find the surface area of the trapezoid

To prove that opposite sides of a quadrilateral are parallel, you have to show that the slopes of both sides are the same.

Slope is a measure of how steep a line is, and it can be found by calculating the ratio of the change in the y-coordinate to the change in the x-coordinate between two points on the line.

If two sides of a quadrilateral have the same slope, then they must be parallel because parallel lines have the same slope. Conversely, if two sides of a quadrilateral are parallel, then they must have the same slope. Therefore, by showing that the slopes of two sides of a quadrilateral are equal, you can prove that they are parallel, and hence, opposite sides of the quadrilateral are parallel.

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Answer:

y = mx + b

Step-by-step explanation:

Answer: The quadrilateral is not a parallelogram.

Step-by-step explanation:

Slope of any line = (Change in y)/(Change in x)

Slope of LM = (9-6)/(5-(-1)) = 3/6 = 1/2

Slope of LN = (2-6)/(0-(-1)) = -4/1 = -4

Slope of LP = (-2-6)/(-8-(-1)) = -8/-7 = 8/7

Slope of MN = (2-9)/(0-5) = -7/-5 = 7/5

Slope of MP = (-2-9)/(-8-5) = -11/-13 = 11/13

Slope of NP = (-2-2)/(-8-0) = -4/-8 = 1/2

Since slopes of LM and NP are the same, they are parallel lines.

Parallelograms have two sets of parallel lines. However, there only exists one set of parallel lines for this quadrilateral. Thus, this quadrilateral is not a parallelogram.

Answer:

-563

Step-by-step explanation:

a = -7 , b = 9 , c = 4

9ab +C

9 × -7 × 9 + 4

81 × -7 + 4

-567 + 4

-563

The completed table in tabular form

X    Y

0    -3

1 -1

2 1

3 3

To complete the table for the equation y = 2x - 3, we can substitute the given x values into the equation to find the corresponding y values.

X value. 0. 1. 2. 3

by substituting x = 0 into the equation y = 2x - 3, we get:

y = 2(0) - 3

y = -3

by substituting x = 1 into the equation y = 2x - 3, we get:

y = 2(1) - 3

y = -1

by substituting x = 2 into the equation y = 2x - 3, we get:

y = 2(2) - 3

y = 1

by substituting x = 3 into the equation y = 2x - 3, we get:

y = 2(3) - 3

y = 3

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complete question

Complete the table for the equation y = 2x - 3

X value. 0. 1. 2. 3

Y value.

Given:

In a right angle triangle θ is an acute angle and \(\tan\theta =\dfrac{3}{5}\).

To find:

The value of \(\cos \theta\).

Solution:

In a right angle triangle,

\(\tan \theta=\dfrac{Perpendicular}{Base}\)

We have,

\(\tan\theta =\dfrac{3}{5}\)

It means the ratio of perpendicular to base is 3:5. Let 3x be the perpendicular and 5x be the base.

By using Pythagoras theorem,

\(Hypotenuse=\sqrt{Perpendicular^2+base^2}\)

\(Hypotenuse=\sqrt{(3x)^2+(5x)^2}\)

\(Hypotenuse=\sqrt{9x^2+25x^2}\)

\(Hypotenuse=\sqrt{34x^2}\)

\(Hypotenuse=x\sqrt{34}\)

In a right angle triangle,

\(\cos \theta=\dfrac{Base}{Hypotenuse}\)

\(\cos \theta=\dfrac{5x}{x\sqrt{34}}\)

\(\cos \theta=\dfrac{5}{\sqrt{34}}\)

Therefore, the value of \(\cos \theta\) is \(\dfrac{5}{\sqrt{34}}\).

Answer:

6.

Step-by-step explanation:

To round 5.955 to the nearest tenth consider the hundredths’ value of 5.955, which is 5 and equal or more than 5. Therefore, the tenths value of 5.955 increases by 1 to 0.

Answer:

6.0

Step-by-step explanation:

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Answer:

4

0+0+0+5+6=7+10 = 28

28 divided by 7 is 4

To find mean you need to add up all the numbers then divided them by the total number of numbers there are. 0+0+0+5+6=7+10 has 7 numbers so I divided 28 by 7.

Brainliest?

The required requirement of the density curve is should be equal to 1 and the ordinate should not be zero.

Given that,
Two requirements of a density curve are to be determined.

A density curve is defined as a curve on a graph that represents the distribution of values in a dataset.

Here,

The two requirements of a density curve should be,

a. The area under the density curve should be equal to 1.

b. The ordinate of the curve should not be zero i.e. they should always have the vertical height.

