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3 years ago

6

The instructions for building a kite tell you to begin by cutting a strip of wood to 45 cm in length, but your ruler only measur

es inches. How many inches should the piece of wood be? Round to the nearest quarter of an inch. (Recall: 1 in. = 2.54 cm)

2 answers:

Phantasy [73]3 years ago

6 0

If one inch = 2.54 centimeters, then 45 centimeters divided by 2.54 centimeters will give you the amount of inches the piece of wood needs to be.

45/2.54 = 17.72 ---- Rounded to the nearest quarter, would be 17.75 inches.

sergey [27]3 years ago

6 0

Answer: $17\dfrac{23}{32}\text{ inches}$ .

Step-by-step explanation:

Given: The required length of wood strip = 45 cm

Since we know that $\text{One inch = 2.54 centimeters}$

Using Unitary Method ,

$\text{One centimeter}=\dfrac{1}{2.54}\text{ inch}\\\\$

Now, the length of the strip ( in inches ) will be :-

$\dfrac{1}{2.54}\times45\text{ inches}\\\\\\=\dfrac{12512}{32}\text{ inches}\\\\\\=17\dfrac{23}{32}\text{ inches}$

Hence, the length of the piece should be $17\dfrac{23}{32}\text{ inches}$ .

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Check whether the relation R on the set S = {1, 2, 3} is an equivalent

kozerog [31]

Answer:

$R$ isn't an equivalence relation. It is reflexive but neither symmetric nor transitive.

Step-by-step explanation:

Let $S$ denote a set of elements. $S \times S$ would denote the set of all ordered pairs of elements of $S\!$ .

For example, with $S = \lbrace 1,\, 2,\, 3 \rbrace$ , $(3,\, 2)$ and $(2,\, 3)$ are both members of $S \times S$ . However, $(3,\, 2) \ne (2,\, 3)$ because the pairs are ordered.

A relation $R$ on $S\!$ is a subset of $S \times S$ . For any two elements $a,\, b \in S$ , $a \sim b$ if and only if the ordered pair $(a,\, b)$ is in $R\!$ .

A relation $R$ on set $S$ is an equivalence relation if it satisfies the following:

Reflexivity: for any $a \in S$ , the relation $R$ needs to ensure that $a \sim a$ (that is: $(a,\, a) \in R$ .)

Symmetry: for any $a,\, b \in S$ , $a \sim b$ if and only if $b \sim a$ . In other words, either both $(a,\, b)$ and $(b,\, a)$ are in $R$ , or neither is in $R\!$ .

Transitivity: for any $a,\, b,\, c \in S$ , if $a \sim b$ and $b \sim c$ , then $a \sim c$ . In other words, if $(a,\, b)$ and $(b,\, c)$ are both in $R$ , then $(a,\, c)$ also needs to be in $R\!$ .

The relation $R$ (on $S = \lbrace 1,\, 2,\, 3 \rbrace$ ) in this question is indeed reflexive. $(1,\, 1)$ , $(2,\, 2)$ , and $(3,\, 3)$ (one pair for each element of $S$ ) are all elements of $R\!$ .

$R$ isn't symmetric. $(2,\, 3) \in R$ but $(3,\, 2) \not \in R$ (the pairs in $\! R$ are all ordered.) In other words, $3$ isn't equivalent to $2$ under $R\!$ even though $2 \sim 3$ .

Neither is $R$ transitive. $(3,\, 1) \in R$ and $(1,\, 2) \in R$ . However, $(3,\, 2) \not \in R$ . In other words, under relation $R\!$ , $3 \sim 1$ and $1 \sim 2$ does not imply $3 \sim 2$ .

3 0

3 years ago

Find the value of the variable.

nalin [4]

Answer:

The variable, y is 11°

Step-by-step explanation:

The given parameters are;

in triangle ΔABC; ${}$ in triangle ΔFGH;

Segment $\overline {AB}$ = 14 ${}$ Segment $\overline {FG}$ = 14

Segment $\overline {BC}$ = 27 ${}$ Segment $\overline {GH}$ = 19

Segment $\overline {AC}$ = 19 ${}$ Segment $\overline {FH}$ = 2·y + 5

∡A = 32° ${}$ ∡G = 32°

∡A = ∠BAC which is the angle formed by segments $\overline {AB}$ = 14 and $\overline {AC}$ = 19

Therefore, segment $\overline {BC}$ = 27, is the segment opposite to ∡A = 32°

Similarly, ∡G = ∠FGH which is the angle formed by segments $\overline {FG}$ = 14 and $\overline {GH}$ = 19

Therefore, segment $\overline {FH}$ = 2·y + 5, is the segment opposite to ∡A = 32° and triangle ΔABC ≅ ΔFGH by Side-Angle-Side congruency rule which gives;

$\overline {FH}$ ≅ $\overline {BC}$ by Congruent Parts of Congruent Triangles are Congruent (CPCTC)

∴ $\overline {FH}$ = $\overline {BC}$ = 27° y definition of congruency

$\overline {FH}$ = 2·y + 5 = 27° by transitive property

∴ 2·y + 5 = 27°

2·y = 27° - 5° = 22°

y = 22°/2 = 11°

The variable, y = 11°

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lozanna [386]

Answer:

Option c is right.

Step-by-step explanation:

Given is a parabola y =x^2

From that transformation is done to get parabola as

y =(0.2x)^2

We find that instead of x here we use 0.2x

i.e. New x = 5 times old x

Hence there is a horizontal expansion of scale factor 5.

We can check with any point also

When y =4, x=2 in the parent graph

But when y =4 , we have x = 10 in the new graph

i.e. there is a horizontal expansion of scale factor 5.

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Answer: 30:5

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QveST [7]

Answer:

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Step-by-step explanation:

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