a + (16 -1) \times d)\\[/tex]

     [tex]= 8(2a+15d)[/tex]

     [tex]= 8 \times 80[/tex]

     [tex]= 640[/tex]

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In this problem, we are looking for the doubling time of the wage of the Toyota automobile assembly line workers. Initially, their wage is $6.70 and by the end of 15 years, their salary is now $29.59.

What we can find here first is the rate of the increase of the salary of the workers. We can use the equation

We are looking for the value of r. We have to derive an equation solving for r. We have

Now, we solve for the value of r given y = 29.59, y0 = 6.70, and t = 15 years. We get

The doubling time is computed as

Substitute the value of r on the equation above and solve, we get

Hence, the doubling time for this problem is equal to 7 years.

Answer: 7 years

Solution

Step 1:

Write the rational expression:

Step 2:

Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of the function ( note: this only applies if the numerator t(x) is not zero for the same x value).

Step 3

Step 4:

\ertical} Asymptote is =-8,\ =3,

Answer:

The answer is A, 3

Answer:

4 is the answer

Step-by-step explanation:

the perimeter of a triangle is 84 cm and its area is 36 CM square if one its side is 30 cm find the length of remaining two side

The values of the trigonometry formulas are sin(240) = -sin(60), cos(225) = -cos(45) and tan(225) = tan(45)

The trigonometry ratios are given as

sin(180 - ∅) = sin(∅)

cos(180 - ∅) = -cos(∅)

tan(180 - ∅) = -tan(∅)

Also, we have the following trigonometry ratios are given as

sin(180 + ∅) = -sin(∅)

cos(180 + ∅) = -cos(∅)

tan(180 + ∅) = tan(∅)

Using the above trigonometry ratios, we  have

sin(240) = sin(180 + 60)

By comparison, we have

sin(240) = sin(180 + 60)

sin(180 + ∅) = -sin(∅)

This gives

∅ = 60

So, we have

sin(180 + 60) = -sin(60)

Evaluate

sin(240) = -sin(60)

Using the above trigonometry ratios, we  have

cos(225) = cos(180 + 45)

By comparison, we have

cos(225) = cos(180 + 45)

cos(180 + ∅) = -cos(∅)

This gives

∅ = 45

So, we have

cos(180 + 45) = -cos(45)

Evaluate

cos(225) = -cos(45)

Using the above trigonometry ratios, we  have

tan(225) = tan(180 + 45)

By comparison, we have

tan(225) = tan(180 + 45)

tan(180 + ∅) = tan(∅)

This gives

∅ = 45

So, we have

tan(180 + 45) = tan(45)

Evaluate

tan(225) = tan(45)

Hence, the value is tan(225) = tan(45)

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⇒Plug in the given values of the variables in order and then simplify the expression

Given that a= 3 and b=4

⇒[tex]=(3)^{3} -(4)+7\\=27-4+7\\=23+7\\=30[/tex]

⇒The expression evaluated at the given known variables gives 30.

we'll start by moving the recurring part to the left of the decimal point hmmm so the recurring part is 0.14 so if we just multiply that by 100, that'll give us 14.141414...., now let's make the recurring part a variable

[tex]x=0.\overline{14}\hspace{5em} \begin{array}{llll} 100x&=&14.\overline{14141414}\\\\ &&14+0.\overline{14141414}\\\\ &&14+x \end{array} \\\\[-0.35em] ~\dotfill\\\\ 100x=14+x\implies 99x=14\implies x=\cfrac{14}{99}[/tex]

Answer:

2070707/500000

Step-by-step explanation:

rational no. simply means a fraction.

Answer:

68°

Step-by-step explanation:

Alternate exterior angles have the same measurement.

he standard form of a quadratic efunctionis:

Since the y-intercept is (0, -1.4), it follows that:

Substitute c = -1.4 into the equation:

Since the x-intercept is (0.905, 0), it follows that:

Since the graph passes through the third point (2, 0.6), it follows that:

Substitute equation (2) into equation (1):

Substitute a = -0.5 into equation (2), therefore,

Therfore the function is given by:

The equation of the parabola is y = -0.5x² + 2x - 1.4

.

Answer:

n= -16/25

Step-by-step explanation:

Solution:

The cube is numbered from 1 to 6

The probability that any of the numbers from 1 to 6 will show will be

The expected value will be calculated below as

The unit rate of what Sarah bought is 0.8 dollars per pepper.

The equation relating cost in dollars, c to the number of red peppers is c = 0.8p

A unit rate describes the ratio of two different units for the quantity of one.

In other words, the unit rate can be defined as the ratio between two measurements with the second term as 1.

Therefore, the unit rate when Sara buys 7 red peppers for $5.60 can be calculated as  follows

unit rate = cost of pepper / number of pepper

unit rate = 5.60 / 7

unit rate = 0.8 dollars per pepper

Let's use the unit rate to write an equation relating the cost in dollars c to the number of red peppers, p.

Therefore,

c = 0.8p

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Adult tickets cost $7 each

Student tickets cost

Answer: 16

Step-by-step explanation: 8 ÷ 2(2 + 2)

Domain is number of minutes water has been added .

Range is amount in the pond

The domain and range of a relation are, respectively, the sets of all the x-coordinates and all the y-coordinates of ordered pairs. For example, if the relationship is R = (1, 2), (2, 2), (3,), (4, 3), then

Domain is the set of all x-coordinates that is all with values of 1, 2, 3, and 4.

The set of all y-coordinates in the range is equal to 2, 3.

