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3 years ago

(5,-6) after a rotation of 90 digres

Mathematics

1 answer:

vlada-n [284]3 years ago

7 0

Answer:

depends which way you rotate it

Step-by-step explanation:

counterclockwise rotation: (6,5)

clockwise rotation: (-6,-5)

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Help please because i am very dumb

Sloan [31]

A) 7000
B) 20000
C) 300000

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3 years ago

Given that k // I, identify the congruent angles in the

muminat

V 23 is the correct answer

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2 years ago

Find the equations of the tangents to the curve y = x²-x-12 at each of the points where the curve crosses the x-axis.

poizon [28]

Step-by-step explanation:

First, find the zeroes of the parabola

${x}^{2} - x - 12$

${x}^{2} - 4x + 3x - 12$

$x(x - 4) + 3(x - 4)$

$(x + 3)(x - 4) = 0$

$x = - 3$

$x - 4 = 0$

$x = 4$

So the zeroes or where the curve crosses the x axis is at 4 and -3.

Now, we take the derivative of the function.

$\frac{d}{dx} ( {x}^{2} - x - 12) = 2x - 1$

Plug in -3, and 4 into the derivative function

$2( - 3) = - 7$

$2(4) - 1 = 7$

So at x=-3, our slope of the tangent line is -7 and must pass through (-3,0). So we use point slope formula.

$y - y _{1} = m(x - x _{1})$

$y - 0 = - 7(x - ( - 3)$

$y = - 7x - 21$

At x=4, our slope of tangent line is 7, and pass through (4,0) so

$y - 0 = 7(x - 4)$

$y = 7x - 28$

So the equations of tangent is

$y = - 7x - 21$

$y = 7x - 28$

6 0

2 years ago

Tori has already jarred 8.24 liters of jam and will jar an additional 7.36 liters of jam every day.How much jam did Tori jar if

gayaneshka [121]

Answer:

Step-by-step explanation:24 liters of jam after 4 days. How much jam did Alexa jar if she spent 8 days making jam? Assume the relationship is directly proportional.

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3 years ago

Consider the following probability distribution function of the random variable X which represents the number of people in a gro

Troyanec [42]

Answer:

(a) 3.55

(b) 3.45 and 1.86

(d) 0.016

Step-by-step explanation:

The random variable <em>X</em> denotes the number of people in a group (party) at a restaurant.

(a)

The formula to compute the mean is:

$\mu=\sum {x\cdot P(X=x)}$

Consider the Excel sheet attached.

The mean is, 3.55.

(b)

The formula to compute the variance is:

$\sigma^{2}=[\sum {x^{2}\cdot P(X=x)}]-(\mu)^{2}$

Consider the Excel sheet attached.

Compute the variance as follows:

$\sigma^{2}=[\sum {x^{2}\cdot P(X=x)}]-(\mu)^{2}\\\\=16.05-(3.55)^{2}\\\\=3.4475\\\\\approx 3.45$

The variance is, 3.45.

Compute the standard deviation as follows:

$\sigma=\sqrt{\sigma^{2}}\\\\=\sqrt{3.45}\\\\=1.85742\\\\\approx 1.86$

The standard deviation is, 1.86.

(c)

Compute the probability that the next party will be over 4 people as follows:

$P(X>4)=P(X=5)+P(X=6)+P(X=7)+P(X=8)\\\\=0.10+0.05+0.05+0.05\\\\=0.25$

Thus, the probability that the next party will be over 4 people is 0.25.

(d)

Compute the probability that the next three parties will each be over 4 people as follows:

It is provided that the three parties are independent.

P (Next 3 parties will be each over 4) = [P (X > 4)]³

$=(0.25)^{3}\\=0.015625\\\approx 0.016$

Thus, the probability that the next three parties will each be over 4 people is 0.016.

3 0

3 years ago