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3 years ago

If y = 4 x - 1 find the value of y when x = -2

Mathematics

2 answers:

velikii [3]3 years ago

8 0

Use the substitution method for x

y= 4(-2)-1

y= -8-1

y= -9

Answer is y=-9

Contact [7]3 years ago

8 0

X=-9
Because when you substitute -2 into x
You would multiply 4 times -2 which equals -8 plus the -1 which equals -9

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Please answer this I will give u

satela [25.4K]

Answer:

Step-by-step explanation:

The 3 angles must add up to 180. So

6x + 4x + 2x = 180

12x = 180

x = 15

Plug this into all the angles and you have your answers

5 0

3 years ago

Read 2 more answers

Find the derivative of f(x) = negative 9 divided by x at x = -8.

marusya05 [52]

Answer:

$f'(-8)=\frac{9}{64}$

Step-by-step explanation:

Given the function

$f(x)=\frac{-9}{x}$

We can rewrite it as

$f(x)=-9x^{-1}$

Now we can apply the power rule

$f'(x)=9x^{-2}$

Now we can rewrite it

$f'(x)=\frac{9}{x^{2} }$

Now we can plug in x=-8

$f'(-8)=\frac{9}{(-8)^{2} }\\f'(-8)=\frac{9}{64}$

7 0

3 years ago

The lengths of the sides of a triangle are consecutive integers and the largest angle is twice the smallest angle. Find the meas

eduard

Answer:

41°

Step-by-step explanation:

I could not think of an easy way to solve this, apart from having a graphing calculator do it. In the end, I found I could solve it analytically using a combination of the law of sines and the law of cosines.

Let x represent the length of the shortest side, and θ the smallest angle. Then the <em>law of sines</em> tells you ...

sin(θ)/x = sin(2θ)/(x+2)

Cross-multiplying and using the trig identity for sin(2θ), we have ...

(x +2)sin(θ) = 2x·sin(θ)cos(θ)

Dividing out sin(θ), we see that ...

cos(θ) = (x+2)/(2x)

___

The law of cosines for the shortest side and smallest angle tells you ...

x^2 = (x+1)^2 + (x+2)^2 - 2(x+1)(x+2)·cos(θ)

Substituting the above expression for cos(θ), this can be rewritten as ...

0 = (x^2 +2x +1) +(x^2 +4x +4) -x^2 -(x+1)(x+2)^2/x

0 = x^2 +6x +5 -(x+1)(x+2)^2/x . . . . . . collect terms outside the fraction

0 = x(x+5)(x+1) -(x+1)(x+2)^2 . . . . . . . . factor and multiply by x

We know that x=-1 is not a solution, so we can divide by that factor:

0 = x^2 +5x -(x^2 +4x +4) . . . . . multiply it all out

0 = x -4 . . . . . . . . . . . . . . . . . . . . collect terms

4 = x

so, cos(θ) = (4+2)/(2·4) = 6/8 = 3/4

and the angle of interest is ...

θ = arccos(3/4) ≈ 41.40962° ≈ 41°

_____

The attachment shows a triangle-solver's result using the consecutive integers for side lengths. It confirms the answer we have here.

7 0

3 years ago

Waiting on the platform, a commuter hears an announcement that the train is running five minutes late. He assumes the arrival ti

natima [27]

Answer:

D. 91%

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Less than 15 minutes.

Event B: Less than 10 minutes.

We are given the following probability distribution:

$f(T = t) = \frac{3}{5}(\frac{5}{t})^4, t \geq 5$

Simplifying:

$f(T = t) = \frac{3*5^4}{5t^4} = \frac{375}{t^4}$

Probability of arriving in less than 15 minutes:

Integral of the distribution from 5 to 15. So

$P(A) = \int_{5}^{15} = \frac{375}{t^4}$

Integral of $\frac{1}{t^4} = t^{-4}$ is $\frac{t^{-3}}{-3} = -\frac{1}{3t^3}$

Then

$\int \frac{375}{t^4} dt = -\frac{125}{t^3}$

Applying the limits, by the Fundamental Theorem of Calculus:

At $t = 15$ , $f(15) = -\frac{125}{15^3} = -\frac{1}{27}$

At $t = 5$ , $f(5) = -\frac{125}{5^3} = -1$

Then

$P(A) = -\frac{1}{27} + 1 = -\frac{1}{27} + \frac{27}{27} = \frac{26}{27}$

Probability of arriving in less than 15 minutes and less than 10 minutes.

The intersection of these events is less than 10 minutes, so:

$P(B) = \int_{5}^{10} = \frac{375}{t^4}$

We already have the integral, so just apply the limits:

At $t = 10$ , $f(10) = -\frac{125}{10^3} = -\frac{1}{8}$

At $t = 5$ , $f(5) = -\frac{125}{5^3} = -1$

Then

$P(A \cap B) = -\frac{1}{8} + 1 = -\frac{1}{8} + \frac{8}{8} = \frac{7}{8}$

If given the train arrived in less than 15 minutes, what is the probability it arrived in less than 10 minutes?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{7}{8}}{\frac{26}{27}} = 0.9087$

Thus 90.87%, approximately 91%, and the correct answer is given by option D.

3 0

3 years ago

PLS HELP I WILL GIVE YOU Brainliest

Sindrei [870]

Answer:

3/2

Step-by-step explanation:

Because the problem tells you that the two triangles are similar, the value of a/b would be equivalent for both triangles. The fact that they are right triangles also indicates which sides are which in case the image was not drawn to scale. A is proportional to 2.1 and b is proportional to 1.4. So a/b= 2.1/1.4. This can reduce itself to 3/2 because both are divisible by .7

5 0

3 years ago