Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left.
Write an equation to determine the number of friends (x) at Jack's party.

Equation which is equivalent to the given equation 6x + 9 = 12 is given by 2x + 3 = 4.

As given in the question,

Given equation is equal to :

6x + 9 = 12

Simplify by writing each number into prime factors of the given equation 6x + 9 =12 to get the equivalent equation,

( 2 × 3 )x  + ( 3 × 3 ) = ( 2 × 2 × 3 )

3 is the common factor in all we get,

3 ( 2x + 3) = 3(4)

Divide by 3 both the side of the equation we get,

2x + 3 = 4

Therefore, equation which is equivalent to the given equation 6x + 9 = 12 is given by 2x + 3 = 4.

The complete question is:

Which equation is equivalent to the equation 6x + 9 = 12?

A. x +9=6

B. 2x + 3 = 4

C. 3x + 9 = 6

D. 6x + 12 = 9​

E. 6x = 3

F. 3 = 2x + 4

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A linear equation in two variable can be written in general form as y = mx + c. The slope and y-intercept are 1 / 2 and 30 respectively.  

A linear equation is an equation having only one variable.

Its degree is one and it can  be used to find the value of only one unknown quantity.

Suppose, the cost be y and the number of minutes be x.

Then, the slope from the given table can be found by by taking the ratio of the difference of cost and minutes from any two rows of the table as given below,

Slope = (50-40)/(40-20)

=> slope = 1/2

Now, the equation for the line representing the given table can be given as,

(y-40)/(x-20) = 1 / 2

=> y - 40 = 1 / 2 (x - 20)

=> y = x / 2 - 10 + 40

=> y = x / 2 + 30

The y-intercept is given at x = 0.

therefore y-intercept is given as,

y = 0 / 2 + 30

y = 30.

Hence, the slope is given as 1 / 2 and the y-intercept is 30.

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Answer: If the graph of a relationship is a line or a ray through the origin, then it is proportional. If it is a line or ray that does not pass through the origin, then it is not proportional. Also, if it is not linear, then it is not proportional.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The y-intercept is the y-coordinate with x = 0, this is 2 on the table:

Use one more of points, (2, 6.5) to find the slope:

The line is:

Correct choice is A.

Answer:

25

Step-by-step explanation:

5x5 =25 25-5=20

After 12 months for Emma and 10 months for Evie they will have the same amount of money that is $ 2,600

Given:

Case 1 : Amount of money Emma already has = $ 2000

Amount she plans to save per month = $ 50

Thus according to the above data after 12 months Emma would have

12 × 50 = 600 + 2000

this is equal to $ 2600

Case 2 : Amount of money Evie has = $ 1,600

Amount of money she plans to save every month = $ 100

Thus after 10 months she will have 10 multiplied by 100 which is $ 1000

Thus the total amount she will have = 1000 + 1600

which is equal to $ 2,600

Thus after 12 months for Emma and 10 months for Evie they will have the same amount of money that is $ 2,600

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The dimensions of the rectangle such that the rectangle have the greatest area is length  = 8 and width = 4   .

In the question ,

it is given that ,

a rectangle is inscribed with its base on the x axis , and its upper corner on the parabola y = 12 − x²  ,

let the coordinate of the upper right corner be P(x,y) ,

and A be the area of the rectangle .

the point P lies on the parabola , given y = 12 − x² ,

So,  P = P(x,12−x²)

Due to symmetry of the rectangle,  the width of rectangle is half the distance between P and the y axis ,

that means width = 2x   and length = y .

Area of the rectangle = width × Length

= 2x * y

= 2x (12 − x²)

= 24x - 2x³

To maximize the area we differentiate Area with respect to x ,

we get ,

dA/dx = 24 - 6x²

for critical point dA/dx = 0 ,

24 - 6x²  = 0

6x² = 24

x² = 4

x = ±2 ,

since length cannot be negative ,

So , x = 2 .

to check for maximum and minimum ,we differentiate Area with respect to x,

we get

d²A/dx² = -12x

substituting , x = 2 ,

we get -12 < 0, So , the area is maximum .

hence the width = 2*2 = 4

and length = 12 - 4 = 8

and the maximum area is 32 .

Therefore , The dimensions of the rectangle such that the rectangle have the greatest area is length  = 8 and width = 4   .

The given question is incomplete , the complete question is

A rectangle is inscribed with its base on the x axis and its upper corners on the parabola y = 12 − x² . What are the dimensions of such a rectangle with the greatest possible area ?

