The quilt is made of squares with diagonals.
The length of BD is 4.
a. Find the length of AE. Round answer to the hundredths.
b. Find the area of square ABCD.

Answer:

To summarize:

√3 - 6x: Domain is all real numbers (-∞, +∞).

√13 - (13 - 2x): Domain is all real numbers (-∞, +∞).

1/√x - 2: Domain is all real numbers except x = 0, represented as (-∞, 0) U (0, +∞).

Step-by-step explanation:

To find the domain of each expression, we need to identify any restrictions or limitations on the variables that would result in undefined values.

√3 - 6x:

Since square roots are defined for non-negative numbers, the expression is defined as long as the value inside the square root (√3) is non-negative. The square root of 3 is a positive value, so there are no restrictions on the domain of this expression. Therefore, the domain is all real numbers (-∞, +∞).

√13 - (13 - 2x):

Similar to the previous expression, the square root (√13) is defined for non-negative values. However, we also need to consider the expression (13 - 2x) inside the parentheses. This expression does not have any limitations since it is defined for all real numbers. Therefore, the domain of this expression is all real numbers (-∞, +∞).

1/√x - 2:

For this expression, we need to consider both the square root (√x) and the denominator (1/√x). The square root (√x) is defined for non-negative values of x. However, the denominator 1/√x will become undefined if the value of x is zero because division by zero is undefined. Therefore, we need to exclude x = 0 from the domain. For all other non-zero values of x, the expression is defined. Therefore, the domain of this expression is all real numbers except x = 0, represented as (-∞, 0) U (0, +∞).

The numeric value of the expression in this problem is given as follows:

-77.

The expression in the context of this problem is defined as follows:

[tex]2^5[/tex] x (-2) - 4 x 5 + 7.

Considering the PEMDAS acronym, the power operation has the precedence over the remaining operations, hence:

[tex]2^5[/tex] x (-2) - 4 x 5 + 7 = 32 x (-2) - 4 x 5 + 7.

Then, following the same acronym, we have that the multiplication operation has precedence over the addition/subtraction operations, hence:

32 x (-2) - 4 x 5 + 7 = -64 - 20 + 7.

Finally, we can just subtract and add the numbers to obtain the numeric value of the expression as follows:

-64 - 20 + 7 = -77.

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The reasoning of the student is wrong because the claim doesn't abide by the sine rule and formula.

The sine rule states that in a triangle, side “a” divided by the sine of angle A is equal to the side “b” divided by the sine of angle B is equal to the side “c” divided by the sine of angle C.

That is;

a/sinA= b/sinB = c/sinC

Therefore, the proper equation to find X = 5/sin98° = X/sin20°

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Option C is the table of values representing a proportional relationship in the context of this problem.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

For item c, we have that the output is equals to the input, hence the proportional relationship is given as follows:

y = x.

The problem asks for which table represents a proportional relationship.

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On July 20, the journal entry to record the reissuance of treasury stock is: Debit Cash for $4,140 and credit Treasury Stock for $4,140.

To record the reissuance of treasury stock on July 20, the company needs to make the following journal entry:

Date: July 20

Account Debit Credit

Cash $4,140

Treasury Stock $4,140

Explanation:

Debit to Cash ($46 per share * 90 shares) to record the cash received from the reissuance of 90 shares of treasury stock: $46 * 90 = $4,140.

Credit to Treasury Stock to remove the cost of the 90 reissued shares from the treasury stock account.

This journal entry reflects the cash inflow from the reissuance of treasury stock and reduces the balance in the treasury stock account, indicating a reduction in the number of shares held by the company as treasury stock.

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The expression x²x²x²√x when evaluated is [tex]x^{6\frac{1}{2}}[/tex]

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

x²x²x²√x

The above expression can be evaluated using the law of indices

Using the above as a guide, we have the following:

x²x²x²√x = x⁶√x

So, we have

x²x²x²√x = x⁶ * √x

When evaluated, we have

x²x²x²√x =  [tex]x^{6\frac{1}{2}}[/tex]

Hence, the expression when evaluated is [tex]x^{6\frac{1}{2}}[/tex]

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Complete question

Evaluate x²x²x²√x

The measure of the marked central angle for the given circle is 160°.

Given a part of a circle.

This part is 4/9 of the full circle.

We have to find the marked central angle.

We know that,

Total circle can be represented as,

Total circle = 360°

Since the given figure is 4/9 part of the total circle, the marked central angle will be 4/9 of the total central angle.

Marked central angle = 4/9 × 360

                                    = 160°

Hence the marked central angle is 160°.

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The measure of unknown angle of triangle is 28.2°.

From the given triangle, we have sides 11 units, 12 units and 20 units.

The law of cosine states that the square of any one side of a triangle is equal to the difference between the sum of squares of the other two sides and double the product of other sides and cosine angle included between them. The law of cosine states that: a² = b² + c² − 2bc·cosA.

Here, 11²=12²+20²-2×12×20·cosA

121=144+400-480·cosA

121=544-480·cosA

121-544=-480·cosA

-423=-480·cosA

cosA= 423/480

cosA= 0.88125

A=28.2°

Therefore, the measure of unknown angle of triangle is 28.2°.

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Answer:

x = 1 or x = 7

Step-by-step explanation:

-x² + 8x - 7

= -(x² - 8x) - 7

= - [(x - 4)² - 16] - 7

= -(x - 4)² + 16 - 7

= -(x - 4)² + 9.

-(x - 4)² + 9 = 0

-(x - 4)² = -9

(x - 4)² = 9

x - 4 = ±√9

x - 4 = ±3

x = 3 + 4 or x = -3 + 4

x = 7 or x = 1

Answer:

45

Step-by-step explanation:

Plug in the numbers with their variables.

6(5)+5(3)

30+15

45

Hope this helps

The two mathematical symbols that William Oughtred introduced are "×" for multiplication and "::" for proportion.

Given is a statement about William Oughtred.

William Oughtred is most famous not for his mathematical discoveries, but rather for introducing two mathematical symbols.

We have to find those symbols.

William Oughtred is actually an English priest who basically teaches the students in mathematics subject.

He did invent other famous things like slide rule.

But the most famous invention of him is two mathematical symbols which are "×" for multiplication and "::" for proportion which are still widely used symbols.

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Answer:

what is all that?!

floor plan => It is the scale drawing that show the relationship between rooms, spaces, and physical features viewed from the above

THIS PIC WILL ALSO HELP U

Answer:

Hope this saved you ^^

Step-by-step explanation:

To determine the number of babies we can expect among the next 12 children to enroll, we need to calculate the proportion of babies based on the current enrollment data.

Out of the total enrollment so far, there are 3 babies and 6 children of other ages, making a total of 9 children.

Proportion of babies = (Number of babies / Total number of children) = 3 / 9 = 1/3

Now, to estimate the number of babies among the next 12 children, we multiply the proportion of babies by the total number of children to be enrolled:

Number of babies expected = Proportion of babies * Total number of children to enroll

Number of babies expected = (1/3) * 12 = 4

Therefore, based on the current enrollment data, we can expect approximately 4 out of the next 12 children to be babies.

Answer:

76.5 hours

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

Part 1 of 2:

(a) The equation that describes Winona's total take-home pay, P, in terms of the number of hours, x, worked at the first job and the number of hours, y, worked at the second job can be written as:

P = (10x) + (9.25y + 0.7 * 9.25y) - 0.2[(10x) + (9.25y + 0.7 * 9.25y)]

Simplifying the equation:

P = 10x + 9.25y + 0.7 * 9.25y - 0.2(10x + 9.25y + 0.7 * 9.25y)

Part 2 of 2:

(b) If Winona is committed to working 30 hours per week at the first job, let's assume x = 30. We need to find the number of hours per week, y, she would need to work at the second job to reach a biweekly take-home pay of $800.

Using the simplified equation from part (a), we substitute x = 30 and solve for y:

800 = (10 * 30) + (9.25y + 0.7 * 9.25y) - 0.2[(10 * 30) + (9.25y + 0.7 * 9.25y)]

800 = 300 + (9.25y + 0.7 * 9.25y) - 0.2(300 + (9.25y + 0.7 * 9.25y))

Now, we can solve for y:

800 = 300 + 9.25y + 0.7 * 9.25y - 0.2(300 + 9.25y + 0.7 * 9.25y)

Simplify the equation:

800 = 300 + 9.25y + 0.7 * 9.25y - 0.2 * 300 - 0.2 * 9.25y - 0.2 * 0.7 * 9.25y

Combine like terms:

800 = 300 - 60 + 9.25y - 1.85y - 0.1295y

800 = 240 + 7.32y

Subtract 240 from both sides:

560 = 7.32y

Divide both sides by 7.32:

y ≈ 76.5

Therefore, Winona would need to work approximately 76.5 hours per week at her second job to reach a biweekly take-home pay of $800.

When matched, the prompts on asymptotes would be:

The presence of a vertical asymptote at x=0 signifies that the cost of producing pills can never reach a value of 0, remaining persistently positive. Simultaneously, the horizontal asymptote at y=0 serves as a reassuring indication that the cost of producing pills cannot be negative, as it steadfastly remains at or above zero.

This crucial constraint ensures that the cost incurred in the pill production process is always a non-negative quantity. Consequently, the prompt related to the impossibility of negative costs aligns with this notion.

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Given: The equation x² = 5x + 4

We have to draw the the graph for the given equation.

Consider the given equation,

x^2 - 5x - 4 = 0  

The vertex of the parabola of the form f(x) = ax^2 + bx + c   is given by x = -b/2a

Here,

a= 1

b= -5

c= -4

vertex = x = 5/2= 2.5

Also, the y coordinate at x = 2.5 is,

y = (2.5)^2 -5(2.5)-4

y = -10.25

Thus the vertex of parabola is (2.5 , -10.25)

y - intercept is the point where x = 0

put x = 0 in given equation

f(x) = 0 - 0 -4

f(x) = -4

hence y intercept is at (0, -4).

Now, we calculate x- intercept

x- intercept is where y is equal to 0.

Put f(x) = 0

We have,

x^2 - 5x - 4 = 0

by using quadratic formula,

x = -b ±√b² - 4ac/2a

x=5 ±√-5² - 4 (1)(-4)/2

x= 5±√41/2.

Hence with the obtained values the graph of the equation is obtained.

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Every pair of values except (2, y different of 7), (5, y different of 14) and (9, y different of 21) can go in the blanks so that this represents y as a function of x.

A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.

For a point in the standard format (x,y), we have that:

Hence every point can go into the blank, except the ones that map the inputs 2, 5 and 9 to different outputs than the ones already given in this problem.

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Answer:

16x^2 - 1.6x - 5

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

x+2 | 16x^3 + 31.6x^2 - 6.8x - 12

- (16x^3 + 32x^2)

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

-0.4x^2 - 6.8x

+(-0.4x^2 - 0.8x)

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

-6x - 12

+(-6x - 12)

----------

0

Answer:   = 16x²-.4x-6

Step-by-step explanation:

divide 16x³+31.6x²-6.8x-12 by x+2​

Using synthetic division:  Carry first 1 down.  Multiply that by outside -2 and put it under 2nd number.  Add.  Then multiply and repeat until you get to end.

-2    |   16            31.6             -6.8           -12

      |                  -32                  .8             12        

           16              -.4             -6                0

Put back into equation form.  Last number is 0 so remainder is 0

= 16x²-.4x-6

Answer:

49pi cm^2

Step-by-step explanation:

The area of a circle is pi(r)^2

To find our radius, we need to divide the diameter by 2.

14 / 2 = 7

Lets plug that into our equation:

pi(7)^2

Simplify:

pi(49)

rearrange:

49pi

WAIT, we need units!

