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3 years ago

The lines below are perpendicular. If the green line has a slope of 2, what is

Mathematics

1 answer:

Tatiana [17]3 years ago

5 0

Answer: The slope of the red line is -1/2

Step-by-step explanation:

For perpendicular slopes, use the reciprocal of the given slope and reverse the sign (additve inverse)

The reciprocal of 2 is 1/2. Reverse from positive to negative so you have -1/2

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would someone be able to explain to me how to solve these problems? I don't need the solutions, I just need an explanation. I ne

Leni [432]

The first 3 are examples of the difference of 2 squares so you use the identity
a^2 - b^2 = (a + b)(a - b)
x^2 - 49 = 0
so (x + 7)(x - 7) = 0
so either x + 7 = 0 or x - 7 = 0
giving x = -7 and 7.
Number 7 reduces to 3x^2 =12, x^2 = 4 so x = +/- 2
Number 8 take out GCf (d) to give
d(d - 2) = 0 so d = 0 , 2
9 and 10 are more difficult to factor
you use the 'ac' method Google it to get more details
2x^2 - 5x + 2
multiply first coefficient by the constant at the end
that is 2 * 2 = 4
Now we want 2 numbers which when multiplied give + 4 and when added give - 5:- -1 and -4 seem promising so we write the equation as:-

2x^2 - 4x - x + 2 = 0

now factor by grouping
2x(x - 2) - 1(x - 2) = 0

(x - 2) is common so

(2x - 1)(x - 2) = 0
and 2x - 1 = 0 or x - 2 = 0 and now you can find x.

The last example is solved in the same way.

8 0

3 years ago

5/8x + 10 for x = -8

Afina-wow [57]

Answer by JKismyhusbandbae:

$\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a\\=-\frac{5}{8}\cdot \:8+10\\\frac{5}{8}\cdot \:8=5\\=-5+10\\\mathrm{Add/Subtract\:the\:numbers:}\:-5+10=5\\=5$

5 0

4 years ago

Read 2 more answers

A rocket is launched into the air and follows the path, h (t) = -3 * t^2 + 12 * t

DanielleElmas [232]

check the picture below.

so, the rocket will come back to the ground when h(t) = 0, thus

$\bf h(t)=-3t^2+12t\implies \stackrel{h(t)}{0}=-3t^2+12t\implies 0=-3t(t-4)\\\\[-0.35em]~\dotfill\\\\0=-3t\implies 0=t\impliedby \textit{0 seconds when it took off from the ground}\\\\[-0.35em]~\dotfill\\\\0=t-4\implies 4=t\impliedby \textit{4 seconds later, it came back down}$

8 0

4 years ago

Whats 2.5/6 = h/9 what does h equal to

Liula [17]

Answer:

h =2.6

Step-by-step explanation:

2.5/6

2.5+6

2.6

4 0

3 years ago

Read 2 more answers

The population of a city is modeled by the exponential function ƒ (x) = 689,254 · 2.40.014x, where x is the number of years af

Alex Ar [27]

Answer:

Step-by-step explanation:

Given the population of a city is modeled by the exponential function

ƒ (x) = 689,254 · 2.4e^0.014x, where x is the number of years after 2000

In order to determine the year that the city's population will exceed one million, we will substitute f(x) = 1,000,000 and find x first as shown:

1,000,000 = 689,254 2.4e^0.014x,

1000000/689,254 = 2.4e^0.014x,

1.4508 = 2.4e^0.014x,

1.4508 /2.4 = e^0.014x,

0.6045 = e^0.014x,

Apply ln to both sides

ln 0.6045 = lne^0.014x,

-0.5033 = 0.014x

x = -35.95

Since x cannot be negative, lets say x ≈ 36years

<em>This means that the population will exceed one million after about 36 years. The year it will exceed this amount will be 2000+36 = 2036</em>

<em>Note that the exponential equation used was not correctly written but the same calculation can be employed for any exponential functions you might have.</em>

3 0

3 years ago