Solve each equation. 2 1/3(2x-3)=2 1/3

Answers

Answer 1

Answer: x = 2

Step-by-step explanation:

Multiply each term between the parentheses by 2 1/3.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2\frac{1}{3}(2x-3)=2\frac{1}{3} \iff \ 2\frac{1}{3}\times2x+2\frac{1}{3}\times(-3)=2\frac{1}{3} } \end{gathered}$} }[/tex]

We calculate the expression of the multiplication.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2\frac{1}{3}\times2x+2\frac{1}{3}\times(-3)=2\frac{1}{3} \iff \ \frac{14x}{3}+2\frac{1}{3}\times(-3)=2\frac{1}{3} } \end{gathered}$} }[/tex]

We calculate the multiplication and division of rational numbers.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{14x}{3}+2\frac{1}{3}\times(-3)=2\frac{1}{3} \iff \frac{14x}{3}-7=2\frac{1}{3} } \end{gathered}$} }[/tex]

We convert the mixed fraction to improper.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{14x}{3}-7=2\frac{1}{3} \iff \dfrac{14x}{3}-7=\dfrac{7}{3} } \end{gathered}$} }[/tex]

We eliminate the fractions by multiplying by the least common multiple of the denominators of both sides.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\dfrac{14x}{3}-7=\dfrac{7}{3} \iff \ 14x-21=7} \end{gathered}$} }[/tex]

We move the constant to the right side and change the direction of the sign.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x-21=7 \iff 14x=7+21=28, and \ remains \ 14x=28} \end{gathered}$} }[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x=28 \iff \ we \ divided \ x=\frac{28}{14}=x; \Rightarrow x=2. } \end{gathered}$} }[/tex]

Related Questions

Question 8
You decide to begin saving toward the purchase of a new car in five years. If you put
RM1,000 at the end of each of the next 5 years in a savings account paying 6 percent
compounded annually, how much will you accumulate after 5 years?

Answers

If you save RM1,000 at the end of each of the next 5 years in a savings account paying 6 percent compounded annually, the future value or the amount you will accumulate after 5 years is RM5,637.09.

What is the future value?

The future value is the compounded present value of the periodic deposits.

The future value formula or FV table can determine the accumulated future value of periodic investments.

We can also use an online finance calculator to determine the future value.

N (# of periods) = 5 years

I/Y (Interest per year) = 6%

PV (Present Value) = RM0

PMT (Periodic Payment) = RM1,000

Results:

Future Value (FV) = RM5,637.09

Sum of all periodic payments = RM5,000(RM1,000 x 5)

Total Interest = RM637.09

Thus, in 5 years, you will have an accumulated future value of RM5,637.09 in the savings account.

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There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.

Outcome | Frequency
Brown | 13
Black | 9
Green | 7
Gold | 11

Compare the theoretical probability and experimental probability of pulling a gold marble from the bag.
A. The theoretical probability, P(gold), is 25%, and the experimental probability is 27.5%.
B. The theoretical probability, P(gold), is 50%, and the experimental probability is 11.5%.
C. The theoretical probability, P(gold), is 25%, and the experimental probability is 25%.
D. The theoretical probability, P(gold), is 50%, and the experimental probability is 13.0%.

Answers

The correct option is A.

"The theoretical probability, P(gold), is 25%, and the experimental probability is 27.5%."

How to find the probabilities?

First, let's find the theoretical probability.

We know that there are:

10 brown marbles10 black marbles10 green marbles10 gold marbles

For a total of 40 marbles.

The theoretical probability of randomly pulling a gold marble is equal to the quotient between the total number of gold marbles and the total number of marbles, it is:

P = 10/40

P = 1/4 = 0.25

For the experimental probability, we need to take the quotient between the number of times that the outcome of the experiment was a gold marble and the total number of times that the experiment was performed.

The experiment was performed 40 times and 11 times we got the gold marble, then:

E = 11/40 = 0.275

Then the correct statement is A:

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Answer: The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.

