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3 years ago

3) The foot of a ladder is 1.2 m from a fence

Mathematics

1 answer:

VashaNatasha [74]3 years ago

5 0

Answer: $4.5\ meters$

Step-by-step explanation:

Using the data given in the exercise, we can draw the diagram attached, where "h" is the height of the building reached by the top of the ladder.

Notice that there are two similar triangles.

So, you can set up the following proportion:

$\frac{1.8}{1.2}=\frac{h}{(1.2+1.8)}$

Finally, in order to calculate the height on the building reached by the top of the ladder, you must solve for "h".

Therefore, the value of "h" is :

$\frac{1.8}{1.2}=\frac{h}{3}\\\\(3)(\frac{1.8}{1.2})=h\\\\\frac{5.4}{1.2}=h\\\\h=4.5$

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soldi70 [24.7K]

Answer:no

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3 years ago

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Solve 12^x^2+5x-4 = 12^2x+6

faust18 [17]

The solutions for ‘x’ are 2 and -5

<u>Step-by-step explanation:</u>

Given equation:

$12^{x^{2}+5 x-4}=12^{2 x+6}$

Since the base on both sides as ‘12’ are the same, we can write it as

$x^{2}+5 x-4=2 x+6$

$x^{2}+5 x-2 x-4-6=0$

$x^{2}+3 x-10=0$

Often, the value of x is easiest to solve by $a x^{2}+b x+c=0$ by factoring a square factor, setting each factor to zero, and then isolating each factor. Whereas sometimes the equation is too awkward or doesn't matter at all, or you just don't feel like factoring.

<u>The Quadratic Formula:</u> For $a x^{2}+b x+c=0$ , the values of x which are the solutions of the equation are given by:

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Where, a = 1, b = 3 and c = -10

$x=\frac{-3 \pm \sqrt{(-3)^{2}-4(1)(-10)}}{2(1)}$

$x=\frac{-3 \pm \sqrt{9+40}}{2}$

$x=\frac{-3 \pm \sqrt{49}}{2}=\frac{-3 \pm 7}{2}$

So, the solutions for ‘x’ are

$x=\frac{-3+7}{2}=\frac{4}{2}=2$

$x=\frac{-3-7}{2}=\frac{-10}{2}=-5$

The solutions for ‘x’ are 2 and -5

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3 years ago

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Given the graph of a function f. Identify the function by name. Then Graph, state domain & range in set notation:A) f(x) +2B

WARRIOR [948]

The function in the graph has the name of square function.

The domain of a function is all values of x the function can have. The domain of this function is all real numbers:

$\mleft\lbrace x\in\R\mright\rbrace$

The range of a function is all values of y the function can have. The range of this function is all positive numbers, including zero:

$\mleft\lbrace y\in\R\mright|y\ge0\}$

In order to graph f(x) + 2, we just need to translate the graph 2 units up. To find the new points, we need to increase all y-coordinates by 2:

(-2, 6), (-1, 3), (0, 2), (1, 3), (2, 6)

Domain: {x ∈ ℝ}

Range: {y ∈ ℝ | y ≥ 2}

Then, in order to graph f(x) - 2, we just need to translate the graph 2 units down. To find the new points, we need to decrease all y-coordinates by 2:

(-2, 2), (-1, -1), (0, -2), (1, -1), (2, 2)

Domain: {x ∈ ℝ}

Range: {y ∈ ℝ | y ≥ -2}

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1 year ago

Lol please help find the value of x thank you

bagirrra123 [75]

Answer:

x=30

Step-by-step explanation:

that's a 90º angle so 90÷3=30

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2 years ago

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fenix001 [56]

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summing both sets we have one set: (1,6]
so
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b) also represent because all numbers between 4-6 and 6 are in our set
c)also represent, all numbers are in main set
d)also represent

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3 years ago

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