how to complete the square for an equation for example this equation -10x ² +250x-1500=0.

Answer:

  See attached

Step-by-step explanation:

Given trapezoids with midlines, you want to find various values in the figures shown.

The length of a midline of a figure is the average of the parallel edges. That means ...

These relations are used in solving the figures shown. Work and results are given in the attachment.

The square feet of fabric of the portions in the red and blue portions is 10.05 square feet

The missing figure is added as an attachment

We start by calculating the areas of the portions

The red and blue portions form a trapezoid

So, the area is

Red and blue portions = 2 * 1/2 * (2.2 + 4.5) * 1.5  = 10.05

Hence, the red and blue portions is 10.05 square feet

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Answer:

Step-by-step explanation:

tg

Answer:

The solution is 11/8

Step-by-step explanation:

3 1/4 - 1 7/8

= 13/4 - 15/8

= 26-15/8

= 11/8

Answer:  1/4. Based on the given conditions, formulate:: 3/12 Cross out the common factor: 1/4.

Step-by-step explanation:

Answer: 3/12

Step-by-step explanation:

The statements that are true based on the variables around the centroid are; 1)The value of x is 2, 2)The value of y is 6 and 3) The length of KH is 7.6

To find the value of y with the information provided about the various lengths around centroid,

KW : KR - 1:2

(2y - 8.9)/ (0.5y + 3.2) = 1/2

4y - 17.8 = 0.5y + 3.2

3.5y = 21

y =21/3.5

y = 6

KR = 0.5 × 6 + 3.2 = 6.2.

KT : KW = 1/2

7.1 x - 11. 8/ 5x - 5.2 = 1/2
14.2x - 23.6 = 5x -5.2

9.2x = 18.4

x = 2

KW = 5 × 2 - 5.2 = 4.8

KD : KH = 1/2

9w - 23.2/ 4.5w - 5.9 = 1/2

18w - 46.4 = 4.5w -5.9

13.5w = 40.5

w = 3

KH 4.5 x 3 - 5.9 = 7.6

The length of KN

KN = (5x - 5.2)

KN = (5 × 2 - 5.2)

KN = 4.8

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For a sample of born babies' weight in a large hospital, probability that the mean weight of the sample babies would differ from the population mean by greater than 43 grams is equals to 0.5390.

We have a sample of born babies' weight in a large hospital.

Mean of weight = 4090 grams

Variance of weight = 31300

Standard deviations = 560

Sample size or included babies = 64

standard error = [tex]\frac{560}{\sqrt(64)}[/tex] = 70

We have to determine probability that the mean weight of the sample babies would differ from the population mean by greater than 43 grams. Let the population mean would be [tex]\mu[/tex]. Now, the probability, [tex]P ( \bar X - \mu > 43 ) [/tex]. Using Z-score formula, [tex]Z = \frac{X -\mu}{\frac{\sigma}{\sqrt(n)}} [/tex]

Substitute all known values then, z= ± 43/70, z= ± 0.614

P(z<-0.614 or z>0.614) = P(z<-0.614)+ P(z>0.614)

=2 × 0.2695

=0.5390

Hence, required value is 0.5390.

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Answer: 1/4

Step-by-step explanation:

There are 8 possible outcomes

there are 2 possible times that the number is greater than 3

so you have a 2 out of 8 chance of getting a number greater than 3

2/8=1/4

The inverse of the function is g(x) = ( x - 2 )/5 and f(x) = 5x + 2 and g(x) = x - 2/5 are inverse functions of each other

Given data ,

Step 1:

Let the function be represented as f ( x )

Now , f(x) = 5x + 2 as an equation with the variable x:

f(x) = 5x + 2

Step 2:

Switch the variables in the equation from Step 1 and solve for y

Switching x and y:

x = 5y + 2

x - 2 = 5y

Dividing both sides by 5

y = (x - 2)/5

So, the equation with y as the variable is y = (x - 2)/5

Step 3:

Now , the inverse of g(x) = x - 2/5 and f(x) = 5x + 2

The inverse of a function g(x) is denoted as g⁻¹(x) and it is obtained by interchanging x and y and solving for y

Given g(x) = x - 2/5, we can switch x and y:

x - 2/5 = g^(-1)(x)

Now, we can solve for y by isolating it on one side of the equation

x - 2/5 = y

Hence , the inverse of g(x) is y = ( x - 2 )/5

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The area of the regular polygon with 4 sides and an apothem of 12 cm is 576 square cm.

The given apothem of the polygon is 12 cm.

The area of a regular polygon with 4 sides (a square):

Area = 2 × apothem × perimeter / 4

Since a square has four equal sides, the perimeter of the square is given by:

Perimeter = 4 × side length

So, the side length by using the formula for the apothem of a regular polygon with 4 sides:

Apothem = side length / 2

Solving for side length, we get:

side length = apothem × 2 = 12 × 2 = 24 cm

Now we can find the perimeter:

Perimeter = 4 × side length = 4 × 24 = 96 cm

Substituting the values of apothem and perimeter in the area formula, we get:

Area = 2 × 12 × 96 / 4 = 2 × 12 × 24 = 576 square cm

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The requried length of the arc MN is evaluated as 6π.

From the figure,
The area of the shaded sector is given as:

A = ∠NLM/360×πr²

27π= ∠NLM/360×π9²
∠NLM = 120

Now,

length MN = 120/360*2πr

                  = 1/3×2π×9
                  = 6π

Thus, the requried length of the arc MN is evaluated as 6π.

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Answer:

Step-by-step explanation:

In the picture are 2 dots connect the line

I plugged in 0 for x and got (0,-3)

then i plugged in -3/2 for x and got (-3/2, -2)

plotted those 2 points and drew a line connecting those 2 dots

The scale factor of the dilation of the triangles is 2

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

The similar triangles

The scale factor of the dilation is the division of the corresponding sides

So, we have

Scale factor = 6/3

When evaluated, we have

scale factor = 2

Hence the scale factor is 2

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Answer: 1,404 Non-Purple Candies

Step-by-step explanation:

First, you must figure out how many are non-purple in the box of 50:

50*0.22=11

Then, you must figure out how many are NOT purple:

50-11=39

Next, since you are trying to calculate how many non-purples are in 36 boxes of that candy, you must multiply the number of non-purple found in 1 box by 36:

39*36= 1404

So, there are 1,404 Purple Candies in 36 Boxes of Candy (approximately)

The best estimate for the total number of non-purple candy pieces in 36 boxes of the same candy is 1,404.

If 22% of the candy pieces in one box of fruit candy are purple, then 78% (100% - 22%) of the candy pieces are non-purple. To find the best estimate of the total number of non-purple candy pieces in 36 boxes of the same candy, we need to use proportions.

Let x be the total number of candy pieces in one box of fruit candy. Then, the number of non-purple candy pieces in one box is 0.78x. Therefore, the total number of non-purple candy pieces in 36 boxes is:

36 boxes x 0.78x non-purple candy pieces per box = 28.08x non-purple candy pieces

To find the value of x, we can use the fact that the box contains 50 candy pieces in total. Therefore:

22% of x = 0.22x purple candy pieces
78% of x = 0.78x non-purple candy pieces
Total number of candy pieces = 50

Using these equations, we can solve for x:

0.22x + 0.78x = 50
1x = 50 / 0.78
x = 64.1 (rounded to one decimal place)

Therefore, each box contains approximately 64 candy pieces. And the total number of non-purple candy pieces in 36 boxes is:

28.08x non-purple candy pieces = 28.08 x 64.1 = 1802.728 non-purple candy pieces

So the best estimate for the total number of non-purple candy pieces in 36 boxes of the same candy is 1803 (rounded to the nearest whole number).

Let's use the terms you've provided to solve the problem step-by-step.

Step 1: Determine the number of purple candies in one box.
22% of the 50 fruit candy pieces are purple. To find this, multiply 50 by 0.22 (the decimal equivalent of 22%):
50 * 0.22 = 11 purple candy pieces

Step 2: Determine the number of non-purple candies in one box.
There are 50 fruit candy pieces in total. Subtract the 11 purple candies to find the number of non-purple candies:
50 - 11 = 39 non-purple candy pieces

Step 3: Estimate the total number of non-purple candies in 36 boxes.
To find this, multiply the number of non-purple candies in one box (39) by the number of boxes (36):
39 * 36 = 1,404

So, the best estimate for the total number of non-purple candy pieces in 36 boxes of the same candy is 1,404.

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A theoretical hypothesis is a hypothesis that attempts to provide an explanation for a scientific question or phenomenon by proposing a theoretical framework or model. (option b).

Theoretical hypotheses are often used in scientific research to guide investigations and to help researchers make predictions about what they expect to observe. They are essential to the scientific method because they provide a basis for developing testable predictions and designing experiments to confirm or reject them.

A theoretical hypothesis is a hypothesis that attempts to provide an explanation for a scientific question or phenomenon.

This statement is accurate. As discussed earlier, a theoretical hypothesis is a type of hypothesis that proposes a theoretical framework or model to explain a scientific question or phenomenon.

Therefore, statement b is the most accurate description of a theoretical hypothesis.

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Answer:

We can use the formula for conditional probability to solve this problem:

P(Scholarship | Accepted) = P(Scholarship and Accepted) / P(Accepted)

We know that P(Accepted) = 18/25 and P(Scholarship and Accepted) = 13/25 (from the given information). Therefore:

P(Scholarship | Accepted) = (13/25) / (18/25) = 13/18 or approximately 0.722

So the probability that you receive a scholarship, given that you are accepted to your preferred college, is about 0.722 or 72.2%.

Step-by-step explanation:

Answer:

Triangle congruence cannot be determined with the given information.

Answer:

The dimensions of the piece of carpet that Charlotte must purchase is 160.5 feet by 13.5 feet, and the total cost of the carpet, including labor and materials, is $5088.95

Step-by-step explanation:

To determine the dimensions of the piece of carpet that Charlotte must purchase, we need to add the overlap to the length and width of the room.

The overlap is 3 inches, which is 0.25 feet (since there are 12 inches in a foot and 3/12 = 0.25).

So the length of the piece of carpet needed is 160.5 feet (160 + 0.25 + 0.25), and the width is 13.5 feet (13.25 + 0.25 + 0.25).

To find the area of the piece of carpet needed, we multiply the length by the width:

160.5 feet x 13.5 feet = 2166.75 square feet

Now we need to add the extra area needed for the overlap, which is:

0.25 feet x 0.25 feet x 4 (since there are 4 sides) = 0.25 square feet

So the total area of the piece of carpet needed is:

2166.75 square feet + 0.25 square feet = 2167 square feet

To determine the labor and material costs, we need to find the area of the plece (piece) of carpet, including the overlap.

The labor costs are $23 per hour, per person, and the crew can lay 50 square feet of carpet each hour. So the total labor cost will be:

4 people x $23 per hour per person = $92 per hour

To determine how many hours it will take to lay the carpet, we divide the total area of the plece by the rate at which the crew can lay carpet:

2167 square feet ÷ (4 people x 50 square feet per hour) = 10.835 hours

We will need to round up to the nearest whole number since the crew cannot work for a fraction of an hour. So it will take 11 hours to lay the carpet.

The cost of materials will be:

2167 square feet x $1.85 per square foot = $4001.95

The cost of labor and materials will be:

11 hours x $92 per hour = $1012

$1012 + $4001.95 + $75 equipment/materials/supplies fee = $5088.95

Therefore, the dimensions of the plece of carpet that Charlotte must purchase is 160.5 feet by 13.5 feet, and the total cost of the carpet, including labor and materials, is $5088.95.

Build-borrow-or-buy.

The build-borrow-or-buy framework is a conceptual model used by strategists to help them decide whether to build capabilities internally, borrow them through partnerships and alliances, or buy them through mergers and acquisitions. The framework helps organizations identify the most efficient and effective way to acquire the resources, capabilities, and competencies they need to achieve their strategic goals. It is a useful tool for decision-making when considering growth strategies, and can help managers evaluate the costs, risks, and benefits of each option.

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(a) build-borrow-or-buy. This framework helps strategists decide whether to pursue internal development, enter into an alliance, or acquire new resources, capabilities, and competencies.

the build-borrow-or-buy framework suggests that companies have three options when it comes to acquiring new resources and capabilities. First, they can build or develop these resources and capabilities internally through investments in research and development or employee training. Second, they can borrow or enter into strategic alliances with other companies to gain access to new resources and capabilities. Finally, they can buy or acquire companies that already possess the desired resources and capabilities.

the build-borrow-or-buy framework provides a structured approach for companies to evaluate their options when it comes to acquiring new resources and capabilities. By considering the pros and cons of each option, companies can make more informed decisions that align with their strategic goals and objectives.


The build-borrow-or-buy framework is a conceptual model that helps strategists decide whether to seek internal development (build), enter into an alliance (borrow), or acquire new resources, capabilities, and competencies (buy). This model assists organizations in evaluating their options for growth and resource allocation based on their strategic goals and objectives.

the build-borrow-or-buy framework is a valuable tool for strategists when choosing between internal development, alliances, or acquisitions to achieve their organization's growth and resource needs.

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Answer:

The orange is 60 cents.

Step-by-step explanation:

1) Calculate the cost of an apple (45 cents).

2) Take away the cost of the 2 apples from the original problem (45+45=90 cents).

3) You get the cost of 60 cents for one apple.

3A + O - (2A + O) = 1.95 - 1.5
A = 0.45
Now we can substitute this value of A into one of the original equations to solve for O:
2(0.45) + O = 1.5
O = 0.6
Thus, an orange costs $0.60 at the local supermarket.

To find the cost of an orange, we can use the system of linear equations. Let's denote the cost of an apple as "a" and the cost of an orange as "o".

From the given information, we can write two equations:

1) 2a + o = $1.50
2) 3a + o = $1.95

Now, we can solve for "o" using the following steps:

Step 1: Subtract equation 1 from equation 2 to eliminate the "o" variable:

(3a + o) - (2a + o) = $1.95 - $1.50
a = $0.45

Step 2: Substitute the value of "a" back into equation 1 to find the value of "o":

2($0.45) + o = $1.50
$0.90 + o = $1.50

Step 3: Solve for "o":

o = $1.50 - $0.90
o = $0.60

So, the cost of an orange at the local supermarket is $0.60.

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In Seventh grade, 30 students chose Music and 15 students chose World language while in Eight grade, 5 students chose Music and 50 students chose World language.

Total students is 100

Total students that chose music is 35

Total students that chose world language is 100-35 = 65

Total students in eight grade is 55

Total students in seventh grade is 100-55 = 45

Students in eight grade that chose world language is 50

Students in eight grade that chose music is 55 - 50 = 5

Students in seventh grade who chose music is 35 - 5 = 30 (total students who chose music - number of eighth grade students who chose music)

Students in seventh grade who chose world language = 45 - 30 = 15 (total student in seventh grade - students in seventh grade who chose music)

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Answer:

R23

Step-by-step explanation:

1.6kg of bananas= R36.80

1kg= 36.80×1/1.6

= R23

The simplified expression of (7j³ - 2) + (5j³ - j - 3) is 12j³ - j - 5.

To simplify the expression (7j³ - 2) + (5j³ - j - 3), we first combine like terms. The like terms are the ones with the same power of j.

The terms with j³ are 7j³ and 5j³, which add up to 12j³.

The terms with j are -j and -j, which add up to -2j.

The constant terms are -2 and -3, which add up to -5.

(7j³ - 2) + (5j³ - j - 3) = 7j³ + 5j³ - 2 - j - 3 (grouping like terms)

= 12j³ - j - 5 (combining like terms and simplifying)

Therefore, the simplified expression is 12j³ - j - 5.

A simplified expression is an expression in which all like terms have been combined and any unnecessary parentheses or symbols have been removed

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The total amount of wood needed would be -

X = 2w(l + b).

Assume that the total number of windows made by the carpenter are {w}.

Let the dimensions of each of the window be {l} x {b} respectively.

The total amount of wood needed for one window would be -

x = 2(l + b)

For all the windows, the total amount of wood needed would be -

X = 2w(l + b).

Therefore, the total amount of wood needed would be -

X = 2w(l + b).

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An inequality that is represented by this graph include the following: C. y ≤ (4 - x)/2.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 3)/(2 + 2)

Slope (m) = -2/4

Slope (m) = -1/2.

At data point (2, 1) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = -1/2(x - 2)

y = -x/2 + 1 + 1

y = -x/2 + 2

y ≤ (4 - x)/2 (since the solid line is shaded below)

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The range of customers that served on the middle 50 percent of days are from 2994 to 3514 customers, under the condition that mean of 3,250 customers and a standard deviation of 320.

Here,
The middle 50% of days means that we are observing for the range of values that comprise the middle 50%  the data.

In order o find  range, we have to find the z-scores that correspond to the 25th and 75th percentiles and then change these z-scores back to raw scores using the formula
z = (x - μ) / σ
here x = raw score,
μ = mean,
σ = standard deviation

The z-score concerning to the 25th percentile is -0.6745 and the z-score concerning  the 75th percentile is +0.6745.
Using these z-scores and the formula, we evaluate  the raw scores that concerning  the percentiles
z = (x - μ) / σ
-0.6745 = (x - 3250) / 320
x = 2994
z = (x - μ) / σ
+0.6745 = (x - 3250) / 320
x = 3514

The range of customers that served on the middle 50 percent of days are from 2994 to 3514 customers.

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The fraction which exactly half-way between the fractions "2/3" and "1/6", expressed in simplest-form is "5/12".

To find the fraction exactly halfway between 2/3 and 1/6, we first convert the given fractions to fractions with a common denominator.

So, 2/3 = 8/12  and 1/6 = 2/12,

Now we have the fractions "8/12" and "2/12".

To find the fraction exactly halfway between them, we take their average.

So, Average of "8/12" and "2/12" is

⇒ (8/12 + 2/12)/2,

⇒ 5/12.

Therefore, "5/12" is the fraction exactly halfway between 2/3 and 1/6.

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The given question is incomplete, the complete question is

Find the fraction which is exactly half way between 2/3 and 1/6 in it simplest form.

The probability that a person aged 40 or over has a master's degree is 6.15%

Given is table showing the educational qualification of a residential area, we need to find the probability that person aged 40 or over has a master's degree,

P(E) = favorable outcome / total outcome

P(person aged 40 or over has a master's degree) = 475+699 / 19076
= 1174 / 19076

= 0.06154

= 6.15%

Hence, the probability that a person aged 40 or over has a master's degree is 6.15%

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