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neonofarm [45]
2 years ago
8

IF YOU ANSWER THIS RIGHT NOW ILL GIVE YOU 64 POINTS

Mathematics
1 answer:
Anit [1.1K]2 years ago
5 0

Answer:

13 = x

Step-by-step explanation:

\frac{6}{8} = \frac{(x + 2)}{(x + 7)}

6x + 42 = 8x + 16

42 = 2x + 16

\frac{26}{2} = \frac{2x}{2}

13 = x

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BaLLatris [955]

If There is a math equation you can use math-way.

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7 0
3 years ago
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Axis of sym: x =
marta [7]

Answer:

<h2>SEE BELOW</h2>

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>
  • quadratic function
  • PEMDAS
<h3>let's solve:</h3>

vertex:(h,k)

therefore

vertex:(-1,4)

axis of symmetry:x=h

therefore

axis of symmetry:x=-1

  • to find the quadratic equation we need to figure out the vertex form of quadratic equation and then simply it to standard form i.e ax²+bx+c=0

vertex form of quadratic equation:

  • y=a(x-h)²+k

therefore

  • y=a(x-(-1))²+4
  • y=a(x+1)²+4

it's to notice that we don't know what a is

therefore we have to figure it out

the graph crosses y-asix at (0,3) coordinates

so,

3=a(0+1)²+4

simplify parentheses:

3 = a(1 {)}^{2}  + 4

simplify exponent:

3 =  a + 4

therefore

a =  - 1

our vertex form of quadratic equation is

  • y=-(x+1)²+4

let's simplify it to standard form

simplify square:

y =  - ( {x}^{2}  + 2x + 1)  + 4

simplify parentheses:

y =  -  {x}^{2}  - 2x - 1 + 4

simplify addition:

y =  -  {x}^{2}  - 2x + 3

therefore our answer is D)y=-x²-2x+3

the domain of the function

x\in \mathbb{R}

and the range of the function is

y\leqslant 4

zeroes of the function:

-  {x}^{2}  - 2x + 3 = 0

\sf divide \: both \: sides \: by \:  - 1

{x}^{2}  + 2x - 3 = 0

\implies \:  {x}^{2} +   3x  - x  +  3 = 0

factor out x and -1 respectively:

\sf \implies \: x(x + 3)   - 1(x  + 3 )= 0

group:

\implies \: (x - 1)(x + 3) = 0

therefore

\begin{cases} x_{1} = 1 \\  x_{2}  =  - 3\end{cases}

4 0
3 years ago
Los lados de un triángulo rectángulo tienen por medida tres números enteros consecutivos. Calcula los lados del triángulo.
elixir [45]

Answer:

Los lados del triángulo rectángulo miden 3, 4 y 5, respectivamente.

Step-by-step explanation:

Un triángulo rectángulo puede ser descrito mediante el teorema de Pitágoras, para el caso de tres lados representando tres números enteros consecutivos, tenemos que:

(n+2)^{2} = n^{2} + (n+1)^{2} (1)

Donde n es un número natural.

A continuación, expandimos la expresión y resolvemos:

n^{2}+4\cdot n +4 = n^{2} + n^{2} +2\cdot n + 1

n^{2}-2\cdot n -3 = 0

(n -3) \cdot (n+1) = 0

La única solución factible es n = 3. En consecuencia, los lados del triángulo rectángulo miden 3, 4 y 5, respectivamente.

4 0
3 years ago
Trig. help. How does <img src="https://tex.z-dn.net/?f=2sin%20%28%5Cfrac%7B1%7D%7B2%7D%20x%29cos%28%20%5Cfrac%7B1%7D%7B2%7D%20x%
kotegsom [21]
Recall that 2sin(x) cos(x) is actually equal to sin(2x).

We can prove this by expanding sin(2x) to sin(x + x).
sin(x + x) = sin(x) cos(x) + cos(x) sin(x) = 2sinxcosx

Thus, 2sin(x/2)cos(x/2) can be rewritten in the form:
sin(2x/2), and this simplifies down to sinx.
5 0
3 years ago
The sum of two numbers is 128. Their difference is 4. What are the numbers?
Naddik [55]

Answer:

66 and 62

Step-by-step explanation:

128 divided by 2 gives you 64, and by taking two away from one number and giving it to the other, you're final answers are 66 and 62

3 0
3 years ago
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