the cycling team raises money to buy a bike that cost 5,643 the team collects the same amount of money each week for 33 weeks to pay for the bike.
How much money did they make each week?

F and G are inverse if both of them satisfy the condition h(x)=x. f(g(x))=g(f(x))=x, as we discovered. The argument f(x) and g(x) are inverse functions is thus established.

If f (x) and g (x) are inverse functions, it can be determined using one of two ways. For more information, see the explanation.

Explanation:

Instance 1

Inverse functions of both functions can be found using the first method.

Example.

Inverse of f (x) = x + 7 is what we're looking for.

We attempt to determine x using the equation y = x + 7.

y = x + 7

Inferring that g (x) is the inverse of f (x) from the fact that x = y 7

Finding g (x inverse )'s is now necessary.

g( x ) = x − 7

y = x − 7

x = y + 7

As a result, we discovered that f (x) is the inverse function of g (x).

f and g are equal if g is inverse of f and vice versa.

The second approach entails locating the compound functions f ( g ( x ) ) and g ( f ( x ) ). In this case, f and g are inverse if they are both h (x ) = x.

Example:

f ( g ( x ) =  [ x − 7 ] + 7

G ( x ) placed as x is the expression in brackets.

f ( g ( x ) ) = x − 7  + 7 = x

g (f ( x ) =  [ x + 7 ] − 7

f ( x ) inserted as x is the expression in brackets.

g ( f ( x ) ) = x + 7 − 7 = x

The equation f ( g ( x ) ) = g ( f ( x ) ) = x was what we discovered. The argument f (x) and g (x) are inverse functions is thus established.

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Answer:

slope is -1/4

Step-by-step explanation:

We are given the points (-5,2) and (7,-1)

the slope formula is [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

y₂ = -1

y₁ = 2

x₂ = 7

x₁ = -5

[tex]m=\frac{(-1)-2}{7-(-5)}[/tex]

[tex]m=\frac{-3}{12}[/tex]

[tex]m=-\frac{1}{4}[/tex]

Answer:

(1,0)

Step-by-step explanation:

The equation for the red graph is G(x) = 5 - x⁴.

With a graph, the coordinates show where a point is in relation to the x- and y-axes.

The connection between the data drawn on the specified x-axis and y-axis is depicted by the coordinates in a graph.

The red graph is having y = 5, when x = 0

Put x = 0 in G(x) = (2 - x)⁴

= (2 - 0)⁴

= 2⁴

= 16

Now, put in G(x) = 5 - x⁴

= 5 - 0⁴

= 5

Similarly, for G(x) = 2 - x⁴, we get G(x) = 2

For G(x) = (5 - x)⁴

= 5⁴

= 625

When we put x = 0 in all the options, we observe that the equation G(x) = 5 - x⁴ satisfies the condition. So, this is the equation for the red graph.

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The error is to find the solution of system of equations.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The system of equations are,

⇒ a + b = 7   .. (i)

And 1.29a + 0.49b = 6.63 .. (ii)

Now, We can solve the system of equations as;

Here, The system of equations are,

⇒ a + b = 7  

⇒ a = 7 - b .. (i)

And, ⇒ 1.29a + 0.49b = 6.63 .. (ii)

Substitute the value of a from (i) in (ii), we get;

⇒ 1.29a + 0.49b = 6.63

⇒ 1.29(7 - b) + 0.49b = 6.63

⇒ 9.03 - 1.29b + 0.49b = 6.63

⇒ - 0.8b = 6.63 - 9.03

⇒ - 0.8b = - 2.4

⇒ 0.8b = 2.4

⇒ b = 2.4 / 0.8

⇒ b = 3

And, From (i);

⇒ a = 7 - b .. (i)

⇒ a = 7 - 3

⇒ a = 4

Hence, The solution is, 4 pounds of apples and 3 pounds of bananas were bought.

