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Nutka1998 [239]

3 years ago

10

The class collected 3,591 bottle caps in 57 days. The same number of bottle caps were collected each day. How many bottle caps d

id the class collect per day?

1 answer:

ANTONII [103]3 years ago

8 0

The answer is 63 bottle caps.
3,591 divided by 57 is 63

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Suppose f(x)=x^2+3 and g(x)=x-2 find (f-g)(x

SSSSS [86.1K]

Answer:

x^2-x+5

Step-by-step explanation:

(f-g)(x)=f(x)-g(x)

= (x^2 + 3) - (x - 2) (Don’t forget the -1 multiplies to the x AND -2

= x^2 + 3 - x + 2

=x^2-x+5

6 0

3 years ago

Using addition formula solve tan 15

salantis [7]

Answer:

2 - $\sqrt{3}$

Step-by-step explanation:

Using the addition formula for tangent

tan(A - B) = $\frac{tanA-tanB}{1+tanAtanB}$ and the exact values

tan45° = 1 , tan60° = $\sqrt{3}$ , then

tan15° = tan(60 - 45)°

tan(60 - 45)°

= $\frac{tan60-tan45}{1+tan60tan45}$

= $\frac{\sqrt{3}-1 }{1+\sqrt{3} }$

Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.

The conjugate of 1 + $\sqrt{3}$ is 1 - $\sqrt{3}$

= $\frac{(\sqrt{3}-1)(1-\sqrt{3}) }{(1+\sqrt{3})(1-\sqrt{3}) }$ ← expand numerator/denominator using FOIL

= $\frac{\sqrt{3}-3-1+\sqrt{3} }{1-3}$

= $\frac{-4+2\sqrt{3} }{-2}$

= $\frac{-4}{-2}$ + $\frac{2\sqrt{3} }{-2}$

= 2 - $\sqrt{3}$

3 0

2 years ago

Find the value of c such that y= x + c is a tangent to the parabola y = x squared - x - 12

Bond [772]

Answer:

c = –13

Step-by-step explanation:

by property of tangent line, equation

x² – x – 12 = x + c

x² – 2x – 12 – c = 0

has only one solution, which mean

– 12 – c = 1

c = –13

5 0

3 years ago

The sum of 1/6,2/3, and 1/4 is

Bumek [7]

¹³/₁₂

<h3>Further explanation</h3>

<u>Given:</u>

$\boxed{ \ \frac{1}{6} + \frac{2}{3} + \frac{1}{4} = ? \ }$

A fraction represents part of a whole.
A fraction consists of a numerator and a denominator. i.e., $\boxed{ \ \frac{numerator}{denominator} \ }$ .
The numerator = the number of equal parts of a whole.
The denominator = the total number of parts that make up said whole.

From the problems above, the denominator or the bottom numbers are still different. We use the Least Common Multiple (or LCM) to equalize the denominator.

Multiples of 3: $\boxed{ \ \{3, 6, 9, 12, 15, ... \} \ }$
Multiples of 4: $\boxed{ \ \{4, 8, 12, 16, ... \} \ }$
Multiples of 6: $\boxed{ \ \{6, 12, 18, ... \} \ }$

Hence, the LCM for 3, 4, and 6 is 12.

We change the denominator for each fraction to 12.

$\boxed{ \ \frac{1}{6} \rightarrow \frac{multiply \ by \ 2}{multiply \ by \ 2} \rightarrow \frac{2}{12} \ }$

$\boxed{ \ \frac{2}{3} \rightarrow \frac{multiply \ by \ 4}{multiply \ by \ 4} \rightarrow \frac{8}{12} \ }$

$\boxed{ \ \frac{1}{4} \rightarrow \frac{multiply \ by \ 3}{multiply \ by \ 3} \rightarrow \frac{3}{12} \ }$

Then we continue adding fractions.

$\boxed{ \ \frac{1}{6} + \frac{2}{3} + \frac{1}{4} = \frac{2}{12} + \frac{8}{12} + \frac{3}{12} \ }$

$\boxed{ \ \frac{1}{6} + \frac{2}{3} + \frac{1}{4} = \boxed{ \ \frac{13}{12} \ } \ }$

Thus, the result is $\boxed{ \ \frac{13}{12} \ or \ 1\frac{1}{12}\ }$

<h3>Learn more</h3>

²/₇m - ¹/₇= ³/₁₄ solve step by step brainly.com/question/4853649
100 is 1/10 of what? brainly.com/question/96535
Mr. Frye distributed his money equally among his 4 children for their weekly allowance brainly.com/question/13174288#

Keywords: the sum of ¹/₆, ²/₃, and ¹/₄, fraction, adding, numerator, denominator, still different, LCM

6 0

3 years ago

Read 2 more answers

Find the term to term rules for 2,6,18,54,162

faltersainse [42]

Answer:

a, ax3 =b, bx3= c , cx3=d, dx3=e

Step-by-step explanation:

2, 2×3=6, 6x3=18,18 x3 =54, 54x3= 162

Multiplication of three with previous number will give you next number in series.

4 0

2 years ago