please help with portion B. thank you

If the domain of f is ( -1, 1), then the function g defined by g(x) = f((x + 1)/(x - 1)) has a domain of; (-2, 0)

The domain of a function refers to the set of all possible intput values that make the function possible.

Now, we are given the function;

g(x) = f((x + 1)/(x - 1))

The domain would be a set of real numbers excluding 1 because at x = 1, the function is undefined.

Since the domain of  f(x)  is  -1 < x < 1  ,

Then the domain of  f(x + 1)  is  -1 < x + 1 < 1 .

domain of -1 < x + 1 < 1  will simplify to -2 < x < 0

Thus, we can say that the domain of  f(x + 1)  is  (-2, 0).

Thus;

g(x) = f(x + 1) and as such, the domain of  g(x)  is  (-2, 0) .

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Answer:

804,264

Step-by-step explanation:

Evaluate 93×92×94

We have 1 of the number 93

We have 1 of the number 92

We have 1 of the number 94

Group numbers by powers:

93×92×94 = 93[1]92[1]94[1]

93[1]92[1]94[1] = 804,264

Answer:

x=5

you're welcome

Answer:

[tex]\sf -\dfrac{7}{4}[/tex]

Step-by-step explanation:

  (1, -5)    ⇒ x₁ = 1    ; y₁ = -5

  (-3, 2)  ⇒ x₂ = -3  ; y₂ = 2

[tex]\sf \boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

            [tex]\sf =\dfrac{2-[-5]}{-3-1}\\\\= \dfrac{2+5}{-4}\\\\=\dfrac{7}{-4}\\\\= -\dfrac{7}{4}[/tex]

From the figure given the required prove is achieved using transitive property of equality to show that 2 ≅ ∠3

The term transitive property of equality is used in situation where say three values: x, y, and z are related as follows

given data

Given: ∠1 ≅ ∠4

Information deduced from the figure

Hence we can say that ∠2 ≅ ∠3 using the transitive property of equality

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Answer:

-1, 1, 3

Step-by-step explanation:

Let x equal the first odd integer.

The three consecutive odd integers would be represented by x, then x+2, then x+4.

So 3x + 2(x + 4) = 4(x + 2) - 1

Solve for x

3x + 2x + 8 = 4x + 8 -1

5x + 8 = 4x + 7

x = -1

Answer:

Inequality

Step-by-step explanation:

An expression is a mathematical phrase that contains numbers, variables, or both. Expressions never have an equal sign. An equation is a mathematical sentence that says two expressions are equal.

The point (1, 60). on the graph how's the speed that the car travels.

It should be noted that car traveled at a constant speed. The distance traveled is 210 miles and the time to travel is 3.5 hours.

Therefore, it should be noted that the point (3.5, 120) shows the distance.

The slope of the like which is the speed will be:

= Distance / Time

= 210 / 3.5

= 60 mph

Therefore, it should be noted that the point B(1, 60) lies on the graph.

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Based on the dilation, the scale factor of dilation of the point is 1/3

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

From the question, we have the following parameters

Dilation rule: Do,k

Point = (9, 6)

Image = (3, 2)

As a general rule of dilation, the following are the properties of a scaled copy of another figure

Using the above as a guide, the scaled factor is calculated as

Scaled factor = Image/Poins

This gives

Scaled factor, k = (3, 2)/(9, 6)

This gives

Scaled factor, k = 1/3

Hence, the scale factor is 1/3

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Answer:

C. Lines l and m appear to be skew--they are not parallel, and they are not intersecting each other.

Value of the function [ f(x+ h) - f(x) ] /h in simplest form when f(x) = -2x -1 is equal to -2.

As given,

Given function:

f(x) = -2x -1

Express value of  in simplest form:

f( x + h ) = -2 (x + h ) - 1

             = -2x -2h -1                   ___(1)

Simplify the function by substituting value of f(x +h and f(x),

[f(x + h) - f(x) ] /h

= [ (-2x -2h -1 )- ( -2x -1 ) ] /h

= ( -2x -2h -1 +2x +1 ) /h

= -2h /h

= -2

Therefore, value of the function [ f(x+ h) - f(x) ] /h in simplest form when f(x) = -2x -1 is equal to -2.

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Answer:

7,492.5

Step-by-step explanation:

Solve the problem

A = (50+50)

B=(85*85+A)

C = (15*0.9+B)

D = (10*15+4+C)

10*15+4+15*0.9+85*85+50+50=

150+4+13.5+7,225+100=

7,492.5

Answer:

A= 100

B= 7,325

C= 7,338.5

D= 7,492.5

The inequality which represents the possible values for the number of peaches and mangos purchased will be;

⇒ $0.75p + $1.75m = $15

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

Avni and her children went into a grocery store and will buy peaches and mangos.

