Explain what the construction does and list the steps to creating the construction. Be as detailed as possible :D

Answer:

y = 4x² - 43x + 178

Step-by-step explanation:

Given that data:

1 __ 137

2 __ 110

3 __ 93

4 __ 70

5 __ 65

6 __ 77

Usibg technology, the quadratic regression equation obtained is written in the form:

Ax² + Bx + C

A = 4.34 = 4 ( nearest whole number)

B = - 43.46 = - 43 (nearest whole number)

C = 178.3 = 178 ( nearest whole number)

Hence, the quadratic model is

y = 4x² - 43x + 178

By rounding the coefficients to the nearest whole number, the quadratic function that models the data is[tex]f(x) = 5x^2 - 42x + 174[/tex]

To find a quadratic function that models the data,  use a quadratic equation of the form:

[tex]f(x) = ax^2 + bx + c[/tex]

Let's use the given data points to form a system of equations and solve for the coefficients a, b, and c.

Using the first data point (month 1 with 137 births):

[tex]f(1) = a(1)^2 + b(1) + c = 137[/tex]

a + b + c = 137 (Equation 1)

Using the second data point (month 2 with 110 births):

[tex]f(2) = a(2)^2 + b(2) + c = 110[/tex]

4a + 2b + c = 110 (Equation 2)

Using the third data point (month 3 with 93 births):

[tex]f(3) = a(3)^2 + b(3) + c = 93[/tex]

This simplifies to:

9a + 3b + c = 93 (Equation 3)

Solve this system of equations will give us the values of a, b, and c.

Subtract Equation 1 from Equation 2

3a + b = -27 (Equation 4)

Subtract Equation 1 from Equation 3

8a + 2b = -44 (Equation 5)

Now  solve Equations 4 and 5 simultaneously.

Multiply Equation 4 by 2 and subtracting it from Equation 5:

8a + 2b - (6a + 2b) = -44 - (-54)

2a = 10

Divide both sides by 2:

a = 5

Now substitute the value of a back into Equation 4:

3(5) + b = -27

15 + b = -27

Subtract 15 from both sides:

b = -42

Finally, substitute the values of a and b into Equation 1

5 + (-42) + c = 137

-37 + c = 137

Add 37 to both sides:

c = 174

Therefore, the quadratic function that models the data is:

[tex]f(x) = 5x^2 - 42x + 174[/tex]

Rounding the coefficients to the nearest whole number, the quadratic function becomes:

[tex]f(x) = 5x^2 - 42x + 174[/tex]

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Answer:

76°,60°

Step-by-step explanation:

sum of angles of a triangle=180

x+64+x+80+44=180

2x+188=180

2x=180-188=-8

x=-8/2=-4

so angles are -4+60=60°

and -4+80=76°

Step-by-step explanation:

divide the divisor and dividend by 10

Answer:

the answer is rotation hope it helps ahhaha

Answer:

I think yes

Step-by-step explanation:

12/4=3

36/12=3

-6/-2=3

and so on

If “the notation arcsin x represents the inverse function to sine” is true when the sine function is to the interval [ -pi/2, pi/2 ].

The sine function is one of the three primary functions in trigonometry, the others being cosine, and tan functions.

The confusion is compounded by the fact that we use the notation sin⁻¹(x) interchangeably with arcsin(x), and we call it the inverse sine.

Here is a counterexample disproving your given statement:

Let x = π.

The value π is in the domain of sin(x).

arcsin[sin(π)] = arcsin(0) = 0

arcsin[sin(π)] ≠ π

Therefore arcsin(x) is not the inverse of sin(x).

If you restrict the sine function to the interval [ -pi/2, pi/2 ]. Otherwise, arcsin will not be a function.

Hence, If “the notation arcsin x represents the inverse function to sine” is true when the sine function is to the interval [ -pi/2, pi/2 ].

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Answer:

35 miles

Step-by-step explanation:

Total Miles driven at full tank = 230 miles

Miles drive at full tank from Austin to Dallas = 195 miles

How many miles will be left once he arrives in Dallas?

Number of miles remaining at full tank = Total Miles driven at full tank - Miles drive at full tank from Austin to Dallas

= 230 miles - 195 miles

= 35 miles

Answer:

i don't see anything so i cant help you sorry

Step-by-step explanation:

Answer:

5 3 3 2 2

Step-by-step explanation:

180

90 2

45 2 2

15 3 2 2

5 3 3 2 2

Answer:

180 = 5 × 3² × 2²

Step-by-step explanation:

Starting with 180, the prime factors are in bold

180 = 90 × 2

      = 45 × 2 × 2

      = 15 × 3 × 2 × 2

      = 5 × 3 × 3 × 2 × 2

Then

180 = 5 × 3 × 3 × 2 × 2 = 5 × 3² × 2²

The distance traveled depends on the amount of time Marlene rides her bike

The function f(t) = 16t represents the scenario

Answer:

options (2), (3) and (5)

Step-by-step explanation:

2.

the distance traveled depends upon the amount of time she rides her bike.

as she travels 16 miles in 1 hr. she'll ride 32 miles in 2 hrs. so all values of distance traveled by her depends upon the time she takes.

3.

yes the initial is 16 miles per hour as the output of 1hr will be 16 and that's what the initial value is 16 miles for one hour. or 16 miles per hour.

5.

f(t) = 16t represents the scenario

where f(t) will be the output of the function that is d, distance when the output is t that is time.

Answer:

12%

Step-by-step explanation:

well when you get 72/6 and to make it into a easier full number/ (not a fraction) you get 12 then you put the % behind it and now you have 12%

Step-by-step explanation:

149......hshdbhdhsbhsjsusvshhs

Answer:

one point 4 inchs

Step-by-step explanation: yessuh

Answer:

one and six hundred four thousandths

The solution for x is x = (y + 49)/7.

Given that an equation 7x - 49 = y, we need to determine the equation in for of x,

To solve for x in the equation 7x - 49 = y, we'll isolate x on one side of the equation.

Here's the step-by-step process:

Start with the given equation: 7x - 49 = y.

Add 49 to both sides of the equation to isolate the term with x:

7x = y + 49.

Divide both sides of the equation by 7 to solve for x:

(7x)/7 = (y + 49)/7.

Simplify:

x = (y + 49)/7.

Therefore, the solution for x is x = (y + 49)/7.

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Answer:

Vertex= (-5,-4)

Another point=(0, -129)

Step-by-step explanation:

The vertex is also the maximum, and the point is also the y-intercept.

Answer:

wait what???

Step-by-step explanation: Is that even a question?

Answer:

x-2

Step-by-step explanation:

Dividing 3x2 – 10x + 8 by 3x-4 we get x-2.

Step-by-step explanation:

hope it helps

Answer:

10 km/hr

Step-by-step explanation:

Average speed = Total distance travelled / Total time taken

Ardi:

Total distance travelled = 70 km

Total time taken = 35 minutes = 35/60 hour

Average speed = Total distance travelled / Total time taken

= 70 km ÷ 35/60 hr

= 70 × 60/35

= 4,200/35

= 120 km/hr

Lei:

Total distance travelled = 585 km Total time taken = 9:05 - 13:35 = 4 hours 30 minutes

= 4.5 hours

Average speed = Total distance travelled / Total time taken

= 585 km / 4.5 hours

= 130 km/hr

Difference, in km/h, between the average speed of their trains = Lei's train - Ardi's train

= 130 km/hr - 120 km/hr

= 10 km/hr

Answer:

20

Step-by-step explanation:

the perimeter of the square and the triangle are the same

4×(x + 10) = 3×4x

4x + 40 = 12x

40 = 8x

x = 5

=>

a triangle side is 4x = 4×5 = 20

Answer:

14 $1 coin

12 quarter coin

Step-by-step explanation:

Let :

x = $1 dollar coin

y = $0.25 (1 quarter) coin

x + y = 26 - - - (1)

1x + 0.25y = 17 - - - - (2)

From (1) :

x = 26 - y

Put x = 26 - y in (2)

1(26 - y) + 0.25y = 17

26 - y + 0.25y = 17

-y + 0.25y = 17 - 26

-0.75y = - 9

Divide both sides by - 0.75

-0.75y /- 0.75 = - 9 / - 0.75

y = 12

Put y = 12 in (1)

x = 26 - 12

x = 14

Answer:

Option c. 59°

Step-by-step explanation:

<W+<Y=180

121+<Y=180

<Y=180-121

<Y=59

Answered by GAUTHMATH

Answer:

you did not apply an expression

Step-by-step explanation:

Answer:

Office personnel refers to the office chief, sectional chiefs and assistants that carry out all the administrative as well as clerical functions jointly to archive the objectives of an organization.

[tex](f\circ g)(x)=f(g(x))=4(x^2-5)+1=4x^2-19[/tex]

[tex](f\circ g)(4)=4\cdot4^2-19=64-19=\boxed{45}[/tex]

Hope this helps.

Answer:

no it is not perpedicular

Step-by-step explanation:

I plugged the equation into a graphing calculator and the line does not appear to be perpendicular

Answer:

3y = 5x+4

3y=9x

yx=9/3

yx=3

Answer:

Step-by-step explanation:

True. The function appears to be f(x) = x/4.

Step-by-step explanation:

a)

g(3) = 9

b)

g(-1) = 1

c)

g(-x) = x²

d)

g(2y) = 4y²

e)

g(1 + h) = 1 + h² + 2h

using the identity (a +b)² = a² + b² + 2ab

Answer:

a) g(3) = 9

b) g(-1) = 1

c) g(-x) = x²

d) g(2y) = 4y²

e) g(1+h) = 1 + 2h + h²

Step-by-step explanation:

a) when x = 3 ,

   g(3) = 3² = 9

b) when x = -1 ,

   g(-1) = (-1)² = 1

c) when x = -x ,

   g( -x ) = (-x)² = x²

d) when x= 2y ,

   g( 2y ) = (2y)² = 4y²

e) when x = 1 + h ,

   g( 1 + h ) = ( 1 + h )² = 1 + 2h + h²