The perimeter of a rectangle is 168 feet. Find the length and width if the length is an integer and the width is 4 times the next consecutive integer.

Answer:

9

Step-by-step explanation:

Because it is multiplication, the parenthesis are not important. It is the equivalent of 3*9*8 = 8*3*n. From here, you can tell that the 9 is missing.

The system has no solution.

The solution to the system would be the intersection point of the two lines.  Since these lines don't appear to intersect, there's no solution.

Answer:

1) 3/4 x 7/6
2) 21/24
3) 7/8

Step-by-step explanation:

1) KCF, Keep change flip. 3/4 stays the same, division sign changes into multiplication, and 6/7 changes into its reciprocal.
2) Multiply numerator by numerator and denominator by denominator
3) Find their greatest common factor (GCF) and divide the numerator and denominator by it. There's your simplified answer.

Answer:

7/8

Step-by-step explanation:

Divide 3/4 with 6/7

3

4

÷

6

7

is

7

8

.

Steps for dividing fractions

Find the reciprocal of the divisor

Reciprocal of

6

7

:

7

6

Now, multiply it with the dividend

So,

3

4

÷

6

7

=

3

4

×

7

6

=

3 × 7

4 × 6

=

21

24

After reducing the fraction, the answer is

7/8

The value of a for system ax + 12y = −6, 2x − 6y = 4 having no solution is a = -4.

Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.

Given:

ax + 12y = −6

2x − 6y = 4

Calculate the value of a by using the condition of no solution of the system given below,

[tex]a_1 / a_2 = b_1 / b_2 \neq c_1/c_2[/tex]

So, a₁ / a₂ = b₁ / b₂

a / 2 = 12 / (-6)

a / 2 =  - 2

a = -4

And -4 / 2 ≠ -6 / 4

Therefore, the value of a for system ax + 12y = −6, 2x − 6y = 4 having no solution is a = -4.

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Answer:

The two numbers are 44 as the smaller number and 89 as the larger number.

Step-by-step explanation:

Hope it helps!

Let's call the larger number x, and the smaller number y. We know that y is one more than half of x, so we can write y = x/2 + 1. We also know that the sum of the two numbers is 133, so we can write x + y = 133. We can use these two equations to solve for the values of x and y. Substituting the first equation into the second, we get:

x + (x/2 + 1) = 133

Combining like terms, we get:

1.5x + 1 = 133

Subtracting 1 from both sides, we get:

1.5x = 132

Dividing both sides by 1.5, we get:

x = 88

Substituting this value for x in the first equation, we get:

y = 88/2 + 1 = 44 + 1 = 45

Therefore, the two numbers are 88 and 45, and we can check our solution by verifying that the sum of these numbers is indeed 133.

x + y = 88 + 45 = 133

This confirms that our solution is correct.

The range of possible lengths for the third side is  [46.13,57.27] .

What is pythagoras theorem?

The Pythagorean theorem or Pythagoras' theorem could be a elementary relation in parabolic geometry between the 3 sides of a trigon.

Main Body:

To find range of possible lengths for the third side , we will use Pythagoras theorem : a²+b² = c²

given =   24 ft , 52 ft​

24² =576

52² =2704

2704+576=3280

√3280 =57.27

AND

52² = 24²+b²

b²= 2704-576

b=√2128

b = 46.13

range of possible lengths for the third side is [46.13,57.27]

Hence the range of third side is found out.

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Answer:4f+3t=7.95  2f+10t=9.50

Step-by-step explanation:

Let the cost of fudge be f and taffy be t.

Chris bought 4 pieces of fudge and 3 pieces of taffy for a total of $7.95

 4 f + 3 t = 7.95

Samantha bought 2 pieces of fudge and 10 pieces of taffy for a total of $9.50

 2 f + 10 t = 9.5

The following complex number (1-i)³ in a+ bi form is -2+4i

In mathematics, a complex number is a part of a number system that includes an element with the symbol I often known as the imaginary unit, and extends the real numbers. Complex numbers satisfy the equation that any complex number can be represented as a + bi, where a and b are real numbers. Rene Descartes referred to me as an imaginary number because no real number can satisfy the aforementioned equation. A and b are referred to as the real and imaginary parts, respectively, of the complex number a+bi. Complex numbers are accepted in the mathematical sciences as being just as "real" as real numbers despite the historical appellation "imaginary."

(1-i)³

=1³-i³-3(1)(i)(1-i)

=1+i-3(1-i)

=1+i-3+3i

=-2+4i

Therefore, the following complex number (1-i)³ in a+ bi form is -2+4i.

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The solution to the given system of linear equations is x = 2, y = 6.

From the question, we are to solve the given system of linear equations

The given system of linear equations is

-x +5y = 28

x+3y=20

To solve the equation, add the equations

  -x +5y = 28

+  x + 3y=20

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

8y = 48

Divide both sides by 8

8y/8 =48/8

y = 6

Substitute the value of y into the second equation

x+3y=20

x + 3(6) = 20

x + 18 = 20

x = 20 - 18

x = 2

Hence, the solution is x = 2, y = 6

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Answer:

This is a solution to the linear inequality.

Step-by-step explanation:

(-8, 9)

x + y ≤ 4

-8 + 9 ≤ 4

1 ≤ 4

This is a solution to the linear inequality.

Answer:

Step-by-step explanation:

According to the graph that I graphed online, the point (-8,9) is a solution to the linear inequality. To find out that, (-8,9) is a solution you have to look if that point is shaded if it is shaded then it is a solution to the inequality.

(-8 is the x variable and 9 is the y variable, to find out if that is a point you look for the -8 in the graph but you would look down on the the x side and then you go up looking for a 9.)

The system of equations that could be used to solve the problem are;

400a + 1000p = 8800

a + p = 13

Where a is associate and p is partner

Let the variables be defined as:

Associate is denoted by a

Partner is denoted by p

We are told that the daily rate charged to the client for each associate is $400 and the daily rate for each partner is $1000. Thus, the equations are:

400a + 1000p = 8800   -----(1)

a + p = 13   ------(2)

Make a the subject in eq 2 to get;

a = 13 - p   -----(3)

Put 13 - p for a in eq 1 to get;

400(13 - p) + 1000p = 8800

5200 - 400p + 1000p = 8800

5200 + 600p = 8800

5200 + 600p = 8800

600p = 3600

p = 6 partners

a = 13 - p

a = 13 - 6

a = 7 associates

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The solution is h⁴ for the equation h⁻⁵ / h⁻⁹.

Given equation,

h⁻⁵ / h⁻⁹

We know that ,

According to law of exponents ,

xᵃ / xᵇ = xᵃ⁻ᵇ

So here

h⁻⁵ / h⁻⁹ = h⁻⁵ ⁺⁹

= h⁴

Therefore the solution of the equation h⁻⁵ / h⁻⁹ is h⁴.

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(3, 11) is the coordinate of the point that is most likely an outlier

How to draw a scatter diagram?

A scatter diagram is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data

Given: The Age and Value as shown in the question

Age (years)        4   6    5   4   2   8  3   3  5   7    1    5

Value (£ 000's) 46 37 52 60 74 21 65 11 67 27 86 40

The values of Age against Value will then be plotted on a scatter plot as shown in the image attached. Note that Age will be on the horizontal while Value will be on the vertical.

Therefore, the coordinate of the point that is most likely an outlier is (3, 11). This is because it is too far from the line

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The Tangents of the three circles  passing though point P and A are attached below

2.

The circle is inscribed in the triangle and is the largest circle which will fit within the triangle. The line from each triangle vertex to the center of the circle bisects each angle of the triangle

What is a tangent ?

A tangent in geometry is a line that originates at an outside point and travels through a curve's Centre. When you ride a bicycle, every point on the wheel's circumference forms a tangent with the road, providing a practical illustration of a tangent. Let's use an illustration to better grasp what a tangent is. The arc S and point P outside of S are depicted in the following figure. S has been reached via a tangent from P. This serves as an illustration of a tangent.

Two crucial characteristics of the tangent are:

A tangent only hits a curve once.

A line that never reaches the inside of the circle is known as a tangent.

At the point of tangency, the tangent makes a right angle contact with the circle's radius.

A tangent to the circle also has mathematical theorems linked with it, which are needed when doing important computations in geometry in addition to the qualities mentioned above. Let's go into further depth on a couple tangents to circle theorems.

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Answer:

Step-by-step explanation:

perp. -1/5

y - 6 = -1/5(x + 3)

y - 6 = -1/5x - 3/5

y - 30/5 = -1/5x - 3/5

y = -1/5x + 27/5

parallel: 5

y - 6 = 5(x + 3)

y - 6 = 5x + 15

y = 5x + 21

1.22ft is the length, in feet, of the model.

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.

Main Body:

Length of Clark house = 30.5 ft

Dimensions of the model were 1/25 the dimension of Clark's actual home.

so , we can write as -

Write and solve an equation of ratios:

 1          x

---- = ----------

25      30.5 ft

Then 30.5 ft = 25 x, and x = 1.22 ft, or 14.64 inches.

Hence 1.22ft is the length, in feet, of the model.

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Answer:

A) The equation y = 2x represents a proportional relationship. This is because the values of y are directly proportional to the values of x. In other words, as x increases, y also increases by the same factor. This is the definition of a proportional relationship.

B) The unit rate of change for this situation is 2 hot dogs per minute. This is because the equation y = 2x represents a linear relationship, where the rate of change (the slope) is constant. The unit rate of change is the slope of the line, which in this case is 2. This means that for every 1 minute that passes, Peter eats 2 hot dogs.

Answer:

Step-by-step explanation:

For an equation or function be linear, it should be in the form:

Y= mX +b

then

a) YES Linear

b) NO linear

c) YES Linear

d) NO linear

Answer: No

A correlation is a relationship between two variables that tend to move in the same direction. Therefore, a positive correlation will describe two variables that increase together. However, correlation does not always equal causation, and in this case, this conclusion cannot be made. A more probable explanation is that there is some third variable causing an increase in population, so more people are buying more cars, not the other way around.

The variables in an experiment that tests the distance honey flows at different temperatures is the distance honey flows is the dependent variable and temperature is the independent variable .

Given :

In the experiment " Temperature" is dependent variable and the distance honey flows is independent variable.

What is independent variable ?

It is the factor that one can purposely control or change to observe its effect , is called independent variable.

What is dependent variable ?

It respond to the change in the independent variable , is called dependent variable.

Hence temperature is dependent and distance honey flow is independent variable.

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Answer:

  p = 8

Step-by-step explanation:

Given 4 equations in 4 unknown values, you want to find the value of p.

Substituting for c in the second equation, we have ...

  ts = (t +s) +t -s

  ts = 2t . . . . . . simplify

  s = 2 . . . . . . . divide by 2

Substituting for c and s in the third equation, we have ...

  3(t +2) = t +10·2

  2t = 14 . . . . . . . . . subtract t+6

  t = 7

Substituting for c, t, s in the equation for p gives ...

  p = ((t +s) +t)/s = (2·7 +2)/2 = 8

The value of p is 8.

__

Additional comment

The variable values are (c, p, s, t) = (9, 8, 2, 7).

The volume of the cube with a mass of 20 grams and a density of 6 g/cm³ is 3.33 cm³

From the question, we are to determine the volume of the given cube

From the given information,

The mass of the cube is 20 grams

and

The density of the cube is 6 g/cm³

From the formula,

Density = Mass / Volume

Then, we can write that

Volume = Mass / Density

Thus,

The volume of the cube is

Volume = 20/6

Volume = 3.33 cm³

Hence, the volume is 3.33 cm³

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The answer to this question would be (B)

Answer: csc^2x+sec^2x=1

Step-by-step explanation:

The confidence interval gets broader as the confidence level rises because the error bound rises as well. The confidence interval gets narrower as the confidence level is reduced since the error bound is also reduced.

This can be the reason why  you might want to increase the confidence level, even though it means that precision is lost and the interval widens.

We must widen the distance in order to obtain greater trust. The multiplier, which rises with confidence level, shows this clearly. The width of confidence intervals will rise when sample size is increased.

An unknown population parameter's likely range of values is known as a confidence interval. A certain proportion of the confidence intervals will include the population mean if you repeatedly take random samples. The confidence level is expressed as this percentage.

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We know that Martin earn $81 last week by raking 27 bags using simple mathematical operations.

A mathematical expression known as an "operation" in mathematics is one that transforms zero or even more input data into a precisely specified actual output.

The number of arithmetic determines the difficulty of the operation.

The four basic operations in arithmetic are addition, subtraction, multiplication, and division, according to the majority of people.

So, money was earned by raking 27 bags.

Martin earns $15 for raking 5 bags.

The amount earned by raking 1 bag:

15/5 = $3

Now, the amount earned by raking 27 bags:

27 * 3 = $81

Therefore, we know that Martin earn $81 last week by raking 27 bags using simple mathematical operations.

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The inverse of the given relation  {(5, 1), (4, -3), (3, -1)} is  {(1, 5), (-3, 4), (-1, 3).

The inverse of a relation is a relation obtained by interchanging or swapping the elements or coordinates of each ordered pair in the relation.

The ordered pair (x, y) of f(x) becomes (y, x) of f⁻¹(x).

Given, A relation in form of a set of ordered pairs {(5, 1), (4, -3), (3, -1)} let this be f(x).

∴ The ordered pair of f⁻¹(x) will be {(1, 5), (-3, 4), (-1, 3).

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Answer:

Length (L) = 50 m

Step-by-step explanation:

Given information,

→ 400 m long fencing wire is required to surround square flower garden 2 times.

Now the fence taken for 1 time,

→ 400 ÷ 2

→ 200 m

Formula we use,

→ P = 4 × L

[Perimeter of square]

Then the length of the garden is,

→ P = 4 × L

→ 200 = 4L

→ 4L = 200

→ L = 200/4

→ [ L = 50 m ]

Hence, length of garden is 50 m.

Answer: B

Step-by-step explanation:

Multiply matrices

AB = [ 4    5 ]       x    [   3   ]

        [ 8    7 ]             [   9   ]

4 x 3 + 5 x 9 = 12 + 45 = 57

8 x 3 + 7 x 9 = 24 + 63 = 87

[ 57 ]

[ 87 ]

Answer:

6p+3q

Step-by-step explanation:

1.5(4p+2q)

Distribute property

1.5(4p)+1.5(2q)

6p+1.5(2q)

6p+3q

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Answer:

3 x (2p+q)

Step-by-step explanation:

STEP 1:

                3

Simplify   —

                 2

The equation at the end of step 1:

 3

 — • (4p + 2q)

 2

STEP 2:

Pulling out like terms

3.1     Pull out like factors :

  4p + 2q  =   2 • (2p + q)

Final result :

 3 • (2p + q)