Explain how the distributive property can be used to solve the equation 3(x+4)=36

Answer:

N = 14

Step-by-step explanation:

Let the number be N.  Then:

N + 7 = 21

Now solve this equation for N:

Subtract 7 from both sides.  We get:

N = 14

Answer:

1. n = 14

2. n = 3

3. n - 7 = 21; n = 28

Answer:

It is 3.5 x 10^2 and 9.4x10^4

Step-by-step explanation:

350 = 3.5 x 10^2

which implies 3 - hundred

5 - tens

0 - units

94000 = 9.4x10^4

which implies 9 - ten thousand

4 - thousand

0 - hundred

0 - tens

0 - units

Answer:

Repost: 350.94

Step-by-step explanation:

three hundred: 3__

fifty: _5_

And: Is for the decimal point

Ninety (Thousandths): ___.9_

Four (Thousandths): ___._4

Now just put it all together and you get 350.94

Hopes this helps in the future ^_^

Answer:

1/2

Step-by-step explanation:

you put it in slope form which is y1-y2/x1-x2 to get 9-3/7+5 which simplifies to 1/2

Answer: x = 12

Step-by-step explanation:

First you must simplify:

x + (x + 4) = 28

Reorder the terms:

x + (4 + x) = 28

Remove parenthesis around (4 + x):

x + 4 + x = 28

Reorder the terms:

4 + x + x = 28

Combine like terms: x + x = 2x

4 + 2x = 28

Solving

4 + 2x = 28

Now we must solve for the variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.

4 + -4 + 2x = 28 + -4

Combine like terms: 4 + -4 = 0

0 + 2x = 28 + -4

2x = 28 + -4

Combine like terms: 28 + -4 = 24

2x = 24

Divide each side by '2'.

x = 12

Simplifying

x = 12

Hope this helps! :)

Answer:57

Step-by-step explanation:

Conversion factor is

1 US bushel = 4 US pecks

76 rows x 3 pecks= 228 pecks

228 pecks / 4 = 57

To plant 76 rows of seed potatoes, with 3 pecks per row, we would need a total of 57 bushels, as there are 0.75 bushels per row and this is multiplied by the number of rows.

To answer this question, we first need to understand the relationship between bushels and pecks. There are 4 pecks in one bushel. If 3 pecks are planted per row, then each row requires 0.75 bushels (because 3/4 = 0.75). So, to find the number of bushels needed for 76 rows, we multiply 76 by 0.75.

The final calculation is: 0.75 bushels/row * 76 rows = 57 bushels.

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Answer:

width =4.5ft

length=6ft

Step-by-step explanation:

w = x

L = 2x-3

area = L*w

27 = x(2x-3)

[tex]27=2x^{2} -3x[/tex]

[tex]2x^{2} -3x-27=0[/tex]

[tex]2x^{2} +6x-9x-27=0[/tex]

2x(x+3)-9(x+3)=0

(2x-9)(x+3)=0

2x-9=0

2x=9

x=9/2

x=4.5

L=2x-3=2*4.5-3 =9-3=6

The dimensions of the rectangle are; width = 4.5ft and length = 6ft.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

The length of the rectangle is 3ft less than twice the width.

Let width = x

Length = 2x - 3

The area of the rectangle = length × Width

27 = x(2x-3)

2x² - 3x = 27

2x² - 3x - 27 = 0

2x(x + 3) - 9(x + 3) = 0

(2x-9)(x+3)=0

The solutions are;

2x-9=0

2x=9

x=9/2

x = 4.5

(x+3) = 0

x = -3

The width cannot be negative.

So,

Length = 2x-3 = 2*4.5-3 = 9 - 3

Length = 6

Hence, The dimensions of the rectangle are; width = 4.5ft and length = 6ft.

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Final answer:

The value of the discriminant is 36, which means that the quadratic equation -2x = -8x + 8 has two distinct real solutions.

Explanation:

The given equation -2x = -8x + 8 can be rearranged into a quadratic equation: -8x + 8 + 2x = 0. Combining like terms gives: -6x + 8 = 0. To find the discriminant of this quadratic equation, we look at the coefficient of x^2, which is 0. Since the discriminant D = b^2 - 4ac, where a = coefficient of x^2, b = coefficient of x, and c = constant term, in this case, a = 0, b = -6, and c = 8. Plugging these values into the formula, we have: D = (-6)^2 - 4(0)(8) = 36 - 0 = 36.

