The triangle and the square shown have the same perimeter. Solve the equation 3x+4x+5x=4(x+2)

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:

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 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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Answer:

  (x, y) ≈ (3.4, 1.8)

Step-by-step explanation:

You want the point of intersection of the lines through (0, 1), (4.3, 2) and (2.1, 3), (5.4, 0).

The first attachment shows a graph of the lines and the coordinates of the point of intersection. The solution is ...

  (x, y) ≈ (3.42, 1.8)

  (x, y) = (3.4, 1.8) . . . . accurate to 1 decimal place

__

Additional comment

For each pair of points, the equation of the line can be written as ...

  (y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0

  (2 -1)(x -0) -(4.3 -0)(y -1) = 0   ⇒   x -4.3y +4.3 = 0

and

  (0 -3)(x -2.1) -(5.4 -2.1)(y -3) = 0   ⇒   -3x -3.3y +16.2 = 0

The calculator result in the second attachment shows the exact solution to be ...

  (x, y) = (3 229/540, 1 43/54) ≈ (3.42407, 1.79630)

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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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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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 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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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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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:

x=−5+ 21 ,−5− 21

Step-by-step explanation:

x= 4−20+4= 214−20−4 =21

​

​

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:

13.9375

Step-by-step explanation:

this is your answer 1234

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 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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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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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 area of any circle is directly proportional to the square of the radius thus there are proportional relationships between the area of a circle and to the radius of the circle.

The ratio is the division of the two numbers.

Proportion is the relation of a variable with another. It could be direct or inverse.

The area of a circle with radius "r" is given as,

A = πr²

Since,π = constant.

Removing constant by proportionality.

A ∝ r²

Hence "The area of any circle is directly proportional to the square of the radius thus there are proportional relationships between the area of a circle and to the radius of the circle".

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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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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]

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 money spent by Mr. Dunston is $ 35.

Given that:-

Money spent by Mr. Dunston and Mr. Dolland = $ 45

Money spent by Mr. Dunston and Ms. Campbell = $ 65

Ms. Campbell spent 3 times as much as Mr. Dolland.

We have to find the money spent by Mr. Dunston.

Let the money spent by Mr. Dunston be $ x,

Let the money spent by Mr. Dolland be $ y and,

Let the money spent by Ms. Campbell be $ 3y

Hence, from the data given in the question, we can write,

x + y = 45  ...(1)

x + 3y = 65 ... (2)

By elimination method, we can write,

(2) - (1)

2y = 20

y = 10

x + 10 = 45

x = 45 - 10 = 35

x = 35

Hence, the money spent by Mr. Dunston is $ 35.

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Answer:

Charlie gets paid more then Derek. Charlie gets paid per hour $52.25

The sum form of the trigonometric function 2 · sin 2x · sin 2x by product-to-sum formula is 1 - cos 4x.

Herein we find the definition of a trigonometric function defined as a product of trigonometric function, this can be transformed into a sum of trigonometric functions by means of the following product-to-sum formula:

sin α · sin β = [cos (α - β) - cos (α + β)] / 2

First, write the trigonometric function defined in the statement:

2 · sin 2x · sin 2x

Second, use the product-to-sum formula by considering α = β = 2 · x:

2 · [[cos (2x - 2x) - cos (2x + 2x)] / 2]

cos 0 - cos 4x

1 - cos 4x

Third, write the resulting expression:

2 · sin 2x · sin 2x = 1 - cos 4x

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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 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 table has been shown using the function rule y = 5x - 2. (Refer to the table attached below).

So, the rule is y = 5x - 2:

Now calculate values as follows:

(A) When x = 0:

(B) When x = 1:

(C) When x = 2:

(D) When x = 3:

Therefore, the table has been shown using the function rule y = 5x - 2. (Refer to the table attached below)

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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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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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