Kendrick is trying to determine if a painting he wants to buy will fit in the space on his wall. If the rectangular frame's diagonal is 76. 84 inches and forms a 51. 34° angle with the bottom of the frame, what is its height? Round your answer to the nearest inch. 96 inches 60 inches 50 inches 48 inches.

The employee's gross pay is $816.08.

None of the answer choices provided matches the result obtained.

To determine the employee's gross pay, we have to use the information given. We'll multiply the employee's regular hourly rate by the hours worked in a week, then add any overtime earnings. Here's the given information:

- Regular hourly rate: $12.75
- Overtime hourly rate: $19.13
- Hours worked in a week: 56

First, we'll calculate the employee's earnings for regular time:

$12.75/hour × 40 regular hours worked = $510.00

Next, we'll calculate the employee's earnings for overtime:

$19.13/hour × 16 overtime hours worked = $306.08

Now we'll add the employee's earnings for regular time and overtime together to find the gross pay:

$510.00 (regular earnings) + $306.08 (overtime earnings) = $816.08

Therefore, the employee's gross pay is $816.08.

None of the answer choices provided matches the result obtained.

To know more about gross pay visit:

https://brainly.com/question/13793671

#SPJ11

9. The original price of the television is approximately $462.20. 10. Daniel will pay approximately $1,548.53 for the refrigerator including sales tax. 11. The tip amount is $15.48

9. To find the original price of the television, we can use the formula:

Original price = Sale price / (1 - Discount percentage)

Given:

Sale price = $379

Discount percentage = 18%

Plugging in the values:

Original price = $379 / (1 - 0.18)

Original price = $379 / 0.82

Original price ≈ $462.20

Therefore, the original price of the television is approximately $462.20.

10. To calculate the sales price Daniel will pay for the refrigerator after a 10% discount, we can use the formula:

Sales price = Original price - (Original price * Discount percentage)

Given:

Original price = $1,580

Discount percentage = 10%

Plugging in the values:

Sales price = $1,580 - ($1,580 * 0.10)

Sales price = $1,580 - $158

Sales price = $1,422

Daniel will pay $1,422 for the refrigerator after the 10% discount.

To calculate the total price including 8.875% sales tax, we can use the formula:

Total price = Sales price + (Sales price * Tax percentage)

Given:

Sales price = $1,422

Tax percentage = 8.875%

Plugging in the values:

Total price = $1,422 + ($1,422 * 0.08875)

Total price ≈ $1,548.53

Daniel will pay approximately $1,548.53 for the refrigerator including sales tax.

11. To determine which store has the better sales price for the car stereo, we need to compare the prices after the respective discounts.

Electronic Depot:

Sale price = $140

Discount percentage = 30%

Sales price after discount = $140 - ($140 * 0.30) = $140 - $42 = $98

The Beatbox:

Sale price = $135

Discount percentage = 25%

Sales price after discount = $135 - ($135 * 0.25) = $135 - $33.75 = $101.25

The better sales price is from Electronic Depot, as they offer the stereo for $98 compared to The Beatbox's price of $101.25.

12. To calculate the tip amount, we can multiply the bill amount by the tip percentage:

Tip amount = Bill amount * Tip percentage

Given:

Bill amount = $86.00

Tip percentage = 18%

Plugging in the values:

Tip amount = $86.00 * 0.18

Tip amount = $15.48

The tip amount is $15.48.

To know more about discounts, click here: brainly.com/question/13501493

#SPJ11

When Triangle ABC is dilated with a center of dilation at (0,0) and a scale factor of 2, the coordinates of point A' can be found by multiplying the original coordinates of point A by the scale factor.

In this case, if the coordinates of point A are (x, y), then the coordinates of A' would be (2x, 2y).

Dilation involves scaling an object by a factor while preserving its shape. When the center of dilation is at (0,0), the dilation occurs relative to the origin. By applying a scale factor of 2, the x-coordinate of point A is multiplied by 2, and the y-coordinate of point A is also multiplied by 2. This scaling operation results in the coordinates of A' being (2x, 2y).