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A rental company charge $65 a day and 20 cent a mile for renting a truck. Michael rented a truck for 3 day, and he bill came to $275. He drive 400 mile.

In the given question we have to find how many mile did he drive.

From the given question, a rental company charge $65 a day and 20 cent a mile for renting a truck.

Michael rented a truck for 3 day, and he bill came to $275.

The rental company charges for three days renting

$(65×3)=$195

Also there is a expense of a mile for renting the truck is

20 cents =$0.20

Let Michel drove x miles in 3 days.

Therefore total bill in 3 days is $(0.20x+195).

According to the question,

0.20x+195 = 275

Subtract 195 on both side we get

0.20x = 80

Divide by 0.20 on both side we get

x = 400

Hence, he drive 400 mile.

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Answer:

MN = 130

Step-by-step explanation:

since M is at the midpoint of LN , then

LM = MN

7x - 24 = 6x - 2 ( subtract 6x from both sides )

x - 24 = - 2 ( add 24 to both sides )

x = 22

Then

MN = 6x - 2 = 6(22) - 2 = 132 - 2 = 130

Step-by-step explanation:

function 1 :

simple, you put 3 into every place of x and then calculate.

y = -4×3 + 2 = -12 + 2 = -10

function 2 :

the only one where we need to think a little.

so, x = 3.

from the center of the coordinate axes we go on the x-axis to 3.

from there we go up out down to intersect the line. then we look to the left to the y-axis and see what value we have there : -1

y = -1 when x = 3

function 3 :

the solution is already written there in full sight.

input = 3.

so, we look in the table. where is the line with input = 3 ?

it is the last but one line. what value is in the output column of that line ? -3

output = -3

The slope of the line is 1/5 which is positive.

From the graph:

slope:

Slope is the steepness of a line as it moves from LEFT to RIGHT. Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line. The slope of a line is always constant (it never changes) no matter what 2 points on the line you choose.

Take any points:

(0,0) and (5,1)

slope m = y2 - y1 / x2 -x1

= 1 - 0 / 5 - 0

= 1/5

Therefore the slope of the line is 1/5 which is positive.

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Distance between starting and end point. The hiker descends the distance is [tex]124.1m[/tex]

What is depth?

The distance between the nearest end and farthest end of an object is its depth.

Here given that, the depth of the mammoth cave is [tex]-124.1m[/tex].

When the hiker is at the maximum depth it is traveling to the bottom of the cave.

As it is given the depth of the cave [tex]-124.1m[/tex]. Since the hiker is traveling down to the bottom and covering the total depth and the hiker must have covered the same distance corresponding to the depth in the cave which would be [tex]124.1m[/tex].

Hence, the hiker must have descended the distance that is [tex]124.1m[/tex]

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The temperature when the plane reaches an altitude of 7,000ft is 47.3 degree.

What is temperature?

Temperature, measure of hotness or coldness expressed in terms of any of several arbitrary scales and indicating the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature).

Given,

there is temperature decrease in every thousand feet = 1.7f

temperature decrease in 7000 ft = 7(1.7) = 11.9 f

Therefore, temperature = 59.2- 11.9

=47.3

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The speed of the fish in still water is 5 Km/h.

The speed of the current is 1 km/hr.

For the given question.

Total distance travelled by fish = 12 miles.

Let the speed of the fish in still water be 'x km/h.'

Let the speed of the current be 'y km/hr'.

Time taken by fish in moving down steam is 2 hours.

Time taken by fish in moving up steam is 3 hours.

Use formula;

Distance = speed x time

Part a:  system of linear equations

Down steam; 2(x + y) = 12   ...eq 1

Up steam; 3(x - y) = 12   ...eq 2

Part b: speed of the fish in still water.

Solve equation 1 an d 2 by elimination.

2(x + y) = 12

3(x - y) = 12

Divide equation 1 by 2 and multiply it by 3, Then add to eq 2.

6x = 30

x = 5

Speed of fish in still water = 5 Km/h.

Part c: speed of the current

Put value of x in eq 1.

x = 5

2y = 12 - 10

2y = 2

y = 1

Thus, speed of the current is 1 km/hr.

Part d: If the speed of the current is not constant than, then the value of speed of the fish in still water can not be found.

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Answer:

Step-by-step explanation:15(x+2) =25

15x+30=25

15x=5

3x=1

x=1/3

The different ways used to display misleading information on a graph is done by skipping a number or doesn't begin at zero. There are incorrect labels on the graph. Data is missing.

