Find the zeros with multiplicity for the function p(x) = (x^3 – 8)(x^5 – 4x^3)

Please show steps

PART A:

The function in vertex form by completing the square is:

            [tex]f(t)=(t+3)^2-29[/tex]

PART B:

The vertex is located at (-3,-29)

and the vertex is the minimum point of the graph.

PART C:

      The axis of symmetry of f(t) is:

                    t= -3

The function f(t) is given by:

             [tex]f(t)=t^2+6t-20[/tex]

We know that the vertex form of a equation is given by:

           [tex]f(t)=a(t-h)^2+k[/tex]

where a,h and k are real numbers.

and the vertex is located at (h,k)

The function is given by:

        [tex]f(t)=(t+3)^2-29[/tex]

Hence, the vertex is given by:

            (-3,-29)

Also, as the leading coefficient is positive.

Hence, the parabola is upward open parabola.

Hence, the vertex will be the minimum point of the graph.

Also, the axis of symmetry of a graph is given by:

                          t=h

Hence, here the axis of symmetry is:  t= -3

Answer:

B. The graph of g is the graph of f translated to the left 3 units and down 7 units.

Step-by-step explanation:

f(x) = x²  to g(x) = (x + 3)² - 7

Notice the difference:

from 'x' to 'x + 3'

and then from 'x²' to '(x+3)² - 7'

The transformation that changes 'x' to 'x + 3' is the translation across the x-axis, three units to the left. The transformation that changes 'x²' to (x + 3)² - 7' is the translation across the y-axis, seven unit down. Refer to the graph attached below to visualize the transformation. Take the vertex of f(x) = x² and translate it three unit left and seven unit down to get g(x).

The length of the hypotenuse is 20 centimeters.

In order to solve this question, we'll use the Pythagoras formula which will be:

a² + b² = c²

where,

First leg = a = 12 centimeters

Second leg = b = 16 centimeters

Hypothenuse = c = Unknown

It should be noted that the hypothenuse is the longest side and therefore the formula will be:

a² + b² = c²

12² + 16² = c²

144 + 256 = c²

400 = c²

Therefore, c = ✓400

c = 20

Therefore, the length of the hypotenuse is 20 centimeters.

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Answer:

[tex]30-(1.79a+0.36b+2.99)[/tex]

Step-by-step explanation:

Let  a represents the number of pounds of apples Abigail buys

Cost of 1 pound of apple = $1.79

So, Cost of a pounds of apple = 1.79a

Let b represents the number of bananas she buys,

Cost of 1 pound of banana = $0.36

Cost of b pounds of banana = 0.36b

Abigail buys 3 pounds of potatoes

Cost of 3 pounds of potatoes = $2.99

So, Total cost = [tex]1.79a+0.36b+2.99[/tex]

Abigail has $30.00 to buy groceries.

So, the amount of change she receives after her purchases=[tex]30-(1.79a+0.36b+2.99)[/tex]

So,Option C is correct.

Hence The  expression represents the amount of change she receives after her purchases is [tex]30-(1.79a+0.36b+2.99)[/tex]

11(y-10) = 4y-5

11y-110 = 4y-5

7y -110 = -5

7y =105

y = 105/7 = 15

PTS = 11(15-10) = 11*5 = 55 degrees

Answer:

55

Step-by-step explanation:

We are given with two lines that intersects each other .

the vertical opposite angles are same.

So we equate the angles and solve for y

[tex]11(y-10)= 4y-5[/tex]

[tex]11y-110=4y-5[/tex]

Subtract 4y from both sides

[tex]7y-110=-5[/tex]

Now we add 110 on both sides

[tex]7y=105[/tex]

Now we divide by 7 on both sides

y=15

now we find m∠PTS

m∠PTS=[tex]11(y-10)[/tex]

Plug in 15 for y

m∠PTS=[tex]11(15-10)=55[/tex]

The maximum possible length it could have been 44.49cm.

Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.

here, we have,

44cm is rounded to the nearest whole cm.

as, it is rounded to the nearest whole cm.

so, we get,

The maximum possible length it could have been 44.49cm.

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To find the length of MF, the distance formula is used after calculating the midpoint M of CF with coordinates C(3,7) and F(5,5), resulting in MF being √2 units.

The question asks to find the distance MF, where M is the midpoint of segment CF given the coordinates of the points C(3,7) and F(5,5). To find the coordinates of M, we need to use the midpoint formula:

Midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2)

Using the given points C(3,7) and F(5,5), we get:

M = ((3 + 5)/2, (7 + 5)/2) = (4, 6)

Now, we will use the distance formula to calculate MF:

Distance formula: D = √((x2 - x1)² + (y2 - y1)²)

Since M(4,6) and F(5,5) are the points in question, plugging in these values yields:

MF = √((5 - 4)² + (5 - 6)²) = √((1)² + (-1)²) = √(1 + 1) = √2

So, the length of segment MF is √2 units.

the equation for a line is y = mx+b

 m = slope

b = y intercept

 you know the slope is 2/3 and the y intercept is 7 so just replace them in the equation:

 y =2/3x +7

the answer is c. 25

expalnation: A 3:2 ratio can be used in a proportion.

3/2=15/girls, girls =15*2÷3=10.

10÷15=25

To calculate the maximum speed a subway train can reach between stations, given the maximum tolerable acceleration, we use the equation Vmax = sqrt(2 × a × d), resulting in a maximum velocity of approximately 40.21 m/s.

To find the maximum speed a subway train can attain between stations, given a maximum tolerable acceleration for passengers, we need to use the equations for uniformly accelerated motion. Since the train starts and ends at rest at the stations and because the stations are 930 meters apart, we can think of the train's trip as two identical parts: an acceleration phase and a deceleration phase.

Let's denote the maximum speed as Vmax, the acceleration as a, and the distance for each phase as d (half the distance between stations). We have:

Using the equation Vmax2 = 2ad, we can solve for the maximum speed (Vmax) as follows:

Vmax = sqrt(2 × a × d)

Substituting the values, we get:

Vmax = sqrt(2 × 1.74 m/s2 × 465 m)

Vmax ≈ sqrt(1617) m2/s2 ≈ 40.21 m/s

Therefore, the maximum speed the subway train can attain between stations is approximately 40.21 m/s.

Answer:  2

Step-by-step explanation:

Let Set A represents the number of employees cooked​ food.

Set B represents the number of employees washed​ dishes.

Set C represents the number of employees operated the cash​ register .

Given : n(A)=9 ; n(B)=14 ; n(C)=22

n(A∩B)=4 ; n(A∩C) = 2 ; n(B∩C)=7 ; n(A∩B∩C)=1

Using the given information, we have made a Venn diagram below.

Using Venn diagram , we have

n(only A)= n(A)-(n(A∩B)+n(A∩C)+n(A∩B∩C))

⇒n(only A)=9-(4+2+1)=9-7=2

Hence, 2 employees only cooked​ food.

divide 1623 by 3

1623 / 3 = 541

now subtract 1 from that

541-1=540

then add one to 541, 541+1 = 542

540 + 541 + 542 = 1623

 the numbers are 540, 541, 542

Answer:

all you got 2 do is plug in 4 for the value of x.

Step-by-step explanation:

Final answer:

The quotient when dividing 6x³ + 13x² + x - 2 by x - 1 is 6x² + 19x + 20, and the remainder is 18. This solution can be found using synthetic division.

Explanation:

The question asks to find the quotient and remainder when the polynomial 6x³ + 13x² + x - 2 is divided by x - 1. To solve this, we can use polynomial long division or synthetic division. As the divisor is in the form of x - a, where a is 1, synthetic division is a streamlined approach.

We set up our synthetic division with 1 as our key number outside the division symbol and the coefficients of our polynomial (6, 13, 1, -2) inside:

Bring down the 6.

Multiply 1 by 6 to get 6, add this to the next coefficient 13 to get 19.

Continue the process: Multiply 1 by 19 to get 19, add this to 1 to get 20.

Repeat: Multiply 1 by 20 to get 20, add this to -2 to get 18.

The numbers now inside the division symbol represent the coefficients of the quotient polynomial, giving us 6x² + 19x + 20 with a remainder of 18. Therefore, the quotient is 6x² + 19x + 20, and the remainder is 18.