PLEASE PLEASE PLEASE HELP TIMEDCan you prove that DE F = HGF Justify your answer. A. Yes, the triangles are congruent by SAS. B. Yes, the triangles are congruent by SSS. C. Yes, the triangles are congruent by SSA. D. No, not enough information is given.

Answer:

a. (24 ln 2 − 7) / 9

b. x tan x + ln|cos x| + C

Step-by-step explanation:

a. ∫₁² x² ln x dx

Integrate by parts.

If u = ln x, then du = 1/x dx.

If dv = x² dx, then v = ⅓ x³.

∫ u dv = uv − ∫ v du

= (ln x) (⅓ x³) − ∫ (⅓ x³) (1/x dx)

= ⅓ x³ ln x − ∫ ⅓ x² dx

= ⅓ x³ ln x − ¹/₉ x³ + C

= ¹/₉ x³ (3 ln x − 1) + C

Evaluate between x=1 and x=2.

[¹/₉ 2³ (3 ln 2 − 1) + C] − [¹/₉ 1³ (3 ln 1 − 1) + C]

⁸/₉ (3 ln 2 − 1) + C + ¹/₉ − C

⁸/₉ (3 ln 2 − 1) + ¹/₉

⁸/₃ ln 2 − ⁸/₉ + ¹/₉

⁸/₃ ln 2 − ⁷/₉

(24 ln 2 − 7) / 9

b. ∫ x sec² x dx

Integrate by parts.

If u = x, then du = dx.

If dv = sec² x dx, then v = tan x.

∫ u dv = uv − ∫ v du

= x tan x − ∫ tan x dx

= x tan x + ∫ -sin x / cos x dx

= x tan x + ln|cos x| + C

Answer:

Step-by-step explanation:

[tex]\frac{x-1}{2} =t\\\frac{y-2}{3} =t\\\frac{z-3}{4} =t\\so~eq.~of~line~L_{1}~is\\\frac{x-1}{2} =\frac{y-2}{3} =\frac{z-3}{4} \\its~d.r's~are~2,3,4\\again~\frac{x-2}{1} =s\\\frac{y-4}{2} =s\\\frac{z+1}{-4} =s\\so~eq. ~of~line~L_{2}~is\\\frac{x-2}{1} =\frac{y-4}{2} =\frac{z+1}{-4} \\its~d.r's ~are~1,2,-4\\let ~the ~d.r's~of~line~perpendicular~to~both~L_{1}~and~L_{2}~be~a,b,c,~then~\\2a+3b+4c=0\\1a+2b-4c=0\\solving\\\frac{a}{3*-4-4*2} =\frac{b}{4*1-2*-4} =\frac{c}{2*2-3*1} \\[/tex]

[tex]\frac{a}{-20} =\frac{b}{-4} =\frac{c}{1} \\d.r's~of ~reqd~line~is~-20,-4,1~or~20,4,-1[/tex]

now you find the point of intersection.

then calculate the angle.

Answer:

Mars

Step-by-step explanation:

America

Answer:

the dimensions that will minimize the cost of constructing the box is:

a = 5.8481  in ;   b = 5.848 in  ; c = 10.234 in

Step-by-step explanation:

From the information given :

Let a be the base if the rectangular box

b to be the height and c to be the  other side of the rectangular box.

Then ;

the area of the base is ac

area for the front of the box is ab

area for the remaining other sides   ab + 2cb

The base of the box is made from a material costing 8 ac

The front of the box must be decorated, and will cost 10 ab

The remainder of the sides will cost 4 (ab + 2cb)

Thus ; the total cost  C is:

C = 8 ac + 10 ab + 4(ab + 2cb)

C = 8 ac + 10 ab + 4ab + 8cb

C = 8 ac + 14 ab + 8cb   ---- (1)

However; the volume of the rectangular box is V = abc = 350 in³

If abc = 350

Then b = [tex]\dfrac{350}{ac}[/tex]

replacing the value for c in the above equation (1); we have :

[tex]C = 8 ac + 14 a(\dfrac{350}{ac}) + 8c(\dfrac{350}{ac})[/tex]

[tex]C = 8 ac + \dfrac{4900}{c}+\dfrac{2800}{a}[/tex]

Differentiating C with respect to a and c; we have:

[tex]C_a = 8c - \dfrac{2800}{a^2}[/tex]

[tex]C_c = 8a - \dfrac{4900}{c^2}[/tex]

[tex]8c - \dfrac{2800}{a^2}=0[/tex] --- (2)

[tex]8a - \dfrac{4900}{c^2}=0[/tex]   ---(3)

From (2)

[tex]8c =\dfrac{2800}{a^2}[/tex]

[tex]c =\dfrac{2800}{8a^2}[/tex] ----- (4)

From (3)

[tex]8a =\dfrac{4900}{c^2}[/tex]

[tex]a =\dfrac{4900}{8c^2}[/tex]   -----(5)

Replacing the value of a in 5 into equation (4)

[tex]c = \dfrac{2800}{8*(\dfrac{4900}{8c^2})^2} \\ \\ \\ c = \dfrac{2800}{\dfrac{8*24010000}{64c^4}} \\ \\ \\ c = \dfrac{2800}{\dfrac{24010000}{8c^4}} \\ \\ \\ c = \dfrac{2800*8c^4}{24010000} \\ \\ c = 0.000933c^4 \\ \\ \dfrac{c}{c^4}= 0.000933 \\ \\ \dfrac{1}{c^3} = 0.000933 \\ \\ \dfrac{1}{0.000933} = c^3 \\ \\ 1071.81 = c^3\\ \\ c= \sqrt[3]{1071.81} \\ \\ c = 10.234[/tex]

From (5)

[tex]a =\dfrac{4900}{8c^2}[/tex]   -----(5)

[tex]a =\dfrac{4900}{8* 10.234^2}[/tex]

a = 5.8481

Recall that :

b = [tex]\dfrac{350}{ac}[/tex]

b = [tex]\dfrac{350}{5.8481*10.234}[/tex]

b =5.848

Therefore ; the dimensions that will minimize the cost of constructing the box is:

a = 5.8481  in ;   b = 5.848 in  ; c = 10.234 in

The dimensions that will minimize the cost of constructing this box are: a = 5.8481 inches, b = 5.848 inches, and c = 10.234 inches and this can be determined by using the given data.

Given :

According to the given data the total cost is given by:

C = 8ac + 14ab + 8cb   --- (1)

The volume of the rectangular box is (V = abc = 350 inch cube). So, the value of b is given by:

[tex]\rm b = \dfrac{350}{ac}[/tex]

Now, substitute the value of 'b' in the equation (1).

[tex]\rm C = 8ac + \dfrac{4900}{c}+\dfrac{2800}{a}[/tex]

First differentiating the above equation with respect to c.

[tex]\rm C_c = 8a-\dfrac{4900}{c^2}[/tex]   --- (2)

Now, differentiating the above equation with respect to a.

[tex]\rm C_a = 8c-\dfrac{2800}{a^2}[/tex]    --- (3)

Now, equate equation (2) and equation (3) to zero.

From equation (2):  

[tex]\rm a=\dfrac{4900}{8c^2}[/tex]    ----- (4)

From equation (3):

[tex]\rm c=\dfrac{2800}{8a^2}[/tex]   ----- (5)

Now, from equations (4) and (5).

[tex]\rm c = \dfrac{2800}{8\left(\dfrac{4900}{8c^2}\right)^2}[/tex]

Now, simplifying the above expression in order to get the value of c.

c = 10.234

Now, put the value of 'c' in equation (5) in order to get the value of 'a'.

a = 5.8481

The value of 'b' is given by:

[tex]\rm b = \dfrac{350}{5.8481\times 10.234}[/tex]

b = 5.848

So, the dimensions that will minimize the cost of constructing this box are: a = 5.8481 inches, b = 5.848 inches, and c = 10.234 inches.

For more information, refer to the link given below:

https://brainly.com/question/19770987

Answer:

Option A is the correct option.

Step-by-step explanation:

[tex] \frac{3}{x } = \frac{6}{x - 4} [/tex]

Apply cross product property:

[tex]3(x - 4) = 6 \times x[/tex]

[tex]3(x - 4) = 6x[/tex]

Hope this helps...

Best regards!!

Answer:

3 * (x - 4) = 6 * x.

Step-by-step explanation:

3 / x = 6 / (x - 4)

3 * (x - 4) = 6 * x

3x - 12 = 6x

6x = 3x - 12

6x - 3x = -12

3x = -12

x = -4.

Hope this helps!

Hey there! I'm happy to help!

First of all, if one bill weighs on gram, a million would weigh one million grams. Let's divide this by 1,000 to see how many kilograms it is.

1,000,000/1,000=1,000

Now, we need to convert 1,000 kilograms into pounds. We see that 1 kilogram is equal to about 2.205 pounds, so we multiply 1,000 kilograms by 2.205 to get our pounds.

1,000*2.205=2205

Therefore, one million dollar bills weigh about 2205 pounds.

Have a wonderful day! :D

Answer:

see below.

Step-by-step explanation:

1st row has four small boxes

2nd row has three big boxes

big box 1 has no items ragged in it.

big box 2 has small box 1 and also small box 1 dragged into it.

big box 3 has small box 3 and small box 4 dragged into it.

Answer:

h = -9

Step-by-step explanation:

5h+2(11-h)= -5

Distribute

5h +22 -2h = -5

Combine like terms

3h +22 = -5

Subtract 22 from each side

3h +22-22 = -5-22

3h = -27

Divide by 3

3h/3 = -27/3

h = -9

The linear equation defines the arithmetic sequence is an = -8 + 4(n - 1). The correct option is A.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that, the sequence is -8, -4, 0, 4, 8, ...

a = -8

d = +4

The expression for the nth term will be written as,

an = a + ( n - 1 ) d

= -8 + ( n - 1 ) 4

To know more about arithmetic progression follow

https://brainly.com/question/6561461

#SPJ5

Answer:

❄️The answer is 7.0 or 7❄️

Step-by-step explanation:

It mostly depends on how many zeros will you put in 7.0

It actually doesn’t matter how many zeros you put after the decimal point.

Below I attached a picture of how to solve this kinds of problem.

Hope this helps! ^-^

By:❤️BrainlyMagic❤️

Note:if you ever need help, you can always ask me!

Answer:

It’s 7.0 or 7

Step-by-step explanation:

Trust me I got it right in my homework.

Answer:

Interval notation is

[tex]\left(-\infty, -5\right)\cup \left(0,1)[/tex]

Solutions:

[tex]\left(-\infty, -5\right)[/tex]

[tex]\left(0,1)[/tex]

Step-by-step explanation:

[tex]x^3 + 4x^2 - 5x < 0[/tex]

In this inequality, luckly we can easily factor it.

[tex]x^3 + 4x^2 - 5x[/tex]

[tex]x(x^2+4x-5)[/tex]

[tex]x(x-1)(x+5)[/tex]

So we have

[tex]x(x-1)(x+5)<0[/tex]

In exercises of this kind I usually do in my mind, but just to make it clear, let's do a table to organize. This table represents the x-intercepts in order to evaluate the inequality.

Consider [tex]x(x-1)(x+5)=0[/tex]. Here, those are the possible values for [tex]x[/tex] for each factor to be 0:

The first step to complete the table is the x value where the factor will be equal to zero.

       [tex]x<-5[/tex]       [tex]x=5[/tex]         [tex]-5<x<0[/tex]        [tex]x=0[/tex]      [tex]0<x<1[/tex]      [tex]x=1[/tex]      [tex]x>1[/tex]                                                                  

[tex]x[/tex]                                                                        0

[tex]x-1[/tex]                                                                                                    0        

[tex]x+5[/tex]                      0

Then, just consider the signal:

  [tex]x<-5[/tex]       [tex]x=5[/tex]         [tex]-5<x<0[/tex]        [tex]x=0[/tex]      [tex]0<x<1[/tex]      [tex]x=1[/tex]      [tex]x>1[/tex]                                                                  

[tex]x[/tex]    -                -                       -                   0               +                 +             +

[tex]x-1[/tex]  -             -                      -                   -               -                  0             +

[tex]x+5[/tex]  -             0                     +                   +                +               +              +

[tex]x(x-1)(x+5)[/tex]    -     0       +     0      -      0     +

When [tex]x(x-1)(x+5)<0[/tex] ?

It happens when [tex]x<-5[/tex]     and when [tex]0<x<1[/tex]

The solution is

[tex]\{x \in \mathbb{R} | x<-5 \text{ or } 0<x<1 \}[/tex]

[tex]\left(-\infty, -5\right)\cup \left(0,1)[/tex]

Answer:

72 cents.

Step-by-step explanation:

The expected winnings is the amount times the probability that you will get that amount.

2,000 * (1/10,000) = 2,000 / 10,000 = 2 / 10 = 0.2.

700 * (4 / 10,000) = 2,800 / 10,000 = 28 / 100 = 0.28.

300 * (8 / 10,000) = 2,400 / 10,000 = 24 / 100 = 0.24.

0.2 + 0.28 + 0.24 = 0.72.

Hope this helps!

Answer:

B.77.4%

Step-by-step explanation:

Mean wage (μ) = $4.50

Standard deviation (σ) = $0.50

For nay given salary X, the z-score is given by:

[tex]z=\frac{X-\mu}{\sigma}[/tex]

For X = $3.75, the z-score is:

[tex]z=\frac{3.75-4.50}{0.50}\\z=-1.5[/tex]

For X = $5.00, the z-score is:

[tex]z=\frac{5.00-4.50}{0.50}\\z=1[/tex]

A z-score of -1.5 corresponds to the 6.68th percentile, while a score of 1 corresponds to the 84.13th percentile. Therefore, the percentage of workers getting paid between $3.75 and $5.00 an hour is:

[tex]P=84.13-6.68\\P=77.45\%[/tex]

The answer is alternative B.77.4%

Answer:

try 3x=30 or 10

Step-by-step explanation:

Answer:

[tex]B(a)=\frac{a}{5} -7[/tex]

Step-by-step explanation:

The input it taken as the unknown base value, while the output here is the area of the trapezoid. b is therefore the base value, and A( b ) is the area of the trapezoid. Let's formulate the equation for the area of the trapezoid, and isolate the area of the trapezoid. To find the inverse of this function, switch y ( this is A( b ) ) and b, solving for y once more, y ➡ y ⁻ ¹.

y = height [tex]*[/tex] ( ( unknown base value ( b ) + 7 ) / 2 ),

y = 10 [tex]*[/tex] ( ( b + 7 ) / 2 )

Now switch the positions of y and b -

b = 10 [tex]*[/tex] ( ( y + 7 ) / 2 ) or [tex]b=\frac{\left(y+7\right)\cdot \:10}{2}[/tex] - now that we are going to take the inverse ( y ⁻ ¹ ) or B( a ), b will now be changed to a,

[tex]y+7=\frac{a}{5}[/tex],

[tex]y^{-1}=\frac{a}{5}-7 = B(a)[/tex]

Therefore the equation that represents the inverse function will be the following : B(a) = a / 5 - 7

Answer:

complementary because 2 angles that add up to 90º is a complementary angle and x=9 :)

Step-by-step explanation:

90=46+5x-1

45=5x

x=9

Answer:

x = 9 Complementary

Step-by-step explanation:

The angles are compplementary cause the angle add up to 90°

Well to find x we need to make the following equation,

46 + (5x - 1) = 90

We need to simplify and combine like terms,

46 - 1 = 45

45 + 5x = 90

-45 to both sides

5x = 45

Divide 5 by both sides

x = 9

Thus,

x is 9.

Hope this helps :)

Answer:

Option (2)

Step-by-step explanation:

In the two triangles ΔWVZ and ΔYXZ,

If the sides WV and XY are parallel and the segments WY and VX are the transverse.

∠X ≅ ∠V [Alternate angles]

∠W ≅ ∠Y [Alternate angles]

Therefore, ΔWVZ ~ ΔYXZ [By AA postulate of the similarity]

Option (2) will be the answer.

None of these options seem to be correct. You can check each result by differentiation:

[tex](e^x\sec^2x)'=e^x(\sec^2x+2\sec^2\tan x)=e^x\sec^2x(1+\tan x)[/tex]

[tex](e^x\sec x)'=e^x(\sec x+\sec x\tan x)=e^x\sec x(1+\tan x)[/tex]

[tex](e^x\tan^2x)'=e^x(\tan^2x+2\tan x\sec^2x)=e^x\tan x(\tan x+2\sec^2x)[/tex]

[tex](e^x\tan x)'=e^x(\tan x+\sec^2x)[/tex]

But none of these are equivalent to [tex]e^x(\sec x+\tan^2x)[/tex]...

Answer:

Step-by-step explanation:

when h(t)=0

-4.9 t²+19.6t=0

4.9t(-t+4)=0

either t=0 or t=4

so domain is 0≤t≤4

for range

h(t)=-4.9t²+19.6t

=-4.9(t²-4t+4-4)

=-4.9(t-2)²+19.6

so range is 0≤h≤19.6

Domain = 0<t<4, make sure to use less than or equal to signs not just less than signs.

Range = 0<h<19.6, again, use less than or equal to signs.

Answer: [tex]S=0.087p[/tex] .

Step-by-step explanation:

Equation for direct proportion:

y=kx

, where x= independent variable ,

y=dependent variable.

k= proportionality constant

Here, State sales tax S  is directly proportional to retail price p.

Also, dependent variable= S,  independent variable =p

Required equation: S= kp

Put S= 12.32 and x= 142

[tex]S=12.32=k(142)\\\\\Rightarrow\ k=\dfrac{12.32}{142}\approx0.087[/tex]

Hence, the required equation is [tex]S=0.087p[/tex] .

Answer:

Sample size

Step-by-step explanation:

Central Limit Theorem states that population with mean and standard deviation and if the sample size is large then the distribution of sample mean will be will be normally distributed. The central limit theorem holds assumptions that the factors to be considered when assessing central limit theorem is sample size.

The CLT is the factor(s) to be considered when assessing if the central theorem holds are sample.

It is given that the objective that central limit theorem assumptions. the factor(s) to be considered when assessing if the central theorem holds.

It is required to describe the above theorem.

It is defined as the in statistics the assumption holds that the sample means distribution of arbitrary variables follows a normal distribution or close to normal distribution if the sample size is big.

We have an objective:

The CLT is the factor to be considered when assessing if the CLT holds a large sample size.

If we draw the random sample data and its measures, the Central limit theorem explains the distribution will explain the normal bell curve, the mean of the parameters and the distribution will be the same.

Thus, the CLT is the factor(s) to be considered when assessing if the central theorem holds are sample.

Learn more about the Central limit theorem here:

https://brainly.com/question/5027686

Answer:

(2,0)

Step-by-step explanation:

From the information the first equation is y = 0.5 x  - 1 and the the line through (3,1) and (-5,-7) is  

y = x - 2  .   From those two equations you get

x - 2 = 0.5 x -1     and     x = 2  , y = 0.  So  it is the last point.   (2,0)

Answer:

D. (2,0)

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

If we call each team, A, B, C and D, each team has to play each other team once. Let's call each pairing between 2 teams the 2 teams' letters next to each other, e.g. AB is A playing against B. A has to play against B, C and D so we have AB, AC and AD. So we have 3 so far.

