A right triangle has legs measuring 20 in. and 28 in. what is the length of the hypotenuse? round to the nearest tenth. responses 8.0 in. 8.0 in. 19.6 in. 19.6 in. 34.4 in. 34.4 in. 1184.0 in.

The slope of segment EF and AB is same but the length of segment EF is half of the length of segment AB.

What is Line segment ?

An unmoving portion of a line is called a line segment. Two points serve as its ends. By the termination points, it is identified.

Let's assume the length of EF to be "x"

from the figure, we can clearly see that AB is made up of two segments which are of same length as EF.

So, we can say that AB = 2 times of the length of EF

i.e. AB = 2 x

Hence, By comparing, we conclude that AB's length is double of EF.

Now, if we look at slope,

Slope of EF = CE/CF

and, Slope of AB = BC/AC

But, we know that AC = 2 CF and BC = 2 CE

So, Slope of  EF = CE/CF

and, Slope of AB = 2 CE / 2 CF

                             = CE/CF.

Hence, Both segments have same slope direction.

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The equation 5x + 6y = 4, 10x + 12y = 8 has infinitely many solution.

System of equation can be solved using elimination method, substitution method and graphical method.

Therefore, let's solve the system of equation using elimination method.

5x + 6y = 4

10x + 12y = 8

multiply equation(i) by 2

Hence,

10x + 12y = 8

10x + 12y = 8

subtract the equations

0 = 0

Therefore, the equation has infinitely many solution.

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Answer:

see explanation

Step-by-step explanation:

given sinΘ = - [tex]\frac{3}{5}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]

the negative sign indicates sinΘ is in the third quadrant where sinΘ < 0

this is a 3- 4- 5 right triangle with opposite = 3 and hypotenuse = 5

then the adjacent side = 4

cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = - [tex]\frac{4}{5}[/tex] ( since cosΘ < 0 in third quadrant )

secΘ = [tex]\frac{1}{cos0}[/tex] = [tex]\frac{1}{-\frac{4}{5} }[/tex] = - [tex]\frac{5}{4}[/tex]

tanΘ

= [tex]\frac{sin0}{cos0}[/tex]

= [tex]\frac{-\frac{3}{5} }{-\frac{4}{5} }[/tex]

= - [tex]\frac{3}{5}[/tex] × - [tex]\frac{5}{4}[/tex]

= [tex]\frac{3}{4}[/tex]

Answer:

$1.89/gal

Step-by-step explanation:

The average rate of change of f(x) over the interval 3≤x≤4 is 15

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

The table of values

On the table, we have

f(3) = -4

f(4) = 11

The average rate is then calculated as

Average rate = [f(4) - f(3)]/[4 - 3]

Substitute the known values in the above equation, so, we have the following representation

Average rate = (11 + 4)/(4 - 3)

Evaluate

Average rate = 15

Hence, the average rate is 15

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Complete question

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3\le x \le 43≤x≤4.

X f(x)

3 -4

4 11

5 8

6 10

7 11

8 14

Answer:

[tex]\frac{y^2}{4x^5}[/tex]

Step-by-step explanation:

Used Exponents Properties :

[tex]\blacksquare \left( a\times b\right)^{n} =a^{n}\times b^{n}\\\blacksquare \left( a^{n}\right)^{m} =a^{n\times m}\\\blacksquare \left( \frac{a}{b} \right)^{n} =\frac{a^{n}}{b^{n}}[/tex]

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

[tex]\begin{aligned}\left(\frac{256 \times x^{20}}{y^8}\right)^{-\frac{1}{4}} & =\left(\frac{y^8}{2^8 \times x^{20}}\right)^{\frac{1}{4}} \\& =\frac{\left(y^8\right)^{\frac{1}{4}}}{\left(2^8 \times x^{20}\right)^{\frac{1}{4}}} \\& =\frac{y^{8 \times \frac{1}{4}}}{\left(2^8\right)^{\frac{1}{4}} \times\left(x^{20}\right)^{\frac{1}{4}}} \\& =\frac{y^{\frac{8}{4}}}{2^{\frac{8}{4}} \times x^{\frac{20}{4}}} \\& =\frac{y^2}{2^2 x^5}\\& =\frac{y^2}{4 x^5}\end{aligned}[/tex]

Answer:

The equation of the line of symmetry of triangle ABC is:

Step-by-step explanation:

The line of symmetry of an isosceles triangle bisects the vertex angle (the angle opposite the base) and is perpendicular to the base of the triangle.

As AB = AC, then angle A is the vertex angle of the isosceles triangle ABC.

If B and C lie on the line with equation 3y = 2x + 12, then the line of symmetry is the line that is perpendicular to this line and passes through A (4, 37).

Rearrange the given equation 3y = 2x + 12 to slope-intercept form by dividing both sides by 3:

[tex]\implies y=\dfrac{2}{3}x+4[/tex]

Perpendicular lines have slopes that are negative reciprocals of one another.  Therefore, the slope of the perpendicular line is -³/₂.

Substitute the found slope and point A (4, 37) into the point-slope formula:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-37=-\dfrac{3}{2}(x-4)[/tex]

Rearrange the equation to standard form:

[tex]\implies 2y-74=-3(x-4)[/tex]

[tex]\implies 2y-74=-3x+12[/tex]

[tex]\implies 3x+2y-74=12[/tex]

[tex]\implies 3x+2y=86[/tex]

Therefore, the equation of the line of symmetry of triangle ABC is:

The hare can afford to nap for approximately 3686.33 seconds if he does not want to lose the race.

We can use the time it takes the hare to run 100 m to determine how long he can afford to nap.

First, let's find the time it takes the hare to run the 100 m:

t = d / v

Where t is the time, d is the distance, and v is the velocity (speed) of the hare.

t = 100 m / 15 m/s

t = 6.67 s

Next, let's find the time it takes the tortoise to run 1 km (1000 m):

t = d / v

Where t is the time, d is the distance, and v is the velocity (speed) of the tortoise.

t = 1000 m / 0.27 m/s

t = 3700 s

So, the time it takes the tortoise to run the race is 3700 s. The time it takes the hare to run the first 900 m is 7 s. Therefore, the time the hare has left to nap is:

3700 s - 7 s = 3693 s

And the time it takes the hare to run the last 100 m is 6.67 s. Therefore, the hare can afford to nap for:

3693 s - 6.67 s = 3686.33 s

So, the hare can afford to nap for approximately 3686.33 seconds if he does not want to lose the race.

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At its earliest stages, a logistic growth curve closely resembles an exponential growth curve - True

It is true that at its earliest stages, a logistic growth curve closely resembles an exponential growth curve.

The logistic growth curve shows the logistic population growth rate, the logistic growth curve on a line graph is similar to a S-shaped and it's observed that there is a slow increase, rapid population growth, and finally, the reduction in the growth.

On the other hand, the exponential growth curve is a J-shaped curve that shows us that there is a rapid and consistent or steady growth in the population over the duration of a specific period.

It could be said that an exponential growth curve is opposite of a slow and steady success.

Both the curve start along with the same pattern but with time gradually change their constrain over the graph.

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Approximately 70 miles separated Harold's home at his grandparents' home from his own home. Accordingly, Harold travelled the following distance overall on his birthday: 70 + 74.46 + 70 ≈ 214.46

What is a distance? . Regardless of the start or end point, distance can be defined as the amount of space object has to cover.

The metre serves as the SI unit of distance (m). Centimeters (cm) are a common unit of measurement for short distances, whereas kilometres (km) are used for longer distances (km). You could measure a piece of paper's length in centimetres, for instance, by measuring from the bottom to the top.

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The correct option is a. The equation used to find Vanessa's age is v + 2 = 32.

A mathematical statement known as an equation utilises the equals sign to demonstrate the equality of two expressions. It may be used to address a variety of issues and can contain both numbers and variables. Algebraic operations including addition, subtraction, multiplication, division, and exponentiation are frequently used in equations.

In the given question, Vanessa's age may be calculated using the equation a. v+2=32. This equation shows that Vanessa's age plus 2 equals 32, implying that Vanessa's age is 30. We may solve this equation by removing 2 from both sides, yielding v=30. This equation is valid for determining Vanessa's age because it specifies that Vanessa's age plus Monique's age equals 32.

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Answer:

83%

Step-by-step explanation:

To find the percentage divide 40 by 48

40/48 = 0.83333333333333

Round to 0.83

Multiply by 100

The patient has only eaten 83% of her daily intake.

Answer:

2x(5x+7)

Step-by-step explanation:

[tex]x^2+2x^2+14x+7x^2\\=10x^2+14x\\=2x(5x+7)[/tex]

The primary tool or measure for determining whether the assumed regression model is appropriate is the residual plot.

A residual plot is a graph that shows the residuals, or the differences between the observed values and the predicted values from the regression model, plotted against the predictor variable(s). If the residuals are randomly scattered around zero, with no discernible pattern, then the regression model is a good fit for the data.

However, if there is a pattern in the residuals, such as a curved or U-shaped relationship, then the regression model may not be appropriate and a different model may need to be considered.

In addition to the residual plot, other measures such as the coefficient of determination (R-squared), the p-values of the regression coefficients, and the normality of the residuals can also be used to evaluate the goodness of fit of a regression model.

However, the residual plot is often considered the primary tool for assessing the adequacy of a regression model.

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The largest square that Mr. Stanley can use to plant in his farm is a square with a side length of 8 meters.

To find the greatest common factor of 24 and 40, we can list the factors of both numbers and find the highest factor that they have in common:

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

The highest factor that 24 and 40 have in common is 8.

Factors are numbers that can be multiplied together to get a given number. For example, the factors of 6 are 1, 2, 3, and 6 because 1 x 6 = 6 and 2 x 3 = 6. Factors can be prime or composite. Prime factors are those that are only divisible by 1 and themselves. Composite factors are those that have more than two factors.

Factors are important in math because they can be used to simplify fractions, find common denominators, and solve equations. They also play a crucial role in number theory and cryptography, where they are used to encrypt and decrypt messages. 150 is a composite number, which means it has factors other than 1 and itself. The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150. To find these factors, you can divide 150 by each number smaller than it and see if the remainder is 0.

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Answer:

[tex]-\dfrac{4}{5}[/tex]

Step-by-step explanation:

We have the following expression

[tex]3 \;\dfrac{1}{2} x - 5\;\dfrac{1}{2}x[/tex]

and asked to evaluate this expression at  [tex]\[x = {2\over\displaystyle 5\][/tex]

First convert [tex]3 \; \dfrac{1}{2}[/tex]   and  [tex]5 \; \dfrac{1}{2}[/tex]  to mixed fractions

[tex]3 \; \dfrac{1}{2} = \dfrac{3 \times 2 + 1}{2} = \dfrac{7}{2}\\[/tex]

[tex]5 \; \dfrac{1}{2} = \dfrac{5 \times 2 + 1}{2} = \dfrac{11}{2}[/tex]

Therefore
[tex]3 \;\dfrac{1}{2} x - 5\;\dfrac{1}{2}x\\\\= \dfrac{7}{2}x - \dfrac{11}{2}x\\\\= \dfrac{7 - 11}{2} x\\\\= -\dfrac{4}{2}x \\\\= -2x\\\\[/tex]

[tex]\mathrm{For \;x =\dfrac{2}{5}},\\\\= -2x \\= - 2 \times \dfrac{2}{5}\\\\= -\dfrac{4}{5}[/tex]

The angle that the ladder makes with the ground is ∠B = 67.38°.

The distance between the ladder from the building is 5 feet.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Given that a 13-foot ladder is placed up against a wall.

The ladder's top touches the wall at a height of 12 feet.

As per the given question, we have the right triangle ΔABC

Using sine ratio to find angle ∠B as:

sin ∠B = AC/ AB

sin ∠B = 12/13

∠B = sin ⁻¹(12/13)

∠B = 67.38°

Now, using Pythagoras's theorem to find distance x as:

AC² + BC² = AB²

12² + x² = 13²

144 + x² = 169

x² = 169 - 144

x² = 25

x = 5

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If there are 15000 average passengers on domestic flights daily, then 1/20 of the passengers are tourists, which means there are 15000 * (1/20) = 750 tourists daily.

And if 1/15 of the tourists are travel bloggers, then there would be 750 * (1/15) = 50 travel bloggers daily.

If there are 15000 average passengers on domestic flights daily, then 1/20 of the passengers are tourists, which means there are

15000 * (1/20) = 750 tourists daily

So, there would be a total of 50 tourist passengers on domestic flights who are travel bloggers.

It is important to note that these are average numbers and the actual number of tourists and travel bloggers on domestic flights can vary from day to day. However, this calculation provides a general idea of the proportion of tourist passengers who are travel bloggers on domestic flights.

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The division can be written as: x³ + 9x² + 12x - 5 = (x + 7)(x² + 7x + 10) - 75

What is synthetic division ?

Synthetic division is a simplified method of polynomial division that can be used to divide a polynomial by a linear binomial. It's used to find the quotient and remainder of a polynomial division without having to perform long division.

