what improper fraction is equivalent to 3 and 7/12

Answer: 8x + 2

Step-by-step explanation:

Answer:

8x+2

Step-by-step explanation:

x3+2x2+x+2

=3x+4x+x+2

=8x+2

Answer:

x=4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

0.75x+3=6(x−3)

0.75x+3=(6)(x)+(6)(−3)(Distribute)

0.75x+3=6x+−18

0.75x+3=6x−18

Step 2: Subtract 6x from both sides.

0.75x+3−6x=6x−18−6x

−5.25x+3=−18

Step 3: Subtract 3 from both sides.

−5.25x+3−3=−18−3

−5.25x=−21

Step 4: Divide both sides by -5.25.

−5.25x/-5.25    =    -21/-5.25

Answer: x=4

The value of x from the given equation is 4.

The given equation is 0.75x + 3 = 6 (x - 3).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation can be solve for x as follows:

0.75x + 3 = 6x - 18

⇒ 6x-0.75x = 3+18

⇒ 5.25x=21

⇒ x=21/5.25

⇒ x=4

Therefore, the value of x from the given equation is 4.

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The standard form for the equation of this line is equal to 3A - 4B = 12.

A linear equation can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).

In Mathematics, the standard form of a linear equation is given by the following:

Ax + By = C.

When C = 24, the line passes through point (4, 0) and we have;

Ax + By = C.

4A + B(0) = 24.

4A = 24

A = 24/4

A = 6

When C = 24, the line passes through point (0, -3) and we have;

A(0) + B(-3) = 24

-3B = 24

B = -24/3

B = -8

Therefore, the standard form for the equation of this line is given by:

6A - 8B = 24

Dividing all through by 2, we have:

3A - 4B = 12

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Answer:

1. Median

2. Altitude

3.  Altitude

4. Neither

Step-by-step explanation:

Median- splits the side into two congruent parts

Altitude- Makes a right  angle

1. Splits the side. Median

2. Makes a right angle. Altitude

3.  Makes a right angle. Altitude

4. Doesn't make a right  angle or split the sides. Neither

Answer:

17

Step-by-step explanation:

Let the number of 2 point shots be t.

Let the number of 3 point shots be h.

Allison made 87 shots and scored 191 total points. This implies two things:

t + h = 87 ________(1)

2t + 3h = 191 ______(2)

Let us eliminate t by multiplying (1) by 2 and subtracting from (2):

=> 2t + 3h = 191

 -  2t + 2h = 174

               h  = 17

Therefore, she made 17 three point shots.

The result of the sum of positive integer and negative integer are found as;

8 + (-8) = 0.

Integers are a term used to describe whole numbers, or numerical expressions without fractions or decimals.

Types:

For the stated sum.

= 8 + (-8)

Open the brackets.

= 8 - 8

= 0

Thus, the result of the sum of two positive and negative integer is 0.

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The explicit solution for y = e^(x^2/2).

The explicit solution for the given differential equation is y = e^(x^2/2) * e^(C), where C is an integral constant. Substituting the initial condition, y(0) = 1, gives C = 0, thus the solution is y = e^(x^2/2).

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Answer:

put -4,-8 and -6 go on blue and 1, 2, 3 and 7 in red.

The decimals that are equivalent to 5x10 +2x1/100 is: E. 50.02.

Given :

5 x 10 +2 x 1/100

Now let calculate or determine the decimal that are equivalent to 5 x 10 +2 x 1/100 :

Hence :

Decimal=(5 × 10) + (2 × 1/100)

Decimal=50+2/100

Decimal=50+0.02

Decimal=50.02

Based on the above calculation we can conclude that  5 x 10 +2 x 1 /100 is the same as 50.02 which in turn means that the correct option to the question is option E which is 50.02.

Therefore the decimals that are equivalent to 5x10 +2x1/100 is: E. 50.02.

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The complete question is:

which decimals are equivalent to ( 5 x 10) + (2 x 1/100) select all that apply A. 50.020 B. 50.002. c. 5.02. D. 50.20. E. 50.02

An outcome refers to the result of an experiment, whereas an event refers to a combination of outcomes that satisfy a specific condition. Outcomes and events can be used to represent probability and are important in determining the probability of specific events.