We have already counted that B is playing A but we haven't counted B playing C and D yet so we also have BC and BD. So we have 5 in total

Lastly, C needs to play D, we have already counted C playing B and C playing A so we have CD left. In total that gives 6.

Now we have already included D playing every other team so we don't include any other pairings.

In total, now every team has played every other team giving a total of 6.

(another way of solving this is doing "3!2 but if you haven't learnt factorials yet stick to the first method.

Answer:

6 games.

Step-by-step explanation:

The answer is the number of combinations of 2 from 4

= 4*3 / 2*1

= 6.

Answer: The average rate of change for this function for the interval from x=3 to x=5 is 12.

Step-by-step explanation:

Complete question is provided in the attachment below.

Formula: The average rate of change for this function y=f(x) for the interval from  x= a to x= b :

[tex]Rate =\dfrac{f(b)-f(a)}{b-a}[/tex]

Let y= f(x) for the given table:

At x= 3 , f(3)=8 and f(5)=32

Then, the average rate of change for this function for the interval from x=3 to x=5:

[tex]Rate=\dfrac{f(5)-f(3)}{5-3}\\\\=\dfrac{32-8}{2}\\\\=\dfrac{24}{2}=12[/tex]

Hence, the average rate of change for this function for the interval from x=3 to x=5  is 12.  (Option A is correct.)

The answer is A. Dilate circle A by a scale factor of 3

I took the test :)

Answer:

$15,842

Step-by-step explanation:

We use the Present value formula

Present Value = Future value/(1 + r)ⁿ

r = 6% = 0.06

n = 4 years

Future value = $20,000

Present value = 20,000/(1 + 0.06)⁴

= $15841.873265

≈ $15,842

Answer:

probability of getting both are unripe

= 0.15

probability of getting both are ripe

= 0.375

Probability of one ripe and one unripe

=0.234375

Probability of at least one unripe

=0.625

Step-by-step explanation:

50 mangoes 20 of which are unriped in the first basket .

Riped = 50-20= 30

Probability of unripe = 20/50

Probability of unripe= 0.4

Probability of ripe = 30/50

Probability of ripe = 0.6

40 mangoes of which 15 are unripe In the second basket

Number of riped= 40-15= 25

Probability of unriped= 15/40

Probability of unriped= 0.375

Probability of riped= 25/40

Probability of riped= 0.625

probability of getting both are unripe

= 0.4*0.375

probability of getting both are unripe

= 0.15

probability of getting both are ripe

= 0.6*0.625

= 0.375

Probability of one ripe and one unripe

= 0.625*0375

= 0.234375

Probability of at least one unripe

= 1- probability of no unripe

= 1 - probability of both ripe

= 1-0.375

= 0.625

Answer:

x=6.28 inches

y=191.08 inches

Step-by-step explanation:

Let the dimensions of the rectangle be x and y

Area of the rectangular sheet

x*y=1200 in^2}

x = circumference of the cylinder

This means x=2πr

Volume of a cylinder=πr^2h

h=y

Volume of the cylind=πr^2(y)=600 in^3

From x=2πr

r=x/2π

Substitute r=x/2π into Volume=πr^2(y)=600 in^3

We have,

Volume of the cylinder=πr^2(y)=600 in^3

π*(x/2π)^2(y)=600

(x^2/4π)y=600

Recall, x*y=1200

y=1200/x

Substitute y=1200/x into (x^2/4π)y=600

(x^2/4π)y=600

(x^2/4π)(1200/x)=600

1200x/4π=600

Multiply both sides by 4π

(x^2/4π)(1200/x)(4π)=600*4π

1200x=2400π

Divide both sides by 1200

1200x/1200 = 2400π/1200

x=2π

Substitute x=2π into y=1200/x

We have,

y=1200/2π

y=600/π

The dimensions are x=2π and y=600/π

Let π=3.14

x=2π

=2(3.14)

=6.28 inches

y=600/π

=600/3.14

=191.08 inches

Answer:

no tiene mas informaion?

Step-by-step explanation: