what is 2(3x+4)=x-7​

Answer:

50 to 60 seconds is the answer

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:  Therefore, at the start of the game, Peter had 80 marbles and Jack had 80 marbles.

Step-by-step explanation:

Answer C -16 is the answer

The total amount of soap that needs to be sold in order to cover the cost of the equipment is 10 kilograms.

Two things are equal, according to an equation. The equals sign "=" will appear as in the formula: x + 2 = 6.

According to that equation, what is on the right is equivalent to what is on the left (x + 2).

A mathematically based fact or rule is called a formula.

Typically, it will have: two or more variables (x, y, etc.) with the equals symbol (=) representing values we don't yet know

A statement like "this equals that" is an equation.

Let the amount of soap in kilogram = x.

Given that, She initially spent $60 to purchase soap-making equipment, and the materials for each kilogram of soap cost $13. This is represented as:

A = 60 + 13x

She sells the soap for $19"

S = 19x

To cover the cost the initial investment must be equal to the number of soap sold:

60 + 13x = 19x

60 = 6x

x = 10

Hence, the total amount of soap that needs to be sold in order to cover the cost of the equipment is 10 kilograms.

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Answer:

Step-by-step explanation:

Make the length of one side = 'x'

The other side = 3xPerimeter = 2 x one side + 2 x the other side

79 cm = 2(x) + 2(3x)

79 cm = 2x + 6x

8x = 79

x = 9.875

One side = 9.875 cm

Other side = 29.625 cm

Answer:

Step-by-step explanation:

To find the two consecutive natural numbers whose sum is 575, we can set up the following equation:

x + (x+1) = 575

where x and x+1 are the two consecutive natural numbers.

We can solve this equation by combining like terms:

2x + 1 = 575

Subtracting 1 from both sides, we get:

2x = 574

Dividing both sides by 2, we get:

x = 287

Therefore, the two consecutive natural numbers are 287 and 288. Our final answer is 287, 288.

Answer:

287,288

Step-by-step explanation:

Question

The sum of two consecutive natural numbers is 575. Find the numbers

soln

x +( x + 1) = 575

x + x + 1 = 575

2x + 1 = 575

2x = 575 – 1

2x = 574

\( \frac{2x}{2} = \frac{574}{2} \)

x = 287

since we got x as 287, lets solve(x+1)

by substituting

287 + 1 = 288

hence the consecutive numbers are 287,288

Check

287 + 288 = 575

we are correct.

i hope this helps

Answer:

See below

Step-by-step explanation:

a)

\( \frac{20}{ \sqrt{10} } = \frac{20 \sqrt{10} }{ \sqrt{10} \times \sqrt{10} } = \frac{20 \sqrt{10} }{10} = 2 \sqrt{10} \)

b)

\( \frac{ \sqrt{2} }{2 \sqrt{5} - 1 } \\ \\ = \frac{ \sqrt{2} \times (2 \sqrt{5} + 1 )}{(2 \sqrt{5} - 1)(2 \sqrt{5} + 1) } \\ \\ = \frac{ \sqrt{2} \times 2 \sqrt{5} + \sqrt{2} \times 1 }{(2 \sqrt{5} ) ^{2} - (1)^{2}} \\ \\ = \frac{ 2 \sqrt{10} + \sqrt{2}}{20 - 1} \\ \\ = \frac{ 2 \sqrt{10} + \sqrt{2}}{19} \\ \\ equating \: it \: with \: \\ \frac{ a + \sqrt{b}}{c} \\ \\ a = 2 \sqrt{10} \\ \\ b = 2 \\ \\ c = 19\)

Answer:

The above answer is correct

Answer:

1. -7.5

2. $1

3. 40

Step-by-step explanation:

For number 1, it can be solved by using the PEMDAS method, or see explanation below:

6x - 4x - 36 = 6 - 2x

2x - 36= -2x + 6

4x + 36 = 6

4x = -30

x = -15/2 or -7.5

For number 2, substitute 3 into both equations:

f(x) =1.50(3) + 2.00

and

f(x) = 2.00(3) + 1.50

This would get $6.50 and $7.50, which, if subtracted, gets $1.

