4.
49%
6x
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83°
33°

The standard equation of a conic section with its center or vertex at the origin is x² = 4ay.

The graph of this conic section is a parabola that opens upward with with its vertex at the origin (0, 0).

In Euclidean geometry, a conic section can be defined as a curve that is generated as the intersection of the surface of a right circular cone with a plane.

In Mathematics, the standard equation of a conic section is represented or modeled by the following mathematical equation:

(x - h)²/a² - (y - k)²/b² = 1

Where:

Based on the information provided about the vertex at (0, 0), the foci would be at (0, a) and the directrix would be represented by a horizontal line at y = -a. Therefore, the required equation of a conic section in standard form is given by:

x² = 4ay.

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Answer:its b 6,12

Step-by-step explanation:

Therefore , the solution of the given problem of quadratic equation comes out to be x = 2, -3 + √(5)i, -3 - √(5)i.

Regression modelling uses the polynomial answer x = ax2 + b + c=0 for one-variable equations. The First Proposition of Algebra claims that since this proposition has a second order, there can only be one solution. There are simple and complicated solutions available variable . Even as the name suggests, a "non-linear formula" has four factors. According to this, there might be just one squared term. In the formula ax2 + bx + c = 0

Here,

The provided polynomial equation can be rewritten as follows:

=> x³ + 4x² - 7x - 28 = 0

The constant term in this situation is -28, with components of 1, 2, 4, 7, 14, and 28, and a leading coefficient of 1. Therefore, 1, 2, 4, 7, 14, and 28 are among the polynomial's potential rational solutions.

It is possible to factor the polynomial by discovering that x = 2 is one of its roots.

=> (x - 2)(x² + 6x + 14) = 0

The quadratic formula can be used to calculate the quadratic factor:

=> x = (-6 ± √(6² - 4114)) / (2*1)

=> (-6 ± √(-20)) / 2

=>  -3 ± √(5)i

Thus, the following are the answers to the algebraic equation:

=> x = 2, -3 + √(5)i, -3 - √(5)i.

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The value of the perimeter:

1. 97. 3 units

2. 27. 8 units

The formula for the perimeter of a triangle is expressed as;

P = a + b + c

Given that;

From the diagram shown, we have that;

Using the tangent identity;

tan 44 = BC/29

find the value and cross multiply

BC = 28. 00

Also, AC ²= 29² + 28²

AC = √1625 = 40. 3

Then, the perimeter = 29 + 28. 00 + 40. 3 = 97. 3 units

For the second diagram;

Note that the perimeter of a rectangle is expressed as 2(length + width)

Substitute the values

Perimeter =2 ( 4 + 3) = 14 units

For triangle;

sin 45 = 4/t

cross multiply

t = 5. 7 units

To determine the adjacent side;

5.7² - 4² = x²

32. 5 - 16 = a²

a = √16. 49

a = 4. 1

Then, the perimeter = perimeter of rectangle + perimeter of triangle

= 14 + 13. 8

= 27. 8 units

Note that no specific unit was given as thus, we used 'units' as the measuring scale.

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Step-by-step explanation:

f(X)=ax+q

domain: X element of real numbers

In the given diagram, using the tangent theorem, the value of x to the nearest tenth is 16.6

From the question we are to determine the value of x.

From one of the tangent theorems, we have that

The tangent to the circle is perpendicular to the radius of the circle at the point of contact.

Thus, the triangle is a right triangle

From the Pythagorean theorem which states that, in a right triangle, the square of the hypotenuse equals sum of squares of the other two sides.

Then, we can write that

x² = 9² + 14²

x² = 81 + 196

x² = 277

x = √277

x = 16.6433

x ≈ 16.6 (to the nearest tenth)

Hence, the value of x is 16.6

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Answer:

approx 20% of the department faculty have 20 or more years of service

Step-by-step explanation:

To find the percentage of the department faculty with 20 or more years of service, we need to add up the number of faculty members in the "20-24.9" and "25 or more" year categories, since anyone with 20 or more years of service would fall into one of these categories.

Looking at the histogram, we see that there are 24 faculty members in the "20-24.9" year category, and an additional 4 in the "25 or more" year category. Therefore, the total number of faculty members with 20 or more years of service is 24 + 4 = 28.

To calculate the percentage of faculty members with 20 or more years of service, we need to divide this number by the total number of faculty members in the department, which we can find by adding up the heights of all the bars in the histogram. Based on the heights of the bars in the histogram, we can estimate that the total number of faculty members is approximately 140.

Therefore, the percentage of faculty members with 20 or more years of service is:

(28/140) x 100% = 20%

So, approximately 20% of the department faculty have 20 or more years of service.

Answer:

ok, what do you want me to answer?

Answer:

18.4

Step-by-step explanation:

ur welcome

The volume of Eli's trophy case is 64.4 cubic feet.

Eli's trophy case's length, breadth, and height must be multiplied to determine its volume. The case has the following measurements:

Length = 4 3/5 feet

Width = 2 feet

Height = 3 1/2 feet

We can sum the improper fractions after converting the mixed integers to fractions to arrive at:

Length = 4 3/5 feet = (5*4 + 3)/5 = 23/5 feet

Height = 3 1/2 feet = (2*3 + 1)/2 = 7/2 feet

Now that we have the volume, we can multiply the length, width, and height:

Volume equals length, width, and height

= (23/5) feet x 2 feet x (7/2) feet

= (23 x 2 x 7)/(5 x 2) cubic feet

= (644/10) cubic feet

= 64.4 cubic feet

Eli's trophy case therefore has a 64.4 cubic foot volume.

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In descending order in terms of y, the expression is -x³y⁵ - 2x²y³ + 4xy + x⁴.

When a pattern of numbers in mathematics has a decreasing value, the numbers are said to be in descending order. It indicates that the numbers are sorted from highest to lowest. Information is considered to be in descending order if it is arranged from highest to lowest. For example 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 are ordered in descending order. In other terms, it is considered to be in descending order if the numbers are listed from greatest to smallest.

The given expression is:

x⁴- x³y⁵+ 4xy - 2x²y³

To arrange in descending order, place the highest value first followed by the smaller value.

Therefore, in decreasing order in terms of y, the expression is -x³y⁵ - 2x²y³ + 4xy + x⁴.

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The five-number summary of the class, determined by the results of the final test, is:

Minimum = 60

Lower quartile = 71.5.

Median = 85.

Upper Quartile = 94.

Maximum = 98

The median, a measure of the center of gravity, reflects the center of value in the collection when values are sorted in either ascending or descending order. The value that distinguishes the lower 50% of the information from the upper 50% of the data is, in other words, the value.

The lowest score is 60, which is the minimum. The highest score, 98, will serve as the maximum.

The formula: can be used to determine the lower quartile.

= (Second score + Third score) / 2

= (65 + 78) / 2

= 71.5.

The upper quartile is:

= (Third to last score + Second to last score) / 2

= (93 + 95) / 2

= 94

The median is:

= (5th score + 6th score) / 2

= (82 + 88) / 2

= 85

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Answer:

Option B

3&5, 4&6

Step-by-step explanation:

An interior angle is an angle inside a shape

a) The speed at which the car gets maximum gas mileage is given as follows: 48 miles per hour.

b) The max gas mileage is given as follows: 29.5 miles per gallon.

The gas mileage is modeled as a function of the velocity x according to the quadratic function presented as follows:

m(x) = -0.028x² + 2.688x - 35.012.

The coefficients are given as follows:

a = -0.028, b = 2.688, c = -35.012.

The leading coefficient a is negative, hence the vertex represents the point at which the maximum mileage is obtained.

The velocity is given as follows:

x = -b/2a

x = -2.688/[2(-0.028)]

x = 48 miles per hour.

The max gas mileage is obtained as follows:

m(48) = -0.028(48)² + 2.688(48) - 35.012.

m(48) = 29.5 miles per gallon.

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The length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.

Applying the Pythagorean Theorem, the length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.

From the information given, we know the following:

Triangles AED and CED are right-angled triangles

Thus:

AC = AE + CE

Find AE and CE using the Pythagorean Theorem , where c if the hypotenuse of the right triangle.

Length of AE:

AE = [tex]\sqrt{5^2 -4^2}[/tex]

AE= [tex]\sqrt{9}[/tex]

AE= 3

Length of CE:

CE = [tex]\sqrt{7^2 -4^2}[/tex]

CE= [tex]\sqrt{33}[/tex]

CE= 5.7

Length of AC:

AC = AE + CE

Put the values together:

AC = 3 + 5.7

= 8.7cm

Therefore, the length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.