Thus, the required requirement of the density curve is mentioned above.

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a)The value of f f(5) is  6

b) The third derivative of the Taylor polynomial is  -5

c)  The value of f(5.1) using the Taylor polynomial is T₄(5.1) ≈ 5.8252

d) The value of f'(4.9) using the Taylor polynomial T₄ is f'(4.9) ≈ -5.158

a) To find the value of f(5), we need to look at the constant term in the Taylor polynomial T₄(x). We see that the constant term is 6, so f(5) = 6.

b) The third derivative of T₄(x) is -30(x-5), which means that the third derivative evaluated at x = 5 is -30(0) = 0. This means that the correct choice is 3. f ⁽³⁾(5) = 30.

c) To estimate f(5.1) using T₄(x), we plug in x = 5.1 into the expression for T₄(x) and simplify. The calculation is as follows:

T₄(5.1) = 6 − 4(0.1) + 3(0.1)² − 5(0.1)³ + 2(0.1)⁴

= 6 - 0.4 + 0.03 - 0.0005 + 0.00008

= 5.6252 (rounded to four decimal places)

Therefore, the correct choice is 5. f(5.1) ≈ 5.6252.

d) To estimate f'(4.9) using T₄(x), we need to differentiate T₄(x) and evaluate the derivative at x = 4.9. The derivative of T₄(x) is as follows:

T'₄(x) = -4 + 6(x-5) - 15(x-5)² + 8(x-5)³

To evaluate T'₄(4.9), we substitute x = 4.9 into the expression for T'₄(x) and simplify:

T'₄(4.9) = -4 + 6(4.9 - 5) - 15(4.9 - 5)² + 8(4.9 - 5)³

= -4 - 0.6 + 0.25 - 0.008

= -5.158

Therefore, the correct choice is 1. f'(4.9) ≈ -5.158.

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Answer:

b

Step-by-step explanation:

Answer:

I did this. But there's only 5 points . But it's ok

Answer:

what is the full number supposed to be when you add the a and b together?

The center of mass of the region R, bounded by the graphs of

\(f(x) = sin x\) and \(g(x) = cos x\)over the interval [**, ], is (x,y) = (π/4, 0.8540). This can be calculated by taking the area-weighted average of the region's two boundaries.

The area of R can be calculated using the formula: A = \(∫f(x) - g(x)dx.\) Then, the x-coordinate of the center of mass is calculated using the formula: x = \((1/A) * ∫x * [f(x) - g(x)]dx.\)

Finally, the y-coordinate of the center of mass is calculated using the formula:

y = \((1/A) * ∫y * [f(x) - g(x)]dx\). With the given boundary equations and constant density d, the center of mass can be determined to be (x,y) = (π/4, 0.8540).

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Answer:

24

Step-by-step explanation:

i quessed

Supercomputers are the most powerful computers at any given time, but are built especially for assignments that require arithmetic speed.

The supercomputers, which are the most advanced and high-performance computers available, are specifically constructed to handle assignments that demand rapid arithmetic processing.

These machines are optimized for executing complex mathematical operations and simulations, enabling them to tackle problems that require immense computational power.

By harnessing parallel processing, massive memory capacities, and specialized architectures, supercomputers excel in solving scientific, engineering, and research challenges that necessitate exceptional arithmetic speed.

Their capabilities contribute to advancements in various fields, including weather forecasting, molecular modeling, astrophysics, and cryptography.

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Step-by-step explanation:

can u type ur question in english?

Answer:157/10

Step-by-step explanation:

Make 15 into an improper fraction (every number is a fraction over 1) so multiply the numerator(15) and the denominator(1) by 10 to get 150/10 then add 150/10 to 7/10 to get 157/10

Answer:

\(\frac{157}{10}\)

Step-by-step explanation:

Step 1

Multiply the denominator by the whole number

10 × 15 = 150

Step 2

Add the answer from Step 1 to the numerator

150 + 7 = 157

Step 3

Write answer from Step 2 over the denominator \(\frac{157}{10}\)

Answer:

x=-15

Step-by-step explanation:

Answer:

1 solution

Step-by-step explanation:

2x-7+3x+8

add 7 to both sides

2x=3x+15

subtract 3x from both sides

-1x=15

divide both sides by -1

x=-15

Step-by-step explanation:

3/2(4x-1)-3x = 5/4-(x+2)

6x -3/2 -3x = 5/4 -x -2

3x -3/2 = 5/4-2-x

4x=5/4 -2 +3/2

4x= (5-8+6)/4

4x=3/4

x=3/16

For

Example 1: Pair of lines are parallel.

Example 2: Pair of lines are perpendicular.

Example 3: Pair of lines are not parallel nor perpendicular.

Example 4: Pair of lines are perpendicular.

Example 5: Pair of lines are parallel.

Example 6: Pair of lines are parallel.

Example 7: Pair of lines are perpendicular.

Example 8:  Pair of lines are not parallel nor perpendicular.

What is the slope of the line in the slope-intercept form of the line?

If y = mx + c line is given then 'm' represents the slope of the line. If any pair of lines are given and if they have the same value of the slopes then we can say that the given pair of lines will be parallel in nature and if the slope of the one line is the negative inverse of the other line then we can say that the pair of lines are perpendicular to each other.

For example 1:

      y = 3x + 4 and y = 3x +7

     The slopes of both lines are equal hence, these pair of lines are parallel.

For example 2:

     y = -4x + 1 and 4y = x + 3

    Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.

For example 3:

     y = 2x - 5 and y = 5x -5

   In this, the slopes are not equal so we can say that the graph of this pair of equations is not parallel nor perpendicular.

For example 4:

     y = -1/3x + 2 and y = 3x - 5

     Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.

For example 5:

     y = 3/5x - 3 and 5y = 3x - 10

    The slopes of both lines are equal hence, these pair of lines are parallel.

For example 6:

     y = 4 and 4y = 6

     The slopes of both lines are equal hence, these pair of lines are parallel.

For example 7:

     y = 7x + 2 and x + 7y = 8

     Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.

For example 8:

     y = 5/6x - 6 and x + 5y = 4

    In this, the slopes are not equal so we can say that the graph of this pair of equations is not parallel nor perpendicular.

Hence,

Example 1: Pair of lines are parallel.

Example 2: Pair of lines are perpendicular.

Example 3: Pair of lines are not parallel nor perpendicular.

Example 4: Pair of lines are perpendicular.

Example 5: Pair of lines are parallel.

Example 6: Pair of lines are parallel.

Example 7: Pair of lines are perpendicular.

Example 8:  Pair of lines are not parallel nor perpendicular.

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Answer:

i dont see the question

Step-by-step explanation:

Rex's bike distance in kilometers is calculated to be 104.65 kilometers

Given that:

rex rides his bike for 13 miles each day for 5 days

1 mile = 1.61 kilometers

Rex's total ride in five days

13 miles * 5 days = 65miles

1 mile = 1.61 kilometers

65 miles = ? kilometers

cross multiply gives

? kilometers * 1 mile = 1.61 kilometers * 65 miles

? kilometers = 106.65 kilometers

Hence the unknown distance in kilometers represented as ? is solved to be 106.65 kilometers to the nearest hundredth

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Answer:

b 104.65

Step-by-step explanation:

i did the exam

The length of side BD which is the altitude of the triangle is 2√(70)

The length of BD is solved using similar triangles. This is defined by triangles formed from triangle ABC and they include

Let the altitude be h, hence we have the formula of the proportions as

AD / h = h / DC

plugging the values gives

20 / h = h / 14

h^2 = 20 * 14

h = √(20 * 14 )

h = √(280)

h = 2√(70)

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Answer:

The system has one solution,

Both lines have the same y-intercept,

The solution is the intersection of the 2 lines.

Step-by-step explanation:

Answer:

$196

Step-by-step explanation:

Step one

given data

We are told that Noel bought a printer for $10 less than half its original price

let the original price be x

hence Noel paid  =  x/2-10= 88

Step two

amount paid=   x/2-10= 88

Collect like terms

 x/2= 88+10

x/2= 98

cross multiply

x=196

Hence the original price is $196

Answer:

Centroid

Step-by-step explanation:

is it right please  tell me down below thank you

To solve for y as a function of u, we can use the equation: /" - 114" + 24y = 0.

First, we need to isolate y on one side of the equation. Adding 114 to both sides, we get:

24y = 114 - /"

Then, dividing both sides by 24, we get:

y = (114 - /") / 24

Now, we need to use the initial conditions to find the value of y at u = 0. We have:

y(0) = 3
7(0) = 3
7'(0) = 6

Substituting u = 0 into our equation for y, we get:

y(0) = (114 - /") / 24 = 3

Solving for /", we get:

114 - /" = 72

/" = 42

So our equation for y becomes:

y = (42 / 24)u + 3

Simplifying, we get:

y = (7 / 4)u + 3

Therefore, y is a function of u given by y = (7 / 4)u + 3, with initial conditions y(0) = 3, 7(0) = 3, and 7'(0) = 6.

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