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Answer:

=-64

Step-by-step explanation:

8+13-85 = 21-85 = -64

Answer:

= -64

Step-by-step explanation:

+ * - = -

+ -85 = -85

then:

8 + 13 + -85 = 8 + 13 - 85 = 21 - 85

= -64

In option, D number line shows the sum of -1 and +1 equals zero.

What is the number line?

A number line is a type of line that can be used to show the positions of all numbers. It has two ends which start with -∞, and stops at +∞. A directed number is a number that is either negative or positive. Thus all directed numbers can be located on the number line.

When you have two opposite numbers on a number line, that is, a digit that has a negative value and the same digit having a positive value, when you add them together, you would have 0.

i.e. -a + b = 0

In the above options given, the number line that shows this particular case is the number line in option D.

Hence, In option, D number line shows the sum of -1 and +1 equals zero.

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Solution

Step 1:

The number 2 appears 3 times in the multiplication.

Step 2:

So 2 × 2× 2= 8

Step 3:

The expression 8 has a base of 2 and an exponent of 3.

[tex]2 \times 2 \times 2 \\ = {2}^{3} [/tex]

Answer:

a₆ = -13

Step-by-step explanation:

A recursive formula for a sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.  Therefore, when giving a recursive rule, we need to define the first term of the sequence, as it is not part of the formula.  

Given recursive rule:

[tex]\begin{cases}a_1=7\\a_n=a_{n-1}-4\end{cases}[/tex]

To find the value of a₆, use the recursive formula to find the first 6 terms of the sequence:

[tex]a_1=7[/tex]

[tex]a_2=a_1-4=7-4=3[/tex]

[tex]a_3=a_2-4=3-4=-1[/tex]

[tex]a_4=a_3-4=-1-4=-5[/tex]

[tex]a_5=a_4-4=-5-4=-9[/tex]

[tex]a_6=a_5-4=-9-4=-13[/tex]

Therefore, the value of a₆ is -13.

Answer:

4!/(1! 1! 1! 1!) = 24

Step-by-step explanation:

None of your answers are correct!

Answer: y = 7x + 7

Step-by-step explanation:

The lines equation is y = 7x + 7

Here is a picture of graphing it (desmos)

The length of the line segment AC is 20 units.

A line segment is bounded by two distinct points on a line.

The length of AC is x + 9. The actual length of the line segment AC can be found as follows:

Therefore, using equations,

AB + BC = AC

AB = 3x - 15

BC = x - 9

AC = x + 9

Hence,

AC = AB + BC

x + 9 =  3x - 15 + x - 9

x + 9 = 3x + x - 15 - 9

x + 9 = 4x - 24

x - 4x = -24 - 9

-3x = -33

divide both sides by -3

x = -33 / -3

x = 11

Therefore,

AC = 11 + 9 = 20 units

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Answer:

X=5y+6

Step-by-step explanation:

Answer:

the answer is x = 6 + 5y

Answer:

1,110,000

Step-by-step explanation:

I hope this helps!

The sinusoidal function can be represented as:

[tex]$y = A \sin(Bx + C) + D$[/tex]

Where A is the amplitude, B is the b, C is the phase shift, and D is the vertical shift.

Given that the y-intercept is 2, the vertical shift D is 2.

Given that the midline y = 2, the average value of the function is 2, so the sum of the maximum and minimum value is 4 which means the maximum value is 4, the amplitude of the function is 4-2 = 2.

Given that the maximum value of 4 is at [tex]π/4[/tex] , the phase shift C is π/4.

Given that it completes 2 cycles in the interval [0,2π], the frequency B is

[tex]2/(2π) = 1/π[/tex]

So, the sinusoidal function is:

[tex]$y = 2 \sin(x + \frac{\pi}{4}) + 2$[/tex]

This function starts at y-intercept 2, oscillates between 2+2 =4 and 2-2 = 0, and completes 2 cycles in the interval [0,2π].

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Answer:

1 + 7 = 8

The answer is 8.

Answer:

1+7=8

Step-by-step explanation:

Variable amount include costs of goods sold (COGS), raw materials and production inputs, packaging, wages and commissions, and certain utilities.

The variable cost is calculated using the following formula:

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We can start solving this problem using algebra. Let x be the price of the lower section seats. Then the price of the upper level seats is x - 10.

We know that there are a total of 8000 seats in the arena, and 3000 of them are upper level seats. So the remaining seats are in the lower section, which means there are 5000 lower section seats.

We also know that the total revenue for a sellout is $194,000. We can use this information to set up an equation to represent the total revenue:

(x - 10) * 3000 + x * 5000 = 194000

Now we can use this equation to solve for the price of the lower section seats (x).

3000(x-10) + 5000x = 194000

3x - 30,000 + 5x * 10^4 = 194000

8x = 224,000

x = 28000/8 = 3500

Therefore, the price of the lower section seats is $3500 and the price of the upper level seats is $3500 - $10 = $3490.

Answer: 8 fifteenths of the rain gauge will be filled

Answer:

3/100

Step-by-step explanation:

100 pennies equals 1 dollar so 3 over 100 is the fraction

230p-1010=650p-400-p and 2.3p-10.1=6.49p-4 are the correct options that have the same solution with the parent equation.

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: The expression 2.3p-10.1=6.5p-4-0.01p

                                              -4.19p=10.1-4

                                                     p= -1.4558

Now 230p-1010=650p-400-p

              -419p=1660

                     p=-1.4558

Similarly 2.3p-10.1=6.49p-4

                 -4.19p=10.1-4

                         p=-1.4558

Hence, 230p-1010=650p-400-p and 2.3p-10.1=6.49p-4 are the correct options that have the same solution with the parent equation.

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Answer: 4,5, and 6

Step-by-step explanation:

Answer:

2.5r - 2.5

Step-by-step explanation:

Step 1: Apply the Distributive Property

2.5(r - 1)

2.5 * r - 2.5 * 1

Step 2: Solve

2.5r - 2.5

the correct answer is No

Step-by-step explanation:

it's not equal

Answer:

[tex]\frac{1}{3}\neq\frac{3}{3}[/tex]

Step-by-step explanation:

The two numbers are different

The single shift is 1.5 hours long if 2+3/4 hours equals 1+5/5 equal length shift.

Fractions are referred to in mathematics as the components of a whole. The entire can be a single item or a collection of items. When we slice a cake in real life, the portion represents the proportion of the cake that was originally cut. The word "fraction" has its roots in Latin. "Fractus" is the Latin word for "broken." The fraction was first expressed verbally in antiquity. Later, a numerical form was developed.

Paola contributed to the community garden for 2 + 3 / 4 hours this week, or a 1 + 5 / 6 times length of shift.

We must determine the duration of a single shift.

The correct fraction of the given mixed fractions must first be determined.

Numerator and denominator combine to form a fraction.

The numeral that appears above the division symbol is referred to as the numerator, while the numeral that appears below the division symbol is referred to as the denominator.

2+3/4=(8+3)/4=11/4

1+5/6=(6+5)/6=11/6

Let's say a shift lasts for x hours.

So,

11/4=11*x/6

11/4=11/6 x

66/44=x

x=3/2

x=1.5 hours.

As a result, the single shift is 1.5 hours long if 2+3/4 hours equals 1+5/5 equal length shift.

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The rate of total amount to pounds of meat is 33:11. Option B

The unit rate of total amount to pounds of meat is 3:1. Option F

$33.00 for 11 pounds of meat

The rate of total amount to number of pounds = 33/11

= 33 : 11

The unit rate which refers to the rate of each pound of meat = Total cost / number of pounds

= 33/11

= 3/1

= 3 : 1

Hence, the rate and unit rate of the cost to pounds of meat is 33 : 11 and 3 : 1

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Therefore , the solution of the given problem of inequality comes

out to be  x <-2.

In mathematics, an inequality is a linking of two equations or numbers when there isn't an equal sign. Unbalance therefore precedes inequity. When two numerical values are not equal, an inequality results in a relationship between them. Egality and inequality are not the same. Where variables are not similar or equal, have used the most common symbol (). There are various inequalities that can be utilized to contrast values regardless of how small or huge they are. Switching the two sides it until variables represent all that is left can address a variety of basic inequality problems. The combination or division with low values from both sides are only a few examples of the many factors that might cause inequality. You switch sides and the left.

Here,

Given : 2x-7 < -11

=> 2x < -11 + 7

=> 2x < -4

=> x <-2

Therefore , the solution of the given problem of inequality comes

out to be   x <-2.

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The weekly gross pay is 1040. The solution is obtained using arithmetic operations.

What are arithmetic operations?

There are four basic operations which are listed as follows:

•Addition(‘+’): This operation deals with finding the sum.

•Subtraction(‘-’): This operation deals with finding the difference.

•Multiplication(‘×’): This operation deals with finding the product.

•Division(‘÷’): This operation deals with finding the quotient.

Assumption: Weekly working hours are 40.

Since, the hourly rate is 20 per hour and working hours per week are 40

So, the weekly pay comes out to be 40*20= 800

The overtime rate is time and a half which comes out to be

20*1.5= 30 per hour

The overtime hours are 48-40=8 hours

So, the weekly overtime pay comes out to be 8*30= 240

The total pay= 800+240= 1040

Hence, the weekly gross pay is 1040.

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t should have constraint as in the real world, t is the number of years from 2000,  

T { t ∈ N U {0} | 0 ≤ t ≤ 20} and W = { w ∈ R | w = 0.5t + 47 and 0 ≤ t ≤ 20}

What is the constraint?

A constraint is a condition of an optimization problem that should be satisfied the condition. A cost constraint means that you're limited to a specific project budget, while a time constraint means you must complete your project within a specified timeframe.

The equation W(t) = 0.5t + 47 models the percentage of the population in Guatemala that has access to safe drinking water,

where t represents the number of years since 2000, and W represents the percentage of the population that has access.

Because the data has been collected from 2000 to 2020 and the modelling function is developed on the basis of the collected data. Hence, t should have constraint as in the real world, t is the number of years from 2000.

Because t is the number of years from 2000. Data is collected til 2020, i.e. t=0 to 20,

Let T be the set of all values of t.

T { t ∈ N U {0} | 0 ≤ t ≤ 20}

Because W(t) = 0.5t + 47

Let W be the set of all values of W.

W = { w ∈ R | w = 0.5t + 47 and 0 ≤ t ≤ 20}

Hence, t should have constraint as in the real world, t is the number of years from 2000,  

T { t ∈ N U {0} | 0 ≤ t ≤ 20} and W = { w ∈ R | w = 0.5t + 47 and 0 ≤ t ≤ 20}

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Complete question:

From 2000 to 2020, a world health organization collected data on the percentage of a country's population that had access to safe drinking water. The function W(t) = 0.5t + 47 models the percentage of the population in Guatemala that has safe drinking water where  is the number of years since 2000 and W is the percentage of the population that has access. 5. Explain why the values of  should have a constraint. 6. Write the constraint for the values of t using set builder notation. 7. Write the constraint for the values of W using set builder notation.

An inequality equivalent to 6x+12≥48 is 3x+6≥24.

What is inequality?

Inequality means not equal. Generally, if two values are not equal, we use the “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.

This is because dividing both sides of the original inequality by 6 results in 3x + 6 ≥ 24.

In option B, C and D, the inequality is not equivalent to the original inequality, as they have different values on one side of the inequality sign.

In option B: 3x+12≥24, the left side of the inequality is greater than the left side of the original inequality.

In option C: 3x+12≥18, the right side of the inequality is lesser than the right side of the original inequality.

In option D: 3x+21≥24, the left side of the inequality is greater than the left side of the original inequality and the right side of the inequality is greater than the right side of the original inequality.

Hence, An inequality equivalent to 6x+12≥48 is 3x+6≥24.

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