Gerry is a restaurant manager and plans to advertise her restaurant. The advertising budget is $5000, and she plans to run television and online ads. She would like to run at least 5 television ads and 10 online ads. A television ad costs $500 and an online ad costs $150. Let x represent the number of television ads and y represent the number of online ads. Two of the constraints for this situation are x≥5 and y≥10 . What is the other constraint for this situation?

Answers

Answer 1

We are given the two constraints:

x ≥ 5 and y ≥ 10

 

Now the other constraint must of course be based on the sum of the two. It was given that the budget is $5000 so the sum must be greater than that, that is:

 

500 x + 150 y ≤ 5000


Related Questions

A long piece of wood of length 2.0 m is broken into 4 pieces with two pieces of length a and the other two pieces of length
b. the four pieces are put together to form a rectangle. find b if your aim is to have a rectangle with the maximum area.

Answers

Best Answer: 2a+2b=4 a+b=2 a=2-b Let area of the rectangle is A so A=a*b A=(2-b)b A=2b-b^2 taking derivative of both sides of above equation with respect to b we get, dA/db=2-2b for maximum A dA/db=0 2-2b=0 b=1 so, b=1 meter

The value of b is 0.5 m if your aim is to have a rectangle with the maximum area.

What is the area of the rectangle?

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.

It is given that:

A long piece of wood of length 2.0 m is broken into 4 pieces with two pieces of length a and the other two pieces of length b.

Total wooden length:

2a + 2b = 2

a + b = 1

Area = ab  

A = a(1 - a)

dA/da = 0

1 - 2a = 0

a = 0.5 m

b = 0.5 m

Thus, the value of b is 0.5 m if your aim is to have a rectangle with the maximum area.

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What is the value of x?
Enter your answer in the box.

Answers

Answer:

x = 9 and y = 5

Step-by-step explanation:

From the given figure :

In ΔLNM ,

LN = NM = LM

This shows that all the sides of the triangle are given to be equal.

And the triangle whose all sides are equal is called equilateral triangle and in an equilateral triangle the measure of its each angle is 60°

⇒ ∠L = ∠N = ∠M = 60°

Now, ∠N = 60°

⇒ 7x - 3 = 60

⇒ 7x = 63

⇒ x = 9

Also, ∠M = 60°

⇒ 11y + 5 = 60

⇒ 11y = 55

⇒ y = 5

Answer: x=9

Step-by-step explanation:

i did the test and got it right lol

You have a $50 bill. you and your friend ordered two cheeseburgers for $4.25 each, two fries for $1.28 each, and two colas for $1.98 each. including 4% sales tax and 15% tip, what is the change you will receive from $50?

Answers

Answer: 32.13

Step-by-step explanation:

Answer:

The answer is:  $32.13

When you are finding the slope of a line using two points, it doesn't matter which point you choose to be (x1,y1) and which point you choose to be (x2,y2)?

Answers

Typically if it is a linear function then it doesn't matter. However if it is a quadratic, cubic, and so on and so forth....([tex] x^{2},x^{3},x^{4} [/tex]) you may want to used the distance formula if you are not given any other points (with the exception of the vertex, asymptote or roots... etc).

The correct scientific notation for the number 0.00050210 is:

Answers


5.0210 × 10-4





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Final answer:

The correct scientific notation for the number 0.00050210 is 5.0210 x 10^(-4).

Explanation:

The correct scientific notation for the number 0.00050210 is 5.0210 x 10-4. In scientific notation, the decimal point is moved to the right, and the number is multiplied by a power of 10. The exponent indicates how many places the decimal point was moved.

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What are the roots of the quadratic equation 0 = 2x^2 + 12x –14?

2, 12, –14
–7, 1
–1, 7
1, 6, –7
Can you explain what it is wanting or asking?

Answers

It is basically asking you to find where the equation crosses the d-axis. 2x^2 + 12x -14 = (x-1)(2x-14). x-1=0. x=1. 2x-14=0. 2x=14. x=7. The solution/roots/zeros would be 1 and 7

Answer:

-7, 1

Step-by-step explanation:

Given quadratic equation,

[tex]2x^2+12x-14=0[/tex]

By middle term splitting,

[tex]2x^2+(14-2)x-14=0[/tex]

[tex]2x^2+14x-2x-14=0[/tex]

[tex]2x(x+7)-2(x+7)=0[/tex]

[tex](2x-2)(x+7)=0[/tex]

By the zero product property,

[tex]2x-2=0\text{ or }x+7=0[/tex]

[tex]\implies x=1\text{ or }x=-7[/tex]

Hence, the roots of the given equation are -7 and 1.

Second option is correct.

One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 9 hours. how long will it take the pipe to fill the pool if the drain is left open?

Answers

inlet pipe can fill the pool in 6 hours, means: every hour the pool is filled 1/6 
a drain can empty the pool in 9 hours, means: every hour the pool is drained 1/9
If the inlet and the drain are both left open, every hour the pool is filled 1/6-1/9=1/18
It will take 18 hours to fill up the pool.

There are 5 red marbles four blue marbles and three yellow marbles in a bag what is the probability of a blue marble being randomly chosen

Answers

total number of marbles : 12
amount of blue marbles : 4

4/12 = 1/3 or 33%

the probability of choosing a blue marble 1/3 or 33%

Evaluate -8 × |2|.

-10
10
-16
16

Answers

-8 * | 2 | =
-8 * 2 =
-16 <==
Here is your answer:                                                                                                                                                                                                                                                      -8*2=-16                                                                                                                                                                                                                                               Your answer is -16 or C

Mariah has been hired as a receptionist. She is paid a flat rate of $225 each week and earns an additional $11.25 for every hour that she works. If her goal is to make $675 in one week, how many hours must Mariah work? 36 40 60 72

Answers

(675 - 225) / 11.25 = 40
Ans- 40

Hope this helps! good luck!
(675 - 225) / 11.25 = h


40 is your answer

Mr. furley has 27 coins that are all dimes and quarters. the value of the coins is 4.35. how many dimes and how many quarters does mr. furley have

Answers

A) d + q = 27
B) .10d + .25q = 4.35
Multiplying equation A by -.1
-.1d -.1q = -2.7  then adding it to equation B
.1 d + .25q = 4.35 equals
.15q = 1.65
The number of quarters = 11
putting 11 quarters into equation A
d + 11 = 27
dimes = 16





The original price of the DVD is nine dollars the sale price is 80% of the price what is the sale price of the DVD?

Answers

multiply $9 by 80%

80% = 0.80

9 * 0.8 = 7.20

 subtract that from original price

9 - 7.20 = 1.80

 Sale price is $1.80

Let's rewrite the information then figure out the answer. 

DVD: $9.00 originally but on sale with an 80% discount. 
80%=0.80
9.00(0.80) = $7.20
$9.00 - $7.20 = $1.80

Thus, the sales price is: $1.80

If a+bi is a zero of a function and the coefficients of the polynomial are real, what will be the other complex zero of the function?

1. -a + bi

2. a - bi

3. -a - bi

4. a

Answers

the conjugate of a binomial is simply the same binomial with a different sign in the middle, so the conjugate of x + y, is just x - y, and the conjugate of w - z is just w + z and so on.

now, complex roots never come all by their lonesome, her sister, the conjugate, is always along with her, so if the root a + bi is there, then her sister a - bi is also there too.

The surface area of a cone is given by the formula
S = πl + πr2. Solve the formula for l.

Answers

Start my moving terms to one side of the equation to isolate the term with 'l' in it.

(pi)(l)=S- (pi)(r^2)

Then divide to get the 'l' term alone.

l = (S/(pi)) - r^2

Answer:

l = (S - πr²) / π

Step-by-step explanation:

The problem gives us the formula for the surface area of a cone S, we will solve the formula for l.

The formula is

S = πl + πr²

If we take the πr² to the other side, we get:

S - πr² = πl

Now we divide by π, and we get:

(S - πr²) / π = l

Therefore solving for l, we get that

l = (S - πr²) / π.

Calculate δe, if q= 0.769 kj and w= -860 j .

Answers

Final answer:

The change in internal energy (δe) of the system, calculated using the first law of thermodynamics, and considering that the heat and work quantities are converted to the same unit, is 1629 J.

Explanation:

The query you've presented seems to be about the first law of thermodynamics, which states that the change in internal energy (ΔE or in your notation, δe) of a system is equal to the heat (q) added to the system minus the work (w) done by the system. Both heat and work quantities need to be in the same units for this calculation, whereas your values are given in different units: kJ for heat and J for work. To facilitate this calculation, let's first convert the heat quantity from kJ to J (1 kJ equals 1000 J).

So, q = 0.769 kJ = 0.769 * 1000 J = 769 J.

Given, w = -860 J.

Now, according to the first law of thermodynamics, δe = q - w.

Substituting the given values, we get δe = 769 J - (-860 J) = 769 J + 860 J = 1629 J.

Therefore, the change in internal energy, δe, is 1629 J.

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Find the GCF of the following monomials.
-50m⁴ n⁷ and 40m² n¹⁰

Answers

Greetings!

We can factor this expression/ the GCF is:
[tex]-10m^2n^7[/tex]

[tex](-10m^2n^7)(5m^2-4n^3)[/tex]

Hope this helps.
-Benjamin

Answer:  [tex]10\ m^2\ n^7[/tex]

Step-by-step explanation:

The given monomials : [tex]-50m^4n^7\text{ and }40 m^2 n^{10}[/tex]

The prime factorization of coefficients :-

[tex]50=5\times5\times2\\\\40=5\times2\times2[/tex]

GCF(50, 40)=[tex]2\times5=10[/tex]

The greatest common degree of m is 2

The greatest common degree of n is 7

So , the GCF of the given monomilas will be :-

[tex]10\ m^2\ n^7[/tex]

You need to strengthen a 19% alcohol solution with pure alcohol solution to obtain 40% solution. How much pure alcohol should you add to 100 milliliters of the 19% solution.

Can anyone solve this problem???

Answers

Let x be the number of mm of pure alcohol to be added:

I will add the mm to express the volume in mm
100mm.(19%) + (100%).x mL = (100 mL+x mL).(40%).
Now right again without the %
100.(0.19) + x.(1) = (100+x).(0.4)

19 + x = = 40 + 04x
x - 0.4x = 40 - 19
0.6 x = 21
x = 21/0.6  and x = 35 mL. This te quantity of pure alcohol should to be added to get a solution at 40%.



How many ways can six friends be arranged around a circular dinner table?

Answers

A question such as this one is a little tricky since the people seated are not in a straight line. 

For a circular table seating question, (n-1)! formula is used. Without restrictions 5! people can be seated. 

You might be wondering why it is not 6!, this is because the first person will the the 6 person so you are accounting for the same person twice. 

Hope I helped :) 

The mass of the sun is about 2x10^27 metric tons or 2x10^30 kilograms. How many kilograms are in one metric ton

Answers

1 metric ton *2*10^30 kg/ 2*10^27 metric ton=1000 kg

Can I get some help on these please ?

Answers

Q1
Divide each distance by its time to find the speed for each driver.
T: 380 km / 4 hr = 95 km/h
M: 530 km / 5 hr = 106 km/h
Martine's average speed was greater.

Q2
Bronze to aluminum is 25:2
The alloy is bronze plus aluminum, so by adding 25 + 2 you get 27.
Bronze to total is 25:27

25 is 27 as x is to 55

25/27 = x/55

27x = 25 * 55

x = 50.926

Answer: 50.926 kg of bronze

Q3
Manipulative toys to art toys is 30:40
Total toys = 30 + 40 = 70

manipulative toys are 30 out of 70

30/70 * 100 = 42.9%

graph y=4x please i need help

Answers

start from the origin and go over 4

Find the measure of an angle whose measure is 18 degrees less than one-half of the measure of its complement.Find the measure of an angle whose measure is 18 degrees less than one-half of the measure of its complement.

Answers

The measure of the angle in question is 18 degrees, as found by setting up an equation based on the relationship between an angle and its complement, and solving for the angle.