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The ordered pair (2,6) means that 2 plain rings and 6 initial rings were purchased, and the total cost would be 23 + 64 = 24 dollars.

In mathematics, an ordered pair is a collection of two objects, which are arranged in a specific order. The order of the objects in the pair is important, as the ordered pair (a, b) is different from the ordered pair (b, a) if a and b are not equal.

The two objects in an ordered pair can be anything, such as numbers, variables, or other mathematical entities. The ordered pair (x, y), for example, can represent a point on a two-dimensional coordinate plane, where x represents the horizontal coordinate and y represents the vertical coordinate.

The ordered pair notation is commonly used in set theory and other branches of mathematics to represent relationships between two objects. Ordered pairs can also be used to define functions, where the first object in the pair represents an input to the function, and the second object represents the output.

Here's the completed table and ordered pairs:

Cost of plain rings (x) Cost of initial rings (y) (Ordered Pairs (x,y))

              0                                 4                              (0,4)

               1                                 5                              (1,5)

               2                                 6                              (2,6)

               3                                 7                              (3,7)

               4                                 8                              (4,8)

In each ordered pair, the first number represents the number of plain rings purchased (x) and the second number represents the number of initial rings purchased (y). For example, the ordered pair (2,6) means that 2 plain rings and 6 initial rings were purchased, and the total cost would be 23 + 64 = 24 dollars.

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By answering the presented question, we may conclude that As a result, fraction the answer is nine thirty-fifths.

A whole can be represented by any number of equal sections or fractions. In standard English, fractions represent the number of units of a specific size. 8, 3/4. A whole contains fractions. In mathematics, numbers are stated as the ratio of the numerator to the denominator. Each of these is an integer in simple fractions. A fraction exists in the numerator or denominator of a complex fraction. True fractions have numerators that are smaller than their denominators. A fraction is a sum that represents a piece of a total. You may assess it by dividing it up into smaller chunks. Half of a whole number or object, for example, is represented as 12.

We can simplify both fractions to have a common denominator of 12 for the first problem:

Four-sixths = Eighteenths

Three-twelfths + three-twelfths = three-twelfths

As a result, the phrase becomes: 8/12 - 3/12 = 5/12

As a result, the answer is five-twelfths.

For the second case, we may reduce both fractions again such that they have a common denominator of 16:

Seventy-eighths = fourteenteenths

Nineteenths + nineteenths = nineteenths

As a result, the equation becomes: 14/16 - 9/16 = 5/16.

As a result, the answer is five-sixteenths.

We can simplify both fractions to obtain a common denominator of 35 for the third problem:

Two-fifths = 14-thirty-fifths

One-seventh Equals thirty-fifths

As a result, the phrase becomes: 14/35 - 5/35 = 9/35

As a result, the answer is nine thirty-fifths.

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Answer:

Step-by-step explanation:

Use SAS congruency; AD=DC, and they both share side BD. Also, BD is the perpendicular bisector to AC, so it also forms 2 right angles. Proof using SAS.

Or, if you don’t know SAS congruency, you may use SSS congruency;

Use the Pythagorean theorem. Side length AB^2 = AD^2 + BD^2
BC^2 = DC^2 + BD^2.

AD=DC, so therefore AB = BC. Use SSS congruency, and there you go.

Answer:

Rounding to the nearest hundredth of a foot, the change in altitude is approximately 514.77 feet.

Step-by-step explanation:

To solve this problem, we can use trigonometry. The angle of climb is 15 degrees, which means that the ratio of the change in altitude to the horizontal distance traveled is the tangent of 15 degrees:

tan(15°) = change in altitude / horizontal distance

We can rearrange this equation to solve for the change in altitude:

change in altitude = horizontal distance x tan(15°)

Substituting the given values, we get:

change in altitude = 2 miles x tan(15°)

We can convert the distance to feet by multiplying by 5280:

change in altitude = 2 miles x 5280 feet/mile x tan(15°)

Using a calculator, we get:

change in altitude ≈ 514.77 feet

Rounding to the nearest hundredth of a foot, the change in altitude is approximately 514.77 feet.

