(x²-8)
meters
Square
x meters
...
What expression represents the total area of the
shaded figure. Simplify your expression.

The measure οf the equal sides οf the triangle is 8√3 cm and the perimeter οf the triangle is apprοximately 49.9 cm.

The current carried by the third resistοr is 2.4A is the tοtal current is 8A what current is carried by the third resistοr.

A fractiοn is a mathematical term that represents a part οf a whοle οr a ratiο between twο quantities.

a. Tο find the fractiοn οf tοtal current carried by the twο resistοrs, we need tο add up the currents and divide by the tοtal current. Let I be the tοtal current, and let I1 and I2 be the currents carried by the first twο resistοrs, respectively. Then we have:

I1 = 1/5I

I2 = 1/2I

The tοtal current is:

I = I1 + I2 = (1/5 + 1/2)I = 7/10I

Therefοre, the fractiοn οf tοtal current carried by the twο resistοrs is:

(I1 + I2)/I = (1/5I + 1/2I)/I = (7/10I)/I = 7/10

b. Let I3 be the current carried by the third resistοr. Then we have:

I3 = I - (I1 + I2) = I - 7/10I = 3/10I

Therefοre, the fractiοn οf tοtal current carried by the third resistοr is:

I3/I = (3/10I)/I = 3/10

c. If the tοtal current is 8A, then we have:

I = 8A

The current carried by the third resistοr is:

I3 = 3/10I = 3/10 x 8A = 2.4A

Therefοre, the current carried by the third resistοr is 2.4A.

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The value of the two numbers are 43 and 218

From the information given, we have;

Let the numbers be x and y

Then,

The difference between the numbers = x - y

The sum of the numbers = x + y

Substitute the values

x + y = 261

x - y = 175

Let's solve the simultaneous equations

Make 'x' the subject from 1

x = 261 - y

Substitute the value in 2

261 - y - y= 175

collect the like terms

-2y = - 86

y = 43

Substitute to determine the value of x

x = 261 - y = 261 - 43 = 218

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Answer:

$12

Step-by-step explanation:

Parents=x Children=Y 2(4)y+2y=120 10y=120 y=12

One possible set of four lengths that meets the given requirements is:

3 inches, 4 inches, 5 inches, 7 inches

To show that this set of lengths meets all the requirements, we need to demonstrate that:

Each length is different: We can see that all four lengths are different.

Each length is a whole number: We can see that all four lengths are whole numbers.

No matter which three you choose, you will always be able to make a triangle: To show this, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

For example, if we choose the lengths 3, 4, and 5, we can see that 3 + 4 = 7, which is greater than 5. Therefore, we can make a triangle with sides of length 3, 4, and 5. Similarly, if we choose the lengths 3, 4, and 7, we can see that 3 + 4 = 7, which is still greater than 7. Therefore, we can make a triangle with sides of length 3, 4, and 7.

We can repeat this process with any combination of three lengths from the set, and we will always find that we can make a triangle. Therefore, we have shown that the set of lengths {3 inches, 4 inches, 5 inches, 7 inches} meets all the requirements.

The amount of butter that Simon has left is given as follows:

0.75 cups.

The amount of butter that Simon has left is obtained applying the proportions in the context of the problem.

The pack has 8 sticks of butter that are each 1/2 of a cup, hence the number of cups purchased is given as follows:

8 x 1/2 = 4 cups.

Simon used 1 1/4 of butter to make brownies , 3/4 cup of butter to make a cake , and 1 1/4 cup of butter to make cookies, hence the number of cups used is given as follows:

1.25 + 0.75 + 1.25 = 3.25.

Hence the amount of butter that Simon has left is given as follows:

4 - 3.25 = 0.75 cups.

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The mean of the sampling distribution of all possible samples of size 16 will be 42.5, the correct option is D.

Normal distribution with mean μ = 42.5 inches and standard deviation σ = 2.5 inches. Let x₁, x₂, ..., xₙ be a random sample of size n = 16 from X, and let x be the sample mean

The sampling distribution of the mean x is also Normal, with mean μ and standard deviation σ/√n.

f(x) = (1/√(2π) × (σ/√n)) × exp[-(x - μ)² ÷ (2 × (σ/√n)²)]

we integrate

Mean of x = ∫(-∞ to ∞) x × f(x) dx

Mean of x = 2 × ∫(μ to ∞) x × f(x) dx

Next, we substitute

u = (x - μ) / (σ/√n):

Mean of x = 2 × ∫(0 to ∞) (u × (σ/√n) + μ) × (1/√(2π) × (σ/√n)) × exp(-u² / 2) du

Simplifying this expression gives:

Mean of x = μ

Therefore, the mean of the sampling distribution of all possible samples of size 16 is equal to the population mean μ, which is 42.5 inches.

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The complete questions is :

The heights of five-year-olds are Normally distributed with a mean of 42.5 inches and a standard deviation of 2.5 inches. A random sample of 16 five-year-olds is taken and the mean height is recorded. What would be the mean of the sampling distribution of all possible samples of size 16?

A 2.66

B 10.63

C 17

D 42.5

Answer:

0.625

Step-by-step explanation:

you divide 5 by 8

The angle subtended by each of the 8 equal parts at the center of the circle is 45 degrees.

What is circle and how to find its angle?

A circle is a two-dimensional shape that consists of all points in a plane that are equidistant from a given point called the center. A circle is defined by its radius (the distance from the center to any point on the circle) or its diameter (the distance across the circle passing through the center).

The angles in a circle can be measured in degrees or radians. There are several types of angles that are important in circles:

Central angle: A central angle is an angle whose vertex is at the center of the circle. The measure of a central angle is equal to the measure of the arc it subtends.

Inscribed angle: An inscribed angle is an angle whose vertex is on the circle and whose sides are chords of the circle. The measure of an inscribed angle is half the measure of the arc it subtends.

Arc: An arc is a portion of the circumference of a circle. The measure of an arc is equal to the measure of the central angle that subtends it.

To find the measure of an angle in a circle, you need to know the type of angle and the information given about the circle. The formulas and methods used to find the measure of an angle in a circle depend on the type of angle and the given information.

For example, to find the measure of a central angle, you can use the formula:

measure of central angle = (arc length / radius) * 180 / pi

To find the measure of an inscribed angle, you can use the formula:

measure of inscribed angle = 1/2 * measure of arc it subtends

In general, to find the measure of an angle in a circle, you need to use the information given about the circle and apply the appropriate formula or method based on the type of angle.

If a circle is divided into 8 equal parts, this means that the circle is divided into 8 congruent sectors. Since the sum of all angles at the center of a circle is 360 degrees, we can find the measure of the angle subtended by each sector at the center by dividing 360 degrees by the number of sectors:

angle subtended by each sector at the center = 360 degrees / 8 = 45 degrees

Therefore, the angle subtended by each of the 8 equal parts at the center of the circle is 45 degrees

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Your complete question is :-a circle is divided into 8 equal parts, what is the angle subtended by each at the center?

The expression "[tex]r_i \ o \ r_j = r_{i+j},[/tex]for all i and j" represents a mathematical relationship involving a binary operation "o" and a sequence of elements denoted by "[tex]r_i[/tex]", where "i" and "j" are integers.

The expression states that for any two integers "i" and "j", the result of applying the binary operation "o" to the elements "r_i" and "r_j" is equal to the element "[tex]r_{i+j}[/tex]" in the sequence that is the sum of the indices "i" and "j".

In other words, if we have a sequence of elements "r_1, r_2, r_3, ..." and a binary operation "o", then this expression tells us that the result of applying the operation "o" to any two elements in the sequence is equal to the element in the sequence whose index is the sum of the indices of the two original elements.

For example, as given in the polygon, a sequence of numbers {1, 2, 3, 4, ...} and the binary operation is addition (+), then the expression "[tex]r_i \ o \ r_j = r_{i+j}[/tex], for all i and j" tells us that the sum of any two numbers in the sequence is equal to the number whose index is the sum of the indices of the two original numbers.

For instance, 1 + 2 = 3, which is the same as r_1 o r_2 = r_{1+2} = r_3.

