how many roots does the polynomial function y=(x-2)(x+3)^2 have

Answer:

A. Distributive Property

Step-by-step explanation:

I'm taking the exam right now. :)

Answer:

53 minutes.  

Step-by-step explanation:

We have been given that Payton leaves  to go on an 85 minute bike ride at 3:27 pm.

Let us find when Payton will finish biking by 85 minutes after 3:27 pm.

Since 85 minutes equals to 1 hour and 25 minutes. 1 hour after 3:27 pm will be 4:27 pm. Now let us add 25 minutes to 4:27 pm.

So Payton will finish biking at 4:(27+25) pm= 4:52 pm.

Payton's family eats dinner at 5:45 pm. Now let us find remaining time between dinner and 4:52 pm.

[tex]\text{Minutes between dinner and finishing bike ride}=5:45 pm- 4:52 pm[/tex]  

[tex]\text{Minutes between dinner and finishing bike ride}=53[/tex]  

Therefore, Payton have 53 minutes between finishing her bike ride and eating dinner.  

Answer:

The vertices of A'B'C are  A'(-1,2), B'(-4,6) and C'(-4,2).

Step-by-step explanation:

Triangle ABC has vertices at A(1, 2) B(4, 6) and C(4, 2).

If a figure reflected over x-axis, then

[tex](x,y)\rightarrow (x,-y)[/tex]

Therefore the vertices of triangle ABC after reflection over x-axis are:

[tex]A(1,2)\rightarrow A'(1,-2)[/tex]

[tex]B(4,6)\rightarrow B'(4,-6)[/tex]

[tex]C(4,2)\rightarrow C'(4,-2)[/tex]

Rotation 180 degrees about the origin is defined as

[tex](x,y)\rightarrow (-x,-y)[/tex]

Therefore the vertices of triangle ABC after reflection over x-axis followed by rotated 180 degrees about the origin are:

[tex]A(1,-2)\rightarrow A'(-1,2)[/tex]

[tex]B(4,-6)\rightarrow B'(-4,6)[/tex]

[tex]C(4,-2)\rightarrow C'(-4,2)[/tex]

Therefore the vertices of A'B'C are  A'(-1,2), B'(-4,6) and C'(-4,2).

Answer:

C

Step-by-step explanation:

If ur not trying to look at all that but you should

Using exterior angle formula, you get that ∠CAD=36+123=159°

Exterior angle formula says that the angles facing CAB (ACB and ABC) sum to CAD.

We are given that revenue of Tacos is given by the mathematical expression [tex]-7x^{2}+32x+240[/tex].

(A) The constant term in this revenue function is 240 and it represents the revenue when price per Taco is $4. That is, 240 dollars is the revenue without making any incremental increase in the price.

(B) Let us factor the given revenue expression.

[tex]-7x^{2}+32x+240=-7x^{2}+60x-28x+240\\-7x^{2}+32x+240=x(-7x+60)+4(-7x+60)\\-7x^{2}+32x+240=(-7x+60)(x+4)\\[/tex]

Therefore, correct option for part (B) is the third option.

(C) The factor (-7x+60) represents the number of Tacos sold per day after increasing the price x times. Factor (4+x) represents the new price after making x increments of 1 dollar.

(D) Writing the polynomial in factored form gives us the expression for new price as well as the expression for number of Tacos sold per day after making x increments of 1 dollar to the price.

(E) The table is attached.

Since revenue is maximum when price is 6 dollars. Therefore, optimal price is 6 dollars.

Answer:

If we are to treat these as two ordered pairs, then the rate of change is 1.25.

Step-by-step explanation:

To find this, use the slope equation with the ordered pairs.

m(slope) = (y2 - y1)/(x2 - x1)

m = (11 9/16 - 9 1/16)/(12 - 10)

m = (2 8/16)/2

m = 2.5/2

m = 1.25

Now we know that this could be a function since we have a constant slope.

The rate of change between these two sets of measurements is 1 1/4 inch. Additionally, the relation is indeed a function because each x-value corresponds to exactly one y-value.

The rate of change in a relationship between two variables is a measure of how much one variable changes in relation to a change in the other variable. Here, we are dealing with pairs of measurements in inches. To find the rate of change, we subtract the y-values (the second number in each pair) and divide by the difference of the x-values (the first number in each pair).

We calculate as follows: (11 9/16 - 9 1/16) / (12 - 10), which simplifies to 2 1/2 / 2 or 1 1/4.

