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uranmaximum [27]
3 years ago
6

Are the expressions 3/4a + 8 - 1/4a - 2 and 1/2(a + 12) equivalent? Show why or why not.

Mathematics
1 answer:
natta225 [31]3 years ago
4 0

Answer:Yes they are equivalent.

Step-by-step explanation:

3/4a + 8 - 1/4a - 2 1/2(a + 12)

Combine like terms Distributive property

2/4a+6 1/2a+6

2/4=1/2 (simplify)

1/2+6=1/2+6

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I have 8 pennies and some quarters, nickels, and dimes. The number of pennies plus nickels equals the number of dimes. I have 3
Darina [25.2K]

There are five nickels.

Let <em>w</em> = the number of pennies; <em>x</em> = the number of nickels; <em>y</em> = the number of dimes; <em>z </em>= the number of quarters.

Then, we have three equations with four unknowns:

(1) <em>w</em> + <em>x = y </em>

(2) 3<em>w</em> = 2<em>z</em>

(3) 2<em>y</em> = 3<em>z</em>

However, there is a fourth <em>unstated </em>condition: <em>w</em>, <em>x</em>, y, and <em>z</em> must all be integers.

Assume that z = 6 (to avoid fractions).

From Equation (2), w = 4.

From Equation (3), y = 9.

Insert the values for <em>w</em> and <em>y</em> into equation (1).

4 + <em>x</em> = 9

x = 9 – 4 = 5

Thus, there are 4 pennies, 5 nickels, 9 dimes, and 6 quarters.

<em>Check</em>: 4 pennies + 5 nickels = 9 dimes

6 quarters + 4 pennies = 3 quarters for every 2 pennies

9 dimes + 6 quarters = 3 dimes for every 2 quarters

5 0
3 years ago
Read 2 more answers
Name the coordinates for the reflection. Reflect point (4, -1) over the x-axis.
inysia [295]

Answer:

i just took the test its (4,1)

Step-by-step explanation:

6 0
3 years ago
Solve for x to the nearest ten
swat32

Answer:

in right angled triangle ABC

by using Pythagoras law

h²=p²+b²

x²=7²+10²

x=√149=12.21cm

5 0
3 years ago
In triangle abc, AC=15 BC=11 and m
Oksana_A [137]

Answer: 10

Step-by-step explanation:

In a right angle triangle

Hypothenus ^2= opposite ^2+ adjacent ^2

According to a diagram below

Hypothenus =15

Opposite =?

Adjacent =11

Substitute for the values

15^2=11^2+opp^2

Opp^2=15^2-11^2

0pp^2= 225-121

Opp2=104

Opp= square root of 104

Opp= 10.2

Opp= ~10

3 0
3 years ago
Una parte de 25 000 dólares se invierte al 10% de interés, otra parte al 12 % y el resto al 16%. El ingreso anual total de las t
Drupady [299]

Answer:

  • $5000 at 10%, $10000 at 12% and 10000 at 16%

Step-by-step explanation:

  • <em>One part of $ 25,000 is invested at 10% interest, another part at 12%, and the rest at 16%. The total annual income from the three investments is $ 3,200. Also, the income from the investment at 16% is equal to the income from the other two investments combined. How much was invested at each interest rate?</em>

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

Let the parts be x, y and z

<u>As per given we get below system of equations:</u>

  • x + y + z = 25000
  • 0.1x + 0.12y + 0.16z = 3200
  • 0.1x + 0.2y = 0.16z

<u>Substitute 0.1x + 0.2y in the second equation:</u>

  • 0.16z + 0.16z = 3200
  • 0.32z = 3200
  • z = 3200/0.32
  • z = 10000

<u>Now we have:</u>

  • x + y + 10000 = 25000 ⇒ x + y = 15000

and

  • 0.1x + 0.12y + 0.16*10000 = 3200 ⇒ 0.1x + 0.12y = 1600

<u>Multiply the second equation and then subtract the first one:</u>

  • 10(0.1x + 0.12y) = 10(1600) ⇒ x + 1.2y = 16000
  • x + 1.2y - (x + y) = 16000 - 15000
  • 0.2y = 1000
  • y = 10000

Then

  • x = 15000 - 10000 = 5000

<u>So the parts are:</u>

  • $5000 at 10%, $10000 at 12% and 10000 at 16%
4 0
3 years ago
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