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3 years ago

. Write an algebraic expression for the following. the sum of 12 and 3 times a number

Mathematics

1 answer:

mariarad [96]3 years ago

4 0

let "a number" = n

"3 times a number" = 3n

"the sum of 12" = "+ 12

Combine the two terms

3n + 12, or (B) is your answer

hope this helps

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ABC and EDC are straight lines. EA is parallel to DB. EC = 8.1 cm. DC = 5.4 cm. DB = 2.6 cm. (a) Work out the length of AE. cm (

harkovskaia [24]

By applying the knowledge of similar triangles, the lengths of AE and AB are:

a. $\mathbf{AE = 3.9 $ cm}\\\\$

b. $\mathbf{AB = 2.05 $ cm} \\\\$

See the image in the attachment for the referred diagram.

The two triangles, triangle AEC and triangle BDC are similar triangles.
Therefore, the ratio of the corresponding sides of triangles AEC and BDC will be the same.

This implies that:

AC/BC = EC/DC = AE/DB

Given:

$EC = 8.1 $ cm\\\\DC = 5.4 $ cm\\\\DB = 2.6 cm\\\\AC = 6.15 $ cm$

a. Find the length of AE:

EC/DC = AE/DB

Plug in the values

$\frac{8.1}{5.4} = \frac{AE}{2.6}$

Cross multiply

$5.4 \times AE = 8.1 \times 2.6\\\\5.4 \times AE = 21.06$

Divide both sides by 5.4

$AE = \frac{21.06}{5.4} = 3.9 $ cm$

b. Find the length of AB:

$AB = AC - BC$

AC = 6.15 cm

To find BC, use AC/BC = EC/DC.

Plug in the values

$\frac{6.15}{BC} = \frac{8.1}{5.4}$

Cross multiply

$BC \times 8.1 = 6.15 \times 5.4\\\\BC = \frac{6.15 \times 5.4}{8.1} \\\\BC = 4.1$

Thus:

$AB = AC - BC$

Substitute

$AB = 6.15 - 4.1\\\\AB = 2.05 $ cm$

Therefore, by applying the knowledge of similar triangles, the lengths of AE and AB are:

a. $\mathbf{AE = 3.9 $ cm}\\\\$

b. $\mathbf{AB = 2.05 $ cm} \\\\$

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brainly.com/question/14327552

3 0

3 years ago

Solve each of the following system of equations by substitution!!! x-5y=-49 y=-2x+1

saul85 [17]

Answer:

(-4,9)

Step-by-step explanation:

substitute the given value for y into the first equation

x-5(-2x+1)=-49

distribute

x+10x-5=-49

add like terms

11x-5=-49

add 5 to both sides

11x=-44

divide both sides by 11

x=-4

now plug x into into the second equation

y=-2(-4)+1

y=8+1

add like terms

y=9

8 0

3 years ago

Night Owl Motel rents rooms with 2 beds for $68 per night and rooms with 1 bed for $57 per night. One evening Night Owl Motel re

mixer [17]

1 bed room = 12
2 bed room = 15

68 x 15 = 1020
57 x 12 = 684
-----------
1020 + 684 = $1704 (total made)

15 two-bed room + 12 one-bed room = 27 rooms in all

5 0

4 years ago

Someone please help me with this. thanks. and please explain.

just olya [345]

It would be 190 km because you do 5 x 3 to get 15 add a 0 at the end of it. Than at 40 because .8 of 150 is 40. Then 150+40= 190

4 0

3 years ago

Read 2 more answers

If DF = 170, find the value of x. Then find DE and EF. DE=3x + 20 EF=2x + 40

Julli [10]

9514 1404 393

Answer:

DE = 86

EF = 84

Step-by-step explanation:

We assume that point E lies on segment DF, so that ...

DE + EF = DF

(3x +20) +(2x +40) = 170

5x = 110 . . . . . . . . . . . . . . . collect terms, subtract 60

x = 22 . . . . . . . . . . . . divide by 5

DE = 3×22 +20 = 66 +20 = 86

EF = 2×22 +40 = 44 +40 = 84

7 0

3 years ago