The relation is indeed a `function` because each input (x-value) corresponds to exactly one output (y-value). In other words, if you insert a particular measurement of the x-value into this relationship, you will always get the same corresponding y-value. In the context of mathematical functions, this is known as the vertical line test.

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If x = the first number (equal to 1x) then the second number is 75% more than this.

This means the value of the bigger number is 100 + 75 (because 100 is the starting number and 75 is the percent bigger)

This can be shown with the following equation:

Amount * [tex]\frac{percentage}{100}[/tex]

x *  [tex]\frac{175}{100}[/tex] = 1.75x

1.75x is the value of the bigger number.

Answer:

The correct answer option is a. 14∑1 (-28+3n)

Step-by-step explanation:

The summation notation for the given series is 14∑1 (-28+3n) where [tex]i[/tex] (the index of summation or the lower limit of summation) is 1 and [tex]n[/tex] (the upper limit of summation) is 14.

Putting in the values of the limit from 1 to 14 in the notation to get the first 14 terms of the series:

[tex]-28+3(1)=-25\\\\-28+3(2)=-22\\\\-28+3(3)=-19\\\\-28+3(4)=-16\\\\-28+3(5)=-13\\\\-28+3(6)=-10\\\\-28+3(7)=-7\\\\-28+3(8)=-4\\\\-28+3(9)=-1\\\\-28+3(10)=2\\\\-28+3(11)=5\\\\-28+3(12)=8\\\\-28+3(13)=11\\\\-28+3(14)=14\\[/tex]

Therefore, first option is the correct one.

Answer:

A is the correct one hope ive been of help

Answer:

1. 756 / 108 = 7 inches (the width of the first roof);

2. 954 / 106 = 9 inches (the width of the second roof);

Step-by-step explanation:

Answer:

y = -2x + 25/2

Step-by-step explanation:

Slope intercept form is y = mx + b.

You must solve the equation for y.

4x + 2y = 25

Subtract 4x from both sides.

2y = -4x + 25

y = -2x + 25/2

Answer:

solution given:

4x+2y=25

we know that

slope intercept form is

y=mx+c

so

4x+2y=25

2y=-4x+25

y=-4/2 x+25/2

y=-2x+25/2 is a required answer.

The smallest possible whole number length for the third side of a triangle with sides of length 20 and 2, based on triangle inequalities, is 19.

The subject of your question revolves around triangle inequalities, a fundamental concept in geometry. Triangle inequalities state that the length of any one side of a triangle must be less than the sum of the lengths of other two sides. In this case, you have two sides of lengths 20 and 2. This means the third side must be less than 22 but more than 18 (since it also needs to be more than the difference of two sides).

However, your question asks for the smallest whole-number length possible for the third side. Hence, the smallest possible whole number length for the third side of the triangle is 19.

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The smallest possible whole-number length for the third side of the triangle is 18.

To determine the smallest whole-number length for the third side of a triangle with sides of length 20 and 2, one must consider the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.Let's denote the lengths of the sides as [tex]\( a \), \( b \), and \( c \)[/tex] , where [tex]\( a = 20 \) and \( b = 2 \)[/tex]  . We are looking for the smallest whole number [tex]\( c \)[/tex]  that satisfies the triangle inequality theorem:  

1. [tex]\( a + b > c \)2. \( a + c > b \)3. \( b + c > a \)[/tex] . Substituting the known values of [tex]\( a \) and \( b \), we get: 1. \( 20 + 2 > c \)[/tex]

2.[tex]\( 20 + c > 2 \)[/tex]

