In the diagram of AABC shown below, DE || BC.
B
A
3) 3
4) 15
E
If AB= 10, AD = 8, and AE = 12, what is the
length of EC?
1) 6
2) 2
C
dd or create
k as done
nments
As
to Susan Guha

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

What does the information want:

Let's gather some information:

             ⇒ Angle B is shared by both triangles

             ⇒ Angle A' and A are the same, as they are both on parallel

                   lines, A'C' and AC, and both angles are formed with the

                   same line AB

                 ⇒ by the Angle-Angle Theorem*, they are similar triangles

If they are similar triangles:

   ⇒ their side lengths are proportional to each other

          ⇒ let's set up a proportion

                 [tex]\frac{A'B}{AB} =\frac{A'C'}{AC} \\\frac{30}{x+30} =\frac{14}{22} \\14(x+30) = 30*22\\14x + 420 = 660\\14x = 240\\x = 17.143[/tex]

          ⇒ let's set up a proportion

                 [tex]\frac{BC'}{BC} =\frac{A'C'}{AC} \\\frac{y}{y+15} =\frac{14}{22} \\22y=14(y+15)\\22y=14y+210\\8y=210\\y=26.25[/tex]

Answer:

Hope that helps!

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The area of the base of cube B is 25/9 times larger than the area of the base of cube A.

Because the cubes are similar, then we know that the dimensions of cube B are a dilation of scale factor K of the dimensions of cube A.

Then, the volume of cube B is K³ times the volume of cube A.

The area of any face of cube B is K² times the area of any face of cube A

From this we can write:

125 in³ = K³*27in³

(125/27) = K³

If we apply the cubic root in both sides, we get:

∛(125/27) = K = 5/3

Then the relation between the areas is equal to:

K² = (5/3)^2 = 25/9

The area of the base of cube B is 25/9 times larger than the area of the base of cube A.

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Answer:

25/9

Step-by-step explanation:

I Just Took the Test.

Answer:

4x -51

Step-by-step explanation:

m(n(x)) = m(x - 10) = 4(x-10) - 11 = 4x -40 -11 = 4x -51

Answer:

m[n(x)] = 4x - 51

Given following:

Solving steps:

Answer:

3 nikels and 2 cents

Step-by-step explanation:

1 niquel = 5 cents

5+5+5= 15

15+ 2= 17

The correct option is the second one:

We know that:

We have the operation:

x - y + (-z)

Notice that because y is negative, then -y is positive.

Because z is positive, -z is negative.

Then we have:

positive + positive + negative

Or, in the number line:

right, right, left.

Second question:

Can we conclude the sign of the outcome?

No, we can't, the sign will depend on the values of x, y, and z.

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Answer:The correct option is the second one:i) right, right, left.ii) Undefined.

Step-by-step explanation:

[tex](d) \: \: y = - x - 1[/tex]

[tex]a \times \frac{ - 2}{3} = - 1 \\ a = \frac{3}{2} [/tex]

[tex](d) \: \: \: \: y = \frac{3}{2} x - 4[/tex]

Answer:

1. y = -x - 1

2. y = (3/2)x - 4

Step-by-step explanation:

1. Let y = ax + b be the equation of the line

that passes Through (4,-5) and parallel to y = -x + 1

Where ‘a’ is the slope and b the y value of the y-intercept point.

The lines are parallel

then

they have the same slope

then

a = -1

we get :

y = -x + b and the point (4 , -5) lies on the line

then

-5 = -(4) + b

Then

b = -5 + 4 = -1

Conclusion:

y = -x - 1

………………………………………

2. Let y = mx + p be the equation of the line

that passes Through (2,-1) and perpendicular to y = -2/3x + 5

Where ‘m’ is the slope and p the y value of the y-intercept point.

The lines are perpendicular  

then

The product of their slopes = -1

Then

m × (-2/3) = -1

Then

m = 3/2

we get :

y = 3/2x + p and the point (2 , -1) lies on the line

then

-1 = (3/2)×(2) + p

Then

p = -1 - 3 = -4

Conclusion:

y = (3/2)x - 4

a)

Gain on disposal=$12,900

b)

Loss on disposal=$5,900

Prepare a tabular summary to show the cost of equipment disposed of, the accumulated depreciation, and gain or loss recorded on disposal?

Note that initially when the equipment was purchased, it would be debited to an asset account, whereas, it would be credited upon disposal since the company no longer owns it.

The accumulated depreciation was originally a credit entry in the balance sheet and needs to be debited now that the equipment has been sold.

Note that the excess of the sum of the accumulated depreciation and the cash received over the initial cost of the equipment is a gain and the reverse means a loss was recorded on disposal.

Account                                DR                  CR

Asset                     $49,600

Gain on disposal      $12,900

Accumulated depreciation                               $24,600  

Cash received                                              $37,900  

gain on disposal=$24,600+$37,900-$49,600

gain on disposal=$12,900

Account                                 DR                    CR

Asset                                                           $49,600

Accumulated depreciation   $24,600  

Cash received                         $19,100  

Loss on disposal                     $5,900  

Loss on disposal=$49,600-$24600-$19,100

Loss on disposal=$5,900

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This is a very simple transformation problem and can be solved by observation. The correct answer is Option D where g(x) = f(x-3) + 6. See the attached graph for the full question.

In mathematics, transformation is the process of converting one figure, expression, or function into another of equivalent value.

Note that on an x-axis, moving past zero to the left gets you into the negative, and vice versa.

On the y-axis moving upwards past zero gets you into the positive.

Recall that g(x) is a transformation of f(x). This means that the original image is f(x).

Notice that F(x) is transformed three degree beyond 0 on the -axis and 6 degrees beyond zero on the y-axis. Hence the correct equation is:

g(x) = f(x-3) + 6.

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A percentage is a way to describe a part of a whole. The percetage decrease in the price of CD is 33.33%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

The price of the CD decreases from $18 to $12. Therefore, the percentage decrease is,

Percentage Decrease = ($18-$12)/$18 × 100% = 33.33%

Hence, the percetage decrease in the price of CD is 33.33%.

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The miles Sophia drove is 60 miles

The distance Sophia drove is represented in fractions.

A number is expressed as a quotient where a numerator is divided by a denominator. In a simple fraction, both are integers.

A fraction consists of a numerator and a denominator. An example of a fraction is 1/2 where 1 is the numerator and 2 is the denominator.

In order to determine the miles Sophia drove, the total distance of the trip would be multiplied by the fraction of the time Sophia drove.

Miles Sophia drove = 3/5  x 100

                                = 60 miles

So sophia drove 60 miles in 500 miles.

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Answer: 14.25

Step-by-step explanation:

Because 14 and 10 inches don't indicate that the ruler can measure to the nearest 0.25 inches. They indicate that the ruler can measure to the nearest inch.

14.2598 inches cannot be measured with this ruler.

That leaves 14.25.

Hope this helped.

Answer: False

Step-by-step explanation:

[tex]\sqrt{5x}=\sqrt{x} \sqrt{5} \neq x\sqrt{5}[/tex]

Answer:

C.

Step-by-step explanation:

The boundary of a circle is the circle itself.

The radius of a circle is a segment from the center of the circle to any point of the circle.

In a circle, every radius has the same length.

Answer: C.

Calculations:

Normal pop has mean of 20.0

standard deviation = 4.0

XNN(20.0, 4.0)

a).

[tex]z=\frac{x-h}{z}[/tex]

[tex]=\frac{25-20}{4.0} =\frac{5}{4} =1.25[/tex]

Z = 1.25

b).

The proportion between 20 and 25 is P(20 <x<25.0)

[tex]=p(\frac{20-20}{4} < z < \frac{25-0}{4} )[/tex]

[tex]=P(0 < z < 1.25)[/tex]

[tex]=P(Z < 1.25)-P(z < 0)[/tex]

[tex]=0.8944-0.5000[/tex]

P(20 < x < 25)=0.3944

c).

The proportion value is less than 18 when

[tex]P(x < 18)=p(\frac{x--4}{6} < \frac{18-20}{4}[/tex]

[tex]=P(z < \frac{-2}{4})[/tex]

[tex]=P(z < -0.5)[/tex]

P(x<18) = 0.3085

Answer:

2

Step-by-step explanation:

2.is best possible answer as it.says below 1000...

Answer:

the answer is

x^2 – 2y ≥ 7000

2x + 5y < 1000

so it would be the second option

Step-by-step explanation:

just took the test:)

Answer:

B

Step-by-step explanation:

[tex](f-g)(x)=4x^2+5x-3-(4x^3-3x^2+5)\\\\=-4x^3+7x^2+5x-8[/tex]

Hence B is correct.

Answer:

Let the angle be x

∘

. Then it's complement = (4x)

∘

.

We know that if the sum of two angles is equal to 90

∘

then the angles are said to be complementary.

Step-by-step explanation:

4x+x=90°

5x=90°

x=90°/5

x=18

4×18=72°

This is the complete solution!

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Answer:

[tex]\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}[/tex]

Step-by-step explanation:

The width of a square is its side length.

The width of a circle is its diameter.

Therefore, the largest possible circle that can be cut out from a square is a circle whose diameter is equal in length to the side length of the square.

Formulas

[tex]\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}[/tex]

[tex]\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}[/tex]

[tex]\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}[/tex]

If the diameter is equal to the side length of the square, then:
[tex]\implies \sf r=\dfrac{1}{2}s[/tex]

Therefore:

[tex]\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}[/tex]

So the ratio of the area of the circle to the original square is:

[tex]\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}[/tex]

Given:

[tex]\implies \sf \textsf{Area of square}=6^2=36\:in^2[/tex]

[tex]\implies \sf \textsf{Area of circle}=\pi \cdot 3^2=28\:in^2\:\:(nearest\:whole\:number)[/tex]

Ratio of circle to square:

[tex]\implies \dfrac{28}{36}=\dfrac{7}{9}[/tex]

I'm guessing you mean

[tex]S_{k+1} = S_k + a_{k+1}[/tex]

and that [tex]S_k[/tex] is the sum

[tex]S_k = 6 + 12 + 18 + \ldots + 6k = 6 (1 + 2 + 3 + \ldots + k) = 3 k (k+1)[/tex]

using the well-known formula

[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]

Then by substitution,

[tex]S_{k+1} = 6 (1 + 2 + 3 + \cdots + k + (k+1)) = 3 (k+1) (k+2)[/tex]

and hence

[tex]a_{k+1} = S_{k+1} - S_k[/tex]

[tex]a_{k+1} = 3 (k+1) (k+2) - 3k (k+1)[/tex]

[tex]a_{k+1} = 3 (k+1) \bigg((k+2) - k\bigg)[/tex]

[tex]\implies \boxed{a_{k+1} = 6 (k + 1)}[/tex]

The maximum concentration is greatest at; t = 4.926 hours

We are given the equation that represents the concentration as;

C = (3t² + t)/(50 + t³)

The maximum value of C is obtained when the slope of C' is zero (can be a local maxima too). So we are going to find solutions of C'.

C' = (-3t⁴ - 2t³ + 300t + 50)/(50 + t³)

At C' = 0, we have;

-3t⁴ - 2t³ + 300t + 50 = 0

Using online polynomial root calculator, the only valid root of this is;

t = 4.926 hours

Thus, the maximum concentration is greatest at t = 4.926 hours

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Combine the fractions and factorize.

[tex]\dfrac{3a^2b}{a-b} + \dfrac{3ab^2}{b-a} = \dfrac{3a^2b}{a - b} - \dfrac{3ab^2}{a - b} \\\\ ~~~~~~~~ = \dfrac{3a^2b - 3ab^2}{a - b} \\\\ ~~~~~~~~ = \dfrac{3ab (a - b)}{a - b} \\\\ ~~~~~~~~ = 3ab[/tex]

The relationship between temperature and the coffee sales is a negative exponential of temperature

relation is subject of order between to sets or how the connected to each other.

The temperature of liquid is essential in the  process of brewing because its affects the rate of evaporation or extraction. it refers to the test and matters that are dissolved from the coffee beans. The hot is the water, the quick it is to extract. At a high temperature, it’s tougher to control the rate of extraction. This can lead to over-evaporation of liquid, making your coffee taste too bitter since the heat strips away a lot of oxygen.

since the temperature varies over the year, which implies the taste of coffee also vary in a manner that in cold days people love coffees and in hotter days the people love to drink cold drinks instead of coffees
so in cold days the sales of coffees is grater in comparison with hot days

Thus the relationship between the sales of coffees and temperature is negative exponential of temperature.

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Using the hypergeometric distribution, it is found that there is a 0.0002 = 0.02% probability that exactly 6 patients will die.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters for this problem are:

N = 25, k = 6, n = 8.

The probability that exactly 6 patients will die is P(X = 6), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 6) = h(6,25,8,6) = \frac{C_{6,6}C_{19,2}}{C_{25,8}} = 0.0002[/tex]

0.0002 = 0.02% probability that exactly 6 patients will die.

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The correct information based on the equation is that the functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.

From the graph of f(x):

⇒ Axis of symmetry will be at x = 2

⇒ The maximum value of f(x) = 4

From the table of g(x):

⇒ Axis of symmetry will be at x = 2

⇒ The maximum value of g(x) = 3

The graph is attached.

The functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.

Here is the other part of the question:

Which statement is true?

The functions f and g have the same axis of symmetry, and the maximum value of f is less than the maximum value of g.

The functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.

The functions f and g have different axes of symmetry and different maximum values.

The functions f and g have the same axis of symmetry and the same maximum values.

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The type of transformation that preserves the symmetry of an even function f(x) but does not preserve the symmetry of an odd function g(x) is vertical translation.

Vertical translation of a graph is done by moving the base graph up or down in the y-axis direction. Each point on a graph is moved k units vertically to translate the graph by that many units.

The vertical translation is the movement of the curve along the y-axis by a certain number of units without altering the function's shape or domain.

The function's form is preserved in the case of vertical translation.

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Answer:

D.  -924 feet

Step-by-step explanation:

For this problem, we'll need the relationship [tex]d=vt[/tex] where "d" is the distance traveled, "v" is the velocity the object is traveling, and "t" is the amount of time that it traveled.

Velocity is a "vector" quantity, which has both a magnitude and a direction.  The magnitude is the speed (42 feet per second) and the direction is downward.  Collectively, the velocity is -42 feet per second.  This will address the change in altitude and signify that the change in altitude is downward.

All quantities should be using units that match.

In this case, the distances provided in the answers are all measured in feet, and the speeds are measured in feet per second, so the feet match.

Also, the times are measured in seconds, and the speeds are measured in feet per second, those also match.

[tex]d=vt[/tex]

[tex]d=(\frac{-42\text{ feet}}{\text{second}})(22\text{ seconds})[/tex]

[tex]d=-924 \text{ feet}[/tex]

Answer:

-0.61

Step-by-step explanation:

0.55/2=0.275

Read 0.275 from normal distribution tables

Gives -0.61

Answer:

A 256/3

Step-by-step explanation:

1/3 * 4^4 =

1/3 * (4*4*4*4) =

1/3 * 256 = 256/3

Answer:

A = 256/3

Step-by-step explanation:

F(x) = 1/3 × 4ˣ = 4ˣ/3

F(4) = 4⁴/3 = 256/3

Answer:

Mikhail is 44 years old.

Step-by-step explanation:

Set both Gabrielle and Mikhail's age to a variable.

Gabrielle is x, Mikhail is also x.

Now create an equation using the variables with the sum.

Age1 + Age2 + 15 = 103

x + x + 15 = 103

Now we solve.

1. Combine like terms

2x + 15 = 103

2. Make all the numbers on one side of the equation, and the variables of the other, so subtract.

2x + 15 - 15 = 103 - 15

2x = 88

3. Simplify further by dividing.

x = 44

Mikhail is 44 years old.

Check your work:

44 + (x + 15) = 103

x + 15 = 59

x = 44

Answer:

Step-by-step explanation:

Let Gabrielle's age be x.

The age of the milk will be x - 15.

x + (x - 15) = 103.

2x - 15 = 103

2x = 118

x = 59

The milk's age = x - 15 = 59 - 15 = 44.