The scale drawing has a scale of 1 inch:9yards. What is the total area of the composite figure.
The figure is a right triangle with a height of 6 in and the height of 6 inches. The rectangle has a length of 7 inches and a width of 6 inches.
How do you solve?

The solution of the equation by factoring is x = 6.645 and x = 1.355.

The breaking or breakdown of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics. An algebraic expression is factorised when it is written as the product of its factors. Certain variables, factors, or algebraic expressions might be present.

The given equation is:

x² - 8x + 16 = 7

x² - 8x + 16 - 7 = 0

x² - 8x + 9 = 0

Using the quadratic formula we have:

x = 8 ±√(8)² - 4(1)(9) /2(1)

x = 8 ± 5.29/2

x = 8 + 5.29/2 and x = 8 - 5.29/2

x = 6.645 and x = 1.355

Hence, the solution of the equation by factoring is x = 6.645 and x = 1.355.

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The appropriate price for the second poster is $1.37.  The dimensions is not equal but less than that of the first poster

From the information given, we have that the poster takes form of a rectangle.

The formula that is used to calculate the area of a rectangle is usually expressed with the equation;

A = lw

The parameters are enumerated as;

For the first poster, we have;

Area = 55(70)

Multiply the values

Area = 3850 cm^2

Then, we have that;

3850 cm^2 = $5.49

Then, 27.5(35) = x

cross multiply the values

x = $1. 37

The dimensions of the first poster is two times greater than that of the second.

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As a result, the vertical asymptotes of the function's curve will be at x=-5 and x=1 of quadratic equation .

A function in mathematics is a formula that associates each element from a set (referred to as the domain) with a single element from another set (called the range). A machine that generates an outcome from an input (the independent variable) can be compared to a function (the dependent variable). Algebraic expressions or equations are frequently used to describe functions, such as f(x) = x2 + 3x - 2. In a coordinate plane, where the x-axis denotes the input values and the y-axis denotes the output values, they can also be graphically depicted as a curve or line.

given

Since division by zero is undefined, we must search for the values of x that cause the denominator of the function to equal zero in order to determine the vertical asymptote of a rational function.

The function is undefined at x=-5 and x=1 because the denominator of f(x) = (x-2)/(x2+4x-5) is a quadratic equation that can be factored as (x+5)(x-1).

As a result, the vertical asymptotes of the function's curve will be at x=-5 and x=1 of quadratic equation .

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By the hypotenuse-leg congruence theorem (HL theorem), triangles ABD and CBD are congruent.

What is Trapezoid ?

A trapezoid is a four-sided polygon with at least one pair of parallel sides. It is also known as a trapezium in some countries.

To prove that BD is congruent to AC, we will use the fact that the opposite sides of a trapezoid are parallel.

Since AB and CD are parallel, and BC is a transversal, we know that angles ABC and DCB are supplementary (they add up to 180 degrees).

From the given information, we know that angle ABC is congruent to angle DCB. Therefore, both angles must be equal to 90 degrees (since their sum is 180 degrees).

Now consider the right triangles ABD and CBD.

In triangle ABD, we have a right angle at angle ABD, and we know that AB is congruent to CD (given).

In triangle CBD, we have a right angle at angle BCD, and we know that BC is congruent to BC (reflexive property).

We also know that angle ABD is congruent to angle BCD (since they are both equal to 90 degrees minus angle ABC/DCB).

Therefore, by the hypotenuse-leg congruence theorem (HL theorem), triangles ABD and CBD are congruent.

This means that BD is congruent to AC (the corresponding sides of congruent triangles are congruent).

Therefore, we have proven that BD is congruent to AC in trapezoid ABCD.

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An object's size in real life and its size on a map or a blueprint are compared using a scale factor, which is a mathematical concept. The scale factor may exceed, fall short of, or be equal to 1.

The size of the object is decreased and becomes smaller if the scale factor is between 0 and 1. This is so because the scale factor only approximates the object's true size. The size of the thing on the map will be half that of the real object, for instance, if the scale factor is 0.5.

When the scale factor is 1, the object's size is said to remain constant. As a result, the map or blueprint is created using the same dimensions.

In other words, the map or blueprint is created at the exact same scale as the final product.

The size of the thing is enlarged and made larger if the scale factor is greater than 1. This is so because the scale factor is a multiple of the object's actual size. The size of an object on a map will appear twice as large as it is in reality, for instance, if the scale factor is 2.

In general, it's crucial to comprehend scale variables in order to appropriately depict an object's size on maps, blueprints, and other scaled representations.

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The sοlutiοn tο the given prοblem οf expressiοn cοmes οut tο be  1.2516883 x 10⁴ is the abbreviated fοrmula in scientific nοtatiοn.

There is a need fοr mathematical οperatiοns like multiplying, splitting, adding, and even deleting. They wοuld result in the fοllοwing assertiοn if cοmbined: A mathematical fοrmula, sοme data, and an equatiοn A declaratiοn οf truth is made up οf values, elements, and mathematical οperatiοns like additiοns, erasures, algebraic expressiοns, and divisiοns. It is pοssible tο rate and analyze wοrds and sentences.

Here,

The priοr respοnse was cοndensed,

[tex]\frac{[(0.0070)(50)(55)]} {[(1.4)(0.0011)(.25)]} = 12516.883[/tex]

We can describe the following respοnse in scientific notatiοn as the sum of a decimal number between 1 and 10 and a pοwer of 10:

12516.883 = 1.2516883 x 10⁴

Therefοre, 1.2516883 x 10⁴ is the abbreviated fοrmula in scientific notation.

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Answer:

[tex]12 = 13 + p \\ 12 - 13 = p \\ - 1 = p \\ [/tex]

Answer:

x is greater than or equal to 9.

Step-by-step explanation:

This is because the dot is going above 9 and it's a closed dot. The closed dot means the greater than or equal to and the x represents all real numbers at and after the 9

The statement that a factor goes into a larger number is true.

A factor is a number that can be divided into another larger number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because these are the numbers that can be evenly divided into 12. Similarly, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. 5 is a factor of 20 because 20 can be divided evenly by 5:

20 ÷ 5 = 4.

In contrast, 7 is not a factor of 20 because 20 ÷ 7 leaves a remainder:

Factors are important in mathematics because they are used to find common denominators, simplify fractions, and solve equations.

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Using the addition operation, the sum of 40 + 5 is 45.

The addition operation is one of the basic mathematical operations.

Other mathematical operations include subtraction, division, multiplication, exponentiation, and functions.

The addition operation involves two addends added using the addition operand (+) and the  equal symbol (=) we show the result of the algebraic operation called the sum or total.

Thus, when five is added to forty (40 + 5), the result or sum is forty-five (45).

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Fabian has $0.05x + $0.01y in total.

If Fabian has 130 nickels, his collection is worth:

130 nickels at $0.05 each translate to $6.50.

Moreover, if he has 120 cents, the total amount is:

120 pennies multiplied by the price of a penny ($0.01) equal $1.20.

Combining these two numbers, Fabian has:

$6.50 + $1.20 = $7.70

Fabian now has $7.70 in total.

If Fabian owns x nickels, the worth of those nickels is:

x nickels * 0.05 cents each nickel = 0.05x

Moreover, if he possesses y cents, the total worth is:

y pennies * $0.01 per penny = $0.01y

Combining these two numbers, Fabian has:

$0.05x + $0.01y

Fabian therefore has a total of $0.05x + $0.01y.

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The distance from frank's house to john's house and then back to frank's house is less than a mile by 1/5 units.

Simply multiplying the distance between two points while travelling from one location to another and back will give you the total distance travelled when travelling from one location to another and returning to the starting point.

The distance from frank's house to john's house = 4/10.

The distance back to Frank's house = 4/10.

Total distance = 4/10 + 4/10

Total distance = 8/10

The distance is thus,

1 - 8/10

Take the LCM:

(10 - 8) / 10

2/10 = 1/5

Hence, the distance from frank's house to john's house and then back to frank's house is less than a mile by 1/5 units.

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Answer: There are no questions posted

Step-by-step explanation:

15% of the people in the city visited the food pantry last month.

What is the percentage?

A percentage is a way of expressing a number as a fraction of 100. It is a ratio that compares a number to 100, and it is often denoted using the % symbol. For example, if there are 25 blue marbles in a jar of 100 marbles, we can say that 25% of the marbles are blue. This means that 25 out of every 100 marbles are blue.

To calculate the percentage of people who visited the food pantry last month, we can use the following formula:

Percentage = (Part / Whole) x 100%

where "Part" is the number of people who visited the food pantry last month, and "Whole" is the total number of people in the city.

Plugging in the given values, we get:

Percentage = (150 / 1,000) x 100%

Percentage = 0.15 x 100%

Percentage = 15%

Therefore, 15% of the people in the city visited the food pantry last month.

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The volume of the sphere according to the question will be approximately 7232.752cm³.

What is a sphere?

A geometric shape with a sphere-like appearance. In three dimensions, the sphere is defined. The sphere is a three-dimensional solid with a volume and surface area.

What is the Volume of sphere?

A sphere is a perfectly round geometrical 3D object. The formula for its volume equals:

              Formulae of  Volume of sphere = (4/3) × π × r³

So according to the question:

                            r = 12cm(given)

Substitute in above formulae:

                    =(4/3)×3.14×12×12×12 cm³           [Here 4/3= 1.333, π=3.14,r=12]

                    = 1.333×3.14×12×12×12 cm³

      Volume of sphere will be =7232.752 cm³

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Based on the information in the graph, the perimeter of the figure would be 48.

To find the perimeter of the figure we must add the value of all the sides. In this case, this figure has 8 sides. However, in essence it is a rectangle because all the angles are 90°, so we could assume that the sides on the right add up to 6 as the side on the left. Also the bottom sides would add up to 18 like the top.

According to the above, we could infer that the perimeter of the figure is:

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The value of x that corresponds to f(x) = 500 lies between 0 and 1. The whole numbers between 0 and 1 are 0 and 1, so the answer whole numbers are 0 and 1.

Exponential growth is a mathematical concept that describes a process where a quantity grows at an increasing rate proportional to its current value. In other words, the larger the quantity, the faster it grows. This leads to a graph that is characterized by a rapid upward curve that becomes steeper and steeper over time.

Exponential growth is often represented by the equation y = abˣ, where y is the final amount, a is the initial amount, b is the growth factor or base, and x is the time or number of periods.

The function f(x) = a(1 - r)ˣ represents exponential decay, where "a" is the initial value, "r" is the decay rate as a decimal, and "x" is the time variable.

In this case, the initial value is 1,000, and the decay rate is 20%, or 0.20 as a decimal. Therefore, the equation for the function becomes:

f(x) = 1,000(1 - 0.20)ˣ = 800ˣ

To find the whole numbers that correspond to a value of f(x) = 500, we can set the equation equal to 500 and solve for x:

500 = 800ˣ

Taking the natural logarithm of both sides, we have:

ln(500) = ln(800ˣ)

Using the property of logarithms, we can bring down the exponent:

ln(500) = x ln(800)

Solving for x, we divide both sides by ln(800):

x = ln(500) / ln(800) ≈ 0.717

Therefore, the value of x that corresponds to f(x) = 500 lies between 0 and 1. The whole numbers between 0 and 1 are 0 and 1, so the answer is:

The whole numbers are 0 and 1.

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The student's percentile will be 28.

Calculating percentiles is a common practise. The majority of the time, we can define percentile as a score below which a predetermined percentage of other scores fall. We might be able to tell when someone received a test score of 65 out of 90. But without knowing what percentile he belongs to, this number is meaningless. When a score is in the 90th percentile, it signifies that it is higher than the scores of 90% of test-takers.

Given : Student's rank = 144 out of 200

So, there are 56 (200-144) students whose rank is below that student.

We know that, percentile

= no. of ranks below that rank / total no. of ranks * 100

So, his percentile = 56/200 * 100

                             = 28 percentile.

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Create four angles by drawing a straight line that meets another straight line at an angle. To keep track of the angles, assign letters to each one. Make a note of the angles' measurements using a protractor.

A right angle is created when two perpendicular lines cross at an exact 90-degree angle. Four 90-degree right angles are formed by intersecting perpendicular lines.

A right angle is a right angle if one of the four angles created by two intersecting lines is a right angle. Straight lines that are perpendicular to one another intersect at a 90° angle.

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Answer:

y=x+1

Step-by-step explanation:

y=mx+b

y=mx+1

2/2=1

y=1x+1

y=x+1

Angle AXC is congruent to both angle CAX (78 degrees) and angle CDX (102 degrees), its measurement is also 102 degrees.

To find the measurement of angle AXC, we need to consider that it is an inscribed angle subtended by the same arc CX as arc CA and arc DB.

Inscribed angles that subtend the same arc are congruent. Therefore, we can conclude that angle AXC is congruent to both angle CAX and angle CDX.

Since angle CAX and angle CDX are supplementary angles (they add up to 180 degrees) and we know the measurement of angle CAX, we can find the measurement of angle CDX.

angle CAX + angle CDX = 180 degrees

78 degrees + angle CDX = 180 degrees

angle CDX = 180 degrees - 78 degrees

angle CDX = 102 degrees

Since angle AXC is congruent to both angle CAX (78 degrees) and angle CDX (102 degrees), its measurement is also 102 degrees.

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Answer:

To determine which supermarket offers the best value for money, we need to compare the cost per kilogram (kg) of potatoes from both supermarkets.

For Supermarket A:

4.5 kg cost R20, so 1 kg costs R20/4.5 kg = R4.44 per kg (excluding VAT)

For Supermarket B:

1.8 kg cost R8, so 1 kg costs R8/1.8 kg = R4.44 per kg (excluding VAT)

As both supermarkets offer potatoes at the same cost per kg, they are equal in terms of value for money. Therefore, Betty and Valencia can choose either supermarket to purchase their potatoes for the mini tuck shop.

Step-by-step explanation:

The tοtal amοunt earned, including cοmmissiοn and base pay, is $63.50, rοunded tο the nearest hundredth.

Tο answer this questiοn, we need tο knοw the cοmmissiοn rate fοr the lοbster raviοli and k salads. Let's assume the cοmmissiοn rate is 10% fοr bοth items.

If the lοbster raviοli cοst $15 each and the steak salads cοst $12 each, then the tοtal cοmmissiοn earned wοuld be:

3 x $15 x 0.10 + 5 x $12 x 0.10 = $13.50

Therefοre, the cοmmissiοn earned is $13.50.

Tο find the tοtal amοunt earned, including cοmmissiοn and base pay, we simply add the cοmmissiοn earned tο the base pay:

$50 + $13.50 = $63.50

Therefοre, the tοtal amοunt earned, including cοmmissiοn and base pay, is $63.50, rοunded tο the nearest hundredth.

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The correct method to calculate the number of cubic units(volume) of cake batter needed to fill the mold is option (a) , i.e V equals 355 over 113 times 5 squared times 7.

Mensuration is the branch of mathematics concerned with the study of various geometric shapes, their areas and volumes. In a broad sense, it is about the process of measurement. Measurement is a branch of mathematics. That is measurement. 

Solution:

Given, Diameter = 10 inches

               Radius = 5 inches

                Height = 7 inches

Volume of cylinder = πr²h

                                = (355/113)×5²×7

                                = 3.14×25×7

                                 = 549.77 inches³

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Answer:

Step-by-step explanation: OK so I don't know if I'm exactly right on this  but what I would do is I would first read it more than 1 time and I would see that the sandwich shop offers 4 types of bread, that's 4 different types of bread. Then it says 5 meats, 7 cheeses, 4 condiment options, and you can pick veggies or no veggies. So what I did was I multiplied 4 by 5 and got 20, then I multiplied 7 by 4 and got 28, then I added 20 and 28 and got 48 sandwiches are possible. Then to make sure I was correct I  did 4 times 5 times 7 times 4 by accident and I got 560. So I don't know which one is correct but I just thought that I could at least try to help you because even I have problems with problems like this one too. So I hope I helped you even a little bit.                                      

Answer: You always put the whole number over 1

Step-by-step explanation:

ex: 31= 31/1

By using the future value of a series formula, you can calculate the future value of your investment. In this case, if you invest $600 annually in a 401k mutual fund with a 9% annual return, you will have approximately $132,204.02 after 40 years.

To solve this problem, we can use the future value of a series formula (also known as an annuity), which is common in business finance. The formula is:

FV = P * [((1 + r)^n - 1) / r]

Where:
FV is the future value of the money you have invested.
P is the annual investment (in this case, $600).
r is the annual rate of return (which is 9% or 0.09 as a decimal).
n is the number of years the money is invested (which is 40 in this scenario).

Applying these numbers to the formula we get:

FV = 600 * [((1 + 0.09)^40 - 1) / 0.09]

After performing the calculations, the future value (which is the amount of money you'll have at the end of 40 years) comes out to be approximately $132,204.02. Thus, if you invest $600 annually in a 401k which invests in an international stock mutual fund with a 9% annual rate of return, you will have $132,204.02 in the fund when retiring in 40 years.

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The required slope of the tangent line to the graph of the function at the point (-1, 5) is -2.

A line that only touches a circle or an ellipse at one place is said to be tangential in geometry. If a line touches a curve at point P, that place is referred to as the point of tangency. In other words, it is described as the line that, at that particular point, depicts the slope of a curve.

The slope of the tangent line to the graph of a function at a given point is equal to the derivative of the function at that point.

So, to find the slope of the tangent line to the graph of the function f(x) = -2x at the point (-1, 5), we need to find the derivative of the function at x = -1.

Using the power rule for derivatives, we can find the derivative of f(x) = -2x as:

[tex]$f'(x) = \frac{d}{dx}(-2x) = -2$$[/tex]

So, the slope of the tangent line to the graph of the function f(x) = -2x at x = -1 is:

f'(-1) = -2

Therefore, the slope of the tangent line to the graph of the function at the point (-1, 5) is -2.

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Answer: Infinitely many solutions

Step-by-step explanation:

Solve by Substitution :

Solve equation [2] for the variable  y

y = 2x + 4

Plug this in for variable  y  in equation [1]

4•(2x+4) - 8x = 16

0 = 0 =>  Infinitely many solutions

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