1. A supermarket display consists of boxes of soda. The bottom row has 38 boxes. Each row has four fewer boxes than the row below it. The display has eight rows.
a) Write and use the function to determine how many boxes are in the top row. Show your work.
b) Use the appropriate formula to determine the number of boxes in the entire display. Show your work.

Answer:

The polynomial will be P(x) = - 5 (x + 2)²(x - 3)

Step-by-step explanation:

The degree of the polynomial P(x) is 3 and it has zeros at x = - 2 with multiplicity 2 and at x = 3 with multiplicity 1.

Therefore, (x + 2)² and (x - 3) are the factors of the equation.

Let the polynomial is

P(x) = a(x + 2)²(x - 3) ........... (1)

Now, the polynomial passes through the point (2,80).

So, from equation (1) we gat,

80 = a(4)²(-1)

⇒ a = - 5

Therefore, the polynomial will be P(x) = - 5 (x + 2)²(x - 3) (Answer)

The required polynomial is [tex]P(x) = - 5 (x + 2)^{2} (x - 3)[/tex]

Any polynomial have number of roots equal to its degree of polynomial.

Since, the degree of the polynomial P(x) is 3. it means that it has 3 roots.

it has zeros at x = - 2 with multiplicity 2, it means that factor (x - 2) have power 2 and at x = 3 with multiplicity 1 means that factor (x - 3) have power of 1 .

Thus, [tex](x + 2)^{2}[/tex] and (x - 3) are the factors of the equation.

Let us consider the polynomial is [tex]P(x) = k(x + 2)^{2} (x - 3) .[/tex]

Since,  the polynomial passes through the point (2,80).

So, substituting point (2, 80)  in above polynomial equation.

   We get,   [tex]80 = a(4)^{2} (-1)[/tex]

                      a = - 5

Therefore, the polynomial is [tex]P(x) = -5(x + 2)^{2} (x - 3) .[/tex]

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Answer:

368.94

Step-by-step explanation:

New value =

258 + Percentage increase =

258 + (43% × 258) =

258 + 43% × 258 =

(1 + 43%) × 258 =

(100% + 43%) × 258 =

143% × 258 =

143 ÷ 100 × 258 =

143 × 258 ÷ 100 =

36,894 ÷ 100 =

368.94

To increase 258 by 43% using the multiplier method, multiply 258 by 1.43. The result is 369.14.

To use the multiplier method to increase 258 by 43, you simply need to calculate 258 times the multiplier. The multiplier is 1 plus the rate of increase, which is 43% in this case. So, the multiplier is 1+0.43=1.43.

Here is the calculation:

258 * 1.43 = 369.14

So, 258 increased by 43% is approximately 369.14.

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Answer:

if C = 56pi, you do plug in the given by using the formula C = 2pi(r)

56pi = 2pi(r)

56/2 = r

r= 28

the radius is 28

Answer:

y = - 17

Step-by-step explanation:

[tex]y = 1 - 2x[/tex]

When x = 9

[tex]y = 1 - 2(9)[/tex]

[tex]y = 1 - 18[/tex]

[tex]y = - 17[/tex]

Therefore, given equation y = 1 - 2x; when x = 9, y = - 17

Answer:

Pie

Step-by-step explanation:

Answer:

pi

Step-by-step explanation:

Answer:

  use the Pythagorean theorem

Step-by-step explanation:

The slant height is the hypotenuse of a right triangle whose legs are the height of the pyramid and the distance from the edge of the base to the center of the pyramid (where the height segment reaches the base).

For h = pyramid height, b = base edge length, s = slant height, the Pythagorean theorem tells you ...

  h² + (b/2)² = s²

Solving for h gives ...

  h = √(s² -(b/2)²) . . . . . the height of the pyramid

Answer:

42 miles

Step-by-step explanation

Distance = Speed * Time

X=12mph*3.5h

X=42 miles

Distance he can travel is 42 miles.

Step-by-step explanation:

⇒ Distance = 12 × 7/2 = 42 miles

Answer:

The average rate of change is = - 4

Step-by-step explanation:

If y = f(x) is a function then the average rate of change for f(x) between the interval a ≤ x ≤ b is given by

[tex]\frac{f(b) - f(a)}{b - a}[/tex].

Now, in this case the function is given by f(x) = - 4x + 40 and the interval is 1 ≤ x ≤ 3.

Therefore, f(1) = - 4(1) + 40 = 36 and f(3) = - 4(3) + 40 = 28

So, the average rate of change is = [tex]\frac{28 - 36}{3 - 1} = - \frac{8}{2} = - 4[/tex] (Answer)

Answer:

−30

Step-by-step explanation:

−30 is the average rate of change for ƒ(x) = −4x + 40 over the interval 1 ≤ x ≤ 3.

ƒ(b) − ƒ(a)

b − a

=  ƒ(3) − ƒ(1)

3 − 1

=  −24 − 36

2

=  −60

2

= −30

Degree of polynomials:

[tex]6x^2 = 2\\\\18x^3+5ab-6y = 3\\\\4x^3y +3x^2-xy-4 = 4\\[/tex]

Least to greatest based on degree:

[tex]6x^2[/tex]

[tex]18x^3+5ab-6y[/tex]

[tex]4x^3y +3x^2-xy-4[/tex]

Solution:

The degree of the polynomial is the highest degree of any of the terms

Know that the degree of a constant is zero

Option I

[tex]6x^2[/tex]

Here the highest degree is 2 ( x power 2)

In this case, degree of polynomial is 2

Option II

[tex]18x^3+5ab-6y[/tex]

To find the degree of the polynomial, add up the exponents of each term and select the highest sum.

[tex]Degree\ of\ 18x^3 = 3[/tex]

[tex]Degree\ of\ 5ab = 5a^1b^1 = 1+1 = 2[/tex]

[tex]Degree\ of\ 6y = 6y^1 = 1[/tex]

Thus the highest degree is 3

Option III

[tex]8a^{-5}[/tex]

This is not a polynomial

A polynomial does not contain variables raised to negative

Option IV

[tex]4x^3y +3x^2-xy-4[/tex]

To find the degree of the polynomial, add up the exponents of each term and select the highest sum.

[tex]Degree\ of\ 4x^3y = 4x^3y^1=3+1 = 4\\\\Degree\ of\ 3x^2 = 2\\\\Degree\ of\ xy = x^1y^1 = 1+1 = 2\\\\Degree\ of\ 4 = 0[/tex]

Thus highest degree is 4

Then organize the expressions from least to greatest based on their degree

Least to greatest based on degree:

[tex]6x^2[/tex]

[tex]18x^3+5ab-6y[/tex]

[tex]4x^3y +3x^2-xy-4[/tex]

Answer:

lower case p

Step-by-step explanation:

The law of sines: [tex]\frac{sinA}{a} = \frac{sinB}{b}[/tex]

Therefor look for which sides and angles are accounted for. If we are given angle P, Angle R, and Side r, then Side p is the last term that fits into the law of sines equation.

Answer:

4:3, 32:24, 8:6

Step-by-step explanation:

for 4:3, you divide both sides of 16:12 by 4

for 32:24 you mutiple both sides by 2

for 8:6 you multiply both sides by 2

Hope this helps :)

8th term is 0.30

Step-by-step explanation:

⇒ r = a2/a1 = 216/648 = 1/3

⇒ 8th term =  648 × (1/3)^8-1 = 648 × (1/3)^7 = 648/2187 = 0.30

Answer:

Step-by-step explanation:

4 - 2b = 2

collect terms

4 - 2 = 2b

2 = 2b

divide both side by 2

2/2 = 2b/2

b = 1

First, we need to find out how many siblings the students have in total and how many siblings the teachers have in total.

The students: (1 x 4) = 4 + (2 x 7) = 18 + (3 x 5) = 33 + (4 x 2) = 41. The students have a total of 41 siblings.

The teachers: (1 x 3) = 3 + (2 x 2) = 7 + (3 x 4) = 19 + (4 x 5) = 39 + (5 x 3) = 54 + (6 x 1) = 60 + (8 x 1) = 68. The teachers have a total of 68 siblings.

Now that we have this information, we know that the answer is option 1, the students tend to have fewer siblings than the teachers. This is because the students had a total of 41 siblings and the teachers had a total of 68 siblings, and 41 is less than 68 so the students have fewer siblings than the teachers.

I really hope I could help! I put a lot of work into this answer! :D

QT = 36

Step-by-step explanation:

Step 1 :

Lines RT and SV are the diagonals of the parallelogram RSTV.

Step 2 :

The diagonals of a parallelogram bisect each other . (Properties of a parallelogram)

Step 3 :

Given that the diagonals RT and SV intersect at Q, we have QT = RQ.

=> 5 x + 1 = 3 x + 15

=> 5 x - 3 x = 15 -1

=> 2 x = 14

= > x = 7

Step 4:

QT = 3 x + 15

=> QT = 3 * 7 + 15

=> QT =  21 + 15 = 36

Applying the properties of the diagonal of a parallelogram, the length of QT = 36 units.

Therefore,

RQ = QT

5x + 1 = 3x + 15

5x - 3x = -1 + 15

2x = 14

x = 7

QT = 3x + 15

QT = 3(7) + 15

QT = 36

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Answer:

The least possible number of coins that Pirate Jack has is 77.

Step-by-step explanation:

i) let the number of coins in the piles for the parrots be x.

ii) therefore we can say that the total number of coins be 7x + 4

iii) let the number of coins in the piles for for the pirates be y.

iv) therefore we can say that the total number of coins be 11y + 4

v) therefore we can say that 7x + 4 = 11y + 4

vi) therefore 7x = 11y

vii) therefore the least possible number of coins that Pirate Jack has is equal to the LCM of 11 and 7 which is 77.

viii) x = 11 and  y = 7

Answer:

158 coins

Step-by-step explanation:

Jack's number has to be an even number, because he can split his gold and silver coins evenly.

77 is the LCM of 11 and 7 and add 4 (the remainder) to get 81.

But it has to be an even number since he can split his coins evenly.

You can then do 77 times 2, and add 4 to get 158, which is the answer.

Answer: 18 months or a year and a half

Step-by-step explanation:

2.5 centimeters every 2 months, so...

1.25 centimeters every month.

22.5 ÷ 1.25 = 18

So it will take 18 months to grow 22.5 centimeters of hair

Answer:

Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt((P^2)/(4 R^10) - (P T)/(R^7))

Step-by-step explanation:

Solve for Q:

T = sqrt((P Q)/R) - Q R^2

T = sqrt((P Q)/R) - Q R^2 is equivalent to sqrt((P Q)/R) - Q R^2 = T:

sqrt((P Q)/R) - Q R^2 = T

Add Q R^2 to both sides:

sqrt((P Q)/R) = Q R^2 + T

Raise both sides to the power of two:

(P Q)/R = (Q R^2 + T)^2

Expand out terms of the right hand side:

(P Q)/R = Q^2 R^4 + 2 Q R^2 T + T^2

Subtract Q^2 R^4 + 2 Q R^2 T + T^2 from both sides:

(P Q)/R - Q^2 R^4 - 2 Q R^2 T - T^2 = 0

Collect in terms of Q:

-Q^2 R^4 - T^2 + Q (P/R - 2 R^2 T) = 0

Divide both sides by -R^4:

Q^2 + T^2/R^4 - (Q (P/R - 2 R^2 T))/R^4 = 0

Subtract T^2/R^4 from both sides:

Q^2 - (Q (P/R - 2 R^2 T))/R^4 = -T^2/R^4

Add (P/R - 2 R^2 T)^2/(4 R^8) to both sides:

Q^2 - (Q (P/R - 2 R^2 T))/R^4 + (P/R - 2 R^2 T)^2/(4 R^8) = (P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4

Write the left hand side as a square:

(Q - (P/R - 2 R^2 T)/(2 R^4))^2 = (P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4

Take the square root of both sides:

Q - (P/R - 2 R^2 T)/(2 R^4) = sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)

Add (P/R - 2 R^2 T)/(2 R^4) to both sides:

Q = (P/R - 2 R^2 T)/(2 R^4) + sqrt(((P/R - 2 R^2 T)^2)/(4 R^8) - (T^2)/(R^4)) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)

(P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4 = P^2/(4 R^10) - (P T)/R^7:

Q = (P/R - 2 R^2 T)/(2 R^4) + sqrt((P^2)/(4 R^10) - (P T)/(R^7)) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)

Add (P/R - 2 R^2 T)/(2 R^4) to both sides:

Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt(((P/R - 2 R^2 T)^2)/(4 R^8) - (T^2)/(R^4))

(P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4 = P^2/(4 R^10) - (P T)/R^7:

Answer: Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt((P^2)/(4 R^10) - (P T)/(R^7))

Angle A and Angle B are identical, so AC and BC are also identical.

ABC = AC

3x -7 =20

Add 7 to both sides:

3x = 27

Divide both sides by 3:

x = 9

Step-by-step explanation:

[tex] \frac{r}{32} = \frac{5}{8} =\frac{30}{t} \\ \\ \therefore \: \frac{r}{32} = \frac{5}{8} \\ \\ \therefore \: r = \frac{32 \times 5}{8} \\ \\\therefore \: r = 4 \times 5\\ \\ \huge \orange{ \boxed{\therefore \: r = 20}} \\ \\ \frac{5}{8} =\frac{30}{t} \\ \\ \therefore \: t = \frac{8 \times 30}{5} \\ \\ \therefore \: t = 8 \times 6 \\ \\ \huge \purple{ \boxed{ \therefore \: t = 48}}[/tex]

Yo sup??

m3 and m6 for a supplementary pair therefore

m3+m6=180

122+m6=180

m6=58

Hope this helps

The required measure of the angle m∠6 is given as 58 degrees. Option B is correct.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
For the bisection of parallel line by transversal line,
Corresponding angles always have an equal measure,
So, ∠2 = ∠6

Now,
∠2 + ∠3 = 180

∠6 + 122 = 180
∠6 = 58°

Thus, the required measure of the angle m∠6 is given as 58 degrees. Option B is correct.

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To calculate the percentage of Zachary's pay that his deductions comprise, divide the total amount of deductions by the total pay, then multiply by 100.

To find out what percent of Zachary's pay his deductions compromise, you need to divide the total amount of deductions by the total amount of his pay, and then multiply by 100 to get the percentage.

Let's use an example. If Zachary's total deductions are $300 and his total pay is $1000, you would do the following calculation:

In this example, Zachary's deductions comprise 30% of his total pay.

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Answer:

30

Step-by-step explanation:

a right angle is 90 degrees so if it split into two parts and one is 30 degrees and the other is x (an unknown) you could do 90-30 to get 60 but since it is 2x but has to equal 60 it is going to be 30 because 30 times 2 is 60

Answer:

The answer is 30

Step-by-step explanation:

hope this helps!

Answer:

32.24 gallons

Step-by-step explanation:

From the question,Jed’s shower head releases

6.2 gallons = 1 minute

x gallon = 5 mins 12 secs

First convert 12 secs to minutes and add it to 5 mins .

1 minute = 60secs

x minute = 12 secs

x = 12/60

= 0.2 mins + 5 mins

= 5.2 mins

Therefore,

6.2 gallons = 1 minute

x gallons = 5.2 mins

Cross multiply

x = 6.2 x 5.2 /1

= 32.24/1

= 32.24 gallons

Answer:288

Step-by-step explanation:32 x 9 = 288

Answer:-18x-24

Step-by-step explanation:Use the PEMDAS method

explanation:-18x-24

Answer:

Step-by-step explanation:

4.75 x [tex]10^{2}[/tex]

Answer:

Step-by-step explanation:

[tex]4.75 x 10^{2}[/tex]

Answer: Its width is 6inches.

Step-by-step explanation:

The given information can be used to construct a right angled triangle. Now applying the Pythagoras theorem,

10^2 = W^2 + 8^2

where w represents the width.

100 = w^2 + 64

100 - 64 = w^2

36 = w^2

find the square root of both sides,

6 = w

Therefore, w = 6 inches

Thus the width of the rectangle is 6 inches.

Answer: B

Step-by-step explanation: you multiply 25 x 13 + 150