Ken and Ivan had some sweets. After Ken gave away 5/7 of his sweet, he had 2/3 as many sweets as Ivan. Ivan then gave away 120 sweets and he had 1/4 as many sweets as Ken. How many sweets did each of them have at first?

Answer:

Step-by-step explanation:

[tex]2x^{99}+3x^{98}+2x^{97}+3x^{96}+.......+2x+3 = [2x^{99}+2x^{97}+...2x]+[3x^{98}+3x^{96}+......3]\\\\=2x*[x^{98}+x^{96}+...+1]+3[x^{98}+x{96}+....1]\\\\= [x^{98}+x^{96}+..+x^{2}.+1](2x+3)\\\\=( [x^{98}+x^{94}+...+x^{2}]+[x^{96}+x^{92}+.......+1])*(2x+3)\\\\=(x^{2}*[x^{96}+x^{92}+.......+1]+[x^{96}+x^{92}+.......+1])*(2x+3)\\\\=[x^{96}+x^{92}+.......+1](x^{2}+1)(2x+3)[/tex]

Answer:

x = 5/2

Step-by-step explanation:

4x-2 = 8

Add 2 to each side

4x-2+2 = 8+2

4x = 10

Divide by 4

4x/4 =10/4

x = 5/2

Answer:

x = 2.5

Step-by-step explanation:

4x - 2 = 8

4x = 8+2

4x = 10

x = 10/4

x = 2.5

Answer:

Step-by-step explanation:

the second number be 2x. Therefore, the number 80 is divided in the ratio of 3:2 is, 48 and 32.

Answer:

125 people

Step-by-step explanation:

P( green) = number of green / total

                = 25/120

                 =5/24

Multiply this probability by 600

5/24 * 600 =125

Answer:

out of 120 people 25 people has chosen green

out of 1 people green will be chosen by 25/120 people

out of 600 people green colour will be chosen by( 25/120)×600 people =25×5=people

[tex]\longrightarrow{\green{D.\:(x²+5)(x-3)}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] {x}^{3} - 3 {x}^{2} + 5x - 15[/tex]

Taking [tex]x²[/tex] as common from first two terms and 5 from last two terms, we have

[tex]➝ \: {x}^{2} \: (x - 3) + 5 \: (x - 3)[/tex]

Taking the factor [tex](x-3)[/tex] as common,

[tex]➝ \: ( {x}^{2} + 5)(x - 3)[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]

Answer:

y = -5/6x + 6

Step-by-step explanation:

Slope intercept form is: y = mx + b

- where m is the slope

- where b is the y-intercept.

The problem already gives you the slope and y-intercept, so all you have to do is put it in for m and b respectively. Therefore, we have:

y = -5/6x + 6

Answer:

[tex]y = - \frac{5x}{6} + 6[/tex]

Step-by-step explanation:

1: Formulate equations/expressions:

[tex]based \: on \: the \: given \: conditions \: formulate[/tex]

[tex]m = - \frac{5}{6} \\ b = 6[/tex]

2: Write the equation:

[tex]write \: the \: equation \: of \: linear \: function[/tex]

[tex]y = mx + b[/tex]

3: substitute:

[tex]y = mx + b \\ m = - \frac{5}{6} \: b = 6 \\ y = - \frac{5}{6} x + 6[/tex]

4: rewrite the equation:

[tex]y = - \frac{5}{6} x + 6 \\ slope - intercept \: form \\ fin \: the \: required \: form: \\ y = - \frac{5x}{6} + 6[/tex]

Answer:

I think y=,48x+2 is correct

The equation y = 2x - 48 represents y, the profit earned by the hot dog stand for x hot dogs sold. Hence, 3rd option is the right choice.

Equations are relations between two equal expressions, usually used to find the values of unknown variables using the constants and the values of other variables (if any).

In the question, we are informed that the profit earned by a hot dog stand is a linear function.

We are also informed that it costs the owner $48 each morning for the day's supply and that he earns $2 profit on each hot dog he sells.

We are asked to find the equation of profit y, for the number of hot dogs sold x.

The basic cost to the owner is $48. This will be his fixed cost, irrespective of the number of hot dogs he sells.

His profit on one hot dog is $2. So, his profit on x number of hot dogs sold will be $2x.

His total profit will be equal to the profits he earned by selling x hot dogs minus the basic cost he needs to pay.

∴ Profit earned = Profit on x hot dogs - Basic cost

or, y = 2x - 48.

∴ The equation y = 2x - 48 represents y, the profit earned by the hot dog stand for x hot dogs sold. Hence, 3rd option is the right choice.

Learn more about equations at

https://brainly.com/question/21405634

#SPJ2

Answer:

C

Step-by-step explanation:

CCCCCCCCCCC

Answer:

y= 4x-7

Step-by-step explanation:

I could be wrong this is what I got so I apologize if this is incorrect

Answer:

It does since lets say X and Y equal 10 it works

Step-by-step explanation:

Answer:

-4 is the larger integer

Step-by-step explanation:

n = smaller integer

n + 2 = larger integer

4(n+2) = n-10

4n + 8 =  n - 10

3n + 8 = -10

3n = -18

n = -6

n+2 = -4

Answer:

[tex]\frac{47}{2} \to 6[/tex]

[tex]\frac{60}{12} \to 5[/tex]

[tex]\frac{40}{10} \to 4[/tex]

[tex]\frac{56}{8} \to 7[/tex]

[tex]\frac{64}{8} \to 8[/tex]

Step-by-step explanation:

Given

See attachment

Required

Complete the blanks

To do this, we simply carry out the division operation.

So, we have:

[tex]\frac{47}{2} \to 6[/tex]

[tex]\frac{60}{12} \to 5[/tex]

[tex]\frac{40}{10} \to 4[/tex]

[tex]\frac{56}{8} \to 7[/tex]

[tex]\frac{64}{8} \to 8[/tex]

The rates of the given equivalent unit rates are properly matched as follows:

42/7 = 6

60/12 = 5

40/10 = 4

56/8 = 7

64/8 = 8

To find the unit rate, the numerator is divided by the denominator such that the denominator is reduced to 1.

Thus, let's find the unit rates that matches with the equivalent rates given (see attachment below).

Divide the numerators by the denominators such that the value of the denominators are reduced to 1.

Learn more about unit rate on:

https://brainly.com/question/18296886

Answer:

Step-by-step explanation:

Since the triangle is inscribed in a semicircle, then angle x is a right angle. That means that angle y is 180 - 90 - 31, which is 59.

Answer:

3/5

Step-by-step explanation:

[tex]Sin A = \frac{4}{5}=\frac{oppsite side}{hypotenuse}[/tex]

Adjacent side² = hypotenuse² - opposite side²

= 5² - 4²

= 25 - 16

= 9

Adjacent side = √9 = 3

Cos A = [tex]\frac{Adjacent side}{hypotenuse} = \frac{3}{5}[/tex]

Sin = 4/5 = Perpendicular/hypotenuse

CosA = Base/hypotenuse

Base = √hyp. ^- prep.^

Base= 3/5

Answer:

Volume of the cylinder = 250π inch²

Step-by-step explanation:

Surface area of the cylinder is given by,

Surface area = 4πr²

Here, r = radius of the sphere

Since, surface area = 100π square inches

100π = 4πr²

r² = 25

r = 5

From the picture attached,

Height of the cylinder = diameter of the sphere

                                    = 2(r)

                                    = 2(5)

                                    = 10 inches

Volume of the cylinder is given by,

Volume = πr²h

Here, r = radius of the cylinder

h = height of the cylinder

Therefore, Volume of the cylinder = π(5)²(10)

                                                          = 250π square inches

Answer:

a=3

Step-by-step explanation:

Given :

1:a :: 5: 15

To find a

a=15×1/5

a=3

Therefore, value of a =3

Answer:

35x^2-5x^4

Step-by-step explanation:

You have to multiply the numbers on the outside to the numbers on the inside.

For example, 5x^2 times 7 would be 35x^2.

Answer:

I think it's option B ...

Answer:

A.) F(x)=1/x-5

Step-by-step explanation:

Answer:

option 2

in the first equation y is greater than so it would be shaded above the line and in the second equation y is less than so it would be shaded below the line

Step-by-step explanation:

Answer:

Expression

Step-by-step explanation:

Given expression :

4a+3b-6cx9

So this is expression not equation because equation consist zero on the righ side

Example: ax+b=0 (This is equation )

And

ax+b (This is expression)

f(-3)=g(-4) 123456789012345

Answer i think it is 4

Evaluate the Function Evaluate x : − 2 x − 5 , then set it equal to 4 . = 4

Step-by-step explanation:

Answer:

x = - 9/2

Step-by-step explanation:

-2x - 5 = 4

-2x - 5 + 5 = 4 + 5        [add 5 both sides ]

- 2x = 9                        [ -5 + 5 = 0]

[tex]\frac{-2x}{-2} = \frac{9}{-2}\\\\x = \frac{9}{2}[/tex]                      [ divide both sides by - 2 ]

Answer:

The half-life of the substance is of 1600 years.

Step-by-step explanation:

Amount of the substance:

The amount of the substance after t years is given by the following equation:

[tex]C(t) = A(0.999567)^t[/tex]

In which A is the initial amount.

Find the half-life:

This is t for which [tex]C(t) = 0.5A[/tex], that is, the amount is half the initial amount. So

[tex]C(t) = A(0.999567)^t[/tex]

[tex]0.5A = A(0.999567)^t[/tex]

[tex](0.999567)^t = 0.5[/tex]

[tex]\log{(0.999567)^t} = \log{0.5}[/tex]

[tex]t\log{0.999567} = \log{0.5}[/tex]

[tex]t = \frac{\log{0.5}}{\log{0.999567}}[/tex]

[tex]t = 1600[/tex]

The half-life of the substance is of 1600 years.

Answer:

14 - .5d

Step-by-step explanation:

To determine the amount of gas in the tank, take the amount in the tank to start and subtract the amount used per day

14 - .5d

Answer: There are 14 gallons total, and you would be using 0.5 gallons a day, which is expressed by 14 - 0.5d. Example = 8 days, 14 - 0.5(8) = 10 gallons left

Answer:

3

Step-by-step explanation:

x=(5x-13)

so you work that equation out

take the 5x to the side of x and equate it to what you get

x=5x-13

5x+x=13+5

6x = 18 = x=3

6 6

x=3

Answer:

(C).

[tex]height = \sqrt{ {29}^{2} - {21}^{2} } \\ = \sqrt{400} \\ = 20 \: units[/tex]

Answer:

5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

0.3y + y/z

y = 10

z = 5

Step 2: Evaluate

Answer:

The mapping statements (-3,7) -> (-9,10) and (1, -5)-> (-5, -2) describe the same translation.

Step-by-step explanation:

In a translation, we have that:

(x,y) -> (x+a,y+b)

In which a and b are how much the values change.

(6.-9) -> (0,1)

x subtracted by 6, y added by 10. So, the translation rule is:

(x,y) -> (x - 6, y + 10).

(-3,7) -> (-9,10)

x subtracted by 6, y added by 3. So

(x,y) -> (x - 6, y + 3).

(1, -5)-> (-5, -2)

x subtracted by 6, y added by 3. So

(x,y) -> (x - 6, y + 3)

Same rule as the above, so the mapping statements (-3,7) -> (-9,10) and (1, -5)-> (-5, -2) describe the same translation.

(2, 4) -> (-4,1)

x subtracted by 6, y subtracted by 3. So

(x,y) -> (x - 6, y - 3)