Please answer soon. Include Statement and Reason if possible.
Given: ΔABC, AC = BC, AB = 3
CD ⊥ AB, CD = √3
Find: AC

Answer:

AC ≅ AE

Step-by-step explanation:

According to the SAS Congruence Theorem, for two triangles to be considered equal or congruent, they both must have 2 corresponding sides that are of equal length, and 1 included corresponding angle that is of the same measure in both triangles.

Given that in ∆ABC and ∆ADE, AB ≅ AD, and <BAC ≅ DAE, the additional information we need to prove that ∆ABC ≅ ADE is AC ≅ AE. This will satisfy the SAS Congruence Theorem. As there would be 2 corresponding sides that are congruent, and 1 corresponding angle in both triangles that are congruent to each other.

Answer:

A).   AC ≅ AE

Step-by-step explanation: took test on edge

Answer:

option: D

51200

Step-by-step explanation:

64000 x 80/100 = 51200

Answer:

Hi there!!!

your required answer is option D.

explanation see in picture.

I hope it will help you...

Answer:

31 and -31

Step-by-step explanation:

The two numbers with a difference of 62 and whose product is a minimum are; 31 and -31

We are told that their difference is 62.

Thus; x - y = 62  ---(1)

f(x,y) = xy

From eq, making y the subject gives us;

y = x - 62

Thus;

f(x) = x(x - 62)

f(x) = x² - 62x

f'(x) = 2x - 62

At f'(x) = 0

2x - 62 = 0

2x = 62

x = 62/2

x = 31

Thus;

y = 31 - 62

y = -31

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Answer:

Q(1,1), N(3,2) A(2,5)

Step-by-step explanation:

we need to add 64 on both sides and required equation is x=-8±2√5-8

Two or more expressions with an Equal sign is called as Equation.

The given equation is x²+16x=-44

Now we need to make the coefficient of x variable half and to square it.

(16/2)²=8²=64

Now add 64 on both the sides

x²+16x+64=-44+64

x²+16x+64=20

(x+8)²=20

x+8=±√20

x+8=±2√5

Now subtract 8 on both sides

x=-8±2√5-8

Hence, we need to add 64 on both sides and required equation is x=-8±2√5-8

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Answer:

The equivalent expression of [tex]\ln(6\cdot a + 9\cdot b)[/tex] is [tex]\ln 3 + \ln (2\cdot a + 3\cdot b)[/tex].

Step-by-step explanation:

Let be [tex]r = \ln (6\cdot a + 9\cdot b)[/tex], which is now solved as follows:

1) [tex]\ln(6\cdot a + 9\cdot b)[/tex] Given.

2) [tex]\ln [3\cdot (2\cdot a + 3\cdot b)][/tex] Distributive property.

3) [tex]\ln 3 + \ln (2\cdot a + 3\cdot b)[/tex] ([tex]\ln (x\cdot y) = \ln x + \ln y[/tex]) Result.

The equivalent expression of [tex]\ln(6\cdot a + 9\cdot b)[/tex] is [tex]\ln 3 + \ln (2\cdot a + 3\cdot b)[/tex].

We want to find an equivalent expression to ln(6a + 9b). We will get:

ln(6a + 9b) = ln(3) + ln(2a + 3b)

Here we will be using the rule:

ln(x) + ln(y) = ln(x*y)

Now let's see our expression:

ln(6a + 9b) = ln(3*(2a + 9b))

Now we use the above rule to write:

ln(3*(2a + 3b)) = ln(3) + ln(2a + 3b)

Then the equivalent expression is:

ln(6a + 9b) = ln(3) + ln(2a + 3b)

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Answer:

the answer is

[tex]3 \sqrt{2} + 2 \sqrt{3} [/tex]

Step-by-step explanation:

the explanation is given in the image.

Answer:

[tex]\huge\boxed{\dfrac{\sqrt6}{\sqrt3-\sqrt2}=3\sqrt2+2\sqrt3}[/tex]

Step-by-step explanation:

[tex]\dfrac{\sqrt6}{\sqrt3-\sqrt2}\\\\\text{use}\ (a-b)(a+b)=a^2-b^2\\\\\dfrac{\sqrt6}{\sqrt3-\sqrt2}\cdot\dfrac{\sqrt3+\sqrt2}{\sqrt3+\sqrt2}=\dfrac{\sqrt6(\sqrt3+\sqrt2)}{(\sqrt3-\sqrt2)(\sqrt3+\sqrt2)}=\dfrac{(\sqrt6)(\sqrt3)+(\sqrt6)(\sqrt2)}{(\sqrt3)^2-(\sqrt2)^2}[/tex]

[tex]\text{use}\ \sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\ \text{and}\ (\sqrt{a})^2=a[/tex]

[tex]=\dfrac{\sqrt{(6)(3)}+\sqrt{(6)(2)}}{3-2}=\dfrac{\sqrt{18}+\sqrt{12}}{1}=\sqrt{9\cdot2}+\sqrt{4\cdot3}\\\\=\sqrt9\cdot\sqrt2+\sqrt4\cdot\sqrt3=3\sqrt2+2\sqrt3[/tex]

Solve for one half on the triangle with height 6 and base would be 4/2 = 2

Use the Pythagorean theorem:

X = sqrt( 6^2 + 2^2)

X = sqrt( 36 + 4)

X = sqrt(40)

The answer is D

Answer:

See below

Step by step explanation

[tex] \tan( \frac{\pi}{4} + A) \tan( \frac{3\pi}{4} + A) = - 1 [/tex]

L.H.S

[tex] \tan( \frac{\pi}{4} + A) \tan( \frac{3\pi}{4} + A ) [/tex]

We know that ,

[tex] \tan(A + B) = \frac{tan \: A + tan \: B}{1 - \tan \: A \: \tan \: B } [/tex]

[tex]( \frac{ \tan( \frac{\pi}{4} + \tan \: A ) }{1 - \tan \frac{\pi}{4} \tan \: A} ) \: (\frac{ \tan \frac{3\pi}{4} + \tan \: A}{1 - \tan \frac{3\pi}{4} \tan( \: A) } )[/tex]

[tex]( \frac{1 + \tan \: A }{1 - \tan\: A} )( \frac{ \tan( x - \frac{x}{4} + \tan \: A ) }{1 - \tan(\pi - \frac{\pi}{4} ) \: \tan \: A }) [/tex] (tan π / 4 = 1 )

[tex]( \frac{1 + \tan \: A}{ -1 - \: \tan \: A } )( \frac{ - \tan( \frac{\pi}{4} + \tan \: A ) }{1 - ( - \tan \: \frac{\pi}{4}) \: \tan \: A } )[/tex] [ tan ( π - B ) = - tan∅ ]

[tex]( \frac{1 + tan \: A}{1 - tan \: B} )( \frac{ - 1 + \tan\: A }{1 + \tan \: A } )[/tex]

[tex] = \frac{ - (1 - \tan\: A)}{(1 - \tan \: A) } [/tex]

[tex] = - 1[/tex]

Hope this helps..

Best regards!!

Answer:

See below.

Step-by-step explanation:

First, distribute:

[tex]=\frac{1}{x(x+1)}[/tex]

Now, perform partial fraction decomposition. This is only two factors, so we only need linear functions:

[tex]\frac{1}{x(x+1)} =\frac{A}{x}+\frac{B}{x+1}[/tex]

Now, multiply everything by x(x+1):

[tex]1=A(x+1)+B(x)[/tex]

Now, solve for each variable. Let's let x=-1:

[tex]1=A(-1+1)+B(-1)[/tex]

[tex]1=0A-B=-B[/tex]

[tex]B=-1[/tex]

Now, let's let x=0:

[tex]1=A(0+1)+B(0)[/tex]

[tex]A=1[/tex]

So:

[tex]\frac{1}{x(x+1)}=\frac{1}{x}-\frac{1}{(x+1)}[/tex]

Double Check:

[tex]\frac{1}{x}-\frac{1}{(x+1)}=\frac{(x+1)}{x(x+1)}-\frac{x}{x(x+1)}[/tex]

[tex]=\frac{x-x+1}{x(x+1)} =\frac{1}{x^2+x}[/tex]

Answer:

(a d)/(bc)

Step-by-step explanation:

a/b ÷ c/d

Copy dot flip

a/b * d/c

ad / bc

Answer: Estimated the standard deviation α  = 5.35

Step-by-step explanation:

According to Empirical rule, the largest value is approximately:

ц + 3α

And the smallest value is approximately:

ц + 3α

Based on the given figures in the question, we can say

ц + 3α = 140.6

ц - 3α = 108.5

Now subtracting these two; we have

ц + 3α - ( ц - 3α  ) = 140.6 - 108.5

ц + 3α - ц + 3α = 32.1

6α = 32.1

α = 32.1 / 6

α = 5.35

Estimated the standard deviation α  = 5.35

Answer:

Point C

Step-by-step explanation:

Point c is the only point on the number line which is in between 2 and 3.

Thus,

point c is the answer.

Hope this helps :)

Answer:Explanatory help v

Step-by-step explanation:The question gives you V0 as 220, so plug that in first.

h=-16t2+220t.

Then it says to find the time (solve for t), when the height is 400 ft. Plug 400 ft in as h and solve for t.

400=-16t2+220t.

To solve this, set the quadratic equal to 0 by subtracting 400 from both sides (0=-16t2+220t-400) and use the quadratic formula!

Answer:

The arrow reaches 400 feet in its way up at about 2.2 seconds after being launched.

Step-by-step explanation:

Since we want to find the time at which the arrow will reach 400 feet, we use this information in the equation for the height;

[tex]400=-16\,t^2+220\,t\\16\,t^2-220\,t+400=0[/tex]

and now use the quadratic equation to solve for the unknown time (t). Notice that been a quadratic equation we expect up to two answers, and then we will need to decide which answer to pick.

[tex]t=\frac{220}{2\,(16)} +/- \frac{\sqrt{(-220)^2-4 \,(16)(400)}}{2\,(16)} \\ \\t= 2.156\,sec\,\,\,or\,\,\, t=11.594\,sec[/tex]

This means that as the arrow goes up, it takes 2.156 seconds to reach 400 feet, and afterwards, after the arrow reaches it maximum height, it falls back due to acceleration of gravity, going through the same 400 feet height before reaching the ground.

We round the answer to the nearest tenth as requested.

Answer:

[tex] \boxed{\sf \frac{3x}{ {x}^{2} - 4x + 4}} [/tex]

Step-by-step explanation:

[tex] \sf Product \: of \: the \: rational \: expression: \\ \sf \implies \frac{x}{x - 2} \times \frac{3}{x - 2} \\ \\ \sf \implies \frac{3x}{(x - 2)(x - 2)} \\ \\ \sf (x - 2)(x - 2) = (x)(x - 2) - 2(x - 2) : \\ \sf \implies \frac{3x}{ \boxed{ \sf (x)(x - 2) - 2(x - 2)}} \\ \\ \sf (x)(x - 2) - 2(x - 2) = (x)(x) - (2)(x) - 2(x) - (2)( - 2) : \\ \sf \implies \frac{3x}{ \boxed{ \sf (x)(x) - (2)(x) - 2(x) - (2)( - 2) }} \\ \\ \sf \implies \frac{3x}{ \boxed{ \sf {x}^{2}} - 2x - 2x - (2)( - 2)} \\ \\ \sf (2)( - 2) = - 4 : \\ \sf \implies \frac{3x}{ {x}^{2} - 2x - 2x - \boxed{ \sf - 4}} \\ \\ \sf - ( - 4) = 4 : \\ \sf \implies \frac{3x}{ {x}^{2} - 2x - 2x + \boxed{ \sf 4}} \\ \\ \sf - 2x - 2x = - 4x : \\ \\ \sf \implies \frac{3x}{ {x}^{2} - 4x + 4} [/tex]

X/(x - 2) × 3/(x - 2) = 3x/(x² + 4x + 4). So, the correct option is A.

The product of the rational expressions shown here X/x-2•3/x-2

X/(x - 2) × 3/(x - 2)

3x/(x - 2)²

by the (a - b)² = a² + b² -2ab

(x - 2)² = x² + 4 - 4x

3x/(x² + 4 -  4x).

Therefore, the correct answer is 3x/(x² + 4 -  4x).

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Answer:

72 degrees.

Step-by-step explanation:

The angle marked as 72 degrees and the angle of JOK are considered vertically opposite angles in relation to each other. This relationship means that the angles are equal.

Answer:

[tex]\boxed{Option \ C}[/tex]

Step-by-step explanation:

Congruent arcs subtend congruent central angles.

So,

∠GOH ≅ ∠JOK

∠JOK = 72 degrees

Answer:

Hey there!

1/2 x (4+8)

1/2 x (12)

6

Hope this helps :)

Answer: 6x

Step-by-step explanation:

.5x*(4+8)

.5x*(12)

6x

Hope it helps <3

Answer:

Continous distributions:

- A probability distribution showing the average number of days mothers spent in the hospital.

- A probability distribution showing the weights of newborns.

Step-by-step explanation:

A probability distribution showing the number of vaccines given to babies during their first year of life will have a discrete distribution as only a natural number can represent the number of vaccines (0, 1, 2 vaccines and so on).

A probability distribution showing the average number of days mothers spent in the hospital can be described as continous because we are averaging days and this average can be fractional, so it is not discrete.

A probability distribution showing the weights of newborns is continous, as the weights are a continous variable (physical measurement), not discrete.

A probability distribution showing the amount of births in a hospital in a month is a discrete distribution, as the number of births can only be represented by natural numbers.

The option that describes a continuous distribution include:

A continuous distribution simply means the probabilities of the values of a continuous random variable.

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Answer:

Solving the system of linear equations Mark tries to apply elementary transformations in order to eliminate one variable.

He makes such steps:

1. He multiplies equation (1) x+y+z=2 by 7 and adds it to equation (3) 4x-y-7z=16. This gives him:

7x+7y+7x+4x-y-7z=14+16,

11x+6y=30.

2. He multiplies equation (3)  4x-y-7z=16 by 2 and adds it to equation (2) 3x+2y+z=8. This step gives him:

8x-2y-14z+3x+2y+z=32+8,

11x-13z=40.

Thus, he did not eliminate the same variables in steps 1 and 2.

Answer: correct choice is he did not eliminate the same variables in steps 1 and 2.

Hope this helps you :)! If you would mark me brainliest, that would be awesome!

Answer:

correct answer is c

Step-by-step explanation:

edge 2020

Answer:

Step-by-step explanation:

put x=r cos θ

y=r sin θ

r²cos²θ-r²sin²θ=3rsin θ

r²(cos²θ -sin²θ)=3r sin θ

r²cos 2θ=3rsinθ

r cos 2θ=3 sin θ

r=3sec 2θ sin θ

Answer:

A.50,000 units

B.62,500 units

C.Process A with a profit of $700,000 to maximize profit

Step-by-step explanation:

A.Calculation for the breakeven volume for Process A

Using this formula

Breakeven volume for Process A= Fixed cost/(Sales per units-Variable cost per units)

Let plug in the formula

Breakeven volume for Process A=500,000/(35-25)

Breakeven volume for Process A=500,000/10

Breakeven volume for Process A=50,000 units

B.Calculation for the breakeven volume for Process B

Using this formula

Breakeven volume for Process B= Fixed cost/(Sales per units-Variable cost per units)

Let plug in the formula

Breakeven volume for Process B=750,000/(35-23)

Breakeven volume for Process B=750,000/12

Breakeven volume for Process B=62,500 units

C. Calculation for what the company should do if the total demand (volume) is 120,000 units

Using this formula

Profit=(Total demand*(Sales per units-Variable cost per units for Process A)- Process A fixed cost

Let plug in the formula

Profit =120,000*($35-$25)-$500,000

Profit=120,000*10-$500,000

Profit=1,200,000-$500,000

Profit= $700,000

Therefore If total demand (volume) is 120,000 units, then the company should select Process A with a profit of $700,000 to maximize profit.

Answer:

98.5

Step-by-step explanation:

The dude above do be wrong doh

Answer:

[tex]\frac{\sqrt{21}}{3}[/tex] is the answer.

Step-by-step explanation:

To rationalize the denominator of [tex]\sqrt{\frac{7}{3}}[/tex] we will remove the square root or cube root from the denominator.

For which we multiply with the same value given in the denominator to numerator and denominator both.

[tex]\sqrt{\frac{7}{3}}=\frac{\sqrt{7} }{\sqrt{3} }[/tex]

[tex]\frac{\sqrt{7}}{\sqrt{3}}=\frac{\sqrt{7}}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}[/tex]

    [tex]=\frac{\sqrt{7\times 3}}{(\sqrt{3})^2}[/tex]

    [tex]=\frac{\sqrt{21}}{3}[/tex]

[tex]\frac{\sqrt{21}}{3}[/tex] is the rationalized form.

Therefore, [tex]\frac{\sqrt{21}}{3}[/tex] will be the answer.

Answer:

1.580 Liters

Step-by-step explanation:

We know that  1000 mL = 1 Liter

1580 ml * 1L/1000 ml

1.580 Liters

Answer:

1.58

Step-by-step explanation:

1 milliliter = .001 liter

Answer:

the answer is C. 12

Step-by-step explanation:

Answer:

This driver's insurance premium should be at least $990.43.

Step-by-step explanation:

We are given that the probability of a driver getting into an accident is 6.4%, the average cost of an accident is $13,991.05, and the overhead cost for an insurance company per insured driver is $95.

As we know that the expected cost that the insurance company has to pay for each of driver having met with the accident is given by;

The Expected cost to the insurance company = Probability of driver getting into an accident [tex]\times[/tex] Average cost of an accident

So, the expected cost to the insurance company = [tex]0.064 \times \$13,991.05[/tex]

                                                                                  = $895.43

Also, the overhead cost for an insurance company per insured driver = $95. This means that the final cost for the insurance company for each driver = $895.43 + $95 = $990.43.

Hence, this driver's insurance premium should be at least $990.43.

Answer:115

Step-by-step explanation:

Answer:

Measure of angle W + measure of angle Z = 180°

Step-by-step explanation:

The reason is that angles in a straight line add up to 180° and angles at a point add up to 360° (i.e the sum of measure of angles W, X, Y, Z is 360°)

Answer:

D is your answer

Step-by-step explanation:

I have no explanation

Answer:

With calculator;√24.5 = 4.9497

With differentials;With calculator;√24.5 = 4.95

The value of the square root gotten using differentials is an approximate value of the one gotten with a calculator

Step-by-step explanation:

With calculator;√24.5 = 4.9497

Using differentials;

The nearest number to 24.5 whose square root can be taken is 25, so let us consider that x = 25 and δx = dx = - 0.5

Now, let's consider;

y = √x - - - (eq 1)

Differentiating with respect to x, we have;

dy/dx = 1/(2√x) - - - - (eq 2)

Taking the differential of eq 2,we have;

dy = (1/(2√x)) dx

Using the values of x = 25 and dx = 0.5,we have;

dy = (1/(2√25)) × 0.5

dy = 0.05

Now;

√24.5 = y - dy

√24.5 = √x - dy

√24.5 = √25 - 0.05

√24.5 = 5 - 0.05

√24.5 = 4.95

Answer:

0.75x+15=2+0.5x-1

0.25x=1-15

0.25x=-14

x=-56

Step-by-step explanation:

Given Information:

Starting population = P₀ = 47,597

rate of growth = 1.8%

Required Information:

Equation that defines the population t years = ?

Answer:

The following equation defines the population t years after 2010.

[tex]$ P(t) = 47,597e^{0.018t} $[/tex]

Step-by-step explanation:

The population growth can be modeled as an exponential function,

[tex]$ P(t) = P_0e^{rt} $[/tex]  

Where P₀ is the starting population in 2010, r is the rate of growth of the population and t is the time in years after 2010.

We are given that the starting population is 47,597 and rate of growth is 1.8%

So the population function becomes

[tex]$ P(t) = 47,597e^{0.018t} $[/tex]

Therefore, the above function may be used to estimate the population for t   years after 2010.

For example:

What is the population after 10 years?

For the given case,

t = 10

[tex]$ P(10) = 47,597e^{0.018(10)} $[/tex]

[tex]$ P(10) = 47,597e^{0.18}$[/tex]

[tex]$ P(10) = 47,597(1.1972)$[/tex]

[tex]$ P(10) = 56,984[/tex]