Which is the vertex form of the equation for the quadratic function y = 2x2 - 20x +47?

Answer:

Area = 346.2yd²

Perimeter = 72.1yd

Step-by-step explanation:

AREA

Split it into three shapes: (1) the semi-circle, (2) the triangle, and (3) the rectangle. Find the area of each and then add them together for the area of the whole shape.

Area₁ = πr² = (6²)π = 36π = 113.1 yd²

Area₂ = (1/2)bh = (1/2)(11.3)(14) = 79.1 yd²

Area₃ = lw = (11)(14) = 154 yd²

154 + 79.1 + 113.1=346.2yd²

PERIMETER

The perimeter consists of the length of the curve on the semi-circle, the top , the right side, the bottom, and the slanted line.

length of the curve on the semi-circle = half the cicumference of circle with radius 6 = (2π(6))/2 = 6π = 18.8

the top = 22.3

the right side = 14

the bottom = 11

the slanted line = the hypotenuse of triangle(2) - the diameter of circle(1) = (√(11.3²+14²))-12= (√(323.69))-12=18-12=6

18.8+22.3+14+11+6=72.1yd

Answer: 18(a)-89=217

Step-by-step explanation:

If a = 17 then you substitute/replace the a with the 17. Making 18(a) into 18(17). 18(17)= 306 - 89 = 217.

Hope this helped.

Answer:217

Step-by-step explanation:

putting the value of a in the equation.

18×17-89= 217

Answer: 9/14

Step-by-step explanation:

hope this helps!

The ratio between 'a' and 'b', when 'b' is not zero, is:

and you read this "a is to b"

In this case, we have that the ratio of adults to children is:

Answer:

\(40\%\)

Step-by-step explanation:

\( \frac{2}{5} \times 100 = 40\%\)

Divide 2 by 5 to get a decimal, then multiply the decimal by 100 to get a percent.

2/5 = 0.4

0.4x100 = 40

2/5 = 40%

Answer:

45%

trust me i took this test before

Step-by-step explanation:

Answer: 4y^2y-80+y^2/4y

Step-by-step explanation:

The probability of landing on the dark blue target is 2/5.

Probability is the ratio of required to the total possible outcomes of an event.

P(dark blue ) = 40/100

divide through by 20

P(dark blue ) = 2/5

Therefore, the probability of landing on target is 2/5

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The arc length of the curve on the given interval is 4√61.

The Parametric Equations are x = 6t + 5 and y = 7 - 5t.

Differentiate the equation x = 6t + 5 and y = 7 - 5t with respect to t.

dx/dt = 6, dy/dt = -5

The interval is -1 ≤ t ≤ 3.

To find the arc length of a curve, you need to first define the curve in terms of its equation. Then, you need to take the integral of the equation from the starting point to the ending point. The integral will calculate the length of the arc.

Arc length of the curve

L = \(\int \sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2} dt\)

L = \(\int_{-1}^3 \sqrt{(6)^2+(-5)^2} dt\)

L = \(\int_{-1}^3 \sqrt{36+25} dt\)

L = \(\int_{-1}^3 \sqrt{61} dt\)

L = √61 · \([t]_{-1}^3\)

L = √61 · [3 - (-1)]

L = √61 · [3 + 1]

L = 4√61

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The complete question is:

Find the arc length of the curve on the given interval. (round your answer to three decimal places.)

Parametric Equations  Interval

x = 6t + 5, y = 7 − 5t               −1 ≤ t ≤ 3

For the rectangle to have a perimeter of 36 units, the sum of the length and the width must equal 18 units

The given parameter is:

Perimeter = 36 units

The perimeter of a rectangle is:

Perimeter = 2 * (Length + Width)

So, we have;

36 = 2 * (Length + Width)

Divide both sides by 2

Length + Width = 18

This means that for the rectangle to have a perimeter of 36 units, the sum of the length and the width must equal 18 units

So, the possible table of values is:

Length  Width

  5           13

  8           10

  9           9

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Answer:

281.25 miles

Step-by-step explanation:

2=250

1=125

0.5=62.5

0.25=31.25

250+31.25=281.25

Answer:

Step-by-step explanation:

12.874752 kilometers

Answer:

≈ 12.872 km

Step-by-step explanation:

Step 1: Find the conversion

1 mile ≈ 1.609 km

Step 2: Multiply

8 mi(1.609 km/mi) = 12.872 km

The CHOOSE function that will determine a date in cell A1 occurs on a weekday or weekend can be written as: CHOOSE ( WEEKDAY (A1), "Weekend", "Weekday",  "Weekday",  "Weekday",  "Weekday"

An excel sheet is a Microsoft spreadsheet that contains cells that are used in the arrangement, ordering, and sorting of data into rows and columns.

The excel function performs statistical as well as Logic operations through a well-defined preset formula and instructions.

From the information given; we are to write a CHOOSE function that will determine whether a date in cell A1 occurs on weekdays or weekends.

Suppose we select a Date within the weekday function, it returns a number between 1 - 7, assuming that:

The CHOOSE function will therefore use this number to return the corresponding value in the list.

Therefore, the CHOOSE function that will determine a date in cell A1 occurs on a weekday or weekend can be written as: CHOOSE ( WEEKDAY (A1), "Weekend", "Weekday",  "Weekday",  "Weekday",  "Weekday"

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Answer:

Given the information you provided, we can model cellular phone usage over time with an exponential growth model. An exponential growth model follows the equation:

`y = a * b^(x - h) + k`

where:

- `y` is the quantity you're interested in (cell phone usage),

- `a` is the initial quantity (34 million in 1995),

- `b` is the growth factor (1.22, representing 22% growth per year),

- `x` is the time (the year),

- `h` is the time at which the initial quantity `a` is given (1995), and

- `k` is the vertical shift of the graph (0 in this case, as we're assuming growth starts from the initial quantity).

So, our specific model becomes:

`y = 34 * 1.22^(x - 1995)`

To find the cellular usage in 2003, we plug 2003 in for x:

`y = 34 * 1.22^(2003 - 1995)`

Calculating this out will give us the cellular usage in 2003.

Let's calculate this:

`y = 34 * 1.22^(2003 - 1995)`

So,

`y = 34 * 1.22^8`

Calculating the above expression gives us:

`y ≈ 97.97` million.

So, the cellular phone usage in 2003, according to this model, is approximately 98 million.

\(-5x^2+3x = -3x^2 +3x -50\\\\\implies 5x^2-3x^2 +3x-3x -50 =0\\\\\implies 2x^2 -50 =0\\\\\implies x^2 -25 = 0\\\\\implies x^2 = 25\\\\\implies x = \pm5\\\\\text{Hence}~ x = 5~ \text{or}~ x = -5\)

Answer:

X = 5, —5

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

Angle C is 54 degrees

Step-by-step explanation:

Angle B is 67 degrees and Angle A is 59 degrees. You add those two together to get 126 and subtract that from 180 to get the measure of Angle C

The measure of angle C is 54°.

From the diagram given, triangle A'B'C is a reflection of triangle ABC, therefore, triangle A'B'C' is similar to triangle ABC.

angle A = angle A' = 59°

angle B = angle B' = 67°

angle C = angle C' = ?

angle C = 180 - (angle A + angle B) ---> Sum of angles in a triangle equals 180°.

angle C = \(180 - (59 + 67)\\\)

angle C = 54°

Therefore, the measure of angle C is 54°.

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Answer:

C and D are both correct

hope that helps

here are the answer choices if anyone needs it :)

4 ÷ n

14n

n4

4n

Answer:

4/15

Step-by-step explanation:

2/5 drive

1/3 bus

and rest walk

fraction of those who walk is 1-(2/5+1/3)

2/5+1/3=(6+5)/15=11/15

15/15-11/15=4/15

Answer:

the value of the expression is 22

Step-by-step explanation:

a2 + 12 + b

- input numbers..

(-2)2 + 12 + 14

-4 + 12 + 14

8 + 14

22

final answer 22

Answer:

18 (see picture for detailed explanation)

Step-by-step explanation:

Plato/Edmentum

n⁴ - 2n³ - 23n² + 24n + 144 is the standard form of given zeroes.

What is a linear equation in mathematics?

A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables.

                              A linear equation is an equation that raises a variable to the first power. ax+b = 0 is an example of a 1 variable. x is a variable and a and b are real numbers.  

Roots : -3(mult . 2), 4(mult.2)

the function is given as

     f(n) = (n + 3)² (n - 4)²

         = (n + 3) (n + 3 ) ( n - 4 ) ( n - 4)

        = (n² + 6n + 9) (n² - 8n + 16 )

        = n⁴ - 8n³ + 16n² + 6n³ - 48n² + 96n + 9n² - 72n + 1

collecting like term,

    f(n) = n⁴ - 2n³ - 23n² + 24n + 144

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After translate the sentence into equation, the equation is,

⇒ 8b - 9 = 7

Where, b is any number.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The algebraic expression is,

⇒ Nine less than the product of 8 and a number is 7.

Now, Let a number = b

So, We can formulate the mathematical expression as;

⇒ 8 × b - 9 = 7

⇒ 8b - 9 = 7

Thus, The equation is,

⇒ 8b - 9 = 7

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Answer:

B

Step-by-step explanation:

6x -8y = - 16y

6x = -8y

8y = 17x + 4

-8y = -17x - 4

6x = -17x - 4

23x = -4

x = -4/23

x² + 3 / (x-1)(x-3) is simplest form of the given expression

Given: x-3/x-1 + 6/x-3

First, find the LCM of x-1 and x-3. The LCM is c

(x-3)(x-3) + 6(x-1) / (x-1)(x-3)            

Remove the bracket of the numerator

x² - 6x + 9 + 6x - 6 / (x-1)(x-3)        

Add and subtract like terms

x² + 3 / (x-1)(x-3)

Therefore, the expression has the simplest form of x² + 3 / (x-1)(x-3). This shows the concept of expression.

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Answer:

he needs to collect at least 56 more

Step-by-step explanation:

c+64\(\geq\)120

c\(\geq\)120-64

c\(\geq\)56

Answer:56 more

Step-by-step explanation:

Answer: =279/10

Step-by-step explanation: look at the picture

This is the same as writing y = sqrt(4(x+5)) - 1

===============================================

Explanation:

The given graph appears to be a square root function.

The marked points on the curve are:

Reflect those points over the line y = x. This will have us swap the x and y coordinates.

Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.

----------

Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).

Plug the coordinates of each point into the template y = ax^2+bx+c.

For instance, plug in x = 1 and y = -4 to get...

y = ax^2+bx+c

-4 = a*1^2+b*1+c

-4 = a+b+c

Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c

Repeat for (5,4) and you should get 4 = 25a+5b+c

We have this system of equations

Use substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.

In other words

a = 1/4, b = 1/2, c = -19/4

We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4

----------

Next we complete the square

y = (1/4)x^2+(1/2)x-19/4

y = (1/4)( x^2+2x )-19/4

y = (1/4)( x^2+2x+0 )-19/4

y = (1/4)( x^2+2x+1-1 )-19/4

y = (1/4)( (x^2+2x+1)-1 )-19/4

y = (1/4)( (x+1)^2-1 )-19/4

y = (1/4)(x+1)^2- 1/4 - 19/4

y = (1/4)(x+1)^2 + (-1-19)/4

y = (1/4)(x+1)^2 - 20/4

y = (1/4)(x+1)^2 - 5

The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.

----------

The last batch of steps is to find the inverse.

Swap x and y. Then solve for y.

y = (1/4)(x+1)^2 - 5

x = (1/4)(y+1)^2 - 5

x+5 = (1/4)(y+1)^2

(1/4)(y+1)^2 = x+5

(y+1)^2 = 4(x+5)

y+1 = sqrt(4(x+5))

y = sqrt(4(x+5)) - 1

I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.

You can also use a tool like GeoGebra to verify the answer.

Answer:

c

Step-by-step explanation:

Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12