The sum of three lengths of a fence ranges from 45 to 60 inches. Two side lengths are 9 and 18 inches. If the length of the third side is x inches, write and solve a compound inequality to show the possible lengths of the third side.

9 ≤ x ≤ 18
18 ≤ x ≤ 33
36 ≤ x ≤ 42
45 ≤ x ≤ 60

The sum to infinity of the terms of this sequence is -36/5

The given parameters are

T3 = -1/6

T6 = -1/1296

The nth term of a geometric sequence is

Tn = a * r^(n-1)

So, we have

T3 = ar^2

T6 = ar^5

Divide both equations

T6/T3 = ar^5/ar^2

Evaluate the quotient

T6/T3 = r^3

Substitute T3 = -1/6 and T6 = -1/1296 in T6/T3 = r^3

(-1/1296)/(-1/6) = r^3

Evaluate the quotient

1/216 = r^3

Take the cube root of both sides

r =1/6

Substitute r =1/6 in T3 = ar^2

T3 = a(1/6)^2

This gives

T3 = a/36

Substitute T3 = -1/6 in T3 = a/36

a/36 = -1/6

This gives

a = -6

The sum to infinity of the terms of this sequence is

S = a/(1 - r)

This gives

S = -6/(1 - 1/6)

This gives

S = -6/(5/6)

Evaluate

S = -36/5

Hence, the sum to infinity of the terms of this sequence is -36/5

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Step-by-step explanation:

This is due to the fact that a parallelogram consists of both a triangle and rectangle .

The base of a parallelogram is rectangular

The statement "Is $24 Dave’s after 3 weeks;$52 saved after 7 weeks equivalent" is false

This is further explained below.

Generally, Expressions are considered to be equivalent if their function is the same despite their appearance being distinct.

If two algebraic expressions are equivalent to one another, then those two expressions will provide the same result when we use the same value for the variable in each expression.

In conclusion,

Firstly, we consider what Dave saves in one week will be,

Since $24 Dave’s after 3 weeks we have

One week =24/3

one week=$8

Therefore

7 weeks =$56

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the rate of change of the linear equation in the table is 120.

Remember that for any linear equation with an slope (also called rate of change) s and it passes through the points (a, b) and (c, d), then the slope can be written as:

s = (d - b)/(c - a)

Using that relation and the first two points on the table (0.5, 60) and (1.5, 180)

We get that the rate of change is:

s = (180 - 60)/(1.5 - 0.5) = 120

So the rate of change is 120.

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The standard form for the Parabola is given as

[tex]y=-\frac{1}{7} x^2+\frac{6}{7} x+\frac{33}{7}[/tex]

This is further explained below.

Generally, the equation for is  mathematically given as

x^2-6 x+7 y-33=0

Solve for y.

Move all terms not containing y to the right side of the equation.

7 y=-x^2+6 x+33

Divide each term into 7 y=-x^2+6 x+33 by 7 and simplify.

[tex]y=-\frac{x^2}{7}+\frac{6 x}{7}+\frac{33}{7}[/tex]

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

y=a x^2+b x+c

Reorder terms.

[tex]y=-\left(\frac{1}{7} x^2\right)+\frac{6}{7} x+\frac{33}{7}[/tex]

[tex]y=-\frac{1}{7} x^2+\frac{6}{7} x+\frac{33}{7}[/tex]

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Answer:

its 40° because they're linear pairs

Step-by-step explanation:

both angle 1 and 3 are 40°

Answer:

The answer is 40°

Step-by-step explanation:

Angles that are opposite of each other are always equal.

The area of shaded region is calculated as: 112.5 cm².

The area of the shaded region in the diagram above is:

Area of shaded region = area of rectangle - area of triangle = (length)(width) - 1/2(base)(height).

