Caesar finished 12 problems in
20 minutes. At that rate, how many problems
can he do in 60 minutes?

Answer:

$222.08

Step-by-step explanation:

To find the original price, divide 193.21 by 0.87:

193.21/0.87

= 222.08

So, the non-markup price was $222.08

There's probably a more efficient way to do it, but the following method works.

First, note that

x² - x - 2 = (x + 1) (x - 2)

Now use synthetic division to divide

a x⁴ + b x³ - x² + 2x + 3

by the two factors above.

Division by x + 1 :

-1   |   a           b               -1                   2                3

…   |               -a          a - b      -a + b + 1      a - b - 3

= = = = = = = = = = = = = = = = = = = = = = = = = = = = =

…   |   a      b - a     a - b - 1      -a + b + 3           a - b

which is to say,

(a x⁴ + b x³ - x² + 2x + 3) / (x + 1)

= a x³ + (b - a) x² + (a - b - 1) x + (-a + b + 3) + (a - b) / (x + 1)

Division by x - 2 :

2   |    a        b - a           a - b - 1          -a + b + 3

…   |                 2a          2a + 2b       6a + 2b - 2

= = = = = = = = = = = = = = = = = = = = = = = = = = =

…   |    a       a + b        3a + b - 1       5a + 3b + 1

meaning,

(a x³ + (b - a) x² + (a - b - 1) x + (-a + b + 3)) / (x - 2)

= a x² + (a + b) x + (3a + b - 1) + (5a + 3b + 1) / (x - 2)

Putting everything together, we have

(a x⁴ + b x³ - x² + 2x + 3) / (x² - x - 2)

= a x² + (a + b) x + (3a + b - 1) + (5a + 3b + 1) / (x - 2) + (a - b) / (x² - x - 2)

Combine the remainder terms:

(5a + 3b + 1) / (x - 2) + (a - b) / (x² - x - 2)

= ((5a + 3b + 1) x + (6a + 2b + 1)) / (x² - x - 2)

We're given that the remainder is 3x + 5, so

5a + 3b + 1 = 3

6a + 2b + 1 = 5

Solve this system for a and b :

5a + 3b = 2

6a + 2b = 4

5a + 3b = 2

3a + b = 2

5a + 3b = 2

-9a - 3b = -6

(5a + 3b) + (-9a - 3b) = 2 + (-6)

-4a = -4

a = 1

5 • 1 + 3b = 2

3b = -3

b = -1

Answer:

A    No Annual Fee

Step-by-step explanation:

Edge 100%

Pappi

Answer:

Step-by-step explanation:

-3x + 7y = -16   (-3)  to eliminate x

-9x + 5y = 16

9x - 21y = 48

      -16y = 64

           y = 64/-16

           y = -4

substitute y= -4 into eq. 1

-3x + 7y = -16

-3x + 7(-4) = -16

-3x = -16 + 28

  x = 12 / -3

  x = -4

check:

-3(-4) + 7(-4) = -16

- 16 = -16 ok

-9x + 5y = 16

-9(-4) + 5(-4) = 16

16 = 16  ok

Answer:

x=44/3, y=4

Step-by-step explanation:

Assuming you have to solve for x and y

-3x+ 7y = -16 (1)

-9x+ 5y =16 (2)

multiply (1) by -3 and add it to (2)

9x-21y=48

-9x+5y=16

Add up and get

-21y+5y=48+16 combine like terms

16y=64 divide both sides by 16 and get

y=4

Substitute y=4 in (1)

-3*x+7*4=-16

28+16=3x

44=3x

x=44/3

Answer:

65 mins

Step-by-step explanation:

I well help anyone because I’m a hero and I well always be one thanks to all of you

Answer:

6.66666666667

Step-by-step explanation:

Answer: 6.66

Step-by-step explanation: because you have to divide 24/3.6

Answer:

x = -4

Step-by-step explanation:

Equation of the Line

It can be written in the slope-intercept form as:

y = mx + b

Where m is the slope of the line and b is the y-intercept.

For horizontal lines, m=0. For slanted lines, m can have any real value.

Vertical lines have an infinite slope and the above equation cannot be used.

Vertical lines have a fixed value for x, thus the equation is:

x = h

If the vertical line goes through the point (-4,1), then its equation is:

x = -4

Answer:

Answer- 432

Step-by-step explanation:

a= 3

b=4

c=12

(2(12) + (3)(4))12

(24 + 12)12

288 +144 = 432

Answer:

4/5

Step-by-step explanation:

Okay, I'm pretty sure about this one! I might be wrong but:

If the number is prime and LESS than 13 (so it can't be 13 either), it's either 2, 3, 5, 7, or 11. Those are 5 numbers in all, and 4 of those are odd. So the fraction would be 4/5!

I might have done this wrong, but I hope it helps!! Have a nice day c:

Answer:

g= -4 is correct answer

Answer:

The scale model giraffe is 5 inches tall.

Step-by-step explanation:

To determine the size of the giraffe sculpted by the artist, knowing that it has been built on a scale of 1 inch for every 4 feet, and knowing that the real giraffe in the zoo is 20 feet, the following calculation must be performed:

20 feet / 4 inches = X

5 = X

Therefore, the size of the giraffe sculpted to scale by the artist is 5 inches.

Answer:

Step-by-step explanation:

Answer:

2 is GCF

Step-by-step explanation:

The greatest common factor of 72 and 34 is 2

What is greatest common factor ?

GCF means Greatest Common Factor.

By one examples we can understand this concept more easily.

We are taking four numbers 20,50,70,100.

By prime factorisation,

[tex]20 = 2 \times 2 \times 5 \\ 50 = 2 \times 5 \times 5 \\ 70 = 2 \times 5 \times 7 \\ 100 = 2 \times 2 \times 5 \times 5[/tex]

Here greatest common factor of 20,50,70 and 100 is [tex](2 \times 5) = 10[/tex]

So,GCF of 20,50,70 and 100 is 10.

Here numbers are 72 and 34

By prime factorisation,

[tex]72 = 2 \times 2 \times 2 \times 3 \times 3 \\ 34 = 2 \times 17[/tex]

So, greatest common factor of 72 and 34 is 2

So,GCF of 72 and 34 is 2

Greatest common factor related one more question:

https://brainly.com/question/11444998

#SPJ2

angle 1 - 78

angle 2- 102

angle 3- 78

angle 4- 102

angle 5- 38

angle 6- 142

angle 8- 142

angle 9- 78

angle 11- 78

angle 12- 102

angle 13- 38

angle 14- 142

angle 15- 38

angle 16- 142

Answer:

Step-by-step explanation:

24^2 + b^2 = 40^2

576 + b^2 = 1600

b^2 = 1024

b = 32

32

Step-by-step explanation:

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

a= 24 , b= b , c=40

In order to find b, you have to change the equation a bit. Your new equation will look like [tex] {c}^{2} - {a}^{2} = {b}^{2} [/tex]

here is the step by step now

[tex] {40}^{2} - {24}^{2} = {b}^{2} [/tex]

[tex] {1600} - {576} = {b}^{2} [/tex]

[tex] {1024} = {b}^{2} [/tex]

**now you need to take the square root of both sides and you get 32**

Answer:

[tex]Probability = 0.30[/tex]

Step-by-step explanation:

Given

Represent Black with B and White with W

[tex]B = 14[/tex]

[tex]W = 6[/tex]

Required

Probability of the second selection being white

This means that: The first selection could be white or black but the second must be white.

This probability would be represented as thus:

[tex]Probability = (P(W)\ and\ P(W))\ or\ (P(B)\ and\ P(W))[/tex]

And it is calculated as:

[tex]Probability = (\frac{n(W)}{Total} * \frac{n(W)-1}{Total - 1}) + (\frac{n(B)}{Total} * \frac{n(W)}{Total - 1})[/tex]

Notice that, the second selection has total -1 has its denominator. This is so because, the first selection was made without replacement

So, the formula becomes

[tex]Probability = (\frac{6}{20} * \frac{6-1}{20- 1}) + (\frac{14}{20} * \frac{6}{20- 1})[/tex]

[tex]Probability = (\frac{6}{20} * \frac{5}{19}) + (\frac{14}{20} * \frac{6}{19})[/tex]

[tex]Probability = \frac{30}{380}+ \frac{84}{380}[/tex]

[tex]Probability = \frac{30 + 84}{380}[/tex]

[tex]Probability = \frac{114}{380}[/tex]

[tex]Probability = 0.30[/tex]

The probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball is 0.33.

Given :

The formula given below can be used in order to determine the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball.

[tex]\rm P = \left(\dfrac{n(W)}{Total}\times \dfrac{n(W)-1}{Total-1}\right)+ \left(\dfrac{n(B)}{Total}\times \dfrac{n(W)}{Total-1}\right)[/tex]

Now, substitute the values of known terms in the above formula.

[tex]\rm P = \left(\dfrac{6}{20}\times \dfrac{6-1}{20-1}\right)+ \left(\dfrac{14}{20}\times \dfrac{6}{20-1}\right)[/tex]

Simplify the above expression.

[tex]\rm P = \dfrac{30}{380}+\dfrac{84}{380}[/tex]

[tex]\rm P =\dfrac{114}{380}[/tex]

P = 0.33

So, the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball is 0.33.

Therefore, the correct option is a).

For more information, refer to the link given below:

https://brainly.com/question/23044118

Answer:

2x+9=-17

Step-by-step explanation:

hopefully this helps :)

Answer: I’m not sure what the number is but it’s a negative number, probably somewhere around 26. Take 9 from it and you will get 17.

Step-by-step explanation:

Answer:

2 goes to a type of ratio that compares two different kinds of quantities or numbers

Step-by-step explanation:

a type of ratio that compares two different kinds of quantities or numbers

Answer:

There are 16 winning tickets and 64 losing tickets

Step-by-step explanation:

Total no of tickets in a bag = 80

The ratio of winning tickets to losing tickets is 2:8.

Let there are 2x winning tickets and 8x losing tickets.

ATQ,

2x+8x=80

10x=80

x = 8

Winning tickets = 2x = 2(8) = 16

Losing tickets = 8x = 8(8) = 64

Hence, there are 16 winning tickets and 64 losing tickets.

Answer:

B: k = 12.1

C: k = 13.0

D: k = 19.9 ARE THE CORRECT ANSWERS

Step-by-step explanation:

Answer:B: k = 12.1

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The answer would be D

Answer:

1,2,3

Step-by-step explanation:

you cant let them be equal its an inequality

Answer:

5.004493

Step-by-step explanation:

Answer:

2.27 kg is about 5 pounds.

Step-by-step explanation:

1 kilogram = 2.2 pounds

So, we have to multiply 2.2 by the amount of kilograms, which in this case, is 2.27.

2.27 x 2.2 = 4.994 or 5 when rounded to the nearest whole number.

Therefore, 2.27 kg = 5 lbs

Hope this helps! :)

Answer: 2

Step-by-step explanation:

3/5 of 30 = 18(AL)

2/6 of 30 = 10 (ML)

18+10 = 28 (AL+ ML)

the remainder

30-28 = 2 (CL)

Answer:

one pencil cost  $0.15

Step-by-step explanation:

Answer:

Right angled triangle

Step-by-step explanation:

Longest side = hypotenuse = 26

26² = 676

24² + 10² = 576+ 100

               = 676

               = hypotenuse²

As Pythagorean rule is satisfied, this makes an right angled triangle

Answer:

After solving the pair of simultaneous equations we get x=5 and y=1. Solution Set = {5,1}

Step-by-step explanation:

We need to solve the pair of simultaneous equations

[tex]0.6x-4y=-1\\0.8x-3.5y=0.5[/tex]

We can solve using substitution method.

Let:

[tex]0.6x-4y=-1--eq(1)\\0.8x-3.5y=0.5--eq(2)[/tex]

Find value of x from eq(1) and put it in eq(2)

[tex]From \ eq(1):\\0.6x-4y=-1\\0.6x=-1+4y\\x=\frac{-1+4y}{0.6}[/tex]

Putting in equation 2

[tex]0.8x -3.5y =0.5\\0.8(\frac{-1+4y}{0.6})-3.5y=0.5\\1.33(-1+4y)-3.5y=0.5\\-1.33+5.32y-3.5y=0.5\\-1.33+1.82y=0.5\\1.82y=0.5+1.33\\1.82y=1.83\\y=\frac{1.83}{1.82}\\y=1.00[/tex]

So, we get value of y= 1.00

Now finding value of x by putting value of y in eq(1)

[tex]x=\frac{-1+4y}{0.6}\\x= \frac{-1+4(1.00)}{0.6}\\x=\frac{3}{0.6}\\x=5[/tex]

We get value of x = 5

So, After solving the pair of simultaneous equations we get x=5 and y=1. Solution Set = {5,1}