In synthetic division, the coefficients of the polynomial are arranged in a table along with the coefficients of the divisor, and then divided and multiplied using the same rules as in long division. The remainder of the division is the last entry in the table, and the quotient is the polynomial whose coefficients are the entries in the table, excluding the remainder.

To perform synthetic division, we divide x³ + 9x² + 12x - 5 by x + 7 by dividing each coefficient by x + 7 and then writing the result in a table with the dividend on top and the divisor on the bottom. Here's what the table would look like:

 + 7 |  1  9  12 -5

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

x^3  | x^3  9  12 -5

x^2  | x^2 +7x  3 -35

x    |  x +7  10 -70

   -------------------

       10  43 -75

The quotient of the division is x² + 7x + 10, and the remainder is -75.

Therefore, the division can be written as: x³ + 9x² + 12x - 5 = (x + 7)(x² + 7x + 10) - 75

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Answer:

8

Step-by-step explanation:

8x3 = 24

24 + 4 = 28

The dimensions are 5 units each

The area of the rectangle is 25 units

It is important to note that algebraic expressions are defined as expressions that are composed of variables, terms, cofficients, constants and factors.

They are also described as expressions with mathematical operations.

From the information given, we have that;

x² - 5x + 3x - 15

To solve the quadratic equation, let us use the factorization method

Group the values in pairs

(x² - 5x) + (3x - 15)

factor the terms

x(x -5) +3(x - 5)

Then, x + 3 = 0

x = -3

And x - 5 = 0

x =5

But area of a rectangle is;

= Length× width

= 5 × 5

= 25 square units

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(a) The number of possible schedules that the student can create from the offerings is 96.

(b) the number of possible schedules that the student can create from the offerings if two of the math 100 sections are closed is 48.

(c) the number of possible schedules that the student can create from the offerings if two of the math 100 sections and four of the English 105 sections are closed is 4.

(a) To find the total number of possible schedules, we need to multiply the number of choices for each class:

Number of schedules = 4 x 2 x 3 x 4 = 96

So, there are 96 possible schedules that the student can create from the offerings.

(b) If two of the math 100 sections are closed, then there are only two choices for that class. So, we have:

Number of schedules = 2 x 2 x 3 x 4 = 48

So, there are 48 possible schedules that the student can create from the offerings with two of the math 100 sections closed.

(c) If two of the math 100 sections and four of the English 105 sections are closed, then there are only two choices for math 100 and one choice for English 105. So, we have:

Number of schedules = 2 x 2 x 1 x 1 = 4

So, there are 4 possible schedules that the student can create from the offerings with two of the math 100 sections and four of the English 105 sections closed.

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The equation will be:

t = b - 2

And we can see that:

Here we have two variables:

t = taner's age

b = age of Tanner's brother.

The independent variable is the one that does not depend on the other, in this case (for how it is worded) is the brother's age.

The dependent variable depends on the other, on this case, Tanner's age.

Now let's write the equation, we know that Taner's age is 2 years less than his brother, then:

t = b - 2

That is the equation.

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Answer:

Remainder:

Step-by-step explanation:

Step 1: Divide 5843 by 11.

5843/11 = 530.272727

Step 2: Find the quotient.

Quotient = 530

Step 3: Find the remainder.

Remainder = 3

The probability of randomly selected patient selected for coronary, oncology or both is equal to P( H∪C ) = 0.24.

Let patient admitted with heart disease represented by P(H)

P(H) = 12%

       = 0.12

And patient admitted for cancer disease represented by P(C)

P(H) = 16%

       = 0.16

Percent of patient received both coronary and oncology = 4%

P( H∩C ) = 0.04

Probability of randomly selected patient admitted for coronary, oncology or both is :

P( H∪C ) = P(H) + P(C) - P(H∩C )

⇒P( H∪C ) = 0.12 + 0.16 - 0.04

⇒ P( H∪C ) = 0.24

Therefore, the probability of randomly selected patient getting treatment for coronary, oncology or both is given by  P( H∪C ) = 0.24.

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Answer:

(-x+2)(2x+1) — first option

Step-by-step explanation:

The rectangles represent an x, red means negative and yellow is positive.

The squares represent a unit (the number 1).

The diagram attached below demonstrates how this works.

Basically the top row of this tile equation is (-x + 2)And the column is (2x+1).

Expanding this makes -2x²+3x+2