y = 3x² - 24x + 57

find the coordinates of the vertex

Answer:
2. Total Hours= 38+5 = 43

Step-by-step explanation:

2. Wage at Normal rate80 *38 = 3040
Extra Sum of Money then Normal wage 3640-3040 = 600

Overtime rate 80*1.5= 120
Overtime hours 600/120=5

3. (a) 210/3 = 70km/hr
        140/(2.75*) = 50.91 km/hr
         *2.75= 2+ (45/60)
 

The result of simplifying this answer is (x - 1)2 = 16(y - 7) (y - 7) The equation for the parabola is presented here in vertex form.

A parabola is a U-shaped curve in mathematics that is produced by the graph of a quadratic function. It is a particular kind of conic section, which is a circle made when a plane and a cone cross each other. A quadratic function with the following standard form can depict a parabola: Y = ax2+bx+c where are constants a, b, and c. Which way the parabola expands depends on the sign of the coefficient a.

given

We can use the following formula to express the equation of a parabola given a focus and a directrix:

where (h,k) is the parabola's vertex, p is the separation between it and the centre, and the directrix is represented by the horizontal line y = k - p.

The centre in this instance is (1,11), and the directrix is y=3.

We also understand that p is the distance, in this instance 4 units, between the vertex and the focus (since the focus is 4 units above the vertex). Therefore, we can enter the numbers into the formula to obtain:

(x - 1)^2 = 4(4)(y - 7) (y - 7)

The result of simplifying this answer is (x - 1)2 = 16(y - 7) (y - 7) The equation for the parabola is presented here in vertex form.

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The linear function that models the scatter plot is given as follows:

y = 7/8x + 6.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For the equation in this problem, we have that:

Hence the option that satisfies the sign of the slope and the intercept is given as follows:

y = 7/8x + 6.

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Answer:

See below.

Step-by-step explanation:

We are asked for the diameter, radius, and area of a circle.

We are given the Circumference.

We should know that;

[tex]Circumference = (diameter)\pi[/tex]

[tex]Circumference = 24\pi[/tex] (Exact)

This means that the Diameter is 24.

The Radius is [tex]\frac{1}{2}[/tex] of the Diameter.

This means that the Radius is 12.

The area of a circle is represented as;

[tex]Area = \pi(radius)^2[/tex]

We have the requirements to find the area, with the value of the radius.

Solve for the area;

[tex]Area = \pi(12)^2[/tex]

[tex]Area = 144 \pi[/tex] (Exact)

[tex]Area = about \ 452.39.[/tex] (Approx.)

The central angles for each category are approximately: Red: 100°, Blue: 150°, Green: 50° and Purple: 60°

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

To find the central angle of each category, we first need to calculate the total number of people:

Total = 20 + 30 + 10 + 12 = 72

Next, we can calculate the percentage of people who prefer each color:

Red: 20/72 = 0.278, or 27.8%

Blue: 30/72 = 0.417, or 41.7%

Green: 10/72 = 0.139, or 13.9%

Purple: 12/72 = 0.167, or 16.7%

To find the central angle for each category, we can multiply the percentage by 360°:

Red: 0.278 × 360° = 100.08°

Blue: 0.417 × 360° = 150.12°

Green: 0.139 × 360° = 50.04°

Purple: 0.167 × 360° = 60.48°

Therefore, the central angles for each category are approximately:

Red: 100°, Blue: 150°, Green: 50° and Purple: 60°

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Answer:

25%

Step-by-step explanation:

$30-$24 =$6

$6×100

________ =25 percent

24

The total amount that Rahul will have is 108,006.20.

Compound interest is a type of interest where the interest earned on a principal amount is added to the principal, and the new total amount becomes the basis for calculating interest in the next period.

In other words, the interest is earned not only on the principal amount but also on the accumulated interest.

The formula for compound interest is:

Here we have, Rahul's plans to invest $25,000 in a retirement account that compounds 6% monthly.

From the data,

The principal amount, P = 25000

Rate of interest, r = 6% = 6/100 = 0.06

Time period, t = 25 years  

Number of compounds, n = 12  [ Since compounded annually ]

By using the formula, A = P (1 + r/n)^(n×t)  

A = 25000 [ 1 + 0.6/12]⁽¹²ˣ²⁵⁾

A = 25000 [ 1 + 0.005]⁽³⁰⁰⁾

A = 25000 [1.005]⁽³⁰⁰⁾  

A = 108,006.20 (rounded to the nearest cent)  

Therefore,

The total amount that Rahul will have is 108,006.20.

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The mistake is in the second step, the negative signs shouldn't be on the diagonal elements.

Here we can see that someone is trying to find an inverse matrix.