3. [tex]\( 2 + c > 20 \)[/tex] From inequality 1, we have: [tex]\( 22 > c \)[/tex] This means [tex]\( c \[/tex] must be less than 22.From inequality 2, we have:[tex]\( 20 + c > 2[/tex]  Since [tex]\( c \)[/tex]  is a positive number, this inequality will always hold true for any positive \( c \).From inequality 3, we have:[tex]\( 2 + c > 20 \)[/tex].  Solving for  [tex]\( c[/tex] , we get: [tex]\( c > 18[/tex]) .Since  [tex]\( c \)[/tex] must be a whole number and the smallest whole number greater than 18 is 19, one might initially think that the smallest possible length for [tex]\( c \)[/tex]  is 19. However, we must also consider that [tex]\( c \)[/tex]  must be less than the sum of the other two sides (inequality 1). The smallest whole number less than 22 is 21, but since [tex]\( c \)[/tex] cannot be equal to [tex]\( a \)[/tex]  or [tex]\( b[/tex]) (as this would not form a triangle), the next smallest whole number is 20, which is also not possible as it would make two sides equal and the triangle degenerate. Therefore, the next smallest whole number is 19. However, we must also consider that for a valid non-degenerate triangle, the difference between the lengths of any two sides must be less than the length of the third side. Since  [tex]\( a = 20 \) and \( b = 2 \)[/tex] , the difference between  [tex]\( a \). and \( b \)[/tex] is 18, which means [tex]\( c \)[/tex] must be greater than 18 to satisfy this condition.Thus, the smallest possible whole-number length for the third side [tex]\( c \)[/tex] is 19, but since we are looking for the smallest whole number greater than 18, the correct answer is actually 18, as it is the smallest whole number that satisfies all the conditions of the triangle inequality theorem and the condition that the difference between the lengths of any two sides must be less than the length of the third side.

Answer:

168

Step-by-step explanation:

2x45=90

6x13=78

78+90=168

Answer:

69

Step-by-step explanation:

23 times 3

Answer: weclome

Step-by-step explanation:

Average movie ticket prices in the united states are, in general, lower than other countries. It would cost in $77.87 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $73.83. How much does an average movie ticket cost in each of these countries?  

Let ticket in japan cost x

Let ticket in Switzerland cost y  

3x+2y=77.87 ------1

3y+2x=73.83------2  

Subtract the equations  

x-y= 4.04 ---4

3y+2x=73.83------5

Answer:

Step-by-step explanation:

Average movie ticket prices in the united states are, in general, lower than other countries. It would cost in $77.87 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $73.83. How much does an average movie ticket cost in each of these countries?  

Let ticket in japan cost x

Let ticket in Switzerland cost y  

3x+2y=77.87 ------1

3y+2x=73.83------2  

Subtract the equations  

x-y= 4.04 ---4

3y+2x=73.83------5

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Answer:

The equation of this line would be y = -6

Step-by-step explanation:

In order to find this, we must first find the slope. For that we use the two points and the slope equation.

m(slope) = (y2 - y1)/(x2 - x1)

m = (-6 - -6)/(7 - 3)

m = 0/4

m = 0

Given that slope, we can use it along with a point in point slope form. From there we can solve for y and get the equation.

y - y1 = m(x - x1)

y + 6 = 0(x - 7)

y + 6 = 0

y = -6

Final answer:

To find the equation of a line passing through given points, calculate the slope, use the point-slope formula, and simplify to obtain the final equation. In this case, the line passing through (7,-6) and (3,-6) results in the equation y = -6.

Explanation:

To find the equation of the line passing through the points (7,-6) and (3,-6):

Calculate the slope (m) using the formula: m = (y₂ - y₁) / (x₂ - x₁)

Substitute one of the points and the slope into the point-slope formula: y - y₁ = m(x - x₁)

Simplify the equation to get the final answer: y = mx + b

The equation of the line passing through those two points is y = -6.

Answer:

34 miles is the distance from point A will they meet.

Step-by-step explanation:

Proportion states that the two ratios or fractions are equal.

Given the statement:

Distance between point A and B (i.e AB) = 200 mi.

Let the cyclist speed be c, and motor- speed be m;

then;

c = 17 mph and m=83 mph

Let they meet at distance x miles from a point A.  

By definition of proportion, we have;

[tex]\frac{x}{17} =\frac{200-x}{83}[/tex]

By cross multiply;

[tex]83x = 17(200-x)[/tex]

Using distributive property, [tex]a\cdot(b+c) =a\cdot b+ a\cdot c[/tex]

[tex]83x = 3400 - 17x[/tex]

Add 17x both sides we get;

[tex]83x+ 17x= 3400 - 17x +17x[/tex]

Simplify:

100x = 3400

Divide by 100 on both sides we get;

x = 34 miles

Therefore, the distance from point A will they meet is, 34 miles.

