The diagram below shows the first four of a series of designs that an artist draws on artwork.

The artist wants to use a design with a maximum of 15 shaded circles. What number of design should the artist use?

The factorized polynomial 6x² + 15xy -14x -35y is given as (2x + 5y) (3x - 7)

A polynomial is an expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power.

To solve this problem, we simply need to factorize the polynomial given.

[tex]6x^2 + 15xy - 14x - 35y[/tex]

[tex]6x^2 + 15xy - 14x - 35y\\(2x + 5y) (3x - 7)[/tex]

This is the the reduced or factorized form of the given polynomial.

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The range of values that a bottle could contain to pass inspection will be 7.840 - 8.160 ounces.

It was stated that the toy company that makes bubbles fills its 8-ounce bottles using a machine.

The bottle passes inspection if the percent error of the amount is 2% or less. The minimum range will be:

= 8 ounces - (2% × 8 ounces)

= 8 ounces - 0.16 ounces

= 7.84 ounces

The maximum range will be:.

= 8 ounces + (2% × 8 ounces)

= 8 ounces + 0.16 ounces

= 8.16 ounces.

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The allowable range for the toy company is [7.84, 8.16].

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, the allowable percentage error is 2% or less.

Now, 2% of 8 ounces is,

= (2/100)×8.

= 0.16 ounces.

So, the allowable range is from (8 - 0.16) = 7.84 ounces to

(8 + 0.16) = 8.16 ounces.

As it is being given that it is 2% or less we'll use include the least value too.

So, the allowable range of the bottles is [7.84, 8.16].

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Answer: they should be 2cm apart

Step-by-step explanation: This means that 1 cm on the map represents an actual distance of 50 000 cm (or 500 m or 0.5 km). We saw above that if a map has a scale of 1 : 50000, then 1 cm on the map is 50000 cm in real life.

The Area of a Rectangle as a Sum and as a Product are as follows:

21. Area as sum = 12x + 60

Area as Product = 12(x + 5)

22. Area as sum = 5x + 20

Area as Product = 5(x + 4)

As a product, we can multiply the height and the base of the rectangle.

As a sum, we can estimate the area finding the sum of the areas of each piece of the rectangle.

The missing pieces that will fill into the circles exists shown in the diagram attached below. The Area of a Rectangle as a Sum and as a Product are as follows:

21. Area as sum = 12x + 60

Area as Product = 12(x + 5)

22. Area as sum = 5x + 20

Area as Product = 5(x + 4)

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The value of the expression will be;

⇒ log₅ (1/25) = - 2

Option D is true.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ log₅ (1/25)

Now,

Solve the expression as;

⇒ log₅ (1/25)

Since, log (a/b) = log a - log b

Hence,

⇒ log₅ (1/25) = log₅ 1 - log₅ 25

Since, log 1 = 0

⇒ log₅ (1/25) = 0 - log₅ 25

⇒ log₅ (1/25) = - log₅ 5²

Since, log a² = 2 log a

⇒ log₅ (1/25) = - 2 log₅ 5

Since,  log₅ 5 = 1

⇒ log₅ (1/25) = - 2 x 1

⇒ log₅ (1/25) = - 2

Thus, The value of the expression will be;

⇒ log₅ (1/25) = - 2

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Answer:

(3, - 4 )

Step-by-step explanation:

under a reflection in the line y = x

a point (x, y ) → (y, x ) , then

(- 4, 3 ) → (3, - 4 )

There will be 15724800 computer passwords possible with 1 letter followed by 7 digits without any repetition of letters or digits.

It is given to us that -

A computer password is required to be 8 characters long

The computer password requires 1 letter(s) followed by 7 digits

The 7 digits are from numbers 0-9.

It is also mentioned that there will be no repetition of any letter or digit

We know that,

The total number of English alphabets = 26 (from a-z)

The total number of digits = 10 (from 0-9)

Since it is given that the computer password has

1 letter followed by 7 digits without any repetition of any letters or digits

So, the number of computer passwords that are possible can be -

[tex]26*10*9*8*7*6*5*4\\= 15724800[/tex]  (1 letter and 7 digits with no repetition)

Thus, 15724800 computer passwords are possible that contains 1 letter followed by 7 digits where no repetition of any letter or digit is allowed.

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Answer: Choice A.  [tex](5\text{x}^2+2)(3\text{x}-1)[/tex]

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

Work Shown:

[tex]15\text{x}^3-5\text{x}^2+6\text{x}-2\\\\(15\text{x}^3-5\text{x}^2)+(6\text{x}-2)\\\\5\text{x}^2(3\text{x}-1)+2(3\text{x}-1)\\\\(5\text{x}^2+2)(3\text{x}-1)\\\\[/tex]

Explanation:

The idea is to pair up the terms into two groups. Factor each group separately. Then we pull out the overall GCF (3x-1) to finish up the factorization. You can use the FOIL rule to expand out the answer to get the original expression again, which helps confirm the answer.

[tex]{\Large \begin{array}{llll} i^4=1 \end{array}} \\\\[-0.35em] ~\dotfill\\\\ -i^{32}\implies -i^{4\cdot 8}\implies -(i^4)^8\implies -(1)^8\implies \text{\LARGE -1}[/tex]

Answer:

The number is 9

Step-by-step explanation:

6n + 11 = 9n -16  Subtract 6n from both sides of the equation

11 = 3x -16  Add 16 to both sides of the equation

27 = 3n   Divide both sides of the equation by 3

9 = n

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

The value of t exists [tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex].

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Expressions have the following structure: (Number/variable, Math Operator, Number/variable).

Given: [tex]$275000=\frac{3001-\left(1+\frac{0.038}{12}\right)^{(-12 t)}}{\left(\frac{0.038}{12}\right)}$$[/tex]

Multiply both sides by 0.038 / 12, we get

[tex]$275000 \cdot \frac{0.038}{12}=\frac{3001-\left(1+\frac{0.038}{12}\right)^{-12 t}}{\frac{0.038}{12}} \cdot \frac{0.038}{12}$$[/tex]

Simplifying the above equation, we get

[tex]$\frac{5225}{6}=3001-\left(1+\frac{0.038}{12}\right)^{-12 t}$$[/tex]

Add [tex]$\left(1+\frac{0.038}{12}\right)^{-12 t}$[/tex] to both sides

[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}=3001-\left(1+\frac{0.038}{12}\right)^{-12 t}+\left(1+\frac{0.038}{12}\right)^{-12 t}$$[/tex]

Simplifying the above equation, we get

[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}=3001$$[/tex]

Subtract 5225 / 6 from both sides

[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}-\frac{5225}{6}=3001-\frac{5225}{6}$$[/tex]

Simplify

[tex]$\left(1+\frac{0.038}{12}\right)^{-12 t}=\frac{12781}{6}$$[/tex]

By using exponent rules, we get

[tex]$-12 t \ln \left(1+\frac{0.038}{12}\right)=\ln \left(\frac{12781}{6}\right)$$[/tex]

Solve [tex]$-12 t \ln \left(1+\frac{0.038}{12}\right)=\ln \left(\frac{12781}{6}\right): \quad t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$[/tex]

[tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex]

Therefore, the value of t exists [tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex].

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The fraction expression given as  -1/3-4/5  is a negative number

The fraction expression is given as

-1/3 - 4/5

From the above expression, we observe that:

The sum of two negative numbers will result in another negative number

This means that the value of -1/3 - 4/5 is a negative expression

Solving further, we have:

-1/3 - 4/5

Evaluate the expression

-1/3 - 4/5 = -17/15

See that 17/15 is negative

Hence, -1/3 - 4/5 is negative

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The study of the correlations between triangles' side lengths and angles is known as trigonometry. x= 0.11

The study of the correlations between triangles' side lengths and angles is known as trigonometry. The field was created in Hellenistic era in the third century BC as a result of the use of geometry in astronomical research. While Indian mathematicians produced the earliest tables of values for trigonometric ratios (also known as trigonometric functions), such as sine, the Greeks concentrated on chord calculation.

Trigonometry has been used historically in the fields like geodesy, surveying, celestial mechanics, and navigation.

Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric identities are frequently employed to rewrite trigonometrical expressions.

xsin45º. cos45°. tan60° = tan² 45° - cos²60⁰​

x0.7*0.70*1.73 =1*1-0.5*0.5

x = [tex]\frac{0.7*0.70*1.73}{1*1 - 0.5*0.5}[/tex] = 0.11

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Answer:

y=1x-5

Step-by-step explanation:

Use rise/run

Answer:

[tex]y=x-5[/tex]

Step-by-step explanation:

Just look at the slope and the y-intercept.

The y-intercept is b, and it's -5. The slope is 1, so it is x.

Answer:+0.82 and -0.8

Step-by-step explanation:

The length of the legs of the sun shade is 8√2 feet.

The equation used is option b , y = 1/2x² and y = 64

Isosceles triangle: What is it?

A triangle with two sides that have the same length is said to be isosceles.

Given,

Area of triangle = 64 sq.ft

Here, an isosceles triangle has two equal sides 

Let

x is equal to the length side of a right isosceles triangle's leg.

y is the area of a right isosceles triangle at position

Currently, the legs of a right isosceles triangle are equal.

Area of triangle = 1/2 ×  base × height

y = 1/2 × (x) × (x)

y = x²/2

64 = x²/2

128 = x²

x = √128

x = 8√2

The length of the legs of the sun shade is 8√2 feet.

The equation used is option b , y = 1/2x² and y = 64

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Answer:

Step-by-step explanation:

first part: B.

second part: -11.3 or 11.3, 11.3

Answer:

x = 8.3

Step-by-step explanation:

We look at the final place of the decimal to round, in this case the thousandths place (underlined)

8.27

If the final place of the decimal is greater than or equal to 5, we round up the decimal to the left, otherwise we round down.

Because 7 > 5, round 2 up to 3, therefore giving 8.3

Answer:

Your answer is 8.3!

Step-by-step explanation:

Step 1: Locate and underline the tenths place (2) then look at the digit to the right (7):

8.27

Step 2: In this case, the digit to the right (7) is 5 or above. So, we add 1 to the tenth place (2). The digit(s) after the (2) are replaced by zeros (or dropped). Thus, we get 8.3 as the answer.

In short: 8.27 rounded to the nearest tenth is 8.3.

The possible coordinates of the point C are : (-6,-2) and (2,-2).

A stiff transition called a rotation involves turning the item around a center point. The direction is changed, but the shape is still oriented in the same way. You can spin a form in any direction. A 180 degree rotation of the triangle is made around point C. A rigorous transition like this one may be seen here.

Rotation and translation are the only two elements of a rigid transformation. It does not alter the size or shape of an input object, nor does it involve reflection.

Hence as the graph shows, the coordinates of C' could be:

(-6,-2) and (2,-2)

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Answer:

175.259 cm

Step-by-step explanation:

ANSWER:

  4x-1=27

or,4x=27+1

or, x=28/4

or, x=7

Approximately, the unit cost of the plastic cups is $0.25

Here, we want to get the unit rate of the plastic cups

By unit rate, we mean the price of 1

From the question, the total 72 costs $17.99

The cost of one is thus;

The probability that a day requires more water than is stored in city reservoirs will be; 0.965

The z-score is a numerical measurement used in statistics to refer to how much a given value differs from the standard deviation.

Given that Water use in the summer is normally distributed with a mean of 310 million gallons and a standard deviation of 45 million gallons.

Let X be the random variable that shows the quantity of water required on a particular day.

Z-score :

[tex]Z = \dfrac{X - \mu}{\sigma},[/tex]

Now, the probability that a day requires more water than is stored in city reservoirs will be;

[tex]Z = \dfrac{350 -310}{45},[/tex]

Z = 0.965

We can see that the above value to the given P(X > 350)= 1 - P(Z < b), we get the value of b is; 0.965.

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Answer: I think it’s t{(-3,2).(5.5).(3.3).(3.-2)}

Step-by-step explanation:

Eyesight is key m’lady

The first graph represents the same relation as the set {(-3,2).(5.5).(3.3).(3.-2)}

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given relation is {(-3,2).(5.5).(3.3).(3.-2)}

We have to find the graph which represents the relation of the set

A binary relation on a set may, or may not, hold between two given set members.

The first number in the ordered pair represents the x coordiantes

The second number in the ordered pair represents the y coordiantes

When we match the ordered pairs with the given graphs

The first graph matches with the given relation

Hence, the first graph represents the same relation as the set {(-3,2).(5.5).(3.3).(3.-2)}

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Answer:

100.00

Step-by-step explanation:

it's 100.00 because the roof is being repaired and the person will have to pay after

How many pounds of walnuts that cost $.80 per pound must be mixed with 8 pounds of cashews that cost $1.25 per pound to make a mixture of nuts that cost $1.00 per pound?​

Let

x ------> pounds of walnuts

we have that

0.80x+

Using combination, there are 1932 arrangments possible.

A combination is a mathematical approach that counts the number of potential configurations in a box containing objects, regardless of their order.

In combinations, we can select items in any order. In combinations, the order doesn’t matter.

The combination formula of given as: n! / r!(n-r)!

Each candy would be distributed in three different ways if there were no limits on how many candies might fit in a bag. 3⁷ different ways to distribute the sweets in this scenario. However, only empty blue and red bags count in this scenario.

There are 2⁷ methods to distribute candy if the red bag is left empty.

Similarly, for the blue bag.

Hence there are 2⁷ +2⁷ – 1 ways to distribute candy such that either blue or red bag is empty.

The total amount of circumstances and ways to deliver the sweets

= 3⁷ – (2⁷ + 2⁷ -1)

= 1932

Therefore, there are a total of 1932 arrangements possible.

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Let's first write both numbers in their fraction form:

then, we can write the division like this:

Now, given the general rule for the division of fractions, we have:

also notice that we are dividing two negative numbers, then our final result will be positive according to the law of signs. Then, we have in this case:

therefore the final result is 360

Step-by-step explanation:

the 2 triangles are similar.

that means their corresponding angles are equal, and their side lengths (and heights and so on) have all the same constant scaling factor.

so, we see that the side with the length 6 must corresponds to the side with the length 3 (factor 1/2).

as then the side with the length 5 corresponds to the side with the length 2.5, and the side with the length 4 corresponds to the side with the length 2 (all have the same factor 1/2).

a is the angle between 6 and 5 (the 2 longest sides).

the angle between the 2 longest sides in the smaller triangle (3 and 2.5) is d.

so, a and d correspond.

b is the angle between 6 and 4 (the longest and the shortest side).

the angle between the corresponding sides 3 and 2 is c.

so, b and c correspond.

therefore, the 4th and last answer choice is correct.

Answer:

always

never

always

always (not 100% sure)

sometimes

sometimes (not 100% sure)

Step-by-step explanation:

this is what I got, hope it helps

3. 300

4. $180

5. $23.75

6. $102.6

Answer: 1 is 300 2 is 180 3 is 23.75 and the fourth one is 102.6

Step-by-step explanation: dont forget to add your $ signsss