Solving a rational equation that simplifies to linear: Denominat Solve for v. 6=(5)/(v-8)

The Pythagorean Theorem is proven.

The reason that we can make the statement BC/AC = CD/AC is because corresponding sides of similar triangles are proportional. This is represented by option D. Corresponding sides of similar triangles are proportional.

To complete the proof of the Pythagorean Theorem, a² + b² = c², we can use the following steps:

As similar triangles have proportional sides, we can write the proportions AB/AC = AC/BC and AB/BC = BC/AC.
By the cross-product property, AB * BC = AC * AC and AB * AC = BC * BC.
By the addition property of equality, AB² + BC² = AC² + BC².
By the segment addition postulate, AC + BC = c.
By factoring, (AC + BC)² = c².
By the distributive property, AC² + 2*AC*BC + BC² = c².
By rearranging the terms, AC² + BC² = c² - 2*AC*BC.
By substituting the values of AC and BC from the proportions in step 1, we get a² + b² = c² - 2*a*b.
By simplifying, we get a² + b² = c².

Therefore, the Pythagorean Theorem is proven.

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ABCD is the square base and A is the apex. As you can see, the apex is not directly above the center of the base, which makes this an oblique square pyramid.

An oblique square pyramid is a type of three-dimensional geometry that has a square base and four triangular faces that meet at a point, called the apex, but the apex is not directly above the center of the base. In other words, the pyramid is "tilted" or "leaning" to one side.

The key difference between an oblique square pyramid and a regular square pyramid is the location of the apex. In a regular square pyramid, the apex is directly above the center of the base, while in an oblique square pyramid, the apex is off-center.

Here is a diagram of an oblique square pyramid:

In this diagram, ABCD is the square base and A is the apex. As you can see, the apex is not directly above the center of the base, which makes this an oblique square pyramid.

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The simplified form is 3/(x+7) + 14/(x)(x+7).

Simplified form of a fraction is the form of a fraction in which the numerator and denominator are in their lowest form, or the greatest common factor has been taken out of both the numerator and denominator. For example, the fraction 24/36 can be simplified to 2/3.

To subtract the two fractions, we need to find a common denominator. The common denominator of (x+7) and (x) is (x)(x+7). We can then rewrite the two fractions with this common denominator and subtract the numerators:

(x+8)/(x+7) - (x-2)/(x) = (x+8)(x)/(x)(x+7) - (x-2)(x+7)/(x)(x+7)

= (x^2+8x)/(x^2+7x) - (x^2-2x+7x-14)/(x^2+7x)

= (x^2+8x - x^2+2x-7x+14)/(x^2+7x)

= (3x+14)/(x^2+7x)

= 3x/(x^2+7x) + 14/(x^2+7x)

= 3/(x+7) + 14/(x)(x+7)

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Part A: In this situation, a Type II error would take place if the council failed to reject the null hypothesis even if it was untrue (i.e., less than 40% of children under the age of 5 could pass a swim test).

If the researcher does not reject a null hypothesis that is actually wrong in the population, this is known as a type II error (false-negative). Notwithstanding the fact that type I and type II mistakes cannot be completely prevented, the researcher can lessen their risk by increasing the sample size.

from the question:

Part A: In this situation, a Type II error would take place if the council failed to reject the null hypothesis even if it was untrue (i.e., less than 40% of children under the age of 5 could pass a swim test). This would result in a lost chance to provide these kids with more swim safety training, perhaps placing them in danger of drowning or other swimming-related mishaps.

Part B: We are unable to reject the null hypothesis since the p-value (0.8438) exceeds the significance level (0.05). This indicates that there is insufficient information to draw the conclusion that less than 40% of children under the age of five can pass a swim test. But, since the test only looked at the alternative hypothesis that the fraction is less than 40%, we cannot draw the conclusion that it is exactly 40%.

Part C: One possible defect in the study is the use of a volunteer sample. The children who volunteered to take the swimming test may not be representative of the entire population of children under 5 in Bloomburg City. For example, parents who are more concerned about their children's swimming abilities may be more likely to volunteer their children for the test, leading to a biased sample. To obtain a more representative sample, a random sample of children under 5 could be selected from the population and asked to take the swimming test.

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The function [tex]g(x) = \frac{x}{x^2+3}[/tex] is neither even nor odd.

To determine if a function is even, we can use the following test:

f(x) = f(-x)

If this is true, then the function is even.

For the given function, [tex]g(x) = \frac{x}{x^2+3}[/tex], let's plug in -x for x and see if the function is equal to itself:

[tex]g(-x) = \frac{-x}{(-x)^2+3} = \frac{-x}{x^2+3}[/tex]

As we can see, g(x) does not equal g(-x), so the function is not even.

To determine if a function is odd, we can use the following test:

f(x) = -f(-x)

If this is true, then the function is odd.

For the given function, let's plug in -x for x and see if the function is equal to the negative of itself:

[tex]g(x) = \frac{-x}{(-x)^2+3} = \frac{-x}{x^2+3}\\\\ -g(-x) = \frac{x}{-x^2+3}[/tex]

As we can see, g(x) does not equal -g(-x), so the function is not odd.

After the algebraic analysis, we can conclude that the function g(x) is neither, i.e., it is neither even nor odd.

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Alice will receive £80 and Brian will receive £320

When dividing an amount of money in a given ratio, we need to first determine the total number of parts that the ratio is divided into.

In this case, the ratio between Alice and Brian is 1:4. This means that for every 1 unit of money that Alice receives, Brian receives 4 units of money. Therefore, the total number of parts in this ratio is 1 + 4 = 5.

To divide £400 in the ratio of 1:4, we need to find out how much of the total amount each part represents. To do this, we divide the total amount by the total number of parts:

£400 ÷ 5 = £80

So each part in this ratio represents £80.

Now that we know the value of each part, we can calculate how much Alice and Brian will receive.

Alice's share is one part, which represents £80. Therefore, Alice will receive

1 part x £80 = £80

Brian's share is four parts, which represents 4 x £80 = £320. Therefore, Brian will receive:

4 parts x £80 = £320

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Answer:

Step-by-step explanation:

sum of all angles in quadrilateral = 360

So, x+48+48+132 =360

x =132

Answer:

6(x)-5=90

Step-by-step explanation:

Move all terms that don't contain x to the right side and solve.

Exact Form:

x=95/6

Decimal Form:

x=15.83

Mixed Number Form:

x= 15 5/6

tbh i don't know if this is right

IQR difference = 5

The interquartile range (IQR) is a measure of variability that describes the spread of a set of data. It is calculated by finding the difference between the third quartile (Q3) and the first quartile (Q1) of the data.

The formula for calculating the IQR is:

IQR = Q3 - Q1

The Upper Quartile - Lower Quartile is the definition of the interquartile range.

The answer to the query is

Mount Vernon data set: 55, 60, 65, 70, 75, 80, 85 and 90

Lakewood data set = 65, 70, 75, 80 and 85

Mount Vernon median = 70+75/2 = 77.5

55+60+65+70/4 = 62.5 is the median for the lower half of the collection.

Upper half of set median: 82.5 (75, 80, 85, 90 divided by 4).

Mount Vernon's IQR is 82.5 minus 62.5, or 20.

Likewise, in the instance of Lakewood,

Average: 75

Lower half of the set median equals 65+70/2 = 67.5

Upper half of set median equals 80+85/2 = 82.5

IQR = 82.5 - 67.5 = 15

Hence, IQR difference = 20-15 = 5

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[tex]\huge\begin{array}{ccc}a_1=-2\\a_2=1\\a_3=6\\a_{10}=97\end{array}[/tex]

[tex]a_n=n^2-3[/tex]

Find the first 3 terms and the 10th term.

Substitute

n = 1, n = 2, n = 3 and n = 10:

[tex]a_1=1^2-3=1-2=-2\\\\a_2=2^2-3=4-3=1\\\\a_3=3^2-3=9-3=6\\\\a_{10}=10^2-3=100-3=97[/tex]

The following functions can be simplify as follows:

(a) f+g=x²+3x+8

(b) f-g=x²-13x-8

(c) fg=x³+3x²-40x-40

(d) f/g= (x-5)/(x+8) domain is x≠-8.

