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3 years ago

ABCD is a parallelogram. If AB is equal to 2x + 1 and CD is equal to x + 13, find x.

Mathematics

1 answer:

morpeh [17]3 years ago

6 0

Hi!

Because this is a parallelogram, we know that AB is equal to CD.

2x + 1 = x+13

Now solve by isolating x on one side.

Subtract 1 from both sides.

2x + 1 - 1 = x + 13 - 1

2x = x + 12

Subtract x from both sides.

2x - x = x - x + 12

x = 12

The answer is x = 12

Hope this helps! :)

-Peredhel

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nikdorinn [45]

Answer:

see explanation

Step-by-step explanation:

There is a common difference d in the values, that is

9 - 5 = 13 - 9 = 17 - 13 = 21- 17 = 4

To obtain a term in the sequence add 4 to the previous term, thus

t₉ = t₈ + 4 → C

(b)

Given the n th term formula 3n - 8

To find any term, substitute the term position n into the formula

(i) first term (n = 1), then

3(1) - 8 = 3 - 8 = - 5

(ii) tenth term (n = 10, then

3(10) - 8 = 30 - 8 = 22

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3(100) - 8 = 300 - 8 = 292

5 0

3 years ago

Which expressions are equivalent to x + 2y + x + 2 ? Choose all answers that apply:

Inga [223]

Answer:

2(x+y+1)

Step-by-step explanation:

x + 2y + x + 2

= 2x + 2y + 2

= 2(x + y + 1)

Answer:

2(x+y+1)

8 0

3 years ago

A box contains $7.45 in nickels, dimes, and quarters. There are 43 coins in all, and the sum of the numbers of nickels and dimes

kari74 [83]

Answer:

Number of nickels = 6

Number of dimes = 14

Number of quarters = 23

Step-by-step explanation:

Total number of coins = 43

Let number of nickels = n

Let number of dimes = d

Let number of quarters = q

$n+d+q=43 ...... (1)$

Money in n nickels = $n \times 0.05$

Money in d dimes = $d \times 0.10$

Money in q quarters = $q \times 0.25$

Total money = $7.45

$0.05n +0.10d+0.25q = 7.45\\\Rightarrow 5n +10d+25q = 745 .... (2)$

The sum of the numbers of nickels and dimes is 3 less than the number of quarters.

i.e.

$n+d=q-3$

Let us put the value in (1):

$q-3+q=43\\\Rightarrow 2q= 43+3\\\Rightarrow q =23$

Putting the value of q in (1) and (2):

n+d = 20 .... (3)

$5n+10d+575 =745\\\Rightarrow 5n+10d =170\\\Rightarrow n+2d =34 .... (4)$

(4) - (3):

d = 14

Now, from (3):

n = 6

Number of nickels = 6

Number of dimes = 14

Number of quarters = 23

5 0

3 years ago

The elevation was –12 feet at the beginning of your hike at 10:00 a.m. The elevation rose 4 feet every hour until 7:00 pm. At wh

uranmaximum [27]

Answer:

7:00 pm

Step-by-step explanation:

-12+4= -8

-8+4= -4

-4+4=0

0+4=4

4+4=8

8+4=12

12+4=16

Hope this helps!

7 0

3 years ago

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Marcus bought r movie posters for $4 each write a algebraic expression for the total amount Marcus spent

dlinn [17]

4r

That is the expression. Every poster costs $4, so multiply that by however many posters he buys (r).

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3 years ago