Step-by-step explanation:

I question below and select the best answer choice. *
What property was used to simplify the expression?
12 × 47 = 12 × (40 + 7)
= 12 X 40 + 12 × 7
= 480 + 84
= 564

Answers

The property used to simplify the expression is 12 × 47 = 12 × (40 + 7) is distributive property.

What is distributive property?

The distributive property states that an expression which is given in form of x (y + z) can be solved as x × (y + z) = xy + xz.

In other words, distributive property is a rule that states that you can distribute the terms of an expression.

Therefore, let's check the property used on the expression as follows:

12 × 47 = 12 × (40 + 7)

12 × 40 + 12 × 7

480 + 84

564

Hence, the property used on the expression is distributive property.

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One aircraft has a capacity of 64 more seats than a second aircraft. A third aircraft has 152 seats less than twice the seating capacity of the second aircraft. If their total number of seats is 1900, find the number of seats for each aircraft.

Answers

The number of seats in the first, second and third aircraft are 561 seats, 497 seats and 842 seats respectively

How to find the number of seats for each aircraft?

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Let F, S and T represent number of seats in the first, second and third aircraft respectively

We can set up three equations to represent the situation:

F = 64 + S --- (1)

T = 2S - 152 --- (2)

F + S + T = 1900 --- (3)

Put (1) and (2) in (3):

F + S + T = 1900

(64 + S) + S + (2S - 152) = 1900

64 + S + S + 2S - 152 = 1900

4S - 88 = 1900

4S = 1900 + 88

4S = 1988

S = 1988/4

S = 497 seats

F = 64 + S

F = 64 + 497 = 561 seats

F + S + T = 1900

561 + 497 + T = 1900

1058 + T = 1900

T = 1900 -1058 = 842 seats

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Borrowed 600$ from the bank. Interest is $14.25 for 90 days. What is interest rate?

Answers

Answer:

0.01 %

Step-by-step explanation:

The interest rate is the percentage of the principal (the amount borrowed) that is charged as interest over a certain period of time.

To find the interest rate, we can use the formula:

Interest Rate = Interest / Principal x Number of days / 365

We know that the principal is 600$, the interest is 14.25$ and the number of days is 90

so we can substitute the values into the formula:

Interest Rate = 14.25 / 600 x 90 / 365

Interest Rate = 0.02375 * 90 / 365

Interest Rate = 0.0104

Rounded to the nearest thousandth, the interest rate is 0.010 or 0.01 %

There is 25 pounds of dog food in a bag. There are approximately 2.2 kilograms in 1 pound. PLEASE HELP ME !! THANK YOU SMM!!

Which statement is true?

A. There is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 55/22.

B. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 25/11.36

C. There is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 25/11.36

D. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 11.36/25

Answers

According to the given information, there is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 25/55

Conversion between units: Calculating kilograms of dog food

From the question, we are to determine the statement that is true

From the given information,

There is 25 pounds of dog food in a bag.

and

There are approximately 2.2 kilograms in 1 pound.

If there are 2.2 kilograms in 1 pound

Then,

There would be x kilograms in 25 pounds

x = 2.2 × 25

x = 55 kilograms

Hence, there are 55 kilograms

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pls help w geometry (see picture)

Answers

The given geometry of the figure does not show any of the options, so option D is correct.

What is a triangle?

A polygon with three vertices and three sides is called a triangle. The triangle's angles are created by joining its three sides end to end at a single point. The sum of the three angles of the triangle is 180 degrees.

Given a ΔSTU

a line from point T intersects at SU at point V and divides SU, given SV is 60 units and UV is 42 units.

The line TV is not a median, because a median divides the side into two equal halves, and the figure does not have SV equal to UV.

The line TV is not an attitude because the figure has not specified the angle of V in line SU, if given that the ∠TVU = ∠TVS = 90° then TV will be called altitude.

The line is not a perpendicular bisector because The line segment drawn from a vertex to the opposite side of a triangle, bisecting that side at a right angle, is known as the perpendicular bisector of the triangle.

