A triangle has rotation symmetry that can take any of its vertices to any of its other vertices. Select ALL conclusions that we can reach this.

A. All sides of the triangle have the same length


B. All angles of the triangle has the same measure

C. All rotations take one half of the triangle to the other half of the triangle

D, it is a right triangle

E. None of the sides of the triangle have the same length

F. None of the angles of the triangle have the same measure

Answer:

158

Step-by-step explanation:

I'm pretty sure it's this. I know it's either this or 4, but this is more likely

Answer:

The answer is 4

Step-by-step explanation:

2+2=4. Brainly patrol, stop deleting my answer!

The probability of overfilling a 34 ounce cup from the soft drink machine, we can use the properties of the normal distribution. The probability of overfilling a 34 ounce cup is approximately 0.0228, rounded to four decimal places.

Given that the machine's output is normally distributed with a mean of 26 ounces and a standard deviation of 4 ounces, we want to calculate the probability that the cup contains more than 34 ounces. To do this, we need to standardize the cup size using the formula z = (x - μ) / σ, where x is the cup size, μ is the mean, and σ is the standard deviation.

In this case, we have z = (34 - 26) / 4 = 2.

Next, we need to find the probability corresponding to a z-score of 2. We can look up this probability in the standard normal distribution table or use a calculator.

Using either method, we find that the probability of a z-score of 2 or greater is approximately 0.0228.

Therefore, the probability of overfilling a 34 ounce cup is approximately 0.0228, rounded to four decimal places.

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Answer: The answer is (264)×(261)(525), because (264)×(261) are the possibilities for choosing 4 red cards and 1 black card from a deck of 52 cards, while (525) are the possibilities for choosing 5 cards from a deck of 52 cards.

So, your first solution is almost correct. On why your second solution is wrong, you'll have to explain your thought process.

Step-by-step explanation:

Answer:

x = -7

Step-by-step explanation:

So we are asked to find what x is equal to in the equation:

\(\frac{x}{7}-4=-5\)

In other words, we are asked to solve for x.

\(\frac{x}{7}-4=-5\)

Add 4 to both sides of the equation.

\(\frac{x}{7}=-1\)

Multiply both sides by 7.

x = -7

So we have solve the equation for x and have found that x = -7.

I hope you find my answer and explanation to be helpful. Happy studying.

The constant of proportionality in table four is -1/3

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".

In each of the table, we can check if proportionality exists.

In the first table, there's no proportionality.

In the second table, there's no proportionality

In the third table, there's no proportionality

In the fourth table, proportionality exist here which we can find the constant of proportionality.

When x = 6, y = -2

y = ax

a = constant of proportionality

-2 = a(6)

a = -1/3

The constant of proportionality is -1/3

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7.071 is the length, in inches, of each side of the square.

What is meant by "square"?

The term "square" refers to a regular quadrilateral having four equal-length sides and angles. Angles in the square are at right angles or are separated by 90 degrees. The diagonals of the square are also equal and meet at a 90-degree angle.

                             Having equal length sides and right angles on all four, a square is a quadrilateral. Due to the fact that a square's sides are all the same length, it may be distinguished from other types of rectangles. Every square consequently becomes a rectangle since it is a quadrilateral with right angles at all four of its angles.

If the side od=f a square is s, the diagonal is  s√2

  This comes from Pythagoras as diagonal is

   √s² + s²  = √2s² = s√2

 as such s√2 = 10

           s = 10/√2

        = 10 * √2/√2  * √2

         = 5√2

    5 * 1.4142  = 7.071

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Answer:

The inverse is 1/7x +2

Step-by-step explanation:

y = 7x - 14

Exchange x and y

x = 7y-14

Solve for y

Add 14 to each side

x+14 = 7y-14+14

x+14 = 7y

Divide each side by 7

(x+14)/7 = 7y/7

1/7x +2 = y

The inverse is 1/7x +2

Answer:

g^-1(x)=x/7+2

Step-by-step explanation:

y=7x-14

7y-14=x

7y=x+14

y=1/7x+2

g^-1(x)=x/7+2

Answer:

x = 18

Step-by-step explanation:

2x - 8 = x + 10

- x       - x

x - 8 = 10

 + 8   + 8

x = 18

\(\huge\mathfrak{\underline{Answer:}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{=20 }\)

__________________________________________

\(\large\bf{\underline{Given:}}\)

\(\large\bf{\underline{To\: find :}}\)

\(\large\bf{\underline{Construction:}}\)

\(\setlength{\unitlength}{0.8cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf 12}\put(2.8,.3){\large\bf 16}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf D}\put(.8,.3){\large\bf C}\put(5.8,.3){\large\bf E}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\put(3.8,1.3){\large\bf $\Theta$}\end{picture}\)

\(\setlength{\unitlength}{0.75cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 16 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 38 cm}\put(-0.5,-0.4){\bf B}\put(-0.5,3.2){\bf C}\put(5.3,-0.4){\bf A}\put(5.3,3.2){\bf E}\end{picture}\)

\(\large\bf{\underline{Hence,}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹CD = 50 - 38

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹CD = 50 - 38

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹CD = 12

\(\large\bf{Since,}\)

\(\large\bf{\underline{Therefore}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹ CE = 16

\(\large\bf{\underline{In\: triangle\:DCE}}\)

\({\large\bf{Using\: Pythagoras\: theorem:}\)

\(\boxed{\large\bf\pink{DE^2 = CD^2 + CE^2}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟹x^2 = 12^2 + 16^2}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟹x^2 = 144 + 256}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟹x^2 = 400}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\( \large \bf \:⟹ {x} = \sqrt{400} \)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\boxed{\large\bf{⟹x= 20}}\)

Answer:

there is no equation

plz edit the question

The value of x for the expression 3x² = 12 are 2 and -2.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation

We have,

3x² = 12

Divide both sides by 3.

x² = 4

x = √4

x = ±2

Thus,

The value of x is 2 or -2.

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The complete question is:

Solve the following equation algebraically 3x² = 12.​

There are 10 faculties in the committee and 12 students.

To find a certain quantity out of many including quantities when their ratios is given use the following formula.

{(ratio of the particular quantity/sum of all the given ratios) × Total quantity}

According to the given question

The ratio of student to faculty on the First Year College Experience Committee at a certain university is 1.2 : 1.

Total number number of people in the committee is 22.

The ratio 1.2 : 1 can also be written as 12 : 10 to remove the decimal.

∴No. of students is

(12/22) × 22 = 12

AND

No. of faculty is

(10/22) × 22 = 10

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the solution to the system of linear equations is:

(x1, x2, x3) = (2, 3, 1)

[  1  -2   4 |  0 ]

[ -1   1  -2 | -1 ]

[  1   3   1 |  2 ]

Applying Gaussian elimination:

Row2 = Row2 + Row1

Row3 = Row3 - Row1

[  1  -2   4 |  0 ]

[  0  -1   2 | -1 ]

[  0   5  -3 |  2 ]

Row3 = 5  Row2 + Row3

[  1  -2   4 |  0 ]

[  0  -1   2 | -1 ]

[  0   0   7 |  7 ]

Dividing Row3 by 7:

[  1  -2   4 |  0 ]

[  0  -1   2 | -1 ]

[  0   0   1 |  1 ]

```

Now, we'll perform back substitution:

From the last row, we can conclude that x3 = 1.

Substituting x3 = 1 into the second row equation:

-1x2 + 2(1) = -1

-1x2 + 2 = -1

-1x2 = -3

x2 = 3

Substituting x3 = 1 and x2 = 3 into the first row equation:

x1 - 2(3) + 4(1) = 0

x1 - 6 + 4 = 0

x1 = 2

Therefore, the solution to the system of linear equations is:

(x1, x2, x3) = (2, 3, 1)

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Answer:

x ≥ 2

Step-by-step explanation:

Given expression:

         –4x + 7 ≤ –1

Now let us solve this problem;

           –4x + 7 ≤ –1

  Add (-7) to both sides of the expression;

           –4x + 7 + (-7) ≤ –1 + (-7)

              -4x  ≤ - 8

Now multiply both sides by \(-\frac{1}{4}\) this will change the inequality sign

             \(-\frac{1}{4}\) x  -4x  ≤ - 8 x  \(-\frac{1}{4}\)

                   x ≥ 2

For all values of x greater than or equal to 2, the inequality is true.

Given:

The equation is,

Explanation:

Taking out 2 as common from the expression.

Factorise the equation by splitting the middle term.

So answer is 2(x + 4)(x + 6)

To construct the phase plane for the given system of differential equations x' = x(5 - x) and y' = y(6 - y), we plot the nullclines (x = 0, x = 5, y = 0, y = 6), label the equilibria (0, 0), (5, 0), (0, 6), and (5, 6) with black dots, and indicate the direction of the vector field to understand the system's behavior.

Constructing the phase plane for the system of differential equations:

The given system of differential equations is x' = x(5 - x) and y' = y(6 - y). To construct the phase plane, we need to plot the nullclines, label the equilibria with a black dot, and indicate the direction of the vector field.

To find the nullclines, we set x' and y' equal to zero and solve for x and y. For x' = 0, we have x(5 - x) = 0, which gives us two nullclines at x = 0 and x = 5. Similarly, for y' = 0, we have y(6 - y) = 0, resulting in two nullclines at y = 0 and y = 6.

Next, we locate the equilibria by solving the system of equations x(5 - x) = 0 and y(6 - y) = 0 simultaneously. We find four equilibria at (0, 0), (5, 0), (0, 6), and (5, 6), which we label with black dots on the phase plane.

To indicate the direction of the vector field, we can select a few representative points in each region defined by the nullclines and observe whether the vectors are pointing towards or away from the equilibria. By doing so, we can sketch the vector field on the phase plane, showing the behavior of the system in different regions.

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Answer:

solution,

\( \sqrt{16 {a}^{8} {b}^{ - 2} } \\ \)

Use negative power rule:

\( {x}^{ - a} = \frac{1}{ {x}^{a} } \)

\( \sqrt{ {16}^{8} \times \frac{1}{ {b}^{2} } } \\ \)

Simplify:

\( \sqrt{ \frac{ {16a}^{8} }{ {b}^{2} } } \\ = \frac{ \sqrt{ {16a}^{8} } }{ \sqrt{ {b}^{2} } } \\ \)

Use this rule:

\( \sqrt{ab} = \sqrt{a} . \sqrt{b} \)

\( \frac{ \sqrt{16. \sqrt{ {a}^{8} } } }{ \sqrt{ {b}^{2} } } \)

Since, 4*4=16 ,the square root of 16 is 4

\( \frac{ \sqrt{ {4}^{2} } \sqrt{ {a}^{8} } }{ \sqrt{ {b}^{2} } } \\ = \frac{4 \sqrt{ {a}^{8} } }{ \sqrt{ {b}^{2} } } \)

Simplify:

\( \frac{4 \: \sqrt{ {(a}^{4) ^{2} } } }{ \sqrt{ {b}^{2} } } \\ = \frac{4 {a}^{4} }{b} \)

Hope this helps...

Good luck on your assignment...

the value of P(A∩B) in terms of x and y is xy.

The correct option is D. xy.

To determine the value of P(A∩B) in terms of x and y, we can use the definition of conditional probability and the fact that P(A∩B) = P(A|B) * P(B).

Given that P(A|B) = x and P(B) = y, we can substitute these values into the equation:

P(A∩B) = P(A|B) * P(B)

        = x * y

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Answer:

First

Step-by-step explanation:

I appologize if this is incorrect I'm not sure what graphs you are talking about :)

After combining like terms in the equation, the next step would be to simplify and solve for 'x' by simplifying further.

In the given equation, "3 - 15x + 24 - 16x" on the left side of the equation is equal to "4x - 24 - 4x" on the right side. To continue solving, we need to simplify and combine like terms on both sides of the equation.

On the left side, combining like terms -15x and -16x gives us -31x. Similarly, combining like terms on the right side, 4x and -4x cancel each other out, leaving us with 0.

The simplified equation becomes -31x + 27 = 0. To finish solving for 'x', we would proceed by isolating the variable 'x' by performing further algebraic operations such as moving the constant term to the other side of the equation and dividing by the coefficient of 'x'. However, the next step would depend on the specific instructions or desired outcome of the equation.


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Answer:

\( \sf \: -2x² + 6x + 4 \)

Step-by-step explanation:

Given problem,

→ (3x² + 8x - 7) - (5x² + 2x - 11)

Let's solve the problem,

→ (3x² + 8x - 7) - (5x² + 2x - 11)

→ 3x² + 8x - 7 - 5x² - 2x + 11

→ (3x² - 5x²) + (8x - 2x) + (-7 + 11)

→ (3 - 5)x² + (8 - 2)x + 4

→ -2x² + 6x + 4

Hence, answer is -2x² + 6x + 4.

The point (5, 10) has not been translated in the given figure.Hence this statement is false.

The graph shows five points.

A point has been translated right and up.

