The sum of 3 consecutive numbers is 126. Find the numbers.

Answer: The value of \((g - f)(x)=4 .\)

Step-by-step explanation:

Given functions :  \(f(x) = x + 4\) and \(g(x) = x + 7\)

To find : \((g - f)(x)\)

Difference between two functions: \((u-v)(x)=u(x)-v(x)\)

Then, \((g-f)(x)=g(x)-f(x)\)

\(=(x+7)-(x+4)=x+7-x-4\\\\=7-4=3\)

Hence, the value of \((g - f)(x)=4 .\)

Answer:

4 and 9 hundreths

Step-by-step explanation:

Answer:

It should be 90

Step-by-step explanation:

Because 270 divided by 3 is 90

The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

Answer:

5  

+   0.6

+   0.02

+   0.009

Step-by-step explanation:

5 × 1  

+ 6 ×   0.1

+ 2 ×   0.01

+ 9 ×   0.001

5 × 100

+ 6 × 10-1

+ 2 × 10-2

+ 9 × 10-3

all of them are correct

For the linear function built from the scatter plot, it is found that:

The slope-intercept representation of a linear function is the rule presented as follows:

y = mx + b

The coefficients of the function and their meaning are listed as follows:

From the graph, we have that when x = 0, y = 500, hence the intercept of the line is:

b = 500.

When the input increases by 200, the output increases by 1000, hence the slope is:

m = 1000/2 = 5.

Thus the equation is:

y = 5x + 500.

The graph is given by the image at the end of the answer.

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Answer:

A

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (4, 1 ) and r = 2 , then

(x - 4)² + (y - 1)² = 2² , that is

(x - 4)² + (y - 1)² = 4 ← equation of circle

The new area would be 40 square inches. When a scale factor dilates a polygon, the area is multiplied by the square of the scale factor. If the original area is 10 square inches and the scale factor is 4, the new area would be 10 x 4^2 = 10 x 16 = 40 square inches.

The product of 5 × 5ab × 5, a, b is 125ab5 when written in its most Simple form

The expression 5 × 5ab × 5, a, b is equal to 125ab5. The reasoning is that when we multiply 5 by 5ab, we get 25ab, which we then multiply by 5 to get 125ab. Since a, b are variables, the product 125ab5 is the product of 5 × 5ab × 5, a, b, when written in its most simple form.

The expression 5 × 5ab × 5, a, b is an algebraic expression, which consists of numbers, variables, and operators. Variables are usually represented by letters or other symbols, while operators such as +, -, ×, ÷, ^ are used to indicate mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. In algebra, expressions can be simplified by combining like terms, expanding brackets, and applying other rules of arithmetic.

The most simple form of an expression is the one that cannot be further simplified.In the given expression, 5 × 5ab × 5, a, b, we can see that the number 5 appears three times, so we can simplify the expression by multiplying the numbers together.

Similarly, we can multiply the variables a and b together to get the term ab. Finally, we write the result as 125ab5, which is the product of 5 × 5ab × 5, a, b, in its most simple form.

Therefore, the product of 5 × 5ab × 5, a, b is 125ab5 when written in its most simple form.

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(i) In decimals: 0.65

(ii) In percentage: 65%

The graph shows that after the spinner is spun after 40 times. The Fraction of wins is 0.65 out of 1. Look at the very end of the graph to look at the conclusion for probability. Similar cases when, after the spinner is spun after 20 times, the probability is 0.65.

Answer:

0.65 or 65%

Step-by-step explanation:

round 5.7255 to thousands place

place after thousands place (5) rounds up the 5 before it

therefore 5.726 ur ans

MARK above ANS as branliest

Answer: There are no possible solutions because

If you were to plot these two equations on the graph you would notice they are parallel because both have the same slope (3x) but still have different intercepts. This means there are no possible solutions as in order to have a solution for x and y they need to intercept and the point of interception is the solution for x and y but that cannot happen in a system of equations that result in parallel lines ( they’ll never intercept)

Answer:

Ø

Step-by-step explanation:

These equations are parallel, meaning they have SIMILAR rate of changes [slopes]. To prove it, convert the second equation from Standard Form to Slope-Intercept Form:

\(\displaystyle y - 3x = -13 \hookrightarrow y = 3x - 13 \\ \\ \left \{ {{y = 3x - 13} \atop {y = 3x - 11}} \right.\)

As you can see, both equations have a rate of change of 3, meaning we CANNOT obtain a solution here, therefore we have no solution.

I am joyous to assist you at any time.

9514 1404 393

Answer:

  direct variation

Step-by-step explanation:

The given equation can be written in the direct variation form ...

  y = kx

  y = -8x . . . . rewrite of the given equation (multiply by -4)

This is an example of direct variation.

Answer:

x=√154 over 7 , −√154 over 7

Step-by-step explanation:

Answer:

the answer is that x=positive or negative square root of 22 over square root of 7

Step-by-step explanation:

The area of the rectangle of length 26 inches and width of 14 inches is 2348.4 cm²

Area is the total region bounded by a plane shape.

To calculate the area of the rectangle, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hene, the area of the rectangle is 2348.4 cm²

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The number of times Jennifer rolls a number less than 3 in a number cube when she rolls it 60 times is 40.

The probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

The probability of rolling a number less than 3 on a number cube is 2/6.

\(P( > 3)=\dfrac{2}{6}\)

Here, the Jennifer rolls a number cube 60 times. Thus, the number of times she rolled the number less than 3 in this cube is,

\(n=\dfrac{2}{3}\times60\\n=40\)

Thus, the number of times Jennifer rolls a number less than 3 in a number cube when she rolls it 60 times is 40.

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Complete Question :

An application is using a two-dimensional list defined as follows: 1. Write a statement that creates an empty two-dimensional list named values with 4 rows and 3 columns. 2. Write nested loops that get an integer value from the user for each element in the list, for example: values= [[1, 2, 3], [10, 20, 30], [100, 200, 300],[1000, 2000, 3000]] 3. Write a function named row_values that accepts values as argument and returns the sums of each row and displays the result as a list named row 4. Write a function named column_values that accepts values as arguments and returns the sums of each column and displays the result as a list named column 5. Write a function called sum_values that sums all the elements of the array and displays the result.

Sum of rows : [ 6, 60, 600, 6000 ]

Sum of columns : [ 1111, 2222, 3333]

Sum of all elements : 6666

The nested loops are :

Enter a number at row 0, and column 0 : 1

Enter a number at row 0, and column 1 : 2

Enter a number at row 0, and column 2 : 3

Enter a number at row 1, and column 0 : 10

Enter a number at row 1, and column 1 : 20

Enter a number at row 1, and column 2 : 30

Enter a number at row 2, and column 0 : 100

Enter a number at row 2, and column 1 : 200

Enter a number at row 2, and column 2: 300

Enter a number at row 3, and column 0 : 1000

Enter a number at row 3, and column 1 : 2000

Enter a number at row 3, and column 2 : 3000

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The square feet of paper that will cover the model is 56 ft squared.

The model above is a square base pyramid. Therefore, the square feet of papers he will need to cover the model is the surface area of the model.

Therefore,

surface area of the square base pyramid = A + 1 / 2 ps

where

Therefore,

p = 4 × 4 = 16 ft

s = 5 ft

A = 4² = 16 ft²

Therefore,

surface area of the square base pyramid = 16 + 1 / 2 × 16 × 5

surface area of the square base pyramid = 16 + 40

surface area of the square base pyramid = 56 ft²

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Answer: n=1

Step-by-step explanation:

The value of n such that the given expression equals 216 is n = 1.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given expression is,

(216)ⁿ⁻² / (1/36)³ⁿ.

We have to find the value of n such that the expression equals to 216.

Let,

(216)ⁿ⁻² / (1/36)³ⁿ = 216

[(216)ⁿ (216)⁻²] / [(1/36)³ⁿ] = 216

[(216)ⁿ / (216)²] / [(1)³ⁿ / (36)³ⁿ] = 216

Taking the reciprocal and sign changes to multiplication,

[(216)ⁿ (36)³ⁿ] / (216)² = 216

[(216)ⁿ (36)³ⁿ] = (216)³

(216)ⁿ (36³)ⁿ = (216)³

(6³)ⁿ ((6²)³)ⁿ = (6³)³

(6³)ⁿ (6⁶)ⁿ = (6³)³

(6)³ⁿ (6)⁶ⁿ = (6)⁹

(6)³ⁿ⁺⁶ⁿ = (6)⁹

So, 3n + 6n = 9

9n = 9

n = 1

Hence the value of n is 1.

