Writing a Polynomial Function of a Graph:
use the fact that the graph passes through (0,36) to find the coefficient a in f(x)=a(x+3)(x+1)(x-2)(x-3)
a=???

y = x² + 6x + 5

Use the formula: -b/2a

a = 1

b = 6

- 6 / 2

= -3

The x-coordinate of the vertex is -3

Plug the x value back into the original equation to find the y-coordinate of the vertex

y = (-3)² + 6(-3) + 5

y = -4

Answer:

Real numbers

0≤ t ≤17

Step-by-step explanation:

Khan academy said

The domain of d in the given problem is time (T) in minutes since Tanya left home and is the set of all real numbers greater than or equal to 17.

The domain of d in the given problem is time (T) in minutes since Tanya left home.

Since Tanya walked for 17 minutes, the domain of d is the set of all real numbers greater than or equal to 17.

Answer:

Bus drop him off 64 miles far from the school.

Explanation:

 Total distance traveled by Nigel from Home to school each day = 312 miles

 Distance from bus stop to his home = 14 miles

Distance traveled by Nigel on the city bus = 234 miles.

Distance from bus drop off position to school = X miles

We have Total distance traveled by Nigel = 14+234+X = 248+X

Equating both total distances

          248+X = 312

            X = 64 miles.

 So bus drop him off 64 miles far from the school.

Answer:

[tex]x = \frac{2}{3} + \frac{\sqrt{10} }{3} , x = \frac{2}{3} - \frac{\sqrt{10} }{3}[/tex]

Step-by-step explanation:

Multiplying the coefficient of x by the constant to get:

3 x (-2) = -6

Find factors of -6 that equal the middle term -4.

Since, no such factors can be found so we can solve the equation by completing the square.

To complete the square, divide the equation by the coefficient of x^2 which is 3 to get:

[tex]x^{2} - \frac{4}{3} x - \frac{2}{3} = 0[/tex]

[tex]x^{2} - \frac{4}{3} x = \frac{2}{3}[/tex]

Now divide the coefficient of x by 2 and add the square of the result to both sides of the equation:

[tex]x^{2} - \frac{4}{3} x + (-\frac{2}{3} )^{2} = \frac{2}{3} +  (-\frac{2}{3} )^{2}[/tex]

[tex](x - \frac{2}{3} )^2 = \frac{2}{3} + \frac{4}{9}[/tex]

[tex](x - \frac{2}{3} )^2 = \frac{4}{9}[/tex]

[tex]\sqrt{(x - \frac{2}{3} )^2} = \sqrt{\frac{4}{9} }[/tex]

[tex]x - \frac{2}{3} = \sqrt{\frac{10}{9} }[/tex] , [tex]x - \frac{2}{3} = -\sqrt{\frac{10}{9} }[/tex]

[tex]x = \frac{2}{3} + \frac{\sqrt{10} }{3} , x = \frac{2}{3} - \frac{\sqrt{10} }{3}[/tex]

First you must know that is i∧2= -1

x∧3-4x∧2+4x-16 = x∧2 (x-4) + 4 (x-4) = (x-4) (x∧2+4) = (x-4) (x∧2-(-4)) =

= (x-4) (x∧2-(-1) *4) = (x-4) (x∧2- i∧2*2∧2) = (x-4) (x∧2-(2i)∧2) = (x-4) (x-2i) (x+2i)

Good luck!!!

[tex]\frac{-5 + 2x^{2}}{7 - 8x}[/tex]

The denominator cannot equal zero.

7 - 8x ≠ 0

7       ≠  8x

    [tex]\frac{7}{8} \neq \frac{8x}{8}[/tex]

[tex]\frac{7}{8} \neq x[/tex]

Answer: [tex]\frac{7}{8}[/tex] is not in the domain

d - e = 2d - e      add e to both sides

d - e + e = 2d - e + e

d = 2d      subtract d from both sides

d - d = 2d - d

0 = d

Answer: D = 0

Thus meaning D has to equal 0.

I hope this helps!

Answer:

13  all three angles =60 in total they equal 180

14) I believe x = 32.5 Am not sure though.

Step-by-step explanation:

That is the only question i can answer but to help you with this all triangles big or small the total of all the angles combined = 180

For this one, plug in your x and y intercepts for the corresponding letters and see which one is true.  I always start with the first equation and then see which ones solve it first, that will cut your time down on a test.

Lets start with A. (4,5)

and the first equation y=x+1

5=4+1, which is true so A is a potential answer

B. (2,3)

3=2+1, B is a potential as well

C. (-2,1)

1=-2+1, which is false so C is out

D. (-4,-3)

-3=-4+1, which is true.

To cut down on time, do the same thing with the second equation and your final answer will be A. (4,5)

Solving the system, we find [tex]\(x = 2.5\) and \(y = -1\)[/tex]. The product of [tex]\(x\) and \(y\) is \(-2.5\)[/tex]. Answer: C) [tex]\(-\frac{2}{5}\).[/tex]

To find the product of [tex]\(x\) and \(y\)[/tex], we need to solve the given system of equations:

2x - 5y = 10

4x + 3y = 7

Let's solve this system using the substitution method:

From the first equation, we can express [tex]\(x\) in terms of \(y\)[/tex]:

[tex]\[2x = 10 + 5y\][/tex]

[tex]\[x = \frac{10 + 5y}{2}\][/tex]

[tex]\[x = 5 + \frac{5}{2}y\][/tex]

Now, substitute this expression for [tex]\(x\)[/tex] into the second equation:

[tex]\[4(5 + \frac{5}{2}y) + 3y = 7\][/tex]

[tex]\[20 + 10y + 3y = 7\][/tex]

[tex]\[13y = -13\][/tex]

[tex]\[y = -1\][/tex]

Now, substitute [tex]\(y = -1\)[/tex] into the expression for \(x\):

[tex]\[x = 5 + \frac{5}{2}(-1)\][/tex]

[tex]\[x = 5 - \frac{5}{2}\][/tex]

[tex]\[x = 5 - 2.5\][/tex]

[tex]\[x = 2.5\][/tex]

Finally, find the product [tex]\(xy\):[/tex]

[tex]\[xy = 2.5 \times (-1)\][/tex]

[tex]\[xy = -2.5\][/tex]

So, the product of [tex]\(x\) and \(y\) is \(-2.5\)[/tex], which corresponds to option C) [tex]\(-\frac{2}{5}\).[/tex]

Answer:

(1,2) (-1,-2)

Step-by-step explanation:

Given the equation of curve as y= 2x³ and slope of tangent line as 6 then

Find dy/dx

[tex]\frac{d}{dx} (y)=\frac{d}{dx}(2x^3)[/tex]

Apply the power rule

[tex]\frac{d}{dx} (x^n)=nx^{n-1}[/tex]

where n=constant

Hence, our equation will be;

[tex]\frac{dy}{dx} =2*3x^{3-1} \\\\\\\frac{dy}{dx} =6x^{2}[/tex]

But you know that dy/dx=slope=6

6x²=6--------------------divide both sides by 6

6x²/6=6/6

x²=1

x=√1=±1

x=1 and -1

Remember y=2x³

Substitute value of x to get value of y

y=2x³

y=2×1³

y=2×1=2

y=2

For x=-1, find y coordinate

y=2×-1³=2×-1=-2

coordinate will be (-1,-2)

Coordinates of the points will be (1,2) ,(-1,-2)

The simplified form of the expression (25x^2-14xy+4)-(7x^2-9y)+(2xy+7) is 18x^2 - 12xy + 20 + 9y. We achieved this by applying the distributive property, grouping like terms, and simplifying each group.

To simplify the expression (25x^2-14xy+4)-(7x^2-9y)+(2xy+7), we first apply the distributive property and place minus signs before each of the terms inside the bracket:

25x^2 -14xy + 4 - 7x^2 + 9y + 2xy + 7.

From here, group like terms together:

(25x^2 - 7x^2) + (-14xy + 2xy) + (4 + 9y + 7).

Finally, simplify each group of like terms to achieve the simplified expression:

18x^2 - 12xy + 20 + 9y.

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Insert x = 100 and x = 200 in the function

f(100) = 20,000 - 40*100

= 20,000 - 4000

= 16,000

f(2)) = 20,000 - 8,000 = 12,000

So its choice C  ,  All reals between 12,000 and 16,000 inclusive.

Answer:

Option C.

Step-by-step explanation:

The given function is

[tex]f(x)=20000-40x[/tex]

where x represents the number of minutes the painter has worked from the 100-minute mark through the 200-minute mark of the project.

We need to find the practical range of the function.

The value of x lies from 100 to 200.

At x=100,

[tex]f(100)=20000-40(100)=20000-4000=16000[/tex]

At x=200,

[tex]f(200)=20000-40(200)=20000-8000=12000[/tex]

It means the practical range of the function is all real numbers between 12,000 and 16,000 inclusive.

Hence, the correct option is C.

I believe the answer is a Penny.

A penny, I'm pretty sure...

ANSWER

The factorization of   [tex]100x^2-20x+1[/tex]

 is [tex](10x-1)^2[/tex].

EXPLANATION

We want to factor [tex]100x^2-20x+1[/tex]

Comparing this to [tex]ax^2+bx+c[/tex]

[tex]a=100,b=-20,c=1[/tex]

[tex]ac=100[/tex]

We look for factors of 100  that add up to [tex]-20[/tex].

These factors are [tex]-10,-10[/tex]

We now split the middle term to obtain;

[tex]100x^2-10x-10x+1[/tex]

We factor to obtain;

[tex]10x(10x-1)-1(10x-1)[/tex]

This simplifies to  [tex](10x-1)(10x-1)=(10x-1)^2[/tex]

Answer:B

Step-by-step explanation:

B. The pickup truck would travel 252 miles in 6 hours.

The truck travels 210 miles in 5 hours.

To find the speed, we divide the distance by the time:

210 miles / 5 hours

= 42 miles/hour.

Now, let's calculate the distance for 6 hours.

The truck travels at 42 miles/hour.

To find the distance in 6 hours, we multiply the speed by the time:

42 miles/hour * 6 hours

= 252 miles.

Answer is BF...hope this helps

What is 3/5 of $40 restaurant bill equals $

the answer is $24

I think you can google that really easily.

Answer:

1800 ÷ 6

Step-by-step explanation:

18,000 ÷ 60 is the same as;

18,000 ÷ 10 ÷ 6 and is the same as;

1,800 ÷ 6

False since 7/9 is the equivalent of 0.7777777 which is less than 1 which in this case acts as 100% so 7/9 is about 77.7% so it is less than 100% so the answer is false.

1. The Great Wall of China is 13,170.696

2.how many feet are in a mile= 5,280= 1 mile  

3. 19,536,000=3700 miles

ANSWER

[tex]2y-x-20=0[/tex]

or

[tex]y=\frac{1}{2}x+10[/tex]

EXPLANATION

Let the rectangle be oriented as shown in the diagram.

The line segment AD passes through [tex]A(2,11)[/tex].

All we need now is the slope of AD then we can find its equation.

Since AD is perpendicular t AB, we determine the slope of AB and then use it to find the slope of AD.

[tex]Slope_{AB}=\frac{1-11}{7-2}[/tex]

[tex]Slope_{AB}=\frac{-10}{5}=-2[/tex]

The slope of AD is the negative reciprocal of the slope of AB because they are perpendicular.

[tex]Slope_{AD}=\frac{-1}{-2}=\frac{1}{2}[/tex]

The equation of AD is given by;

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-11=\fra[1}{2}(x-2)[/tex]

Multiplying through by 2 gives,

[tex]2y-22=(x-2)[/tex]

[tex]2y-x-22+2=0[/tex]

[tex]2y-x-20=0[/tex]

or

[tex]y=\frac{1}{2}x+10[/tex]

x² + y² = 16

the equation of a circle centred at the origin is

x² + y² = r² ( where r is the radius )

here r = 4, hence

x² + y² = 16 ← is the equation of the circle

$50

the sale price is [tex]\frac{5}{12}[/tex] × $120

[tex]\frac{5(120)}{12}[/tex] = $50

Answer:50

Step-by-step explanation:

you would do number of devisions (denominator of fraction) divided by the number of the original price then multiply it by the numer of the devision (numerator of fraction)

120/12=10*5=50