Put the function y=8x2+16x+20
in vertex form f(x)=a(x-h)2+k
and determine the values of a,h
and k

Answer:

To calculate how much Joe would earn for working a 35-hour week, you need to multiply his hourly wage by the number of hours he worked123. For example, if Joe is paid $19.26 per hour, then his weekly pay is:

$19.26 x 35 = $673.10

This is his gross pay, which means it does not include any deductions for taxes or other benefits. His net pay, or take-home pay, may be lower depending on his filing status, allowances, withholding information and voluntary deductions1. You can use an hourly paycheck calculator to estimate his net pay1.

I hope this helps you understand how to calculate hourly pay. If you have any other questions, please let me know.

Answer:  

Worth in 2019 is $12423.75

Explanation:

Current worth is C=$28000

Depreciation rate is D=15%

Time in years is T=19

Worth (W) 2019: W=C(1−D100)T=2800⋅(1−15100)19=$12423.75 [Ans]

Answer:

  decreasing 0.5 m/s

Step-by-step explanation:

You want the rate at which the height of a shadow on a wall is decreasing as a 2 m tall man walks at 1.3 m/s toward the wall. The shadow is cast by a light 12 m from the wall, and the man is 4 m from the wall at the time of interest.

In the attached diagram, triangles ABC and LMA are similar. This lets us write the proportion ...

  y/x = 2/(12 -x)

  y = 2x/(12 -x) . . . . . . multiply by x to get expression for y

Taking the derivative with respect to time gives ...

  y' = (2/(12 -x) +2x/(12-x)²)x'

At x = 4, this is ...

  y' = (2/8 +8/8²)x' = (3/8)x'

When x' = -1.3 m/s, the rate of change of the shadow height is ...

  y' = (3/8)(-1.3 m/s) = -0.4875 m/s

The length of the shadow is decreasing at about 0.5 m/s.

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The sum of magnitude of u + v is 15.99.

The  magnitude or size of a mathematical object is described as a property which determines whether the object is larger or smaller than other objects of the same kind.

Given that, magnitude of u =  5

Magnitude of v = 11

The angle between them i= 40°

we represent u and v in vector form,

u = 5 ( cos 40° i + sin 40° j ) = 3.83 i + 3.21 j

v = 11 ( cos 40° i + sin 40° j ) = 8.42 i + 7.07 j

The sum of two vectors is given by

u + v = 3.83 i + 3.21 j +  8.42 i + 7.07 j

u + v = 12.25 i + 10.28 j

Magnitude of u + v = √(12.25²+10.28²)

Magnitude of u + v

Magnitude of u + v   = √( 150.063 + 105.678)

Magnitude of u + v = 15.99

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complete question:

Given the magnitudes of vectors u and v and the angle θ between them, find sum of . Give the magnitude to the nearest tenth when necessary and give the direction by specifying the angle that the resultant makes with u to the nearest degree. ∣ u∣ = 5, ∣ v∣ = 11, θ = 40°

Answer:

3 coins each row

Step-by-step explanation:

if you put 3 coins in 4 rows it we'll be equivalent to 12

[tex]1/2 * 2 * 1 = 1[/tex] square unit.

Step-by-step explanation:

To find the maximum area of the triangle, we need to locate the vertex of the parabola. This occurs when x=1. The y-coordinate at x=1 is 1. We can then use this as the height of the triangle. The base of the triangle is the distance between x=0 and x=2, which is 2. Therefore, the maximum area of the triangle is 1/2 * 2 * 1 = 1 square unit.

We need 1.5 yards of 3000 psi air entrained concrete for the footings, dug with a 24'' bucket.

We need to determine the dimensions of the footings. Since the footings are 8 inches thick, we can convert this to feet by dividing by 12:

8 inches / 12 inches/foot = 0.67 feet

The dimensions of the footings will depend on the size of the building, but let's assume for this example that the footings are 2 feet wide and 30 feet long.

Volume = length x width x thickness

= 30 ft x 2 ft x 0.67 ft

= 40.2 cubic feet

Convert the volume to cubic yards.

Since there are 27 cubic feet in a cubic yard, we can divide the volume by 27:

40.2 cubic feet / 27 cubic feet/cubic yard = 1.49 cubic yards

Adding 10% as instructed, we get:

1.49 cubic yards + 0.149 cubic yards = 1.639 cubic yards

Therefore, we need 1.5 yards of 3000 psi air entrained concrete for the footings, dug with a 24'' bucket.

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For the month of April, the park is expected to get an average of 826 thousand people every day.

To predict the average daily attendance at the park for the month of April, we need to substitute x = 4 in the given polynomial and simplify:

-24x² +337x-138 = -24(4²) + 337(4) - 138

= -24(16) + 1348 - 138

= -384 + 1210

= 826

Therefore, the predicted average daily attendance at the park for the month of April is 826 thousand visitors per day.

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The future value of the investment is equals to $[tex]32,582.78[/tex].

The number of monthly payments over 4 years is:

= 4 years x 12 months/year

= 48 months.

We will use future value of an annuity formulae to solve which is FV = PMT x [(1 + r)^n - 1] / r

Plugging in the values, we get:

FV = 650 * [(1 + 0.022/12)^48 - 1] / (0.022/12)

FV = 650 * (0.09190014604/0.00183333333)

FV = 650 * 50.1273524766

FV = 32582.7791098

FV = $32,582.78.

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Answer:

If Marco completely filled a box with 36 unit cubes with no gaps or overlap, then the box must have a volume of 36 cubic units.

The box could have different dimensions depending on how the cubes are arranged. For example, the box could be a cube with side length 3 units, since 3 x 3 x 3 = 27. Then, Marco could add another layer of 3 x 3 cubes on top of the first layer, giving a total of 3 x 3 x 4 = 36 cubes.

Alternatively, the box could have dimensions 6 x 1 x 6, since 6 x 1 x 6 = 36. This box would have two layers of 6 x 6 cubes stacked on top of each other.

There are many other possible dimensions for the box, but all of them must have a volume of 36 cubic units to accommodate the 36 unit cubes with no gaps or overlap.

Answer:

So the bearing from C to A is approximately 87° to the nearest degree.

Step-by-step explanation:

(a) To find the distance from C to A, we can use the cosine rule. Let's call the distance from A to B "d1" and the distance from B to C "d2". Then:

d1² = (600 km/h * 1 hour)² = 360,000 km²

d2² = (400 km/h * 1 hour)² = 160,000 km²

Now, let's find the angle between d1 and d2. We know that the angle between the two bearings is 130° - 35° = 95°. We also know that the angle between d1 and d2 is 180° - 95° = 85° (because the three angles in a triangle add up to 180°).

Using the cosine rule:

d² = d1² + d2² - 2d1d2cos(85°)

d² = 360,000 + 160,000 - 2(600)(400)cos(85°)

d ≈ 1,013 km

So the distance from C to A is approximately 1,013 km to the nearest kilometre.

(b) To find the bearings from C to A, we can use trigonometry. Let's call the bearing from C to A "x". Then:

cos(x) = (d2/d)

cos(x) = 160,000/1,013,000

x ≈ 87°

So the bearing from C to A is approximately 87° to the nearest degree.

A cat weighing 10 4/5 pounds on earth will weigh 1 1/2 pounds on the moon.

Given that, an object will weigh 1/6 of its weight on moon of earth,

So, a cat having a weight of 10 4/5 pound will weight =

10 4/5 × 1/6

= 54/6 × 1/6

= 54 / 36
= 9/6

= 3/2

= 1 1/2

Hence a cat weighing 10 4/5 pounds on earth will weigh 1 1/2 pounds on the moon.

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We can use the box plots to make inferences about plant heights at the two nurseries because; "The random samples are likely to be 4) representative of the population of plants at each nursery." (Option C)

A box plot, often known as a boxplot, is a method in descriptive statistics for graphically displaying the localization, spread, and skewness groups of numerical data through their quartiles.

The box plot is useful for examining the range and distribution of numerical data sets. The box plot is useful for organizing vast volumes of data and seeing outlier values.

Disadvantages: Because it deals with a summary of the data distribution, the box plot is ineffective for thorough data analysis.

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Answer:

Step-by-step explanation:

You want the solution to right triangle RST with RS = 15, R = 72°, T = 90°.

The mnemonic SOH CAH TOA reminds you ...

  Sin = Opposite/Hypotenuse   ⇒   r = 15·sin(72°) ≈ 14.3

  Cos = Adjacent/Hypotenuse   ⇒   s = 15·cos(72°) ≈ 4.6

The acute angles in a right triangle are complementary, so ...

  S = 90° -R = 90° -72° = 18°

smaller leg is the smaller side

longer leg is the longer side

hypotenuse is the longest side

triangle a example:
smaller leg: 8-5 = 3

longer leg: 2-(-8) = 10

hypotenuse: use the formula a^2 + b^2 = c^2 (not needed since the side lengths are already given)

Answer:

He made 7 black-and-white drawings and 2 color drawing

Step-by-step explanation:

10x+25y=120

x+y=9

Multiply bottom by ten,

10x+25y=120

10x+10y=90

--------------------

15y=30

y=2

Now find x

x+2=9

x=7

Answer:  7 black and white, 2 color

Step-by-step explanation:

Let b= black and white drawings 10 min

Let c= color 25 min

She make 9 total drawings

b+c=9

She takes 2 hrs  = 120 min

10b + 25c =120

Now you have 2 equations.  Solve the system of equations.  They want you to use elimination.  Take the 1st equation multiply both sides by -10 so when you add it to next it will eliminate b

-10(b+c=9)                 multiply -10 to both sides

-10b-10c=-90             add to other equation

-10b-10c=-90

10b+25c=120

        15c=30

c=2                  >substitute back into an original equation

b+c=9    c=2    >substitute

b+2=9              > subtract 2 from both sides

b=7

Out of Maria's total expenses, the proportion of expenses for her car would be 0. 57 .

To find the proportion, the formula would be :

= Maria total car expenses / Maria total expenses for the month

Maria total car expenses = $ 290. 02

Maria total expenses for the month =  $ 507. 59

The proportion of expenses for her car would be :

= 290. 02 / 507. 59 x 100 %

= 0. 57 x 100 %

= 57 %

In conclusion, Maria's car alone takes over 0. 57 or 57 % of her total expenses.

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Answer: 62 words/ 1 minute

Step-by-step explanation:

186 words/3 minutes is basically 186 divided by 3. So divide the numerator by the denominator.

Example: $35 for 5lbs of flour. 35/5 in the simplest form is 7/1; therefore it is the unit rate.

Answer:

Each package will contain 1/2 pound of meat.

Step-by-step explanation:

To divide 8 1/2 pounds of hamburger meat into 17 equal packages using fractions, you need to divide the total weight by the number of packages:

First, convert the mixed number 8 1/2 to an improper fraction:

(8 * 2) + 1 = 16 + 1 = 17

So, 8 1/2 = 17/2

Now, divide 17/2 pounds by 17 packages. Since division is the same as multiplying by the reciprocal, we'll multiply by the reciprocal of 17, which is 1/17:

(17/2) * (1/17)

Multiply the numerators together (17 * 1 = 17) and the denominators together (2 * 17 = 34):

17/34

Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (17):

17 ÷ 17 = 1

34 ÷ 17 = 2

So, the simplified fraction is 1/2.

Answer:

24%

Step-by-step explanation:

The diameter of the circle, given the radius of 8 m, can be found to be 16 m.

One can discover the diameter of a circle, based on its radius, by multiplying the radius value with 2 since the length of the diameter is twice that of the former.

Comparatively, another segment of equal distance measured between the central position of the same given circle to only one point found within the border outline is called the radius. Henceforth, simply duplicating the established radius equivalent will provide conclusive knowledge of its corresponding diameter measure.

The diameter is therefore :

= 8 x 2

= 16 meters

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The value of probability of getting a bowl of chicken soup is,

⇒ 52.1%

Given that;

Two way frequency table is shown.

Hence, We get;

The value of probability of getting a bowl of chicken soup is,

⇒ 642/1233

⇒ 0.5206 x 100%

⇒ 52.1 %

Thus, The value of probability of getting a bowl of chicken soup is,

⇒ 52.1%

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Answer:

13/38

Step-by-step explanation:

To find the odds in favor of selecting a comedy, we divide the number of comedies by the total number of plays. In this case, there are 13 comedies out of a total of 38 plays  Therefore, the odds in favor of selecting a comedy are 13/38. I hope that helps!

The first three terms of the given sequence is 7, 21 and 63. Therefore, option D is the correct answer.

Given that, the sequence can be generated using aₙ=3aₙ₋₁ and a₁=7.

Here, n is a whole number greater than 1.

So, a₂=3a₂₋₁

a₂=3a₁

a₂=3×7

a₂=21

a₃=3a₂

a₃=3×21

a₃=63

So, the first three terms are 7, 21, 63

Therefore, option D is the correct answer.

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We can use the recursive formula to find the values of the sequence:

g3 = 3·g2 + g1 = 3·5 + 3 = 18

g4 = 4·g3 + g2 = 4·18 + 5 = 77

g5 = 5·g4 + g3 = 5·77 + 18 = 395

g6 = 6·g5 + g4 = 6·395 + 77 = 2457

g7 = 7·g6 + g5 = 7·2457 + 395 = 17276

Therefore, the 7th term of the sequence is g7 = 17276.

The solution is:

Break-even point in units= 1,000 units

Here, we have,

Explanation:

Giving the following information:

The variable cost of a new computer keyboard is $25 per unit, and the fixed costs to produce the keyboard are $20,000 per year. If the selling price of the keyboard is $45.

To calculate the break-even point in units, we need to use the following formula:

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 20,000 / (45 - 25)

Break-even point in units= 1,000 units

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complete question:

The variable cost of a new computer keyboard is $25 per unit, and the fixed costs to produce the keyboard are $20,000 per year. If the selling price of the keyboard is $45, how many units must the company sell to break?

The y-intercept represents the base price of $200 for airfare from NYC.

The slope represent a cost of $0.30 cents per mile traveled.

According to the equation given, someone who traveled 2000 miles from NYC would pay $800 for their fare.

According to the equation given, someone who paid $500 for airfare from NYC would have traveled 1000 miles.

If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be y = 50 + 0.30x.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided about this trip, a linear equation that models the situation is given by;

y = mx + c

y = 0.30x + 200

When x = 2000, the price of airfare (y) is given by;

y = 0.30(2000) + 200 = $800.

When y = 500, the distance traveled (x) is given by;

500 = 0.30x + 200

300 = 0.30x

x = 1000 miles.

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A)  The equation of the line of the best fit is y = -1.5x + 3024.3

B)  The number of turtles to be hatched in 2011 = 8

Let us assume that x represents the years since 2003 and y represents the  number of turtles hatched each year.

From the table of data values we draw a scatter plot.

The scatter plot for the data of  the number of turtles hatched each year since 2003 is shown below.

From the scatter plot, the equation of the line of the best fit is:

y = -1.5x + 3024.3

Now we need to find the number of turtles to be hatched in 2011.

i.e., we find the value of y for x = 2011

y = -1.5x + 3024.3

y = -1.5(2011) + 3024.3

y = 7.8

y ≈ 8

Thus, the number of turtles to be hatched in 2011 = 8

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The ordered pair that shows an equivalent ratio of hours to miles is (1, 12) and Jing will complete a 60-mile trip in approximately 5 hours.

To find an equivalent ratio of hours to miles, we need to divide the number of miles by the number of hours.

For example, for the first 4 hours of the bike trip, Jing rode 48 miles, which is equivalent to a rate of 12/4 = 3 miles per hour.

Since Jing rode 60 miles in the first 4 hours of the trip, we can use this rate to find the time it takes her to ride 60 miles.

We can set up a proportion:

12 miles / 1 hours = 60 miles / x hours

Cross-multiplying, we get:

12x = 60

Dividing by 12, we get:

x = 60/12

x = 5

Therefore, Jing will complete a 60-mile trip in approximately 5 hours.

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The missing figure is attached below.