Hence option D is correct.

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If P = 4s represents the square’s perimeter in terms of the square’s side length (in inches), write a formula that represents the perimeter’s side length 's' in terms of the square’s perimeter 'P.'

Answers

The side of the square in terms of the perimeter is P/4.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

P = 4s

Where s is the side of the square and P is the perimeter of the square.

Now,

The side of the square.

P = 4s

Divide 4 into both sides.

s = P/4

Thus,

The side of the square is P/4.

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Is -2 a solution of 6g-14>21

Answers

Answer:

-2 is not a solution of the inequality 6g - 14 > 21.

Step-by-step explanation:

To determine if -2 is a solution of the inequality 6g - 14 > 21, we need to substitute -2 for g in the inequality and see if it is true.

6g - 14 > 21

6(-2) - 14 > 21

-12 - 14 > 21

-26 > 21

This inequality is not true. Because -26 is not greater than 21.

[tex]6g-14 > 21[/tex]

Substitute -2 for g:

[tex]6(-2)-14 > 21[/tex]

[tex]-12-14 > 21[/tex]

[tex]-26 > 21[/tex]

-2 is not a solution because -26 is not greater than 21.

Use the parallelogram to find m
m

Answers

The angles in the parallelogram are as calculated below

How to find the angles in the parallelogram?

A parallelogram is a quadrilateral with opposite sides parallel. This means that both pairs of opposite sides are parallel and of equal length. The opposite angles of a parallelogram are also equal in measure.

m ∠BEA = 60° (alternate angles)

m ∠BAE = 42° (alternate angles)

m ∠DAE = 40° (alternate angles)

m ∠ABE = 180 - m ∠BEA - m ∠BAE = 78° (angle in a triangle)

m ∠CBE = 78° (vertically opposite angles)

m ∠ABD = 180 - m ∠ABE = 102° (angle on a straight line)

m ∠CBE = 102° (vertically opposite angles)

m ∠BEC = 180 - m ∠CBE - m ∠BEC = 38° (angle in a triangle)

m ∠ADB = 38° (alternate angles)

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PLS HELP ME PLSSS plsssss

Answers

Answer:

The circumference of a tire can be found by using the formula C = πd, where C is the circumference, and d is the diameter.

For the old bicycle with 12 inch diameter tires, the circumference is:

C = π * 12 = 12 * π inches

For the new bicycle with 16 inch diameter tires, the circumference is:

C = π * 16 = 16 * π inches

To find the difference in the circumference of the tires, we subtract the circumference of the old tire from the circumference of the new tire:

16π - 12π = 4π inches

So the difference in the circumference of the two tires is 4π inches.

It's around 12.56 inches.

k=3/2
y=kx
y=3/2x

what is the table of x and y
x -0 y-0
x___ y___
x___ y____

Answers

Using the proportionality relationship equation, y = 3/2x, the complete table is:

x | y

0 0

1 3/2

2 3

How to Complete a Table Using the Constant of Proportionality?

The equation of a proportional relationship between x and y can be represented as y = kx, which means that the constant of proportionality, k, is y/x.

For example, if the constant of proportionality between two variables x and y is given as 4, therefore, the equation of the proportional relationship will be stated as y = 4x.

Given the following:

Constant of proportionality, k = 3/2.

The equation of the proportional relationship is: y = 3/2x

Use the equation, y = 3/2x to complete the table by substituting the values of x into the equation:

For x = 1:

y = 3/2(1)

y = 3/2

For x = 2:

y = 3/2(2)

y = 3

Therefore, the complete table is:

x | y

0 0

1 3/2

2 3

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What are the dimensions of this matrix? I WILL MARK BRAINLIEST.

Answers

Answer:

1 * 3 ==> 4th option

Step-by-step explanation:

Matrix dimensions are:

number of rows by number of columns

The number of rows is 1 : ( -4 1/4 -1 is the row)

The number of columns is 3 : (-4, 1/4, and -1 are the columns)

Hence, the dimensions is 1 * 3.

Answer:

1 x 3

Last choice

Step-by-step explanation:

The dimensions of a matrix are represented by number of rows x number of columns

There is only one row here (don't be confused by the 1/4) and there are three columns

So 1 x 3

(last choice)

2 people push a box from different directions, why doesnt the box move?

Answers

Answer:

Newton's 3rd law of motion

Step-by-step explanation:

Newton's 3rd law of motion states that for every force in nature there is an equal and opposite reaction.

So, assuming the people are both pushing with the same force, their forces are basically canceling each other out, and a net force of 0 is acting uponm the box, which explains why it is not moving.

The box doesn't move when two people push it from different directions because the forces acting on the box are in opposite directions and are equal in magnitude. Newton's first law of motion states that an object at rest will remain at rest and an object in motion will remain in motion with a constant velocity, unless acted upon by an unbalanced force. In this case, the two opposing forces acting on the box balance each other out and create an unbalanced force of zero, resulting in no net force acting on the box, and the box remains at rest.

a dealer gains 7% by selling a sofa set for rs 3852 .find his gain percent if he sells it for rs 4050

Answers

The gain percentage is 12.5%

First, let`s find the Cost price (C.P) of the sofa.

Let C.P of the sofa be x.

Now, according to the question:

x+ 7% of x=Rs.3852

x + (7/100 * x) = 3852

x + 0.07x = 3852

1.07x = 3852

x=3852/1.07,

x = Rs 3600.

Now the dealer sells it for Rs 4050.

so, the Formula for gain% is=(Selling price-Cost price/Cost price)x100

Gain %= (4050-3600/3600)x100

Gain%=(450/3600)x100

Gain%=(450/36)

i.e = 12.5%.

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The diagram shows solid pyramid ABCDE.
The base BCDE of the pyramid is a horizontal square w side lengths 12cm
The vertex A of the pyramid is vertically above the midpoint of BD
The volume of the pyramid is 768cm3
Calculate the size of the angle between AB and the base of the pyramid.

Answers

Id the base BCDE of the pyramid is a horizontal square w side lengths 12cm . The size of the angle between AB and the base of the pyramid is 62 degree.

How to find the size of the angle between AB and the base of the pyramid?

Side of square of base BCDE =12cm

Area of base =12² =144cm²

Volume of pyramid = 768cm³

1/3 a² × h= 768

1/3 × 144 × h =768cm³

h =768 × 3 /144

h =16 cm

BD² =BC² +CD²

BD² = 12² + 12²

BD² = 288

BD =√288 cm

BD = 16.97cm

BD = 17cm

So,

BF = 1/2 BD

BF = 1/2 × 17

BF =8.5cm

So since ΔABF is angle between AB and base of pyramid

tan <ABF = Tan-1 (16/8.5) = 62°

Therefore the size of the angle between AB and the base of the pyramid is 62 degree.

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Which set of numbers is correctly ordered from greatest to least?
221
07,207.36, 2.4-√3x
7.36, 221, 2.4-√3x
30
0 7 1,7
O 2.4√√3,7.36, 221 1,7/1/1
30
221
O
○ 2.4-√3x, 230, 7. 36,7

Answers

The set of number that is correctly ordered from the question in the attachment is option D.

How to solve for the solution in order to get the ordering

1. [tex]7\frac{1}{3}[/tex] = 7 + 0.3333

= 7.3333

2. 221 / 30 = 7.3666

3. 7.36 = 7.36363636

4. [tex]2.4\sqrt{3\pi }[/tex] = 2.4 * [tex]\sqrt{9.43}[/tex]

= 7.36999

We would have to arrange all of the values from their highest to the least values

7.36999, 7.3666, 7.36363636, 7.3333

[tex]2.4\sqrt{3\pi }[/tex], 221 / 30, 7.36 , 7.3333

Hence the last option is the answer. It shows how the solution is ordered from the greatest to the smallest value

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simplify 7m-2(3m^2 +mn)