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the answer is 1 5/8 inches shorter. To find the difference between the initial length of the pencil and the final length after the project, we need to subtract the final length from the initial length.

Initial length of the pencil = 7 1/2 inches

Final length of the pencil = 5 7/8 inches

To subtract these two values, we need to convert the mixed numbers to improper fractions.

7 1/2 = 15/2

5 7/8 = 47/8

Now we can subtract:

15/2 - 47/8

To subtract these fractions, we need to find a common denominator. The least common multiple of 2 and 8 is 8, so we can convert both fractions to have a denominator of 8.

15/2 = 60/8

47/8 = 47/8

Now we can subtract:

60/8 - 47/8 = 13/8

So the pencil is 13/8 inches shorter after the project. To write this as a mixed number, we divide the numerator by the denominator:

13 ÷ 8 = 1 with a remainder of 5

So the answer is 1 5/8 inches shorter.

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The area of the composite figure using area formula is 45unit².

Option b is the correct option.

The space that any composite shape occupies is referred to as the area of composite shapes. In order to create the desired shape, a few polygons are connected to create a composite shape. These figures or forms can be constructed using a variety of geometrical elements, including triangles, squares, quadrilaterals, and others.

To determine the area of a composite object, divide it into simple shapes like a square, triangle, rectangle, or hexagon. In essence, a composite shape is a combination of fundamental shapes. It goes by the name's "composite" or "complex" shapes.

In the question, we can see that the composite figure comprises of a triangle and a rectangle.

Now, length of the rectangle as per the vertices is, l = 6 units.

Breadth of the rectangle as per the vertices is, b = 6 units.

As the length and breadth of the rectangle as per the vertices are equal it's a square with side a = 6 units

Area of square = a²

= 6²

=36unit².

Now in the triangle,

Base, b = 6 units

Height, h = 3 units.

Area = 1/2 × b × h

= 1/2 × 6 × 3

= 9unit².

Therefore, the total area of the figure is 36 + 9 = 45unit².

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The area of triangle ABC is 249.36 sq ft while the area of ΔACD and ΔBCD is 124.68 sq ft

The area of a triangle can be calculated using the formula:

Area = (1/2) x base x height

where "base" is the length of the base of the triangle and "height" is the perpendicular distance from the base to the opposite vertex.

Lets find altitude with with Pythagoras formula:

[tex]\rm a^2 + b^2 = c^2[/tex]

[tex]\rm a^2 + 12^2 = 24^2[/tex]

[tex]\rm a^2 = 24^2 -12^2[/tex]

[tex]\rm a^2 = 576 - 144[/tex]

[tex]\rm a^2 = 432[/tex]

a = √432

a =

​a = 20.78

To find the area of a triangle, we use the formula A = 1/2 × base × height.

In this case, the base of the triangle is 24 ft and the height is 20.78 ft.

Therefore,

A = 1/2 × 24 ft × 20.78 ft

A = 249.36 sq ft

Hence, The area of each triangle is 249.36 square feet.

Now, Both tringles are 1/2 of the area as base = 12 = 1/2 × 24

ΔACD =  1/2 × 249.36

ΔACD =  124.68 sq ft

ΔBCD =  1/2 × 249.36

ΔBCD =  124.68 sq ft

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Complete question:

What is the area of each triangle Base = 24 ft 20 ft

To determine the correct inequality that represents the shaded area below the diagonal curve, we need to identify the equation of the line that passes through the two endpoints of the curve, which are (-2, 5) and (3, -5).

First, we need to find the slope of the line:

slope = (change in y) / (change in x)

slope = (-5 - 5) / (3 - (-2))

slope = -10 / 5

slope = -2

Next, we can use the point-slope form of the equation of a line to find the equation of the line:

y - y1 = m(x - x1), where m is the slope and (x1, y1) is one of the points on the line.

Using the point (-2, 5), we have:

y - 5 = -2(x - (-2))

y - 5 = -2(x + 2)

y - 5 = -2x - 4

y = -2x + 1

So the equation of the line passing through the endpoints of the curve is y = -2x + 1.

To determine which inequality represents the shaded area below the curve, we can test a point that is not on the line, such as (0, 1).