In probability theory, an event and an outcome are two distinct terms. An outcome is a specific result of an experiment or a trial, whereas an event is any combination of outcomes or results. Here is an explanation of the difference between events and outcomes and an example of each using the sample space of tossing a coin 50 times. Difference between events and outcomes: Outcomes are the specific and individual results of an experiment or trial, whereas events are combinations of outcomes that define whether the result is favorable or not.Favorable outcomes, which are outcomes that satisfy the specified criteria, are included in the event. If the result does not meet the criteria, it is not included in the event. Example of an outcome:When a coin is tossed 50 times, there are two possible outcomes: heads or tails. Example of an event:If we toss a coin 50 times and look for the event that has 30 or more heads, we can construct an event called "heads greater than or equal to 30."  

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Answer:

14≤x

Step-by-step explanation:

-6(x-4) ≤-4(x+1)

Distribute

-6x+24 ≤-4x-4

Add 6x to each side

24 ≤-4x-4+6x

24 ≤ 2x-4

Add 4 to each side

24+4≤2x

28≤2x

Divide by 2

28/2≤2x/2

14≤x

Step-by-step explanation:

3.1.

your question

75x-25=5x+125

collect like terms

70x=150

Divide both side by the coefficient of x

70x/70=150/70

70 ti cancel 70 on x side to leave x alone

:. x=150/70 or 2.14

3.2.

6×(3x-2)=7×(x+3)

multiply by the bracket

18x-12=7x+21

collect like terms

18x+7x=21+12

25x=33

divide by the coefficient of x

25x/25=33/25

x=33/25 or 1.32

3.3.

10/x-3=8

cross multiply(know that 8 is /1)

x‐3×8=10×1

8x-24=10

8x=10+24

8x=34

divide both sides by coefficient of x

8x/8=34/8

8x=34/8 or 4.25

3.4.

x+7=5x-13

collect like terms

7+13=5x-x

20=4x

divide both sides by the coefficient of x

20/4=4x/4

5=x

:.x=5

3.5.

20x+4=4x-46

collect like terms

20x-4x=-46-4

16x=-52

divide both sides by the coefficient of x

16x/16=-52/16

:.x=52/16 or 3.25

The statement that , "The set Span{u,v} is always visualized as a plane through the origin" is False because if vectors are scalar multiples of each other, then set Span{u,v} is a line through origin .

The set Span{u,v} is defined as the set of all linear combinations of vectors "u" and "v" . This set can be visualized as a plane in three-dimensional space if the vectors are not scalar multiples of each other.

The plane may not necessarily pass through the origin, unless one of the vectors is the zero vector .

If the vectors are scalar multiples of each other, then the set Span{u,v} is a line through the origin, and if one of the vectors is the zero vector, then the set Span{u,v} is a plane through the origin.

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Given

Six payments each year

$ 115

Procedure

If 6 payments are made in one year then each payment is made every two months.

We now know that a year has a total of 52 weeks.

Therefore, the monthly budget should be as follows:

The answer would be $13.27

Answer:

The question needs more information but you can see that all the numbers in the 1st column are multiplied by 6 to equal the number in column 2

Step-by-step explanation:

3 x6 =18

6 x 6= 36

9 x6= 54

12 x6 =72

Answer:

-1 and -1

Step-by-step explanation:

-1*-1= 1 and -1+-1=-2

The result of this division is x + 7, and the remainder is 3x - 4. Therefore, we can write: x² + 6x - 4

How to divide given polynomials?

To divide the given polynomials, we will use long division. The first step is to divide the highest degree term of the numerator, which is x², by the highest degree term of the denominator, which is x:

      x

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

x - 1 | x² + 6x - 4

     | x² - 1x

     | -------

          7x - 4

The result of this division is x, and we write it above the long division bar. Then, we multiply the divisor x-1 by x, which gives us x² - x. We write this below the numerator, and subtract it from the numerator:

      x

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

x - 1 | x² + 6x - 4

     | x² - 1x

     | -------

          7x - 4

          ---------

               7x - 4

Now we bring down the next term of the numerator, which is -4, and repeat the process:

      x + 7

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

x - 1 | x² + 6x - 4

     | x² - 1x

     | -------

          7x - 4

          ---------

               3x - 4

The result of this division is x + 7, and the remainder is 3x - 4. Therefore, we can write:

x² + 6x - 4

x - 1 = x + 7 + (3x - 4)/(x - 1)

So, the answer is p(x) = x + 7 and k = 3. Therefore:

x² + 6x - 4

x - 1 = x + 7 + 3/(x - 1)

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Answer:

7>0x

0x<7

Step-by-step explanation:

4x-6>6x-20

-6>2x-20

14>2x

7>x

The solutions for the system of equations: 7x - 4y = -12 and x - 2y = 4, x - y = 4 and 2x + y = 5, 4x - 3y = 17 and 2x - 5y = 5, 5x + 6y = -6 and 7x - 3y = -54

by elimination are respectively:

x = -4, y = -4

x = 3, y = -1

x = 5, y = 1

x = -6, y = 4

we shall write the equations as:

7x - 4y = -12...(1)

x - 2y = 4...(2)

multiply equation (2) by 7 to get equation (3)

7x - 14y = 28...(3)

subtract equation (1) from (3) to eliminate x

7x - 14y - 7x + 4y = 28 + 12

-10y = 40

divide through by -10

y = -4

put the value -4 for y in equation (2) to get y

x - 2(-4) = 4

x + 8= 4

x = -4

x - y = 4...(1)

2x + y = 5...(2)

Add equations (1) and (2) to eliminate y

2x + y + x - y = 5 + 4

3x = 9

divide through by 3

x = 3

put the value 3 for x in equation (1) to get y

3 - y = 4

y = -1

4x - 3y = 17...(1)

2x - 5y = 5...(2)

multiply equation (2) by 2 to get equation (3)

4x - 10y = 10...(3)

subtract equation (3) from (1) to eliminate x

4x - 3y - 4x - 10y = 17 - 10

7y = 7

divide through by 7

y = 1

put the value 1 for y in equation (2) to get y

2x - 5(1) = 5

2x - 5 = 5

x = 5

5x + 6y = -6...(1)

7x - 3y = -54...(2)

multiply equation (1) by 7 to get equation (3) and equation (2) by 5 to get equation (4)

35x + 42y = -42...(3)

35x - 15y = -270...(4)

subtract equation (4) from (3) to eliminate x

35x + 42y - 35x + 15y = -42 + 270

57y = 228

divide through by 57

y = 4

put the value for y in equation (1) to get x

5x - 6(4) = -6

5x + 24 = -6

x = -6

Therefore, the solutions for the system of equations: 7x - 4y = -12 and x - 2y = 4, x - y = 4 and 2x + y = 5, 4x - 3y = 17 and 2x - 5y = 5, 5x + 6y = -6 and 7x - 3y = -54

by elimination are:

x = -4, y = -4

x = 3, y = -1

x = 5, y = 1

x = -6, y = 4

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Answer:

hhhhhhhhhhhhhhhhhhh

Step-by-step explanation:

x=9

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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Answer:

The value of sin theta is 5/13

Step-by-step explanation:

In the second quadrant, sin is positive and cos is negative

Cos theta = -12/13 = adjacent/hypotenuse

Sin theta = opposite/hypotenuse

opposite = sqrt(hyp² - adj²) = sqrt (13² - 12²) = sqrt (169 - 144) = sqrt (25) = 5

Sin theta = opposite/hypotenuse = 5/13

The input values are all the values of the x-coordinates and the output values are all the values of the y-coordinate corresponding the x-value: (0, 3), (2, 2), (-1, 1).

An ordered pair (a, b) is a pair of objects in mathematics. Because the ordered pair (a, b) differs from the ordered pair (b, a) unless a = b, the order in which the items occur in the pair is important. The unordered pair a, b, on the other hand, equals the unordered pair b, a.

Ordered pairs are sometimes known as 2-tuples, or sequences of length 2 (or, in computer science, sometimes, lists). 2-dimensional vectors are occasionally used to refer to ordered pairs of scalars.

The input values are all the values of the x-coordinates and the output values are all the values of the y-coordinate corresponding the x-value.

Some of the input, output pair are:

(0, 3)

(2, 2)

(-1, 1)

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Given:Expression to be checked whether it makes sense mathematically.15. Solution: Firstly, let us understand the terminologies used in this question. A set of numbers or terms that are related by addition and subtraction are called expressions.