Domain : Let y = f(x) be a function with an independent variable x and a dependent variable y.

Range :  a function represents a defined relationship between an independent variable (x) and a dependent variable (y). The formula to find the range of a function is y = f(x).

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Surface area of rectangular box is 78 inches².

The surface area of an object is the sum of the areas of all of its faces, or the exterior surfaces of its three dimensions. It is calculated in square units. The total area of all faces (or surfaces) on a 3D form is the surface area. The six rectangular faces of a cuboid. Add the areas of each of the cuboid's six faces to determine its surface area. Additionally, we can label the prism's length (l), width (w), and height (h), and then calculate its surface area using the formula SA=2lw+2lh+2hw.

Given Data

rectangular box with measurements as shown below 5 inches 3 inches 3 inches

Length = 5 inches

Width = 3 inches

Height = 3 inches

Surface area formula

2lw + 2lh+2hw

Equating values

2(5)(3) + 2(5)(3) +2(3)(3)

30 + 30 + 18

78

Surface area of rectangular box is 78 inches².

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Rewrite the given equation in slope intercept form, y=mx+c. Where the slope is m and the y-intercept is c.

Rewrite the given equation as follows:

Simplify the equation:

Compare to the equation y=mx+c, to get:

Hence, the slope is 6/9 and the y-intercept is -8/9.

You can also write the y-intercept as an ordered pair (0,-8/9) since the x-value at the y-intercept is zero.

Answer:

1 Greatest Common Factor

We have to find out the greatest common factor, of the given polynomial to factorise it. This process is nothing but a type of reverse procedure of distributive law.

2. Grouping

This method is also said to be factoring by pairs. Here, the given polynomial is distributed in pairs or grouped in pairs to find the zeros.

3. Using Identities

The factorisation can be done also by using algebraic identities. The most common identities used in terms of the factorisation are:

(a + b)2 = a2 + 2ab + b2

(a – b)2 = a2 – 2ab + b2

a2 – b2= (a + b)(a – b)

4. Zero Factor Property :The Zero Factor Property (also called the Zero Product Property) says that if the product of two quantities is zero, then at least one of those quantities is zero. The only way to get a product equal to zero is to multiply by zero itself.

5. Greatest Common Factor (GCF) Method:

This is almost always the first method applied to factoring polynomials. Look at all of the terms and see if they all have something in common that can be removed.

6. Sum or Difference in Two Cubes

A cube is a term that has been multiplied by itself twice.

[tex] {3}^{3} {x}^{3} and \: \: \: {27x}^{3} [/tex]

are all cubed terms. The trick to remembering how to factor cubed terms is S.O.A.P. S = same sign, O = opposite sign A.P. = always positive.

The area of the walkway in square yards is 22.77 yards²

The cost of painting the walkway will be $85.37.

The square yards of the walkway can be determined by adding the areas of the two rectangles and the area of the quarter of a circle together.

Area of a rectangle = length x width

Area of the first rectangle = 9.5 x 1.5 = 14.25 yards²

Area of the second rectangle = 4.5 x 1.5 = 6.75 yards²

Area of a circle = πr²

Area of quarter of a circle = 1/4 ×  πr²

Where:

π = pi = 3.14

r = radius

1/4 x (3.14 x 1.5²) = 1.77 yards²

Area of the walkway = 1.77 yards² + 6.75 yards² +  14.25 yards² = 22.77 yards²

The cost of the painting can be determined by multiplying the area of the walkway by the cost per square yard.

Total cost = 22.77 yards² x 3.75 = $85.37

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Answer:

1(-3) = -3, 1f(-2) = -2

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

well, the logic is simply that the sum of the parts must be the same as the whole.

so,

8 + (x + 2) = 4x - 2

10 + x = 4x - 2

12 = 3x

x = 4

therefore,

MK = 4x - 2 = 4×4 - 2 = 16 - 2 = 14

The addition of the fraction 1/10 + 11/20 based on the computation will be 13/20.

In mathematics, a fraction is defined as a portion of the whole. If a pizza is cut into four equal pieces, each slice is represented by ¼.

It should be noted that a fraction simply means a part of a whole number. It should be noted that it's usually expressed as a/b where a is the numerator and b is the denominator.

In this case, we want to add 1/10 + 11/20. This will be illustrated thus:

= 1/10 + 11/20

= 2/20 + 11/20

= 13/20

Therefore the addition is 13/20.

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The probability of a gorilla living less than 23.9 years is 0.84 (84%) if the lifespans of gorillas in a particular zoo are normally distributed.

A probability is also called as a numerical representation of the likelihood or chance that any kind of specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. Probability refers to potential.

Any random event's occurrence is the exact subject of this area of mathematics. The range of the value varies from 0 to 1. Mathematics has been incorporated probability to forecast the likelihood of various types of events.

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas.

We need to find the z-score herein of 23.9 years in the kind of standard normal distribution of the lifespans of gorillas in this particular zoo.

z score can be further be calculated using the equation

z = (X-M)/s

and it has been given that X is 23.9 years

M is also called the average gorilla life (20.8 years)

s is given as the standard deviation (3.1 years)

Thus, putting up the values, we have

Z = 1

The Empirical rule that is present here states that 68% of the total lifespans lie within 1 standard deviation from the other mean.

Then Half of it, 68/2 = 34 % lies right side of 1 standard span of the mean.

Since this lifespan is less than mean is 50%, 50%+34% =84% lies less than total z-score 1, that is the probability of a gorilla living less than 23.9 years.

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