Each peach costs $0.75 and each mango costs $1.75.

And, Avni has a total of $15 to spend on peaches and mangos.

Now,

Let number of peaches purchased = p

And, Number of Mangos purchased = m

Since, Each peach costs $0.75.

Hence, Total cost of peaches purchased = $0.75p

And, Each mango costs $1.75.

Hence, Total cost of mangos purchased = $1.75m

Since, Avani has a total of $15 to spend on peaches and mangos.

So, An inequality that would represent the possible values of peaches and mangos will be;

⇒ $0.75p + $1.75m = $15

Thus, The inequality which represents the possible values for the number of peaches and mangos purchased will be;

⇒ $0.75p + $1.75m = $15

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The situation best met through long term saving is retirement (Option B).

In many cases, the retirement fund is taken out of the paychecks at your job and is accumulated over years of your service and job till retirement, it is a long-term saving.

The purpose of long-term saving is the type of saving for long term financial goals. The other options are not long-term financial goals rather unexpected expenses. Hence, a situation best fulfilled through long term saving is retirement.

There are several long-term saving accounts use to save for long term financial goals such as retirement, buying a house, children’s education, or similar one-time, long-term expenses.

Hence, the correct answer is retirement – Option B

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The price of one adult ticket is $5 and one student ticket is $14

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every area of mathematics, including coordinate geometry, calculus, and trigonometry. A straightforward algebraic expression is 2x + 4 = 8.

Given that : first day of ticket sales the school sold 14 adult tickets and 5 student tickets for a total of $140. The school took in $190 on the second day by selling 10 adult tickets and 10 student tickets.

Let the price for adult ticket x and for student ticket y

we have ,

14x + 5y =140.....(i)

10x  + 10y = 190....(ii)

10 x + 10y = 190

x + y = 19

y = 19-x .....(iii)

put the value of y in equation i

14x + 5(19-x) = 140

14x + 95 - 5x = 140

9x = 45

x = 5

Now put value of x in equation iii

y = 19 - 5

y = 14

The price of one adult ticket is $5 and one student ticket is $14

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The flagpole is 35ft tall.

Given,

A 5ft tall person casts a shadow that is 4 ft long.

Flagpole has a 28-foot shadow.

Solution:

Let x be the height of the flagpole.

5/x = 4/28

x = 35ft

The flagpole is 35ft tall.

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Answer:

48

Step-by-step explanation:

3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48

6 12 18 24 30 36 40 48

16 32 48

The lower and upper bounds of c- d are 42.0 and 43.0 respectively.

For the given question;

A number, c, rounded to 1 decimal place is 47.3

Another number, d, rounded to 1 decimal place is 4.6

c- d = 47.3 - 4.6

c- d = 42.7

Lower bound = 42.0

Upper bound = 43.0.

Thus, the lower and upper bounds of c- d are 42.0 and 43.0 respectively.

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Answer:

70°

Step-by-step explanation:

Since m∠JKH and m∠LKM are verticle angles, they are equal to each other.

[tex](\stackrel{x_1}{-10}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-10)}}} \implies \cfrac{-9}{2 +10} \implies \cfrac{ -9 }{ 12 }\implies -\cfrac{3}{4}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{3}{4}}(x-\stackrel{x_1}{(-10)}) \implies y -4= -\cfrac{3}{4} (x +10) \\\\\\ y-4=-\cfrac{3}{4}x-\cfrac{15}{2}\implies y=-\cfrac{3}{4}x-\cfrac{15}{2}+4\implies {\Large \begin{array}{llll} y=-\cfrac{3}{4}x-\cfrac{7}{2} \end{array}}[/tex]

Answer:

[tex]\textsf{Slope-intercept form}: \quad y=-\dfrac{4}{3}x+\dfrac{5}{3}[/tex]

[tex]\textsf{Standard form}: \quad 4x+3y=5[/tex]

Step-by-step explanation:

Given linear equation:

[tex]y-11=-\dfrac{4}{3}(x+7)[/tex]

The given linear equation is point-slope form.

[tex]\boxed{\begin{minipage}{3.7cm}\underline{Slope-intercept form}\\\\$y=mx+b$\\\\where $m$ is the slope\\ and $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

To write the equation in slope-intercept form, isolate y:

[tex]\implies y-11=-\dfrac{4}{3}(x+7)[/tex]

[tex]\implies y-11=-\dfrac{4}{3}x-\dfrac{28}{3}[/tex]

[tex]\implies y-11+11=-\dfrac{4}{3}x-\dfrac{28}{3}+11[/tex]

[tex]\implies y=-\dfrac{4}{3}x+\dfrac{5}{3}[/tex]

[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Standard form}\\\\$Ax+By=C$\\\\where $A, B$ and $C$ are constants and $A$ must be positive.\\\end{minipage}}[/tex]

To write the equation in standard form, eliminate the fraction, bring the terms in x and y to the left of the equation, and the constants to the right:

[tex]\implies y-11=-\dfrac{4}{3}(x+7)[/tex]

[tex]\implies (y-11) \cdot 3=-\dfrac{4}{3}(x+7) \cdot 3[/tex]

[tex]\implies 3y-33=-4(x+7)[/tex]

[tex]\implies 3y-33=-4x-28[/tex]

[tex]\implies 3y-33+4x=-4x-28+4x[/tex]

[tex]\implies 3y-33+4x=-28[/tex]

[tex]\implies 3y-33+4x+33=-28+33[/tex]

[tex]\implies 4x+3y=5[/tex]

The graph that represents the solution to inequality 2(b + 2) ≥ 24 is given by the statement "number line with closed point at 10 with arrow pointing right" .

In the question ,

the inequality is given as

2(b + 2) ≥ 24

Solving the inequality further , we get

2b + 2*2 ≥ 24

2b + 4 ≥ 24

Simplifying further we get

2b ≥ 24-4

2b ≥ 20

b ≥ 10 .

Since the inequality has equal to sign, hence number line representing the inequality will have a closed point 10 ,

And on number line as the number increases the value move towards right ,

hence the arrow will point Right .

Therefore , the graph that represents the solution to inequality 2(b + 2) ≥ 24 is given by the statement "number line with closed point at 10 with arrow pointing right" .

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Answer: C number line with closed point at 10 with arrow pointing right

Step-by-step explanation:

I took the test and I got it right. :)

hope this helps

WE WILL USE THE FORMULA OF CALCULATING GRADIENT

[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{j - 1}{9 - 6} \\ \frac{1}{3} = \frac{j - 1}{3} [/tex]

I WILL USE CROSS MULTIPLICATION

[tex]3(j - 1) = 3 \\ \frac{3(j - 1)}{3} = \frac{3}{3} \\ j - 1 = 1 \\ j = 1 + 1 \\ j = 2[/tex]

ATTACHED IS THE SOLUTION

BE ALERT I INSERTED THE KNOWN VALUES IN THE FORMULA OF FINDING THE GRADIENT.

Answer:

[tex]90a+10b[/tex]

Step-by-step explanation:

[tex](100a+10b+c)-(10a+c) \\ \\ =100a+10b+c-10a-c \\ \\ =90a+10b[/tex]

Answer:

137°

Step-by-step explanation:

By the exterior angle theorem, [tex]m\angle JKX=93^{\circ}+44^{\circ}=137^{\circ}[/tex].

For every mile the car is driven, the cost increases by 0.52 units.

Consider a line that passes through the origin at a distance 'a' from the Y-axis and has a slope of m. In this situation, the distance an is the definition of the line's y-intercept. At this moment, the line will cross the y-axis (0, a). The equation for the line will then be y = mx + a. The same goes for a line that crosses the X-axis at a position b from the origin and has a slope of m. (b,0). The distance b is the line's x-intercept. The equation for the line will be y = m* (x-b)

Given, the equation that relates cost of renting and miles driven is
y = 0.52 x + 186
Therefore, for a car travelling one mile, cost is y₁ = 0.52*1 + 186 = 186.52
For a car travelling two miles, cost is y₂ = (0.52*2) + 186 = 187.04
Thus, for every next mile the cost increases by = y₂ - y₁ = 187.04 - 186.52 = 0.52 units

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Answer: A.

Step-by-step explanation:

Something is a function if the x value is not repeated. The y value can be repeated however.

The amplitude of the function y = sin 5лx is found as 1.

The sine (or cosine) function can be written as,

x = A sin (ωt + ϕ)   or   x = A cos (ωt + ϕ)

To find the variables used to calculate the amplitude, use the formula;

y = asin(bx - c) + d.

Where a is the amplitude.

The given equation of function is y = sin 5лx.

Comparing the function with the standard form

a = 1

Thus, the amplitude of the function y = sin 5лx is found as 1.

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