Determine if the following angles are congruent. What theorem proves them to be congruent. Explain your reasoning.

Answer:

Given:

[tex]\displaystyle \int\limits_{1}^{3} x^2 \:dx[/tex]

Trapezium Rule

[tex]\displaystyle \int\limits_{a}^{b} y \:dx \approx \dfrac{1}{2}h\left[(y_0+y_n)+2(y_1+y_2+...+y_{n-1})\right] \quad \textsf{where }h=\dfrac{b-a}{n}[/tex]

Calculate the width of each strip (h).

Given:

[tex]\implies h=\dfrac{3-1}{5}=0.4[/tex]

Create a table with the x and y values:

[tex]\large\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} x & 1 & 1.4 & 1.8 & 2.2 & 2.6 & 3\\\cline{1-7} y & 1 & 1.96 & 3.24 & 4.84 & 6.76 & 9\\\cline{1-7}\end{array}[/tex]

Put all the values into the formula:

[tex]\begin{aligned}\displaystyle \int\limits_{1}^{3} x^2 \:dx & \approx \dfrac{1}{2}(0.4)\left[(1+9)+2(1.96+3.24+4.84+6.76)\right]\\& = 0.2\left[10+2(16.8)\right]\\\\& = 0.2\left[10+33.6\right]\\\\& = 0.2\left[43.6\right]\\\\& = 8.72 \end{aligned}[/tex]

[tex]\begin{aligned}\displaystyle \int\limits_{1}^{3} x^2 \:dx &=\left[\dfrac{1}{3}x^3\right]^3_1\\& = \dfrac{1}{3}(3)^3-\dfrac{1}{3}(1)^3\\& = 9-\dfrac{1}{3}\\& = \dfrac{26}{3}\end{aligned}[/tex]

The exact area as a decimal is [tex]\sf 8.\dot{6}[/tex].  Therefore, the estimated answer of 8.72 is an overestimate.

Answer to (a) = 8.72

To find the maximum possible error:

Therefore, the maximum possible error for 8.72 is 0.005.

Trapezoid Error formula

[tex]|E| \leq \dfrac{(b-a)^3}{12n^2}\left[\textsf{max}|f''(x)|\right],\quad a \leq x \leq b[/tex]

Calculate the second derivative:

[tex]f(x)=x^2[/tex]

[tex]f'(x)=2x[/tex]

[tex]f''(x)=2[/tex]

Input the values into the formula:

[tex]\implies |E| \leq \dfrac{(3-1)^3}{12n^2}(2) < 0.001[/tex]

[tex]\implies 16 \leq 0.012n^2[/tex]

[tex]\implies 36.5148...\leq n[/tex]

[tex]\implies 37\leq n[/tex]

The answer is 1.29029.

       [tex]log_{5}8=log(8)/log(5)[/tex]

       As we know, [tex]log8=0.9030899[/tex] and [tex]log(5)=0.69897000[/tex]

     So equating is the above equation, we get;

     [tex]log_{5}8=0.9030899/0.6989700[/tex]

    [tex]log_{5}8=1.292029[/tex]

Hence, The answer of [tex]log_{5}8[/tex] is [tex]1.29029[/tex].

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By using the pythagoras theorum you can find an unknown leg of right angled triangle.

Hypotenuse side is in the front of the 90 degree angle and other two sides can be taken as base and perpendicular, so formula goes as :-

(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2

H^2 = B^2 + P^2

Step-by-step explanation:

Answer:

[tex]\boxed{ \sf x=\dfrac{4\pm\sqrt{43}}{2}}[/tex]

Explanation:

[tex]\rightarrow \sf \dfrac{1}{x-5}+\dfrac{3}{x+2}=4[/tex]

make the denominators same

[tex]\rightarrow \sf \dfrac{1(x+2)}{(x-5)(x+2)}+\dfrac{3(x-5)}{(x+2)(x-5)}=4[/tex]

join the fractions together

[tex]\rightarrow \sf \dfrac{x+2+3x-15}{(x-5)(x+2)}=4[/tex]

cross multiply

[tex]\rightarrow \sf x+2+3x-15=4(x-5)(x+2)[/tex]

simplify

[tex]\rightarrow \sf 4x-13=4x^2-12x-40[/tex]

group the variables

[tex]\rightarrow \sf 4x^2-16x-27 = 0[/tex]

use quadratic formula

[tex]\rightarrow \sf x = \dfrac{-\left(-16\right)\pm \sqrt{\left(-16\right)^2-4\cdot \:4\left(-27\right)}}{2\cdot \:4}[/tex]

simplify the following

[tex]\rightarrow \sf x=\dfrac{4\pm\sqrt{43}}{2}[/tex]

Answer:

[tex]x=\dfrac{4 \pm \sqrt{43}}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]\dfrac{1}{(x-5)}+\dfrac{3}{(x+2)}=4[/tex]

Make the denominators of the algebraic fractions the same, then combine them into one fraction:

[tex]\begin{aligned}\implies \dfrac{1}{(x-5)} \cdot \dfrac{(x+2)}{(x+2)}+\dfrac{3}{(x+2)}\cdot \dfrac{(x-5)}{(x-5)} & =4\\\\\implies \dfrac{x+2}{(x-5)(x+2)}+\dfrac{3(x-5)}{(x-5)(x+2)} & = 4\\\\ \implies \dfrac{x+2+3(x-5)}{(x-5)(x+2)} & = 4\\\\ \implies \dfrac{4x-13}{(x-5)(x+2)} & = 4 \end{aligned}[/tex]

Multiply both sides of the equation by [tex](x-5)(x+2)[/tex]:

[tex]\begin{aligned}\implies \dfrac{(4x-13)}{(x-5)(x+2)}\cdot (x-5)(x+2) & = 4(x-5)(x+2)\\\\\dfrac{(4x-13)(x-5)(x+2)}{(x-5)(x+2)} & = 4(x-5)(x+2)\\\\4x-13 & = 4(x-5)(x+2)\\\\4x-13 & =4x^2-12x-40\\\\4x^2-16x-27 & = 0\end{aligned}[/tex]

Solve using the Quadratic Formula:

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\implies a=4\\\implies b=-16\\\implies c=-27[/tex]

Therefore:

[tex]\implies x=\dfrac{-(-16) \pm \sqrt{(-16)^2-4(4)(-27)} }{2(4)}[/tex]

[tex]\implies x=\dfrac{16 \pm \sqrt{688}}{8}[/tex]

[tex]\implies x=\dfrac{16 \pm 4 \sqrt{43}}{8}[/tex]

[tex]\implies x=\dfrac{4 \pm \sqrt{43}}{2}[/tex]

The probability that a person older than 35 years has a hemoglobin level less than 9 is 0.47.

The probability that a person younger than 25 years has a hemoglobin level above 11 is 0 .50

the probability that a person in the 25-35 age group has a hemoglobin

level less than 9 is 0.25.

The probability that a person older than 35 years has a hemoglobin level between 9 and 11 is 0.28.

The probability that a person older than 35 years has a hemoglobin level less than 9 = number of people order than 35 that have a hemoglobin level less than 9 / total number of people over 35

= 76 / 167 = 0.47

The probability that a person younger than 25 years has a haemoglobin level above 11 = people over 25 that have a haemoglobin level above 11 / total number of people above 25

69/139 = 0 .50

The probability that a person in the 25-35 age group has a hemoglobin

level less than 9 = people between 25 - 35 that have a haemoglobin level less than 9 / total number of people between 25 - 35

=  32/128  = 0.25

The probability that a person older than 35 years has a hemoglobin level between 9 and 11=  number of people order than 35 that have a hemoglobin level 9 - 11 / total number of people over 35

46 / 162 = 0.28

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LSA

The value of the expression 7xy-y+x-1, when x = -2 and y = -1 is 12.

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.

To evaluate the given mathematical expression, we substitute the values of the unknown into the expression.

Substitute these values into the expression

Therefore,

Applying BODMAS,

Hence, the evaluation of  7xy-y+x-1 is 12

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When Leonardo and his wife file married filing jointly in 2021, the average tax rate will be 15.63 percent

In the question above, Leonardo's taxable income = $80,000

Theresa's taxable income = $15,000

Total taxable income for both of them will be:

$ 80,000 + $ 50,000 = $ 130,000

When you make use of the Schedule Y-1,

The amount of the tax on total income shall be said as:

Tax liability = $9,086 + (($130,000 - $78,950) * 22%)

= $9,086 +($51,050 * 22%)

= $9,086 + $11,231

= $ 20,317

To get the Effective tax rate, it will be:

= tax liability / Total taxable income Effective tax rate

= [tex]\frac{20,317}{30000}[/tex]  that is also written as $20,317/ $130,000

So, the  average tax rate is = 15.63%

Therefore, the average tax rate will be = 15.63 percent

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Answer:

see the attachment photo!

prefix kilo means 1000

so 1 kilogram = 1000 grams

14 kilograms = 14000 grams

14000 g > 1600 g

Maria's suitcase has a greater mass because 14,000 grams is greater than 1,600 grams.

The minimum number of sides that the polygon at the base of the prism must has 4 sides.

This refers to the plane figure in geometry that has three or more sides and angles in a finite straight line.

As we know the minimum number of sides a polygon does the base of the polygon have 4 side.

Now, as the plane intersect a prism parallel to base of the prism so the polygon of 5 sides will form then at least the base of the polygon will have 4 sides.

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Answer:

  d

Step-by-step explanation:

Answer:

i wish i knew

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

Consecutive interior angles need to add up to 180 degrees.