(a) To find f+g, we simply add the two functions together:

f+g=x^{2}-5x+x+8= x^{2}+3x+8

(b) To find f-g, we subtract g from f:

f-g=x^{2}-5x-(x+8)= x^{2}-6x-8= x^{2}-13x-8

(c) To find fg, we multiply the two functions together

:fg=(x^{2}-5x)(x+8)= x^{3}+3x^{2}-40x-40

(d) To find f/g, we divide f by g:

f/g= (x^{2}-5x)/(x+8)= (x-5)/(x+8)

The domain of this function is all real numbers except for -8, since dividing by zero is undefined. So the domain is x≠-8.

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When the smaller circle has a radius οf 6 cm, the area οf the shaded regiοn is 339.3 cm², rοunded tο the nearest tenth.

The cοllectiοn οf all pοints in a plane that are equally spaced frοm a specific pοint knοwn as the centre is referred tο as a circle in geοmetry. It is usually represented by a clοsed, rοunded curve in twο dimensiοns. The radius is the distance acrοss the centre οf the circle, and the diameter is the distance frοm the centre οf the circle tο any spοt οn the curve. The area encircled by a circle is determined by the fοrmula A = r2, where r is the radius. The circumference οf a circle is alsο referred tο as its edge. Circles are a key idea in geοmetry and have many uses in bοth mathematics and daily living.

given:

We must deduct the area οf the smaller circle frοm the area οf the bigger circle in οrder tο determine the area οf the shaded area.

The bigger circle has a 12 cm radius, sο the fοllοwing is its area:

A = πr² = π(12 cm) (12 cm)

A ≈ 452.39 cm²

The smaller circle has a radius οf 6 centimetres, sο the fοllοwing is its area:

A = πr² = π(6 cm) (6 cm)

A ≈ 113.1 cm²

As a result, the shaded regiοn's size is:

113.1 cm² - 339.3 cm² = 452.39 cm²

When the smaller circle has a radius οf 6 cm, the area οf the shaded regiοn is 339.3 cm², rοunded tο the nearest tenth.

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Answer:

The third one

Step-by-step explanation:

The only one which gives the last number of the sequence is the third one as subbing in 16 you get 3×16 + 3 = 48 + 3 = 51

The range of allowable values 24; can vary by 3.5% is 0.9.

The difference between the highest and lowest values for a given data set is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3.

As a result, the range can also be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.

In statistics, we must put the given values, set of data, or set of observations in ascending order in order to determine the range. That indicates that you should start by writing the observations from lowest to highest value. The formula must now be used to determine the range of observations.

24 × 3.5% =0.84

so round to nearest tenth is 0.9.

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Complete question:

Find the range of allowable values based on the given information. Round to the nearest tenth.

24; can vary by 3.5%

Answer:

20%

Step-by-step explanation:

600÷3 of 100 = 20%

600/3 of 100 = 20%

The measures of arcs and segments are

NK = 12, MLK = 41.5 degrees, JK = 24 and JPK = 277 degrees

Length NK

Given the triangle as the parameter.

Using the Pythagoras theorem, we have

NK = √(KL² - LN²)

So, we have

NK = √(15² - 9²)

Evaluate

NK = 12

The arc measure MK

Here, we start by calculating the central angle MLK

This is done using the following cosine ratio

cos(MLK) = NK/KL

cos(MLK) = 9/12

cos(MLK) = 0.75

Evaluate

MLK = 41.5 degrees

This means that

Arc MK = 41.5 degrees

Length JK

This is calculated as

JK = NK * 2

So, we have

JK = 12 * 2

JK = 24

The arc measure JPK

This is calculated as

JPK = 360 - 2 * MK

So, we have

JPK = 360 - 2 * 41.5 degrees

Evaluate

JPK = 277 degrees

Hence, the arc measure is 277 degrees

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The end behavior is as x approaches negative infinity, f(x) approaches negative infinity as x approaches positive infinity, f(x) approaches negative infinity The only x-intercept of f(x) is x = 3.

The given function is f(x) = -x³ + 2x² + 3

1. End behavior:

As the leading coefficient of f(x) is negative, -x^3 dominates the behavior of the function as x approaches negative or positive infinity. Therefore, the end behavior of the function is:

2. X-intercepts:

To find the x-intercepts of f(x), we need to solve the equation f(x) = -x^3 + 2x^2 + 3 = 0. We can factor out a common factor of -1 to simplify the equation:

-x^3 + 2x^2 + 3 = 0

x^3 - 2x^2 - 3 = 0

Using synthetic division or long division, we can find that one of the roots of this equation is x = 3. We can then factor out (x - 3) using polynomial division to find the other two roots:

x^3 - 2x^2 - 3 = (x - 3)(x^2 + x + 1)

The quadratic factor x^2 + x + 1 has no real roots, so the only x-intercept of f(x) is x = 3.

3. Positive/negative:

To determine the sign of f(x) for different values of x, we can look at the sign of each factor in the polynomial:

Putting these together, we can make the following sign chart for f(x):

x                         f(x)

x < 0                   -

0 < x < 3                  +

x > 3                  -

4. Multiplicity:

The only root of f(x) is x = 3, which has multiplicity 1. This means that the graph of f(x) crosses the x-axis at x = 3 and changes sign at that point.

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When A U B = C & A ∩ B = φ, then A = C - B. The solution has been obtained by using properties of sets.

What is a set?

In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Curly brackets are typically used to represent sets.

We know that

A - B = (A ∪ B) - B

On substituting A U B = C in this, we get

A - B = C - B       ...(1)

Similarly,

A - B = A - (A ∩ B)

On substituting  A ∩ B = φ in this, we get

A - B = A        ...(2)

From (1) and (2), we get

A = C - B

Hence, when A U B = C & A ∩ B = φ, then A = C - B.

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When a=6, the value of b is equals to -43.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, which can be simplified and evaluated.

In other words, an algebraic expression is a collection of terms and coefficients that are connected by mathematical operators.

Substitute the value of a=6 into the expression for b:

b = -1 - 7a

b = -1 - 7(6)

b = -1 - 42

b = -43

Therefore, when a=6, the value of b is -43.

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Answer:

1/2

Step-by-step explanation:

Our answer options are: 0, 1, 1/2

0 = 0/100

1 = 100/100

1/2 = 50/100

Comparing the 3 options, we see that 1/2 is the closest to 48/100!

So, the answer is 1/2

Answer: A maximum height corresponds to:

B. h(t) = 26,200 - 16t^2

A minimum height corresponds to:

C. h(t) = 6 for 7 ≤ t ≤ 8

Height staying the same corresponds to:

D. h(t) = 12 for 2 ≤ t ≤ 3

Starting height corresponds to:

A. h(0) = 7

Using the provided data, we can find the function values that correspond to the given times:

h(1.5) = 26,200 - 16(1.5)^2 = 26,157

h(4) = 16

Therefore, the statement that corresponds to "6-7" is missing from the given options.

Step-by-step explanation:

Answer:

The given function is f(x) = √(x-2) - 2.

The graph that represents this function will have the following characteristics:

The domain of the function is x ≥ 2, since the expression inside the square root must be non-negative.

The function approaches the x-axis but never touches it as x approaches positive infinity, since the square root will always be positive.

The function has a vertical asymptote at x = 2, since the expression inside the square root becomes zero at x = 2.

The function has a horizontal asymptote at y = -2, since the square root term dominates the function as x gets large, and the -2 term remains constant.

Based on these characteristics, you can compare the given graphs to see which one matches the given function.

When BD is perpendicular tο AC, the value οf x is fοund tο be 19°.

When twο lines crοss at a straight angle οr 90 degrees, perpendicular lines are created. Perpendicularity is the name given tο this characteristic οf lines. A straight line that fοrms a right angle (90 degrees) with anοther line is referred tο as being perpendicular.

In οther wοrds, twο lines are perpendicular tο οne anοther if they cοnnect at a right angle. The term "perpendicular tο all pοints in the plane" οr "perpendicular tο each line it intersects" is used tο describe a line that is perpendicular tο the plane.  Perpendicular lines always intersect at 90 degrees but nοt all intersecting lines are perpendicular.

Given a vectοr diagram.

It is given that BD is perpendicular tο AC.

m∠CBE = (5x - 42)°

m∠CBE = (2x - 1)°

Since BD is perpendicular tο AC,

m∠DBC = m∠DBA = 90°

Nοw,

m∠DBC = 90°

m∠CBE + m∠CBE = m∠DBC

Then we can write,

m∠CBE + m∠CBE =  90°

(5x - 42)° +  (2x - 1)° = 90°

7x - 43 = 90

7x = 133

x = 133 / 7 = 19°

Therefοre when BD is perpendicular tο AC, the value οf x is fοund tο be  19°.

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The number that was excluded from the 10 consecutive numbers would be = 228.

Let's take the smallest number of the 10 consecutive number to be = X

Then, the 10 consecutive numbers are x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, and x+9.

If we exclude one of these numbers, then the sum of the remaining 9 numbers would be:

(x) + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8)

Collect the like terms and add up.

= 9x + 36

Recall that the sum of the remaining 9 numbers = 2023.

That is:

= 9X + 36 = 2023

=9x = 1987

x = 221

Therefore, the smallest number in the consecutive sequence is 221, and the 10 numbers are 221, 222, 223, 224, 225, 226, 227, 228, 229, and 230.

If we exclude the number 228, then the sum of the remaining 9 numbers is 2023.

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We can conclude that the Ratio of arc = scale factor of dilation.

An arc in mathematics is a section of a circle's or curve's perimeter. An open curve is another name for it.

The circumference of a circle, sometimes referred to as its perimeter, serves as its boundary. The distance between any two locations traced along the circle of an arc is hence its length.

Given : Radius of original circle A = 3

            Radius of Dilation circle B = 9

We know that, Scale factor of dilation =

Dimension of Dilation shape / Dimension of original shape

So, Scale factor of given dilation = Radius of Circle B / Radius of Circle A

                                                      = 9/3

                                                      = 3.

Now, we know that arc of a circle can be found by using formula:

= Ф × π/180° × r

Arc of Circle A=  90 × π/180 × 3

                       = 3π/2

Arc of Circle B = 90 × π/180 × 9

                        = 9π/2

So, Ratio of arc = Arc of Circle B/Arc of Circle A

                         = 9π/2 ÷ 3π/2 = 3.

Hence, we can see that Ratio of arc = scale factor of dilation.

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The equation of the line passing through the point (8,3) that is parallel to the line y=-3/4+4 is y = (-3/4)x + 9.

The slope of the given line is -3/4. The desired line will likewise have a slope of -3/4 because it is parallel to this line.

The equation of the line travelling through the point (8,3) with a slope of -3/4 may be found using the point-slope form of a line's equation:

y - y1 = m(x - x1)

where the provided point is (x1, y1), and m is the slope.

When we change the values, we obtain:

y - 3 = (-3/4)(x - 8)

Making the right side simpler:

y - 3 = (-3/4)x + 6

To each sides, add 3:

y = (-3/4)x + 9

Hence, y = (-3/4)x + 9 is the equation of the line going through the point (8,3) that is parallel to the line y=-3/4+4.

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Answer: 9

Step-by-step explanation:

The factors of the form (x - c) are (x - 2) and (x² + 49).

To factor the polynomial f(x) = x³ - 2x² + 49x - 98 into factors of the form (x - c), we can use synthetic division with the given zero of 2.

2 | 1 -2 49 -98
  |     2  0  98
    1  0 49   0

The result of the synthetic division gives us the quotient (x² + 49) and a remainder of 0, confirming that 2 is indeed a zero of the polynomial.

Now we can write the polynomial as the product of (x - 2) and the quotient (x² + 49):

f(x) = (x - 2)(x² + 49)

Since the quadratic factor (x² + 49) cannot be factored further using real numbers, the final factorization of the polynomial is:

f(x) = (x - 2)(x² + 49)

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