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2 years ago

A shop sells packets of envelopes.

Mathematics

1 answer:

Ivanshal [37]2 years ago

5 0

9514 1404 393

Answer:

5x +20y = T

Step-by-step explanation:

There are 5 envelopes in each of x small packets, for a total of 5x envelopes in small packets.

There are 20 envelopes in each of y large packets, for a total of 20y envelopes in large packets.

The total number envelopes is then ...

T = 5x +20y

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What is 6=- x/8<br> Plz help

nekit [7.7K]

Answer:

1 .Multiply both sides by 88.

6\times 8=-x6×8=−x

2 .Simplify 6\times 86×8 to 4848.

48=-x48=−x

3. Multiply both sides by -1−1.

-48=x−48=x

4. x=−48

Step-by-step explanation:

5 0

2 years ago

Given f(x)=cos c and g(x)=cot x, what are the domain and range of f(g(x))?

Evgesh-ka [11]

Answer:

Option C

Step-by-step explanation:

We know that the function $y = cos(x)$ has as its domain all real numbers, and as a range $-1\leq y\leq 1$

We know that the function $cot(x) = \frac{cos(x)}{sin(x)}$

The denominator of the function can not be equal to 0. But $sin(x) = 0$ for all $x = n\pi$ where n is an integer number.

Therefore the domain of cot(x) are all real numbers except $x = n\pi$

The range of cot(x) are all real numbers

Then, the domain of f(g(x)) is:

x ∈ Domain g and g(x) ∈ Domain of f

Where:

Domain of g: All reals except $x = n\pi$

Domain of f: All reals.

This is:

Domain of f(g(x)):

All real numbers except $n\pi$

Range of f(g(x)):

$-1\leq y\leq 1$

Therefore the correct option is:

C. Domain: All real numbers x except x does not equal npi for all integers n; Range: -1 is less than or equal to and is less than or equal to 1.

7 0

2 years ago

How to do this question plz

hjlf

Answer:

$\underline{ \boxed{ \underline{part \: a}}}. \\the \: required \: distance \: a part \: be \to \: \boxed{\underline {\overline{p } =79.23 \: km} } \\ \\ \underline{ \boxed{ \underline{part \: b}}}. \\ the \: bearing \: of \: \boxed{ B } \: \: from \: \boxed{ \underline{A}} \: is \to \boxed{ \underline{324 }\degree }$

Step-by-step explanation:

$\underline{ \boxed{ \underline{part \: a}}}. \\ l et \: the \: required \: distance \: apart \: be \to \: \boxed{ \overline {p}} \\ let \: \boxed{ \angle \: P} \: be \: the \: angle \: of \: seperation \: between \: both \: ships :given \: by \to \\ P = (244 - 180) - (196 - 180 )= (64 -16) = \boxed{48 \degree} \\ if \: ship \: A \: and \: B \: left \: the \: port\: at \: (10:30) \: \\ then \: at \: (14 :00) \: their \: time \: interval \: would \: be \to \\ (14 : 00) - (10 : 30) = \boxed{ 3.5 \: hrs} \\ ship \: \boxed{A }\: distance \: from \: the \: port =( v \times t) = (30 \times 3.5) = \boxed{105 \: km} \\ ship \: \boxed{B }\: distance \: from \: the \: port =( v \times t) = (24 \times 3.5) = \boxed{84\: km} \\n ow........we \: cant \: do \: much \: if \: their \: are \: no \: angles \: to \: work \: with \to \\ applying \:t he \: cosine \: rule : we \: have \to \\ \cos(P) = \frac{ {a}^{2} + {b}^{2} - \overline{{p}^{2} } }{2(ab)} \\ {a}^{2} + {b}^{2} - \overline{{p}^{2} } = 2(ab) \cos(P) \\ \overline{{p}^{2} } = {a}^{2} + {b}^{2} - \{2(ab) \cos(P) \} \\ \overline{{p}^{2} } = {84}^{2} + {105}^{2} - \{2(84)(105) \cos(48 \degree) \} \\\overline{{p}^{2} } = 18,081 - 11,803.463897 \\ \overline{{p}^{2} } = 6,277.536103 \\ \overline{p } = \sqrt{6,277.536103} \\ \boxed{\underline {\overline{p } =79.23 \: km} } \\ \\ \underline{ \boxed{ \underline{part \: b}}}. \\ to \: sove \: this : we \: first \: find \: angle \: \angle \: B : by \: applying \to \\ \frac{ \sin(B) }{b} = \frac{ \sin(P) }{p} \\ p \ast \sin(B) = b \ast \sin(P) \\ B = \sin {}^{ - 1} ( \frac{ b \ast \sin(P)}{p} ) \\ B = \sin {}^{ - 1} ( \frac{ 105 \times \sin(48 \degree)}{79.230903712} ) \\ \\ B = \sin {}^{ - 1} ( \frac{ 78.030206678}{79.230903712} ) \\ \\ B = \sin {}^{ - 1} (0.9848455971) \\ \boxed{B = 80 \degree} \\ hence \ : the \: bearing \: of \: \boxed{ B } \: \: from \: \boxed{ \underline{A}} \: is \to \\ 360 - \{180 - (80 + 48 + 16) \} \\ 360 -(180 - 144 )\\ 360 -36 = \boxed{324 \degree }$

♨Rage♨

7 0

2 years ago

HELP ME PLZ

Marta_Voda [28]

Step-by-step explanation:

1.78 . 1012. 4.55 . 1013

ANS. 1,801.36. ANS. 4,609.15

4609.15 - 1801.36 = 2,80679 kilogram

they are 2,806.79 kilogram aparts

6 0

1 year ago

Round to 2 decimal places *

EleoNora [17]

Answer: The circumference of the dome is therefore 149.15 feet or 47.5π feet

Step-by-step explanation:

A scale is basically referred to as the ratio of the dimensions of an object as represented in a draft to the real or true dimensions of the object being drafted.

The figure(s) on the left of the ratio sign represents the size and dimensions of the model with respect to the actual size or dimensions of the object. On the other hand, the figure on the right hand size represents the actual dimensions and size of the real object.

So, if an object is being drawn with the ratio, 1cm : 5cm it means that the size of the object is being reduced because every 5cm of the actual object will always be represented by 1cm in the drawing. If the object is being drawn with a scale of 5cm : 1cm then the actual size of the object will be increased in the drawing. That is, for every 1cm in the actual dimensions of the object, there will be a 5cm representation in the drawing.

Now, the architect draws with a scale of 0.25 inches : 1 foot. If the diameter of the hemispherical dome is 23.75 inches in the scale model, then the actual diameter of the dome is:

0.25 inches ------- 1 foot

23.75 inches ------- ? feet

= 23.75/0.25 × 1

= 95 feet

Therefore, the actual diameter of the dome is 95 feet. We are now required to find the circumference of this dome.

The dome is a hemisphere which literally means half of a sphere. So, if the formula for finding the circumference of a sphere is πd, that of a hemisphere will then be πd/2. Since the diameter is already known to be 95 feet, the circumference of the hemisphere =

(π × 95)/2

=47.5π feet

If π = 3.14, then the circumference = (3.14 × 95)/2 = 149.15 feet

The circumference of the dome is 149.15 feet or 47.5π feet

5 0

2 years ago