The value of the discriminant is 36. The discriminant tells us about the number of real number solutions the equation has. If the discriminant is positive (D > 0), then the equation has two distinct real solutions. If the discriminant is zero (D = 0), then the equation has one real solution. If the discriminant is negative (D < 0), then the equation has no real solutions.

In this case, since the discriminant is positive (D = 36), the quadratic equation has two distinct real solutions.

Answer:

D) .h(x)= 6x+ 13

Step-by-step explanation:

We are given that,

Function representing number of students from A,

Function representing number of students from B,

It is required to find the total number of students in the fair.

So, we have,

Total number of students =

i.e. Total number of students =

i.e. Total number of students =

i.e. Total number of students =

Hence, the function representing the total number of students in the fair is .

Thus, option D is correct.

Answer:

6x + 13.

Step-by-step explanation:

That is the sum of R(x) and g(x)

= 4x + 5 + 2x + 8

= 6x + 13.

C. 3.16 is the right answer

Step-by-step explanation:

The distance formula used in coordinate geometry is derived from the Pythagorean theorem.

The distance formula is give by:

[tex]d=\sqrt{(x_2-x_2)^2+(y_2-y_1)^2}[/tex]

Here (x1,y1) are the coordinates of first point and (y1,y2) are the coordinates of second point

Here,

(x1,y1) = (5,-3)

(x2,y2) = (6,0)

Putting the values in the formula

[tex]AB = \sqrt{(6-5)^2+(0-(-3))^2}\\=\sqrt{(1)^2+(0+3)^2}\\=\sqrt{(1)^2+(3)^2}\\=\sqrt{1+9}\\=\sqrt{10}\\=3.16\ units[/tex]

The distance between two points is 3.16 units.

Hence,

C. 3.16 is the right answer

Keywords: Coordinate geometry, Pythagorean Theorem

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Answer:

constant

It is the unchanging value, and the coefficiant is the numbers with the variables because the variable changes the number. The variable is the letter that is either alone or with a number.

The combined volume of both tanks is: Option A: 15x^2

Step-by-step explanation:

Given

Volume of larger tank = V_L =  [tex]8x^2+2x-1[/tex] in^3

Volume of smaller tank = V_S= [tex]7x^2-2x+1[/tex] in^3

To find the combined volume, we have to add both volumes

[tex]V = V_L+V_S\\=8x^2 + 2x - 1 + (7x^2 - 2x + 1)\\=8x^2+2x-1+7x^2-2x+1\\Combining\ like\ terms\\=8x^2+7x^2+2x-2x-1+1\\=15x^2[/tex]

Hence,

The combined volume of both tanks is: Option A: 15x^2

Keywords: Expressions, Polynomials

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Answer:

$5.89

Step-by-step explanation:

29.45/5=5.89

Answer:

$5.89

Step-by-step explanation:

I divided 29.45 and 5 and got the product+cost of a single pair of the gloves; $5.89

Answer:

B

Step-by-step explanation:

-2x + 9 < x - 9 simplifies to x < 6

Answer:

A is the answer

Step-by-step explanation:

Solve the equation and the answer would come out to be 6

open dot that goes to the right

Answer:

I would line up the numbers in order

The coefficient of skewness is 0.26, indicating slight positive skewness and the kurtosis is approximately -0.84, indicating a platykurtic distribution.

We have,

To calculate the coefficient of skewness and kurtosis, we first need to organize the data into a frequency distribution table.

Age | Frequency

10 | 3

12 | 2

13 | 4

14 | 5

15 | 5

16 | 5

17 | 4

18 | 6

19 | 4

20 | 3

22 | 4

24 | 4

25 | 1

27 | 3

28 | 1

30 | 2

31 | 4

32 | 3

34 | 3

35 | 3

37 | 1

38 | 1

40 | 1

43 | 1

44 | 2

To calculate the coefficient of skewness, we use the formula:

Coefficient of Skewness = (mean - mode) / standard deviation

Mean = (10 * 3 + 12 * 2 + 13 * 4 + ... + 44 * 2) / 100 ≈ 20.49

Mode = 18 (the most frequent value in the dataset)

Standard Deviation

= √[((10 - mean)² * 3 + (12 - mean)² * 2 + ... + (44 - mean)² * 2) / 100]

≈ 9.63

Coefficient of Skewness = (20.49 - 18) / 9.63 ≈ 0.26

To calculate the kurtosis, we use the formula:

Kurtosis = ∑[((x - mean) / standard deviation)⁴ * frequency] / (n * standard deviation⁴) - 3

Kurtosis = [((10 - mean) / standard deviation)⁴ * 3 + ((12 - mean) / standard deviation)⁴ * 2 + ... + ((44 - mean) / standard deviation)⁴ * 2] / (100 * standard deviation⁴) - 3 ≈ -0.84

Interpretation:

Coefficient of Skewness:

The coefficient of skewness is positive (0.26), indicating that the data is slightly skewed to the right (positively skewed). This means that there is a longer tail on the right side of the distribution.

Kurtosis:

The kurtosis value is approximately -0.84. Since it is less than 3, the distribution is considered platykurtic. This means that the distribution has lighter tails and is flatter compared to a normal distribution.

Thus,

The coefficient of skewness is 0.26, indicating slight positive skewness and the kurtosis is approximately -0.84, indicating a platykurtic distribution.

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Answer:

sqrt(x+3)

Step-by-step explanation:

Answer:

d=50

Step-by-step explanation:

-d+100=-3d+200

Subtract 100 from both sides

-d+100-100=-3d+200-100

Simplify

-d=-3d+100

Add 3d to both sides

-d+3d=-3d+100+3d

Simplify

2d=100

Divide both sides by 2

\frac{2d}{2}=\frac{100}{2}

Simplify

d=50

Answer:

In 50days

Step-by-step explanation:

Since the equation below can be used to find the number of days (d) until they will have the same number of pages left in their journals −d + 100 = −3d + 200, this equations will be solved to get 'd'

Given the equation;

−d + 100 = −3d + 200

Collecting like terms we will have;

-d+3d = 200-100

2d = 100

d = 50

This shows that Max and Pat will have the same number of pages left in their journals in 50days.

The total number of boxes will be 60 that the girls have sold in one hour.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

We have to determine the total number of boxes will the girls have sold in one hour

Let Kate sold x boxes in 60 minutes

As per the given situation, we can write the ratio would be as:

27 boxes : 45 minutes = x boxes :  60 minutes

⇒ 27/45 = x/60

Apply the cross-multiplication operation,

⇒ x = (60×27)/45

⇒ x = 36

Let Miley sold y boxes in 60 minutes

⇒ 12/30= y/60

Apply the cross-multiplication operation,

⇒ y = (12×60)/30

⇒ y = 24

So, the total number of boxes = x + y = 36 + 24 = 60

Thus, the total number of boxes will be 60 that the girls have sold in one hour.

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Final answer:

Kate sells 36 boxes and Miley sells 24 boxes in one hour. So, they will have sold a total of 60 boxes in one hour.

Explanation:

To find the total number of boxes sold by both Kate and Miley in one hour, we need to calculate the rate at which each of them sells boxes. Kate sells 27 boxes in 45 minutes, which can be converted to 0.6 boxes per minute (27 boxes / 45 minutes = 0.6 boxes per minute). Miley sells 12 boxes in 30 minutes, which can be converted to 0.4 boxes per minute (12 boxes / 30 minutes = 0.4 boxes per minute).

To find the total number of boxes sold in one hour, we add the number of boxes each of them sells in one minute and multiply it by 60 (the number of minutes in an hour). Kate sells 0.6 boxes per minute, so in one hour she would sell 0.6 boxes/minute * 60 minutes = 36 boxes. Miley sells 0.4 boxes per minute, so in one hour she would sell 0.4 boxes/minute * 60 minutes = 24 boxes. Therefore, the total number of boxes sold by both Kate and Miley in one hour would be 36 + 24 = 60 boxes.

Answer:

At least 55 tickets must be sold to cover the remaining cost of the party.

Step-by-step explanation:

Total money needed for the party  = $350

The money already with the committee  = $75

Now, the money yet to be collected = Total Party Budget - Money present

                                                              = $350  = $75  = $275

Now, the cost of 1 ticket  = $5

Let us assume the number of tickets sold to cover the cost of party = m

⇒ The cost of m tickets   = 5 m

The renaming cost = Total cost of m tickets

or, 5 m =  $275

⇒ m = 275/5  = 55

or, m = 55

Hence, at least 55 tickets must be sold to cover the remaining cost of the

party by Josef.

