Peyton and her children went into a restaurant and where they sell drinks for $3 each
and tacos for $4 each. Peyton has $40 to spend and must buy at least 10 drinks and
tacos altogether. If Peyton decided to buy 4 drinks, determine all possible values for
the number of tacos that she could buy. Your answer should be a comma separated
list of values. If there are no possible solutions, submit an empty answer.

Answer:

If you want to use the Rational Zeros Theorem, as instructed, you need to use synthetic division to find zeros until you get a quadratic remainder.

P: ±1, ±2, ±3, ±6  (all prime factors of constant term)

Q: ±1, ±7              (all prime factors of the leading coefficient)

P/Q: ±1, ±2, ±3, ±6, ±1/7, ±2/7, ±3/7, ±6/7  (all possible values of P/Q)

Now, start testing your values of P/Q in your polynomial:

f(x)=7x4-9x3-41x2+13x+6

You can tell f(1) and f(-1) are not zeros since they're not = 0Now try f(2) and f(-2):

f(2)=7(16)-9(8)-41(4)+13(2)+6

       112-72-164+26+6 ≠ 0

f(-2)=7(16)-9(-8)-41(4)+13(-2)+6

       112+72-164-26+6 = 0  OK!! There is a zero at x=-2

This means (x+2) is a factor of the polynomial.

Now, do synthetic division to find the polynomial that results from

(7x4-9x3-41x2+13x+6)÷(x+2):

-2⊥ 7   -9   -41    13     6

         -14   46   -10    -6          

      7  -23   5       3     0     The remainder is 0, as expected

The quotient is a polynomial of degree 3:

7x3-23x2+5x+3

Now, continue testing the P/Q values with this new polynomial.  Try f(3):

f(3)=7(27)-23(9)+5(3)+3

      189-207+15+3 = 0  OK!!  we found another zero at x=3

Now, another synthetic division:

3⊥ 7   -23    5     3

          21   -6   -3_

    7    -2    -1    0  

The quotient is a quadratic polynomial:

7x2-2x-1  This is not factorable, you need to apply the quadratic formula to find the 3rd and 4th zeros:

x= (1±2√2)÷7

The polynomial has 4 zeros at x=-2, 3, (1±2√2)÷7

Step-by-step explanation:

Answer:

SAS postulate says that if two sides and the included angle of a triangle are equal to two sides and the included angle of another triangle, then the two triangles are said to be congruent.

Answer:

No

Step-by-step explanation:

when checking to see if a point satisfies a system of equations

plug in x and y values from your point into the system

(2, 10)

x y

-3(2) - 4(10) = 4. and. -5.2 + 10 = 2

-6-40 = 4. 4.8. = 2

-46 = 4.

invalid statement. invalid statement

therefore the point (2, 10) does not satisfy this system of equations.

answer:

p = 6

1. pull out like factors

7p - 42  =   7 • (p - 6)

2. solve it

7=0

this equation can't be solved, therefore has no solution.

Answer:

21

Step-by-step explanation:

The reason why the answer is 21 is because a minus with minus makes a positive.

-2 - -17 - -6

-2 + 17 + 6

15 + 6

= 21

Answer:

wat

Step-by-step explanation:

Answer:

To what exactly...?

Step-by-step explanation:

20s + 3m = 73

5s + 17m = 197

Eliminate s terms: Multiply second equation by -4, then add to first equation:

-20s - 68m = -788

 20s + 3m = 73

—————————-

-65m = -715

m = (-715)/(-65) = 11

20s + 3(11) = 73

20s = 40

s = 2

A movie download costs $11. A song download costs $2

Answer:

They walk 9 laps

Step-by-step explanation:

If the run for 6 laps you need to multiply how many times they walked when they ran for 2 laps by 3 (3*3) which should give you 9

Answer:

5

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

The only viable solutions for the given condition are (4.5, 1.35) and (8, 2.40).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Since the fee is charged at a rate of $0.30 per day, if a book is x days late, the total fee charged would be y = 0.30x.

We can check each ordered pair given to see if it satisfies this equation:

For (-3,-0.90), y = 0.30x = 0.30(-3) = -0.90.

This satisfies the equation, but the fee cannot be negative, so this is not a viable solution.

For (-2.5, -0.75), y = 0.30x = 0.30(-2.5) = -0.75.

Again, this satisfies the equation but the fee cannot be negative, so this is also not a viable solution.

For (4.5, 1.35), y = 0.30x = 0.30(4.5) = 1.35.

This satisfies the equation and the fee is positive, so this is a viable solution.

For (8, 2.40), y = 0.30x = 0.30(8) = 2.40.

This satisfies the equation and the fee is positive, so this is also a viable solution.

Therefore, the viable solutions are (4.5, 1.35) and (8, 2.40).

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ7

Answer:

- 8/3

Step-by-step explanation:

Simply subtract 4 from 4/3

4/3 - 4 = 4/3-12/3=-8/3

Lets check of our answer is correct:

4 - 8/3 = 12/3 - 8/3 = 4/3. So our answer is correct.

Answer:

8x-16

Step-by-step explanation:

multiple the 4 and the -2 by everything in the parentheses beside them then add them together to simplify

Answer:

I can not see it well

Step-by-step explanation:

i don't see what your asking but thanxs for the points

i'll give you free point about 40 just look asap because people may snag it

Answer:

so i hope im understanding this. for every 1 bouqet there is 4 roses 6 white carnations so the amount of roses in total you will need for the 4 bouques is 16 and the amount of carnations is 24

Step-by-step explanation:

1 b= 4r an 6c   r= roses c=carnations

sooo                        4+4+4+4=16      6+6+6+6= 24

1b= 4r 6c

1b= 4r 6c

1b= 4r 6c

1b= 4r 6c

Answer:

Step-by-step explanation:

Interest in 1 year:

Interest in 5 years:

The difference between 1-year interest and 5-year interest:

Answer:

Step-by-step explanation:

To calculate the missing sides square the  side length of the legs of the  triangles(  the lines that form a 90 degree angle) then add them together, then take the sqr root of that to find the hypotunse( the slanted side). In simplier terms, here how it look.

[tex]a^{2}+b^{2} =c^{2}[/tex]

where a and b are the legs, and c is the hypotunese.   For example, Ill do 3. The bases are 22, and 11 so plug them in the equations.

[tex]a^{2}+b^{2} =c^{2}[/tex]

11^2+22^2=c^2

121+484=c^2

605=c^2

c=about 24.6

Answer:

Emergency Fund

Step-by-step explanation:

Isabel has setup fund for her emergency needs. She has started saving with named as emergency fund so that she can use her savings when she is in severe needs. Isabel has saved money and then she is now saving her money in saving accounts in the bank.

The correct answer is,

[tex] \frac{1}{64} [/tex]

Answer:

1/64

Step-by-step explanation:

when exponents are separated by parentheses, multiply them

so (2³)^-2 = 2^-6

whenever an exponent is negative, change into fraction form with one as the numerator and the other term goes into the denominator and the exponent now becomes positive

2^-6 = [tex]\frac{1}{2^6}[/tex] = [tex]\frac{1}{64}[/tex]

Answer:

The answer is 2592 ft squared

Step-by-step explanation:

Brainliest?

Answer:

The answer is 2592:)

Step-by-step explanation:

Answer:

488.4 cm²

Step-by-step explanation:

Area of cling film needed = surface area of the triangular prism = 2(B.A) + P×H

Where,

B.A = triangular base area = ½*base*height

height = 10.5 cm

base = √(13.7² - 10.5²) = √77.44 = 8.8 cm

B.A = ½*8.8*10.5 = 46.2 cm²

P = perimeter of the triangular base = 10.5 + 13.7 + 8.8 = 33

H = height of prism = 12 cm

Surface area of triangular prism = 2(46.2) + 33*12

= 92.4 + 396

= 488.4 cm²

Answer:

mk 50- (7.50x2)

50-15=35

then 1.50 can be shoved in 35.00

a)23

it will only go up to 34.5

Step-by-step explanation:

sorry your answer is a)23

Answer:

1000÷11=90.9

So,29th September

Answer:

Step-by-step explanation:

A)5200*54/12*7.36/100=5440.44

b)5200+5440.4410,640.44

Answer:

a. $1722.24 b. $6922.24

Step-by-step explanation:

for a: 5200*0.0736*54/12= 1722.24

for b: 1722.24+5200= 6922.24

Answer:

[tex]Expression = x + 18x\%[/tex]

[tex]Expression = 1.18x[/tex]

Step-by-step explanation:

Given

Represent their goal with x

Additional = 18%

Required

Write two expressions to describe the total percentage

The expression is derived using:

[tex]Expression = Goal + Additional[/tex]

This gives:

[tex]Expression = x + 18\% * x[/tex]

[tex]Expression = x + 18x\%[/tex]

Solving further (Express percentage as decimal)

[tex]Expression = x + 0.18x[/tex]

[tex]Expression = 1.18x[/tex]

Answer:

5: 40.6

6: 26.57

7: 22.21

8: 66.35

Step-by-step explanation:

I am going to assume that you know

SOH CAH TOA (if you don't just ask)

For 5: we have the adjacent and opposite side, we need the angle

I think here it's easiest to use TOA

so we have

tanx=60/70

take the arctan or tan^-1 and get

arctan(60/70)=x x= 40.6

For number 6 it's just the same deal

tanx=10/20

arctan(10/20) =x =26.57

For number 7 we have the adjacent side and we need to find the oppsoite side

for this I will once again use TOA

tan(48)=x/20

20tan(48)=x=22.21

For number 8 it's the same deal as 7

tan53=x/50

50tan53=x=66.35

Answer:

88.50

Step-by-step explanation:

59 divided by 2 (50%) = 29.50

59+29.50=88.50