Which is the correct comparison of solutions for 2x + 6 < 10 and -2x + 22

A circle has a circumference of 616 cm.

Ray Of Light [21]

Answer:

π =14 cm

Step-by-step explanation:

Given:

circumference of a circle =616 cm

pie(π)=22/7

circumference of a circle=πr^2

616=22/7 *r^2

616*7/22 =r^2

4312/22 =r^2

196=r^2

$\sqrt{196}$ =r

14 =r

4 0

3 years ago

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6- Nov 19 P1 #

denis23 [38]

Answer:

a=14

b=6

c=5

Step-by-step explanation:

$x-6\sqrt{x} + 4 = 0$

$x +4 =6\sqrt{x}$

$x^2 + 8x + 16 = 36x$

$x^2 - 28x + 16 = 0$

14 ±6 $\sqrt{5}$

4 0

3 years ago

Suppose T is a transformation from ℝ2 to ℝ2. Find the matrix A that induces T if T is reflection over the line y=1/2x

trapecia [35]

Answer:

$A = \left[\begin{array}{cc}1&\frac{4}{5}\\\frac{4}{3}&-\frac{3}{5}\end{array}\right]$

Step-by-step explanation:

We have to see how the canonical vectors are transformed throught T. Lets first define T in any basis.

Since T is a reflection, then any element of the line y = x/2 if fixed by T. Therefore T(2,1) = (2,1).

On the other hand, any vector perpendicular to the line direction should be sent to its opposite value. We can take, for example, (-1,2) (note that the scalar product (2,1) * (-1,2) = -2+2 = 0). As a consecuence T(-1,2) = (1,-2). We have

T(2,1) = (2,1)
T(-1,2) = (1,-2)

By summing the first vector with the double of the second one we get, using linearity

T(0,5) = T( (2,1) + 2(-1,2)) = T(2,1) + 2T(-1,2) = (2,1) + 2(1,-2) = (4,-3)

Hence, T(0,1) = (4/5,-3/5)

Now, we take the second vector and substract it the double of the first one (to kill the second variable)

T(-3,0) = T( (-1,2) - 2*(2,1) ) = T(-1,2) -2T(2,1) = (1,-2)-2(2,1) = (-3,-4)

Therefore, T(1,0) = (1,4/3)

The matrix A induced by T has in its first column T(1,0) and in its second column T(0,1). We conclude that

$A = \left[\begin{array}{cc}1&\frac{4}{5}\\\frac{4}{3}&-\frac{3}{5}\end{array}\right]$

3 0

3 years ago

Select the correct answer from the drop-down menu. A vertical pole is supported by two ropes staked to the ground on opposite si

Ainat [17]

Answer:

6.78 m

Step-by-step explanation:

Since the set up forms a triangle with length of ropes two sides of the triangle a = 8 m and b = 7 m respectively, the distance between them which is c = 6 m forms the third side of the triangle.

To find the height of the pole, we need to find the angle between any of the ropes and the ground. So, choosing the 8 m long rope side and using the cosine rule,

b² = a² + c² - 2accosФ where Ф is the angle opposite the 7 m long side which is also the angle between the 8 m long side and the ground.

So, making, Ф subject of the formula, we have

b² - (a² + c²) = 2accosФ

cosФ = [b² - (a² + c²)]/2ac

Ф = cos⁻¹{[b² - (a² + c²)]/2ac}

substituting the values of the variables into the equation, we have

Ф = cos⁻¹{[b² - (a² + c²)]/2ac}

Ф = cos⁻¹{[7² - (8² + 6²)]/2(8)(6)}

Ф = cos⁻¹{[49 - (64 + 36)]/96}

Ф = cos⁻¹{[49 - 100]/96}

Ф = cos⁻¹{-51/96}

Ф = cos⁻¹{-0.53125}

Ф = 122.09°

Since the height of the pole, h is a perpendicular bisector to the base of the triangle, and the 8 m long side form a triangle with it and the ground and the 8 m long side being the hypotenuse side of this triangle, we have that

sinФ = h/a where a = 8 m and Ф = 122.09° = the angle between the 8 m long side and the ground.

h = asinФ

substituting the values of the variables into the equation, we have

h = asinФ

h = (8 m)sin122.09°

h = 8 m × 0.8472

h = 6.78 m

3 0

3 years ago

Which statement correctly describe the data shown in the scatter plot?

pentagon [3]

Answer:

Option C is correct, The scatter plot shows a positive association because y increases as x increases.

Step-by-step explanation:

We are given a graph of scatter plot of points. We need to choose correct option using graph.

Option A: The point (18,2) is an outlier. This point is not shown on graph.

False.

Option B: The scatter plot show linear association. This is not linear association because points are not col-linear.

False

Option C: The scatter plot shows a positive association. This is positive association because y increases as x increases.

True

Option D: The scatter plot shows no association. This is false because it shows positive association.

False

7 0

3 years ago

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Which is the correct comparison of solutions for 2x + 6 < 10 and -2x + 22 < 18?