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Dmitry_Shevchenko [17]
1 year ago
13

Use translation (x, y) (x - 8, y + 4) to answer the question. What is the image of B(- 1, 5)?

Mathematics
1 answer:
shutvik [7]1 year ago
3 0

Translation involves changing the position of a shape.

The image of B is (-9, 9)

<h3>How to translate a point ?</h3>

If we know the direction and how far the figure should be moved, we can draw the translation in the coordinate plane. P'(x+a,y+b) is used to translate the point P' (x,y) a unit right and b unit up.

Translation involves changing the position of a shape.

The image of B is:

The translation rule is given as:

(x, y) → (x - 8, y + 4)

The point is given as: B(- 1, 5)

Substitute -1 for x and 5 for y

(x, y) → (x - 8, y + 4)

(-1, 5) → (-1 - 8, 5 + 4)

(-1, 5) → (-9, 9)

i.e. B' → (-9, 9)

Hence, the image of B is: (-9, 9)

To learn more about Translations refer,

brainly.com/question/15123583

#SPJ1

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Write the trigonometric expression sin(sin−1u−tan−1v) as an algebraic expression in u and v. Assume that the variables u and v r
igomit [66]

Answer:

[u – v√(1 – u²)]/√(1 + v²)

Step-by-step explanation:

Let sin^-1(u) = A, therefore sinA = u.

We know that sin(theta) = opposite/hypothenuse

Therefore, sinA = u/1 and u is the opposite side to angle A while 1 is the hypotenuse. Draw an acute triangle placing u opposite to angle A and 1 as the hypotenuse. By Pythagoras theorem the adjacent would be √(1 – u²).

By doing this, it means cosA = adjacent/hypotenuse = √(1 – u²)/1 = √(1 – u²)

Also, let tan^-1(v) = B, therefore tanB = v.

We know that tan(theta) = opposite/adjacent

Therefore, tanB = v/1 and v is the opposite side to angle B while 1 is the adjacent. Draw an acute triangle placing v opposite to angle B and 1 as the adjacent. By Pythagoras theorem the hypothenuse would be √(1 + v²).

Therefore, sinB = opposite/hypotenuse = v/√(1 + v²) and cosB = adjacent/hypotenuse = 1/√(1 + v²)

Now,

sin[sin^–1(u) – tan^–1(v)] =

sin(A – B) =

sinAcosB – sinBcosA =

u[1/√(1 + v²)] – [v/√(1 + v²)][√(1 – u²)] =

[u/√(1 + v²)] – [v√(1 – u²)/√1 + v²)] =

[u – v√(1 – u²)]/√(1 + v²).

8 0
2 years ago
In the equation (x^2+y)^5, what is the coefficient of the term x^4y^3? what is the coefficient of the same term in the expansion
lys-0071 [83]

\displaystyle&#10;(x+y)^n=\sum_{k=0}^n\binom{n}{k}x^{n-k}y^k

<em>-------------------------------------------------------------</em>


\displaystyle&#10;(x^2+y)^n=\sum_{k=0}^n\binom{n}{k}x^{2n-2k}y^k\\&#10;n=5\\&#10;k=3\\\\\binom{5}{3}=\dfrac{5!}{3!2!}=\dfrac{4\cdor5}{2}=10

<u>It's 10.</u>

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

\displaystyle&#10;(3x^2+y)^n=\sum_{k=0}^n\binom{n}{k}(3x)^{2n-2k}y^k=\sum_{k=0}^n\binom{n}{k}\cdot 3^{2n-2k}\cdot x^{2n-2k}y^k\\\\&#10;n=5\\&#10;k=4\\\\&#10;\binom{5}{3}\cdot3^{2\cdot5-2\cdot4}=10\cdot3^{2}=10\cdot9=90

<u>It's 90</u>

6 0
3 years ago
Shane has a garden box that is 4 feet long, 4 feet wide, and foot deep.
OverLord2011 [107]

Answer:

How much soil for a raised bed?

Answer: The cost to fill a raised bed with bagged fertile soil (planting mix) adds up quickly. The volume of soil you need is 12 feet times 4 feet times 1.5 feet (length times width times depth equals volume), which comes to 72 cubic feet

Step-by-step explanation:

4 0
3 years ago
Solve the equation using the order of operations.<br><br> 5+{2×[(5−1)+6]}÷4
creativ13 [48]

Answer:

The order of operations is PEMDAS

First step is to do everything is parenthesis or brackets

5+{2*[(5-1)+6]}/4

{2*[(5-1)+6]}

First you would go 5-1=4, because that is the first equation that is in parenthesis by itself.

{2*[4+6]}

Next you would go 4+6=10, because that is your next smallest bracket

{2*10}

Last you would go 2*10=20

Your equation now looks like this

5+{20}/4

In PEMDAS your next step is exponents, but we don't have any so we go on to the next one which is multiply/division

5+5

You would go 20/4=5

Last step is to add/subtract

5+5=10

Your final answer would be 10

Hope this helps ;)

Step-by-step explanation:

5 0
2 years ago
How do you solve and check x/4 = -5
Mashutka [201]

Rearrange x/4-(-5)=0

Simplify x/4

-5 = -5/1 = -5*4/4

x- (-5*4)/4 = x+20/4

x+ 20/4 = 0

x+20/4 * 4 = 0*4

The equation now takes the shape: x+20=0

subtract 20 from both sides of the equation: x=-20

Answer: x=-20

6 0
3 years ago
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