Answer: a. To find the earnings per share (EPS), we can use the formula:

P/E ratio = Price per share / Earnings per share

Rearranging this formula to solve for EPS, we get:

Earnings per share = Price per share / P/E ratio

Substituting the given values, we have:

Earnings per share = $53.21/13.26 ≈ $4.01

Therefore, the earnings per share were approximately $4.01.

b. To determine if the stock is overpriced, underpriced, or about right given the historical P/E ratio of 12-14, we can compare the current P/E ratio to this range. Since the current P/E ratio is 13.26, which falls within the historical range, the stock seems to be about right in terms of valuation. However, it's important to note that other factors should also be considered before making any investment decisions.

Step-by-step explanation:

To calculate the total amount paid over two years, we first need to determine the annual premium increase percentage. Let's assume the insurer increases the premium by 5% per year to keep up with inflation.

After the first year, the new premium would be:

R450 + (5% of R450) = R472.50 per month

After the second year, the new premium would be:

R472.50 + (5% of R472.50) = R496.13 per month

To calculate the total amount paid over two years, we can use the following formula:

Total amount paid = (monthly premium x 12 months x number of years)

= (R450 x 12 x 2) + (R472.50 x 12 x 1) + (R496.13 x 12 x 1)

= R10,800 + R5,670 + R5,953.56

= R22,423.56

Therefore, you would have paid a total of R22,423.56 over two years.

The ratio for 2 quantities of flour and milk is given as follows:

d. 6:4.

The ratio 2 quantities of flour and milk is obtained applying the proportions in the context of the problem.

A proportion is applied as to obtain the ratio between two amounts, you simply divide one amount by the other. The ratio is expressed as a fraction, and can also be expressed as a decimal or a percentage.

The amounts for a single recipe are given as follows:

Hence for two quantities, the amounts are multiplied by two as follows:

Meaning that the ratio is given as follows:

6:4.

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Step-by-step explanation:

Interchange just means to switch really. The first 3 will stay the same be cause they are the same numbers.

The last one will be (2,8) because that's (8,2) but with the numbers switched

Heather's account balance will be approximately $1,340.55 after 7 years if the interest is compounded 6 times each year.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the account balance after a certain amount of time

P is the principal or initial amount invested

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time period in years

Given tha data in the question;

First, convert R as a percent to r as a decimal

r = R/100

r = 3.5/100

r = 0.035 rate per year.

Substituting these values into the formula solve for accrued amount, we get:

A = P(1 + r/n)^(nt)

A = 1,050(1 + 0.035/6)^(6 × 7)

A = 1,050(1 + 0.005833333333333)⁴²

A = 1,050(1.005833333333333333)⁴²

A = $1,340.55

Therefore, the accrued amount is $1,340.55.

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Answer:

Step-by-step explanation:

(y^2)/1600-(x^2)/81=1. y21600−x281=1 y 2 1600 - x 2

Answer: y21600x281=1 y 2 1600 - x 2

Step-by-step explanation: for sure chfjjgffjfj ;)

Answer:

[tex]d^{2}[/tex] - 16.

Step-by-step explanation:

To solve for the product of (d + 4) and (d - 4), we can use the FOIL method.

This means we multiply the first terms, then the outer, then the inner, and finally the last terms, then we add all the products together.

So, (d + 4) (d - 4) can be expanded like this:

Adding all of them together, we get: [tex]d^{2}[/tex] - 4d + 4d - 16, which simplifies to [tex]d^{2}[/tex] - 16.

Therefore, (d + 4)(d - 4) = [tex]d^{2}[/tex] - 16.

The percentage of bicyclists that finished the race in less than 56 minutes is 96 %

Percentage is a ratio out of hundred

If in a​ race, 24 out of the 25 bicyclists finished in less than 56 minutes. To find what percent of bicyclists finished the race in less than 56 ​minutes, we first write it in a fraction as number/total

Since

We have that

fraction = number/total

= 24/25

Now to write it as a percentage, we multiply by 100.

So, we have that percentage = fraction × 100 %

So, we have that in percentage = 24/25 × 100 %

= 24 × 4 %

= 96 %

So, the percentage is 96 %

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There are 252 different ways to assemble the committee.

Permutation:

A simple definition of permutation is the various ways to arrange some or all of the members in a particular order.

It is the process of orderly disorganisation.

A permutation is what is meant by this.

Combination: Combination is the process of choosing one or more objects from a group of objects so that, unlike permutations, the order in which the objects are chosen is irrelevant.

It describes the combination of N items drawn randomly from a collection of K items at a time.

Hence, There are 252 different ways to assemble the committee.

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