49pi cm^2

~~~Harsha~~~

Altogether they have 85 marbles.

Given,

Randy's marbles = 50

Randy's marbles is 5/2 of Andy's marbles.

Randy's marbles is 10/3 of Peter's marbles.

Now form the linear equations,

Let Andy has x marbles.

So,

5/2 × x = 50

x = 20

Andy's marbles = 50

Let Peter has y marbles.

So,

10/3 × y = 50

y = 15

Peter's marbles = 15

Thus total marbles of Randy , Andy , Peter is 85.

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Answer:

85 marbles

Step-by-step explanation:

Andy has 20

Randy has 50

Peter has 15

If Erin had 150m/ of buttermilk and recipe require 0.25 cups of buttermilk, she has more than the required amount, so she has sufficient buttermilk for the recipe.

1.2 To determine if Erin has enough buttermilk for the recipe, we need to convert the given quantities to a common unit.

150 ml of buttermilk is equivalent to 0.15 liters (since 1 liter = 1000 ml).

Now, let's convert 0.25 cups to liters. Since 1 cup is approximately 0.2366 liters, we have:

0.25 cups ≈ 0.25 * 0.2366 liters = 0.05915 liters.

Comparing the amount of buttermilk Erin has (0.15 liters) with the amount required by the recipe (0.05915 liters), we can see that Erin has enough buttermilk. She has more than the required amount, so she has sufficient buttermilk for the recipe.

1.3.1 To determine the total mass of the ingredients, we need to convert the given quantities to a common unit, kilograms.

0.8 kg of flour is already in kilograms.

650 g of sugar is equivalent to 0.65 kg (since 1 kg = 1000 g).

900,000 mg of butter is equivalent to 900 g (since 1 g = 1000 mg), which is 0.9 kg.

Adding up the masses of the ingredients:

0.8 kg (flour) + 0.65 kg (sugar) + 0.9 kg (butter) = 2.35 kg.

Therefore, the total mass of the ingredients is 2.35 kilograms.

1.3.2 If sugar comes in 150 g bags at a cost of R5.95 per 150 g, we can calculate the total cost of the sugar needed for the recipe.

The recipe requires 650 g of sugar. Since each bag contains 150 g of sugar, we divide the required amount by 150 g:

650 g / 150 g = 4.3333 bags.

Since we cannot purchase a fraction of a bag, we need to round up to the nearest whole number. So, we'll need to buy 5 bags of sugar.

The total cost of the sugar is calculated by multiplying the number of bags by the cost per bag:

5 bags * 5.95 per bag = 29.75.

Therefore, the total cost of the sugar needed for the recipe is 29.75.

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Yes, because it is practical to obtain that many aspirin because the number is relatively small. The correct option is B.

The minimum sample size required to be 99% confident that the sample standard deviation (s) is within 10% of the population standard deviation (σ) is 336, according to the table provided.

This means that in order to have a high level of confidence (99%) that the sample standard deviation is within a reasonable range of the population standard deviation, a minimum sample size of 336 is needed.

In this case, the sample size requirement is met with a relatively small number, 336, compared to the larger values provided in the table for higher levels of confidence.

Therefore, it can be considered practical to obtain that many aspirin tablets for the purposes of this study.

Thus, the correct option is B.

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By using this absolute value equation, the chef can determine the range of cake diameters that meet the desired margin of error of 3 inches and make an informed decision when purchasing the cake.

The absolute value of the difference between the actual diameter of the cake and the ideal diameter of 24 inches should be less than or equal to 3 inches.

To describe the statement using an absolute value equation, let's define the variable "d" as the actual diameter of the cake.

The ideal diameter of the cake is given as 24 inches.

The margin of error is specified as 3 inches, which means the chef is willing to accept a cake with a diameter within 3 inches of the ideal size.

Considering the margin of error, we can express the acceptable range of diameters for the cake as follows:

d - 24 ≤

This inequality states that the difference between the actual diameter "d" and the ideal diameter of 24 inches should be less than or equal to 3 inches, indicating that the actual diameter should be no more than 3 inches larger or smaller than 24 inches.

However, to represent this condition using an absolute value equation, we need to remove the inequality signs.

We can rewrite the inequality above using absolute value:

|d - 24| ≤ 3

This absolute value equation states that the absolute value of the difference between the actual diameter "d" and the ideal diameter of 24 inches should be less than or equal to 3 inches.

It encompasses both possibilities of the actual diameter being within 3 inches greater or smaller than 24 inches.

By using this absolute value equation, the chef can determine the range of cake diameters that meet the desired margin of error of 3 inches and make an informed decision when purchasing the cake.

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Answer:

To calculate the value of (-3/4)^-4, we need to apply the exponentiation rules.

When a negative number is raised to an even power, the result is positive. Thus, we can rewrite (-3/4)^-4 as (4/-3)^4.

Now, let's evaluate the expression:

(4/-3)^4 = (4^4)/(-3)^4 = 256/81

So, the value of (-3/4)^-4 is 256/81

Step-by-step explanation:

The statement that correctly compares the centers of the distributions is this:

D. The mean of East Hills HS is greater than the mean of Southview HS.

Since, The statement that correctly describes the centers of the distributions is option D. To find out, we will calculate the mean of the two distributions as follows:

For East Hills HS

25 * 1 + 29 * 1 + 31 * 2 + 33 * 4 + 35 * 5 + 37 * 8 + 39 * 4

= 875

And, Frequency = 1 + 1 + 2 + 4 + 5 + 8 + 4 = 25

Hence,

Mean = 875/25

Mean = 35

For Southview

25 * 2 + 27 * 6 + 29 * 9 + 31 * 6 + 33 * 2

= 725

Frequency = 2 + 6 + 9 + 6 + 2 =25

Hence, Mean = 29

So, from our calculation, the mean of East Hills HS is greater than the mean of Southview HS.

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The percentage is 26%, so the number is 26.

Here we know that the x% of the number 800,000 is equal to 208,000.

Remember that the x% of a number N, is given by the product:

(x%/100%)*N

So in this case we can solve the equation:

(x%/100%)*800,000 = 208,000

Solving that equation for the percentage, we will get:

x% = 100%*(208,000/800,000)

x% = 26%

That is the missing number.

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