Can someone help me solve this?

The sum of the first 26 terms for an arithmetic sequence is 1417.
The sum of the first 8 terms for the same arithmetic sequence is 76.
Find the value of the first term.

Given:

A U.S. Geological Survey map has a scale of 1:24200

There are two buildings that are 3.38 miles apart.

We will find how they are inches apart on the map

First, convert from miles to inches

1 mile = 63 360 inches

So, 3.38 miles = 3.38 * 63 360 inches = 214156.8 inches

The map has a scale of 1:24200

So, using the ratio and the proportions, we will find the length on the map as follows:

Rounding to the nearest hundredth

So, the answer will be: 8.85 inches

If in lixue's garden the green pepper plants grew 5 inches in 3/4 months then at this rate they can grow 0.555 feet in one month

The problem is solved as per the unitary method

In lixue's garden the green pepper plants grew 5 inches in 3/4 months.

In 3/4 months the green pepper grew by 5 inches.

3/4 months can be written as 0.75 months

in 1 month the green pepper plant will grow by (5/0.75) 1

The green pepper plant will grow by 6.66 inches

1 foot is equals to 12 inches

1 inch = 1/12 foot

6.666 inches = (1/12) 6.666

= 0.0833 x 6.666

= 0.555

the plant grew 0.555 feet in 1 month

Therefore, if in lixue's garden the green pepper plants grew 5 inches in 3/4 months then at this rate,they can grow 0.555 feet in one month

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Answer:

1) 267.45

2) 18.48

3) 3472

Constant of proportionality  : [tex]\frac{1}{3}[/tex]

Equation: y = ka

How are the values calculated?

a: 2, 3, 10, and 12

y: 2/3, 1, 10/3, and 4

Let the constant of proportionality = k

If x and y are directly proportional ,

We know , k = [tex]\frac{y}{x}[/tex]

Here, k = [tex]\frac{y}{a}[/tex]

Considering y = 2/3 and a =2

k =   [tex]\frac{2}{3*2}[/tex] =   [tex]\frac{2}{6}[/tex]  =  [tex]\frac{1}{3}[/tex]

Thus, the constant of proportionality ( k) =  [tex]\frac{1}{3}[/tex]

The equation y is given by ,

y =  ka

Let us verify,

For k = 1/3 and a = 12

[tex]y=\frac{1}{3} *12\\\\y=4[/tex]

Thus the equation is y = ka

What is constant of proportionality?

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Yes it is possible for a rectangle to have irrational sides and rational area.

What are rational numbers?

Ration numbers is an ordered pair of integers a, b written in the form a/b where b is not equal to zero.

We are given that sides of rectangle are irrational can the rectangle have rational area

Let us consider that sides of the rectangle be [tex]2\sqrt{2}[/tex] and [tex]\sqrt{2}[/tex]

Hence the area of the rectangle is the product of sides which is [tex]4[/tex] sq. units

Which is a rational number

Hence, Yes it is possible for a rectangle to have irrational sides and rational area

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The area of the first and second circles is 36π m² and 9π m², respectively.

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The most appropriate choice for function and domain and range of a function will be given by -

Domain of y = [tex]\mathbb{R} -[/tex] {[tex]-\frac{1}{2}[/tex]}

Range = [tex]\mathbb{R}-[/tex]{[tex]\frac{1}{2}[/tex]}

What is a function and domain and range of a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

The set of  values for which the function is defined is the domain of the function and the values obtained on substituting the values of domain in the function is the range of the function.

y = [tex]\frac{x -5}{2x + 4}\\[/tex]

For domain of y

y is not defined if 2x  +4 = 0

y is not defined if [tex]x = -\frac{1}{2}[/tex]

Domain of y = [tex]\mathbb{R} -[/tex] {[tex]-\frac{1}{2}[/tex]}

For range of y

let [tex]\frac{x -5}{2x + 4}\\[/tex] = z

[tex]x - 5 = z(2x +4)\\x - 5 = 2zx + 4z\\x - 2zx = 4z + 5\\x(1 - 2z) = 4z + 5\\x = \frac{4z + 5}{1 - 2z}[/tex]

If y = [tex]\frac{1}{2}[/tex]

[tex]\frac{x-5}{2x + 4} = \frac{1}{2}\\2x - 10 = 2x + 8\\-10 = 8\\[/tex]

Not possible

[tex]\frac{1}{2}[/tex] is not in the range of y

Range = [tex]\mathbb{R}-[/tex]{[tex]\frac{1}{2}[/tex]}

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Given that g(x)=2x + 1,

therefore, the value of g(a+h) and g(a) can be written as,g(x)=2x + 1g(a+h)=2(a+h) + 1     
   = 2a + 2h + 1

g(x) = 2x + 1g(a) = 2(a) + 1   
   = 2a + 1

Now, the value of g(a+h)-g(a) will be,

g(a+h) - g(a)= (2a + 2h + 1) - (2a + 1)= 2a + 2h + 1 - 2a - 1= 2h

Hence, the value of g(a+h)-g(a) is 2h.

Using limit definition of the derivative, The value of f'(3) is 2.

By determining the limit of a slope expression, one can get the instantaneous rate of change (derivative).

The derivative of a function f at x is the instantaneous rate of change of the function at x since the derivative is defined as the limit that determines the slope of the tangent line to a function.

Given function

f(x) = x² - 4x.

derivate with respect to x

f'(x) = 2x - 4

put x = 6

f'(x) = 2(3) - 4

= 6-4

=2

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Answer:

5

Explanation:

When we divide A by B, we are calculating how many Bs fit into A. So, if we want to know how many 2/5s fit into 2 yds, we need to divide 2 by 2/5. So:

So, 2 yds of rope can be divide into 5 ropes of 2/5 yd.

Answer:

y = -2x.

Step-by-step explanation:

2y = x - 3

y = 1/2x - 3/2

- so, the slope of this line is 1/2

and the slope of a line perpendicular to it is - 1/ 1/2

= -2.

Using the point slope form of a line the equation of the required line is

y - y1 = m(x - x1)

m = -2, x1 = -1 and y1 = 2.

So,

y - 2 = -2(x - (-1))

y - 2 = -2x - 2

y = -2x - 2 + 2

y = -2x.

The values of the variables are :

10. x = 8 and y = 9

11.  x = 20 /9 and y = - 7/ 9  

12.  x = 3.08 and y = 4x = 12.32

10 . Given equations are ; 7x -5y = 11 ------- equation 1

and y = x + 1

On substituting this value in equation 1

we get 7x - 5 ( x + 1) = 11

7x - 5x - 5 = 11

2x = 16

x = 8 and thus y = 8 + 1 = 9

11. Given equations are : 5x - 4y = 22

x = y+ 3

On again substituting the values we get

5y + 15 - 14 y = 22

- 9 y = 7

y = - 7/ 9 and x = 20 / 9

12. Given equations are 3x + 8y = 108

and y = 4x

On again substituting equations we will get

3x + 32x = 108

35 x = 108

x = 108 / 35

x = 3.08 and y = 4x = 12.32

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Finding the numeric value of the function, the time it will take to read a book of 218 pages is given by:

196.2 minutes.

To find the numeric value of a function, we replace each instance of the variable in the function or in the expression by the desired value in which we want to find the numeric value.

In the context of this problem, the function is given by:

y = 4.5x/5

In which the meaning of the variables is given by:

For a book of 218 pages, the time is found calculating the numeric value at x = 218, that is, replacing the lone instance of x in the function by 218, hence it is given by:

y = 4.5 x 218/5 = 196.2 minutes.

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The equation of the line perpendicular to y = 6x -2 and passes through (6, -2) is y = - 1 / 6 x - 1

The equation of a linear graph can be represented in slope intercept form.

Therefore,

y = mx + b

where

Therefore,  the equation of the line is perpendicular to y = 6x -2 and passes through (6, -2).

Perpendicular lines follows the rule below:

m₁ m₂ = -1

6m₂ = -1

m₂ = - 1 / 6

Therefore, let's find the y-intercept using (6, -2)

y = - 1 / 6 x + b

-2  = - 1 / 6 (6) + b

- 2 + 1 = b

b = -1

Therefore, the equation of the line is y = - 1 / 6 x - 1

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The length of the arc whose central angle is 50° is 10.91.

Here, we are given that a circle has a circumference of 25π.

The length of the arc of a circle is given by the following formula-

(∅/360)*2πr

where ∅ is the measure of the angle that the arc subtends at the center and r is the radius of the circle.

Here, we are already given the circumference, thus, 2πr = 25π.

And, the central angle is given to be 50. Thus, ∅ = 50

Now, substituting the values in the above formula we can calculate the length of the arc as follows-

(50/360)*25π

= 5/36 × 25π

= 125/36 × 22/7

= 2,750/ 252

= 10.91

Thus, the length of the arc whose central angle is 50° is 10.91.

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it D  that the fertilizer with the urea supplement is more effective than the fertilizer without it.

A histogram is the way of representation of data that is utilized to appear the frequency distribution utilizing the rectangle comparable to a bar graph. in order to decide which fertilizer is superior for plant development Farmers conducted a survey consisting of one fertilizer containing an urea supplement, whereas the other does not contain a urea supplement. in which they haphazardly chose 20 plants of the same species developing in their region. ten out of 20 on which the urea-enhanced fertilizer was applied and the rest with the non-urea fertilizer on the other 10 plants.  So After three months At just the beginning of the month, 4 plants showed normal development with the urea supplement, whereas as it were 2 plants appeared to this development when urea isn't supplied. for the second month, 7 plants showed normal development with urea supplement, whereas  4 plants appeared this growth when urea isn't supplied and in the last month of the experiment, 5 plants showed over normal development.

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The price after the discount but before tax, to the nearest dollar and cent, is $18.4.

Given Information:

Price on the tag = $23

Amount of Discount =20%

A % or Percentage is a figure or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred").  A % lacks dimensions and has no associated unit of measurement.

Percentage Formula =[tex]\frac{value}{Total value} *100[/tex]

Calculating the discount,

There is a 20 % discount on the camera

So, the amount of discount by using the percentage formula = [tex]\frac{20*23}{100} = 4.6[/tex]

Hence, the amount of discount is $4.6

Subtracting the discount to calculate the price after the discount =

Initial Price - Discount amount = $23-$4.6 = $18.4

Thus, the price after the discount is $18.4

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Answer:

The right answer choices are B, C, and F

heared about meet, wxa szcx ewn

The fractional equivalent of the repeating decimal n = 0.1515... is 5/33, with two repeating digits.

A fractional equivalent is a fraction that shares the same equivalent value with a decimal.

For instance, the equivalent fraction of 0.1515 is 303/2000.  But for a repeating decimal like 0.1515..., the equivalent fraction is 5/33.

When numbers or values are said to be equivalent, it means that they are equal.

By their nature, repeating decimals continue endlessly.

Let x = 0.1515... equation 1

100x = 15.1515... equation 2

Subtract equation 1 from equation 2:

100x = 15.1515...

    x =   0.1515...

99x = 15

x = 15/99

x = 5/33

Thus, n = 0.1515... as a repeating decimal or 5/33 as a fraction.

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The value of the smaller number is 5

From the question, we are to determine the value of the smaller number

Let one of the numbers be x and the other number be y

From the given information,

The difference of two numbers is 1

That is,

x - y = 1

and

Their sum is 11

That is,  

x + y = 11

Now, we will solve the equations simultaneously

From the first equation

x - y = 1

x = 1 + y     ------------- (3)

Substitute into the second equation

x + y = 11

1 + y + y = 11

1 + 2y = 11

2y = 11 - 1

2y = 10

y = 10/2

y = 5

Substitute the value of y into equation (3)

x = 1 + y

x = 1 + 5

x = 6

Hence, the number is 5

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Answer:

86995.5

Step-by-step explanation:

86995.499184 86995.49918

Two angles are complementary. The measure of the larger angle is 10 greater than 9 times the smaller angle, so the measure of both angles will be 8° and 82°.

The two angles' complement and supplement are determined by the sum of their measurements. The two angles are said to be complimentary if their combined measurement equals that of a straight angle.

According to the question, the equation will form :

x = 9x + 10                      (1)

As we know that for complementary angles,

x + y = 90°

9y +10 + y = 90°

10y = 80°

y = 8°

Substitute this value in equation (1)

x = 9(8) + 10

x = 82°.

Hence, the two angles are 8° and 82° respectively.

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Answer:

6

Step-by-step explanation:

4-x/3=2

4-6/3=2

It is to be noted that the amount of cubic yards of topsoil that Helena purchased is 7 Cubic Yards. (Option D) Here is how we arrived at that answer.

Let the compost purchased be x cubic yards

And the topsoil purchased be y cubic yard

Hence

x+y = 10 .......................................1

Also

Total cost incurred = 25x+15y=180

Dividing the whole equation by 5 we get

5x+3y=36 ........................................2

Multiply 1 by 3 and subtract it from 2

5x+3y=36

-

3x+3y=30

2x      =6 Solving for x

x = 3

Plug x back into equation 1, and we have

x+y=10, this become

3+y=10 Solving for y, we have

y=10-3

=7

Hence it is correct to state that Helena purchased 7 cubic yards of topsoil.

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The total volume of water in the two jugs​ is 3.55 liters.

Given,

Jug A has 2.17 liters of water

Jug B has 0.79 liters less than jug A.

Solution:

Since jug B has 0.79 liters less than jug A.

Jug B = 2.17 - 0.79

= 1.38 litres

The total volume of water in the two jugs​ = 2.17 liters + 1.38 liters

The total volume of water in the two jugs = 3.55 liters

Therefore, the total volume of water in the two jugs​ is 3.55 liters.

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The original price of the toy is p.

An easier way to understand this problem is : The original price is 1, or 100%. Now, it's reduced by 15%, so the new price is 100% - 15% = 85%.

85% can be converted to 0.85, or 85/100. Therefore, the answer is 0.85p