2x(4+1)+(3x+5)+(2x+1)

The image of the transformation is R' (-12, 3), S' (-12, 12) and T' (-6, 3)

The complete question is added as an attachment

The coordinates of the triangle are given as

R = (-4, 1)

S = (-4, 4)

T = (-2, 1)

The transformation is given as

The rule of the transformations is

(x, y) = 3(x, y)

So, we have

R' = 3 * (-4, 1) = (-12, 3)

S' = 3 * (-4, 4) = (-12, 12)

T' = 3 * (-2, 1)= (-6, 3)

Hence, the image of the transformation is R' (-12, 3), S' (-12, 12) and T' (-6, 3)

See attachment for the image of the transformation

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

Answer: C, 21

Step-by-step explanation:

After approximately 16 years, the principal amount of $500 double.

So, to find out how many years will a principal of $ 500 double:

The formula for calculating compound interest is as follows:

The value of r is 0.0462. In the equation, substitute this and x:

Therefore, after approximately 16 years, the principal amount of $500 double.

Know more about compound interest here:

https://brainly.com/question/24924853

#SPJ4

Simplify the expression by applying the index rule: a^mx a^n = a^m+n.

y¹/₂ . y³/₁₀

y¹/₂ . y³/₁₀ = y¹/₂ +³/₁₀

¹/₂ +³/₁₀ = 4/5

y¹/₂ +³/₁₀ = y^ 4/5

Find out more on indices at: brainly.com/question/28595166

#SPJ4

Answer:

I'm assuming you inserting the variable x was a mistake.

Step-by-step explanation:

The least common multiple of 18 and 42 is 126.

[tex]\bold{Step-by-step}[/tex]

[tex]\mathrm{"LCM"}[/tex]

[tex]18 \times 7 = 126\\42 \times 3 = 126[/tex]

Any concerns, let me know, have a great day!

Solution of exponential equation is ,  x = 10

In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as  [tex]a^x[/tex] .

where, a is the base of function

           x defines  expression

Mathematically, if  [tex]log_aN = x[/tex] is an logarithmic function then, this can be converted to exponential function as  [tex]a^x = N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.

Some important formulas of exponential :

According to given statement,

5.2³ x =400

=> 5.8 x =400

=> 40x = 400

=> x =10

Thus solution for this equation is x =10.

To know more about exponential equations, visit :

brainly.com/question/28278137

#SPJ4

The complete question is :

What is the solution of each exponential equation? Check your answer.

a. 7⁻⁴x=800

b. 5.2³x=400

In [tex]e^{2x} =10[/tex] , x = 1., by the properties of logarithm.

Now,

In [tex]e^{2x} =10[/tex] , taking natural logarithm on both side.

=>  [tex]log_e(e^{2x})=log_e(10)[/tex]

By properties of logarithm, we know that: [tex]log_b(a)^m = m(log_b(a))[/tex]

=> [tex]2x(log_e(e))=ln(10)[/tex]

Also, as [tex]log_e(e)[/tex] = 1,

=> 2x (1) = ln(10)

=> 2x = 2.302 (approx)

=> x = 1.151

Hence, In [tex]e^{2x} =10[/tex] , x = 1.151, by the properties of logarithm.

To learn more about logarithms, refer to the link: brainly.com/question/25710806

#SPJ4

Two or more expressions with equal sign is called as Equation. If mWVY = 70 is an angle then mYVX =165 we get by solving the equation x-13=70.

Two or more expressions with equal sign is called as Equation.

mWVY = 70

From the figure we can observe that mWVY =x-13

By this we form an equation

x-13=70

x-13=70

x=70+13

x=83.

So value of x is 83.

Now mYVX=2x-1

2(83)-1

166-1

=165

Therefore mYVX is 165 degree when  mWVY = 70.

To learn more on equation click:

https://brainly.com/question/21105092

#SPJ1

After solving, the factors of the equation x²-13x-30=0 are:

So,

Given equation: x²-13x-30=0

Then,

Factors are: (x-15) and (x+2)

Therefore, after solving, the factors of the equation x²-13x-30=0 are:

Know more about equations here:

brainly.com/question/2972832

#SPJ4

Answer:  x  ≤ 4.5

Step-by-step explanation:

Since there is a closed circle on 4.5 and the ray is going left we know that x is ≤ 4.5

If a and b are rational numbers, then the product of (a+√b) and its conjugate is always a rational number.

The conjugate of ( a + [tex]\sqrt{b}[/tex] ) is ( a - [tex]\sqrt{b}[/tex] ) .

Product of  ( a + [tex]\sqrt{b}[/tex] ) and ( a - [tex]\sqrt{b}[/tex] )  =  ( a + [tex]\sqrt{b}[/tex] ) * ( a - [tex]\sqrt{b}[/tex] )

                                                         = ( [tex]a^{2}[/tex] ) - a[tex]\sqrt{b}[/tex] + a[tex]\sqrt{b}[/tex] - [ [tex]\sqrt{b} ^{2}[/tex] ]

                                            = ( [tex]a^{2}[/tex]) - b .

The expression ( [tex]a^{2}[/tex]) - b is rational .

Hence , if a and b are rational numbers, then the product of (a+√b) and its conjugate is always a rational number.

To learn more on rational nos. follow link :

https://brainly.com/question/12088221

#SPJ4

Answer:

Question 1

f(x) = 19 sin(x [tex]\pi[/tex]/38)

Question 2

f( 7) = 10.39ft

f(24) =  17.4ft

Step-by-step explanation:

f(x) = a sin(x+s)

x =  opening length

a = amplitude

s = shift

Question 1

using half of sine

x = opening = 38ft wide

s = 19

f(x) = 19 sin(x [tex]\pi[/tex]/38)

Question 2

road width =  7 + 17 + 7 = 31

height at x = 7 or at x = 7 + 17 = 24

f( 7) = 19 sin(7 π/38) = 10.39ft

f(24) = 19 sin(24 π/38) = 17.4ft

The value of the expression sec (-π) is equal to -1 if the given expression is undefined.

As given in the question,

Given expression: sec (-π)

Standard position of unit circle: -π is representing semicircle with terminal point on negative x-axis with coordinates (-1, 0)

Hypotenuse = √ (-1)² + 0²

                     = 1

Value of the expression is given by

sec α = Hypotenuse / Base (x-coordinate)

⇒sec(-π) = 1 / -1

⇒sec(-π) = -1

Therefore, the value of the expression sec (-π) is equal to -1.

Learn more about expression here

brainly.com/question/14083225

#SPJ1

keeping in mind that a year has 12 months, thus 9 months is really 9/12 of a year.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$960\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years\to \frac{9}{12}\dotfill &\frac{3}{4} \end{cases} \\\\\\ I = (960)(0.09)(\frac{3}{4}) \implies I=64.8[/tex]

Based on the information, it should be noted that there's an increase in percentage of 30%.

Based on the information, it should be noted that the following can be illustrated:

Original amount = 30

New amount = 39

Therefore, it should be noted that the change in percentage will be:

= Change in amount / Old amount × 100

= (39 - 30) / 30 × 100

= 9/30 × 100

= 30%

Therefore, there's a increase in percentage of 30%.

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

The total expenses of Mrs Terry is given as $3160

We have to form the equation as

2632 = 2500 + 20%(x - 2500)

We have to use the multiplicative distributive law here

Such that we would have

2632 = 2500 + 0.2x - 500

We have to rearrange the terms

2632 - 2500 + 500 = 0.2x

632 = 0.2x

Next we have to divide through by 0.2

632 / 0.2 = x

3160 = x

Hence the total expenses of Mrs Terry is given as $3160

Read more on word equation here:

https://brainly.com/question/13818690

#SPJ1

Answer:1314 or 13.14%

Step-by-step explanation:yes

The fact that $45 is enough to make bracelets for 10.44 persons means that the we can make bracelets for 10 friends

What is the total necklace cost function?

The total cost of necklaces that can be made within the total budget of $45 can be modeled using a straight-line equation, which considers the fixed cost of necklace supplies of $21.50 and the total variable cost of supplies, the cost per necklace multiplied by the total number of necklaces possible, defined as x

45=21.50+2.25x

let solve for x to determine whether we can make bracelets for 10 friends

45-21.50=2.25x

23.50=2.25x

x=23.50/2.25

x=10.44

Find out more about total cost on:https://brainly.com/question/14297342

#SPJ1

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (x² + 2y³)⁶ is expanded as x¹² + 12x¹⁰y³ + 60x⁸y⁶ + 160x⁶y⁹ + 240x⁴y¹² + 192x²y¹⁵ + 64y¹⁸.

The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.

The total number of terms in the expansion of (x + y)ⁿ are (n+1).

The sum of exponents of x and y is always n.

nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ.

The binomial coefficients which are equidistant from the beginning and from the ending are equal.

i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.

Let the function be (x² + 2y³)⁶

By using binomial expansion theorem, we get

(x² + 2y³)⁶ = x¹² + 12x¹⁰y³ + 60x⁸y⁶ + 160x⁶y⁹ + 240x⁴y¹² + 192x²y¹⁵ + 64y¹⁸

(x² + 2y³)⁶ is expanded as x¹² + 12x¹⁰y³ + 60x⁸y⁶ + 160x⁶y⁹ + 240x⁴y¹² + 192x²y¹⁵ + 64y¹⁸

To learn more about binomial, refer to:

brainly.com/question/15246027

#SPJ4

Answer:

1/2 is the correct answer

Step-by-step explanation:

7/8 - 3/8 = 7 -3/8 = 4/8=1/2

The definition for the linear piecewise function is given as follows:

B.

A linear function is modeled by the following rule:

y = mx + b

In which:

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

For x to the left of 0, we have a line with intercept of 2, hence:

y = mx + 2.

When x increases by 1, y increases by 2, hence the slope is of m = 2 and:

y = 2x + 2, x ≤ 0.

For x to the right of 0, we have a line with intercept of 4, hence:

y = mx + 4.

When x increases by 3, y decreases by 4, hence the slope is of m = -4/3 and:

y = -4/3x + 4, x > 0.

Hence the definition of the function is given by:

B.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Exponential Form

We've all heard the term "exponential." What does that word mean? Exponential means growing faster and faster. However, in mathematics, it represents a formula with one or more exponents. So, we know it as exponential form. I would say that things can grow exponentially as the items being talked about get bigger and faster and faster.

So, we use the following method to write the given expression in exponential.

Expression 1 = ⁴√x³

Expression 2 = ⁵√y⁴

Use n*sqrt{a}x=a^(x/n) to rewrite 4*sqrt{x}3 as x^ (3/4)

similarly, we can write the second equation as

Use n*sqrt{a}x=a^(x/n) to rewrite 5*sqrt{y}4 as y^ (4/5)

More problems that deal with writing numbers in their exponential form are in the link below.

https://brainly.com/question/6326336?referrer=searchResults

#SPJ4

a. 3.5 x 4.1 (3.5 ×2.8) = -0.7

b.  2.5+ (-4.1) + [(−2.3) × (-1.1)] = 4.29

c. [-5.5 (-6.5) ÷ 2.4]+ (-1.1) = -0.5

Hence the required parentheses are added to make the statement true.

Learn more about Simplification here:

brainly.com/question/723406

#SPJ9

Answer:

For 2 more panes of glass it will cost $5.70.  

Step-by-step explanation:

To find the price of each pane of glass you take the total price/ total panes of glass.  

25.65/ 9 = $2.85.

If he wanted one more pane of glass it would be $2.85 but since you asked for two you multiply by 2 and get $5.70.  Hope this helps!

Answer:

LCD = 30

Equivalent Fractions with the LCD

1/10 = 3/30

1/6 = 5/30

Step-by-step explanation:

Rewriting input as fractions if necessary:

1/10, 1/6

For the denominators (10, 6) the least common multiple (LCM) is 30.

LCM(10, 6)

Therefore, the least common denominator (LCD) is 30.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

1/10 = 1/10 × 3/3 = 3/30

1/6 = 1/6 × 5/5 = 5/30

The area of the rectangular fenced area for dog run is given by:

A = 4x² + 34x + 18.

Considering a rectangle of length l and width w, we have that:

For this problem, the section enclosed by the fence is divided into two triangles, as follows:

Hence the total area is:

A = 8(2x) + (6 + 2x)(2x + 3)

A = 16x + 4x² + 18x + 18

A = 4x² + 34x + 18.

Hence the area of the rectangular fenced area for dog run is given by:

A = 4x² + 34x + 18.

More can be learned about the area of a rectangle at https://brainly.com/question/10489198

#SPJ1

The value of x for the equation log₇343=x will be 3.

Logarithmic function properties. You have encountered several characteristics during your study of algebra, including the commutative, associative, and distributive properties.

These characteristics make it easier to simplify a complex statement or equation. With logarithms, the same holds true.

For log₇343=x

It can be expressed in the form of -

343 = 7ˣ

It can be further expressed as -

7³ = 7ˣ

As base is same,

x = 3

To learn more about logarithmic functions from given link

https://brainly.com/question/13473114

#SPJ4

The slope of the line is 1 / 3

The slope of a line is a measure of its steepness.

The slope of the line is the ratio of the rise to the run, or rise divided by the run.

Mathematically, the slope of a line can be described as follows;

slope = change in y / change in x

Therefore,

slope = y₂ - y₁ / x₂ - x₁

Let's take two points from the graph

(0, 2)(3, 3)

where

x₁ = 0

x₂ = 3

y₁ = 2

y₂ = 3

Hence,

slope = 3 - 2 / 3 - 0

slope = 1 / 3

Therefore, the slope of the line is 1 / 3

learn more on slope here:https://brainly.com/question/23087740

#SPJ1