Answers

Answer: 7m-6m²-2mn

Step-by-step explanation:

Multiply each term in parenthesis by -2

Calculate product (2x3=6)

7m-6m²-2mn

I need to be resolved with the number line

Answers

The solution of the inequality is less than 1.75 which is shown on the diagram.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

5/8 > (1/2)x - 1/4

Simplify the inequality, then we have

5/8 > (1/2) x - 1/4

5/8 + 1/4 > (1/2) x

(5 + 2)/8 > (1/2) x

7 / 8 > (1/2) x

(1/2) x < 7 / 8

x < 7 / 4

x < 1.75

The solution of the inequality is less than 1.75 which is shown on the diagram.

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Please help, having trouble getting answer.

Answers

Answer:

C. 2 ≤ x

Step-by-step explanation:

EDGE

Mark plays field hockey. He makes a goal 55% of the time he shoots. A = the event Mark is successful on his first goal attempt. P(A) = 0.55. B = the event Mark is successful on his second goal attempt. P(B) = 0.55. Mark tends to make goals in streaks. The probability that he makes a second goal given that he made the first goal is 0.80.

If Mark attempts two goals, what is the probability that he makes both goals?

Answers

Answer:

We can use the formula for conditional probability to find the probability that Mark makes both goals:

P(A and B) = P(A) * P(B | A)

We know that:

P(A) = 0.55 (the probability that Mark makes a goal on his first attempt)

P(B | A) = 0.80 (the probability that Mark makes a goal on his second attempt given that he made the first goal)

So:

P(A and B) = 0.55 * 0.80 = 0.44

Therefore, the probability that Mark makes both goals is 0.44.

Diego brought 16candy bars $25. large candy bars cost $1.25 and regular candy bars cost $0.75. How many candy bars of each size did he buy? (with explanation if u can)

Answers

There are 10 and 26 candy bars of each size did he buy.

What is an expression?

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;

Diego brought 16 candy bars $25.

And, large candy bars cost $1.25 and regular candy bars cost $0.75.

Now, Let number of large candy bars = x

And, Number of regular candy bars = y

Here, Diego brought 16 candy bars.

Hence, We get;

⇒ x + y = 16 .. (i)

And, large candy bars cost $1.25 and regular candy bars cost $0.75.

Hence, We get;

⇒ 1.25x + 0.75y = 25 .. (ii)

Multiply by 1.25 in (i) and subtract from (ii), we get;

⇒ 1.25y - 0.75y = 20 - 25

⇒ 0.5y = - 5

⇒ y = - 10

And, from (i);

⇒ x + y = 16

⇒ x - 10 = 16

⇒ x = 26

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Have 5 minutes left!!!!!

Which system of equations below has exactly one solution?
O y = -8x - 6 and y = -8x + 6
O y = -8x -6 and 7y = -4x - 3
O y = -8x - 6 and y = 8x - 6
Q y = -8x - 6 and -y = 8x + 6

Answers

Answer:

Y=-8x-6 and x=-8x+

Step-by-step explanation:

Match each of the equations with their corresponding graph.
a) y= x^3 +2x^2-1
b) 2x^2-x-3
c) 1/x +1
d) 2-3x^2 -x^3

Answers

Answer:

I think so the answer is a)y=x³+2x²-1

Please look at the picture and answer the question thank you

Answers

The respective answers are 5 and 4

What is addition in math?

Addition in math is a process of combining two or more numbers. Addends are the numbers being added, and the result or the final answer we get after the process is called the sum.

Given: 5 means 5+0+0 which equals to 5

4 means 4+0+0+0 which equals 4

Hence the respective answers are 5 and 4

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A Man bought 5 Crates of 60 of drinks. On his way home, he drank 5 bottles and broke 25 bottles what percentage of the bottles are left?

Answers

Answer:50%

Step-by-step explanation:

2. In 2000, Social Security tax was 7.5%, to the maximum income of $53,000. If Mary earned $61,711 in 2000, how
much Social Security did she pay?

Answers

Mary paid Social Security tax of $4,378.325 in 2000. This is calculated by multiplying 7.5% by the amount of income over the maximum taxable income of $4,378.325.

How much Social Security did she pay?

The theory used in this question is the marginal tax rate, which is the tax rate that applies to the income earned over the maximum taxable income. In this case, the marginal tax rate is 7.5%, which is the Social Security tax rate.

Step 1: Calculate the amount of income over the maximum taxable income.

Maximum taxable income: $53,000

Income earned: $61,711

Amount of income over the maximum taxable income: $8,711 ($61,711 - $53,000 = $8,711)

Step 2: Calculate the Social Security tax.

Social Security tax rate: 7.5%

Amount of income over the maximum taxable income: $8,711

Social Security tax paid: $4,378.325 ($8,711 x 0.075 = $4,378.325)

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One serving of Campbell Soup Company's Campbell's® Pork & Beans contains 5 grams of protein and 21 grams of carbohydrates.† A typical slice of white bread provides 2 grams of protein and 11 grams of carbohydrates per slice. The U.S. RDA (Recommended Daily Allowance) is 60 grams of protein each day.
(a)
I am planning a meal of "beans on toast" and wish to have it supply one-half of the RDA for protein and 139 grams of carbohydrates. How should I prepare my meal? (Fractions of servings are permitted.)
beans
serving(s)
bread
slice(s)
(b)
Is it possible to have my meal supply the same amount of protein as in part (a) but only 61 grams of carbohydrates?
Yes
No

Answers

The way we should prepare the meal to supply one half of the RDA for protein and 139 grams pof carbohydrates is 4 beans serving and 5 bread slices (answer A). It not possible to have the same amount of protein as in part A but only 61 grams of carbohydrates.

How to calculate the meal of point A?

To calculate the meal of point A we have to consider the amount of grams of protein and carbohydrates in each food. In this case, we try with 4 servings of beans and 5 slices of bread, and it get the protein and carbohydrates required as shown in the following explanation:

Servings of beans

4 * 5 = 20 grams of protein

4 * 21 = 84 grams of carbohydrates

Slices of bread

5 * 2 = 10 grams of protein

5 * 11 = 55 grams of carbohydrates

Totals

20 + 10 = 30 grams of protein

84 + 55 = 139 grams of carbohydrates

According to the previous explanation the meal have to be composed by 4 servings of beans and 5 slices of bread. On the other hand, if we want to make a meal with the same amount of protein but only 61 grams of carbohydrates, it is imposible because the amount of carbohydrates of each food is bigger than we need.

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( Look at picture) Thx btw

Answers

Step-by-step explanation:

930 = -20×|t - 15| + 1010

one solution is for (t - 15) > 0

930 = -20×(t - 15) + 1010

-80 = -20×(t - 15)

4 = t - 15

t = 19

that means 2019.

the second solution is for (t - 15) < 0

930 = 20×(t - 15) + 1010

-80 = 20×(t - 15)

-4 = t - 15

t = 11

that means 2011.

Write and solve an inequality.
Please show work
Chris earns $8 per hour working on the weekends. He needs at least $320.00 for his class trip. How many hours, h, does Chris need to work on the weekends to be able to go on the class trip

Answers

We can start solving the problem by using the formula:

Hours worked = Total cost / Hourly wage

In this case, we know that Chris needs at least $320.00 for his class trip, and he earns $8 per hour working on the weekends. So, we can plug in these values into the formula:

Hours worked = $320.00 / $8.00

To solve this equation, we divide 320 by 8:

Hours worked = 40

So Chris needs to work 40 hours on the weekends to be able to go on the class trip.

I hope this helps :)

Answer:

Chris needs to work at least 40 hours.

----------------------------------------

Chris earns $8 per hour and he needs at least $320.00 for his class trip.

If he works h hours, he will get 8h dollars.

Set up inequality:

8h ≥ 320

Solving we get:

h ≥ 320/8h ≥ 40

Chris needs to work at least 40 hours.

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