A geologist wants to determine the distance across the widest part of a nearby lake. The geologist marked off specific points around the lake so that the line containing segment DE would be parallel to the line containing BC. The segment BC is selected specifically because it is the widest part of the lake. The segment DE is selected specifically because it is a short enough distance to easily measure. Use this diagram to answer the following questions.

1. Is ADE similar to ABC'? How do you know? *

Yes. All three sides are proportional.
Yes. Two or more angles are equivalent.
No. Side lengths are not proportional.
There is insufficient information to determine similarity.

2. If ADE is similar to ABC, and |AD| = 1,200 ft and |AB| = 3,600 ft, what is the length of segment BC?

2,700 ft
1,600 ft
2,100 ft
2,400 ft

3. If ABC is similar to ADE what is the length of segment AC? *
5 points
2,000 ft
3,000 ft
2,400 ft
2,800 ft

Answer:

The correct answer is B. The rate of 7% compounded quarterly is better.

Step-by-step explanation:

In the case of investment at 7% compounded quarterly, the final result after 4 years of investment arises from the following calculation:

X = 7000 x (1 + 0.7 / 3) 4x3

X = 9,232.16

Therefore, after 4 years of investment, the amount in the account would be $ 9,232.16.

In turn, in the case of the investment at 6.85% compounded monthly, the final result after the same investment period arises from the following calculation:

X = 7000 x (1 + 0.685 / 12) 4x12

X = 9,199.33

Thus, in this case, the amount in the account after 4 years of investment would be $ 9,199.33.

Answer:

diameter ÷ 2 = 8 ÷ 2 = 4

Step-by-step explanation:

Answer:

A.true)

Step-by-step explanation:

Hope this helps!

Answer:

1/26

Step-by-step explanation:

There are two sets colors; red and black.

13 ranks, each rank has 2 black cards and 2 red

but there are only 2 black eights

2/52

Answer:

Option (4) and Option (6)

Step-by-step explanation:

By the zero product property,

If (x - a)(x - b) = 0

Then, (x - a) = 0 ⇒ x = a

(x - b) = 0 ⇒ x = b

By following the zero product property,

From the given equation,

3(x - 4)(2x - 3) = 0

x - 4 = 0 ⇒ x = 4

2x - 3 = 0 ⇒ x = [tex]\frac{3}{2}[/tex]

Therefore, options (4) and (6) will be the correct options.

Answer:

4 and 6 :)

Step-by-step explanation:

edge

Answer:

a. Yes

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Since Riley has already saved 80 dollars and she needs to save 150 dollars.

150-80=70

She earns 14 dollars per week:

70/14=5

I also wrote a equation:

(150-80)/14=x

Hope this was helpful!

Answer:

She will pay $2.

Step-by-step explanation:

Answer: 24

Step-by-step explanation: negative multiples by a negative is a positive

The opposite of -(-24) is -24.

A number is additive inverse of a given number when sum of the two number is zero and a number is a multiplicative inverse of a given number when product of two number is 1.

According to the given question statement we have to determine what is opposite of -(-24).

We know opposite of two numbers sums to zero.

Given -(-24).              ( negative signs will distribute and it'll become 24).

Let the opposite number be x.

∴ 24 + x = 0

x = -24.

So the opposite of -(-24) is - 24.

learn more about additive and multiplicative inverse here :

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Answer:

2) 9/4

Step-by-step explanation:

12/5 in decimal form is 2.4. As a mixed number, 12/5 is 2 2/5. And, 12/5 is just a reduced form of 36/15. So, the only answer it can be is answer 2: 9/4

Answer:

2.94 in

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

cause its a pretty simple question

Answer:

A=-4/3

B=1/5

C=-5/4

Step-by-step explanation:

Answer:

p=2 (l+w)

Step-by-step explanation:

Answer:

She got 63 chocolates.

Step-by-step explanation:

Answer: The unit price is $6.59 per pair of socks

Step-by-step explanation: 26.36. divided by 4 = 6.59

Answer:  

470

Step-by-step explanation:

Replace x with 10:  470

5(10)(10 - 3( = 500 - 30 = 470

470

The answer is A

Hope this helps!

Answer:

12 Notebooks And 16 Erasers

Step-by-step explanation:

Let x represent the number of notebooks and y represent the number of erasers. (x+y=28) Then, input the cent numbers into the equation. (90x+45y=1800) The 1800 represents the amount of dollars spent. Then simplfy the equation, which gives you 12 notebooks and 16 erasers.

Answer:

See explanation

Step-by-step explanation:

Solving (a):

[tex]a_n = 6a_{n-1}[/tex] where [tex]a_0 = 2[/tex]

n = 1

[tex]a_n = 6a_{n-1}[/tex]

[tex]a_1 = 6a_{1-1}[/tex]

[tex]a_1 = 6a_{0}[/tex]

Substitute 2 for [tex]a_0[/tex]

[tex]a_1= 6 * 2[/tex]

[tex]a_1= 12[/tex]

n = 2

[tex]a_n = 6a_{n-1}[/tex]

[tex]a_2 = 6a_{2-1}[/tex]

[tex]a_2 = 6a_{1}[/tex]

Substitute 12 for [tex]a_1[/tex]

[tex]a_2= 6 * 12[/tex]

[tex]a_2= 72[/tex]

n = 3

[tex]a_n = 6a_{n-1}[/tex]

[tex]a_3 = 6a_{3-1}[/tex]

[tex]a_3 = 6a_2[/tex]

Substitute 72 for [tex]a_2[/tex]

[tex]a_3= 6 * 72[/tex]

[tex]a_3= 432[/tex]

n = 4

[tex]a_n = 6a_{n-1}[/tex]

[tex]a_4 = 6a_{4-1}[/tex]

[tex]a_4 = 6a_{3}[/tex]

Substitute 432 for [tex]a_3[/tex]

[tex]a_4 = 6 * 432[/tex]

[tex]a_4 = 2592[/tex]

n = 5

[tex]a_n = 6a_{n-1}[/tex]

[tex]a_5 = 6a_{5-1}[/tex]

[tex]a_5 = 6a_4[/tex]

Substitute 2592 for [tex]a_4[/tex]

[tex]a_5 = 6 * 2592[/tex]

[tex]a_5 = 15552[/tex]

n = 6

[tex]a_n = 6a_{n-1}[/tex]

[tex]a_6 = 6a_{6-1}[/tex]

[tex]a_6 = 6a_{5}[/tex]

Substitute 15552 for [tex]a_5[/tex]

[tex]a_6 = 6 * 15552[/tex]

[tex]a_6 = 93312[/tex]

[tex]a_1= 12[/tex]   [tex]a_2= 72[/tex]   [tex]a_3= 432[/tex]   [tex]a_4 = 2592[/tex]   [tex]a_5 = 15552[/tex]   [tex]a_6 = 93312[/tex]

Solving (b):

[tex]a_n = a^2_{n - 1[/tex] where [tex]a_1 = 2[/tex]

We have

[tex]a_1 = 2[/tex] which serves as the first term

n =2

[tex]a_n = a^2_{n - 1[/tex]

[tex]a_2 = a^2_{2-1}[/tex]

[tex]a_2 = a^2_{1}[/tex]

Substitute 2 for [tex]a_1[/tex]

[tex]a_2 = 2^2[/tex]

[tex]a_2 = 4[/tex]

n = 3

[tex]a_3 = a^2_{3-1}[/tex]

[tex]a_3 = a^2_{2}[/tex]

[tex]a_3 = 4^2[/tex]

[tex]a_3 = 16[/tex]

n = 4

[tex]a_4 = a^2_{4-1}[/tex]

[tex]a_4 = a^2_3[/tex]

[tex]a_4 = 16^2[/tex]

[tex]a_4 = 256[/tex]

n =5

[tex]a_5 = a^2_{5-1[/tex]

[tex]a_5 = a^2_4[/tex]

[tex]a_5 = 256^2[/tex]

[tex]a_5 = 65536[/tex]

n = 6

[tex]a_6 = a^2_{6-1[/tex]

[tex]a_6 = a^2_{5[/tex]

[tex]a_6 = 65536^2[/tex]

[tex]a_6 = 4294967296[/tex]

[tex]a_1 = 2[/tex]   [tex]a_2 = 4[/tex]   [tex]a_3 = 16[/tex]   [tex]a_4 = 256[/tex]   [tex]a_5 = 65536[/tex]   [tex]a_6 = 4294967296[/tex]

Solving (c):

[tex]a_n=a_{n-1}+3a_{n-2};[/tex] [tex]a_0=1[/tex]  ; ;  [tex]a_1=2[/tex]

[tex]a_1=2[/tex] ---- First term

n = 2

[tex]a_n=a_{n-1}+3a_{n-2};[/tex] becomes

[tex]a_2=a_{2-1}+3a_{2-2}[/tex]

[tex]a_2=a_1+3a_0[/tex]

Substitute values for a1 and a0

[tex]a_2=2+3 * 1[/tex]

[tex]a_2=2+3[/tex]

[tex]a_2=5[/tex]

n = 3

[tex]a_n=a_{n-1}+3a_{n-2};[/tex] becomes

[tex]a_3=a_{3-1}+3a_{3-2}[/tex]

[tex]a_3=a_{2}+3a_{1}[/tex]

[tex]a_3=5+3 * 2[/tex]

[tex]a_3=5+6[/tex]

[tex]a_3=11[/tex]

n = 4

[tex]a_n=a_{n-1}+3a_{n-2};[/tex] becomes

[tex]a_4=a_{4-1}+3a_{4-2}[/tex]

[tex]a_4=a_{3}+3a_{2}[/tex]

[tex]a_4=11+3 * 5[/tex]

[tex]a_4=11+15[/tex]

[tex]a_4=26[/tex]

n = 5

[tex]a_n=a_{n-1}+3a_{n-2};[/tex] becomes

[tex]a_5=a_{5-1}+3a_{5-2};[/tex]

[tex]a_5=a_{4}+3a_3[/tex]

[tex]a_5=26+3 * 11[/tex]

[tex]a_5=26+33[/tex]

[tex]a_5=59[/tex]

n = 6

[tex]a_n=a_{n-1}+3a_{n-2};[/tex] becomes

[tex]a_6=a_{6-1}+3a_{6-2}[/tex]

[tex]a_6=a_{5}+3a_4[/tex]

[tex]a_6=59+3*26[/tex]

[tex]a_6=59+78[/tex]

[tex]a_6=137[/tex]

[tex]a_1=2[/tex]   [tex]a_2=5[/tex]   [tex]a_3=11[/tex]   [tex]a_4=26[/tex]   [tex]a_5=59[/tex]   [tex]a_6=137[/tex]

Solving (d):

[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex];     [tex]a_0=1[/tex]; [tex]a_1=1[/tex]

[tex]a_1=1[/tex] --- First term

n = 2

[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex] becomes

[tex]a_2=2 * a_{2-1}+2^2a_{2-2}[/tex]

[tex]a_2=2 * a_1+4*a_0[/tex]

[tex]a_2=2 * 1+4*1[/tex]

[tex]a_2=2 +4[/tex]

[tex]a_2=6[/tex]

n = 3

[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex] becomes

[tex]a_3=3 * a_{3-1}+3^2 * a_{3-2}[/tex]

[tex]a_3=3 * a_{2}+9 * a_{1}[/tex]

[tex]a_3=3 * 6+9 * 1[/tex]

[tex]a_3=18+9[/tex]

[tex]a_3=27[/tex]

n = 4

[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex] becomes

[tex]a_4=4*a_{4-1}+4^2*a_{4-2}[/tex]

[tex]a_4=4*a_{3}+16*a_{2}[/tex]

[tex]a_4=4*27+16*6[/tex]

[tex]a_4=204[/tex]

n = 5

[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex] becomes

[tex]a_5=5 * a_{5-1}+5^2 * a_{5-2}[/tex]

[tex]a_5=5 * a_{4}+25 * a_{3}[/tex]

[tex]a_5=5 * 204+25 *27[/tex]

[tex]a_5=1695[/tex]

n = 6

[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex] becomes

[tex]a_6=6 * a_{6-1}+6^2*a_{6-2}[/tex]

[tex]a_6=6 * a_{5}+36*a_{4}[/tex]

[tex]a_6=6 * 1695+36*204[/tex]

[tex]a_6=17514[/tex]

[tex]a_1=1[/tex]   [tex]a_2=6[/tex]   [tex]a_3=27[/tex]   [tex]a_4=204[/tex]   [tex]a_5=1695[/tex]   [tex]a_6=17514[/tex]

Solving (e):

[tex]a_n= a_{n-1}+a_{n-3};\ a_0=1; a_1=2; a_2=0[/tex]

First term: [tex]a_1=2[/tex]

Second Term: [tex]a_2=0[/tex]

n = 3

[tex]a_n= a_{n-1}+a_{n-3}[/tex] becomes

[tex]a_3= a_{3-1}+a_{3-3}[/tex]

[tex]a_3= a_{2}+a_0[/tex]

[tex]a_3= 0+1[/tex]

[tex]a_3= 1[/tex]

n = 4

[tex]a_n= a_{n-1}+a_{n-3}[/tex] becomes

[tex]a_4= a_{4-1}+a_{4-3}[/tex]

[tex]a_4= a_{3}+a_{1}[/tex]

[tex]a_4= 1+2[/tex]

[tex]a_4=3[/tex]

n = 5

[tex]a_n= a_{n-1}+a_{n-3}[/tex] becomes

[tex]a_5= a_{5-1}+a_{5-3}[/tex]

[tex]a_5= a_{4}+a_{2}[/tex]

[tex]a_5= 3 + 0[/tex]

[tex]a_5= 3[/tex]

n = 6

[tex]a_n= a_{n-1}+a_{n-3}[/tex] becomes

[tex]a_6= a_{6-1}+a_{6-3}[/tex]

[tex]a_6= a_{5}+a_{3}[/tex]

[tex]a_6= 3 + 1[/tex]

[tex]a_6= 4[/tex]

[tex]a_1=2[/tex]   [tex]a_2=0[/tex]   [tex]a_3= 1[/tex]   [tex]a_4=3[/tex]   [tex]a_5= 3[/tex]   [tex]a_6= 4[/tex]

Answer:

Yes, because the plot shows no apparent pattern.

Step-by-step explanation:

Yes, because the plot is a residual plot from a regression of a variable with the independent variable x.

Therefore, the correct option is 1.)Yes, because the plot shows no apparent pattern.

To learn more about regression refer to:

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Answer:

Option C. 2(x + 8)

Step-by-step explanation:

To know which option is the correct answer, let us simplify each expression given in the options to know which will not result to 2x² – 16. This is illustrated below:

For Option A:

2x² + 4x – 4x – 16

= 2x² – 16

For Option B:

2(x² – 8)

Clear bracket

2x² – 16

For Option C:

2(x + 8)

Clear bracket

2x + 8

For Option D:

(4x² – 32) /2

4x²/2 – 32/2

2x² – 16

From the above illustration, option C did not result to 2x² – 16.

Therefore, option C is the answer to the question.

Answer:

Mrs Barnes has the highest

Explanation:

The slope of the line is found by the method: rise/run

You calculate how much the slope rises(goes up) and divide it by run(goes horizontal).

One more thing to note is that: the slope is negative BECAUSE ITS DECREASING.

Your answer:   -3/2

Answer:

Standard Deviation and Below are, in fact, the right answer.

Step-by-step explanation:

Edge. :)

Answer:

The person above is right, they deserve brainliest.

-standard deviations

-below

ED2021

Answer:

8.no answer A. x=8

Step-by-step explanation:

10.no answer B. x= -3

Answer:

8. (A) x = 8 , 10. (C.) x = 3

Step-by-step explanation:

Number 8 you could do 75 - 35 = 40

so what can you multiply 5 by (x) to get 40? you would multiply 5 by 8 or (x) and get 40

then add 35 + 40 to get 75 degrees which is the parallel angle to the other 75 degrees.

Number 10 you just want to get them to the same number.

so you would do ( 97 - 3 ) to get the ANSWER 87.

so x = 3

Answer:

9. -3/4

10. -5/1

11. UNDEFINED

12. 2/3

Answer:

9. -3/4

10. -5

11. undefined

12. 2/3

Step-by-step explanation: