Write the expression ;



The quotient of seven and a number, added to ten.​

Cassidy and Calvin have the same amount of money in 11 months.

The amount is $370.

Cassidy has $425 in her savings account, and she has to pay $5 each month to her parents for her cell phone. This will be:

= 425 - 5m

Calvin has $95 and he saves $25 each month from his job walking dogs for his neighbor. This will be:

= 95 + 25m

where m = number of months

The equation will be:

425 - 5m = 95 + 25m

Collect like terms

425 - 95 = 25m + 5m

330 = 30m

Divide

m= 330/30

m = 11

The number of months is 11.

The amount will be:

= 425 - 5m

= 425 - 5(11)

= 425 - 55.

= 370

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Considering the five number summary of the data-set, we have that:

a. None of the prices were outliers, as all the prices are within 1.5 IQR of the quartiles.

b. That is not a very low price, as it is above the first quartile, while very low prices have to be 1.5 IQR below the first quartile.

The outliers, considering the five number summary of a data-set, are the values that are more than 1.5 Interquartile Ranges from the quartiles, that is, either:

The interquartile range of a data-set is the difference between the third quartile and the first quartile, hence, for the given data-set:

IQR = Q3 - Q1 = 110 - 30 = 80.

Hence the bounds for outliers are given as follows:

Since the maximum value of 200 is less than 230, there are no outliers in the data-set.

The five number summary is given by the image at the end of the answer.

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The depreciation expense under the straight-line method for 2022, for Monty Corp., is $5,450.

Under the straight-line depreciation method, one of the cost-recovery methods, the depreciable amount of an asset is divided by its estimated useful life.

The quotient is the depreciation expense for each year.  However, if the asset is not used for a full year, the depreciation expense is prorated according to the number of months or days that the asset is in use.

Note that the depreciable amount is the difference between the cost of the asset and its salvage value.

Cost of new machine = $124,000

Purchase date = October 1, 2022

Estimated salvage value = $15,000

Depreciable amount = $109,000 ($124,000 - $15,000)

Estimated useful life = 5 years

Estimated working hours = 10,000 hours

Depreciation method = Straight-line

Annual Depreciation Expense = $21,800 ($109,000/5)

October 1, 2022, to December 31, 2022, = 3 months

Depreciation expense for 2022 = $5,450 ($21,800 x 3/12)

Thus, using the straight-line method, Monty Corp. will record a depreciation expense of $5,450 for the new machine it purchased on October 1, 2022.

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The vertex is (-2, 11), then the vertex form of the quadratic is:

f(x) = 5*(x + 2)^2 - 11

A quadratic equation with a leading coefficient a and a vertex (h, k) can be written in vertex form as:

y = a*(x - h)^2 + k

And for a quadratic equation of the form:

y = a*x^2 + b*x + c

The vertex is at:

h = -b/2a

In this case, our equation is:

f(x) =5x^2 + 20x + 9

Then:

h = -20/2*5 = -2

Evaluating in x = -2 we get:

f(-2) = 5*(-2)^2 + 20*-2 + 9

f(-2) = 5*4 - 40 + 9

f(-2) = 20 - 40 + 9 = -20 + 9 = -11

The vertex is (-2, -11), and the leadin coefficient is a = 5, then the vertex form is:

f(x) = 5*(x + 2)^2 - 11

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The multiplication of the given function is  (fg)(x) = 12[tex]x^3[/tex]

What is operations of the function ?

   Similar to how a function's constituent terms can be added, subtracted, multiplied, and divided, so can functions. These are to be noted as follows:

Addition f( x ) + g ( x ) means to combine two functions, and it may alternatively be expressed as ( f + g ) ( x )

It is possible to write ( f g ) ( x ) to represent the operation of subtracting the g(x) function from the f(x) function.

The two functions are multiplied together when you multiply f (x ) g (x), which can also be represented as (f g ) (x).

Division f (x)/g (x) means to split the two functions in half, and it can alternatively be expressed as (f/g)(x).

Here the given function ,

=> f(x) = 4[tex]x^2[/tex]

=> g(x)= 3x

Now (fg)(x) = f(x)*g(x)

=> (fg)(x)=  4[tex]x^2[/tex]*3x

=>  (fg)(x) = 12[tex]x^3[/tex]

Hence the  (fg)(x) = 12[tex]x^3[/tex].

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Answer:

x=−5+ 21 ,−5− 21

Step-by-step explanation:

x= 4−20+4= 214−20−4 =21

​

​

Answer:

--------------------------------------

The graph has two local maximums and two local minimums.

The intervals between those points are the increasing intervals.

Refer to the attached, where the intervals are marked.

The intervals are

The solution is x > -2 and x > 3

x is greater than -2 and x is greater than 3.

This can be represented by the number line Option D.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

(x + 2) (x - 3)² > 0

This can be written as,

x + 2 > 0 and (x - 3)² > 0

x + 2 > 0

x > -2 _____(1)

(x - 3)² > 0

Squaring both sides.

x - 3 > 0

x > 3 _____(2)

From (1) and (2) we get,

x > -2 and x > 3

Thus,

The solution is x > -2 and x > 3

x is greater than -2 and x is greater than 3.

This can be represented by the number line Option D.

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Answer:

64

Step-by-step explanation:

you need to plug the number in subtract and add then multiply the number from the first pair of parenthesis into the main number and after multiply the second pair into it.

The answer that best completes the visual analogy of caliper is the first option (picture attached)

Information given in the question

A polygon of 5 sides

Visual analogy refers to using the power of sight to detect of feel things

A polygon of 5 sides is called pentagon is used to describe the caliper

The movement is forecasted by:

considering these the first option become the best option

The line mark will align where the ? was positioned and the center will not be a dark spot

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The equation of a line perpendicular to -5x + y = 9 that passes through the point (0, -9) is [tex]y = -\frac{1}{5}x -9[/tex]

The equation of the line in slope intercept form can be represented as follows:

y = mx + b

where

Perpendicular lines follows the following rules as follows:

m₁ m₂ = -1

Let's find the slope of -5x + y = 9 .

y = 5x + 9

Hence,

slope = 5

Let's find the slope of the equation of the line that passes through (0, -9) and perpendicular to  -5x + y = 9 .

5m₂ = -1

m₂ = -1 / 5

m₂ = - 1 / 5

Therefore, let's find the y-intercept of the line using (0, -9)

-9 = - 1 / 5(0) + b

b = -9

Therefore, the equation of the line is y = - 1 / 5 x - 9

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Answer:

4x4x4

Step-by-step explanation:

3x4x5= 60

4x4x4= 64

64 is a higher volume than 60

Answer:

In order to find out which box can hold more, we can find the respective volumes of the boxes.

Volume of first box

= 3 inches × 4 inches × 5 inches

= 60 inches³

Volume of second box

= 4 inches × 4 inches × 4 inches

= 64 inches³

∴Since the second box has a greater volume than the first box, the former can hence hold more than the latter.

The classification and the output rule for each function in this problem is given as follows:

1. Output rule: y = 5x + 11. Classification: Linear.

2. Output rule: y = 2^x. Classification: Exponential.

3. Output rule: y = 3 if |x| is even, y = 1 if |x| is odd. Classification: Neither.

A linear function is defined when the increase of 1 in x result in the addition of a constant to y, hence the rule is:

y = mx + b.

In which:

Hence, for the first table, as 5 is added to x when x increases by one, the rule is:

y = f(x) = 5x + 16.

An exponential function is defined when the increase of 1 in x result in the multiplication of a constant to y, hence the rule is:

y = a(b)^x.

In which:

Hence, for the second table, the rule is:

y = 2^x.

For the third table, none of the definitions for linear and for exponential functions are true, hence the function is neither, as it is a piece-wise function that assumes one value for odd numbers and another for even numbers.

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The equation for the word problem the difference of ten times a number and six is fourteen is (10x-6 = 14) and the value of x is 2.

According to the question,

We have the following information:

The difference of ten times a number and six is fourteen.

Now, let's take the number to be x.

So, we have the following expression:

10x-6 = 14

Now, moving 6 from the left hand side to the right hand side will result in the change of the sign from minus to plus:

10x = 14+6

10x = 20

x = 20/10

x = 2

Hence, the equation for the word problem the difference of ten times a number and six is fourteen is (10x-6 = 14) and the value of x is 2.

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The number of boys were playing tag are 5.

What is equation?

Two expressions joined by an equal sign form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

Given: Some students were playing tag on a playground. The number of girls was three less than twice the number of boys. If there were 7 girls.

Suppose the number of boys are x,

So, the number of girls are, 2x - 3.

There are 7 girls.

So, 2x - 3 = 7

2x = 10

x = 10/2

x = 5

Therefore, the number of boys were playing tag are 5.

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The composition (f - g)(x) has a value of (c) (f - g)(x) = -2√x

The definitions of the functions are given as

f(x) = √4x and g(x) = √16x

Evaluate the square roots in the above equations

This gives

f(x) = 2√x and g(x) = 4√x

To find the composition (f - g)(x), we make use of

(f - g)(x) = f(x) - g(x)

Substitute the known values in the above equation So, we have the following equation

(f - g)(x) = 2√x - 4√x

Evaluate the like terms

This gives

(f - g)(x) = -2√x

Hence, the value of the composition is (c) (f - g)(x) = -2√x

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By using the dimensional analysis 580 lb = 263.084 kg.

What is dimensional analysis?

Dimensional analysis, which is used in both engineering and science, examines the links between various physical quantities by determining their foundational quantities and units of measurement and then following these dimensions while computations or comparisons are made.

A technique for analysis that, in the absence of sufficient data to establish accurate equations, expresses physical quantities in terms of their fundamental dimensions.

We have to convert 580 lb into kg along with the dimensional analysis.

Since, 1 pound (lb) is equal to 0.45359237 kilograms (kg).

So,

580 lb = (0.4535927) x 580

580 lb = 263.0835746

580 lb = 263.084 kg

Hence, along with the dimensional analysis 580 lb = 263.084 kg.

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Answer:

25% or 35 rocks.

Step-by-step explanation:

To find this answer, simply add up 40% and 35% to get 75%. Now, 100% is the most we can have. So, 100 - 75 = 25%.

To find even more in depth of exactly how much 25% of 140 is, we can simply move the decimal point from 25 over twice to get 0.25. The term "of" means multiply:

0.25 x 140 = 35 rocks.

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The length of the line segment with endpoints at (0, 3) and  (-6, -5) is 10 units

An equation shows the relationship between two or more numbers and variables.

The distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate plane is:

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

The line segment have endpoints at (0, 3) and  (-6, -5). Hence:

Length = √[(-5-3)² + (-6 - 0)²] = √(8² + 6²) = √100 = 10

The length of the line segment is 10 units

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Answer:

[tex]f(x)=-log_{3}(-x)[/tex]

Step-by-step explanation:

Based on the points given on the graph, I would say this is a Log function, reflected across both x- and y-axes.

And given the point (-3, -1), it must be [tex]-log_{3}(-x)[/tex]

Answer:

  4/3

Step-by-step explanation:

You want the limit as t→1 of (t³+t²-5t+3)/(t³-3t+2).

The fact that each polynomial evaluates to 0 at t=1 tells you that (t-1) is a factor of each. Factoring that out gives ...

  [tex]\dfrac{t^3+t^2-5t+3}{t^3-3t+2}=\dfrac{(t-1)(t^2+2t-3)}{(t-1)(t^2+t-2)}=\dfrac{(t-1)(t-1)(t+3)}{(t-1)(t-1)(t+2)}\\\\=\dfrac{t+3}{t+2}[/tex]

The limit at t = 1 is found by direct substitution:

  lim = (1 +3)/(1 +2) = 4/3

Answer:

13.9375

Step-by-step explanation:

this is your answer 1234

The value of q after solving the expression, q/3+2/3 = 8q/3-5/3, is 1.

According to the question,

We have the following expression:

q/3+2/3 = 8q/3-5/3

Now, taking 3 as the denominator on both the sides:

(q+2)/3 = (8q-5)/3

Now, 3 in the denominator on the left hand side can be divided by 3 in the denominator on the right hand side:

q+2 = 8q-5

Now, changing the sides of this expression:

8q-5 = q+2

Moving q from the right hand side to the left hand side:

8q-q-5 = 2

7q -5 = 2

Moving 5 from the left hand side to the right hand side:

7q = 2+5

7q = 7

q = 7/7

q = 1

Hence, the value of q after solving the given expression is 1.

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The range of function f(x) = 4x + 5 for given input values is {-3, 1, 5, 9, 13}

The correct answer is an option (C)

In this question, we have been given a function f(x) = 4x + 5

We need to find the range of given function for input {-2, -1, 0, 1 , 2}

We know that the range of  a function is the set of all output values for given input.

for x = -2,

f(-2) = 4(-2) + 5

f(-2) = -3

for x = -1,

f(-1) = 4(-1) + 5

f(-1) = 1

for x = 0,

f(0) = 4(0) + 5

f(0) = 5

for x = 1,

f(1) = 4(1) + 5

f(1) = 9

for x = 2,

f(2) = 4(2) + 5

f(2) = 13

Therefore, the range of function f(x) = 4x + 5 for given input values is {-3, 1, 5, 9, 13}

The correct answer is an option (C)

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Answer:

2x-2y=4 that is the best way u can write it

The value of pH of the coffee is 4.89

pH is a measure of hydrogen ion concentration, a measure of the acidity or alkalinity of a solution

Given:  The formula pH= -log₁₀ C,

where is the concentration of hydronium ions in the solution measured in moles per litre

The concentration(C) of Hydronium ions type of coffee is 1.3 x 10⁻⁵ moles per liter

To calculate the pH, we will substitute the value of the concentration (C) into the given formula:

pH= -log₁₀ C                     (C = 1.3 x 10⁻⁵ moles per liter)

pH = -log₁₀(1.3 x 10⁻⁵) = 4.89

Therefore, the pH of the coffee is 4.89

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Using the double-declining-balance method of depreciation, the completion of the table as shown is as follows:

Year Cost   Accumulated   Book Value  Depreciation Accumulated  Book

                  Depreciation        B.O.Y             Expense   Depreciation  Value

                       B.O.Y                                                               E.O.Y       E.O.Y

1    $30,000           $0           $30,000        $12,000          $12,000  $18,000

2   $30,000   $12,000          $18,000          $7,200         $19,200  $10,800

3   $30,000   $19,200          $10,800          $4,320         $23,520   $6,480

The double-declining-balance method is a depreciation method that allocates more cost to the earlier years of the asset's life.

The double-declining-balance method uses twice the straight-line rate and is computed as the product of 100/estimated useful life multiplied by 2.

The double rate is applied at the end of the year's balance for each year's depreciation expense.

The difference between the previous year's ending balance and the residual value is taken as the depreciation expense for the last year.

Auto = $30,000

Estimated life = 5 years

Residual value = $800

Depreciable amount = $29,200 ($30,000 - $800)

Straight-line depreciation rate = 20% (100/5)

Double-declining depreciation rate = 40% (20% x 2)

1st year = $12,000 ($30,000 x 40%)

2nd year = $7,200 ($18,000 x 40%)

3rd year =  $4,320 ($10,800 x 40%)

4th year = $2,592 ($6,480  x 40%)

5th year = $3,088 ($3,888 - $800)

Year Cost   Accumulated   Book Value  Depreciation Accumulated  Book

                  Depreciation        B.O.Y             Expense   Depreciation  Value

                       B.O.Y                                                               E.O.Y       E.O.Y

1    $30,000           $0           $30,000        $12,000          $12,000  $18,000

2   $30,000   $12,000          $18,000          $7,200         $19,200  $10,800

3   $30,000   $19,200          $10,800          $4,320         $23,520   $6,480

4   $30,000  $23,520           $6,480          $2,592           $26,112   $3,888

5  $30,000    $26,112           $3,888           $3,088          $29,200     $800

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Answer:

13 Remainder 44

Step-by-step explanation:

The solution after divide is, 13 and remainder = 44

We have to given that;

954 divided by 70 by using long division and with a remainder.

Now, We can divide as,

⇒ 954 divided by 70

70 ) 954 ( 13

     -70

   ----------

      254

    - 210

     ----------

         44

Therefore, The solution is, 13 and remainder = 44

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