Write the expanded form of the expression y(0.25 +6)

The sum of two numbers is 107, the difference is 51. Find the numbers. Answer : The numbers are

Fynjy0 [20]

Answer:

The answer is 56.

Others are 50 + 57 = 107, 44 + 63 = 107, and 39,68

Step-by-step explanation:

107-51 = 56

8 0

3 years ago

7 pt 1 c + 4 pt 1 c

kaheart [24]

ANSWERS

1. B

2. B

3. A

4. C
5. B

6. A

WORKINGS

QUESTION 1

7 pt 1c + 4pt 1c (pt for Pints; c for Cups)
= 7pt + 1c + 4pt + 1c

Collecting like terms

= 7pt + 4pt + 1c + 1c

= 11pt + 2c

1pt = 2c

Therefore,

11pt 2c = 11pt + 1pt

= 12 pt (OPTION B)

QUESTION 2

7c 3fl oz – 3c 4fl oz (c for Cups; oz for Ounce)
= 7c + 3fl oz – (3c + 4fl oz)

= 7c + 3fl oz – 3c – 4fl oz

Collecting like terms

= 7c – 3c + 3fl oz – 4fl oz

= 4c – 1fl oz

1c = 8fl oz

Therefore, 4c can be rewritten as 3c + 8fl oz

4c – 1fl oz = 3c + 8fl oz – 1fl oz

= 3c + 7fl oz

= 3c 7fl oz (Option B)

QUESTION 3

4lb 4oz – 2lb 7oz (lb for Pounds; oz for Ounce)

= 4lb + 4oz – (2lb + 7oz)

= 4lb + 4oz – 2lb – 7oz

Collecting like terms

= 4lb – 2lb + 4oz – 7oz

= 2lb – 3oz

1lb = 16oz

Therefore, 2lb can be rewritten as 1lb + 16oz

2lb – 3oz = 1lb + 16oz – 3oz

= 1lb + 13oz

= 1lb 13oz (Option A)

QUESTION 4

7T 200lb – 2T 700lb (T for Tons; lb for Pounds)

= 7T + 200lb – (2T + 700lb)

= 7T + 200lb – 2T – 700lb

Collecting like terms

= 7T – 2T + 200lb – 700lb

= 5T – 500lb

1T = 2,000lb

Therefore, 5T can be rewritten as 4T + 2,000lb

5T – 500lb = 4T + 2,000lb – 500lb]

= 4T + 1,500lb

= 4T 1,500lb (Option C)

QUESTION 5

7 d 12 h – 5 d 18 h (d for Days; h for Hours)
= 7d + 12h – (5d + 18h)

= 7d + 12h – 5d – 18h

Collecting like terms

= 7d – 5d + 12h – 18h

= 2d – 6h

1d = 24h

Therefore, 2d can be rewritten as 1d + 24h

2d – 6h = 1d + 24h – 6h

= 1d + 18h

= 1d 18h (Option B)

QUESTION 6
3 h 42 min – 1 h 12 min (h for Hours; min for Minutes)

= 3h + 42min – (1h + 12min)

= 3h + 42min – 1h – 12min

Collecting like terms

3h – 1h + 42min – 12min
= 2h + 30min

= 2h 30min (Option A)

6 0

3 years ago

Write 80% as a decimal number and as a reduced fraction

GuDViN [60]

Answer:

Decimal: 0.80 Reduced fraction: $\frac{4}{5}$

Step-by-step explanation:

Take 80% and move the decimal two place values to the left.

This makes 0.80 (The decimal point is where the percent sign is.)

0.80 is $\frac{8}{10}$ because the 8 is in the tenths place value.

$\frac{8}{10}$ can be simplified by dividing both the numerator and the denominator by 2.

$\frac{8}{10}$ = $\frac{4}{5}$

7 0

3 years ago

Let <img src="https://tex.z-dn.net/?f=%5Calpha" id="TexFormula1" title="\alpha" alt="\alpha" align="absmiddle" class="latex-form

Margarita [4]

Answer:

$|\alpha| = 2$

Step-by-step explanation:

Since $\alpha$ and $\beta$ are complex conjugates, let's define them as follows:

$\alpha = a+bi$

$\beta = a-bi$

$\frac{\alpha}{\beta^2}=\frac{a+bi}{a^2-b^2-2abi} =\frac{(a+bi)*(a^2-b^2+2abi)}{(a^2-b^2-2abi)*(a^2-b^2+2abi)} =\frac{a^3-3ab^2+(3a^2b-b^3)i}{a^4+2a^2b^2+b^4}$

Since $\frac{\alpha}{\beta^2}$ is a real number, complex part of above result must be zero.

$3a^2b-b^3=0$

From to hold above equality, $b=0$ or $b^2=3a^2$ .

However, since $|\alpha-\beta|=2\sqrt 3$ , $b\neq 0$

So, $b =\sqrt 3 a$ or $b =-\sqrt 3 a$

And since $\alpha$ and $\beta$ are complex conjugates, taking plus or minus sign as found above will not affect the result, so let's write the last version of $\alpha$ and $\beta$ as follows:

$\alpha = a+\sqrt 3 ai$

$\beta = a-\sqrt 3 ai$

Since $|\alpha-\beta|=2\sqrt 3$

$|a+\sqrt 3 ai-a+\sqrt 3 ai|=2\sqrt 3$ ⇒ $a = 1$

Finally, $\alpha = 1+\sqrt 3 i$ ⇒ $|\alpha| = \sqrt{(1^2+\sqrt 3^2)}=2$

3 0

3 years ago

The air pressure inside Jason's bike tires decreases by about 6% each week. The original pressure was 45 pounds per square inch

Fudgin [204]

Lets do this week by week
beginning pressure 45 pounds
end of week 1
45 *.06 = 2.7
45 - 2.7 = 42.3
end of week 2
42.3 * .06 = 2.538
42.3 - 2.538 = 39.762
end of week 3
39.762 *.06 = 2.38
39.762 - 2.38 = 37.37
end of week 4
37.37* .06 = 2.2425
37.37628 - 2.2425= 35.12
end of week 5
35.12 * .06 = 2.107
35.12 - 2.107 = 33.012
end of week 6
33.012* .06 = 1.98
33.012 - 1.98 =31.03

Here is the fast way to get to this answer.
do 1-.06 = .94

then do
45(.94)(.94)(.94)(.94)(.94)(.94) = 31.04

8 0

4 years ago