To find the measure of an angle that is 18 degrees less than one-half of the measure of its complement, first let's define the angle as x. Since the angle and its complement add up to 90 degrees, the complement is 90 - x. The given information tells us that x is 18 degrees less than half of its complement. Therefore, we can set up the equation:

x = (1/2)(90 - x) - 18

Doubling both sides gives:

2x = 90 - x - 36

Adding x to both sides and adding 36 to both sides gives:

3x = 54

Dividing by 3, we find that:

x = 18 degrees.

Therefore, the measure of the angle is 18 degrees.

Line segments JK and JL in the xy-coordinate plane both have a common endpoint J (-4,11) and midpoints at M1 (2,16) and M2 (-3,5). What's the distance between M1 and M2?

Answers

distance formula : sqrt ((x2 - x1)^2 + (y2 - y1)^2)
(2,16)...x1 = 2 and y1 = 16
(-3,5)...x2 = -3 and y2 = 5
time to sub and solve
d = sqrt ((-3 - 2)^2 + (5 - 16)^2)
d = sqrt ((-5^2) + (-11^2))
d = sqrt (25 + 121)
d = sqrt 146
d = 12.08 <=

Answer:

12.08 units.    

Step-by-step explanation:

We have been given that line segments JK and JL in the xy-coordinate plane both have a common endpoint J (-4,11) and midpoints at [tex]M_1 (2,16)[/tex] and [tex]M_2 (-3,5)[/tex].

To find the distance between [tex]M_1[/tex] and [tex]M_2[/tex] we will use distance formula.

[tex]\text{Distance}=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]

[tex]x_2[/tex] and [tex]x_1[/tex] are x-coordinates of two points.

[tex]y_2[/tex] and [tex]y_1[/tex] are corresponding y-coordinates of two points.    

Let [tex]M_2[/tex] our first point, then  [tex]x_1=-3[/tex] and  [tex]y_1=5[/tex].

Let [tex]M_1[/tex] will be our second point, then [tex]x_2=2[/tex] and [tex]y_2=16[/tex]  

Upon substituting coordinates of point [tex]M_1[/tex] and [tex]M_2[/tex] in distance formula we will get,    

[tex]\text{Distance}=\sqrt{(2--3)^{2}+(16-5)^{2}}[/tex]

[tex]\text{Distance}=\sqrt{(2+3)^{2}+(11)^{2}}[/tex]

[tex]\text{Distance}=\sqrt{(5)^{2}+(11)^{2}}[/tex]  

[tex]\text{Distance}=\sqrt{25+121}[/tex]

[tex]\text{Distance}=\sqrt{146}[/tex]

[tex]\text{Distance}=12.0830459735945721\approx 12.08[/tex]  

Therefore, distance between [tex]M_1[/tex] and [tex]M_2[/tex] is 12.08 units.

Molly walked 3.45 miles on a hike. Her sister walked 1.23 miles. Her brother walked 0.85 miles. How much farther did Molly walk than her brother and sister combined? 0.38 miles 1.37 miles 2.22 miles 5.53 miles

Answers

1.23+0.85 = 2.08 miles
3.45-2.08= 1.37 miles, which is the answer

The distance walked together, is the sum of their distances.

Molly walked 1.37 miles farther  than her brother and sister

The given parameters are:

[tex]\mathbf{Molly = 3.45\ miles}[/tex]

[tex]\mathbf{Sister = 1.23\ miles}[/tex]

[tex]\mathbf{Brother = 0.85\ miles}[/tex]

The combined distance walked by her brother and her sister is:

[tex]\mathbf{Both = Sister + Brother}[/tex]

Substitute known values

[tex]\mathbf{Both =1.23\ miles + 0.85\ miles}[/tex]

Evaluate like terms

[tex]\mathbf{Both =2.08\ miles}[/tex]

The distance Molly walked farther is calculated as follows:

[tex]\mathbf{Farther = Molly - Both}[/tex]

Substitute known values

[tex]\mathbf{Farther = 3.45\ miles - 2.08\ miles}[/tex]

Evaluate like terms

[tex]\mathbf{Farther = 1.37\ miles}[/tex]

Hence, Molly walked 1.37 miles farther  than her brother and sister combined

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Mary has a total of 23 coins made up of nickels and quarters that made a sum of $3.15. How many more nickels than quarters does she have?
A) 10
B) 3
C) 8
D) 7
E) none of these