A misleading graph also referred to as a distorted graph, is one that presents data inaccurately, abusing statistics in the process and potentially leading to an incorrect conclusion.

Sometimes deceptive graphs are created on purpose, and other times it's just a matter of people not comprehending the data that goes into the graph. The "classic" varieties of deceptive graphs include those in which:

The vertical scale does not begin at zero, is too large or too little, skips digits, or all of the above.

The graph's labels need to be updated.

Data is omitted.

Thus, the different ways used to display misleading information on a graph are done by skipping a number or doesn't begin at zero. There are incorrect labels on the graph. Data is missing.

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Answer:

Step-by-step explanation:

 -3x^2 + 24x + 5 in the form 5 (6x - 3)^2 + 18

The recipe  that  will only make 1 dozen cookies is as follows:

.18 cups of peanut butter

.12 cups of vegetable shortening

.30 cups packed light brown sugar

.72 tablespoons of milk

.66 teaspoon vanilla extract

.24 large eggs

.36 cups of flour

.18 teaspoons of baking soda

.6 teaspoons of salt.

This refers to the ingredients for baking a snack or dessert.

From the question:

Original cookie recipe =

1 1/2 cups of peanut butter

1 cup of vegetable shortening

2 1/2 cups packed light brown sugar

6 tablespoons of milk

5 1/2 teaspoon vanilla extract

2 large eggs

3 cups of flour

1 1/2 teaspoons of baking soda

1/2 teaspoon of salt

Note: 1 dozen= 12

The recipe that will only make 1 dozen cookies will be = Original cookie recipe * 12

1 1/2 cups of peanut butter * 12 =

3/2 *12= 18

1 cup of vegetable shortening *12

1 * 12 = 12

2 1/2 cups packed light brown sugar * 12

3/2 * 18 = 30

6 tablespoons of milk *12

6 * 12 = 72

5 1/2 teaspoon vanilla extract * 12

11/2 *12 = 66

2 large eggs * 12

2*12 = 24

3 cups of flour *12

3*12 = 36

1 1/2 teaspoons of baking soda * 12

3/2 *12 = 18

1/2 teaspoon of salt * 12

1/2 * 12= 6

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Answer:

Plug all of the X values on the left of the table in to the equations one by one and calculate.

-2(-4)—5= 3

-2(-2)—5= -1

-2(0)—5= -5

-2(2)—5= -9

Step-by-step explanation:

Answer:

76

Step-by-step explanation:

Let the number of vegetarians be x. Then, the number of non-vegetarians is x-52.

[tex]x+x-52=100 \\ \\ 2x=152 \\ \\ x=76[/tex]

Answer:

Step-by-step explanation:

14. y = -2/3x + 10. This is parallel to 2x -3y because they have the same slope.

15. y = -1/2x and y = -1/2x + 2. These are perpendicular because the slope is the opposite reciprocal to the slope of y = 2x + 3, which is 2.
The slopes of the lines of the 2 equations are the same. Because of that, we can state that 2 lines that are perpendicular to the same line are parallel. This can be further supported by the Perpendicular Transversal Theorem, which says the same thing.

Hope this helps!

Answer:

translation, then rotation

Step-by-step explanation:

TThe 95% confidence interval for the mean spent on books at this university is (160.711, 179.289).

In the given question we have to find the 95% confidence interval for the mean spent on books at this university.

A sample of 50 students was taken from the local university.

So n=50

These students spent an average of $170 on books this semester, with a standard deviation of $25.50.

So x=$170 and σ = $25.50

So the 95% confidence interval for the mean spent on books at this university.

CI=x ± [tex]z_{\alpha /2}[/tex]× σ/√n

Now finding the value of [tex]z_{\alpha /2}[/tex] for 99%=0.99 confidence interval.

[tex]\alpha[/tex] =1−0.99 = 0.01

[tex]\alpha[/tex]/2 = 0.01/2 = 0.005

[tex]z_{\alpha /2}=z_{0.005}[/tex]

[tex]z_{\alpha /2}[/tex] = 2.576

The z critical value at 99% confidence interval is 2.576.

Putting the value

CI=170 ± 2.576× 25.50/√50

CI=170 ± 2.576× 25.50/7.071

CI=170 ± 2.576×3.606

CI=170 ± 9.289

CI=(170 − 9.289, 170 + 9.289)

CI =(160.711, 179.289)

Hence, the 95% confidence interval for the mean spent on books at this university is (160.711, 179.289).

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Answer: The function that has these points is invalid because there can not be 2 different y-values in the same x-value.

Using the ideal gas law, pv=nrt we can find the number of moles (n), pressure (P), volume (V), Kelvin (T).

The relationship between pressure (P), volume (V), amount of gas (n), and temperature (T) is represented by the ideal gas equation, PV=nRT (T). Because it assumes that gas is functioning in an ideal or theoretical way and can therefore be written as a universal gas constant, it is known as "the ideal gas law" (represented by R in the equation).

It is believed that the gas is perfect.

In many cases, pressure (P) is measured in atmospheres (atm). Liters are commonly used to measure volume (V) (L). Mole amounts (n) are frequently used as units of measurement (mol). The unit of temperature is Kelvin (T) (K).

R is the universal constant. The SI value is 8.31 J/mol∗K

The ideal gas law is helpful for comprehending and computing the characteristics and actions of gas, such as when developing cars or airplanes. It is also crucial for understanding thermodynamics. For instance, the pressure can be determined when the temperature, volume, and quantity of gas are known. When the variables are unknown, the ideal gas law equation can be changed to provide a solution for each one.

Hence by using the ideal gas law, pv=nrt compute the characteristics and actions of gas.

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Answer:

French = 5 ; German = 11

Step-by-step explanation:

G + F = 16

G = 6 + F

6 + F + F = 16

6 + 2F = 16

2F = 16 - 6

2F = 10

2/2 F = 10/2

F = 5

G = 5 + 6 = 11

The length of the missing side is 39 units

The parallelogram is a simple 2D-shaped quadrilateral with two pairs of parallel sides. In a parallelogram, the opposite sides and opposite angles are equal.

Here we have,

The length of the sides of a parallelogram is 2x+10, 5x- 20 and 4x-1

As we know parallel lines of a Parallelogram are equal

Take any two sides as equal and find the missing side

Let the sides with lengths be equal 2x+10, 5x- 20

=> 2x+10 = 5x- 20      

=> 5x - 2x = 20+ 10

=> 3x = 30

=> x = 10  

Therefore, the lengths of the 3 sides are  

2x+10 = 2(10) + 10 = 30

5x- 20 = 5(10) - 20 = 30

4x-1 = 4(10) - 1 = 40 - 1 = 39    

The length of the missing side is 39 units

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Answer:

Integer, Rational, Real

Step-by-step explanation:

Let's go through and define what each of these are:

Integer:

An integer is any number (including zero) that is positive or negative. Please note that it cannot be a decimal / fraction.

-1 is a whole, negative number. So, it is an integer.

Rational:

A rational number is any number that can be written as a ratio of 2 numbers. Ex: 1.5 can be 3/2

-1 can be written as -1/1, so it is a rational number.

Real

A real number is *any* number that is not imaginary (the number i is imaginary. i is [tex]\sqrt{-1}[/tex])

-1 has no i so it is a real number

Irrational

An irrational number is any number with a radical at it's end. Ex: 3 [tex]\sqrt{5}[/tex], and [tex]2\sqrt{2}[/tex]

-1 has no radical attached to it, so it is not an irrational number.

Whole:

A whole number is any number that has no decimal and is positive (though zero is included)

-1 has no negative, but is a negative number so it would not be counted as a whole number.

Natural:

Natural numbers were always confusing to me, but I hope this will help you. A natural number is any positive number starting at 1, and going forever. They always increase in a multiple of 1. Examples of natural numbers: 1, 2, 3, 4... It is called a natural number, because counting in multiples of ones is natural to us, like counting the amount of apples in a basket.

-1 is a negative number, so doesn't qualify for the characteristics of a natural number.

Let's go back through all of these explanations and see which ones we said -1 is:

Integer, Rational, Real

The given interval shown on the number line in inequality notation as (3, 6).

What are inequalities on a number line?

Inequalities on a number line allow us to visualise the values that are represented by an inequality.

To represent inequalities on a number line we show the range of numbers by drawing a straight line and indicating the end points with either an open circle or a closed circle.  

An open circle shows it does not include the value.

A closed circle shows it does include the value.

The left endpoint is 3. The right endpoint is 6. Both endpoints are open holes, meaning we do not include them as part of the green shaded solution region. If x is a solution, then the solution can be described as  

3 < X < 6 which converts to the interval notation (3, 6) . The curved parenthesis says "do not include the endpoint".

Note: this is not ordered pair notation (x,y).

The given interval shown on the number line in inequality notation as (3, 6).

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Answer:

Step-by-step explanation: