14. A pole has two wires attached to it, one on each side, forming two right triangles as shown.
How tall is the pole?
26.8 feet
25.7feet
29.6 feet
22.3 feet

x ≥ 3, the value of x is greater than or equal to 3 is the solution of inequality (7x-3)/9 ≥ 8-2x, correct option is C.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

(7x - 3)/9 more than or equal to 8 - 2x

(7x-3)/9 ≥ 8-2x

7x-3 ≥ 9(8-2x)

7x-3 ≥ 72-18x

Add 18x on both sides

7x+18x-3 ≥ 72

25x-3 ≥ 72

Add 3 on both sides

25x ≥ 75

Divide both sides by 25

x ≥ 3

Hence, x ≥ 3, the value of x is greater than or equal to 3 is the solution of inequality (7x-3)/9 ≥ 8-2x, correct option is C.

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The cost of admission to the library for each student will be $0.3125. And the admission cost of the zoo will be $156.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Mrs. Hudson's class of 18 understudies is going to the zoo. Every understudy will pay for confirmation and purchase lunch. Mr. Weaver's class of 24 understudies is going to the library. Every understudy will pay for affirmation and pay for transport passage.

Let 'x' be the cost of admission to the library for each student. Then the equation is given as,

$7.50 + $8.25 × 18 + $5.75 × 18 = 24x + $10.50 × 24

Simplify the equation, then we have

$7.50 + $8.25 × 18 + $5.75 × 18 = 24x + $10.50 × 24

$7.50 + $148.5 + $103.5 = 24x + $252

$259.5 - $252 = 24x

x = $0.3125

And the admission cost of the zoo will be given as,

⇒ $7.50 + $8.25 × 18

⇒ $156

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Answer:

[tex]\frac{-r}{2} +12\\[/tex]

Step-by-step explanation:

Combine multiplied terms into a single fraction, find the common denominator, then combine fractions with the common denominator.

The function's standard form equation is equivalent to

y=(1/2)x²+(-7x)+24.

A mathematical expression (equation) that can be used to define and represent the relationship between two or more variables on a graph is known as a quadratic function.

The standard form of a quadratic equation in mathematics is represented by;

ax² + bx + c = 0

y=ax² + bx + c

The information in the table above would then be used to create a set of equations:

The points are (4, 4), (6, 0), (8, 0), (10, 4)

4=a(4)²+b(4)+c

16a+4b+c=4 ------(1)

0=a(6)²+b(6)+c

36a+64b+c=0  ------(2)

0=a(8)²+b(8)+c

64a+8b+c=0  -------(3)

By solving 2 and 3 equations, we get

Eq2-Eq3,

We get b= -14a

By substituting b value in eq2 we get,

36a+6b+c=0

36a+6(-14a)+c=0

35a-84a+c=0

c=48a

By substituting a, b values in eq1 we get,

16a+4(-14a)+48a=4

16a-56a+48a=4

-40a+48a=4

8a=4

a=1/2

Then, b=-14a

b= -7

c=48a

c=24

Now, by substituting these a, b, c values in,

y=ax² + bx + c

y=(1/2)x²+(-7x)+24

By  checking the above equation is correct or not,

We consider the fourth value x=10

When x=10,

y=(100/2)-70+24

y=50-70+24

y=4

From the given table if x=10 then y=4,

So it satisfies with the equation we get.

Therefore, the function's standard form equation is equivalent to

y=(1/2)x²+(-7x)+24.

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Answer:

3.24

Step-by-step explanation:

The Hundredth is the second decimal place

Since 6 is greater than 5, round up

Answer: 5 small bags and 3 large bags

Step-by-step explanation:  5+5+5+5+5=25    7+7+7=21    21+25=46

Answer:

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

Let the missing side be x.

Use Pythagorean to find its value:

The taxi can travel a maximum distance of 11 miles if we have at most $10 to spend on the cab ride.

What is distance?

The length of the line connecting two places represents the distance between them. Subtracting the different coordinates will reveal the distance if the two points are on the same horizontal or vertical line.

The formula for measuring distance between two lines, the total length of all a polygon's sides, the perimeter of a polygon on a coordinate plane, the area of a polygon, and many other things are all found in analytical geometry. For instance, we can use the distance formula to find the lengths of a triangle's sides and decide if it is scalene, isosceles, or equilateral.

It is given that, a taxi charges a flat rate of $1.75 plus an additional fee of $0.75 per mile.

We have to find the maximum distance it could travel at most with $10

Let the maximum distance be x miles.

Thus, the fare would be

$(1.75 + 0.75x) = 10

⇒ 0.75x = 8.25

⇒ x = 8.25/0.75

⇒ x = 11

The taxi can travel a maximum distance of 11 miles if we have at most $10 to spend on the cab ride.

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Answer:

y = 6x

Step-by-step explanation:

[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

[tex]\frac{24-6}{4-1}[/tex]

[tex]\frac{18}{3}[/tex]

m = 6

y = mx + b

y = 6x + b

6 = 6(1) + b

6 = 6

b = 0

Answer:

$3.25

Step-by-step explanation:

This is division

29.25 divided by 9

9 goes into 29.25 3 times

29.25-27=2.25

2.25 is 1/4 of 9

2.25*4=9 because 2*4=8 and .25*4=1 so 8+1=9

So the answer is 3 1/4 or $3.25

The measure of x is 22.5 and the angle ADE is 67.5 degrees

The complete question is added at the end of this solution as an attachment

From the question, we have the following angle measures that can be used in our computation:

Angle A = x

Angle B = 3x

The sum of angles in a triangle is 180

So, we have

x + 3x + 90 = 180

Evaluate the like terms

4x = 90

Divide by 4

x = 22.5

From the attached figure, we have

Angle ADE = Angle B

So, we have

Angle ADE = 3x

This gives

Angle ADE = 3 x 22.5

Evaluate

Angle ADE = 67.5

Hence. the angle is 67.5 degrees

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Answer:

x= 3.5 and x= -3.5

Step-by-step explanation:

4x^2 -49=0

x^2=49/4

x= 3.5 and -3.5

If the two bikes are racing a distance of 100 feet, the bike that will win the race is: D. Bike 1 will win because the slope of the line for Bike 1 is 3/2, which is greater than the slope of the line for Bike 2.

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would calculate the slope of the line representing the distance covered by each of the bikes based on the data points on their graph.

For Bike 1, the slope is given by;

Slope, m = (6 - 3)/(4 - 2)

Slope, m = 3/2

Slope, m = 1.5.

For Bike 2, the slope is given by;

Slope, m = (10 - 5)/(8 - 4)

Slope, m = 5/4

Slope, m = 1.25.

Therefore, the slope of Bike 1 is greater than the slope of Bike 2.

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We move all the characters to the left:

We add all the numbers and all the variables.

We add all the numbers and all the variables.

Multiply

We add all the numbers and all the variables.

We move all terms containing x to the left side, all other terms to the right side

Answer:

x = 8

Step-by-step explanation:

The combined mass of the Earth and Moon is 6.07342 × 10^24.

Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper.

Mass of Earth = 6 × 10^24

Mass of Moon = 7.342 × 10^22

The combined mass of the Earth and Moon will be:

= (6 × 10^24) + (7.342 × 10^22)

= 6.07342 × 10^24

The mass is 6.07342 × 10^24.

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Landon is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Landon scored a total of 24 points and made 2 more two point shots than three point shots. Graphically solve a system of equations in order to determine the number of two point shots made, x, and the number of three point shots made, y.

x = the number of two point shots made

y = the number of three point shots made

Each two point shot scores 2 points, so x two point shots would score 2x points. Each three point shot scores 3 points, so y three point shots would score 3y points.

Therefore, the total number of points scored 2x + 3y equals 24 :
2x+3y=24

Since Landon made 2 more two point shots than three point shots, if we add 2 to the number of three point shots made, we will get the number of two point shots made, meaning x equals y + 2.

                                                                                    x = y + 2

Write System of Equations:

​2x + 3y = 24

         x = y + 2

Solve for y in each equation:

The midsegment has length 25 then the value of x exists 14.

The length of the midsegment is half that of the base, according to the theorem.

A segment that joins the midpoints of two triangle's sides is referred to as a midsegment. According to the midsegment theorem, the third side of a triangle is parallel to the middle two sides of the triangle, and the midsegment is half its length.

Find the midpoints of two of any triangle's sides. A section joins these midpoints. This section will then be half the length of the third side and parallel to it.

The midsegment has length 25.

The base has length x.

x/2 = 25

simplifying the above equation, we get

x = 12.5

Therefore, the value of x exists 12.5.

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221 pages are read in an average reader's time of 6.1 hours. Depending on your Speed, it can take you longer or less period than 6.1 hours you read 221 pages.

You should try to complete the Speed Problems on your own before checking where you are falling behind. We are aware that an object's speed is just how far it travels in one unit of time. 1. A 25 km (6 h) stroll by a man Find the man's speed, please. 2. A railway travels 70 km 30 minutes, compared to a car's 420 m in a minute.

If you're driving your car at 60 km/h, that indicates that the vehicle will cover 60 kilometres per hour. The total distance of 120 km would have been traveled after two hours of driving at a speed of 60 km/h. Because of this, distance equals speed times time, and understanding the connection between speed, time, and distance is essential to figuring out any questions about speed.

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Answer:

[tex]y<5[/tex]

Step-by-step explanation:

[tex]3y-4<11 \\ \\ 3y<15 \\ \\ y<5[/tex]

The paintings' width-to-length ratios are different because the ratio 3 to 2 is not equal to 9 to 6. The correct option is B.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The width-to-length ratios of the paintings differ because 3 to 2 is not equal to 9 to 6.

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Answer:

Step-by-step explanation:

            400                            ÷                                           80

Number of cookies        Divde by         Number of peanut butter cookies

= 5 Total cups

Answer:

The school ordered more than enough concrete to completely fill in the court, so the number of bags of concrete ordered, represented by x, must be greater than the number of cubic yards of concrete needed to fill the court. This can be represented by the inequality x > 60 cubic yards / 0.5 cubic yards/bag. Solving for x, we get x > 60 * 2 = 120. Therefore, the inequality that describes the problem is x > 120.

Using an algebraic equation to represent the word problem, the smallest integer is 1

This is a way of representing mathematical problems with words. To solve this, we have to use algebraic equations or expressions.

Let the integers be represented as

We can write an equation from the word problem given as

7 × (x + 2) = 15 + [x + (x + 4)]

7x + 14 = 15 + x + x + 4

7x + 14 = 15 + 2x + 4

collect like terms

7x - 2x = 15 - 14 + 4

5x = 5

Divide both sides by coefficient of x

5x / 5  = 5 / 5

x = 1

The smallest integer is 1

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Translation:

Find the smallest of three consecutive odd integers such that 7 times the middle integer is 15 more than the sum of the first and third integers

Answer:

The profit or loss on selling a fixed asset will be

Step-by-step explanation:

We know that,

Depreciation = Original value - Scrap value / Estimated life of an asset

-> 100,000 - 0/ 5

= Rs 20,000 for every year

for 3 years,

Depreciation= 3 * 20,000 = Rs 60,000

The value of the asset after 3 years of depreciation = 100,000- 60,000

=Rs 40,000 ---(1)

If it is sold for Rs 45,000 ---(2)

Profit = (2) - (1)

= 45,000-40000

= Rs 5,000

Answer: first, second, and third images.

Step-by-step explanation:

to determine if something is a function, the domain must not have more than one answer in the range. My class calls it the y axis test, if you were to graph it, you cannot draw a line straight down that will go through two points. it's easy to understand with images like these, because all you need to know is that arrows cannot go from one number on the left to multiple on the right. Vice versa is a function, because it passes the y axis test.

The equivalent equation for the given equation m = ca is a = m/c. The equivalent equation has no effect on the original equation's actual function.

An equivalent equation is one that yields the same solution as the original equation.

The equivalent equation is obtained by removing a variable from the given equation. There will be the same number of equivalent equations as there are variables in an equation.

Given that,

m = ca

Here m, c, and a are the three variables in the given equation.

We can write the equation into two more forms as follows:

W.r.t variable 'c',

m = ca

Dividing both sides by 'a'

⇒ ca/a = m/a

c = m/a

W.r.t variable 'a',

m = ca

Dividing both sides by 'c'

⇒ ca/c = m/c

a = m/c

The missing image is attached with the answer.

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The difference between 96 and 72 by 12 can be expressed as

(96 - 72) / 12 and 24 / 12.

We have to find the difference between  between 96 and 72 by 12.

The difference between 96 and 72 can be expressed as,

96 -72

= 24

Next we have to divide the answer that is 24 by 12.

It becomes,

24/12

= 2

As a result, the required expressions for the following calculation is:

(96 - 72) / 12 and 24 / 12.

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Answer:

Step-by-step explanation:

no

Answer: y= mb + xe

Step-by-step explanation: