The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers. x + (x + 1) + (x + 2) = 42 x + (x + 2) + (x + 4) = 42 (x minus 1) + x + (x + 1) = 42 (x minus 2) + x + (x + 2) = 42 x + 2 x + 3 x = 42

Answer:

12

Step-by-step explanation:

Answer: The sales tax percentage is 10%

Step-by-step explanation:

we find the price by take 429 - 390 = $39

Then we take 39 divided by 390 then timed a 100 = 10%

In linear equation,  { 2x + 3y = 7.20 ,   { 4x + 2y = 8.80 the price per pound for oranges.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                   Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let be "x"  the price per pound for grapefruit, "y" the price per pound for oranges.

We know that Steve buys 2 pounds of grapefruit and 3  of oranges for $7.20.

This means that the sum of the products of 2x and 3y is $7.20. Then, we can write this equation to represent it

                                2x + 3y = 7.20

Kennedy buys 4 pounds of grapefruit and 2 pounds of oranges for $8.80.

This means that the sum of the products of  4x and 2y  is $8.80. Then, we can write this equation to represent this

                  4x + 2y = 8.80

Therefore, we get that the system of equations that models the situation is

           { 2x + 3y = 7.20

            { 4x + 2y = 8.80

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The equation of the line that passes through the point (6,1) and is parallel to the line x+3y=15 is 3y+x=9.

The general equation of a straight line is given by the expression

y = mx + c, where m is the gradient and y = c is the point at which the line intersects the y-axis.

Given,

The line is parallel to the line x + 3y = 15 and passes through the point (6,1).

The procedures listed below can be used to find the equation of the line that runs parallel to the line x + 3y = 15 and passes through the point (6,1).

Step 1 - Keep in mind that two parallel lines have equal slopes.

Step 2: As a result, the line's slope across point (6,1) is -1/3.

Step 3: Accordingly, the equation of a line passing through the point (6,1) and being parallel to the line (x + 3y = 15) may be found using the one-point slope form of a line.

The one-point slope form is shown below in Step 4:

y-y₁=m(x-x₁)

Step 5: In the equation above, substitute the values of the known terms.

y-1=-(1/3)(x-6)

3y - 3 = -x + 6

3y +x = 9

Therefore, the equation of the line that passes through the point (6,1) and is parallel to the line x+3y=15 is 3y+x=9.

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Algebraic expressions -1/3(-3m+6-12+15m) and 2(1-2m) are equivalent as they give same expression of simplifying.

What are equivalent algebraic expressions?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

According the given question:

The given algebraic expressions in variable m are -1/3(-3m + 6- 12 + 15m) and 2(1 - 2m)

Simplifying 1st expression

-1/3(-3m + 6- 12 + 15m)

-1/3(-3m) -1/3(6) -1/3(-12) -1/3(15m)

m - 2 + 4 - 5m

-4m + 2 is the simplified form

Similarly simplifying 2nd expression

2(1 - 2m)

2 - 4m

Clearly both the algebraic expressions are same when simplified.

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The pounds of fruit  he buy if he buys 3 pounds of pears and 2 pounds of apples is $16.75.

In case he buys x pounds of pears and y pounds of apples, then he will have  ($3.50x + $3.25y) number of fruits.

The concept that will be used is the concept of addition.

We were told that the Pears cost $3.50 per pound and apples cost $3 per pound from the question.

We can get the total pounds of fruits bought  by multiplying the pounds of apples  with cost per pound and then add it to the  multiplication of the pounds of blueberries and cost per pound which can e expressed as:

($3.50 x 2) =$ 7

+ (3.25 x 3) = $9.75

Then add together as

($ 7 + $9.75 )= $16.75

Then if  if he buys x pounds of pears and y pounds of apples, the number of pounds friuyt he buys will be

$3.50x + $3.25y

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Answer: Its 130 degrees

The number of days it would take if both Sonia and Jennifer work together on the job is 1 7/8 or 1.875 days.

Let the amount of time (in days) that it would take both Sonia and Jennifer working together to paint Sonia's room be t. Additionally, the amount of work done by both Sonia and Jennifer to paint her room in 1 day is given by:

The amount of work done by Sonia in 1 day is 1/x or 1/3.

The amount of work done by Jennifer in 1 day is 1/y or 1/5.

Therefore, the amount of work done by both Sonia and Jennifer working together to paint Sonia's room in 1 day is given by this mathematical expression:

Combined work done = 1/x + 1/y

Combined work done = 1/3 + 1/5

Combined work done = 8/15

Next, we would calculate the combined time as follows:

8/15 × t = 1

Combined time, t = 15/8

Combined time, t = 1 7/8 or 1.875 days.

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In linear equation,$308 is Mr. Brown leaving a a tip .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                        Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

The amount of hotel bill= $140

He leaves 12% of the hotel bill as a tip for the housekeeping service.

Thus, the amount of tip= 12% of hotel bill

=12% of $140

= 12/100 * 140

= 12 * 14

=    168

Therefore, the total amount Mr. Chin pays, including tip =$140+$168 =$308

Hence, Mr. Chin pays $308, including tip

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The value of x is 5.

A polygon is a flat object whose sides are made up of lines. It is a two-dimensional form called a polygon. The sides of regular polygons are all the same length.

Given the polygon and its exterior angle measures.

The sum of the measures of the exterior angles of a polygon is 360°, therefore, it follows:
(10x + 43)° + 66° + (12x + 39)° + (7x + 15)° + 52° = 360°

29x + 215° = 360°

29x = 360° - 215°

29x = 145°

x = 5

Hence, the value of x is 5.

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Answer:

To find the growth rate for a country with a population of 11,000,000, 320,000 births, and 650,000 deaths, you need to first calculate the natural increase in the population by subtracting the number of deaths from the number of births: 320,000 - 650,000 = -330,000. This means that there are 330,000 more deaths than births in this country.

To calculate the growth rate, you need to divide the natural increase by the total population and multiply by 100 to express the result as a percentage. In this case, the growth rate would be: (-330,000 / 11,000,000) * 100 = -3.0%. This means that the population is decreasing at a rate of 3.0% per year.

To find the growth rate for a country with 60,000 births, 50,000 deaths, 20,000 immigrants, and 10,000 emigrants, you need to first calculate the natural increase in the population by subtracting the number of deaths from the number of births: 60,000 - 50,000 = 10,000. Then, you need to add the number of immigrants to this number to get the total increase in the population: 10,000 + 20,000 = 30,000. Finally, you need to subtract the number of emigrants from this number to get the net increase in the population: 30,000 - 10,000 = 20,000.

To calculate the growth rate, you need to divide the net increase in the population by the total population and multiply by 100 to express the result as a percentage. In this case, the growth rate would be: (20,000 / 20,000,000) * 100 = 0.1%. This means that the population is increasing at a rate of 0.1% per year.

Belgium has a growth rate of 0.1%, which means that its population is increasing by 0.1% per year. To find out how many years it will take for the population to double, you need to divide the growth rate into the number 100. Since 100 / 0.1 = 1000, it will take 1000 years for Belgium's population to double if it continues to grow at a rate of 0.1% per year.

Libya is doubling its population every 19 years, which means that its population is increasing by 100% every 19 years. To find the growth rate, you need to divide the population increase (100%) by the number of years it takes for the population to double (19 years) and multiply by 100 to express the result as a percentage. In this case, the growth rate would be: (100 / 19) * 100 = 5.26%. This means that Libya's population is increasing at a rate of 5.26% per year.

Step-by-step explanation:

Answer:

891 millas en 11 semanas.

Step-by-step explanation:

81* 11 es igual a 891.

:)

The greatest possible number of red sweets in the box is 28.

If the ratio between blue and red sweets is x, then the number of blue sweets equals 2x and the number of green sweets equals 7x. If the ratio between green and red sweets is y, then the number of green sweets equals 3y and the number of red sweets equals y. In this case, the number of green sweets must be the same.

7x = 3y

Additionally, 140 is the sum of all of them,

thus,

2x + 3y + y < 140

2x + 4y < 140

x + 2y < 70

x + 2 × 7x/3  < 70

3x + 14x < 210

17x < 210

x < 12.36

and x ought to be a whole number, therefore x = 12

, and the total number of sweets will equal 136.

y = 7 × 12/3 = 28

thus, The greatest possible number of red sweets in the box is 28.