Therefore, 180 - 75 = 105

Answer:

105°

Consecutive interior angles are always supplementary, they add upto 180°

.

.

Angle A = 75°

Angle B = 180 - 75 = 105°

Step-by-step explanation:

I hope it helps u dear ^_^

(a) The precision of this measurement is 17.64 mm ± 0.01 mm.

(b) he uncertainty of the measurement is 0.057%.

(c) The tolerance of the measurement is 0.02 mm.

(d) The acceptable diameter in the format, nominal value uncertainty is 17.64 mm ± 0.057%.

A micrometer screw gauge is used in the measurement of a wire. The measuring accuracy of a micrometer screw gauge is 0.01 mm.

The precision of the measurement is 17.64 ± 0.01 mm.

The uncertainty of the measurement is calculated as follows;

uncertainty = (error/actual measurement) x 100%

uncertainty =  (0.01/17.64) x 100% = 0.057%

Tolerance = maximum measurement - minimum measurement

                 = (17.64 + 0.01)mm - (17.64 - 0.01)mm

                 = 0.02 mm

0.057% of 17.64 mm = 0.01 mm

Range of uncertainty = (17.64 mm - 0.01 mm) to (17,64 mm + 0.01 mm)

                                    = 17.63 mm to 17.65 mm

Acceptable diameter format, = 17.64 mm ± 0.057%

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The amount of the interest with simple interest of 6.9% will be $ 10.35.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

Miguel Rodriguez borrowed ​$300 from his brother Julio to pay for books and tuition.

He agreed to pay Julio in 6 months with simple annual interest at ​6.9%

Then the amount of the interest will be

Amount = P x R x T / 100

We have

P = $ 300

R = 6.9%

T = 6 months = 0.5 years

Then we have

P = (300 x 6.9 x 0.5) / 100

P = $ 10.35

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The best method of solving two-step equation is "Apply the multiplication property of equality first, and then apply the addition property of equality to isolate the variable"

For instance:

40 = 5(x) - 5

40 = 5x - 5

40 + 5 = 5x

45 = 5x

x = 45/5

x = 9

Therefore, the correct answer is "Apply the multiplication property of equality first, and then apply the addition property of equality to isolate the variable".

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Answer:

The angle Sita here is called Amplitude

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-2)}}} \implies \cfrac{-2}{5 +2} \implies \cfrac{ -2 }{ 7 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{2}{7}}(x-\stackrel{x_1}{(-2)}) \implies y-4=-\cfrac{2}{7}(x+2) \\\\\\ y-4=-\cfrac{2}{7}x-\cfrac{4}{7}\implies y=-\cfrac{2}{7}x-\cfrac{4}{7}+4\implies y=-\cfrac{2}{7}x+\cfrac{26}{7}[/tex]

The dimensions of the original photo is: X = 11

A dimension can be defined as the parameters, measurement, scale  or size of an object or figure.

A dimension is so important as is gives us a visual representation of an object.

(x-3[tex])^{2}[/tex] = 64

(x-3) = [tex]\sqrt{64}[/tex]

x = 8 + 3

x = 11

In conclusion, The dimensions of the original photo is: X = 11

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Answer:

3660

Step-by-step explanation:

'milli..' in the metric system means 1000 th

 there are 1000 milliliters in a liter

   3.66 liters *  1000 ml/liter = 3660 ml

Answer:

it's 0 I think ok hope this helped stay safe

Step-by-step explanation:

2.718281828459045…

Euler's Number 'e' is a numerical constant used in mathematical calculations. The value of e is 2.718281828459045…so on. Just like pi(π), e is also an irrational number.

Answer:

I think 34.

Step-by-step explanation:

It's because, 34 can be a positive integer. Decimals can also be integers, but, this one looks a better option. While, the

O

0 0

O

don't seem to be integers.

¹T¹h¹a¹n¹k¹s¹

Answer:

2 hours

Step-by-step explanation:

Mike has a six hour head start so he is    6 x 2 = 12 miles ahead

 their 'closing speed' is  8-2 = 6 m/hr

    it will take Kim   12 / 6  = two hours to catch Mike

Answer:

5 inches

Step-by-step explanation:

the length of painting is 56/7 = 8in. to find the length of the 2nd painting divide the area by the width: 40/8 = 5

The coordinate grid of the ordered pair is gotten from the combination of the y and X axis of the graph.

Using the coordinates, an ordered pair for the given point is:

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Answer:

3.361     3.361     3.361  cm

Step-by-step explanation:

Minimum surface are will be a cube

LWH = 38

L = cubrt (38) = 3.361   side length    cm

The surface area of the cube with a side length of 2 units is 24 units squared

The side length of the cube is given as:

l = 2

The surface area is calculated as:

Surface area = 6l^2

This gives

Surface area = 6 *2^2

Evaluate

Surface area = 24

Hence, the surface area of the cube is 24 unit squared

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