For number 3, do something similar to the previous problem. Substitute 3 for x. It would be 5(2^3), or 40.

Hope this helps!

Answer:

Step-by-step explanation:

Answer:

(B) {6,6,7}

Step-by-step explanation:

A criterion to determine if each triplet represents a triangle is the Law of Cosine, which states that:

\(a^{2} = b^{2}+c^{2}-2\cdot b \cdot c \cdot \cos \theta\)

Where \(a\), \(b\) and \(c\) are sides of the triangle and \(\theta\) is the angle opposite to side \(a\). Now, let is clear the cosine function:

\(2\cdot a \cdot b\cdot \cos \theta = b^{2}+c^{2}-a^{2}\)

\(\cos \theta = \frac{b^{2}+c^{2}-a^{2}}{2\cdot b \cdot c}\)

Cosine is a bounded function between -1 and 1, a triplet corresponds to a triangle if and only if result is located between upper and lower bounds. Now let is evaluate each triplet:

a) \(a = 2\), \(b = 5\), \(c = 9\)

\(\cos \theta =\frac{5^{2}+9^{2}-2^{2}}{2\cdot (5)\cdot (9)}\)

\(\cos \theta = 1.133\) (Absurd)

The triplet does not represent a triangle.

b) \(a = 6\), \(b = 6\), \(c = 7\)

\(\cos \theta =\frac{6^{2}+7^{2}-6^{2}}{2\cdot (6)\cdot (7)}\)

\(\cos \theta = 0.583\) (Reasonable)

The triplet represents a triangle.

c) \(a = 6\), \(b = 4\), \(c = 2\)

\(\cos \theta = \frac{4^{2}+2^{2}-6^{2}}{2\cdot (4)\cdot (2)}\)

\(\cos \theta = -1\) (Absurd)

The triplet does not represent a triangle, but a straight line.

d) \(a = 7\), \(b = 8\), \(c = 1\)

\(\cos \theta = \frac{8^{2}+1^{2}-7^{2}}{2\cdot (8)\cdot (1)}\)

\(\cos \theta = 1\) (Absurd)

The triplet does not represent a triangle, but a straight line.

Hence, the correct answer is B.

Answer:

To find the linear function with the given properties, we need to determine the slope and y-intercept of the function.

We can use the slope-intercept form of a linear function, which is:

y = mx + b

where m is the slope and b is the y-intercept.

First, we can find the slope using the two given points:

slope = (y2 - y1) / (x2 - x1)

slope = (4 - (-12)) / (-7 - (-3))

slope = 16 / (-4)

slope = -4

Now that we have the slope, we can use one of the given points to find the y-intercept. Let's use the point (-3, -12):

y = mx + b

-12 = (-4)(-3) + b

-12 = 12 + b

b = -24

Therefore, the linear function that satisfies the given properties is:

f(x) = -4x - 24

Answer:

I hope this will be the answer... ✌️

\(\large{\pmb{\underline{\underline{\sf{Refraction:-}}}}}\)

Refraction is the bending of a light or sound wave, or the way the light bends when entering the eye to form an image on the retina.

\(\large{\pmb{\underline{\underline{\sf{Examples~ Of~ Refraction:-}}}}}\)

\({\huge{\underline{\small{\mathbb{\pink{HOPE \ THIS \ HELPED \ UH:)}}}}}}\)

Cheers !! :3

Answer:

no

Step-by-step explanation:

equate the two equations (make them equal to each other)

-2/5x - 7 = 2/5x - 3

get rid of the fractions by multiplying everything by 5

5(-2/5x - 7 = 2/5x - 3)

-2x - 35 = 2x - 15

solve

-2x - 35 = 2x - 15

-2x - 2x = -15 + 35

-4x = 20

x = -5

plug in "x" to one of the starting equations (I'm using the second one)

y = 2(-5) - 15

y = -10 - 15

y = -25

an easier way would be to plug in the point for "x" and "y"

-5 = 2(-5) - 15

-5 = -10 - 15

-5 = -25            FALSE

9514 1404 393

Answer:

  59 3/4

Step-by-step explanation:

The change from the opening price is ...

  -50 1/2 +110 1/4 = 60 -1/4 = 59 3/4 . . . change from opening price

Answer:

Hotdogs is 10

and Tacos  8 in numbers purchased

Step-by-step explanation:

Step one:

given data

Le  x represents the number of hotdogs purchased

and y represents the number of tac

hotdogs = $4 each

and tacos = $2.50 each

The total amount at hand = $60

Step two:

The systems of the equations for the situation is given as

4x+2.5y= 60---------1

x+y=18-----------------2

Required

The number of Hotdogs and Tacos purchased

from 2

x= 18-y

put x= 18-y in eqn  1

4(18-y)+2.5y= 60

72-4y +2.5y=60

collect like terms

-4y+2.5y=60-72

-1.5y= -12

divide both sides by -1.5

y= -12/-1.5

y= 8

put y= 8 in eqn 2

x+8=18

x= 18-8

x= 10

Since AB is parallel to CD, we have alternate interior angles forming when transversal CE intersects the parallel lines. Therefore,

mZDCE = mZECB (Alternate Interior Angles)

(7x + 2) = (x + 8) (Substitute in the given angle measures)

Solving for x, we get:

7x + 2 = x + 8

6x = 6

x = 1

Now, we can use x to find the measure of angle ZDCE:

mZDCE = (7x + 2)

= (7*1 + 2)

= 9

Therefore, the measure of angle ZDCE is 9 degrees.

The sum of expected marks is given as follows:

9375.

Each question has four choices, hence the probability of choosing the correct choice is given as follows:

p = 1/4 = 0.25.

Then the expected number of correct answers is given as follows:

E(X) = 0.25 x 150

E(X) = 37.5.

Then the expected grade for a single student is given as follows:

37.5 - 0.25(150 - 37.5) = 9.375.

The expected sum for the 1000 students is then given as follows:

1000 x 9.375 = 9375.

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The standard form of the equation of the line passing through (8,-3) that is parallel to the line 3y=4x+8 is 4x - 3y = 41

The equation of the line in standard form can be represented as follows:

Ax + By = C

where

Therefore, the standard form of the equation of the line through (8,-3) that is parallel to the line 3y = 4x + 8 is a s follows;

Parallel lines have the same slope.

Hence,

3y = 4x + 8

y = 4  / 3 x + 8 / 3

The slope of the line is 4 / 3. Hence, the line passes through (8, -3). let's find the y-intercept.

y = 4 / 3 x + b

-3 = 4 / 3 (8) + b

b = -3 - 32 / 3

b =  -9 - 32/ 3

b = -41 / 3

Hence,

y = 4 / 3 x - 41 / 3

multiply through by 3

3y = 4x - 41

Therefore, the standard form is 4x - 3y = 41

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Answer

9 and 10

Step-by-step explanation:

Answer:

0 is greater than Negative two-thirds.

Negative 1 less-than negative one-third

Negative one-third greater-than negative two-thirds

Step-by-step explanation:

Two-thirds is equal to Negative two-thirds and Negative two-thirds greater-than one-third are incorrect.

Answer:

a c e

Step-by-step explanation:

Answer:

45 degrees

Step-by-step explanation:

The 4 angles of a quadrilateral will add to 360.

We know 1 of them (angle B) is 90 degrees.

We can set up an equation to solve the others.

2x+3x+x+90 = 360

Now solve for x.

Start by combining the x terms together.

6x+90 = 360

6x = 360-90

6x = 270

(6x/6) = 270/6

x = 45 degrees

Check back to see if that makes sense and if the equation equals 360 when x is 45:

2x+3x+x+90 = 360

2(45)+3(45)+45+90=360.

The students in 8th class who choose music are 16 in number,

The students in 7th class who choose music are 32 in number

The total who choose world language is 270

The totals who are in 7th grade be 194

The number of students who choose world language in 7th class are 162

Let x be the students in 8th class who choose music

x+108=124

x=124-108

x=16 students

Now  y be the students in 7th class who choose music

16+y=48

y=48-16

y=32

Let z be the total who choose world language

48+z=318

z=318-48

z=270

Now the totals who are in 7th grade be A

124+A=318

A=318-124

A=194

B be the number of students who choose world language in 7th class

Now 32+B=194

B=194-32

B=162

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Answer:

The approximate volume of the cone is 14 cube inches.

Step-by-step explanation:

Circumference of the base of the cylinder = 3π inches

Height of the cylindrical piece of wood = 6 inches

volume of a cone = \(\frac{1}{3}\)\(\pi\)\(r^{2}\)h

But,

circumference = 2πr

3π = 2πr

r = \(\frac{3}{2}\)

  = 1.5 inches

Radius of the base of the cylinder is 1.5 inches.

So that;

volume of cone =  \(\frac{1}{3}\) x \(\frac{22}{7}\) x \((\frac{3}{2}) ^{2}\) x 6

                          =  \(\frac{1}{3}\) x \(\frac{22}{7}\) x \(\frac{9}{4}\) x 6

                          = 14.143

volume of cone = 14.143 cube inches

The approximate volume of the cone is 14 cube inches.

The system of equations is inconsistent and has no solution.

Here's a step by step process to check for consistency:

2x + y = -5

82x + 3y = 1

Subtracting the first equation from the second gives us:

80x + 2y = 6, which can not be true for any values of x and y.

Therefore, the system of equations has no solution and no approximation of y can be made.

The arrangement of conditions gave doesn't have an answer, since it prompts clashing responses. Basically, when we plug in values for x, the conditions offer us two unique responses for y, and that implies there is definitely not a solitary point that fulfills the two conditions. This makes it difficult to track down an incentive for y that would make the two conditions right. It's like attempting to adjust two teeter-totters simultaneously with loads, yet the loads are different on each side, making it difficult to adjust the two sides. For this situation, there is no arrangement, so finding an incentive for y that works for the two equations is impractical.

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The solution to the given addition problem is 150.6 ft^9.

Converting everything to the same unit is the simplest solution to this problem.

The conversions are:

1 cubic yard = (27 cubic feet)

1 cubic inch = (0.000578704 cubic feet)

The addition can be performed as,

(6 cu yd × 9 cu ft × 134 cu in) + (1 cu yd × 12 cu ft × 200 cu in)

=  [6(27 cu ft) × 9 cu ft × 134(0.000578704 cu ft)] + [1(27 cu ft) × 12 cu ft × 200(0.000578704 cu ft)]

= 150.6 ft^9

The result of the addition is 150.6 ft^9.

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It would take 370 days to build the wall with the given conditions.

If 60 men can build a wall in 40 days, then the total man-days required to build the wall is:

60 men x 40 days = 2400 man-days

However, 55 men quit every ten days, which means that after 10 days, there are only 60 - 55 = 5 men left to work on the wall. After 20 days, there are only 5 - 55 = -50 men left, which means that the remaining 5 men cannot work any faster than they were already working. Therefore, we can assume that the remaining 5 men complete the wall on their own.

The number of man-days required for the first 10 days is:

60 men x 10 days = 600 man-days

The number of man-days required for the second 10 days is:

5 men x 10 days = 50 man-days

The total number of man-days required for the first 20 days is:

600 man-days + 50 man-days = 650 man-days

The remaining work can be completed by the 5 men in:

2400 man-days - 650 man-days = 1750 man-days

Therefore, the total time needed to build the wall is:

20 days + 1750 man-days / 5 men = 20 + 350 days = 370 days

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Answer:

The answer is the Associative Property of Addition.

Step-by-step explanation:

When you add, you can group the numbers in any combanation.

Such as a + ( b + c ) = ( a + b ) + c

2p = a

3q = b

2 = c

So, if you were to write it out it would match perfectly into the format.