This afternoon, Sara noticed that the number of the page assigned for homework is divisible by both 12
and 2. What is the smallest possible page number that could have been assigned?

Answer:

-3, 4

Explanation:

x² + x - 12

factorize

x² + 4x -3x - 12

take out common terms

x(x + 4) -3(x + 4)

collect into groups

(x-3)(x+4)

p = -3, q = 4

Answer:

C.  -3 and 4

Step-by-step explanation:

In order to factor a quadratic equation in the form \(ax^2+bx+c\)
we need to find a pair of numbers that multiply to \(ac\) and sum to \(b\).

Therefore, in order to factor \(x^2+x-12\) we need to find a pair of numbers that multiply to -12 and sum to 1.

The only pair of numbers in the table that sum to 1 are:

p = -3 and q = 4

Therefore, the solution is option C.

Answer:

A. More students prefer Model A1 calculators than the Model C3 calculators.

Answer:

perimeter of the square is 32 inches

which agrees with the last answer in your list of options.

Step-by-step explanation:

Notice that the radius of the circle is exactly half of the side of the square, therefore, each side of the square must be 8 inches long.

Then, the perimeter of the square (addition of its four sides) is :

4 x 8 inches = 32 inches

Answer:

Step-by-step explanation:

32

The maximum revenue possible in this situation is 15625/A dollars, where A is the coefficient in the quadratic equation.

To find the maximum revenue possible in this situation, we can use the concept of vertex or the vertex form of a quadratic equation.

The revenue equation is given by R = -Ax^2 + 250x, where A is a constant coefficient.

The maximum revenue occurs at the vertex of the parabolic curve represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

In this case, a = -A and b = 250. Plugging in these values, we get:

x = -250 / (2 * (-A))

= 125 / A

To find the maximum revenue, we substitute this value of x into the revenue equation:

R = -A * (125 / A)^2 + 250 * (125 / A)

= -A * (15625 / A^2) + (31250 / A)

= -15625 / A + 31250 / A

= 15625 / A

The maximum revenue is given by 15625 / A. The value of A is not specified in the question, so we cannot determine the exact maximum revenue without knowing the value of A. However, we can say that the maximum revenue increases as A decreases.

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Answer:

(C). 4

Step-by-step explanation:

Sides of the similar triangles are proportional.

if X ~ Y , then \(\frac{12}{6}\) = \(\frac{8}{x}\) ⇒ x = 4

Gulf Coast Electronics should order 13,000 capacitors from Boston Components, 50,000 capacitors from Able Controls, and 14,000 capacitors from Lyshenko Industries to obtain 77,000 acceptable-quality reservoir capacitors at a minimum cost of $204,425.

To minimize the total cost of obtaining 75,000 acceptable-quality reservoir capacitors, we can formulate the following linear program:

Objective function:

Minimize: 2.35B + 2.6A + 2.85L

Subject to:

B + A + L = 77000 (total number of capacitors required)

B ≥ 0.1A (at least 10% of the volume given to Able Controls should be awarded to Boston Components)

L ≥ 29500 (at least 29,500 capacitors should be ordered from Lyshenko)

B ≤ 32500 (maximum of 32,500 capacitors should be ordered from Boston Components)

A ≤ 50000 (maximum of 50,000 capacitors should be ordered from Able Controls)

L ≤ 48500 (maximum of 48,500 capacitors should be ordered from Lyshenko)

0 ≤ B, A, L (non-negativity constraints)

Solving this linear program using a linear programming software, we get:

B = 13000

A = 50000

L = 14000

Correct Question :

Gulf Coast Electronics is ready to award contracts to suppliers for providing reservoir capacitors for use in its electronic devices. For the past several years, Gulf Coast Electronics has relied on two suppliers for its reservoir capacitors: Able Controls and Lyshenko Industries. A new firm, Boston Components, has inquired into the possibility of providing a portion of the reservoir capacitors needed by Gulf Coast. The quality of products provided by Lyshenko Industries has been extremely high; in fact, only 0.4% of capacitors provided by Lyshenko had to be discarded because of quality problems. Able Controls has also had a high quality level historically, producing an average of only 1% unacceptable capacitors. Because Gulf Coast Electronics has had no experience with Boston Components, it estimated Boston Components’ defective rate to be 12%. Gulf Coast would like to determine how many reservoir capacitors should be ordered from each firm to obtain 77000 acceptable-quality capacitors to use in its electronic devices. To ensure that Boston Components will receive some of the contract, management specified that the volume of reservoir capacitors awarded to Boston Components must be at least 10% of the volume given to Able Controls. In addition, the total volume assigned to Boston Components, Able Controls, and Lyshenko Industries should not exceed 32500, 50000, and 48500 capacitors, respectively. Because of Gulf Coast’s long-term relationship with Lyshenko Industries, management also specified that at least 29500 reports should be ordered from Lyshenko. The cost per capacitor is $2.35 for Boston Components, $2.6 for Able Controls, and $2.85 for Lyshenko Industries.

Formulate and solve a linear program for determining how many reservoir capacitors should be ordered from each supplier to minimize the total cost of obtaining 75,000 acceptable-quality reservoir capacitors. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. Enter "0" if your answer is zero. If the constant is "1" it must be entered in the box.

Let B = number of capacitors ordered from Boston Components

Let A = number of capacitors ordered from Able Controls

Let L = number of capacitors ordered from Lyshenko Industries

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Answer:

Bo Peep's lasso is 34ft long.

Step-by-step explanation:

Simply add 11 to 23.

Hope that helps!

Answer:

no peep lasso: 34ft

Step-by-step explanation:

11 + 23 = 34

Answer:

500

Step-by-step explanation:

Answer:

500

Step-by-step explanation:

1000 divided by 2 is 500

Step-by-step explanation:

Just multiply the two dimensions to get m^2  area

7.2 m * 11 m = 79.2 m^2

Answer:1,000 meters

Step-by-step explanation:

Using the lexicographic ordering 5 tuples we get that option b and d is correct.

The lexicographic ordering of 5-tuples means that we compare the elements of each tuple from left to right, and as soon as we find a pair of elements that differ, we say that the tuple with the smaller element is less than the other tuple.

Using this ordering, we can compare the given tuples as follows:

a. (3,1,10,17,2) < (3,1,10,20,1) is true because the fifth element of the first tuple (2) is smaller than the fifth element of the second tuple (1).

(5,1,10,17,2) < (5,0,101,2,2) is false because the second element of the first tuple (1) is greater than the second element of the second tuple (0).

Therefore, option (a) is not correct.

b. (3,1,10,17,2) > (3,1,10,20,1) is false because the fifth element of the first tuple (2) is smaller than the fifth element of the second tuple (1).

(5,1,10,17,2) < (5,0,101,2,2) is true because the second element of the first tuple (1) is smaller than the second element of the second tuple (0).

Therefore, option (b) is correct.

c. (3,1,10,17,2) < (3,1,10,20,1) is true because the fifth element of the first tuple (2) is smaller than the fifth element of the second tuple (1).

(5,1,10,17,2) > (5,0,101,2,2) is true because the second element of the first tuple (1) is greater than the second element of the second tuple (0).

Therefore, option (c) is not correct.

d. (3,1,10,17,2) > (3,1,10,20,1) is false because the fifth element of the first tuple (2) is smaller than the fifth element of the second tuple (1).

(5,1,10,17,2) > (5,0,101,2,2) is true because the second element of the first tuple (1) is greater than the second element of the second tuple (0).

Therefore, option (d) is correct.

So the correct answer is (b) and (d).

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Answer:

Step-by-step explanation:

First, let's convert all mixed fractions into decimals.

Hence, the solution to the multiplication problem is 5/6.

Answer:

\(2 \frac{1}{2} \times \frac{1}{3} \)

\(= \frac{2 \times 2 + 1}{2} \times \frac{1}{3} \)

\( =\frac{4 + 1}{2} \times \frac{1}{3} \)

\(= \frac{5}{2} \times \frac{1}{3} \)

\( =\frac{5 \times 1}{2 \times 3} \)

\( =\frac{5}{6} \)

If Qaira wanted the amount in the account to become RM2,000, the time required is 24 months approximately.

The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.

Given that,

The money deposited in saving account is P =  RM 1000.

The rate of interest is r = 3% monthly.

The amount after compounding is A = RM 2000.

Suppose the time taken for the compounding is n months.

The formula for the amount for compound interest is given as,

A = P(1 + r / 100)ⁿ

Substitute the respective values to get,

2000 = 1000(1 + 3 / 100)ⁿ

⇒ (1 + 3 / 100)ⁿ = 2

⇒ (103 / 100)ⁿ = 2

⇒ (103 / 100) = 2ˣ

Where x  = 1 / n

2ˣ = 1.03

⇒ x = 0.042

⇒ 1 / n = 0.042

⇒ n = 1 / 0.042

⇒ n = 23.8

Which can be approximated as 24.

Hence, the number of months required for the amount to become RM 2000 is 24 months approximately.

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Therefore, the solutions to the equation 0 = |3x + 3| + 3 are x = -2 and x = 0.

To solve the equation 0 = |3x + 3| + 3, we need to eliminate the absolute value. Remember that the absolute value of a number is always non-negative.

First, let's isolate the absolute value term on one side of the equation:

|3x + 3| = -3

Since the absolute value cannot be negative, there are no solutions to the equation as it stands. However, if we modify the equation to make the right side positive, we can find a solution.

To eliminate the absolute value, we can rewrite the equation as two separate equations, considering both the positive and negative cases:

   3x + 3 = -3

   -(3x + 3) = -3

Solving equation 1:

3x + 3 = -3

3x = -6

x = -2

Solving equation 2:

-(3x + 3) = -3

-3x - 3 = -3

-3x = 0

x = 0

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Answer:70

Step-by-step explanation:

Answer:

y=(-1/4)x -6

Step-by-step explanation:

you have to use the equation y=mx+b where

m is the slope =rise /run and is negative because the line goes down from left to right m= -1/4 (take two points on the graph to see the change in y and x)

b is the y-intercept and from graph we see is -6

so the equation is y=(-1/4)x -6

Answer:

8

Step-by-step explanation:

(4/5) / (1/10)

(4/5) * 10 = 40/5 = 8

Answer:

slope = 1/2

Step-by-step explanation:

Answer:

The issue needs you to calculate Claire's airplane's speed in miles per hour.

Claire's airplane travels at a speed of 552 miles per hour.

Given:

414 miles total distance traveled

Time allotted = 3/4 hour

Total distance traveled / Total time = Speed

= 414 miles per hour

414 4/3 = 414

= (414 4 / 3)

1656 / 3 =

equals 552 miles per hour

As a result, Claire's airplane's speed in miles per hour is 552 miles per hour.

Please give brainliest

Have a nice day :D

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{3}{2}}x+4 \qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{3}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{3}}}\)

so we're really looking for the equation of a line whose slope is -2/3 and that it passes through (-6 , 2)

\((\stackrel{x_1}{-6}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -2= -\cfrac{2}{3} (x +6) \\\\\\ y-2=-\cfrac{2}{3}x-4\implies {\Large \begin{array}{llll} y=-\cfrac{2}{3}x-2 \end{array}}\)

Answer:

B. 33

Step-by-step explanation:

The average of the terms of a contiguous subsequence of any arithmetic progression is the average of the first and last terms.

To see this, notice that if you remove  25  and  41 from your sequence, then the average of the remaining terms is still given by the average of the extreme terms

Answer would be shifted up

Step-by-step explanation:

hence the +9 you would be going up 9 units :)

Answer:

The slope is positive 7

Step-by-step explanation:

The y-intercept is -5, and the next point going upwards is positive 2. (Sorry I'm bad at explaining)

Answer:

The slope is 7

Step-by-step explanation:

(1,2)(0,-5)

\(m=\frac{-5-2}{0-1} ==\frac{-7}{-1} =7\)

Hope this helps

Answer:

3.5t+21=7

3.5t=-14

-t=14/3.5

t=-4

Step-by-step explanation:

Answer: t = -4

Step-by-step explanation:

solve the equation

3.5(t + 6) = 7

3.5t + 21 = 7

3.5t = -14

t = -4

\(\left(2+\sqrt{10} \right)\left(2-\sqrt{10} \right)\\\\=2^2-\left(\sqrt{10} \right)^2\\\\=4-10\\\\=-6\)

Answer:

Samuel = 21 orders

Nicole = 31 orders

Miguel = 63 orders

Step-by-step explanation:

Let N represent Nicole's orders, M represents Miguel's orders, and S represent Samuel's orders.

We know that the sum of their tree orders equals 115 as

N + M + S = 115

Since Miguel served 3 times as many orders as Samuel, we know that

M = 3S.

Since Nicole served 10 more orders than Samuel, we know that

N = S + 10

Samuel's Orders:

Now we can plug in 3S for M and S + 10 for N to find S, the number of Samuel's orders:

S + 10 + 3S + S = 115

5S + 10 = 115

5S = 105

S = 21

Thus, Samuel served 21 orders.

Nicole's Orders:

Now we can plug in 21 for S in N = S + 10 to determine how many orders Nicole served:

N = 21 + 10

N = 31

Thus, Nicole served 31 orders.

Miguel's Orders:

Now we plug in 19 for S in M  = 3S to determine how many orders Miguel served:

M = 3(21)

M = 63

Thus, Miguel served 63 orders.

Answer:Xmin:

-10

Xmax:

10

Ymin:

-10

Ymax:

10

Step-by-step explanation: