The graph of a quadratic function with vertex (4, 3)
Find the domain and the range.
Write the domain and range using interval notation.

The area of lengthwise pathway is 610 m²

The area of breadthwise pathway is 360 m²

The total area of the two pathways is 985 m²

Given,

The side of square field = 125 m

The width of the lengthwise path = 3 m

The width of the breadthwise path = 5 m

We have to find the area of the two pathways.

Here,

Area of path on length wise = (125 - 3) × 5 = 610 m².

Area of path on breadth wise = (125 - 5 ) × 3 = 360 m²

Area of rectangle at intersection of paths = 5 × 3 = 15 m².

Thus the Total area of two pathways = 610 + 360+15 = 985 m²

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The end points behavior of the function:

(a) If x goes to positive infinity then the function goes to positive infinity. If x goes to negative infinity then the function goes to negative infinity.

(b) The zeros of the function f(x) are -3, -1, -1, and 1.

(c) The y-intercept is at (0,-3).

What is the endpoint behaviors of a polynomial?

A polynomial function's final behaviour is how its graph behaves as x gets closer to positive or negative infinity. The graph's final behavior is determined by a polynomial function's degree and leading coefficient.

What are zeros of a polynomial?

The locations where a polynomial becomes zero overall are known as the zeros of the polynomial. The term "zero polynomial" refers to a polynomial with a value of zero (-1). The highest power of the variable x is referred to as a polynomial's degree. A linear polynomial is a polynomial with degree 1.

Given function is f(x) = (x+3)(x+1)^2(x-1).

If x = ∞, then f(x) = ∞. The one endpoint of the function will go positive infinity.

If x =- ∞, then f(x) = -∞. The one endpoint of the function will go negative infinity.

To find the zeros of the polynomial, equate f(x) with zero.

(x+3)(x+1)^2(x-1) = 0

Either, x + 3 =0 → x = -3

or, (x+1)^2 =0 → x = -1

or, x-1 = 0 → x = 1

The zeros of the function are -3, -1, and 1.

To find y-intercept, put x=0 in the given function:

f(0) = (0+3)(0+1)^2(0-1)

→ f(0) = -3

The y-intercept is at (0,-3).

The x-intercepts of the function are zeros of the function.

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Terry should mix 29 gallons of the 25%  acid solution and 11 gallons of the 80%  acid solution

Given: 40% acid and 80% acid solutions

Terry needs 40 gal of a 40% acid solution

Let x represent the amount of the 25%  acid solution required in gal

Thus, the amount of the 80% acid solution required will be (40-x) gal

The amount of acid in these solutions is 0.25x + 0.8(40-x)

Since Terry wants exactly 40% or 0.4 of 40 gallons i.e. 0.4×40 gallons

The amount  of acid in these solutions will be:

0.25x + 0.8(40-x) = 0.4×40      Solve for x

0.25x + 32-0.8x  = 16

0.8x-0.25x = 32-16

0.55x = 16

x = 16/0.55 = 29 gallons

40-x = 40 -29 = 11 gallons

Therefore, the amount of the 25%  acid solution required is 29 gallons

and the amount of the 80%  acid solution required is 11 gallons. So she should mix 29 gallons and 11 gallons respectively

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The value of velocity is [tex]v = 7.67\frac{m}{s}[/tex].

The coefficient of restitution is the ratio of the final to initial speed between two bodies after the collision. While a value of 1 indicates a perfectly elastic collision, a value of 0 indicates a perfectly inelastic collision.

The first option is

We can find the displacement by using the area under the graph, which is equal to the displacement. The area of the triangle can be found using the formula below.

[tex]Area = \frac{1}{2} . base . length[/tex]

[tex]Area = 0.5m.50m.50. = 1250 m^{3}[/tex]

The other option is

We use the conservation of energy. So, we equate the potential energy and the kinetic energy.

[tex]E_{pot} = E_{kin}\\ \\ m.g.h = \frac{1}{2}.m.v^{2}[/tex]

The mass is cancelled out in the above equation, and we re-arrange with respect to velocity.

[tex]v^{2} = 2.g.h\\ \\v = \sqrt{2.9.81\frac{m}{s^{2} }.3m } = 7.67\frac{m}{s}[/tex]

Hence the answer is the value of velocity is [tex]v = 7.67\frac{m}{s}[/tex].

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In the right-angled triangle ABC, CA is 4.2cm.

What is a right-angled triangle? How to identify it?

Any angle that is a right angle or has one of its interior angles equal to 90 degrees is considered to be in a right-angled triangle. This triangle is also known as the right triangle or the 90-degree triangle for this reason. Trigonometry heavily utilizes the right triangle. In this article, let's learn more about this triangle.

By applying Pythagoras' theorem, one can determine whether a triangle has a right angle. If the squares of the triangle's two shorter sides equal the square of the hypotenuse, a right angle is present.

Solution explained:

A/Q, we have

BC = 9.2cm and m∠A = 63°

Using the tangent ratio formula (ratio of a side that is not the hypotenuse to a side that is near to an angle), we get

[tex]tanA = \frac{BC}{CA}[/tex]

tan 63° = [tex]\frac{9.2}{CA}[/tex]

CA = [tex]\frac{9.2}{1.96}[/tex]     (tan 63° = 1.96)

CA = 4.687 ≅ 4.7cm

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71.849 feet of fencing are required.

Given:

In a rectangle two sides are 13 feet and 12 feet.

In right angled triangle sides are 15 feet and 13 feet.

Let x be the hypotenuse of the triangle.

From rectangle opposite sides are equal so the other two sides are equal to 12 feet and 13 feet.

According to pythagorean theorem:

[tex]15^{2} +13^{2} =x^{2}[/tex]

x = [tex]\sqrt{225+169}[/tex]

x = 19.849

The perimeter of the pool = 15 + 12 + 13 + 12 + 19.849

= 27 + 13 + 12 + 19.849

= 52+19.849

= 71.849 feet.

Therefore 71.849 feet of fencing are required.

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The vector having a magnitude √61 and direction 140.2° has been shown in the figure.

Given,

Let the vector v have an initial point at (4, 8) and a terminal point at

(-2, 3).

we are asked to  Plot the vector v .

Given that the initial point of the vector is (4,8) and the termination point of the vector is (-2,3).

So, the tail of the vector is at point (4,8) and the head of the vector is at (-2,3).

The vector , v, has been shown.

I v I = √(4-(-2))²+(8-3)²

= √(4+2)²+(8-3)²

= √(6)²+(5)²

= √36+25

= √61

The direction of a vector is the angle made by a vector with the positive direction of the x-axis.

θ =  180° tan⁻¹ I 3-8/-2-4I

θ = 180° tan⁻¹ (5/6)

θ = 180° - tan⁻¹(5/6)

θ = 180° - 39.80°

θ = 140.2°

Hence, the required vector having a magnitude √61  and direction  140.2° has been shown in the figure.

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The linear equation for the monthly charge C dollars , in terms of the number of miles driven(n) is C(n) = 35 + 0.10×n  .

In the question ,

it is given that ,

the fixed rent for a car is = $35 .

the per mile charge for the car is = $0.10 miles

let the number of miles driven is = n miles

the function C that represents the linear equation for the monthly charge C dollars , in terms of the number of miles driven(n) is given by

C(n) = fixed charge + (per mile charge)×(number of miles)

Substituting the values , we get

C(n) = 35 + 0.10×n

Therefore , The linear equation for the monthly charge C dollars , in terms of the number of miles driven(n) is C(n) = 35 + 0.10×n  .

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Answer:
id say, C=0.10=35

Step-by-step explanation:

not really sure, but I tried!

The graph that represents the equation y [tex]=[/tex] (-4/3)x - 2 is drawn below .

In the question ,

it is given that,

the equation of the line is  [tex]y=-\frac{4}{3}x-2[/tex] ,

we need to plot the graph of the given line ,

To sketch the graph we need minimum two points .

when we put x [tex]=[/tex] 3 in the equation , we get

y [tex]=[/tex] (-4/3)(3) - 2

y = -4 - 2

y = -6

the first point is (3,-6)  .

For second point put x [tex]=[/tex] 6 ,

we get

y = (-4/3)(6) - 2

y = -4*2 - 2

y = -8 - 2

y = -10

the second point is (6,-10) .

After plotting and joining the point  (3,-6) and (6,-10) ,

the graph is shown below .

Therefore , The graph that represents the equation y [tex]=[/tex] (-4/3)x - 2 is drawn below .

The given question is incomplete , the complete question is

Draw the graph which represents the equation y [tex]=[/tex] (-4/3)x - 2   ?

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Answer:

5 nickels and 4 dimes

Step-by-step explanation:

5 nickels = 25 (5 x 5)

4 dimes = 40 (4 x 10)

Answer: 20

Step-by-step explanation:

Answer:

the first one

Step-by-step explanation:

one because 13+7= 20 and 20 is a bigger than 5 so there for it i one

Answer:

Below

Step-by-step explanation:

If -5 is one of the roots then that means  (x+5) is one of the factors

divide (x+5) into x^3 + 3x^2 -12x -10

to get   x^2-2x-2   which you can easily  (using Quadratic Formula) find the roots       1 + sqrt 3   and        1 -sqrt 3

('roots'   and 'zeroes'   are the same thing)

Answer:

7,036,363,636,363,635,660,000

Step-by-step explanation:

this one hert my head

Step-by-step explanation:

One taco =$10.20/12=$0.85

The arrow first reach an altitude of 60 meters is 13 seconds.

A General Rule for Solving Equations

h (t) = -2.1t² +32t-0.03 ---(i)

The arrow first reach an altitude of 60 meters:

h(t) = 60 -- (ii)

Equate the (i) and (ii)

60 = -2.1t² +32t-0.03

2.1t² - 32t + 0.03 + 60 = 0

2.1t² - 32t + 600.3 + = 0

t = -13, 13

Hence, The arrow first reach an altitude of 60 meters is 13 seconds.

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The point only can be on the unit circle and on the second quadrant if:

x = -√55/8

We know that we have a point of the form:

P = (x, y)

And the value of y is:

y = 3/8

Then our point is:

P = (x, 3/8)

And it is on the unit circle, then the values of x and y are solutions of:

x^2 + y^2 = 1

x^2 + (3/8)^2 = 1

x^2 = 1 - (3/8)^2 = 1 - 9/64 =

x^2 =  64/64 - 9/64

x^2 = 55/64

x = ±√(55/64) = ±√55/8

And P is on the second quadrant, then we take the negative option:

x = -√55/8

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If She cuts the cucumber into 3/8 inch thick slices and adds them to a salad. The number of 3/8 inch thick slices that  Daisy have  21 1/3.

Given data:

Cucumber length = 3 inches

Second cucumber length = 5 inches

Cucumber slices = 3/8

Now let find the the number of thickness that daisy have

Thickness  = (3+5) ÷ 3/8

Thickness  = 8× 3/8

Thickness  = 64/3

Thickness  = 21 1/3

Therefore the thickness is 21 1/3.

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Answer:

linear

Step-by-step explanation:

Because if you graph it. It creates a line which makes it a linear

The equation of the table is y=2x+8 when the slope and intercept are 2 and 8.

Given that,

In the picture we can see the table.

We have to find the equation of the table.

We know the equation is in the form

y=mx+b

Here,

m is rise/run

Which is slope

b is intercept.

Take the point as (0,8) and (1,10)

Slope is m =(10-8)/(1-0)

m= 2/1

m=2

Then b is

8=2(0)+b

b=8

The equation will be y=2x+8

Therefore, The equation of the table is y=2x+8 when the slope and intercept are 2 and 8.

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It will take the boat going north 16.5hrs and the boat going south will take it 8.25hrs

Step-by-step explanation:

divide 66/4 for the north boat and 66/8 for the south boat

Answer:

39

Step-by-step explanation:

2*3^3+4*3+9

= 39

Mark me as brainliest

Answer:

Step-by-step explanation: √240 = 15.49….    √50 = 7.07…

15.5 x 7.07 = 109.58 rounded to 110. Therefore the area is 110 feet so at least 2 can is needed to fill up the wall. But if the problem is being precise it’s 1 can and 5/6 of a can.

2 cans of paint will be needed to cover 110 square feet area.

The area of Rectangle is length times of width.

Given,

A rectangular wall is √240 ft by √50 ft.

Need to paint the wall twice to cover the area with two coats of paint.

Area of wall=Length×Width

=√240×√50

=√12000

=109.5=110

Given that each can of paint can cover 60 square feet,

110/60=1.83

=2

Hence, 2 cans of paint will be needed to cover 110 square feet area.

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The number local extremas to the function is given as follows:

3.

They are classified as follows:

The local extremas of a function are the turning points of the graph of the function, and they are classified as follows:

The graph of the function has three turning points, and they are defined as follows:

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Answer:

23

Step-by-step explanation:

5^2=25

50/10 = 5

3+25-5

Answer: A

Step-by-step explanation:                                                                                                                        

Answer: m=18 and b=25

Step-by-step explanation:

y = mx + b ==> standard slope intercept equation

y = 18x + 25

Notice any similarities?

y = 18x + 25

m=18 and b=25

The amount of accounts receivable to be reported on the company's budgeted balance sheet at the end of August is $22000.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, the sales of the company for August, September, and October are $110000, $120000, and $130500.

The company collects 20% of total sales in cash, therefore, the cash received by the company for the august month is,

110000×20%

= 110000×20/100

= 22000

Hence, the amount of accounts receivable to be reported on the company's budgeted balance sheet at the end of August is $22000.

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Answer:

D.4

Step-by-step explanation:

You can try replacing x value with the answer one by one.

A. 1(7) > 22 = 7 > 22, false, 7 smaller than 22

B. 2(7) > 22 = 14 > 22, false, 14 smaller than 22

C. 3(7) > 22 = 21 > 22, false, 21 smaller than 22

D. 4(7) > 22 = 28 > 22, true, 28 is larger than 22