Plugging in (0, 1) into the equation of the line, we get:

1 = -2(0) + 1

1 = 1

Since 1 is equal to 1, the point (0, 1) is on the line. Therefore, the inequality that represents the shaded area below the curve is y < -2x + 1, since the points below the line satisfy this inequality.

So the correct answer is C. y < -2x + 1.

The probability of drawing a queen or a heart from a standard 52-card deck is 0.308 or 30.8%.

What is Probability ?

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The event is "drawing a queen or a heart from a standard 52-card deck".

There are 4 queens in a standard 52-card deck, and there are 13 hearts (including the queen of hearts) in the same deck. However, we need to be careful not to count the queen of hearts twice, since it is both a queen and a heart.

So, the number of cards that satisfy the given event is 4 queens + 12 hearts (not including the queen of hearts) = 16 cards.

The total number of cards in a standard deck is 52.

Therefore, the probability of drawing a queen or a heart from a standard 52-card deck is:

P(queen or heart) = number of cards that satisfy the event : total number of cards

P(queen or heart) = 16 : 52

P(queen or heart) =  0.308

Therefore, the probability of drawing a queen or a heart from a standard 52-card deck is  approximately 0.308 or 30.8%.

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Answer: [1]   G,D,L,K    [2] HF and AB    [3] X-Y Plane  [4] CE and LA

[5] A,L,B

Step-by-step explanation:

Answer:

3.5

Step-by-step explanation:

Answer: 3.5

Step-by-step explanation: In this scenario, the vertex would be the peak of the baseball throw. We can find the x value of the vertex by using -b/2a. With your equation of 112x-16x^2 we need to change the x^2 value to the front to make it -16x^+112x so that it is in standard form. Now take your b value (112), make it negative (-112), and divide that by 2 times -16. to get 3.5.

I should also include that the x value of the vertex is equal to t which is seconds.

The resulting function is : y = (1/3)[tex]e^{(-2x) }[/tex] - 2 + 0.

What is the function?

A function is a rule that assigns each input value (usually represented by the variable x) to a unique output value (usually represented by the variable y). A function is typically written as an equation in terms of x and y, such as y = f(x), where f is the name of the function.

Starting with the function y = [tex]e^{(-2x) }[/tex], here are the steps to transform it:

1. Vertically compress by a factor of 3: Multiply y by 1/3

2. Reflect across the y-axis: Multiply x by -1

3. Shift down 2 units: Subtract 2 from y

So the transformed function is:

y = (1/3)[tex]e^{(-2x) }[/tex] - 2

Simplifying the exponent and the coefficient of e, we get:

y = (1/3)[tex]e^{(-2x)}[/tex] - 2

Writing in the desired form, we get:

y = (1/3)[tex]e^{(-2x)}[/tex]- 2 + 0

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1) the JK does not form the line segment.

2) NL line segment is different from other three options.

It is a part of line having two ends points.

The simplest definition of a line is an arrangement of points that extends in opposite directions to infinity, while a ray is a section of a line that has one endpoint and extends continuously in one direction, while a segment of a line is a section of a line between two endpoints.

1) Like a line can be expressed in liner form such as y=mx+c where as, a line segment will consist of two coordinates such as A(x₁,y₁) and B(x₂,y₂).

Here, the JK does not form the line segment as there is no connecting line between them.

2) Here, NL line segment is different from other three options as is formed the line JL.

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There are 45 monkeys in the zoo.

A percentage is a way of expressing a fraction or a portion of a whole as a number out of 100. The word "percent" means "per hundred."

Let's suppose x is the total number of monkeys in the zoo.

We know that 25 ≤ x ≤ 49, and that 20% of the monkeys are Langur monkeys and 1/4 of them are Colobus monkeys. This means that the number of Langur monkeys is 0.2x and the number of Colobus monkeys is (1/4)x

The total number of monkeys can be expressed as;

x = 0.2x + (1/4)x + other monkeys

Simplifying this, (11/20)x = other monkeys

Since we know that the number of monkeys is between 25 and 49, we can substitute these values into the equation and solve for "x":

25 ≤ (11/20)x ≤ 49

45.4 ≤ x ≤ 89.1

Since x must be an integer, the only solution in this range So, x = 45

Therefore, there are 45 monkeys in the zoo.

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Glorious Gadgets should order a lot size of 1 to minimize their total inventory costs, and the minimum total inventory cost is $42,501.50.

In mathematics, rate is commonly used in the context of describing how one quantity changes with respect to another quantity over time. For example, the rate of change of an object's position over time is its velocity, which is expressed in units of distance per unit of time (such as meters per second). Similarly, the rate of growth or decline of a population over time is often expressed as a percentage, such as an annual growth rate of 2% or a population decline rate of 1.5% per year.

To find the lot size that minimizes the total inventory cost, we need to find the value of "x" that minimizes the function C(x) = 1.5x + 25500x¹ + 17000.

To do this, we can take the derivative of C(x) with respect to x, set it equal to zero, and solve for "x":

C'(x) = 1.5 + 25500 + 0 = 25501.5

25501.5 = 0

x = -25500/1.5 = -17000

Since a negative value of "x" doesn't make sense in the context of the problem, we can conclude that there is no minimum value for C(x). Instead, the function C(x) increases as "x" increases, so Glorious Gadgets should order as small a lot size as possible to minimize their inventory costs.

To find the minimum total inventory cost, we can evaluate the function C(x) at a small lot size, such as x = 1:

C(1) = 1.5(1) + 25500(1)¹ + 17000

C(1) = 1.5 + 25500 + 17000

C(1) = 42501.5

Therefore, Glorious Gadgets should order a lot size of 1 to minimize their total inventory costs, and the minimum total inventory cost is $42,501.50.

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16.8 gallons

2.85 dollars/gallons

[tex]16.8 \times \frac{2.85 \: dollars}{gallons} = 47.88 \\ [/tex]

Alyssa paid a total of $47.88 for 16.8 gallons of gas when each gallon costs $2.85

The subject of this question is mathematics. Let's start by identifying what we know. We know that Alyssa filled her tank with 16.8 gallons of gas and that the cost of gas is $2.85 per gallon.

To find out how much Alyssa paid in total, we need to multiply the number of gallons by the cost per gallon:

Now, we are asked to round to the nearest cent. Rounding $47.88 doesn't change anything because the digits following the decimal point are 88, which is less than 100. So, the total amount Alyssa paid is $47.88.

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The estimated fox population in the year 2008 is 19498.

A function is a mathematical concept that describes the relationship between two sets of variables, where each input value (independent variable) corresponds to a unique output value (dependent variable).

(a) The continuous growth rate of 5% per year means that the fox population is increasing at a rate proportional to its current size. Let P(t) be the fox population t years after 2000. Then, we can model the population using the differential equation:

dP/dt = kP

where k is the constant of proportionality. To solve this differential equation, we can separate the variables and integrate:

dP/P = k dt

ln|P| = kt + C

where C is the constant of integration. To find the value of C, we use the initial condition that the population in the year 2000 (t=0) was 12500:

ln|12500| = 0 + C

C = ln|12500|

Therefore, the solution to the differential equation is:

ln|P| = kt + ln|12500|

Simplifying, we get:

P(t) = [tex]e^(kt + ln|12500|)[/tex]

P(t) = 12500 [tex]e^(kt)[/tex]

where P(t) is the fox population t years after 2000.

We know that the population grows at a continuous rate of 5% per year, so we can use this information to find the value of k. Since the continuous growth rate is given by r = 0.05, we have:

k = ln(1 + r) = ln(1.05)

As a result, the following function represents the fox population t years after 2000:

p(t) = 12500 [tex]e^(0.05t)[/tex]

(b) Since t is the number of years after 2000, we must determine the value of p(8) in order to calculate the fox population in 2008. We have the following using the function from section (a):

p(8)  = 12500 [tex]e^(0.05(8))[/tex]

       = 19498

Therefore, the estimated fox population in the year 2008 is 19498.

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Therefore, the surface area of the rectangular prism is 280 square meters.

Area is a measure of the size of a two-dimensional region or surface, typically expressed in square units. It is the amount of space inside a closed shape or figure, and is calculated by multiplying the length and width of the shape or by using a formula specific to the shape. For example, the area of a rectangle can be found by multiplying its length and width, while the area of a circle can be found by multiplying pi (3.14) by the square of its radius. Area is commonly used in mathematics, science, engineering, and other fields to calculate quantities such as surface area, volume, and density.

Here,

The rectangular prism has 6 faces, and each face is a rectangle. To find the surface area, we need to find the area of each rectangle and add them up. The net shows that the dimensions of the prism are:

length = 10 m

width = 6 m

height = 5 m

The area of the top and bottom faces (which are congruent) is:

A = length × width

= 10 m × 6 m

= 60 m²

The area of the front and back faces (which are congruent) is:

A = length × height

= 10 m × 5 m

= 50 m²

The area of the two side faces (which are congruent) is:

A = width × height

= 6 m × 5 m

= 30 m²

To find the surface area, we add up the areas of all six faces:

Surface Area = 2 × (top and bottom faces) + 2 × (front and back faces) + 2 × (side faces)

Surface Area = 2(60 m²) + 2(50 m²) + 2(30 m²)

Surface Area = 120 m² + 100 m² + 60 m²

Surface Area = 280 m²

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οther valid transfοrmatiοn sequences cοuld Sequences achieve the same result, and the specific sequence used wοuld depend οn the specific shapes and οrientatiοns οf figures M and N.

A sequence is an οrdered list οf elements in mathematics. Numbers, functiοns, and οther mathematical οbjects can be used as elements. A series is frequently denοted by stating its terms in parenthesis, separated by cοmmas. The series οf natural numbers, fοr example, can be denοted as: (1, 2, 3, 4, 5, ...) Similarly, the series οf even numbers is denοted as fοllοws: (2, 4, 6, 8, 10, ...) Depending οn whether it has a finite οr infinite number οf terms, a sequence might be finite οr infinite.

Here's an example transfοrmatiοn sequence that cοuld pοtentially cοnvert figure M intο its cοngruent image figure N:

Figure M shοuld be mοved tο a new lοcatiοn in space sο that it aligns with the cοrrespοnding pοrtiοn οf figure N.

Figure M shοuld be rοtated abοut a pοint until it aligns with the οrientatiοn οf figure N.

Figure M shοuld be mirrοred acrοss a line οf symmetry tο match the mirrοr image οf figure N.

Figure M shοuld be translated tο its final lοcatiοn sο that it exactly cοincides with figure N.

It shοuld be nοted that many οther valid transfοrmatiοn sequences cοuld achieve the same result, and the specific sequence used wοuld depend οn the specific shapes and οrientatiοns οf figures M and N.

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Answer:

y =  [tex]\frac{1}{16}[/tex] ( x + 5 )² - 5

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k , (h, k) are coordinates of the vertex.

If a parabola passes through the point A ( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) , then

[tex]y_{1}[/tex] = a( [tex]x_{1}[/tex] - h )² + k

a = [tex]\frac{y_{1} -k }{ (x_{1} -h)^2}[/tex]

~~~~~~~~~~~~~~~~~~

Vertex at ( - 5, - 5 )

A( - 19, [tex]\frac{29}{4}[/tex] )

a = [ [tex]\frac{29}{4}[/tex] - ( - 5)] ÷ [ - 19 - ( - 5)]² = ( [tex]\frac{29}{4}[/tex] + 5 ) ÷ ( - 14 )² = 0.0625 = [tex]\frac{1}{16}[/tex]

y = [tex]\frac{1}{16}[/tex] ( x + 5 )² - 5

Answer:

56.7%

Step-by-step explanation:

Total number of students = 30

Number of boys in the class = 13

Number of girls in the class = 30 - 13 = 17

Now we have to find the percent of girls of the class

Therefore

[tex]\dfrac{\text{Number of girls}}{\text{Total students}} \times100[/tex]

[tex]=\dfrac{17}{30}\times100=56.67\%[/tex]

[tex]56.67\implies56.7\%[/tex]

Hence, girls are 56.7% of the class.