1. Paulina wants to find the width, AB, of a river. She walks along the edge of the river 200 ft and marks point C. Then she walks 60 ft further and marks point D. She turns 90° and walks until her location, point A, and point C are collinear. She marks point E at this location, as shown. (a) Can Paulina conclude that ΔABC and ΔEDC are similar? Why or why not? (b) Suppose DE = 40 ft. Calculate the width of the river, AB. Show all your work and round answer to the nearest tenth. Answer

1. Paulina Wants To Find The Width, AB, Of A River. She Walks Along The Edge Of The River 200 Ft And

Answers

Answer 1

Answer:

Step-by-step explanation:

a). In ΔABC and ΔEDC,

Since, AB and DE are parallel and AE is a transversal,

Therefore, ∠CAB ≅ ∠CED [Alternate interior angles]

m∠D = m∠B = 90°

ΔABC ~ ΔEDC [By AA property of similarity of two triangles]

b). Therefore, by the property of similar triangles,

"Corresponding sides of two similar triangles are proportional"

[tex]\frac{DC}{BC}= \frac{DE}{AB}[/tex]

[tex]\frac{60}{200}=\frac{40}{AB}[/tex]

AB = [tex]\frac{40\times 200}{60}[/tex]

     = 133.33

     ≈ 133.3 ft


Related Questions

Cual es la raiz cudrada de 2

Answers

Answer:

1.4142135

Step-by-step explanation:


a.) x ≥ 2

b.) x > 2

c.) x < 2

d.) x ≤ 2

Answers

Answer:

x < 2

Step-by-step explanation:

There is an open circle at 2 so that means it is not equal to

The line goes to the left so x is less than 2

x < 2

Answer:

c.) x < 2

Step-by-step explanation:

open circle means > or <

the line is going to the left, meaning < or ≤

from this, we know the inequality is x < 2

which expression is equivalent to 10 a+ 3b -2a+b

Answers

Answer:

Step-by-step explanation:

Simplify like terms.

10a-2a+3b+b = 8a+4b

Answer:

8a +4b

4(2a+b)

Step-by-step explanation:

10 a+ 3b -2a+b

Combine like terms

10a-2a   +3b+b

8a +4b

We can factor out 4

4(2a+b)

The temperature on a mountain peak was 7 degreesFahrenheit (F) at 6:00 p.m. By 8:00 p.m., thetemperature had dropped to 0F. If the temperaturecontinued to drop at about the same rate, which isthebestestimate of the temperature at 11:00 p.m
A -20 / B. -14 / C -10 / D -9 /

Answers

Given:

The temperature on a mountain peak was 7°F at 6:00 p.m.

By 8:00 p.m., the temperature had dropped to 0°F.

To find:

The temperature at 11:00 p.m. if the temperature continued to drop at about the same rate.

Solution:

Time between 6:00 p.m. to 8:00 p.m. is 2 hours.

Change in temperature in 2 hours is -7°F.

Change in temperature in 1 hours is [tex]-\dfrac{7}{2}^\circ[/tex]F.

Time between 8:00 p.m. to 11:00 p.m. is 3 hours.

Change in temperature in 3 hours is [tex]3\times \dfrac{-7}{2}^\circ[/tex]F, i.e., [tex]-\dfrac{21}{2}^\circ[/tex]F.

Now, the temperature at 11:00 p.m is:

[tex]0-\dfrac{21}{2}=-10.5[/tex]

Therefore, the temperature at 11:00 p.m. is -10.5°F.

Note: All options are incorrect.

Determine which equations have the same solution set as 2/3 -x +1/6 = 6x by recognizing properties, rather than solving. Check all that apply.

Answers

Answer:

The answer is "0.1190".

Step-by-step explanation:

Given:

[tex]\to \frac{2}{3} -x +\frac{1}{6} = 6x\\\\\to \frac{2}{3} +\frac{1}{6} = 6x+x\\\\\to \frac{4+1}{6} = 7x\\\\\to \frac{5}{6} = 7x\\\\\to x=\frac{5}{6\times 7} \\\\\to x=\frac{5}{42}\\ \\\to x= 0.1190[/tex]

Answer:

A.) 4 - 6x + 1 = 36x

B.) 5/6 - x = 6x

F.) 5 = 42x

Step-by-step explanation:

edge.

if 2x + 3x.find the value of x​

Answers

if 2x + 3x = ? the question is incomplete or is it about traingle

arctanx=arccos(-5/13)
i know that there is no solution but i need to know how to get there

help me solve the trig equation for x!!

Answers

If φ = arccos(-5/13), then cos(φ) = -5/13. Since this is negative, you know φ is an angle that terminates either the second or third quadrant.

arctan(x) has a range of -π/2 < arctan(x) < π/2, which is to say that arctan(x) is an angle that terminates in either the first or fourth quadrant.

These quadrants don't overlap, so there is no solution to the equation.

2(-3-6)+(-7+4)to the power of 2

Answers

I don’t know if it’s correct or not

Which of the following statements is false?

Answers

Answer:

option D is false it's not parallelogram

calcula el valor de A - B, si se sabe que: A=

Answers

Answer:

[tex]P=\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]P=\frac{(x+3)^2-(x-3)^2}{(x+6)^2-(x-6)^2}[/tex]

   [tex]=\frac{[(x+3)-(x-3)][(x+3)+(x-3)]}{[(x+6)-(x-6)][(x+6)+(x-6)]}[/tex]

   [tex]=\frac{6(2x)}{12(2x)}[/tex]

   [tex]=\frac{1}{2}[/tex]

Por tanto, el valor de P será [tex]\frac{1}{2}[/tex]

Help if you know thanks

Answers

x= - 1/2,-1

or

x= - 0.5, -1

Answer:

x = -1/2  x=-1

Step-by-step explanation:

2x( x+1.5) = -1

Distribute

2x^2 + 3x = -1

Add 1 to each side

2x^2 +3x+1 = 0

Factor

(2x+1) (x+1) =0

Using the zero product property

2x+1 = 0   x+1=0

2x = -1    x=-1

x = -1/2  x=-1

Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why AABC= ALMN?
Check all that apply
O A. LL
O B. ASA
I C. LA
D. HL
E AAS

Answers

3 Answers:

Choice A.  LLChoice D.  HLChoice F.  SAS

==========================================================

Explanation:

Let's go through the answer choices one by one.

A) This can be used because LL = leg leg, and this means we have two pairs of congruent legs. Those pairs are AC = LN and CB = NM. The LL theorem only applies to right triangles.B) This cannot be used. We don't have info about two pairs of angles. We only know that one pair of angles are the same (those 90 degree angles). So we can't form the second "A" in "ASA". This idea will come up again in choice C and choice E.C) This cannot be used. Why not? Because the "A" of "LA" refers to "acute angle". But unfortunately we don't know anything about the acute angles (whether they are congruent or not). The LA theorem can only be applied to right triangles.D) This can be used. We can use the HL (hypotenuse leg) theorem because we see that AB = LM are the pair of congruent hypotenuses, and you can use any of the congruent leg pairs to form the L of HL. Similar to LL and LA, the HL theorem only works for right triangles.E) This cannot be used. Like with choice B, we can't form the second "A" of "AAS".F) This can be used because we have two pairs of congruent sides, with a pair of congruent angles between those sides. Those angles being the marked 90 degree angles. It turns out that LL theorem is a special case of the SAS theorem.

In short, we can use choice A, choice D, choice F. We can't use the other three choices because we lack the info about any other pairs of angles.

The congruence theorem or postulate that we can use to show that triangle ABC is congruent to triangle LMN is LL (Side-Side-Side), the correct option is A.

What are congruent triangles?

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]

(|AB| denotes length of line segment AB, and so on for others).

We are given that;

Sides are equal

Now,

Based only on the information given in the diagram, we can use the following congruence theorems or postulates to show that triangle ABC is congruent to triangle LMN:

A. LL (Side-Side-Side): This theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. In this case, we know that AB = LM, AC = LN, and BC = MN, so we can use LL to show that triangle ABC is congruent to triangle LMN.

B. ASA (Angle-Side-Angle): This theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. In this case, we do not know any angle measures, so we cannot use ASA to show that the triangles are congruent.

Therefore, by the  congruent triangles the answer will be LL (Side-Side-Side).

Learn more about congruent triangles here:

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please find the answer
there are options given below
plz give answer asap​

Answers

Answer

33.3

Step-by-step explanation:

if u multiply the 2, and then find the ratio of them in comparison to the number under, you will find the rate decreases by 10 percent every time, the first situation it is 4/8 = 5/10, second situation is it 32/80= 4/10, and htis situation is most like 3/10, right ? so the answer would be 33.3 :)

A girl is 18 years younger than her mother. In 6 years time, the sum of their ages will be 54. How old is the girl now?​

Answers

Answer:

12 yrs.

Step-by-step explanation:

let present age of girl=x

age of mother=x+18

after 6 yrs

age of girl=x+6

age of mother=x+18+6=x+24

according to the condition of question

(x+6)+(x+24)=54

2x+30=54

2x=54-30=24

x=24/2=12

Nigel's age (n) is 3 years more
than his sister's age (s).

A. N = 3N + 3
B. N =3s
C. N = 3 + s
D. S = -3s/n

Answers

Answer:

b

Step-by-step explanation:

n=3s

~~~~~~~~~~~~~~~~~

Describe how (2 cubed) (2 superscript negative 4) can be simplified.

Answers

Answer:

1/2

Step-by-step explanation:

Given:

(2 cubed) (2 superscript negative 4)

= (2³)(2^-4)

= (2³) (1 / 2⁴)

= (2³ * 1) / 2⁴

= 2³ / 2⁴

Both numerator and denominator has the same base. Thus, pick one of the bases

Also, in indices, division sign can be translated to subtraction

Therefore,

2³ / 2⁴

= 2^3-4

= 2^-1

= 1/2¹

= 1/2

(2³)(2^-4) = 1/2

Answer:

D

Step-by-step explanation:

bc i said so

need help with this!!

Answers

Answer: C. 40



Explanation: Since the correct graph is 3 (based on the information given), you would look at the part of the graph where only circles BM and NT overlap. The number inside that section would be the amount of people who watched both Batman and Ninja Turtles but not Looney Tunes. By observing the graph, you can tell that the number 40 is in the section where BM and NT overlap, so therefore the answer would be 40.



Hope that helps シ

3. Express the mixed recurring decimal 15.732 in p/q form.​

Answers

Answer

15717/999

Step-by-step explanation

n=15.732732

10n=157.32732

100n=1573.27327

1000n=15732.732732

n= 15.732732

999n=15717

999 999

Answer:

3933/250

Step-by-step explanation:

A car travels a distance of 800m in 40s find its speed

Answers

Answer:

the answer is 20m/s

Step-by-step explanation:

speed = distance/time which equals to speed = 800/40, so the answer is 20m/s

Answer:

20m /s

Step-by-step explanation:

Speed = [tex]\frac{Distance}{time}[/tex]

             [tex]= \frac{800}{40}=\frac{80}{4}= 20[/tex]

AYUDAAAAA
Un litro de leche de búfala equivale a 1.7 litros de leche de vaca. ¿si tengo
27 litros de leche de búfalo, a cuantos litros de leche de vaca equivaldría?

Answers

Answer:

27 litros de leche de búfalo equivalen a 45.9 litros de leche de vaca.

Step-by-step explanation:

Sabiendo que un litro de leche de búfala equivale a 1.7 litros de leche de vaca, podemos calcular el equivalente de capacidad de la vaca para 27 litros de leche de búfala mediante Regla de Tres Simple:

[tex]x = 27\,L\times \frac{1.7\,L}{1\,L}[/tex]

[tex]x = 45.9\,L[/tex]

27 litros de leche de búfalo equivalen a 45.9 litros de leche de vaca.

write the equation of the line that passes through the point (-2,4) and (5,8). Put your answer in fully reduced point slope form, unless it is a vertical or horizontal line.

Answers

Answer:

y-4=4(x+2)/7

Step-by-step explanation:

slope(m) = (8-4)/(5-(-2)) =4/7

b = 4-(4/7)×(-2) = 36/7

y = mx+b

y = 4x/7+36/7

in point-slope form,

y-4=4(x+2)/7

please help asap, see attached photo. This is due in 1 hour!!! please answer both questions. Both 5 and 6

Answers

Answer:

A and C

Step-by-step explanation:

5) logx+log(x+9)=2

log(x(x+9))=2, log(x^2+9x)=2

6) log(x^2+9x)=2

(x^2+9x)=36 or 6^2

Can someone help with these 2?

Answers

Answer:

a. 25 ft squared

b. 0.3

Step-by-step explanation:

a. if the perimeter is 20 that means that each side would be 5 because its a square and 5 x 5 is 25.

b. 0.3 to the third power is 0.027

pleeaseeee help me !!!

Answers

Answer 3. -7.5 is located to the left of 6.5 on a number line oriented from left to right.

can y’all help me out

Answers

Answer:

B: y = {-13, -5, 3, 15}

Step-by-step explanation:

Let's plug each x-value into this equation: f(x) = 4x + 3

Domain: {-4, -2, 0, 3}

First, let's start with -4:

f(x) = 4x + 3

y = 4x + 3

y = 4(-4) + 3

y = -16 + 3

y = -13

Next, let's do -2:

f(x) = 4x + 3

y = 4x + 3

y = 4(-2) + 3

y = -8 + 3

y = -5

After that, let's do 0:

f(x) = 4x + 3

y = 4x + 3

y = 4(0) + 3

y = 0 + 3

y = 3

Finally, let's do 3:

f(x) = 4x + 3

y = 4x + 3

y = 4(3) + 3

y = 12 + 3

y = 15

Now that we have all our y-values, let's set up the range:

Range (y-values): {-13, -5, 3, 15}

As you can see, the only answer choice that includes this range is B;

{-13, -5, 3, 15}.

In Exercises 1-4, determine whether the dilated figure or the original figure is closer to the center of dilation. Use the given location of the center of dilation and scale factor k.
1. Center of dilation inside the figure; k = 3
Center of ditation inside the figure, k = 1/2
3. Center of dilation outside the figure: = 120%
4. Center of dilation outside the figure; k = 0.1

Answers

When the Center of dilation is inside the figure

The original figure is closer to the center of dilationThe dilated figure is closer to the the center of dilation

When the Center of dilation is outside the figure

    3. The original figure is closer to the the center of dilation

    4. The dilated figure is closer to the center of dilation

The center of dilation is the fixed point from which the distances in a dilation are measured

The scale factor is ratio of the side lengths of an original figure or preimage to  the side lengths of the newly formed image

Center of dilation is inside the figure

Where the center of dilation is inside the figure, and the scale factor is larger than 1, k = 3 > 1,  we have;

The distance of a point on the dilated figure, including the distances from the center of dilation is 3 times the distances of points on the original image from the center of dilation

Therefore, the original figure has a shorter distance to and is therefore closer to the the center of dilation than the dilated figure

     2. Where the center of dilation is inside the figure, and the scale factor is a fraction between 0 and 1 k = 1/2, we have;

The distance of a point on the dilated figure, including the distances from the center of dilation is 1/2 times the distances of points on the original image from the center of dilation

Therefore, the dilated figure has a shorter distance to and is therefore closer to the the center of dilation than the original figure

Center of dilation outside the figure

     3. Given that the center of dilation is outside the figure and the scale factor is larger than 1, k = 120% = 120/100 = 1.2 > 1, we have;

The distance of the dilated figure from the center of dilation is 120% of the distance of the original figure from the center of dilation, therefore, the original figure is closer to the the center of dilation than the dilated figure

     4. Where the center of dilation is outside the figure and the scale factor is a fraction between 0 and 1, k = 0.1 < 1

The distance of the dilated figure from the center of dilation is only 0.1 times the distance of the original figure from the center of dilation, and therefore, the dilated figure is closer to the center of dilation

Learn more about scale factors and center of dilation here;

https://brainly.com/question/12162455

Which best describes the relationship between the lines with equations −6x+8y=−1 and −4x−3y=2?

Answers

Answer:

it is linear

Step-by-step explanation:

Both of these both lines are perpendicular to each other.

We have the two equations of straight lines :

− 6x + 8y = −1 and −4x − 3y = 2.

We have to identify the relation between these two lines.

What is the general equation of a straight line ?

The general equation of a straight line is as follows -

y = mx + c

where -

m - slope of line

c - intercept of line on y - axis.

According to the question, we have -

−6x + 8y = −1           ...(1)

−4x − 3y = 2            ...(2)

Rearranging the terms of the equations we get -

y = [tex]\frac{3}{4} x - \frac{1}{8}[/tex]                 ...(3)

and

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

When compared -

The slope of line −6x + 8y = −1 is m(1) = [tex]\frac{3}{4}[/tex].

The slope of line −4x − 3y = 2  is m(2) = [tex]\frac{-4}{3}[/tex].

We can see that -

m(1) x m(2) = - 1

The product of the slopes of two perpendicular lines is -1.

Hence, these both lines are perpendicular to each other.

To solve more questions on relation between straight lines, visit the link below -

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arc length of an oval that is 6ft by 5ft. i just want 1/4 of the oval. i want to find out how long i would need a wire to go from the ground to the middle of the "dome".
the picture explains it better.

in the end i want to have a wire frame around the garden and than take some netting and use that to keep out the big bugs and birds. i will of course use zip ties to attach the screen/netting to the frame. unless there is a easier and cheaper way to do this.​

Answers

You can model the ellipse with the equation

(x/6)² + (y/5)² = 1

If you're comfortable with calculus, read on.

Let x = 6 cos(t ) and y = 5 sin(t ), with 0 ≤ t ≤ π/2. Then the curve C parameterized by (x(t), y(t)) traces out one quarter of the ellipse. The arc length of this curve is given by the integral,

[tex]\displaystyle\int_C\mathrm ds = \int_0^{\pi/2}\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt \\\\ = \int_0^{\pi/2}\sqrt{36\sin^2(t)+25\cos^2(t)}\,\mathrm dt \\\\ = \int_0^{\pi/2}\sqrt{25+11\sin^2(t)}\,\mathrm dt \\\\ = 5\int_0^{\pi/2}\sqrt{1+\frac{11}{25}\sin^2(t)}\,\mathrm dt[/tex]

Unfortunately, you cannot find the exact value of this integral. (Well, you can, but it involves introducing a special kind of function; I'll link it in a comment.)

But you can approximate it, and the integral above comes out to about 8.657.

I'm not sure if there's a simpler, purely geometric way to estimate the arc length. But since the semiaxes (5 ft and 6 ft) are fairly close, you could try a circle with a radius somewhere in between. The arc length would range between 7.854 ft and 9.425 ft. If the material isn't too expensive, you can always overshoot and trim off the excess or repurpose it.

I’ll mark u as a brainliest!! pls help me

Answers

Answer:

Shorter leg is 7

Bigger leg is 7√3 = 12.1 (rounded to the nearest tenth)

Which graph represents the function f(x)=|x−1|−3 ?

Answers

Answer is B, (the one on the top right)
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