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DIA [1.3K]
3 years ago
15

Help !! I need help with this math

Mathematics
1 answer:
allochka39001 [22]3 years ago
5 0

Answer:

B

Step-by-step explanation:

Transformation that maps triangle XYZ into triangle X'Y'Z' is a translation 3 units to the right and 1 unit down, because

  • X(0,0)→X'(3,-1);
  • Y(2,3)→Y'(5,2);
  • Z(4,-1)→Z'(7,-2).

So, the algebraic ru;e of the transformation is

(x,y)→(x+3,y-1)

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Brainliest to first person WHO GETS IT RIGHT.
Rudiy27

Answer:

124

Step-by-step explanation:

because we have to add numbers of hamburgers and burritos and

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Newton uses two properties ti rewrite the expression (4x23)x25 identify the properties he used why would Newton use these proper
valentinak56 [21]

The two properties newton used to rewrite the <em>expression </em>are;

<u><em>- Associative Property; Because it involves change of grouping of numbers in the expression.</em></u>

<u><em>- Distributive Property; Because it involves distribution of a number outside a bracket to numbers inside that same bracket.</em></u>

  • This involves algebraic <em>properties</em>. There are 3 major types that work on only addition and multiplication namely;

- Associative Property

- Commutative Property

- Distributive Property

Let us define each of them;

1) Associative Property; This property in algebra is one that means that no

matter how we group the numbers, we will still get the same result. e.g.

x + (y + z) = (x + y) + z.

2) Commutative Property; This property means that we can change the

order of <em>operation</em> and still get the same answer. For example;

p × q × r = p × r × q

3) Distributive Property; This property means that multiplying the sum of

two or more which are in a bracket by a number outside the will be equal to

the answer gotten when we multiply each number in the bracket

individually by the number outside and then adding their respective

products together. For example; p(q + r) = (p * q) + (p * r)

Newton has the expression; (4 × 23) × 25

Since it is multiplication, he can use any of the three properties above but let us use the <em>associative and distributive properties </em> as they are most suited to this expression<em>.</em>

  • For the <em><u>associative property</u></em> as shown above, he will arrive at;

(4 × 23) × 25 = 4 × (23 × 25)

  • For the <u><em>distributive property</em></u> as shown above, he will arrive at;

(4 × 23) × 25 = (25 × 4) + (25 × 23)

Read more at; brainly.com/question/20724601

6 0
2 years ago
Help me with trigonometry
poizon [28]

Answer:

See below

Step-by-step explanation:

It has something to do with the<em> </em><u><em>Weierstrass substitution</em></u>, where we have

$\int\, f(\sin(x), \cos(x))dx = \int\, \dfrac{2}{1+t^2}f\left(\dfrac{2t}{1+t^2}, \dfrac{1-t^2}{1+t^2} \right)dt$

First, consider the double angle formula for tangent:

\tan(2x)= \dfrac{2\tan(x)}{1-\tan^2(x)}

Therefore,

\tan\left(2 \cdot\dfrac{x}{2}\right)= \dfrac{2\tan(x/2)}{1-\tan^2(x/2)} = \tan(x)=\dfrac{2t}{1-t^2}

Once the double angle identity for sine is

\sin(2x)= \dfrac{2\tan(x)}{1+\tan^2(x)}

we know \sin(x)=\dfrac{2t}{1+t^2}, but sure,  we can derive this formula considering the double angle identity

\sin(x)= 2\sin\left(\dfrac{x}{2}\right)\cos\left(\dfrac{x}{2}\right)

Recall

\sin \arctan t = \dfrac{t}{\sqrt{1 + t^2}} \text{ and } \cos \arctan t = \dfrac{1}{\sqrt{1 + t^2}}

Thus,

\sin(x)= 2 \left(\dfrac{t}{\sqrt{1 + t^2}}\right) \left(\dfrac{1}{\sqrt{1 + t^2}}\right) = \dfrac{2t}{1 + t^2}

Similarly for cosine, consider the double angle identity

Thus,

\cos(x)=  \left(\dfrac{1}{\sqrt{1 + t^2}}\right)^2- \left(\dfrac{t}{\sqrt{1 + t^2}}\right)^2 = \dfrac{1}{t^2+1}-\dfrac{t^2}{t^2+1} =\dfrac{1-t^2}{1+t^2}

Hence, we showed \sin(x) \text { and } \cos(x)

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

5\cos(x) =12\sin(x) +3, x \in [0, 2\pi ]

Solving

5\,\overbrace{\frac{1-t^2}{1+t^2}}^{\cos(x)} = 12\,\overbrace{\frac{2t}{1+t^2}}^{\sin(x)}+3

\implies \dfrac{5-5t^2}{1+t^2}= \dfrac{24t}{1+t^2}+3 \implies  \dfrac{5-5t^2 -24t}{1+t^2}= 3

\implies 5-5t^2-24t=3\left(1+t^2\right) \implies -8t^2-24t+2=0

t = \dfrac{-(-24)\pm \sqrt{(-24)^2-4(-8)\cdot 2}}{2(-8)} = \dfrac{24\pm 8\sqrt{10}}{-16} =  \dfrac{3\pm \sqrt{10}}{-2}

t=-\dfrac{3+\sqrt{10}}{2}\\t=\dfrac{\sqrt{10}-3}{2}

Just note that

\tan\left(\dfrac{x}{2}\right) =  \dfrac{3\pm 8\sqrt{10}}{-2}

and  \tan\left(\dfrac{x}{2}\right) is not defined for x=k\pi , k\in\mathbb{Z}

6 0
2 years ago
The sum of 30 and twice a number is 48. Find the number?
lesya [120]

Answer:

9 is the number

Step-by-step explanation:

Let's call this number x

The equation is:

30+2x=48

subtract 30 from both sides and you get

2x=18

divide 2 from both sides and you get

x=9

Therefore, 30+2(9)=48

3 0
3 years ago
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