Answers

Nickels n
quarters q
I: 3.15=n*0.05+q*0.25
II: n+q=23

isolate n in II:
n+q=23
n=23-q

substitute n in I:
3.15=n*0.05+q*0.25=
3.15=(23-q)*0.05+q*0.25
3.15=(23-q)*(1/20)+(q/4)
3.15=(23/20)-q/20+(q/4)
3.15=1.15-(4*q/20)
2=q/5
10=q

insert q=10 into II:
n+q=23
n+10=23
n=13

so c) 3 more nickels than quarters

1. the temperature in Montreal was -8C in New York the temperature was 11C. How many degrees warmer was the temperature in New York?

2. mike deposited $200 in to his bank account. He then wrote checks for $20 and $30. The he deposited $40 dollars more. Which of the following represents the changes in the value of mike's account?


Answers

1. (11)-(-8)=11+8=19
2.200-(20+30)+(40)=190
1. New York's temperature is greater by 19 degrees. 

add the absolute values |-8| + 11 = 19

2. The change in Mike's value is -10
(or 190, if you need the final value)
he is subtracting 20 + 30 (50)
he is adding +40 to the -50 (-10)

hope this helps!  have a great day.

Please help!!!!!!!!!
does x/x+6 simplify to 1/6 explain why or why not

Answers

No, it does not.

x and x + 6 are both prime and cannot be factored.

There are no common factors to divide out.

x over x + 6 is already simplified.

If you substitute in a value for x, the fraction will not be equal to 1/6.

The expression x/(x+6) does not simplify to 1/6 because there are no common factors in the numerator and denominator that can be canceled out.

The expression x/(x+6) does not simplify to 1/6. To understand this, we need to recognize that simplification involves reducing a fraction to its simplest form by factoring or canceling common factors in the numerator and the denominator.

If x were a factor in both the numerator and the denominator, then we could simplify by canceling out the x's.

However, in the expression x/(x+6), the term x+6 in the denominator cannot be simplified with x in the numerator because they are not factors of each other. They are connected by the addition of 6, which means that there are no common factors to cancel out.

The only way x/(x+6) would simplify to 1/6 is if 'x' were to be somehow removed from the denominator, leaving only the constant 6. But since this is not the case, the fraction cannot be simplified to 1/6. Therefore, the original expression is already at its simplest form unless a specific value is given for x, which may then allow further simplification.

Which does not describe the same situation?

Answers

y=3+6x is the only one that doesn't mach because the graph and the work problem is y=2+6x

Answer:

y = 3+6x

Step-by-step explanation:

Let us substitute x = 0, then we get

y = 3

This is not the case as the graph clearly shows that when x = 3, then y = 2

y = 2+6x

when x = 0 then y = 2 which valid from the graph

Now put x values from the table into the equation

y = 2+6×-1

⇒y = -4

x = 0 already solved

x = 2

y = 2+6×2

⇒y = 14

All the values fit in the equation. So, the bottom two options are valid.

Hence, the first equation is not valid.

The coordinate grid below shows triangle ABC and it's image after translation, triangle A'B'C':

Which of the following completes the rule for this translation, (x,y)>(x+4,__)?

y+4
y+2
y-4
y-2

Answers

y+4 would complete the rule for this translation.

Answer:

First option : y+4

Step-by-step explanation:

Given triangle ABC and a translated triangle A'B'C'.

Coordinates of triangle ABC are

A(-1,-1)

B(-3,-3) and

C(2,-2).

Coordinates of triangle A'B'C' are

A'(3,3)

B'(1,1)

C'(6,2).

Let us check the translation is being applied there.

A(-1,-1)  ---> A'(3,3)

We can see that A(-1,-1)  ----> A'(-1+4, -1+4) to get (3,3).

Therefore, (x,y) ---> (x+4,y+4) rule is being applied there to get the translated triangle A'B'C'.

So, the correct option is first option:

y+4

What z-score values form the boundaries for the middle 60% of a normal distribution?​?

Answers

This would be -0.84  and 0.84
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