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The length of the arc defined by the central angle of 312 degrees is 26π cm.

The formula for the arc length of a circle is given by:

L = (θ/360) × 2πr

where L is the length of the arc, θ is the central angle in degrees, and r is the radius of the circle.

Substituting the given values, we get:

L = (312/360) × 2π(30)

L = (26/30) × π × 30

L = 26π cm

Therefore, the length of the arc defined by the central angle of 312 degrees is 26π cm.

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Answer:

The rates are not equivalent since Maria saves $0.50 more per month than Ralph.

Step-by-step explanation:

We can determine if two rates are equivalent by comparing the rates at which they save per month.

Maria's savings per month:

Both 50 and 4 can be divided by 2, which gives us 25/2.  As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.

Ralph's savings per month:

Both 60 and 5 can be divided by 5, which gives us 12.  Thus, Ralph saves $12 per month.

Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.

Step-by-step explanation:

1.: Distribute the 3: 3g-24=18

2.: Add 24 to both sides: 3g=42

3.: Divide by 3: 3g/3=42/3

4.: Answer: g=14

Answer:g=14

Step-by-step explanation:

3(g-8)=18

3g-24=18

3g-24+24=18+24

3g=42

\(\frac{3g}{3} =\frac{42}{3}\)

g = 14

Answer:

\( \sf \huge \boxed{ \boxed{(b + \frac{2}{3} )(b - \frac{2}{3} )}}\)

Step-by-step explanation:

Answer:

Solution given:

\(b^{2} -\frac{4}{9}\)=\(b^{2} -\frac{2^2}{3^2}=b^2 -(\frac{2}{3})^2\)

it is in the form of x²-y²=(x+y)(x-y)

so

\(b^2 -(\frac{2}{3})^2=(b+\frac{2}{3})(b-\frac{2}{3})\) is A required polynomial.

Step-by-step explanation:

9514 1404 393

Answer:

  0  (no solutions)

Step-by-step explanation:

Eliminating parentheses, the equation becomes ...

  24s +72 = 24s -112

  184 = 0 . . . . . . . . . . . add 112 -24s to both sides

There is no value of the variable s that will make this true. The equation has no solutions.

Answer:

Step-by-step explanation:

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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The factory will put 441 cans of soda in 7 cases.

If each case of soda contains 7 cans of each flavor, and the factory is putting 7 cases, we can calculate the total number of cans by multiplying the number of flavors, cans per flavor, and cases.

Given:

Number of flavors = 9

Cans per flavor = 7

Number of cases = 7

To calculate the total number of cans, we can multiply these values:

Total cans = Number of flavors × Cans per flavor × Number of cases

Total cans = 9 × 7 × 7

Total cans = 441

To arrive at this answer, we multiplied the number of flavors (9) by the number of cans per flavor (7) to get the number of cans per case (63). Then, we multiplied the cans per case (63) by the number of cases (7) to obtain the total number of cans (441).

Hence, the factory will put 441 cans of soda in 7 cases.

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The amount of cars you need to break even is 5.

To determine the number of cars you need to break even, we can set up an equation where the revenue equals the total cost.

Let's denote the number of cars as x.

Revenue = Number of cars × Price per wash

= x × $10

Total cost = Cost per car × Number of cars + One-time cost

= $3x + $35

To break even, the revenue should be equal to the total cost:

x × $10 = $3x + $35

Now, let's solve this equation to find the value of x:

10x = 3x + 35

Subtract 3x from both sides:

10x - 3x = 3x + 35 - 3x

7x = 35

Divide both sides by 7:

x = 35 / 7

x = 5

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Answer:

angle1 : angle 2:

72                108

Step-by-step explanation:

Supplementary angles add to 180

angle1 : angle 2:

2               3

Multiply each term by x

2x           3x

The total is 180

2x+3x= 180

5x= 180

Divide by 5

5x/5 =180/5

x =36

angle1 : angle 2:

2*36           3*36

72                108