Given the following:

Length of rectangle = 20 cm

Width of the rectangle = 9 cm

Base of triangle = 20 - 3 - 2 = 15 cm

Height of triangle = 9 cm

Plug in the values into the equation, area = (length)(width) - 1/2(base)(height):

Area of shaded region = (20)(9) - 1/2(15)(9)

Area of shaded region = 180 - 67.5

Area of shaded region = 112.5 cm²

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The actual width of the field 80 yard. when proportion is 3 : 2.

What in mathematics is a proportion?

A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

We have the proportion  

                            3/2 = 120/w

where in the numerator are the length and in the denominators the width of the field.

Now ,                        3 . w = 120 . 2

                                  3w = 240

                                    w = 80

Therefore , the actual width of the field 80 yard.

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Answer:

m×w plus x times x and the then 41 times Square 2 minus k

Step-by-step explanation:

x and y compkety le diff so w n m 41 than times b and g equivalent to 24 so asneer 24 negative

Answer:

3(2a+7)

You find the common multiple and then distribute.

The point slope form are as follows:

The point slope equation can be represented as follows;

y - y₁ = m(x - x₁)

where

Therefore, (5, 2)(-1, -6)

m = slope = -6 - 2 / -1 - 5

m = slope = -8 / - 6

m = slope = 4 / 3

Therefore, using (5, 2) the point slope form is represented as follows;

y - 2 = 4 / 3(x - 5)

using (-1, -6) the point slope form is represented as follows;

y + 6 = 4 / 3(x + 1)

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Step-by-step explanation:

let Irene's share be x and Charlie's share be y

x=2y-8

x+y=$47.50

x=$47.50-y

$47.50-y=2y-$8

$47.50+$8=2y+y

$55.50=3y

y=$55.50/3

y=$18.50

x=$47.50-$18.50

x=$29

Answer:

Irene's share = 29

Charlie's share = 18.5

Step-by-step explanation:

R bill = 47.5

Irene's share = (2 × Charlie's share )-8

Irene's share = y

Charlie's share = x

bill = x + y = 47.5

y = 2x -8

x + 2x - 8 = 47.5

3x = 47.5 + 8= 55.5

x = 18.5

y = 29

The absolute values solved for x are:

Absolute value of a number can be defined as the distance of the number from zero on the number lines.

It is also said to be the value of a number irrespective of its sign.

The absolute value of a number must take a positive sign.

It is denoted with the symbol, '| |'

Given the equations;

a. ) |3-|2-x||=6

Take the absolute value

3 + 2 + x = 6

collect like terms

x = 6 - 5

x = 1

b) |3x-2|+x>= 4

Take absolute values

3x + 2 + x = 4

collect like terms

4x = 2

make 'x' the subject

x = 1/ 2

c) ||2x-1|-2|>3

Take absolute values

2x + 1 + 2 > 3

collect like terms

2x > 3 - 3

x > 0

Thus, the absolute values solved for x are x = 1, x = 1/2 and x> 0

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Answer:

2.9 over 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

It's because the latter one is not a approximation, like about, while the first one is.

The scale factor that the drawing use is 3/1000.

From the information, Colleen made a scale drawing of a house and she used the scale 3 millimeters = 1 meter.

It should be noted that 1000 millimeters = 1 meter

Therefore, the scale factor that the drawing use is:

= 3 millimeters / 1 meter

= 3/1000

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Answer:

Mathematics is a fundamental part of human thought and logic, and integral to attempts at understanding the world and ourselves. Mathematics provides an effective way of building mental discipline and encourages logical reasoning and mental rigor. In addition, mathematical knowledge plays a crucial role in understanding the contents of other school subjects such as science, social studies, and even music and art.