To get it, we need to change the order of the elements in the diagonal (thing that has ben done) and change the signs of the elements that are not in the diagonal (in the image we can see that this person changed the signs on the diagonal).

So there is the mistake, the negative signs should be in the 3 and the 5 in the second step.

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Answer:

Step-by-step explanation:

midpoint of AC

[tex]x=\frac{1-1}{2} =0\\y=\frac{4-4}{2} =0\\mid ~point~of~AC=(0,0)[/tex]

midpoint of BD

[tex]x=\frac{4-4}{2} =0\\y=\frac{-1+1}{2} =0\\midpoint ~of~BD=(0,0)[/tex]

so diagonals bisect each other.

The area of a rhombus is 399 in².

What is the area of a rhombus?

A rhombus is a quadrilateral whose four sides all have the same length. Another term for this shape is an equilateral quadrilateral since all of its sides are equal in length.

Here, we have

Given: A rhombus with a base of 21 inches and a height of 19 inches.

We have to find the area of a rhombus.

As per the given rhombus,

Base = 21 inches

Height = 19 inches

The area of the rhombus = base ×  height

⇒ 21 × 19 = 399 in²

Hence, the area of a rhombus is 399 in².

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Answer:

to simplify the other dude, its 399 in2

Step-by-step explanation:

hope this helps your day :P

please give brainleziest

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Answer:

5 miles / Maria's time = 4 miles / Gus's time

Since both Maria and Gus run for equal periods of time, we can set their times equal to each other:

5 miles / t = 4 miles / t

where t is the time it takes both of them to run.

Simplifying this equation, we can see that the distance Maria runs (M) is equal to the distance Gus runs (G) multiplied by 5/4:

M = (5/4)G

Therefore, the correct equation that relates the variables defined is:

M = (5/4)G

This means that Maria's distance is 1.25 times Gus's distance. So, the correct answer is option B: M = 1.25G.

Answer:

Reflection in the x-axis

Step-by-step explanation:

f(x) = √x

Shift left 3 units:

f(x + 3) = √(x + 3)

Reflection in x-axis:

-f(x + 3) = -√(x + 3)

Vertical stretch:

-3.f(x + 3) = -3√(x + 3) = g(x)

g(1) = -3√((1) + 3)

g(1) = -6

The area of the circular flower bed is approximately 78.54 square feet.

The circular flower bed's 10 foot diameter corresponds to a radius of 5 feet, or half the diameter. The area and circumference of the circular flower bed can be determined using the following data:

Circumference:

The formula for calculating a circle's circumference is:

C = 2πr

where the mathematical constant is roughly equivalent to 3.14159 and r is the circle's radius.

Using the values we were provided as replacements, we obtain:

C = 2π(5) \sC = 10π

We may calculate a rough estimate of the circumference using a calculator:

C ≈ 31.42 feet

As a result, the flower bed's circumference is approximately 31.42 feet.

Area:

The area of a circle is determined using the following formula:

A = πr²

Using the values we were provided as replacements, we obtain:

A = π(5)² \sA = 25π

We can calculate the area's value using a calculator as follows:

A area of 78.54 square feet.

Thus, the circumference of the flower bed is about 78.54 square feet.

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The LCD we can use to simplify the equation is (2-r)(2+r) = 4 - r².

The lowest common denominator is defined as the set of fraction denominators with the lowest common multiple. The lowest positive integer with more than one denominator in the set is LCD.

1. We can use the formula:

distance = rate × time

For the upstream journey:

distance = 4 miles

rate = 2 - r (since Dara is paddling against the current)

time = 4/(2-r) hours

For the downstream journey:

distance = 4 miles

rate = 2 + r (since Dara is paddling with the current)

time = 4/(2+r) hours

We can fill in the table as follows:

                       Distance (mi)    Avg Speed (mph)    Time (h)

With Current:            4                     2+r                    (4)/(2+r)

Against Current:       4                    2-r                       (4)/(2-r)

2. We know that the total time for the round trip is 6 hours:

4/(2-r) + 4/(2+r) = 6

3. Multiplying both sides by the LCD (2-r)(2+r), we get:

4(2+r) + 4(2-r) = 6(2-r)(2+r)

Simplifying, we get:

8 = 12 - 2r²

Rearranging, we get:

r² = 2

Taking the square root of both sides, we get:

r = ±√2

Since the current is flowing in one direction, we take the positive square root:

r = √2 ≈ 1.41 miles per hour

The LCD we can use to simplify the equation is (2-r)(2+r) = 4 - r².

4. To the nearest hundredth, the rate of the current is approximately 1.41 miles per hour, which is option B: About 1.15 miles per hour (rounded to two decimal places).

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The equation of a rational function that has been translated left 2 units and shifted up 1 unit is: f(x) = (a(x - 2) + b + 1) / (c(x - 2) + d)

A relation is a function if it has only One y-value for each x-value.

A general form of a rational function is:

f(x) = (ax + b) / (cx + d)

To translate this function left 2 units, we need to replace x with x + 2. This gives us:

f(x + 2) = (a(x + 2) + b) / (c(x + 2) + d)

To shift this function up 1 unit, we need to add 1 to the numerator. This gives us:

f(x + 2) = (a(x + 2) + b + 1) / (c(x + 2) + d)

Therefore, the equation of a rational function that has been translated left 2 units and shifted up 1 unit is: f(x) = (a(x - 2) + b + 1) / (c(x - 2) + d)

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Therefore, 20 overs are bowled if 120 balls are bowled in cricket.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

If 6 balls are bowled in one over, then the number of overs can be determined by dividing the total number of balls by 6.

So, if 120 balls are bowled, the number of overs is:

Number of overs = 120 balls ÷ 6 balls/over

= 20 overs

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Answer:

Chef will have 15 pieces of butter.

Step-by-step explanation:

Chef has 3 blocks of butter,

weight of each block = 1 pound

she cuts each block into fifth pieces,

3 / 1/5 = 15 pieces

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1) If the sales of McDonald's for one year is $650,000 and increasing at 4% annually (exponential growth), their sales after 5 years will be $790,824.

2) If the population of a school is 800 students and is increasing at a rate of 2% per year (exponential growth), after 6 years, the population will be 901.

3) With 70 northern sea otters growing at a rate of 18% annually (exponential growth), after 4 years, the population will be 136.

4) If the annual sales for a furniture stores are $375,000 and increasing (exponential growth) at a rate of 6.75% each year, the sales after 9 years will be $675,060.

5) If the population of Indiana showed an annual growth rate of 0.6% (exponential growth) and their population in 1999 was 273,000, the population in 2007 will be 286,383.

Exponential growth refers to the consistent increase in quantity over time and at a constant growth rate.

Exponential growths are modeled using the exponential growth function y = a(1+r)^t.

1. McDonalds:

y= a(1+r)^t

Where a = $650,000

r = 0.04 (4%)

t = 5 years

Sales after 5 years, y= a(1+r)^t

= $650,000 (1.04)^5

= $650,000 × 1.2166529

= $790,824

2) School Population:

Current population = 800

Annual increasing rate = 2%

a = 800

r = 2%

t = 6 years

Population after 6 years, y= a(1+r)^t

= 800(1.02)^6

=901

3) Northern Sea Otters:

a = 70

r = 18% or 0.18

t = 4 years

Population after 6 years, y= a(1+r)^t

= 70(1.18)^4

= 136

4) Furniture Stores:

a = $375,000

r = 6.75% or 0.0675

t = 9 years

Sales after 9 years, y = a(1+r)^t

= 375,000(1.0675)^9

= $675,060

5) Indiana Population:

a = 273,000

r = 0.6% or 0.006

t = 8 years (2007 - 1999)

Population after 8 years, y = a(1+r)^t

= 273,000(1.006)^8

= 286,383

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Answer: To find the distance between two points on a grid, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, the coordinates of the middle school are (-5, 3), and the coordinates of the library are (2, 3). So we have:

distance = sqrt((2 - (-5))^2 + (3 - 3)^2)

distance = sqrt((2 + 5)^2 + 0^2)

distance = sqrt(7^2)

distance = 7

Therefore, the library is 7 miles away from the middle school.

Step-by-step explanation:

The value of x for the given expression is x = 7 and x = 3.

A mathematical expression with the form ax² + bx + c, where a, b, and c are constants and x is a variable, is known as a quadratic expression. The graph of a quadratic expression can be represented by a U-shaped parabola. The y-intercept of the parabola is determined by the constant term c, whereas the coefficient a decides whether the parabola opens up or down.

The given expression is:

1.5x² - 15x + 31.5x = 0

The quadratic formula is given as:

x = -b ± √b² - 4ac / 2a

x = 15 ± √(15)² - 4(1.5)(31.5) / 2(1.5)

x = 15 ± 6 / 3

x = 15 + 6 / 3 and x = 15 - 6/3

x = 7 and x = 3

Hence, the value of x for the given expression is x = 7 and x = 3.

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The linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.

Temperature is a unit of hotness and coldness that can be described in terms of any number of arbitrary scales. It also represents the direction wherein heat energy will naturally flow, from either a hotter (i.e., higher temperature) body to a colder body.

