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2 years ago

Special right triangles!!! Help

Mathematics

2 answers:

klemol [59]2 years ago

8 0

Answer:

This is a 30, 60, 90, right triangle.

The length of the longest side (this case s), is equal to twice the length of the shortest side.

x $\sqrt{3\\}$ = 27

x = 27/ $\sqrt{3}$

s is twice as that, so the answer is 54/ $\sqrt{3}$

Let me know if this helps!

Archy [21]2 years ago

3 0

Answer:

i think 40 meters

Step-by-step explanation:

i hope this helps

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Describe the congruence transformation that maps ΔABC onto ΔA′B′C′ in the given figure.

babymother [125]

<h3>Answer: Choice B</h3>

Reflection along y axis

Translation: $(x,y) \to (x,y-3)$ which means we shift 3 units down

===========================================================

Explanation:

Let's track point A to see how it could move to point A'.

If we were to reflect point A over the vertical y axis, then A(-4,4) would move to (4,4). The x coordinate flips in sign, but the y coordinate stays the same.

The diagram shows that A' is located at (4,1) instead of (4,4). So a y-axis reflection isn't enough to move A to A', but we can shift that reflected point three units down. That will move (4,4) to (4,1) which is exactly where we want to end up. Note how we subtract 3 from the y coordinate and x stays the same. So that explains the notation $(x,y) \to (x,y-3)$

Overall, this points to choice B as the final answer. If we apply these steps to points B and C, you should find that they'll land on B' and C' respectively. Apply this to all of the points on the triangle ABC, and it will move everything to triangle A'B'C'.

7 0

3 years ago

Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc. Ar

Veseljchak [2.6K]

Answer:

The given relation R is equivalence relation.

Step-by-step explanation:

Given that:

$((a, b), (c, d))\in R$

Where $R$ is the relation on the set of ordered pairs of positive integers.

To prove, a relation R to be equivalence relation we need to prove that the relation is reflexive, symmetric and transitive.

1. First of all, let us check reflexive property:

Reflexive property means:

$\forall a \in A \Rightarrow (a,a) \in R$

Here we need to prove:

$\forall (a, b) \in A \Rightarrow ((a,b), (a,b)) \in R$

As per the given relation:

$((a,b), (a,b) ) \Rightarrow ab =ab$ which is true.

$\therefore$ R is reflexive.

2. Now, let us check symmetric property:

Symmetric property means:

$\forall \{a,b\} \in A\ if\ (a,b) \in R \Rightarrow (b,a) \in R$

Here we need to prove:

$\forall {(a, b),(c,d)} \in A \ if\ ((a,b),(c,d)) \in R \Rightarrow ((c,d),(a,b)) \in R$

As per the given relation:

$((a,b),(c,d)) \in R$ means $ad = bc$

$((c,d),(a,b)) \in R$ means $cb = da\ or\ ad =bc$

Hence true.

$\therefore$ R is symmetric.

3. R to be transitive, we need to prove:

$if ((a,b),(c,d)),((c,d),(e,f)) \in R \Rightarrow ((a,b),(e,f)) \in R$

$((a,b),(c,d)) \in R$ means $ad = cb$ .... (1)

$((c,d), (e,f)) \in R$ means $fc = ed$ ...... (2)

To prove:

To be $((a,b), (e,f)) \in R$ we need to prove: $fa = be$

Multiply (1) with (2):

$adcf = bcde\\\Rightarrow fa = be$

So, R is transitive as well.

Hence proved that R is an equivalence relation.

8 0

3 years ago

The distance between two cities is 600 miles. On a map, they are 4 inches apart. What is the scale of the map?

RSB [31]

1 inch = 150 miles (150*4=600)

6 0

3 years ago

Kim and Daniel are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of

ivanzaharov [21]

There are two equation:

1) From Kim

2) From Daniel

Let:

x be the cost of rolls of plain wrapping paper

y be the cost of rolls of shiny wrapping paper

Kim:

7x + 8y = 140

Daniel:

14x + 7y = 154

<u>Using elimination method:</u>

(7x + 8y = 140) * -2 (Multiplying the equation by -2)

-14x - 16y = -280

-14x -16y = -280

14x + 7y = 154

------------------------------

0x - 9y = -126

9y = 126 (Negative sign cancels from both sides)

y = 126 /9

y = 14

The cost of each shiny wrapping paper is $14.

Now solve x, you pick any two equation to solve for x.

7x + 8y = 140

7x + 8(14) = 140 (You know from above y =14)

7x + 112 = 140

7x = 28

x = 28/7

x = 4

The cost of each plain wrapping paper is $4.

Solution: (4,14)

4 0

3 years ago

Which of the following equations represents the line that is graphed on the coordinate grid below?

tatiyna

Answer:

y = -(1/3)x + 2

Step-by-step explanation:

Keeping in mind the equation of a line: y = mx + c

Notice three discernible points on the graph: (0,2), (3,1), (6,0).

The first and last points mentioned represent the intercept on y-axis and the intercept on x-axis respectively.

Therefore, when x = 0, y = 2. And 2 = m(0) + c

c = 2

Also, when y = 0, x = 6. And 0 = 6m + 2

6m = -2. And m = -(2/6) = -(1/3)

Therefore, y = -(1/3)x + 2

8 0

3 years ago