Step-by-step explanation:

if you need more I can help with that

Answer:

See below

Step-by-step explanation:

From 2 minutes to 5 minutes the pump puts in (200-110) = 90 gallons ...in 3 minutes....so the rate of the pump is    30 gal / min

   at two minutes the pump has put in 30 x 2 = 60 gallons......so there was 50 gallons in the tank to start ( 50 + 60 = 110)

the equation becomes :

   G = 50  +  30 t    

               where t = minutes

   and 50 is the initial volume in the tank

For 13 minutes      G = 50 + 30 (13) = 440 gallons

For 890 gallons      890 = 50 + 30 t

                                840 = 30 t

                                   t = 28  minutes

t intercept occurs when  G = 0

                         0 = 50 + 30 t

                             t = - 5/3   minute    <====this is the amount of time before measurements were taken.....or the time for the pump put in 50 gallons before the  start

9 squares should be shaded to represent the male penguins with red eyes.

Percentage is a fraction or a ratio in which the value of whole is always 100.

Given:

45% of the penguins are male, and 55% are female.

20% of the time, male penguins are born with red eyes,

and 30% of the time, females are born with red eyes.

To find the squares should be shaded to represent the male penguins with red eyes we have to perform the following step

20% of 45

=0.2* 45

=9

Hence, 9 squares should be shaded to represent the male penguins with red eyes.

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Answer:

9 blue squares should be shaded

Step-by-step explanation:

20% of 45 = 9

The value of the expression 6( 3 + 5 ) 2 - 9a when a = 3 is 69

In this question,

we have been given an expression 6( 3 + 5 ) 2 - 9a

We need to evaluate given expression when a = 3 and b = 5

We substitute a = 3 in given expression and solve it.

6( 3 + 5 ) 2 - 9a                 ..........(given expression)

= 6( 3 + 5 ) 2 - 9(3)            ..........(substitute a = 3)

= 6(8) 2 - 27

= 96 - 27

= 69

Therefore, the value of the expression 6( 3 + 5 ) 2 - 9a when a = 3 is 69

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Total number of hours both worked last month is; 28.8 hours

Let the number of hours that Herold worked last month be x. Thus, number of hours that Marley worked = 16 + x

Now, we are told that Marley worked 7 hours for every 2 hours that Herold worked. Thus;

(16 + x)/x = 7/2

Cross multiply to get;

2(16 + x) = 7x

32 + 2x = 7x

7x - 2x = 32

x = 32/5

x = 6.4 hours

Thus, total hours Marley worked = 16 + 6.4 = 22.4 hours

Total number of hours both worked last month = 22.4 + 6.4 = 28.8 hours

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The two representations are:

x > 5

A number line with an open circle at 5 and a line that points to the right.

We start with the inequality:

-3(2x - 5) < 5*(2 - x)

First, we need to solve this for x, expanding both sides we get:

-6x + 15 < 10 - 5x

Now we move the terms with x to the right side and the terms without to the left side.

15 - 10 < 6x - 5x

5 < x

This is a representation of the inequality.

The other will be a graph, to graph this on a number line we need to do an open circle at x = 5, and shade the region to the right (because x is larger than 5).

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Answer:

Answer is 36.8

Step-by-step explanation:

There's something wrong in your question... Because...

5x-2=182

5x=182+2

5x=184

5x/5=184/5

X=36.8

Answer:

The first option (a) is the most approximate

Step-by-step explanation:

The area results:

a = 161.91315 = 162

[tex]e^{5} =148.4[/tex]

then

[tex]14+e^{5} =14+148.4=162.4[/tex]

Hope this helps

The equivalent expression is x raised to the eighth power over quantity 9 times y raised to the tenth power end quantity. Option A

The index form of a number can be defined as the number written as an exponential expression.

It is expressed as a single number raised to another number.

Index forms are also called standard forms or scientific notations.

Index notation is also a way of representing variables or constants multiplied by themselves a number of times.

Equivalent expressions are expression having same solution but different  arrangement of variables.

Given the expression;

(3x^−4y5)^−2

Multiply the exponents

x^8/ 9y10^

Thus, the equivalent expression is x raised to the eighth power over quantity 9 times y raised to the tenth power end quantity. Option A

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Answer:

angles in radians

Step-by-step explanation:

look