Now, the statements that are true based on the graph are as follows:

The point (9, D) has been translated right and up.Answer: False

There is no information given about point (9, D).

So, we cannot say anything about the translation of point (9, D).

The point (1, 8) has been translated right and up.Answer: True

As explained above, the point (1, 8) has been translated 7 units to the right and 2 units up to get the new point (8, 10). So, this statement is true.

The point (2, 9) has been translated right and up.Answer: False

The point (2, 9) has not been translated in the given figure.

So, this statement is false.

Statement 4: The point (8, B) has been translated right and up.Answer: True

The point (8, B) has been translated 1 unit up in the given figure. So, this statement is true.

The point (5, 10) has been translated right and up.Answer: False

The point (5, 10) has not been translated in the given figure.

So, this statement is false.

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Therefore, the vector equation for the line of intersection of the planes is: r(t) = <t, (25t - 91)/4, (t + 13)/2> where t is a parameter and r(t) represents a point on the line.

To find the vector equation for the line of intersection between the planes 2y - 7x + 3z = 26 and x - 2z = -13, we need to find a direction vector for the line. This can be achieved by finding the cross product of the normal vectors of the two planes.

First, let's write the equations of the planes in the form Ax + By + Cz = D:

Plane 1: 2y - 7x + 3z = 26

-7x + 2y + 3z = 26

-7x + 2y + 3z - 26 = 0

Plane 2: x - 2z = -13

x + 0y - 2z + 13 = 0

The normal vectors of the planes are coefficients of x, y, and z:

Normal vector of Plane 1: (-7, 2, 3)

Normal vector of Plane 2: (1, 0, -2)

Now, we can find the direction vector by taking the cross product of the normal vectors:

Direction vector = (Normal vector of Plane 1) x (Normal vector of Plane 2)

= (-7, 2, 3) x (1, 0, -2)

To compute the cross product, we can use the determinant:

Direction vector = [(2)(-2) - (3)(0), (3)(1) - (-2)(-7), (-7)(0) - (2)(1)]

= (-4, 17, 0)

Hence, the direction vector of the line of intersection is (-4, 17, 0).

To obtain the vector equation of the line, we can choose a point on the line. Let's set x = t, where t is a parameter. We can solve for y and z by substituting x = t into the equations of the planes:

From Plane 1: -7t + 2y + 3z - 26 = 0

2y + 3z = 7t - 26

From Plane 2: t - 2z = -13

2z = t + 13

z = (t + 13)/2

Now, we can express y and z in terms of t:

2y + 3((t + 13)/2) = 7t - 26

2y + 3(t/2 + 13/2) = 7t - 26

2y + 3t/2 + 39/2 = 7t - 26

2y + (3/2)t = 7t - 26 - 39/2

2y + (3/2)t = 14t - 52/2 - 39/2

2y + (3/2)t = 14t - 91/2

2y = (14t - 91/2) - (3/2)t

2y = (28t - 91 - 3t)/2

2y = (25t - 91)/2

y = (25t - 91)/4

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The regression equation of the data values is y = 0.3x^2 - 2.8x +4.2

Using a technology such as a graphing calculator, we simply input the data values in the graphing calculator and then wait for the result.

The x coordinates must be entered into the x values and the y coordinates must be entered into the y values

Using a graphing technology, the regression equation of the data values is y = 0.3x^2 - 2.8x +4.2

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Answer:

Below

Step-by-step explanation:

To write this function in the standard form simplify it.

● -4(x+2)(x+3)

● -4 (x^2+3x+2x+6)

●-4(x^2+5x+6)

●-4x^2-20x-24

Answer:

y = -4(x+2.5)²+1

Step-by-step explanation:

Standard form is given by f(x) = a(x-h)²+k, where (h,k) is the vertex. We are already given a = -4, and if we graph the equation given, we can see that the vertex is (-2.5, 1). So, we can set up the equation y = -4(x+2.5)²+1.

The graph that represents the systems of linear equations 2x - y ≥ -3 and y < -2x + 4 is option d

information gotten from the question include

inequality graph showing shaded regions

rearranging the equation to be in the form

y = mx + c

2x - y ≥ -3

2x + 3 ≥ y

y ≤ 2x + 3

The two equations are

y ≤ 2x + 3

y < -2x + 4

some interpretation on the information from the question include

The both inequalities are less than hence the shading for the both will be below the line

This interpretation helps to conclude that last options is the best choice

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Answer:

-14x+6

Step-by-step explanation:

The measure of angle number 1 is 69°.

We know that ∠1 + ∠2 = 180°

We also know that the sum of the interior angles of a triangle is always equal to 180°.

Then we can write simple linear equations to find the missing angles, for example we can write:

21° + 38° + ∠2 = 180°

∠2 = 180° - 21° - 38°

∠2 = 121°

Now we can replace that in the original equation  ∠1 + ∠2 = 180°:

∠1 + 121° = 180°

∠1 = 180° - 121° = 69°

∠1 = 69°

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The value of x in the quadrilateral is 4.

We are given that;

Four angles of quadrilateral 5x, 102, 4y-12, 3x+8

Now,

The sum of all interior angles of quadrilateral is 360degree

So, 5x + 102 + 4y-12 + 3x+8 = 360

Also opposite angles are equal

5x= 3x+8

2x=8

x=4

Therefore, by the properties of quadrilateral the answer will be 4.

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