Temperature is not the same as the energy of such a thermodynamic system; for instance, an iceberg has a significantly larger total heat energy than a match, despite the fact that a match is burning at a significantly higher temperature. The linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.

Therefore, the linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.

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The median value is 26.5, the first quartile is 24, the third quartile is 35.5, and the highest value is 38. The lowest value is thus 20.

We can plot the data on a number line to determine the data's least value, first quartile, median, third quartile, and greatest value:

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38\s| | | |

The leftmost number on the number line and the lowest value is 20.

We can split the data into four equal sections to determine the quartiles. The data's middle value is known as the median. We choose the average of the two middle values because there are an even number of data points. The midpoint is:

(26 + 27)/2 = 26.5 is the median.

We calculate the median of the lower half of the data to determine the first quartile:

(23 + 25)/2 = 24 for the first quartile.

We determine the median of the upper half of the data to determine the third quartile:

Third quartile: (34.5) ((34 + 37)/2)

The rightmost number on the number line, 38, has the highest value.

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The optimal strategy would be to fit several models to the data using equation mathematical software or tools, and then assess the goodness of fit using statistical metrics like R-squared or Mean Squared Error.

In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilised. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.

The following exponential model could be a good fit for the data in the image:

[tex]f(x) = 7.5 * e^(0.1x) (0.1x)[/tex]

The data is assumed to develop exponentially with a base of e in this model, with a growth rate of 10% for each unit increase in x.

It is crucial to remember that this is only one potential model and that other exponential models with other parameters could also be able to satisfactorily match the data. The optimal strategy would be to fit several models to the data using mathematical software or tools, and then assess the goodness of fit using statistical metrics like R-squared or Mean Squared Error.

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The domain and the range of h(n) are the set of whole numbers

Given that

h(n) is the number of houses

The possible values of n and h(n) are whole numbers

So, we have

Based on the patterns in the sequence, we have

h(n) = n

So, we have

h(5) = 5

h(11) = 11

In (b), we have

h(n) = n

Given that

s(n) is the number of segments

Based on the patterns in the sequence, we have

s(n) = 2n

So, we have

s(4) = 8

s(7) = 14

Above, we have

s(n) = 2n

The above equation is a proportional equation

This means that

The growth pattern of s(n) is linear, with a constant rate of change

Above, we have

s(n) = 2n

Hence, the explicit of s(n) is s(n) = 2n

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We can simplify this expression by multiplying the cube roots together:

³√5 × ³√5 × ³√5 = ³√(5 × 5 × 5)

Simplifying the product inside the cube root, we get:

³√(125)

Therefore, the cube root of 5 × 5 × 5 is equal to:

³√5׳√5׳√5 = ³√125 = 5

The loan's simple interest rate when the loan of $2,300 is taken will be 40.17%.

Let P be the principal, R be the rate of interest, and T be the time. Then the interest rate is given as,

The formula for interest is written as,

I = (PRT)/100

The value of the principal is $2,300 and the amount generated in six months is $2,762. Then the percentage rate is calculated as,

($2,762 - $2,300) = [$2,300 x r x (6/12)] / 100

46,200 = 1,150r

r = 40.17%

The loan's simple interest rate when the loan of $2,300 is taken will be 40.17%.

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The angle measure of minor arc QS is 92 degrees, and the angle measure of angle QQS is 46 degrees.

What is Angle?

In geometry, an angle is a figure formed by two rays that have a common endpoint, called the vertex of the angle. The rays that form the angle are called the sides of the angle. Angles are typically measured in degrees or radians and are used to describe the amount of rotation between two intersecting lines or planes.

In a circle, the measure of an inscribed angle is equal to half the measure of the intercepted arc. Since QS intercepts the minor arc QR, the measure of angle QRS is equal to half the measure of the minor arc QS.

Therefore, if m∠QRS = 46, then m(arc QS) = 2×m∠QRS = 2×46 = 92 degrees.

Since the measure of an arc is equal to the measure of the central angle that intercepts it, and the sum of the measures of the central angles in a circle is 360 degrees, we have:

m(arc QS) + m(arc QR) = 360 degrees

Substituting the value of m(arc QS) that we found above, we get:

92 degrees + m(arc QR) = 360 degrees

Solving for m(arc QR), we get:

m(arc QR) = 360 degrees - 92 degrees = 268 degrees

Since QS is a minor arc of the circle, the measure of angle QQS is equal to half the measure of the arc QS. Therefore, we have:

m∠QQS = 0.5×m(arc QS) = 0.5×92 = 46 degrees

Therefore, the angle measure of minor arc QS is 92 degrees, and the angle measure of angle QQS is 46 degrees.

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hi

im pretty sure the answer is:

y= -x+4