Answer:

Image

Step-by-step explanation:

Image

NOTES:

1)⇒    A + B + C = 180°

       A + B + C = π

       A + B        = π - C

2)⇒⇒ sin (A + B) = sin (π - C)

                         = (sin π)(cos C) - (sin C)(cos π)

                          = (0)(cos C) - (sin C)(-1)

                          = 0 - (-sin C)

                          = sin C

3)⇒⇒⇒cos (A + B) = cos (π - c)

                            = (cos π)(cos C) + (sin π)(sin C)

                            = (-1)(cos C) + (0)(sin C)

                            = - cos C              

4)⇒⇒⇒⇒ sin 2A + sin 2B = 2 sin (A + B) cos (A - B)

PROOF (from left side):

sin 2A + sin 2B + sin 2C    =    4 sin A sin B sin C

2 sin (A + B) cos (A - B) + sin 2C     refer to NOTE 4

2 sin (A + B) cos (A - B) + 2 sin C cos C  double angle formula

2 sin C cos (A - B) + 2 sin C cos C   refer to NOTE 2

2 sin C [cos (A - B) + cos C]     factored out 2 sin C

2 sin C [cos (A - B) - (cos(A + B)]   refer to NOTE 3

2 sin C [2 sin A sin B]           sum/difference formula

4 sin A sin B sin C      multiplied 2 sin C by 2 sin A sin B

Proof completed: 4 sin A sin B sin C   =   4 sin A sin B sin C

The answer is C. 3/5

20 girls, 3 boys. 23/40 is about 60 percent, or 3/5.

I wrote the wrong answer on accident for whatever reason when I first sent this, I apologize.

x-2y=6

-2y=-x+6

2y=x-6

y=0.5x-3

Parallel=same slope

y=0.5x+5

Answer: D

Step-by-step explanation:

End behavior is determined by two factor:

1. Coefficient - determines right side:

2. Degree - determines left side:

******************************************************************************************

-x³ + 2

Leading coefficient is NEGATIVE, so right side goes to -∞ (decreases)

Degree is ODD, so left side is opposite of right side → goes to +∞ (increases)

Answer:

[tex]\frac{70+71+72+x}{4}\geq 73[/tex]        

[tex]x\geq 79[/tex]

Step-by-step explanation:    

Let x be the height of 4th plant purchased by Millie.

We have been given that Millie needs the average height of the plants she is buying to be at least 73 inches. She has selected three plants that are 70, 71 and 72 inches tall.

So the average of 4 plants purchased by Millie will be: [tex]\frac{70+71+72+x}{4}[/tex]

We can represent this information in an inequality as: [tex]\frac{70+71+72+x}{4}\geq 73[/tex]        

Therefore, our desired inequality will be [tex]\frac{70+71+72+x}{4}\geq 73[/tex].

Now let us solve our inequality by multiplying both sides of inequality by 4.

[tex]4*\frac{70+71+72+x}{4}\geq 4*73[/tex]  

[tex]70+71+72+x\geq 292[/tex]    

[tex]213+x\geq 292[/tex]

[tex]x\geq 292-213[/tex]    

[tex]x\geq 79[/tex]      

Therefore, the height of 4th plant purchased by Millie must be at least 79 inches.

Given:

b1 = 17 ft

b2 = 20 ft

h = 13 ft

r = 17/2 = 8.5 ft

Area of the Semi-circle = 1/2 π r²

= 1/2 (22/7) (8.5²)

= (11/7) (72.25)

= 113.535 ft²

Area of the trapezium = (h) (b1 + b2) / 2

= (13)(17 + 20)/2

= 240.5 ft²

Total area of the amphitheater stage = Area of Semi-circle + Area of the trazezium = 113.535 + 240.5 = 354.035 ft²

Answer:

The answer is π

Step-by-step explanation:

Not really an explanation, but you can type this in wolframalpha: integrate (x^3 cos x/2 + 1/2) sqrt(4-x^2) dx from x=-2 to 2

The given integral can be solved using numerical calculation methods. The integral by part formula also would be applicable in the given integral.

The value of the given integral is [tex]3.14\rm\: or\: \pi[/tex].

Given:

Write the given integral.

[tex]\int_{-2}^{2}\sqrt{4-x^2}\left(\cos\left(\dfrac{x}{2}\right)x^3+\dfrac{1}{2}\right)\\[/tex]

Write the formula for the integration by part formula.

[tex]\int u.v=u\int vdx-\int u'(\int vdx)dx[/tex]

Let,

[tex]u=\sqrt{4-x^2}[/tex]

[tex]v=\left (x^3\cos\dfrac{x}{2} +\dfrac{1}{2} \right)[/tex]

Now put the value in above formula and integrate.

[tex]\begin{aligned}\int_{-2}^{2}\sqrt{4-x^2}\left(\cos\left(\dfrac{x}{2}\right)x^3+\dfrac{1}{2}\right)&=\left [\dfrac{\frac{x\sqrt{4-x^2}}{2}+2\arcsin\left(\frac{x}{2}\right)}{2}\right]_{-2}^{2}\\&=\left [\dfrac{x\sqrt{4-x^2}}{4}+\arcsin\left(\dfrac{x}{2}\right)\right]_{-2}^{2}\\\end[/tex]

Now, further simplify the expression.

[tex]\int_{-2}^{2}\sqrt{4-x^2}\left(\cos\left(\dfrac{x}{2}\right)x^3+\dfrac{1}{2}\right)\\=\left [\dfrac{2\sqrt{4-2^2}}{4}+\arcsin\left(\dfrac{2}{2}\right)\right]-\left [\dfrac{2\sqrt{4-(-2)^2}}{4}+\arcsin\left(\dfrac{-2}{2}\right)\right]\\=1.57-(-1.57)\\=3.14[/tex]

The value of the given integral is [tex]3.14\rm\: or\: \pi[/tex].

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Answer:

1225.56 kg

Step-by-step explanation:

1 stone = 14 slugs

1 slug = 14.59 kg

[tex]\text{6 stones} ( \dfrac{14 slug}{1 stone})(\dfrac{14.59 kg}{1 slug})[/tex]

numerator 6 * 14 * 14.59 = 1225.56 kg

denominator = 1

Answer 1225.56 kg in 6 stones

w - width

2w - length

60 - perimeter

w + w + 2w + 2w = 6w - perimeter

The equation:

6w = 60    divide both sides by 6

w = 10 → 2w = 2 · 10 = 20

The area: A = width × length

A = (10)(20) = 200

Answer:

It is a factor and a variable.

Step-by-step explanation:

The missing number can be found using Matrix rule. We have to apply addition and subtraction rule to find the missing number form given matrix.

The missing number is -5.

Given:

The given matrix is,

[tex]\left[\begin{array}{cccc}9&38&47&4\\6&35&42&x\\12&21&23&27\end{array}\right][/tex]

Let the missing number is [tex]x[/tex].

Apply the subtraction rule to subtract second row from first row.

[tex]\left[\begin{array}{cccc}9&38&47&4\\3&3&5&4-x\\12&21&23&27\end{array}\right][/tex]

The sum of first three number is equal to the sum of digits of the first three number in the third row,

[tex]1+2=3\\2+1=3\\2+3=5[/tex]

Now from the same pattern.

[tex]2+7=4-x\\x=-5[/tex]

Thus, the missing number is -5.

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Answer:

The sale price is $43.50.

Step-by-step explanation:

58 x .25 = 14.50 off the original price

58 - 14.50 = 43.50

Answer:

The point of change is the point (1,9)

Step-by-step explanation:

The first derivative of the function equated to zero will give you the point where the function changes.

Therefore, to solve this problem find the first derivative of f (x)

[tex]f '(x) = 3*3(x-1)^{3-1}\\\\f '(x) = 9(x-1)^2[/tex]

Now we equate the derivative to 0.

[tex]9 (x-1)^ 2 = 0\\\\x = 1[/tex]

Then the derivative of the function is equal to 0 when x = 1. This means that the concavity of the function changes in x = 1.

When [tex]x = 1, y = 3(1-1) ^ 3 +9\\\\x =1, y = 9.[/tex]

Then the point of change is the point (1,9)

Answer:

The point of inflection is (1,9)

Step-by-step explanation:

We have following  given function

[tex]f(x)=(x-1)^{3} +9[/tex]

The point at which the function changes its curvature is defined by the point of inflection.

To find point of inflection we set 2nd derivative to 0

[tex]f''(x)= 0[/tex]

The first derivative is given by

[tex]f'(x)= \frac{d}{dx} [(x-1)^{3} +9][/tex]

[tex]f'(x)= 3(x-1)^{2}[/tex]     ( using chain rule  and derivative of constant is 0)

now again we take 2nd derivative

[tex]f''(x)=3(2(x-1))[/tex]

[tex]f''(x)=6(x-1)[/tex]

now we equate 2nd derivative to 0

[tex]6(x-1)=0\\x-1=0\\x=1[/tex]

hence point of inflection is at x=1

now we find y coordinate of point of inflection by plugging x=1 in f(x)

[tex]y=f(1)=(1-1)^{3} +9 =9[/tex]

Hence the point of inflection is (1,9)