Segment
B
D
‾
BD
bisects
∠
A
B
C
∠ABC. Solve for
x
x. Round to the nearest tenth, if necessary. (Image not necessarily to scale.)

Therefore , the solution of the given problem of algebra comes out to be

60 garden beds in the students plans.

Algebra, a subfield of mathematics, is concerned with symbols and the mathematical operations carried out on them. Because these symbols don't have predetermined values, they are referred to as variables. These symbols are additionally put through a variety of addition, subtraction, multiplication, and division arithmetic operations in order to obtain the values.

Here,

Given: actual flower bed: 18

This represents 30% of all garden beds.

Assume that x is the size of the entire flowerbed.

So, 30% of x= 18

30/100 x = 18

x= 1800/ 30

x= 60

60 garden beds are therefore planned by the students.

Therefore , the solution of the given problem of algebra comes out to be

60 garden beds in the students plans.

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Using the values for x and y and substituting these values in the expression of equations provided, The answer is 23 and 1728.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.

When a variable (or set of letters) in an algebraic statement is substituted, its numerical value is used instead. The expression's total value can then be calculated.

x=3 and y=4

[tex]x^2 + 2(x+y)\\=3^2 + 2* (3+4)\\=9+2*7\\=9+14\\=23[/tex]

[tex](xy)^3\\=(3*4)^3\\=12^3\\=1728[/tex]

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Dalisay hits the target more.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

Kendra hits the target 3 times every 5 misses.

And, Dalisay hits the target 5 times every 7 misses.

Since, Kendra hits the target 3 times every 5 misses.

Hence, In 1 misses Kendra hits the target = 3/5 times

                                                               = 0.6 times

And,  Dalisay hits the target 5 times every 7 misses.

Hence,  In 1 misses Dalisay hits the target = 5/7 times

                                                               = 0.74 times

Thus, Dalisay hits the target more.

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The baker can make 13 loafs of bread using 85 cups of flour using 6 1/4 c of flour for each loaf of bread.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A baker has 85 cups (c) of flour to make bread she uses 6 1/4 c of flour for each loaf of bread.

Now, The fraction 6 1/4 can be written as 25/4.

Therefore, The number of bread loaf the baker can make is,

= (85/25/4).

= 85×(4/25).

= (17×4)/5.

= 68/5.

= 65/5 + 3/5.

= 13 + 3/5.

So, he can make 13 bread loafs.

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the quadratic equation have been solved and the required graph is attached below.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The equation:

[tex]\frac{x^{2}-7x+12 }{x^{2} -1}[/tex]

Its a quadratic equation in both numerator and denominator, by dividing the x² will be get a graph as given in the attached file.

Hence, the quadratic equation will be solved and the required graph is attached below.

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The value of π can be written with upper and lower limits as -

3.12 ± 0.062.

Significant figures of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something.

Given is that Helen draws a random circle, she then measures the circumference and diameter. She gets a circumference {C} of 405mm correct to 2 significant figures She gets a diameter {D} of 130mm correct to 2 significant figures.

We can write -

Circumference {C} = (405 ± 2) mm

Diameter {D} = (130 ± 2) mm

The value of π can be calculated as -

π = {C}/{D}

π = (405 ± 2)/(130 ± 2)

Now, divide the numbers without errors first -

405/130

3.12

Now, we will calculate the relative errors in each number -

2/405 = 0.004

2/130 = 0.016

Adding the relative errors -

0.004 + 0.016

0.02

Absolute error = 0.02 x 3.12 = 0.062

The value of π can be written with upper and lower limits as -

3.12 ± 0.062

Therefore, the value of π can be written with upper and lower limits as -

3.12 ± 0.062.

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The length of 9/16 of an inch threaded section of the pipe indicates that the new length of the threaded section after 4/32 of an inch is trimmed off obtained by the difference between the fractions is; C. 7/16 of an inch

A fraction is the representation of only a part of a whole of an item in the form of a quotient, consisting of a numerator, being divided by a denominator.

The length of the threaded section of the pipe = 9/16 of an inch

The length of the threaded part trimmed off due to an error = 4/32 of an inch

The new length of the threaded section following the trimming off of 4/32 is therefore;

New length of the threaded section = 9/16 - 4/32

The value of the difference between the fractions is found as follows;

[tex]\dfrac{9}{16} -\dfrac{4}{32} =\dfrac{2 \times 9 - 4}{32} = \dfrac{14}{32}[/tex]

[tex]\dfrac{14}{32}=\dfrac{7}{16}[/tex]

Therefore;

[tex]\dfrac{9}{16} -\dfrac{4}{32} =\dfrac{7}{16}[/tex]

The new length of the threaded section will be 9/16 - 4/32 = 7/16

The correct option that indicates the new length of the threaded section is C. 7/16

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The value of x is 10 yards. The given shape is a trapezoid.

What are trigonometry ratios?

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Draw a line parallel to the base.

Name the corner point of the shape.

Assume that ∠ADG = θ.

Consider △BDF:

BD = 6 + x

DF = 8 + 4.8 = 12.8 yrds.

The cosine of an angle is the ratio of the base to the hypotenuse of the right-angle triangle.

cos θ = DF/BD

cos θ = 12.8 /(6+x)  .....(i)

Consider △CDE:

cos θ = DE/CD

cos θ = 8/x  .....(ii)

Now equate equations (i) and (ii):

12.8 /(6+x) = 8/x

Cross multiply:

12.8 × x = 8(6+x)

12.8x = 48 + 8x

12.8x - 8x = 48

4.8x = 48

Divide both sides by 4.8:

x = 48/4.8

x = 10

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The value of x is 10 yards. The given shape is a trapezoid.

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Draw a line parallel to the base.

Name the corner point of the shape.

Assume that ∠ADG = θ.

Consider △BDF:

BD = 6 + x

DF = 8 + 4.8 = 12.8 yrds.

The cosine of an angle is the ratio of the base to the hypotenuse of the right-angle triangle.

cos θ = DF/BD

cos θ = 12.8 /(6+x)  .....(i)

Consider △CDE:

cos θ = DE/CD

cos θ = 8/x  .....(ii)

Now equate equations (i) and (ii):

12.8 /(6+x) = 8/x

Cross multiply:

12.8 × x = 8(6+x)

12.8x = 48 + 8x

12.8x - 8x = 48

4.8x = 48

Divide both sides by 4.8:

x = 48/4.8

x = 10

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Answer:

Five hours after the museum opens, there are 36 visitors.

Step-by-step explanation:

V(5)=36 means that when h is 5, V is 36. Assuming this is a function from what information this gives.

Answer:

[tex] \sf \: a) \: 1[/tex]

Step-by-step explanation:

Given values of variables,

→ e = 3.2

→ d = 10

→ u = 7

The problem needed to solve is,

[tex] \sf \rightarrow \: \frac{ue}{eu} [/tex]

Let's solve the problem,

[tex] \sf \rightarrow \: \frac{ue}{eu} [/tex]

[tex] \sf \rightarrow \: \frac{(7 \times 3.2)}{(3.2 \times 7)} [/tex]

[tex] \sf \rightarrow \: \frac{22.4}{22.4} [/tex]

[tex] \sf \rightarrow \: \frac{1}{1} = 1[/tex]

Hence, option (a) is correct.

Answer:

Option A ) 1

Step-by-step explanation:

[tex]\frac{ue}{eu} = \frac{3.2X7}{7X3.2} = \frac{22.4}{22.4} = 1[/tex]

Hence , Option A ) is the answer

Answer:

Perpendicular line ⇒ 2x + 9y + 42 = 0

midpoint: (-1,1)

Step-by-step explanation:

Let's find the coordinates of midpoint of AB

Here, from figure, A = (-3,-2), B = (1,4)

So midpoint:

[tex]P = (\frac{-3+1}{2},\frac{-2+4}{2})[/tex]

∴ P = (-1, 1)

Now, given straight line is x - 2y = -8(x-8)

⇒x - 2y = -8x+64

⇒9x - 2y - 64 = 0

Perpendicular line to 9x - 2y - 64 = 0 is 2x + 9y + k = 0

Perpendicular line passes though (6,-6)

Putting the values, we get

2(6) + 9(-6) + k = 0

⇒12 - 54 + k = 0

⇒k = 42

∴ Perpendicular line ⇒ 2x + 9y + 42 = 0

Complete the puzzles with values -4, 0, -3 and 2

Since each row, column, and diagonal adds up to the same total.

For the 1st row, the total is:

3 + (-2) + (-1) = 0

That means each row, column, and diagonal will always adds up to 0.

3 + w + 1 = 0

w = -3-1

w = -4

w + y + 4 = 0

-4 + y + 4 = 0

y = 0

-1 + 4 + t = 0

3 + t = 0

t = -3

1 + h + t = 0

1 + h + (-3) = 0

h -2 = 0

h = 2

(Check the attached image for labeling)

Thus, complete the puzzle with the values accordingly

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Answer:

The magnification is the ratio of the size of the image to the size of the object. In this case, the length of the insect is the size of the object, and the length of the drawing is the size of the image.

To find the magnification, we can divide the size of the image by the size of the object:

Magnification = size of image / size of object

Plugging in the values, we have:

Magnification = 85mm / 23mm

Calculating, we find that the magnification is approximately 3.7. This means that the length of the drawing is 3.7 times the length of the insect.

Step-by-step explanation:

Functions whose inverses are also functions.

Inverse function is represented by [tex]f^{-1}[/tex] with regards to the original function  and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.

If a horizontal line intersects the original function in a single region, the function is a one-to-one function and inverse is also a function.

Every function has an inverse, but not every inverse will be a function. The inverse may fail the vertical line test. If the original function is a one-to-one function, then its inverse will be a function. A one-to-one function not only passes the vertical line test, it also passes a horizontal line test.

Therefore, functions whose inverses are also functions.

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The midpoint and distance between (-3,10) and (15,-2) are ( 6,4 ) and 6√13 respectively.

The midpoint formula is expressed as;

[ (x₁ + x₂)/2, (y₁ + y₂)/2 ]

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Given the data in the question;

Point 1(-3,10)

Point 2( 15,-2 )

Plug the given values into the midpoint formula and simplify.

[ (x₁ + x₂)/2, (y₁ + y₂)/2 ]

[ ( -3 + 15)/2, ( 10 + (-2) )/2 ]

[ ( 12)/2, ( 10 - 2 )/2 ]

[ ( 12)/2, ( 8 )/2 ]

( 12/2, 8/2 )

( 6,4 )

Therefore, the midpoint is (6,4).

Plug the given values into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

D = √( ( 15 - (-3)  )² + ( -2 - 10 )² )

D = √( ( 15 + 3  )² + ( -2 - 10 )² )

D = √( ( 18  )² + ( -12 )² )

D = √( 324 + 144 )

D = √( 468 )

D = 6√13

Therefore, the distance between the points is 6√13.

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========================================================

Explanation:

The left-most rectangle spans from x = 0 to x = 2. It has base 2 and height 2, which means it has an area of 2*2 = 4 square units. Let A = 4 since we'll use it later.

The middle rectangle goes from x = 2 to x = 4. It has base 2 and height 3 (because it goes from y = 0 to y = -3). The area is B = 2*3 = 6

Draw a vertical line through 6 on the x axis. This forms the final rectangle we need. It has base 2 (because it goes from x = 4 to x = 6) and height 5. The area is C = 2*5 = 10.

The small sliver to the right of x = 6 is ignored completely.

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

Summary so far:

Those represent the areas of the rectangles from left to right. We ignore the portion to the right of x = 6.

Since rectangle B is below the x axis, we treat this as a negative area, or we subtract off this area. The positive areas of rectangles A and C are added.

So,

A-B+C = 4-6+10 = 8 is the final answer

We can write [tex]\displaystyle \int_{0}^{6}f(\text{x})d\text{x} = \boldsymbol{8}[/tex]

(20, 2,200) and (5, 3,000) are the viable solutions of the given inequality.

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

Given that the side of the square must be equal to the width of the rectangle, x feet.

The length of the rectangle must be 50 feet longer than its width

The field the farmer wants to build the two fenced sections in has an area of y square feet.

The difference of the area of this field and the area of the fenced, square section needs to be at least 1,000 square feet

the sum of the fenced areas must be less than the area of the field.

y≥x²+1000

y>2x²+50x

(20, 2,200) and (5, 3,000) are the viable solutions

Hence, (20, 2,200) and (5, 3,000) are the viable solutions of the given inequality.

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Using a calculator we can approximate this to be A ≈ 568.89 cm^2.

A regular decagon is a two-dimensional geometric shape with ten sides of equal length and ten interior angles of equal measure. It is a polygon, which is a two-dimensional shape made up of line segments (straight sides).

The approximate area of a regular decagon can be calculated using the formula A = (5/2) * a^2 * tan(π/5), where a is the length of each side. Since the radius of the decagon is 8 cm, the length of each side can be calculated using the formula a = 2r * sin(π/10) where r is the radius.

Plugging these values into the formula we get A = (5/2) * (2 * 8 * sin(π/10))^2 * tan(π/5) which simplifies to A = 320 * sin^2(π/10) * tan(π/5).
Using a calculator we can approximate this to be A ≈ 568.89 cm^2.

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Both of you are correct because using either way can solve the equation for the value of x.

In the case of solving for x in  2/5 x = 14, the goal is to get rid of the fraction that is multiplying x on the left side. This can be done by either multiplying both sides of the equation by the inverse of 2 / 5 ( which is 5 / 2 ) or by dividing both sides by 2 / 5.

Doing either of these things would get rid of the 2 / 5 and give an answer to x as shown below :

Multiplying :

2/5 x = 14

5 / 2 x 2 / 5 x = 14 x 5 / 2

x = 35

Dividing :

2/5 x = 14

2 / 5 x / 2 / 5 = 14 / 2 / 5

x = 35

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Amount of pounds that Ben get back is £75.

Exchange rate is defined as the value of a currency with respect to another currency in order to convert the currency.

Ben changes £800 to Euros before he goes on holiday.

Before holiday, exchange rate is, £1 = 1.25 Euro

£800 = 800 × 1.25 Euros = 1000 Euros

He spends 895 Euros.

Euros left = 1000 - 895 = 105 Euros

Now, the exchange rate is £1 = 1.40 Euro.

or 1.40 Euro = £1

⇒ 1 Euro = £ 1/1.40

⇒ 105 Euros = £ (1/1.40) × 105 = £75

Hence Ben got £75 of pounds back.

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She traveled 6.375 miles by train.

Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time

Given here as per question the formula is x × (4+3×4)=34

∴ x×16=34

       x= 6.375

Hence, She traveled 6.375 miles by train.

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Answer:

A) Angle A. Angle EG.

B) Angle A and Angle F.

C) Angle EG and Angle D.

I hope this helped you!

Answer:

D

Step-by-step explanation:

x²+5x=0

by factorizing;

x(x+5)=0

x=0 or x+5=0

Therefore, x= 0 or x=-5 ---> {0, -5}

Answer: The solution to the system of equations is (1/3,-4/3).

Step-by-step explanation: Yes

The formula is written as (3x+9)(x+9) of + 36x + 81 = 0. A second-degree polynomial equation can be used to define quadratics.

Multiplying a variable by itself is the mathematical operation known as "squaring," which is frequently used to refer to a quadratic issue. This vocabulary is based on the notion that a square's area is equal to the sum of its side lengths. The word "quadratic" derives from the Latin quadratum, which meaning square.

here ,

[tex]= + 36x + 81 = 0\\= 3x^2 + 27x + 9x + 81\\= 3x(x+9) + 9(x+9)\\= (3x+9)(x+9)\\= 3(x+3)(x+9)[/tex]

factorized form is [tex](3x+9)(x+9) of + 36x + 81 = 0 .[/tex]

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Answer:

x=2/3

Step-by-step explanation:

when the three turned into a 2 it removed one third, so we need to remove one third from 1, which gives us 2/3.

Basically, if a rectangle side goes from x to y, we figure out the percent decrease, and subtract that percent from the other side to find the variable we need to find on the other rectangle

Answer: To find the percent increase in pay, you can use the following formula:

percent increase = ((new pay - old pay)/old pay) * 100

Plugging in the values given in the question, you get:

percent increase = ((11.75 - 10.50)/10.50) * 100

= (1.25/10.50) * 100

= 0.119047619 * 100

= 11.9047619%

Therefore, the percent increase in pay is approximately 11.9%.

Step-by-step explanation:

Producing written and visual content for social media can be divided into two items that can be developed as a one-person small business in a little amount of time.

Social media is internet communication that enables real-time information sharing and customer interaction. Social networking can help you: better connect with your audience. building online networks sell and publicise the goods and services you offer.

Social media's effects on business

The social media presence of businesses in order to boost visibility, engagement, positioning, and value creation for their intended audience has been facilitated by the digital revolution.

In order to help businesses establish their strategy in the digital environment, marketing and advertising agencies can quickly produce digital media such posters and catalogues in addition to advertising text as their core offerings.

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On solving the question, we can say that - the probability of given will be P(a/c) = 3/6 = 1/2

A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1. the proportion between the number of events in a comprehensive collection of equally likely outcomes that lead to a certain occurrence and the entire number of outcomes.

here,

the probability that event the dice will roll is 6

and chances of geting even numbers are = 3

so P(a/c) = 3/6 = 1/2

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