Expressions may contain letters or variables, which represent numbers. Expressions can be simple or complex.Let's take each expression one by one.15. (a) u (v w)This expression makes sense mathematically. We can evaluate this expression by using the associative property of addition, which states that if a, b, and c are real numbers, then the sum of a and b, added to c, is the same as a added to the sum of b and c. Hence, u + (v + w) can be written as (u + v) + w and vice versa.(c) llu v This expression does not make sense mathematically as the operator ll is not defined in mathematics.

Therefore, this expression is invalid.(d) (u v)- u This expression makes sense mathematically. We can evaluate this expression by using the distributive property of subtraction, which states that if a, b, and c are real numbers, then the difference of a and b, multiplied by c, is the same as the difference of a times c and b times c. Hence, (u - u) + v can be written as 0 + v, which is equal to v.(a) lul-vThis expression does not make sense mathematically as the operator l is not defined in mathematics. Therefore, this expression is invalid.(b) (u v)-wThis expression makes sense mathematically. We can evaluate this expression by using the distributive property of subtraction, which states that if a, b, and c are real numbers, then the difference of a and b, multiplied by c, is the same as the difference of a times c and b times c. Hence, (u - v) - w can be written as u - (v + w) and vice versa.

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the decay constant for this material is approximately 0.0445.when t = 8 years, the amount of the material remaining is 550 grams.

The formula for radioactive decay is given by:

a = \(e^(-kt)\\\) * A

where a is the final amount,A is the initial amount, t is the time in years, and k is the decay constant.

We can use the given information to solve for k as follows:

When t = 0, a = A. So, we have:

A = \(e^(0 * k)\) * A

Simplifying this gives:

1 = e^0

Therefore, we can see that k = 0 at the start of the decay process.

Now, when t = 8 years, the amount of the material remaining is 550 grams. Therefore, we have:

550 = \(e^(-8k)\) * 700

Dividing both sides by 700 and taking the natural logarithm of both sides, we get:

ln(550/700) = -8k

Simplifying this gives:

k = ln(700/550)/8

Using a calculator, we can evaluate this expression to get:

k ≈ 0.0445

Therefore, the decay constant for this material is approximately 0.0445.

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Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, the population will be 852.78 after another three years.

A logistic model, also known as the Verhulst-Pearl model, is a type of function used to describe population growth that is limited. It’s a form of exponential growth that takes into account the carrying capacity of an environment.

Population growth that is limited and slows down as the population approaches its carrying capacity is modeled using the logistic model. It is given by this equation:

\(P(t) = K / (1 + Ae^{-rt})\)

where P(t) is the population at time t, K is the carrying capacity, A is the constant of proportionality, and r is the growth rate.

Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, substitute this information into the logistic model: \(P(1) = 500\), \(K = 2000\), and \(P(0) = 200\).

\(500 = 2000 / (1 + Ae^{-r(1)})\)

Now, solve for A by dividing both sides by 2000 / (1 + A):

\(1 + A = 4A = 3\)

Substitute the value of A back into the logistic model equation:

\(P(t) = 2000 / (1 + 3e^{-rt})\)

Solve for r by using the data provided in the problem for the first year (t = 1) and second year (t = 4):

\(P(1) = 500 = 2000 / (1 + 3e^{-r(1)})\)

\(P(4) = ? = 2000 / (1 + 3e^{-r(4)})\)

Solve the first equation for r:

\(500 = 2000 / (1 + 3e^{-r})\\1 + 3e^{-r} = 4e^{-r}\\1 + 3e^r = 4e\)

Solve for e using the quadratic formula to get:

e = 0.4274 and e = 1.1713

Let e = 0.4274:

\(1 + 3e^{-r} = 4e^{-r}\\1 + 3(0.4274)^{-r} = 4(0.4274)^{r}\\1 + 0.5746^r = 1.7166^r\)

Take the natural logarithm of both sides:

\(ln(1 + 0.5746^r) = ln(1.7166^r) - lnr\\ln(1 + 0.5746^r) = rln(1.7166) - lnr\)

Use a graphing calculator to solve for r:

\(ln(1 + 0.5746^r) = rln(1.7166) - lnr\);  -0.1568 < r < 0.7534

Solve for r using the second year’s data:

\(2000 / (1 + 3e^{-r(4)}) = P(4)\\2000 / (1 + 3(0.4274)^{-r(4)}) = P(4)\\P(4) = 852.78\)

Thus, the population will be 852.78 after another three years.

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