Answer:

80in^3

Step-by-step explanation:

Answer:

80 in^3

Step-by-step explanation:

I just did this

Answer:

The length is 52 units

Step-by-step explanation:

we know that

The length of the path. is equal to the perimeter of polygon A.B.C.D.E.F

[tex]P=A.B+B.C+C.D+D.E+E.F+A.F[/tex]

The formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

step 1

Find the distance A.B

we have

[tex]A(-7,7),B(6,7)[/tex]

substitute in the formula

[tex]d=\sqrt{(7-7)^{2}+(6+7)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(13)^{2}}[/tex]

[tex]d_A_B=13\ units[/tex]

step 2

Find the distance B.C

we have

[tex]B(6,7),C(6,-2)[/tex]

substitute in the formula

[tex]d=\sqrt{(-2-7)^{2}+(6-6)^{2}}[/tex]

[tex]d=\sqrt{(-9)^{2}+(0)^{2}}[/tex]

[tex]d_B_C=9\ units[/tex]

step 3

Find the distance C.D

we have

[tex]C(6,-2),D(3,-2)[/tex]

substitute in the formula

[tex]d=\sqrt{(-2+2)^{2}+(3-6)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(-3)^{2}}[/tex]

[tex]d_C_D=3\ units[/tex]

step 4

Find the distance D.E

we have

[tex]D(3,-2),E(3,-6)[/tex]

substitute in the formula

[tex]d=\sqrt{(-6+2)^{2}+(3-3)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(0)^{2}}[/tex]

[tex]d_D_E=4\ units[/tex]

step 5

Find the distance E.F

we have

[tex]E(3,-6),F(-7,-6)[/tex]

substitute in the formula

[tex]d=\sqrt{(-6+6)^{2}+(-7-3)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(-10)^{2}}[/tex]

[tex]d_E_F=10\ units[/tex]

step 6

Find the distance A.F

we have

[tex]A(-7,7),F(-7,-6)[/tex]

substitute in the formula

[tex]d=\sqrt{(-6-7)^{2}+(-7+7)^{2}}[/tex]

[tex]d=\sqrt{(-13)^{2}+(0)^{2}}[/tex]

[tex]d_A_F=13\ units[/tex]

step 7

Find the perimeter

[tex]P=A.B+B.C+C.D+D.E+E.F+A.F[/tex]

substitute the values

[tex]P=13+9+3+4+10+13[/tex]

[tex]P=52\ units[/tex]

Answer:

She can make 10 pizzas.

Step-by-step explanation:

8 1/3=25/3

(25/3)/(5/6)=(25/3)(6/5)=150/15=10

Answer:

120°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

A hexagon has 6 sides, thus

sum = 180° × 4 = 720°

To find the measure of each interior angle divide by 6, that is

interior angle = 720° ÷ 6 = 120°

Answer: 120°

Step-by-step explanation: Let's start by finding the sum of the measures of the interior angles. The sum of the measures of the interior angles of a polygon can be found using the formula 180 (n - 2) where n represents the number of sides in the polygon.

Since a regular hexagon has 6 sides, we can plug a 6 in for n in our formula and we have 180 (6 - 2) where 6 represents the number of sides. We can simplify this by subtracting 2 from 6 inside the parentheses to get 180 (4) which is 720.

So the sum of the measures of the interior angles of a regular hexagon is 720°.

However, we want to know the measure of each interior angle. Since the angles of a regular hexagon are all congruent, we simply divide the sum of the measures of the angles which is 720 by the number of angles or sides which is 6 to get 120.

So the measure of each interior angle of a regular hexagon is 120°.

So the formula for finding the measure of each interior angle of a regular polygon is simply the sum of the interior angles 180 (n - 2) divided by the number of sides which is n.

Image provided.

Answer:

Domain f(x)={y:6≥y≤0}

Range of f(x)={x:x≤69}

Cross-check the location of point on your graph this is roughly estimation

Answer:

[tex]t = \frac{100}{r} [\frac{D}{C} - 1][/tex]

Step-by-step explanation:

Assume that the deposited amount C dollars earn r% simple interest annually.

If after t years the deposited amount C dollars grows to D dollars, then we are asked to write a relation using the given terms to calculate t.

Now, using the formula of simple interest we can write

[tex]D = C(1 + \frac{t\times r}{100})[/tex]

⇒ [tex]1 + \frac{t \times r}{100} = \frac{D}{C}[/tex]

⇒ [tex]\frac{t \times r}{100} = \frac{D}{C} - 1[/tex]

⇒ [tex]t = \frac{100}{r} [\frac{D}{C} - 1][/tex]

So, this is the expression for t. (Answer)

Answer:

t= 100/r [d/c-1]

Answer:

D. 47 square units

Step-by-step explanation:

The area of the piece of red paper after the hole for the photograph has been cut is the difference between the area of large square and are of small square.

Area of large square:

The length of the side of large square is

[tex]EF=|-4-4|=8\ units[/tex]

Area of large square [tex]=8^2=64\ un^2.[/tex]

Area of small square:

The length of the side of large square is

[tex]AB=\sqrt{(-3-(-2))^2+(-2-2)^2}=\sqrt{(-1)^2+(-4)^2}=\sqrt{1+16}=\sqrt{17}\ units[/tex]

Area of small square [tex]=\sqrt{17}^2=17\ un^2.[/tex]

Difference:

[tex]64 \ un^2-17\ un^2=47\ un^2[/tex]

Answer:

19

Step-by-step explanation:

8+4=12 +7=19

Answer:

1 and 2 answers are correct

Step-by-step explanation:

2x-y= -8

x-y = -4

ADD BOTH (y is cancelled)

3x= -12

x= -4

-8+y=-8

y=0

    -4-y = -4

     Multiply all by -1

4+y=4

y=0

Answer:

4*1/6=2/3

Step-by-step explanation:

we have 4 of 1/6

so 1/6 +1/6 +1/6 +1/6=4*1/6=4/6=2/3

Answer:

200 ft.

2 jumps

Step-by-step explanation:

The slide is placed at coordinates (-2,0) and the fountain is placed at coordinates (-2,-2).

(A) Therefore, using the distance between two known points formula, the distance from the slide to the fountain is given by  

[tex]\sqrt{(-2 - ( -2))^{2} + (-2 - 0)^{2}} = \sqrt{(0 + 4)} = 2[/tex] units.

Now, given that each unit on the grid represents 100 ft.

So, the distance from slide to the fountain is (100 × 2) = 200 ft. (Answer)

(B) Now, if each jump = 100 ft, then the slide is 2 jumps apart from the fountain. (Answer)

We know the distance between two known points on the coordinate plane ([tex]x_{1},y_{1}[/tex]) and ([tex]x_{2},y_{2}[/tex]) is given by the following formula

Distance = [tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2}  )^{2}}[/tex]

The distance from the slide to the fountain is sqrt(29) units on the grid or 100*sqrt(29) feet. If each unit represents 100 ft, the distance is 100*sqrt(29) feet.

To find the distance from the slide to the fountain, we need to determine the coordinates of both points on the grid. Let's assume the slide is located at point A (2,4) and the fountain is located at point B (7,6).

Using the distance formula, d = sqrt(([tex]x2 - x1)^2 + (y2 - y1)^2)[/tex], we can plug in the coordinates:

d = [tex]sqrt((7 - 2)^2 + (6 - 4)^2)[/tex] = sqrt(25 + 4) = sqrt(29).

So, the distance from the slide to the fountain is approximately sqrt(29) units on the grid or 100*sqrt(29) feet.

To determine the distance in feet if each unit on the grid represents 100 ft, we can simply multiply the distance by 100:

Distance = sqrt(29) * 100 = 100*sqrt(29) feet.

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Total area of the field is 160 ft^2

Step-by-step explanation:

Given

Total workers = 4

Each worker's share of area = 5*8 feet

We will find the area for each worker and then multiply the area with four to find the whole area of field as it was evenly distributed to workers

so,

[tex]Area\ given\ to\ one\ worker = 5*8\\= 40\ ft^2[/tex]

[tex]Total\ area = 40*4 = 160\ ft^2[/tex]

Total area of the field is 160 ft^2

Keywords: Area, Measurement

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Final answer:

The total area of the field being harvested by four workers, each with a plot of 5 by 8 feet, is 160 square feet.

Explanation:

The subject of this question is Mathematics, specifically, it involves calculating the total area of land worked by four workers. Each worker is given a plot that is 5 feet by 8 feet. To find the total area of the field that the four workers are harvesting, you multiply the area of one plot by the number of workers.

To calculate the area of one plot: Area = length * width = 5 feet * 8 feet = 40 square feet.
Now, since there are four workers each with a plot of this size, you multiply the area of one plot by the number of plots/workers:
Total area = 40 square feet/plot  imes 4 plots = 160 square feet.

Therefore, the total area of the field being harvested by the four workers is 160 square feet.