If inflation from last year to this year was 2% and a pair of designer jeans sold for $75 last year, what would you expect to pay for them this year?

Option D:

all real numbers

Solution:

Definition of domain:

The domain of the function is the set of all possible

x-values (independent variable).

Definition of range:

The range of a function is the set of all possible resulting values

of y-values (dependent variable).

i.e The range of a function is the resulting y-values we get after substituting all the possible x-values.

Given function: [tex]y=\log_8x[/tex]

Domain of y: (0, ∞) (or) {x | x > 0}

Range of y: (–∞, ∞) (or) {y | y > R}

i.e all real numbers

Option D is the correct answer.

Hence the range of y is all real numbers.

Answer:

  (x, y) = (-8, -3)

Step-by-step explanation:

If all you want is a quick solution, I find a graphing calculator to be very handy. The one used in the attachment shows the solution to be (x, y) = (-8, -3).

_____

You can use one equation to substitute for y in the other equation:

  -3x -27 = 5 +x

  -32 = 4x . . . . . . add 3x-5 to both sides

  -8 = x . . . . . . . . divide by 4

  y = 5 +(-8) = -3 . . . . . use the second equation to find y

The pair of numbers that satisfies both equations is ...

  (x, y) = (-8, -3)

Answer: [tex]49 = 3x + 7[/tex]

Step-by-step explanation:

Let the daughter's age be x and Kendra's age be y , then from the first statement;

[tex]y = 3x + 7[/tex]

Since Kendra's age is 49 , substitute it into the equation , we have

[tex]49 = 3x + 7[/tex]

subtract t from both sides

[tex]49 - 7 = 3x[/tex]

[tex]42 = 3x[/tex]

divide through by 3

[tex]x = 14[/tex]

Therefore : the daughter's age is 14

Answer:

3x+7=49

Step-by-step explanation:

Answer:

y = -1

Step-by-step explanation:

Add 3y to both sides:

2y + 3y + 6 = 1 - 3y + 3y

Simplify:

5y + 6 = 1

Subtract 6 from both sides to isolate the y value:

5y + 6 - 6 = 1 - 6

Simplify:

5y = -5

Divide by 5 on both sides to solve:

5y/5 = -5/5

Simplify:

y = -1

Answer:

m<=-15

Step-by-step explanation:

Answer:

  AC = 18 mm

Step-by-step explanation:

See the attachment for a diagram.

Since length BD = 24 mm, length BO = 12 mm. Then ΔBOC is a right triangle with one leg 12 and hypotenuse 15. The other leg (OC) is given by the Pythagorean theorem:

  OC² +OB² = BC²

  OC = √(BC² -OB²) = √(225 -144) = √81

  OC = 9

Diagonal AC is twice the length of OC, so is ...

  AC = 2·9 = 18 . . . . mm

_____

It can save a little time if you recognize that the given sides of triangle BOC have the ratio 4:5. This suggests you're dealing with a 3:4:5 right triangle, and that side OC is (3/5)·(15 mm) = 9 mm.

The 20th term is -106

15,9,3,-3,-9,-15,-21,-28,-35,-41,-46 (10) -6 x 10 = -60

-60 + -46

-106

You're just subtracting by 6.

Answer:

-99

Step-by-step explanation:

you subtract by 6 every number.....

-3-6=-9

-9-6=-15

so on and so on until you get to the 20th term.....

Answer:

0.57

Step-by-step explanation:

56.30 divided by 1.57=32.21

Answer:

68$

Step-by-step explanation:

cost of 10 book= 10$ * 10= 100$

now,

Remaining money= 168$-100$

                             =68$

Answer:

$68

Step-by-step explanation:

If each of the 10 books costs $10, you must multiply $10 x 10 to get $100. Then, you do $168 - $100 and get $68.

Answer:

B. y = -1/2 (4x + 2)

Step-by-step explanation:

your welcome :) and sorry that I'm a bit late

Answer:

-11

Step-by-step explanation:

To evaluate an expression with variables, replace the variables with what the question tells you to.

Replace "x" with 3. Replace "y" with -2.

-x + 4y

= -(3) + 4(-2)       Multiply 4 and -2 first to get -8

= (-3) + (-8)         Add normally. -3 + (-8) is the same as (-3) - 8.

= -11             Answer

Therefore the solution is -11.

Answer:

3:7.5 = 1:2.5 = 2:5

4:10 = 2:5

5:12.5 = 10:25 = 2:5

6:15 = 2:5

A and D belong to this set:

A: 1:2.5 = 2:5

D: 8:20 = 2:5

Answer:

[tex]x = \frac{3}{5} \times \frac{5}{7}[/tex] and [tex]y = \frac{16}{21} - \frac{1}{3}[/tex]

Step-by-step explanation:

We have to write a multiplication equation and a subtraction equation that both involve a fraction and have the same solution.

Let the multiplication equation be, [tex]x = \frac{3}{5} \times \frac{5}{7}[/tex].

And the subtraction equation is, [tex]y = \frac{16}{21} - \frac{1}{3}[/tex]

Now,  [tex]x = \frac{3}{5} \times \frac{5}{7} = \frac{3}{7}[/tex] and [tex]y = \frac{16}{21} - \frac{1}{3} = \frac{16 - 7}{21} = \frac{9}{21} = \frac{3}{7}[/tex]

Therefore, in both the equations the solution is [tex]\frac{3}{7}[/tex]. (Answer)

Final answer:

Both a multiplication equation (½ * 2 = 1) and a subtraction equation (1 - ½ = ½) can be constructed to have the same solution, where the multiplication involves doubling the fraction and the subtraction involves a whole number minus the fraction.

Explanation:

Creating a multiplication equation and a subtraction equation with the same solution involves finding a common value that the operations can share. Here's a simple example:

Let's say we have the fraction ½. If we want a multiplication equation, we could multiply this fraction by 2 to get 1 (since ½ * 2 = 1).

Multiplication equation: ½ * x = 1, where x = 2.

For the subtraction equation, we consider the fact that subtracting 0 from any number leaves it unchanged. We can use this to our advantage by creating an equation where we subtract a fraction from itself:

Subtraction equation: y - ½ = ½, where y = 1.

By solving these equations, we can see they have the same solution:

Both equations simplify to the same value, demonstrating that multiplication and subtraction can indeed share the same result when formulated correctly.

The original price of the sweater, before a 20% discount, was found to be $60. This was calculated by dividing the sale price of $48 by 0.80, as the sale price represents 80% of the original price.

The student is asking how to find the original price of a sweater given that the sale price is $48 and this sale price represents a 20% discount from the original price.

To find the original price, we need to understand that the sale price is 80% of the original price (100% - 20% discount). Let's denote the original price as P. We can set up the equation P * 0.80 = $48. Solving for P, we get P = $48 / 0.80

The calculation will give us the original price which is $60. The original price of the sweater was $60 before the 20% discount was applied.

Final answer:

The original price of the sweater was $60.

Explanation:

Let x be the original price of the sweater.

According to the given information, the sale price of the sweater is $48, which is 20% less than the original price.

So, we can set up the equation as follows-

Original Price - Discount = Sales Price

x - 0.2x = $48

Simplifying:

0.8x = $48

Dividing both sides by 0.8, we get:

x = $60

Therefore, the original price of the sweater was $60.

Answer:

I think its c. but i could be wrong

Answer I believe it would just be 8/10

Step-by-step explanation:

You have 2/10 of the worlds ocean which = Indian Ocean

So Your remaining ocean (10-2 = 8)

Also known as 8/10

The remaining oceans make up 4/5 of the world's oceans after subtracting the 1/5 that represents the Indian Ocean.

If the Indian Ocean covers 2/10 (or 1/5 when simplified) of the world's oceans, then the fraction representing the remaining oceans is found by subtracting this fraction from the whole (1, as the whole represents all of the world's oceans).

So, the calculation to find the fraction of the area of the remaining oceans would be:

1 - 2/10 = 1 - 1/5 = 5/5 - 1/5 = 4/5

Therefore, the remaining oceans make up 4/5 of the area of the world's oceans.

Step-by-step explanation:

Let the required number = x

To find, the required number = ?

According to question,

∴ 2x - 16 - 2 × 10 = 0

⇒ 2x - 16 - 20 = 0

⇒ 2x - 36 = 0

⇒ 2x = 36

⇒ x = 18

∴  The required number = 18

Thus, the required number is 18.

Answer: x=18

Explanation:

The given equation describes a linear relationship between temperature and time. The slope, -0.7, indicates that the temperature is dropping at a rate of 0.7 degrees per unit of time.

The equation given, T=42-0.7t, is in the form of a linear equation, y=mx+b, where T is the temperature in degrees Celsius, t is the time, 42 represents an initial temperature, and -0.7 is the slope representing the rate of temperature change over time.

In this equation, the slope, -0.7, tells us that the temperature is decreasing or dropping at a rate of 0.7 degrees per unit of time. This could be per minute, per hour, etc., depending on the context given.

Note that because the '-0.7' is negative, we know that the temperature is decreasing, or dropping, rather than increasing. If it were positive, it would mean the temperature is rising. Thus, when you're asked how fast the temperature is dropping, the answer based on this equation is that it's dropping at a rate of 0.7 degrees per unit of time.

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The temperature drops at a rate of 0.7 degrees per time unit, as indicated by the coefficient of t in the equation T = 42 - 0.7t.

The equation given, T = 42 - 0.7t, suggests a relationship between temperature (T) and time (t), where the temperature drops over time due to some cooling process, such as a cold front arriving. To determine how fast the temperature is dropping, we look at the coefficient of t in the equation, which is -0.7. This means that for every unit of time that passes, the temperature drops by 0.7 units. Thus, the rate of temperature drop is 0.7 degrees per time unit, assuming the temperature is measured in degrees and time in matching time units (likely minutes or seconds).

Answer:

x = 8

Step-by-step explanation:

7x + 2(6x + 9) = 170

2(6x + 9) = 12x + 18

7x + 12x + 18 = 170

19x = 152

152/19 = 8

x = 8

Answer:

  Yes, (x, y) = (0, 3) is a solution

Step-by-step explanation:

You can determine whether a given ordered pair is a solution by substituting those values into the equation, then checking to see if the resulting statement is true.

For x=0 and y=3, the equation becomes ...

  2·0 -3 = -3 . . . . . a true statement

(0, 3) is a solution to the equation

Answer:

Step-by-step explanation:

Let a represent the hours put in my mechanic 1 and b represent that of mechanic 2.

a + b = 25, i.e. a = 25 - b

95a + 70b = 2000

Let's substitute the value of a in the second equation

95(25 - b) + 70b = 2000

2375 - 95b + 70b = 2000

2375 - 25b = 2000

-25b = 2000 - 2375

-25b = -375

b = 375/25

b = 15hrs

If b = 15hrs,

a + 15 = 25

a = 10hrs

Answer:

Step-by-step explanation:

4b+5=t

First, you must get the variable alone! Substract 5 from both sides!

4b+5=t

    -5  -5

The 5 cancels out because 5-5=0

The new equation is 4b=t-5

You must divide by 4 to get the variable alone since your solving for b!

4b=t-5

4      4

b= [tex]\frac{t-5}{4} \\[/tex]

This is your answer!

We have a system of equations in two variables, namely, a and c. Use the substitution to find a and c.

Answer:

The price of 1 adult ticket is $11, while the price of one child ticket is $8.

Step-by-step explanation:

Let's identify what we already know:

1) On the first day of ticket sales, the school sold $159 worth of tickets.

2) On the first day, they sold 5 adults tickets, and 13 adult tickets.

3) The school sold $51 worth of tickets on the second day.

4) The school sold 1 adult ticket, and 5 child tickets.

Let's create two formulas:

(5 times x) + (13 times y) = $159

(1 times x) + (5 times y) = $51

The factor for given equation [tex]3x^2+7x-6[/tex] is (3x-2) and (x+3).

Step-by-step explanation:

To find the factors of the equation,

1) Multiply the coefficient of the [tex]x^2[/tex] and the constant value.

⇒3×(-6)= -18.

2) Now find two numbers that can result is in -18 while multiplying and 7 (middle term or coefficient of x) while adding.

⇒9 × (-2) = -18.

9+(-2)= 7.

Now spit the equation as[tex]3x^2+9x-2x-6[/tex].

=[tex](3x^2+9x)-(2x-6)[/tex].

=3x(x+3) - 2(x+3).

=(x+3)(3x-2).  (by taking out the common term x+3)

∴ The factor for given equation [tex]3x^2+7x-6[/tex] is (3x-2) and (x+3).

Answer:

20 and 22.

Step-by-step explanation:

Let the consecutive integers be a and b

Then b = a + 2

a is the smaller integer.

[tex]\begin{array}{rcl}2a + b & = & 62\\2a + a + 2& = & 62\\3a + 2 & = & 62\\3a & = & 60\\a & = & \dfrac{60}{3}\\\\& = & \mathbf{20}\\\end{array}[/tex]

a               = 20

b = 20 + 2 = 22

The two integers, in ascending order, are 20 and 22.

Check:

2(20) + 22 = 62

    40 + 22 = 62

             62 = 62

OK.

A population with a doubling time of 25 years will grow by a factor of 2 in 25 years, by a factor of 4 in 50 years, and by a factor of 16 in 100 years, based on the exponential growth rule.

If a population has a doubling time of 25 years, by what factor will it grow in various timeframes? Let's calculate this using the rule of exponential growth.

In 25 years, the factor by which the population will grow is 2, because the definition of doubling time implies that the population doubles every 25 years.

In 50 years, which is two doubling periods, the population will grow by a factor of 2^2 (2 raised to the power of 2), which is 4.

In 100 years, which is four doubling periods, the population growth factor will be 2^4 (2 raised to the power of 4), which equals 16.

Thus:

Answer:

40 minutes

Step-by-step explanation:

Elapsed time = end time - start time

Elapsed time = 2:00 - 1: 20

Elapsed time = 40 minutes

Answer:

93

Step-by-step explanation:

s= salads  d= drinks

$6.5s + $2d = $836.5

s + d =209

s = 209-d

6.5 (209-d) + 2d = 836.5

1358.5 - 6.5d + 2d = 836.5

-4.5d = -522

d = 116

s = 209 - 116 = 93