In parallelogram ABCD, AC = 14 and BD = 2x+4. What value of x makes this parallelogram a rectangle?

4

10

2

5

The zeroes of the quadratic equation are [tex]{\displaystyle x= {3-2{\sqrt {2}}}[/tex] and [tex]{\displaystyle x={3+2{\sqrt {2}}}[/tex] for the given quadratic equation.

A second-degree algebraic equation known as a quadratic equation can be found in mathematics (having one or more variables raised to the second power). Ancient Babylonian cuneiform texts from the time of Hammurabi demonstrate a knowledge of how to solve quadratic equations, but it seems that ancient Egyptian mathematicians were not familiar with this technique.

They have played a significant role in the physics of accelerated motion, such as free fall in a vacuum, ever since Galileo's time. The general quadratic equation in one variable is written as ax2 + bx + c = 0, where a, b, and c are arbitrary constants (or parameters) and an is not equal to 0.

Given to solve the quadratic equation

[tex]{\displaystyle x={\frac {6\pm {\sqrt {(-6)^{2}-4(1)(1)}}}{2(1)}}}[/tex]

[tex]{\displaystyle x={\frac {6\pm {\sqrt {36-4}}}{2}}}[/tex]

[tex]{\displaystyle x={\frac {6\pm {\sqrt {32}}}{2}}}[/tex]

[tex]{\displaystyle x={\frac {6-4{\sqrt {2}}}{2}}}[/tex]

[tex]{\displaystyle x= {3-2{\sqrt {2}}}[/tex]

x = 0.171573

[tex]{\displaystyle x={\frac {6+4{\sqrt {2}}}{2}}}[/tex]

[tex]{\displaystyle x={3+2{\sqrt {2}}}[/tex]

x = 5.828427

Thus, the zeroes of the quadratic equation are [tex]{\displaystyle x= {3-2{\sqrt {2}}}[/tex] and [tex]{\displaystyle x={3+2{\sqrt {2}}}[/tex] for the given quadratic equation.

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3 has a mean of 120 and a standard deviation of 3.

Describe standard deviation using an example?

The dispersion of the data around the mean value is measured by the standard deviation. It might be helpful when comparing data sets that may have the same mean but a different range.

                                The means of the two numbers 15, 15, 15, 14, 16, and 2, 7, 14, 22, 30 are the same, for instance. The second is, however, obviously more dispersed.

mean of sample means = true mean = 120

std dev of sample mean = true std / sqrt(n)

                                     = 15/5 = 3

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The equations that are equivalent are:

2 + x = 5

x + 1 = 4

-5 + x = -2

If any two or more equations are equivalent, they would have the same value when evaluated.

To find which equations are equivalent, solve to find the value of x in each given equation.

A. 2 + x = 5

x = 5 - 2

x = 3

B. x + 1 = 4

x = 4 - 1

x = 3

C. 9 + x = 6

x = 6 - 9

x = -3

D. x + (-4) = 7

x  = 7 + 4

x = 11

E. -5 + x = -2

x = -2 + 5

x = 3

The equivalent equations are:

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Answer:

Step-by-step explanation:

t%5Bc%5D=2.055

ME=SE%2At%5Bc%5D

ME=4.118%2A2.055

ME=8.463

.

.

.

(67.7,84.7)

The perimeter of the triangle is 28 cm. The perimeter of the triangle containing the right angle with two sides that differ by 2 cm is 28 cm. This can be determined by using the Pythagorean Theorem to solve for the length of the sides.

Let the two sides of the right triangle be x and x+2

Apply the Pythagorean Theorem:

(x)^2 + (x + 2)^2 = 24

x^2 + x^2 + 4x + 4 = 24

2x^2 + 4x = 20

2x(x + 2) = 20

x(x + 2) = 10

x = 5 and x + 2 = 7

Therefore the perimeter of the triangle is 5 + 7 + 7 = 19 cm.

The perimeter of the triangle is 28 cm.

The perimeter of the triangle containing the right angle with two sides that differ by 2 cm is 28 cm. This can be determined by using the Pythagorean Theorem to solve for the b of the sides. The equation 2x(x + 2) = 20 can be used to solve for x, which is equal to 5. Therefore, the two sides of the triangle are 5 cm and 7 cm. Adding these lengths together, the perimeter of the triangle is 5 + 7 + 7 = 28 cm.

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Super would need 2 premium cars to achieve a productivity ratio of 7.

Let's call the number of premium cars "x".

The total revenue from the regular cars would be $1500 * 19 = $28,500 per month.

The total revenue from the premium cars would be $2500 * x.

The total cost of the regular cars would be $100 * 19 = $1900 per month.

The total cost of the premium cars would be $500 * x.

The Chief of Operations wants the revenue to be 7 times the cost of service operations, so we can write the following equation:

($28,500 + $2500x) / ($1900 + $500x) = 7

Expanding and simplifying the equation, we get:

$2500x + $28,500 = 7($1900 + $500x)

$2500x + $28,500 = $13,300 + 7$500x

$11,200 = 6$500x

$11,200 / $6,500 = x

x = 1.723

Rounding up, Super would need 2 premium cars to achieve a productivity ratio of 7.

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The score of fourth test is 95

The mean, also known as the average or the arithmetic mean, is a measure of central tendency that represents the sum of a set of values divided by the number of values in that set. It is one of the most common ways to summarize a set of data and is often used as a reference point for other measurements such as standard deviation. It is represented by the Greek letter "mu" (µ) for population mean and "x bar" for sample mean.

Given mean of the score is 80.5

mean of score is given as (∑ score) / n

where ∑ score is sum of score of all marks and n is the number of test he had attempted

∑ score  = 62 + 75 +90 +x

where x is marks in fourth subject

so ∑ score = mean * 4

=> 227 + x = 80.5 *4

=> x = 322 -227

so x = 95

so the marks of the fourth test is 95.

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A function named "sum three(x, y, z)" that accepts three integer arguments and returns their sum is defined in the aforementioned code.

The function first determines whether any two or three of the three integers (x, y, and z) are equal and if so, it assigns 0 to the variable "sum".

If not, the variable "sum" is set to the sum of the three integers.

It then gives the value of "sum" back.

The function is finally run four times with various inputs, printing the sum of the inputs each time.

def sum_three(x, y, z):

if x == y or y == z or x==z:

sum = 0

else:

sum = x + y + z

return sum

print(sum_three(2, 1, 2))

print(sum_three(3, 2, 2))

print(sum_three(2, 2, 2))

print(sum_three(1, 2, 3))

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The probability that at least 20 of the novels have fewer than 400 pages is 1 - 0.2266 = 0.7734 or 77.34%.

What is the normal distribution and the cumulative distribution?

The normal distribution, also known as the Gaussian distribution or bell curve, is a probability distribution that describes the distribution of a continuous random variable.

The cumulative distribution function (CDF) is a function that gives the probability that a random variable is less than or equal to a certain value

To solve this problem, we can use the normal distribution and the cumulative distribution function (CDF) of a normal distribution. The normal distribution is a probability distribution that describes how many novels have a certain number of pages.

The mean number of pages in a novel is given as 525 and the standard deviation is 200. We know that 30% of the novels have fewer than 400 pages, which corresponds to a z-score of (400 - 525) / 200 = -0.75.

We can use the cumulative distribution function (CDF) to find the probability that at least 20 of the novels have fewer than 400 pages. The CDF of a normal distribution gives the probability that a random variable is less than or equal to a certain value.

The probability that at least 20 of the novels have fewer than 400 pages is the same as the probability that at most 30 of the novels have more than 400 pages. Using a standard normal table or software, we can find the probability that a standard normal random variable is less than -0.75 as P(X< -0.75) = 0.2266, this is the probability that less than 30 novels have more than 400 pages.

Hence, the probability that at least 20 of the novels have fewer than 400 pages is 1 - 0.2266 = 0.7734 or 77.34%.

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P(at least n times) = 1 - (1 - p)^k, where p is the probability of the event happening and k is the number of trials.

The probability of an event happening at least n times out of k trials can be calculated using the formula P(at least n times) = 1 - (1 - p)^k. Here, p is the probability of the event happening, and k is the number of trials. The formula is based on the principle that the probability of an event happening at least n times is equal to one minus the probability of it happening less than n times. The probability of it happening less than n times is calculated by taking the probability of the event happening once, and then multiplying it by itself k times. This is because each trial is independent, and the probability of the event happening for each trial is the same. The result of this multiplication is then subtracted from one, which gives us the probability of it happening at least n times out of k trials

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Answer:

A rational equation is an equation containing at least one fraction whose numerator and denominator are polynomials, \frac{P(x)}{Q(x)}. Q(x)P(x). These fractions may be on one or both sides of the equation.

Answer:

draw a line between an empty point at 0 and a filled point at 3

Step-by-step explanation:

To graph this inequality we first want to isolate the y variable to make it a bit easier to deal with. This is a compound inequality and when isolating the y variable instead of just doing an operation on both sides, we do it to all sides which follows the same principle of maintaining equality.

We start with the original inequality:
[tex]-4 \le -2(y-1) < 2[/tex]

From here we divide by -2 on all sides, but since we're dividing by a negative we would flip the way the inequality is pointing so we get:
[tex]2\ge y-1 > -1[/tex]

From here we add 1 to all sides.

[tex]3 \ge y > 0[/tex]

Although generally we would write this as:

[tex]0 < y \le 3[/tex]

Now to graph this we would draw a hole on the number line at the point zero, and a filled point on the number line at 3, since 3 is included (since less than or equal to 3) and then just connect the two points. I'll include an image that demonstrates this.

If we mark off a distance t along the unit circle, starting at (1, 0) and moving in a counterclockwise direction, we arrive at the terminal point determined by t.

What is a terminal point?

The ray that has been rotated around the origin to form an angle with the stationary ray that is the initial side of the angle is the ray that has reached its terminal point. The most typical acute-angle measurements are represented by the sine and cosine values.

The coordinates of the terminal point come from the coordinates of the reference point (positive or negative depending on the quadrant.)

We know that a unit circle is the circle of radius 1 which is centered at the origin in the xy-plane.

General equation of a unit circle is: x^2+ y^2 = 1

Starting at the point (1,0),

If t≥0, then, t is the distance along the unit circle in clockwise direction

If t<0, then mod t is the distance along the unit circle in clockwise direction.

Here, role="math" , localid="1648202152711"t is a real number by which a point P(x,y) is generated. This point is known as the terminal point which is determined by the real number t.

Hence, if we mark off a distance t along the unit circle, starting at (1, 0) and moving in a counterclockwise direction, we arrive at the terminal point determined by t.

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y-1/7x-2 & x-7y=4 are intersecting but not parallel or perpendicular lines.

Two lines are parallel if they have the same slope (or no slope at all), and two lines are perpendicular if the product of their slopes is -1. To determine if lines are parallel or perpendicular, you can find their slopes and check if they are equal or if the product of their slopes is -1.

The first line y-1/7x-2 can be rewritten in slope-intercept form y = mx + b as y = 1/7x + 2

The second line x-7y=4 can be rewritten in slope-intercept form y = mx + b as y = x/7 - 4/7

The slopes of the two lines are 1/7 and -1/7 respectively. The product of the slopes of two lines is 1/49 which is not -1, that means that the two lines are not perpendicular. Also, the slopes are not equal, which means that the lines are not parallel.

Therefore, the two lines y-1/7x-2 & x-7y=4 are intersecting but not parallel or perpendicular lines.

Answer:

Bacteria Growth The number N of bacteria in culture is modeled by N= 250e^kt where t is the time in hours. If N = 280 when t= 10, estimate the time required for the population to double in size.

Step-by-step explanation:

(⁠◔⁠‿⁠◔⁠)(⁠◔⁠‿⁠◔⁠)(⁠◔⁠‿⁠◔⁠)

The ratio of a to d can be expressed by multiplying the ratio of a to b, b to c, and c to d. Therefore, a to d = (a to b) x (b to c) x (c to d).

The ratio of a to d can be determined by using the given ratio of a to b, b to c, and c to d. To begin, the ratio of a to b can be expressed as a:b, the ratio of b to c can be expressed as b:c, and the ratio of c to d can be expressed as c:d. Then, the ratio of a to d can be determined by multiplying the ratios of a to b, b to c, and c to d. This can be written as (a:b) x (b:c) x (c:d). Therefore, the ratio of a to d can be expressed as (a:b) x (b:c) x (c:d). For example, if the ratio of a to b is 2:3, the ratio of b to c is 4:5, and the ratio of c to d is 6:7, then the ratio of a to d would be (2:3) x (4:5) x (6:7) or 24:35.

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The dollar is weakening in comparison to the euro, making European goods more expensive for Americans. American consumers must spend more to purchase the same amount of goods from Europe.

When the dollar price of the euro increases from $1.50 to $2.00, it means that the euro has strengthened relative to the dollar. This means that the dollar has weakened in comparison to the euro. This weakened dollar results in American consumers needing to spend more to purchase European goods. As the dollar price of the euro increases, it takes more dollars to purchase the same amount of euros, meaning the same amount of goods from Europe will cost more dollars. This means that European goods become more expensive to Americans as the dollar price of the euro increases. This is a result of the weakened dollar and the strengthened euro in comparison to each other.

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The meaning of the y-intercept of the linear function is given as follows:

The tablet starts with 40 percent of battery remaining.

The two most important features of a linear function are the slope and the intercept, and their meaning is explained as follows:

When x = 0, y = 40, hence the intercept of this function is of 40, representing the initial value of 40 of the percentage of battery remaining.

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The surface area of the cuboid is 94 m² while The surface area of the triangular pyramid is 259.695 in²

An equation is an expression showing the relationship between numbers and variables.

Surface area is the sum of each area of the solid surface.

7) For the cuboid:

Surface area = 2(3 m * 4 m) + 2(3 m * 5 m) * 2(4 m * 5 m) = 94 m²

The surface area of the cuboid is 94 m²

8) For the triangular pyramid:

Surface area = 3(1/2 * 17.4 in * 8.7 in) + (1/2 * 8.7 in * 7.5 in) = 259.695 in²

The surface area of the triangular pyramid is 259.695 in²

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1. Yes, this is a binomial distribution.

2. n = 200, p = 0.25.

3. The mean of X is 50. This means that we can expect to get 50 cherry flavored Starburst candies on average.

4. The standard deviation of X is 7.07. This means that the number of cherry flavored candies is likely to be close to the mean of 50, but it could vary by up to 7.07 in either direction.

5. The probability of getting exactly 60 cherry flavored Starburst is 0.108.

6. The probability of getting at most 60 cherry flavored Starburst is 0.619.

A bag of Starburst candies can be considered an SRS of the whole population of Starburst candies since there are 4 flavors. The probability that each Starburst is cherry flavor is 0.25. Since we are buying one bag of Starburst, the number of cherry flavored candies in the bag can be represented by a binomial distribution with n = 200 and p = 0.25. This means that the mean of X (the number of cherry flavored candies) is 50. The standard deviation of X is 7.07, which means that the number of cherry flavored candies is likely to be close to the mean of 50, but could vary by up to 7.07 in either direction. The probability of getting exactly 60 cherry flavored Starburst is 0.108, and the probability of getting at most 60 cherry flavored Starburst is 0.619.

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The required expression is 4w4w² or Aw.Bw².

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

An expression,

16w³.

To write an answer in the form A or AB, where A and B are constants or variable expressions that have no variables in common:

16w³,

= 4w 4w²

Where A = 4 and B = 4.

So, 16w³ = Aw.Bw².

Therefore, the expression is 4w4w² or Aw.Bw².

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Answer:

-9,-6,6,12

Step-by-step explanation:

The dimensions that maximize the area of the window are:

[tex]$P=2 h+w+\frac{\pi \cdot w}{2}=30$[/tex]

[tex]$2 h+(1+0.5 \pi) w=30$[/tex]

[tex]$h=\frac{30-(1+0.5 \pi) w}{2}=15-(0.5+0.25 \pi) w$[/tex]

With the restriction for the perimeter [tex]$(\mathrm{P}=30)$[/tex], we can express h in function of w. Now, we can express the area only in function of w and maximize its value:

[tex]& A=A_c / 2+A_r=\frac{1}{2} \cdot \frac{\pi w^2}{4}+h w=\frac{\pi w^2}{8}+\left[15-\left(\frac{1}{2}+\frac{\pi}{4}\right) w\right] \cdot w \\[/tex]

[tex]& A=15 w-\left(\frac{1}{2}+\frac{\pi}{4}-\frac{\pi}{8}\right) w^2=15 w-\left(\frac{1}{2}+\frac{\pi}{8}\right) w^2[/tex]

To maximize the area, we derive and equal to 0 :

[tex]$\frac{d A}{d w}=15(1)-\left(\frac{1}{2}+\frac{\pi}{8}\right)(2 w)=0$[/tex]

[tex]$$15-(1+\pi / 4) w=0$$[/tex]

[tex]$w=\frac{15}{1+\pi / 4} \approx 8.4$[/tex]

Now, we can calculate the height as:

[tex]$$h=15-(0.5+0.25 \pi) w$$[/tex]

[tex]$$h \approx 15-(1.2854) \cdot 8.4=15-10.8=4.2$$[/tex]

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Triangles that are congruent have the same size and form.Triangle HGK is congruent to triangle KHJ.

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Triangle HGK is congruent to triangle KHJ if in triangles HGK and KHJ, angle H = angle G, angle H = angle J, and angle HG = HK and GK = KJ

Triangles that are congruent have the same size and form.

Three pairs of matching sides are equivalent in two triangles according to the Side-Side-Side (SSS) Theorem.

Side-Angle-Side (SAS) Theorem: Two triangles have two pairs of matching sides and two pairs of corresponding angles that are congruent.

The triangles are congruent if their included sides are congruent and two of their angles match two of the other triangle's angles. Using labels:

Triangle HGK is congruent to triangle KHJ if in triangles HGK and KHJ, angle H = angle G, angle H = angle J, and angle

HG = HK and GK = KJ

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The amount of money gives to my friend today so that the repayment of $500 in 2 weeks is equivalent to a simple interest loan with a rate of 153% per year is,  $477.10

Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).

Every time we calculate simple interest the principal values will be the same unlike compound interest.

Formula;    Simple Interest(I) =  P × R × T/100

Given that,

Loan agreed on simple interest rate =  153% per year

He knows that he can pay me back $500 in 2 weeks or 2/52 years

Suppose, money given to him = P

So, simple interest of amount P in 2 weeks

I   = P × 125 ×(2/52) /100

   = 0.048P

Total repayment = P + 0.048P

He can pay back only $500

Total repayment = $500

P + 0.048P         = $500

1.048P = 500

P       =    477.10

Hence, the loan amount is  $477.10

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The measure of an angle which is 5 times its supplement is 150.

Supplementary Angles. When the sum of the measures of two angles is 180 then the angles are called supplementary angles. When two angles are supplementary, each angle is said to be the supplement of the other.

thus, x and y two angle which sum is 180 then x and y supplement to each other.

According to the problem,

The measure of an angle which is 5 times its supplement.

Supplementary angles means , sum of angles is 180.

⟹x=5(180 −x)

⟹x=5×180 −5x

⟹6x=5×180

⟹x=5×30

       =150

Hence, x=150

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Answer:

h = 40 cm

Step-by-step explanation:

1. Let's calculate the total volume of 1920 cubes, size 5 x 5 x 5 cm:

V one =  5 cm x 5 cm x 5 cm = 125 cm³
V all = 1920 x 125 = 240,000 cm³

2. Divide this volume by the area of the paper to get the height, given that 1 m = 100 cm:

S paper = 100 cm x 60 cm = 6,000 cm²

h = V all / S paper = 240,000 / 6,000 = 40 cm

Function Table:

x f(x)

0 1

1 3

2 5

3 7

4 9

5 11

6 13

7 15

8 17

9 19

And so on, f(x) will always be 2x + 1.

Answer: 0.002. 0.127 - 0.125 is 0.002