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2 years ago

You spend $4.50 on 5 pounds of apples. What is the unit rate in dollars per pound?

Mathematics

2 answers:

vredina [299]2 years ago

5 0

Answer:

$0.90 per pound.

Step-by-step explanation:

4.50:5

5/5=1

4.50/5=0.90

Mnenie [13.5K]2 years ago

4 0

0.90/pound :) hope this helps!

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If angle 1 and angle 2 are complementary angles and if the measures of angle 1 is 8 more than the measure of angle 2 determine t

babunello [35]

Answer:

41° and 49°

Step-by-step explanation:

Given:

Angle 1 and angle 2 are complementary angles.

The measures of angle 1 is 8 more than the measure of angle 2.

Question asked:

Determine the measures of angle 1 and 2.

Solution:

Let ∠1 = $x$

Then ∠2 = $x+8$ (given)

As we know that sum of complementary angles are 90° and here given that angle 1 and angle 2 are complementary angles which means,

∠1 + ∠2 = 90°

$x+x+8=90$ °

$2x +8=90$ °

Subtracting both sides by 8,

$2x=90$ ° $-8$

$2x = 82$ °

Dividing both sides by 2,

$x=41$ °

∠1 = $x=41$ °

∠2 = $x+8$

∠2 = $41+8$ = 49°

Therefore, the measures of angle 1 and 2 are 41° and 49°

3 0

2 years ago

How can i prove this property to be true for all values of n, using mathematical induction.

chubhunter [2.5K]

Proof -

So, in the first part we'll verify by taking n = 1.

$\implies \: 1 = {1}^{2} = \frac{1(1 + 1)(2 + 1)}{6}$

$\implies{ \frac{1(2)(3)}{6} }$

$\implies{ 1}$

Therefore, it is true for the first part.

In the second part we will assume that,

$\: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} = \frac{k(k + 1)(2k + 1)}{6} }$

and we will prove that,

$\sf{ \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 1 + 1) \{2(k + 1) + 1\}}{6}}}$

$\: {{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 2) (2k + 3)}{6}}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k (k + 1) (2k + 1) }{6} + \frac{(k + 1) ^{2} }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k(k+1)(2k+1)+6(k+1)^ 2 }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)\{k(2k+1)+6(k+1)\} }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2 +k+6k+6) }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2+7k+6) }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(k+2)(2k+3) }{6}$

Henceforth, by using the principle of mathematical induction 1²+2² +3²+....+n² = n(n+1)(2n+1)/ 6 for all positive integers n.

_______________________________

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8 0

1 year ago

the sum of 2 numbers is 56.twice the smaller number exceeds one-half the larger number by 22.find the numbers

Alexxandr [17]

Answer:

the numbers are 18 and 38

Step-by-step explanation:

x =smaller integer and y =larger integer

6 0

2 years ago

Read 2 more answers

What is the solution to the linear equation?

Vikki [24]

Answer:

x=-5

Step-by-step explanation:

7 0

3 years ago

Log (3x+1) - Log (2x+5)= 1

sleet_krkn [62]

Answer:

$\huge \red { \boxed{x = - \frac{49}{17}}}$

Step-by-step explanation:

$log(3x + 1) - log(2x + 5) = 1 \\ \\ log \: \frac{3x + 1}{2x + 5} = log \: 10..( \because \: log \: 10 = 1) \\ \\ \frac{3x + 1}{2x + 5} = 10 \\ \\ 3x + 1 = 20x + 50 \\ 3x - 20x = 50 - 1 \\ \\ - 17x = 49 \\ \\ x = \frac{49}{ - 17} \\ \\ \huge \purple{ \boxed{x = - \frac{49}{17}}} \\$

6 0

2 years ago