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(complete question)

There are only blue sweets, green sweets, and red sweets in the box. The ratio of the number of blue sweets to the number of green sweets is 2:7 The ratio of the number of green sweets to the number of red sweets is 3:1 there are less than 140 sweets in the box. What is the greatest possible number of red sweets in the box? Your final answer must include, 'red sweets'.

Answer:

558

Step-by-step explanation:

93 times 600 divided by 100 equals 558

Daily wage of James is $64.

Students should follow these steps to solve any word puzzle:

1. Read the problem: Students should first give the problem a quick once-over.

2. Highlight facts: After reading the issue through one more, students should underline or highlight crucial information, such as crucial numbers or words that indicate an operation.

3. Visualize the issue; you might find it useful to create a picture or a diagram.

By developing pertinent images, students can begin to visualize either simple or more complicated problems.

4. Identify the operation(s): Identify the operations that must be carried out. Is it division, multiplication, or addition?

James earns a total of $448 in a week, and he work 8 hours day.

Let his daily wage be x

As daily wage of James is X

In a week there are 7 days

Therefore, 7×X = $448

X = [tex]\frac{448}{7} = 64[/tex]

So, daily wage of James is $64.

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Answer:

The 3rd box and 4th box will be checked

Step-by-step explanation:

The ratio 9:7 for apples to oranges means for every 9 apples there will be 7 oranges. So, the 3rd box and 4th box will be checked.

Answer: 28.57% mark up.

Step-by-step explanation:

If you subtract 25.57% from 84.00 you get 60.00

Answer:

14. Original Price = $43.20

15. Original Price = $32.50

we prove the following step using proof by induction

What is proof by induction?

For each and every natural number n, a statement, theorem, or formula can be proved using the mathematical induction technique. By generalizing this into the "Principle of Mathematical Induction," which we would utilize to demonstrate any mathematical assertion.

We are given a statement 1+3+5+. +(2n-1)=n^2

Now first let us prove the statement for n=1 where n is the number of terms

On the left hand side = 1

And on the right hand side = 1^2 = 1

Hence the statement is proved for n =1

Now let us prove the statement for n= k

Therefore we have 1+3+5+....+k=k^2

Now let us prove the statement for n= k+1

Hence we have

1+3+5+....+k+(k+1)=

k^1+k+1

= (k+1)^2

Hence proved

Therefore we prove the following step using proof by induction

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By using the property of congruency of triangles,

[tex]\angle[/tex]PSR = [tex]\angle[/tex]PSQ has been proved

What is congruency of triangles?

Two triangles are said to be congruent if the corrosponding angles are equal and the corrosponding sides are equal.

There are different axioms of congruency. They are

SSS axiom, SAS axiom, AAS axiom, ASA axiom, RHS axiom

PS bisects [tex]\angle[/tex]QPR [Given]

PQ [tex]\cong[/tex] PR [Given]

[tex]\angle[/tex]QPS [tex]\cong \angle[/tex]RPS [PS bisects  [tex]\angle[/tex]QPR]

PS [tex]\cong[/tex] PS [Reflexive property of congruence]

[tex]\Delta[/tex] PQS [tex]\cong \Delta[/tex] PRS [SAS axiom]

[tex]\angle[/tex]PSR = [tex]\angle[/tex]PSQ [Corrosponding parts of congruent triangles are congruent]

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Answer:

66.67

Step-by-step explanation:

(24*100)/36

Answer:

[tex]n < 91[/tex]

Step-by-step explanation:

Move all terms not containing n to the right side of the inequality.

Add 5 to both sides of the inequality.

[tex]\frac{n}{13} < -12+5[/tex]

Add −12 and 5.

[tex]\frac{n}{13} < -7[/tex]

Multiply both sides by 13.

[tex]\frac{n}{13} *13 < -7*13[/tex]

Simplify the left side by canceling the common factor of 13.

[tex]n < -7*13[/tex]

Simplify the right side by multiplying −7 by 13.

[tex]n < 91[/tex]

Las soluciones de las ecuaciones lineales por propiedades algebraicas se listan a continuación:

7) x = 7

8) x = 16 / 7

9) x = - 1 / 4

10) x = 1 / 5

En este caso tenemos cuatro casos de ecuaciones lineales, cuya variable x debe ser despejada mediante propiedades algebraicas. A continuación, se procede a determinar las soluciones correspondientes a cada expresión:

Caso 7:

2 · (x - 1) - 5 = 14 - x

2 · x - 2 - 5 = 14 - x

2 · x - 7 = 14 - x

3 · x = 21

x = 7

Caso 8:

15 · x + 10 = 6 · x - 2 · (x - 7) + 3 · (1 - x)

15 · x + 10 = 6 · x - 2 · x + 14 + 3 - 3 · x

15 · x + 10 = x + 17

14 · x = 32

x = 32 / 14

x = 16 / 7

Caso 9:

x + 3 · (x - 1) = 6 - 4 · (2 · x + 3)

x + 3 · x - 3 = 6 - 8 · x - 12

4 · x - 3 = - 6 - 8 · x

12 · x = - 3

x = - 1 / 4

Caso 10:

6 - 3 · (x + 1) = 4 · x + 2 · (1 - x)

6 - 3 · x - 3 = 4 · x + 2 - 2 · x

3 - 3 · x = 2 · x + 2

- 5 · x = - 1

x = 1 / 5

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The following equation's linear components have no solutions.

Because they contain the same variable term on one side of the equation but distinct constant values on the other, 5-4x-7-10x=-8x-4-6x-10.

A linear polynomial over a field with zero coefficients can be used to create a linear equation. The answers to such an equation are the numbers that, when the unknowns are replaced, make the equality true.

This particular situation, in which the variable is accurately referred to as the unknown, is commonly referred to as a "linear equation."

In the case of two variables, each solution can be thought of as a point's Cartesian coordinates on the Euclidean plane. The answers to a linear equation result in a line.

Given is an equation that reads 5-4x-7-10x=-8x-4-6x-10 and 14x-2=14x-14.

A linear equation has no solutions if both sides of the equation have different constant values but the same variable term.

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Answer:

y = -3x + 10

Step-by-step explanation:

Do you want the equation of the line?

y = mx + b

the b is where the line intersects the y axis.  That is at 10.  The slope is down 3 and right 1.  That would be -3

By evaluating the function in x = 1, we will get:

f(1) = 4

Here we have the following absolute value function:

f(x) = 11 - 7*|x|

We want to find f(1), this just means that we need to evaluate the function in x = 1.

That means that we need to replace the variable in the equation by the number 1, so let's do that:

f(1) = 11 - 7*|1|

Now we just simplify that, we will get:

f(1) = 11 - 7*|1|

   = 11 - 7

   = 4

f(1) = 4

That is the value we wanted to find.

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The height pf telephone pole is 55.2 ft.

What are similar triangles?

Similar triangles are triangles that have constant form, however their sizes could vary. All equal triangles, squares of any facet lengths area unit samples of similar objects. In alternative words, if 2 triangles area unit similar, then their corresponding angles area unit congruent and corresponding sides area unit in equal proportion.

Main body:

according to question :

height of wooden pole = 144 inches  = 12 ft

(as 12 inches = 1 ft

therefore 144 inches = 12 ft)

distance between telephone pole and wooden pole = 45 ft

distance between pole and stake = 57.5 ft

distance between wooden pole and stake = 57.5 - 45 = 12.5 ft

we need to find height of telephone pole =?

as ΔABE are similar to ΔCDE , so

AB/BE = CD/CE

AB/57.5 = 12/12.5

AB = 12*57.5/12.5

AB = 55.2 ft

Hence , the height pf telephone pole is 55.2 ft.

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Answer:

Step-by-step explanation:

If a fair die is rolled 4 times, what is the probability, rounded to the nearest

The cost of the apples per pound is $1.8.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example: 42x = 10 is an equation.

From the question, We were given

9 pounds of apples.

Amount of apples eaten = 3/4 of a pound

This means,

1 pound - 3/4 pound = 1/4 pound left

Now,

The pounds of apples left:

= 8 + 1/4

= 33/4 pounds

33/4 pounds = $15

Multiply 4/33 on both sides.

1 pound = 4/33 x $15

1 pound = $1.8

Thus,

The cost of the apples per pound is $1.8.

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