To learn more about center of dilation: -brainly.com/question/29794240

#SPJ11

The lateral area of the given prism is  450 mm².

The lateral area of any prism is equal to the areas of the sides faces

The base of the prism is triangle

It has 3 side faces

The lengths of the side faces are 5 , 12 , 13 and their height is 15.

The lateral area = (5 × 15) + (12 × 15) + (13 × 15)

The lateral area= 75 + 180 + 195

The lateral area = 450 mm²

Hence, the lateral area of any prism is  450 mm².

To learn more on Three dimensional figure click:

https://brainly.com/question/2400003

#SPJ4

The speed of the kayak in component form is approximately 3.112 meters per second in the east-west direction and 7.368 meters per second in the north-south direction.

The speed of the kayak can be represented in component form, which consists of two perpendicular components: one in the east-west direction (x-component) and the other in the north-south direction (y-component).

Given that the kayak is traveling at a speed of 8 meters per second in the direction of S 67 degrees W, we can use trigonometry to determine the x-component and y-component of the speed.

The x-component represents the east-west direction and can be calculated using the cosine function. The y-component represents the north-south direction and can be calculated using the sine function.

To calculate the x-component:

x-component = speed * cosine(angle)

x-component = 8 * cosine(67 degrees)

x-component ≈ 8 * 0.389

x-component ≈ 3.112 meters per second (rounded to three decimal places)

To calculate the y-component:

y-component = speed * sine(angle)

y-component = 8 * sine(67 degrees)

y-component ≈ 8 * 0.921

y-component ≈ 7.368 meters per second (rounded to three decimal places)

Therefore, the speed of the kayak in component form is approximately 3.112 meters per second in the east-west direction and 7.368 meters per second in the north-south direction.

Learn more about speed here

https://brainly.com/question/26046491

#SPJ11

The length of DE is approximately 4.8 units, and the length of EF is approximately 5.6 units.

In similar triangles, corresponding sides are in proportion. We can set up the following ratios based on the given information:

AB/DE = BC/EF = AC/DF

Substituting the given values, we have:

6/DE = 7/EF = 8/(6.4)

Cross-multiplying, we get:

6EF = 7DE

8EF = 48

Simplifying the second equation, we find that EF = 6.

Substituting EF = 6 into the first equation, we can solve for DE:

6(6) = 7DE

36 = 7DE

DE ≈ 36/7 ≈ 4.8

Therefore, DE is approximately 4.8 units and EF is 6 units.

Learn more about Cross-multiplication here: brainly.com/question/27812904

#SPJ11

The change in Samuel's score is 50

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

Beginning = -14 points

Final = 36 points

Using the above as a guide, we have the following:

Change = Final - Beginning

Substitute the known values in the above equation, so, we have the following representation

Change = 36 + 14

Evaluate

Change = 50

Hence, the change is 50

Read more about expression at

https://brainly.com/question/15775046

#SPJ4

Question

Samuel is playing the Big-Time Builders video game. At the beginning of Samuel's turn, his score was – 14 points. After building a high-rise apartment building, his score rose to 36 points.

What was the change in Samuel's score?

To find the length of the hypotenuse (c) in a right triangle, you can use the Pythagorean theorem, The length of the hypotenuse (c) is √312.

In this case, you have the lengths of the two sides, b and a, where b = 5a and[tex]a^2[/tex] = 12.

Let's go through the steps to find the length of the hypotenuse (c):

Step 1: Square the value of a

[tex]a^2[/tex] = 12

Step 2: Substitute the value of b in terms of a

b = 5a

Step 3: Square the value of b

[tex]b^2 = (5a)^2 = 25a^2[/tex]

Step 4: Apply the Pythagorean theorem

According to the Pythagorean theorem, [tex]c^2 = a^2 + b^2[/tex]

Substituting the values:

[tex]c^2 = a^2 + b^2\\c^2 = 12 + 25a^2[/tex]

Step 5: Simplify the equation

[tex]c^2 = 12 + 25a^2[/tex]

Step 6: Substitute the value of [tex]a^2[/tex]from Step 1

[tex]c^2 = 12 + 25(12)[/tex]

Step 7: Simplify further  

[tex]c^2 = 12 + 300\\c^2 = 312[/tex]

Step 8: Take the square root of both sides to find c

[tex]\sqrt{c^2} = \sqrt{312}\\c = \sqrt{312}[/tex]

The length of the hypotenuse (c) is √312.

Learn more about hypotenuse here:

https://brainly.com/question/16893462

#SPJ11

Nishi invests £2500 at a 4% interest rate per year. After 2 years, her investment will grow to £2650. The amount will increase further to £2806 after 4 years, £3071 after 8 years, and £3123.84 after 9 years.

1. To calculate the amount Nishi will have after a certain number of years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial investment), r is the interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years.

2. In this case, Nishi invests £2500 at a 4% interest rate per year. Since the question doesn't specify the compounding frequency, we'll assume it's compounded annually (n = 1). Plugging in the values, we get:

After 2 years:

A = £2500(1 + 0.04/1)^(1*2)

A = £2500(1.04)^2

A ≈ £2650

After 4 years:

A = £2500(1 + 0.04/1)^(1*4)

A = £2500(1.04)^4

A ≈ £2806

After 8 years:

A = £2500(1 + 0.04/1)^(1*8)

A = £2500(1.04)^8

A ≈ £3071

After 9 years:

A = £2500(1 + 0.04/1)^(1*9)

A = £2500(1.04)^9

A ≈ £3123.84

3. Therefore, Nishi will have approximately £2650 after 2 years, £2806 after 4 years, £3071 after 8 years, and £3123.84 after 9 years, assuming an annual compounding frequency.

Learn more about compound interest here: brainly.com/question/14295570

#SPJ11

The solution of the equation x² - 18x = -117 is x = 9 and x = 13. Hence, the answer is x = 9, 13.

Given, x² - 18x = -117

We need to solve this equation.

Step 1: Move the constant term to the left-hand side of the equation.

x² - 18x + 117 = 0

Step 2: Factorize the quadratic equation

x² - 18x + 117x² - 13x - 9x + 117= 0

x(x - 13) - 9(x - 13) = 0

(x - 9)(x - 13) = 0

Step 3: Equate each factor to zero and solve for x.

x - 9 = 0 or x - 13 = 0

x = 9 or x = 13

The solution of the equation x² - 18x = -117 is x = 9 and x = 13. Hence, the answer is x = 9, 13.

To know more about factor visit:

https://brainly.com/question/14452738

#SPJ11

The measure of the length AB to the nearest tenth is: 21.8  

A right triangle is a triangle with one angle equal to 90 degrees.

The sides and angles of a right triangle can be found using trigonometric ratios.

So, let's find the length AB of the attached right triangle using trigonometry.

Along with that,

Tan ∅ = opposite/adjacent

Opposite side = AB

Adjacent side = 17 units

Along with that,

Tan 52° = AB / 17

multiplication cross

AB = 17 * tan 52

AB = 17 × 1.27994163219

AB = 21.7590077473

For this,

AB ≈ 21.8  

Read more about Trigonometric ratios at: https://brainly.com/question/13276558

#SPJ4

The steps used to solve the system of equations are as follows: Apply the Addition Property of Equality to eliminate the variable y. Solve for x using the Division Property of Equality. Substitute the value of x into one of the equations to find the value of y. Therefore, the solution to the system of equations is x = 1 and y = 1.

To solve the system of equations, we can follow these steps:

Step 1: Apply the Addition Property of Equality to eliminate the variable y.

By adding the two equations together, the y-terms will cancel out, resulting in:

(3x - 2y) + (2x + 2y) = 1 + 4

Simplifying the equation, we get:

5x = 5 (Addition Property of Equality)

Step 2: Solve for x using the Division Property of Equality.

Dividing both sides of the equation by 5, we find:

x = 1 (Division Property of Equality)

Step 3: Substitute the value of x into one of the equations to find the value of y.

Using the first equation, we substitute x with 1:

3(1) - 2y = 1

Simplifying the equation, we have:

3 - 2y = 1

Rearranging the equation, we get:

-2y = -2

Dividing both sides of the equation by -2, we find:

y = 1 (Division Property of Equality)

Therefore, the solution to the system of equations is x = 1 and y = 1.

Learn more about Addition Property of Equality here:

https://brainly.com/question/30148588

#SPJ11

the finance charge is $28.67 and the new balance is $240.41.To calculate the finance charge and new balance using the previous balance method, we need to consider the previous balance, annual interest rate, new purchases, and payments/credits.

Previous balance = $179.32
Annual rate = 16%
New purchases = $117.42
Payments/credits = $85.00

First, let's calculate the finance charge. The finance charge is the interest charged on the previous balance. We can calculate it by multiplying the previous balance by the annual interest rate:

Finance charge = Previous balance * Annual rate
             = $179.32 * 0.16
             = $28.67

Next, we can calculate the new balance by adding the finance charge, new purchases, and subtracting the payments/credits:

New balance = Previous balance + Finance charge + New purchases - Payments/credits
           = $179.32 + $28.67 + $117.42 - $85.00
           = $240.41

Therefore, the finance charge is $28.67 and the new balance is $240.41.

ti learn more about payment click here:brainly.com/question/32320091

#SPJ11

There were 671 liars living on the island initially out of 2013 people living on the island.

Let's assume the number of truthtellers is x and the number of liars is y.

According to the given information, each day one person says that when they leave the island, the number of truthtellers will be equal to the number of liars.

This implies that the person speaking must be a liar.

On the first day, if the person speaking is a liar, then the number of liars on the island will increase by one (y+1) and the number of truthtellers will remain the same (x).

The equation can be written as:

x = y + 1

On the second day, if the second person speaking is also a liar, the number of liars will increase by one again (y+2) and the number of truthtellers will remain the same (x).

The equation becomes:

x = y + 2

We can generalize this pattern for each day:

x = y + k

After 2013 days, there is no one left on the island, so x + y = 0.

Substituting this into the equation, we get:

(y + k) + y = 0

Simplifying, we find:

2y + k = 0

Since y represents the number of liars, we want to find a value of y that satisfies this equation.

To do that, we need to find a value of k such that 2013 + k is divisible by 2.

By observing that 2013 is odd, we can conclude that k must be an odd number.

The smallest odd number that satisfies this condition is k = 1.

Substituting k = 1 into the equation, we get:

2y + 1 = 0

Solving for y, we find:

y = -1/2

However, the number of liars cannot be negative, so we can disregard this solution.

Therefore, there were 671 liars living on the island initially.

Learn more about Equation here:

https://brainly.com/question/29018878

#SPJ11

The true statement is Statement 1: The width of the sidewalk is equal to one-third of its length.

The true statement can be found by examining the relationship between the length of the sidewalk (l) and its width, which is given as l ÷ 3.

Let's consider two possible statements:

Statement 1: The width of the sidewalk is equal to one-third of its length.

Statement 2: The width of the sidewalk is three times its length.

To determine which statement is true, we can substitute a numerical value for the length of the sidewalk (l) and compare the resulting width to the statement.

Let's assume the length of the sidewalk (l) is 9 units.

Statement 1: The width of the sidewalk is 9 ÷ 3 = 3 units.

Statement 2: The width of the sidewalk is 3 × 9 = 27 units.

Comparing the width obtained from the calculation (3 units) with Statement 1 (The width of the sidewalk is equal to one-third of its length), we find that they are equal.

It's important to note that this conclusion is based on the assumption that the relationship between the length and width provided in the question is accurate and consistent.

for more such questions on length

https://brainly.com/question/28322552

#SPJ8

The equation of the line is shown as y = ax + p, where a and p are actual numbers. The slope-intercept form of a line is given as y = mx + b, where m is the slope of the line and b is the y-intercept. The line slope-intercept form can be compared with the equation of the line given as y = ax + p.

We know that the equation of a line in slope-intercept form is given as y = mx + b. Here, we are given the equation of the line as y = ax + p, where a and p are real numbers. Thus, the following is true about a and p.The slope of the line in the slope-intercept form is m = a. Therefore, a is the slope of the given line. The y-intercept of the line in the slope-intercept form is b = p.

p is the y-intercept of the given line. Hence, we conclude that in the equation of the line, y = ax + p, where a and p are real numbers, a is the slope of the line and p is the y-intercept of the line.

To know more about intercept visit:

https://brainly.com/question/14180189

#SPJ11

The normal force exerted by the table on the brick is approximately

73.7 Newtons.

The weight of the brick can be calculated using the formula:

Weight = mass x acceleration due to gravity

Weight = 7.52 kg x 9.8 m/s²

since the brick is in equilibrium, the normal force exerted by the table on the brick is equal in magnitude but opposite in direction to the weight of the brick.

Therefore, the normal force exerted by the table on the brick is:

Normal force = Weight of the brick

Normal force = 7.52 kg x 9.8 m/s²

Simplifying the calculation:

Normal force ≈ 73.696 N

Learn more about normal force  at

https://brainly.com/question/2254109

#SPJ1

she used 4/27 cups of cereal to make the snack mix.

Let's say the amount of cereal Nancy used was "x".

Since she used twice as many peanuts as she did cereal, the number of peanuts she used would be "2x".

Total, she used 6 3/4 cups of peanuts and cereal to make the snack mix.

Thus, we can write an equation as follows:6 3/4 = 2x + x

Convert mixed number 6 3/4 to an improper fraction:6 3/4 = (27/4)

Now we can solve the equation: (27/4) = 3x

(combining like terms)

Multiplying both sides by 4/27 gives us:1 = (4/27) * 3x

Now we can solve for "x":x = 4/27Since "x" represents the amount of cereal Nancy used,

To know more about arithmetic:

https://brainly.com/question/16415816

#SPJ11

The total amount earned in the first 2 years of the contract is k488,400

Given that the salary is k20,000 monthly and there is an increment of k350 per month.

To find out the total amount in the first two years of contact, we need to calculate the salary for 24 months and then add the increments earned during those 24 months.

Salary for 24 months = k20,000 × 24= k480,000

Increment for 24 months = k350 × 24= k8,400

Therefore, the total amount earned in the first 2 years of the contract will be the sum of the salary for 24 months and the total increment earned during the same period= k480,000 + k8,400= k488,400

Thus, the total amount earned in the first 2 years of the contract is k488,400.

To know more about amount, visit:

httpshttps://brainly.in/question/49377126

The total amount you will have in the first 2 years of your contract is k14,000,000.

If your salary is k20,000 monthly and there is an increment of k350 per month, the total amount you will have in the first two years of your contact can be found using simple interest formula:
I = prt
where I is the interest, p is the principal amount, r is the rate of interest and t is the time in years.Therefore, using the above formula, we have;
I = (20,000)(350)(2)
= 14,000,000

Therefore, the total amount you will have in the first 2 years of your contract is k14,000,000.

To know more about simple interest, visit:

https://brainly.com/question/30964674

#SPJ11

Marven and three of his friends rent a car with insurance for 5 days but lost their coupon. If each person spent $75, then which car did they rent The total amount of money they paid is $75 * 4 = $300.

We can further write the above equation as:250x + 300y + 350z + 400u = 300Based on the given condition, we know that Marven and three of his friends spent $75 each, so the total amount of money they paid is $300. Hence:250x + 300y + 350z + 400u = 300Now we can simplify the equation by dividing each term by 50:5x + 6y + 7z + 8u = 6We have to find the values of x, y, z, and u. The simplest way to solve the equation is by trial and error.

We can substitute values and check if they satisfy the equation. We need to consider the following conditions: The variables x, y, z, and u must be non-negative integers. The sum of x, y, z, and u must be 1.The only set of values that satisfies the above conditions is x = 1, y = 1, z = 0, and u = 0. This means that they rented a compact car and a mid-size car for 5 days each, respectively. Therefore, the car they rented is a compact car and a mid-size car.

To know more about equation visit:

https://brainly.com/question/29538993

#SPJ11

The time it takes for the rock to hit the ground can be determined using the equation h(t) = -4.9t^2 + 150, where h(t) represents the height of the rock in meters and t represents time in seconds. By setting h(t) to 0 and solving for t, we can find the time it takes for the rock to hit the ground.

Set the equation h(t) = -4.9t^2 + 150 to 0, since the rock hits the ground when the height is 0.

-4.9t^2 + 150 = 0

Solve the quadratic equation for t by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values for a, b, and c:

t = (-0 ± √(0^2 - 4(-4.9)(150))) / (2(-4.9))

Simplify and calculate the value of t:

t = (√(2940)) / (-9.8) ≈ ±7.23

learn more about:-  quadratic equation here

https://brainly.com/question/30098550

#SPJ11

The ratio of Sam’s shells and Thandeka’s shells, in simplest form is 2:3. To simplify the ratio of Sam’s shells and Thandeka’s shells, we need to divide both numbers by their greatest common factor, GCF.

In this case, we have:Sam’s shells = 8Thandeka’s shells = 12Factors of 8: 1, 2, 4, 8Factors of 12: 1, 2, 3, 4, 6, 12The common factors of 8 and 12 are 1, 2, and 4.

However, we need to find the greatest common factor of 8 and 12 to simplify the ratio. Therefore, the greatest common factor of 8 and 12 is 4.

Hence, dividing both numbers by 4 gives us:

Sam’s shells ÷ GCF = 8 ÷ 4 = 2

Thandeka’s shells ÷ GCF = 12 ÷ 4 = 3

Therefore, the ratio of Sam’s shells and Thandeka’s shells, in simplest form is 2:3.Another way to solve the problem is by finding the ratio between the two numbers.

Thus:Ratio = Sam’s shells :

Thandeka’s shellsRatio = 8 : 12

To simplify the ratio, divide both numbers by the greatest common factor of 8 and 12 which is 4.

Ratio = (8 ÷ 4) : (12 ÷ 4)Ratio = 2 : 3

Therefore, the ratio of Sam’s shells and Thandeka’s shells, in simplest form is 2:3.

To know more about greatest common factor visit:

https://brainly.com/question/29584814

#SPJ11

To find the force, F, needed to move a piano given the amount of work applied, W, and distance moved, d, we can use the equation W = Fd.

Rearranging the equation, we can solve for F by dividing both sides of the equation by d.

The equation W = Fd represents the relationship between work (W), force (F), and distance (d).

In this case, we are given the values of W and d and need to find F.

To isolate F, we can rearrange the equation as F = W/d.

By dividing the work (W) by the distance (d), we obtain the force (F) required to move the piano. The unit of force is typically measured in newtons (N), work in joules (J), and distance in meters (m).

It's important to note that this equation assumes a linear motion, where the force applied remains constant throughout the displacement of the piano. In practical situations, however, additional factors such as friction and the piano's weight distribution may affect the force required to move it.

Learn more about equations:

https://brainly.com/question/32634451

#SPJ11

To simplify the given expression, we can first simplify the height and width separately.

The height is 4w^3 - 4w. This expression does not have any common factors, so it cannot be simplified further.

The width is 5w^2 - 3w - 4. This expression can be factored as (5w + 1)(w - 4).

Now we can substitute these simplified expressions into the formula for the area of a rectangle, which is A = length × width. The length in this case is the height.

Area = (4w^3 - 4w) × (5w^2 - 3w - 4)

To multiply these expressions, we can use the distributive property:

Area = 4w^3(5w^2 - 3w - 4) - 4w(5w^2 - 3w - 4)

Expanding the multiplication:

Area = 20w^5 - 12w^4 - 16w^3 - 20w^3 + 12w^2 + 16w

Combining like terms:

Area = 20w^5 - 12w^4 - 36w^3 + 12w^2 + 16w

Therefore, the simplified expression for the area of the rectangle is 20w^5 - 12w^4 - 36w^3 + 12w^2 + 16w.

Learn more about height here

https://brainly.com/question/28122539

#SPJ11

An area of 18 x 30 = 540 square meters, which is half the area of his backyard.

Steve is turning half of his backyard into a chicken pen. Given that his backyard is a 24 meters by 45 meters rectangle, the area of the whole backyard is

24 x 45 = 1080 square meters.

If half of the backyard is to be turned into a chicken pen, then the area of the chicken pen will be

1080/2 = 540 square meters.

Since the area of a rectangle is calculated by multiplying its length by its width, the dimensions of the chicken pen will depend on the desired shape of the pen.

Steve can decide to make the chicken pen a square or a rectangle or any other shape.

However, if he decides to make the pen a rectangle, he will have to make sure that the length and width are such that their product is equal to 540 square meters.

For example, he can make the chicken pen a rectangle with a length of 18 meters and a width of 30 meters.

This will give an area of 18 x 30 = 540 square meters, which is half the area of his backyard.

To know more about area visit:

https://brainly.com/question/30307509

#SPJ11

The equation of the given parabolic function in vertex form is: y = (x - 4)² - 4. This is because a=1.

The parabolic function going down from the left through the point zero comma twelve and through the point two comma zero and turning at the point four comma negative four and going up through the point six comma zero and continuing towards infinity can be represented by the following equation in vertex form: y = a(x - h)² + k where (h, k) is the vertex of the parabolic function.

From the graph, we can see that the vertex is (4, -4). So, the equation can be written as: y = a(x - 4)² - 4 Now, we need to find the value of a. The parabolic function passes through the point (0, 12). Substituting this point in the equation, we get:12 = a(0 - 4)² - 4 Simplifying, we get: 16a = 16a = 1 So, the equation of the given parabolic function in vertex form is: y = (x - 4)² - 4. This is because a=1.

To know more about parabolic function visit:-

https://brainly.com/question/17257957

#SPJ11

Given that 1/5 of 100 oranges is given to Olu and 1/4 of the remaining oranges is given to Ade. We have to find what fraction of the oranges are left.

We have 100 oranges.1/5 of 100 oranges is given to Olu= 1/5 × 100= 20 orangesLet's find out how many oranges are remaining after giving 1/5 of 100 oranges to Olu.Therefore, the number of oranges left is = 100 - 20 = 80Now, 1/4 of the remaining oranges is given to Ade= 1/4 × 80= 20 oranges

Now, we have given a total of 20+20= 40 oranges.Hence, the fraction of oranges left is: 60/100 or 3/5.Here, the final answer is "The fraction of oranges left is 3/5.

To know more about fraction visit:

https://brainly.com/question/18134643

#SPJ11

Gab paid $855 in interest for the printer repair. Sir gab borrowed 3,600 to finance his printer repair at a rate of 6.25%for 4.75 years.

To calculate the interest Gab paid, we can use the formula for simple interest: Interest = Principal * Rate * Time. In this case, the principal is $3,600, the rate is 6.25% (or 0.0625 as a decimal), and the time is 4.75 years.

Using the formula, we can calculate the interest as follows:

Interest = $3,600 * 0.0625 * 4.75 = $855.

Therefore, Gab paid $855 in interest for the printer repair.

Learn more about interest here

https://brainly.com/question/25720319

#SPJ11

The given system of equations can be solved using the elimination method. The possible solutions to the system are: the only solution is (-32, 4), the only solution is (0, 2), there are an infinite number of solutions, or there is no solution.

To solve the system using the elimination method, we can multiply the first equation by 2 and the second equation by 3 to eliminate the variable x. This gives us the following system:

8x + 6y = 124

6x + 6y = 15

Subtracting the second equation from the first equation, we get:

2x = 109

Dividing both sides by 2, we find:

x = 54.5

Substituting this value of x into either of the original equations, we can solve for y. However, when we substitute x = 54.5 into the second equation, we get a contradiction. The equation becomes:

2(54.5) + 2y = 5

109 + 2y = 5

2y = -104

y = -52

Therefore, the system has no solution. The only solution option that matches this result is "There is no solution."

To learn more about elimination method, click here:

brainly.com/question/13877817

#SPJ11