Find the measure of each acute angle.

Answer:

(Check message's below my answer for link to go to the graph on desmos because this is not allowing the link. :( It'sts not anything bad or of that sort, just trust me please.)

3. A = (0,3) B = (4,2) C = (1,-1)

4. A = (-3,0), B = (1,-1) C = (-2,-4)

Step-by-step explanation

Direction of Rotation: Counterclockwise or clockwise direction. Positive rotations are counterclockwise. Negative rotations are clockwise. For example, to rotate the point (2, 5) counterclockwise about the origin by 90 degrees, we use the rule: (x,y)→(−y,x) ( x , y ) → ( − y , x ) .

Answer:

(Check message's below my answer for link to go to the graph on desmos because this is not allowing the link. :( It'sts not anything bad or of that sort, just trust me please.)

3. A = (0,3) B = (4,2) C = (1,-1)

4. A = (-3,0), B = (1,-1) C = (-2,-4)

Step-by-step explanation

Direction of Rotation: Counterclockwise or clockwise direction. Positive rotations are counterclockwise. Negative rotations are clockwise. For example, to rotate the point (2, 5) counterclockwise about the origin by 90 degrees, we use the rule: (x,y)→(−y,x) ( x , y ) → ( − y , x ) .

Answer:

arrow to the right no filled in dot

Step-by-step explanation:

the (>) shows you which direction the thing is going

in this situation you just have to simplify the problem

4x+2=10

-2. -2

4x=8

x=2

x>2

Answer:

You would put it on 10 and use the arrow pointing the right with a open dot. (The dot should not be filled in and looks like a bubble.)

Step-by-step explanation:

Wei-Ling's fifteenth-generation ancestor is estimated to have around 1,220,703 descendants.

Assuming that each descendant has an average of 2.5 children, we can use the formula:

where n is the number of generations.

In this case, n = 15 (fifteenth-generation), so we can plug in the values and get:

number of descendants = \((2.5)^{15}\)= 1,220,703.125

Therefore, Wei-Ling's fifteenth-generation ancestor is estimated to have around 1,220,703 descendants. However, it is important to note that this is just an estimation and may not be entirely accurate due to various factors such as reproductive rates and other variables.

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6. x=1 , y=2

7. x=-4 , y=5

8. Infinitely Many Solutions

Answer:

-1

Step-by-step explanation:

-7=n-6

n=-7+6

n=-1

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(a) h(2) = -1

(b) h(-1) = -1

(c) h(x+1) = -x^2 - x + 1

The equation represents y as a function of x, and the function values are -1 for all given inputs.

To determine whether the equation represents y as a function of x, we need to check if there is a unique y-value for every x-value.

The equation given is:

h(t) = -t^2 + t + 1

(a) h(2):

To find h(2), substitute t = 2 into the equation:

h(2) = -(2)^2 + (2) + 1

h(2) = -4 + 2 + 1

h(2) = -1

(b) h(-1):

To find h(-1), substitute t = -1 into the equation:

h(-1) = -(-1)^2 + (-1) + 1

h(-1) = -1 + (-1) + 1

h(-1) = -1

(c) h(x+1):

To find h(x+1), substitute t = x+1 into the equation:

h(x+1) = -(x+1)^2 + (x+1) + 1

h(x+1) = -(x^2 + 2x + 1) + x + 1 + 1

h(x+1) = -x^2 - 2x - 1 + x + 1 + 1

h(x+1) = -x^2 - x + 1

Therefore:

(a) h(2) = -1

(b) h(-1) = -1

(c) h(x+1) = -x^2 - x + 1

The equation represents y as a function of x, and the function values are -1 for all given inputs.

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The equation 3+7+2=+2 is actually not true, but false.

The equation 3+7+2=+2 is actually not true, but false. This is because the sum of 3, 7, and 2 is 12, not 2.

In general, an equation is considered true if the expressions on both sides of the equal sign are equivalent in value. In this case, the expressions on the left-hand side (3+7+2) and the right-hand side (+2) are not equivalent, and therefore the equation is false.

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Answer:

A. y - 2 = 2/3 (x - 0)

Step-by-step explanation:

The rate of a molecule's migration through an electric field during electrophoresis is determined by factors such as the molecule's size, shape, and charge, as well as the properties of the electric field and the medium through which the molecule is moving.

The rate of a molecule's migration through an electric field during electrophoresis is determined by several factors. The size and shape of the molecule play a significant role. Larger molecules will migrate more slowly than smaller molecules, and molecules with more complex shapes will also migrate more slowly due to increased resistance to movement through the gel or solution. Secondly, the charge of the molecule is also a determining factor. Molecules with a higher charge will migrate more quickly than those with a lower charge.

The strength of the electric field and the properties of the gel or solution used for electrophoresis can also affect the rate of migration. The rate of a molecule's migration through an electric field during electrophoresis is a complex process with multiple factors influencing the final outcome.

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Answer:

1. \(x = \pm 5\)

2. \(x = \pm i\)

3. \(x = 5, -4\)

Step-by-step explanation:

1.

\(x^2-25=0\)

\(x^2 = 25\)

\(x = \pm \sqrt{25}\)

\(x = \pm 5\)

2.

\(x^2 + 1 = 0\)

\(x^2 = -1\)

\(x = \pm \sqrt{x-1}\)

\(x = \pm i\)

3.

\(x^2=x+20\)

\(x^2 - x - 20 = 0\)

\((x-5)(x+4)=0\)

\(x = 5, -4\)

Answer:

24

Step-by-step explanation:

We can make the equation

225+50x=1425

=

50x=1200

=

x=24

In order to determine the integer that makes true the given expression:

______ x 7 = -14

consider that such integer must be equal to the quotient between -14 and 7:

-14/7 = -2

In fact, you have:

-2 x 7 = -14

Hence, the integer is -2

The t-score to be used to find the 90% confidence interval for the population mean is; \(t_{(0.05,27)}\) = 1.703

The t-score which is representative of a point with n - k (n, and k represents the sample size and the number of groups in the test respectively) degrees of freedom  from the Student's T-distribution is a standard test statistic obtained by applying a T-test

Therefore, the t-score used for a confidence interval is obtained by by making use of the the following information;

The number of degrees of freedom = n - k

Given,

The number of pizza orders in the sample, n = The sample size = 28

The number of samples used in the estimate, k = 1 group of 28 randomly sampled pizza

The level of confidence (the probability) that the interval contains the population mean = 90%

Therefore, the significance level, α = 1 - 90% = 1 - 90/100 = 0.1

∴ The α-level for the upper and lower limit of the interval are α/2 = 0.1/2 = 0.05 long

The degrees of freedom, df = n - k

∴ For the estimation, DF = 28 - 1 = 27

The t-statistic is therefore the t-value at the intersection of the row for DF = 27 and the 0.05 (one-tail) column (0.05 two-tail column) which gives;

\(t_{(\alpha /2, DF)}\) = \(t_{(0.05, 27)}\) = 1.703

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Answer:

− 3 ( x − 5 ) ( x + 2 ) hope this helps

Step-by-step explanation:

Answer:

− 3 ( x − 5 ) ( x + 2

Step-by-step explanation:

The value of q based on the given task content is 30° based on the theorem of vertical opposite angles.

Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines, that is, they are opposite of each other.

Therefore

Angle q = 30° based on the theorem of vertical angles.

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To rotate a coordinate system onto another coordinate system using matrices, you can follow these steps:

1. Determine the angle of rotation: First, determine the angle by which you want to rotate the coordinate system. This angle will be used to create a rotation matrix.

2. Create a rotation matrix: The rotation matrix is a 2x2 or 3x3 matrix that represents the transformation of points in the original coordinate system to points in the rotated coordinate system. The elements of the rotation matrix can be determined based on the angle of rotation.

For a 2D rotation, the rotation matrix is:

 \(\[ \begin{matrix} cos\theta & -sin\theta \\ sin\theta & cos\theta \end{matrix} \]\)

For a 3D rotation around the x-axis, y-axis, and z-axis, the rotation matrices are:

\(Rx = \left[\begin{array}{ccc}1&0&0\\0&cos\theta&-sin\theta\\0&sin\theta&cos\theta\end{array}\right]\)

\(Ry = \left[\begin{array}{ccc}cos\theta&0&sin\theta\\0&1&0\\-sin\theta&0&cos\theta\end{array}\right]\)

\(Rz = \left[\begin{array}{ccc}cos\theta&-sin\theta&0\\sin\theta&cos\theta&0\\0&0&1\end{array}\right]\)

Note that θ represents the angle of rotation.

3. Apply the rotation matrix: To rotate a point or a set of points, multiply the coordinates of each point by the rotation matrix. This will yield the coordinates of the points in the rotated coordinate system.

For example, if you have a 2D point P(x, y), and you want to rotate it by angle θ, the rotated point P' can be obtained by multiplying the column vector [x, y] by the rotation matrix:

  [ x' ]  =  [ cosθ  -sinθ ]   [ x ]

  [ y' ] =   [ sinθ   cosθ  ] * [ y ]

Similarly, for 3D rotations, you would multiply the column vector [x, y, z] by the appropriate rotation matrix.

Rotating a coordinate system onto another coordinate system using matrices involves the use of rotation matrices. These matrices define how points in the original coordinate system are transformed to points in the rotated coordinate system.

The rotation matrices are constructed based on the desired angle of rotation. The elements of the matrix are determined using trigonometric functions such as cosine and sine. The size of the rotation matrix depends on the dimensionality of the coordinate system (2D or 3D).

To apply the rotation, the coordinates of each point in the original coordinate system are multiplied by the rotation matrix. This matrix multiplication yields the coordinates of the points in the rotated coordinate system.

By performing this transformation, you can effectively rotate the entire coordinate system, including all points and vectors within it, onto the desired orientation defined by the angle of rotation.

Matrix transformations provide a mathematical and systematic approach to rotating coordinate systems, allowing for precise control over the rotation angle and consistent results across different coordinate systems. They are widely used in computer graphics, robotics, and various scientific and engineering fields.

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This means that for every unit increase in the x-coordinate, the y-coordinate decreases by 11/12 units.To find the slope of the line that contains the points (-3, -5/2) and (3, -8), we can use the formula for slope:

slope = (y₂ - y₁) / (x₂ - x₁)

Let's plug in the given coordinates into the formula:

slope = (-8 - (-5/2)) / (3 - (-3))

Simplifying the numerator and denominator:

slope = (-8 + 5/2) / (3 + 3)

To combine the fractions in the numerator, we need a common denominator:

slope = (-16/2 + 5/2) / 6

slope = (-11/2) / 6

To divide fractions, we multiply the numerator by the reciprocal of the denominator:

slope = (-11/2) * (1/6)

Simplifying the multiplication:

slope = -11/12

Therefore, the slope of the line that contains the points (-3, -5/2) and (3, -8) is -11/12.

The negative sign indicates that the line is sloping downwards from left to right. The magnitude of the slope (11/12) represents the steepness of the line.

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Answer:

24+p=t

Step-by-step explanation:

If he scored 24 points in the first half, and p in the next half, he scored a total of t points.

\(\text{Answer:}\\\\\text{y = -2x +4 where m=-2 is the slope and b = 4 is the y-intercept.}\\\\\text{Step-by-step explanation:}\\\)

Answer:

y = - 2x + 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

Here m = - 2 and b = 4 , then

y = - 2x + 4

The three methods in solving for the solutions of the systems of linear equations in two variables are:

1) graphing.

2) substitution method.

3) elimination method.

In this question we need to mention the three methods in solving for the solutions of the systems of linear equations in two variables.

We know that a linear equation in two variables is of  the form of ax + by + c = 0.

There are three ways to solve systems of linear equations in two variables: graphing, substitution method and elimination method

In graphing method, we graph both the linear equations. If the two lines intersect, then the point of intersection is the solution to the system. If the two lines are parallel, then there is no solution. And if the two lines lie on top of each other, then they have an infinite number of solutions.

In substitution method, the value of one variable from one equation is substituted in the other equation.

And in elimination method one of the variables in given system of linear equations is eliminated using the addition or subtraction methods.

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Answer:

When radius is doubled:

Circumference becomes double.

Area becomes four times.

When diameter is doubled:

Circumference becomes double.

Area becomes four times.

Step-by-step explanation:

Given that

Radius of a circle is doubled.

Diameter of circle is doubled.

To study:

The effect on circumference and area on doubling the radius and diameter.

Solution/explanation:

Let us discuss about the formula for circumference and area.

Formula for Circumference of a circle in form of radius:

\(C =2\pi r\)

It is a linear equation in 'r'. So by doubling the radius will double the circumference.

Formula for Area of a circle in form of radius:

\(A =\pi r^2\)

It is a quadratic equation in 'r'. So by doubling the radius will make the area as four times the earlier area.

Testing using example:

Let the initial radius of a circle = 7 cm

Initial circumference = \(2 \times \frac{22}{7} \times 7 = 44 cm\)

Initial area = \(\frac{22}{7} \times 7 \times 7 =154 cm^2\)

After doubling:

Radius = 14 cm

circumference = \(2 \times \frac{22}{7} \times 14 = 88 cm\)   (Twice the initial circumference)

area = \(\frac{22}{7} \times 14 \times 14 =616 cm^2\) (4 times the initial area)

------------------------------------

Formula for Circumference of a circle in form of Diameter:

\(C =\pi D\)

It is a linear equation in 'D'. So by doubling the diameter will double the circumference.

Formula for Area of a circle in form of diameter:

\(A =\dfrac{1}{4}\pi D^2\)

It is a quadratic equation in 'D'. So by doubling the Diameter will make the area as four times the earlier area.

Testing using example:

Let the initial diameter of a circle = 28 cm

Initial circumference = \(\frac{22}{7} \times 28 = 88 cm\)

Initial area = \(\frac{1}{4}\times \frac{22}{7} \times 28 \times 28 =616cm^2\)

After doubling:

Diameter = 56 cm

circumference = \(\frac{22}{7} \times 56= 176 cm\)   (Twice the initial circumference)

area = \(\frac{1}{4}\times \frac{22}{7} \times 56 \times 56 =2464cm^2\) (4 times the initial area)

So, the answer is justified:

When radius is doubled:

Circumference becomes double.

Area becomes four times.

When diameter is doubled:

Circumference becomes double.

Area becomes four times.

Answer:

See below.

Step-by-step explanation:

First, you want to turn the percentage into a decimal. To do that, divide the percentage by 100.

\(\frac{5.1}{100} =0.051\)

Next, multiply the percentage by the price.

\(129*.051=6.579\)

\(6.579\) rounded to the nearest cent would be \(6.58\).

Last, you would subtract to find the answer.

\(129-6.58=122.42\)

Answer: $122.42

:)

As per the given rectangle, the length of EG is 5x - 7

We are given that DEFG is a rectangle, which means that its opposite sides are parallel and equal in length. Let's label the sides of the rectangle as follows:

DE = FG = a (since opposite sides of a rectangle are equal in length)

EF = DG = b (since opposite sides of a rectangle are parallel)

Now, we can use the given information to set up an equation for the length of EG:

EG = EF + FG = b + a

But we don't know the values of a and b. However, we are given that FD = 3x - 7 and EG = x + 5. We can use this information to solve for a and b.

We know that FD = DE - EF, so we can substitute the values we have:

3x - 7 = a - b

We also know that EG = FG - DG, so we can substitute the values we have:

x + 5 = a - b

Now we have two equations with two variables (a and b). We can solve for a and b by adding the two equations together:

3x - 7 + x + 5 = 2a

4x - 2 = 2a

a = 2x - 1

Now we can substitute this value for a in one of the earlier equations to solve for b:

3x - 7 = (2x - 1) - b

b = 3x - 6

Finally, we can substitute the values we found for a and b into the equation we set up earlier to find the length of EG:

EG = EF + FG = b + a = (3x - 6) + (2x - 1) = 5x - 7

Therefore, the length of EG is 5x - 7.

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Characteristic polynomial of the matrix \(p(x) = (x+1)(x-2)^2\)

For the matrix [8 -4 0 -4], the characteristic polynomial is found by taking the determinant of the matrix [8-x -4 0 -4; 0 8-x -4 0; 0 0 8-x -4; 0 0 0 8-x] and simplifying it. This results in p(x) = \((x-8)^4\).

For the matrix [3 0 4 -3 -4 -1 0 -1 0], the characteristic polynomial is found by taking the determinant of the matrix [3-x 0 4; -3 -4-x -1; 0 -1 -x 0;] and simplifying it. This results in \(p(x) = (x+1)(x-2)^2\).

The determinant of the matrix (A - lam*I), where I is the identity matrix of the same size as A, is found by computing the characteristic polynomial of a square matrix A, represented by P(lam), which is a polynomial function of a scalar variable lambda. We refer to the eigenvalues of the matrix A as the roots of the characteristic polynomial. Important details about the matrix, including its diagonalizability, rank, trace, and determinant, are revealed by the characteristic polynomial. It frequently appears in applications like systems of linear equations, differential equations, and linear transformations.

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Answer:

1835

Step-by-step explanation:

f(x) = 200x + 50

f(5) = 200(5) + 50

     = 1000 + 50

     = 1050

g(x) = 100x + 85

g(7) = 100(7) + 85

      = 700 + 85

      = 785

f(5) + g(7) =

1050 + 785 =

1835

The sampling distribution of difference between means approximates a normal curve whose mean is zero.

The sampling distribution means the probability distribution based on the large number of samples of size n from the given population

Mean is the average of the given numbers and it is calculated by dividing the sum of observation by the number of observation. Here the term observation represents the given data.

Here they used the normal curve, sot its mean value is zero

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The process of ordering objects or numbers is known as permutation. Combinations are a method of choosing items or numbers from a collection or group of items so that the order of the items is irrelevant.

Combinations are used to group objects or to determine how many subgroups can be formed from the given collection of objects. Additionally, we use permutations to determine the amount of potential combinations of unrelated objects.

Fir example, if we want to select 2 players from 6. This will be:

= 6! / 2! (6 - 2)!

= 15 ways

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