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3 years ago

12

A diagonal support beam is attached to the gate of a fence as shown. Which angles must be congruent in order for the top and bot

tom sides of the gate to be parallel?

1 answer:

Harrizon [31]3 years ago

5 0

Where is the angle? Please post the file attachment.

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Pat borrowed $2000 to help pay college expenses. The interest rate was 5% annually, and she will repay the loan in 4 years. How

valentina_108 [34]

Step-by-step explanation:

5% multipyed by 4 years is 20%

20% of 2000 is 400

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Step-by-step explanation:

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Find the sum of the first 48 terms of the following series, to the nearest integer.

Andru [333]

Answer:

3,672

Step-by-step explanation:

Given the sequence 6, 9, 12...

The sequence is an arithmetic sequence

first term a = 6

common difference d = 9 - 6 = 12 - 9 = 3

number of terms n = 48

Sn = n/2[2a+(n-1)d]

Substitute the given values

S48 = 48/2[2(6)+(48-1)(3)]

S48 = 24(12+(3*47))

S48 = 24(12+141)

S48 = 24(153)

S48 = 3,672

Hence the sum of the first 48terms is 3,672

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3 years ago

Two tailors, Valentina and Laura, sit down to do some embroidery. Valentina can embroider 2 shirts per hour, and Laura can get t

mina [271]

Answer:

Valentina and Laura finished the same total number of shirts in $4$ hours.

Total number of shirts finished by Valentina $=23$

Total number of shirts finished by Laura $=23$

Step-by-step explanation:

Suppose that Valentina and Laura finished the same total number of shirts in $t$ hours.

Valentina can embroider 2 shirts per hour and Valentina has already completed 15 shirts.

Total number of shirts finished by Valentina $=2t+15$

Laura can get through 3 shirts per hour and Laura has completed 11 shirts.

Total number of shirts finished by Laura $=3t+11$

Therefore,

$2t+15=3t+11\\3t-2t=15-11\\t=4$

So,

Valentina and Laura finished the same total number of shirts in $4$ hours.

Total number of shirts finished by Valentina $=2(4)+15=8+15=23$

Total number of shirts finished by Laura $=3(4)+11=12+11=23$

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3 years ago