Find x (in degrees) in the following quadrilateral.

Looking at the diagram, there is a transversal cutting across 2 parallel lines.

Angle 2 and angle 6 lie in similar position on the same side of the transversal. This means that they are corresponding angles. Corresponding angles are equal.

Given that angle 2 = 32 degrees, then angle 6 = angle 2 = 32 degrees

angle 5 and angle 6 are linear pairs. They lie on a straight line. the sum of the angles on a straight line is 180 degrees. It means that

angle 5 + angle 6 = 180

angle 5 + 32 = 180

angle 5 = 180 - 32

angle 5 = 148 degrees

Answer:

C

Step-by-step explanation:

Since C is the largest half, then C is part of the largest whole.

Answer: C

Answer:

The only difference is: If you multiply or divide both sides of an equation by the same negative number, the equation remains the same, but If you multiply or divide both sides of an inequality by the same negative number, the inequality reverses.

Answer:

-2

Step-by-step explanation:

the answer is -2

......................

Answer:

8x-24

Step-by-step explanation:

First you do:

8×x which is 8x

Then you do:

8×-3 which is -24

Then you put it into 1 expression:

8x-24

Answer:

8−24

Thank You!

Using the normal distribution and the central limit theorem, it is found that:

\(P(246 \leq \bar{x} \leq 260) = 0.5693\)

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem:

The probability of a sample mean between 246 and 260 is the p-value of Z when X = 260 subtracted by the p-value of Z when X = 246, hence:

X = 260:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{260 - 250}{8.3333}\)

\(Z = 1.2\)

\(Z = 1.2\) has a p-value of 0.8849.

X = 246:

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{246 - 250}{8.3333}\)

\(Z = -0.48\)

\(Z = -0.48\) has a p-value of 0.3156.

0.8849 - 0.3156 = 0.5693, hence:

\(P(246 \leq \bar{x} \leq 260) = 0.5693\)

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The inequality corresponding to the equation -4x + y = -3 is either y > 4x - 3 or y < 4x - 3, depending on the relationship between 4x - 3 and 0.

To write the inequality represented by the equation -4x + y = -3, we first need to manipulate the equation to express y in terms of x.

Starting with -4x + y = -3, we isolate y by adding 4x to both sides:

y = 4x - 3

Now we have y expressed in terms of x. To form the inequality, we consider the relationship between x and y. The inequality depends on whether the expression 4x - 3 is greater than or less than 0.

If 4x - 3 is greater than 0, then y is greater than 0, and we can write the inequality as:

y > 4x - 3

If 4x - 3 is less than 0, then y is less than 0, and we can write the inequality as:

y < 4x - 3

The inequality represents a region in the coordinate plane where the y-values are either greater than or less than the expression 4x - 3, depending on the direction of the inequality sign.

For example, if we choose a point (x, y) in the region above the line y = 4x - 3, where y is greater than 4x - 3, the inequality y > 4x - 3 will hold true. On the other hand, if we choose a point below the line, where y is less than 4x - 3, the inequality y < 4x - 3 will be satisfied.

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Answer:(x+1)(x+2)(x-3)

Because..

Step-by-step explanation:

OUT of  35 spins   4 + 15 + 3  = 22   were blue or green or purple

 22/35 probability  = 63%

Answer:

Step-by-step explanation:

To find the lower quartile, we need to first order the data set from smallest to largest:

{1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 5}

The lower quartile is the median of the lower half of the data set. Since there are an even number of data points, we take the average of the middle two values:

Lower quartile = (2+2)/2 = 2

Therefore, the lower quartile for this data set is C. 2.

The system of inequalities having the given feasible regions and points at (-5, 0), and (0, 5), and (-2, -9), (-5, 0), and (1, 0) is the option;

y > x² + 4•x - 5

y > x + 5

The coordinates of the given points on the linear inequality are;

(-5, 0), and (0, 5)

Slope, m, of the linear inequality is therefore;

m = (5 - 0)/(0 - (-5)) = 1

The equation of the inequality is therefore;

y - 0 > 1•(x - (-5)) = x + 5

Which gives;

Quadratic Inequality;

The coordinates of the points on the quadratic inequality are;

Vertex point = (-2, -9)

x-intercept = (-5, 0), and (1, 0)

Therefore, we have;

y > (x + 5)•(x - 1) = x² + 4•x - 5

The correct option is therefore;

y > x² + 4•x - 5

y > x + 5

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Answer:

y > x2 + 4x – 5

y > x + 5

Step-by-step explanation:

If you put this system into desmos you will see that it matches the photo shown in the question, and it would need to be both greater than symbols because the dotted lines indicate that it is not included in the solution.

Answer:

Almost equals 28°

Step-by-step explanation:

cos(x)= 12/18

x= cos^-1 (12/18)

So it equals 48.1896°

Answer:

Less than $833.33 per month or greater than $2666.67

Step-by-step explanation:

→ Divide both figures by 12

32000 ÷ 12 = 2666.67

10000 ÷ 12 = 833.33

Answer:

The point ”A“ is the point that corresponds to the last entry in the table.

Step-by-step explanation:

Answer:

12-4i

Step-by-step explanation:

i means √-1

(3 - i)(3 + 1) =

3*3=9

3*1=3

-i*3= -3i

-i*1 = -i

9+3-3i-i=

12-4i <--- answer

(3 - i)(3 + i) =

3*3=9

3*i=3i

-i*3= -3i

-i*i = -(√-1)*(√-1) = -(-1) = 1

9+3i-3i+1 =

10 <--- answer

When the short leg of a right triangle is 10 meters long and the sharp angles are present, the right triangle's longer leg has a measurement of 21.45 meters.

Right angles are created when two straight lines cross at a 90° angle or are perpendicular to one another at the intersection. The sign stands for a right angle. Different right angle formations can be seen in the above image. The proper angles can be found in shapes. Right triangles are triangles with one of the internal angles at a right angle of 90 degrees. Since a triangle's three interior angles sum up to 180 degrees, a right triangle's three interior angles must always add up to 90 degrees since one of them is always 90 degrees.

given

x / sin 65° = 10 / sin 25°

x = 10 sin 65°/ sin 25°

x = 21 .45 meters

as law of sine

a / sinA = b / sinB = c / sinC

When the short leg of a right triangle is 10 meters long and the sharp angles are present, the right triangle's longer leg has a measurement of 21.45 meters.

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Answer:

105°

Step-by-step explanation:

Measure of the third angle

= 180° - 18° - 57° (angle sum of triangle)

= 105°

The number= -25

Step-by-step explanation:

To solve this equation, you can start by expressing the difference between the number and 9 as 2 times the sum of the number and 8 divided by 3. This gives you the equation:

2 * (x + 8) / 3 = x - 9

You can then multiply both sides of the equation by 3 to get rid of the fraction:

6 * (x + 8) = 3 * (x - 9)

This simplifies to:

6x + 48 = 3x - 27

You can then combine like terms on both sides of the equation to get:

3x + 48 = -27

You can then add 27 to both sides of the equation to get:

3x + 75 = 0

You can then subtract 75 from both sides of the equation to get:

3x = -75

You can then divide both sides of the equation by 3 to get the solution:

x = -25

Therefore, the number x is equal to -25.

Hope this helps you??

Answer:

Alternative D - 2407 bacteria

Step-by-step explanation:

The num

The solution is:  the rate of change is 3.

Here, we have,

Since the graph of f(x) is translated 1 unit down, we need to decrease the value of f(x) by 1 to find g(x):

g(x) = f(x) - 1

f(x) = 3|x| – 4

so, we get,

g(x) = 3|x| – 4 - 1

      = 3|x| – 5

Now, to calculate the rate of change over the interval 2 <= x <= 5, we can use the formula below:

rate = g(5) - g(2)/ 5-2

so, we get,

rate = 9/3 = 3

Therefore the rate of change is 3.

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9514 1404 393

Answer:

  17

Step-by-step explanation:

The number of handshakes among n people is n(n -1)/2. Then ...

  n(n -1)/2 = 136

  n(n -1) = 272 = 17×16*

  n = 17

There were 17 people at the party.

_____

* This factoring can be facilitated by recognition that √272 ≈ 16.5, the number midway between the consecutive factors.

Answer: Yes

Step-by-step explanation: They are similar because it the same kind of triangle just ones smaller and the other is bigger.

Answer:

x=-7,1

Step-by-step explanation:

Answer: x=-7,1

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

K = Y/X

\(zeros \begin{cases} x=0\implies &x=0\\ x=9\implies &x-9=0\\ x=9\implies &x-9=0 \end{cases}\qquad \implies a(x)(x-9)(x-9)=\stackrel{y}{0} \\\\\\ \stackrel{\textit{with a coefficient of 1}}{1(x)(x-9)(x-9)=y}\implies x(x-9)^2=y\implies x(x^2-18x+81)=y \\\\\\ ~\hfill {\Large \begin{array}{llll} x^3-18x^2+81x=y \end{array}}~\hfill\)

if we notice the tickmarks on the triangle, we can see the all sides are equal, namely is an equilateral triangle, and if all sides are equal, then all interior angles are equal as well.

Let's recall that the sum of all interior angles in a triangle is 180°, now if we divide that by 3, that gives us 60, namely each angle in the equilateral triangle is 60°, that means

\(10x=60\implies x=\cfrac{60}{10}\implies \boxed{x=6} ~\hfill 12y=60\implies y=\cfrac{60}{12}\implies \boxed{y=5}\)