Point M is the midpoint of AB. The coordinates of point A are (−6, 1) and the coordinates of M are (−4, 1). What are the coordinates of point B?

Answer: Given f(x) = -4x + 9 and g(x) = x^2 - x - 10, the composition of functions fog(x) is defined as fog(x) = f(g(x)).

To find the value of fog(5), we need to evaluate g(5) first:

g(5) = 5^2 - 5 - 10 = 20

Now that we have g(5) = 20, we can substitute it into f(x) to find fog(5):

fog(5) = f(g(5)) = f(20) = -4 * 20 + 9 = -79

So, the value of fog(5) is -79.

Step-by-step explanation:

a) given any two real numbers a and b, there is a real number c such that c is between a and b.

b) for any two real numbers a and b, there exists c such that a < c < b.

What are real numbers?

Simply put, in the number system, real numbers are a combination of rational and irrational numbers. In general, all arithmetic operations can be applied to these numbers, and they can also be represented in a number line.

Imaginary numbers, which cannot be expressed on a number line and are frequently employed to symbolise complex numbers, are also unreal numbers that are not expressed in the real world. The letter "R" stands for real numbers, which can be positive or negative. This group encompasses all natural numbers, fractions, and decimals.

For the given question, in the first part, it is said that there is always a real number between every two real numbers.

Using this statement we have to fill in the following blanks.

If we have two given numbers a and b, then there exists a real number c, such that c is between a and b.

Therefore the complete statement is:

a) given any two real numbers a and b, there is a real number c such that c is between a and b.

b) for any two real numbers a and b, there exists c such that a < c < b.

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Answer:

Step-by-step explanation:

This is just the normal parent sin graph, y = sinx

Answer:

  (x, y) = (-4, 3)

Step-by-step explanation:

You want the solution to the matrix equation ...

  [tex]\left[\begin{array}{cc}2&5\\1&3\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] =\left[\begin{array}{c}7\\5\end{array}\right][/tex]

Perhaps the easiest solution is to let a calculator reduce the augmented matrix to row-echelon form. This is done in the attachment. It shows the solution is (x, y) = (-4, 3).

Alternatively, you can left-multiply the equation by the inverse of the coefficient matrix. The inverse of the 2×2 coefficient matrix is easily found.

The inverse is the transpose of the cofactor matrix, divided by the determinant. For a 2×2 matrix, the transpose of the cofactor matrix negates the off-diagonal terms and swaps the diagonal terms. The determinant is the difference of the products of the diagonal and off-diagonal terms:

  [tex]\left[\begin{array}{cc}2&5\\1&3\end{array}\right]^{-1}=\dfrac{1}{2\cdot3-1\cdot5}\left[\begin{array}{cc}3&-5\\-1&2\end{array}\right] =\left[\begin{array}{cc}3&-5\\-1&2\end{array}\right][/tex]

Multiplying this by the constant vector, we have ...

  x = 3(7) -5(5) = -4

  y = -1(7) +2(5) = 3

__

Additional comment

Using row-reduction avoids the problem of the inverse matrix being undefined — when the determinant is zero. That happens when the equations are dependent or inconsistent. The result of row-reduction will tell you which of those is the case: the bottom row is 0 for dependent equations, and 0 0 1 for inconsistent equations.

La condición para convertir una fracción impropia en una fracción mixta es que el denominador sea menor que el numerador. de modo que en esta pregunta solo (4) se puede cambiar a una fracción mixta.

El número 4 se cambia a una fracción mixta se convierte en:

1 372/1000

Una Fracción Ordinaria cuyo cuantificador es menor que el denominador no se puede convertir en una Fracción Mixta.

Entonces, de los números 1-5, solo el número 4 se puede convertir en una fracción mixta.

4)

Convertido a fracciones comunes se convierte en 1371/1000

Convertido a un número mixto se convierte en 1 371/1000

léase uno - trescientos setenta y uno - por mil.

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Answer:

x = 2

Step-by-step explanation:

To obtain a 40% antifreeze solution, we need to add more antifreeze to the 30% solution. Let's call the amount of pure antifreeze that needs to be added x. Then, the amount of antifreeze in the solution will be 2 + x quarts.

The concentration of antifreeze in the solution will be:

(0.30 * 2) + (0.100 * x) = 0.40 * (2 + x)

Solving for x:

0.60 + 0.100x = 0.40 * (2 + x)

Expanding the right-hand side:

0.60 + 0.100x = 0.80 + 0.40x

Solving for x:

0.100x = 0.20

x = 2

So, 2 quarts of pure antifreeze must be added to obtain a 40% antifreeze solution.

Answer:

  see attached for a graph; see below for the check

Step-by-step explanation:

You want to solve this system of equations by graphing, then check the result.

The graph of the equations is attached. The fist has a slope of 1/4 and a y-intercept of -1; the second has a slope of 1/2 and a y-intercept of -2.

The solution is seen to be (x, y) = (4, 0).

In the first equation:

  -4 +4(0) = -4 . . . . . true

In the second equation:

  0 = 1/2(4) -2 . . . . . true

Using the principle of alternate angles we can say that the value of x will be 120°.

The intersection of two parallel lines by a transversal produces alternate angles.

The alternate angles are equivalent when a transversal cuts two parallel lines.

The total of all the angles created on a transverse that are inside either of the two parallel lines is always 180 degrees.

Alternate interior angles for non-parallel lines don't have any special characteristics.

Angles of the same size that are found on opposing sides of the transversal line are known as alternate angles.

So, do not observe the given image:
We know that it is the pair of alternate angles that is equal.

Then, x = 120°.

Therefore, using the principle of alternate angles we can say that the value of x will be 120°.

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Answer:

Step-by-step explanation:

1. the variable 'y' is absent in the equation given in the condition. It means, the given line is vertical. Then

2. if line is vertical, it is parallel to Y-axis, then no y-interception.

3. if to re-write the given equation into x=1, then x-interception is x=1.

4. graph is in the attachment.

The speed and the direction of the resulting blob of clay is 1.4m/s and 57.46 deg below +ve x-axis respectively.

The Latin word for carrier is vector. Points A and B are transported by vectors. The magnitude of the vector is the length of the line connecting points A and B, and the vector's direction is the direction in which point A moves in relation to point B. Other names for vectors are Euclidean vectors and spatial vectors. In many different domains, including mathematics, physics, engineering, and others, vectors are used.

Since there is no external force applied, So using momentum conservation:

Pi = Pf

Since the wreckage is locked onto each other after collision, So their final velocity will be same

m1*v1 + m2*v2 + m3*v3 = (m1 + m2 + m3)*V

m1 = mass of ball1 = 60 g

m2 = mass of ball2 = 20 g

m3 = mass of ball3 = 30 g

v1 = initial velocity of m1 = 4.0 m/sec towards 45 deg South of east = (4*cos(45deg) i - 4*sin(45 deg) j) m/sec

v2 = initial velocity of m2 = 2.0 m/sec towards North = (2.0 j) m/sec

v3 = initial velocity of m3 = 2.9 m/sec towards west = (-2.9 i) m/sec

V = final velocity of blob = x i + y j

So,

60*(4*cos(45deg) i - 4*sin(45 deg) j) + 20*(2.0 j) + 30*(-2.9 i) = (60+20+30)*(x i + y j)

(60*2.83 - 30*2.9) i + (-60*2.83 + 20*2.0) j = 110x i + 110 j

82.8 i - 129.8 j = 110x i + 110y j

By comparing both sides:

x = 82.8/110 = 0.753 i

y = -129.8/110 = -1.18 j

then, final speed will be:

V = 0.753 i - 1.18 j

Part - A

Speed of resulting blob of clay,

|V| = √((0.753)² + (1.18)²)

|V| = 1.4 m/s

Part-B

Direction after collision will be:

Direction = arctan (Vy/Vx) = arctan (-1.18/0.753) = -57.46 deg

Direction = 57.46 deg below +ve x-axis

Hence, the speed and the direction of the resulting blob of clay is 1.4m/s and 57.46 deg below +ve x-axis respectively.

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The formula in this problem is classified as recursive.

The terms are given as follows:

The features that we are given for the formula are given as follows:

Considering that we need the previous term to obtain the nth term, this is an recursive formula.

Then the terms are given as follows:

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The solution is, the value we get 3:4.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

given that,

1/2 (x+8) -:xy +z

when x=4 y=12 and z=-40

so, we get,

1/2*12 : 48+ (-40)

=6:8

=3:4

Hence, The solution is, the value we get 3:4.

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According to the previous sentence, simple interest is equivalent to $157.92.

With only the starting principal and a fixed interest rate, simple yearly interest of government debt interest is calculated. Compounding, which results in borrowers paying tax on both the principal and interest across a number of payment intervals, is not included. To calculate simple interest, multiply the original by the timeframe, rates of return, and duration.

Due to it,

P = $582.09

R = 8.3%

T = 89 days

Now, Simple Interest = P*R*T/100

Simple Interest = 582.09 * 8.3 * 89/100

Simple Interest = 4299.89

Simple Interest would be $4299.89 as a result.

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The missing number is 20.

An amount of something often expressed as a number out of hundred. It is denoted by the symbol '%'.

25% of 20 = [tex]\frac{25}{100}*20[/tex]

                 =5

Then the another number is 20+5=25

The percentage to the number 25 becomes 20 is,

               [tex]\frac{x}{100} *25=20[/tex]

            ⇒x=[tex]\frac{20}{25} *100[/tex]

            ⇒x=80%

Hence, the missing number is 20 and the missing percentage is 80%.

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There are several strategies that can be used to help students understand that a whole number can be divided into parts:

Remember, it may take time for some students to fully grasp the concept of dividing a whole number into parts. Keep practicing and using different strategies until the concept clicks for them.

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a. The vector equation for the given line is (x,y,z) = (1,0,7) + t(1,3,1) and the parametric equations are x = 1+t, y = 3t, z = 6+t.

b. The vector equation for the given line is

(3 + 3t)i + (2.3 + 3t)j + (3.6 - t)k and the parametric equation is

x = 3 + 3t, y = 2.3 + 3t, z = 3.6 - t.

What is a parametric equation?

A series of equations known as a parametric equation specifies a point's location in the xy plane in terms of a third variable, which is typically referred to as a parameter.

a. We are given that a line passes through the point (1,0,7) and is perpendicular to the plane x + 3y + z = 2.

Now, since the line is perpendicular to the plane, the normal vector (1,3,1) for the plane is parallel to the line.

So the vector equation for the line is

(x,y,z) = (1,0,7) + t(1,3,1)

The parametric equations for the line are

x = 1+t, y = 3t, z = 6+t

b.  We are given that a line passes through the point (3, 2.3, 3.6) and parallel to the vector 3i + 3j - k.

So the vector equation "r" for the line is

r = (3i + 2.3j + 3.6k) + t(3i + 3j - k)

r = (3 + 3t)i + (2.3 + 3t)j + (3.6 - t)k

The parametric equations for the line are

x = 3 + 3t, y = 2.3 + 3t, z = 3.6 - t

Hence, the required vector and parametric equations have been obtained.

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The cost per kg of clay is $0.7 and cost per kg of wood is $ 8.

Linear Equation in two variables:

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Now according to the given question,

Let cost per kg of clay be x and cost per kg of wood be y.

Then according to the given information in  table, we can get two equations,

5x + 4y = 35.50                                   .....(1)

3.5x + 6y = 50.45                               .....(2)

Now multiply equation (1) by 3 and equation (2) by 2, we get,

15x + 12y = 106.50                               ......(3)

7x + 12y = 100.90                                 ......(4)

Now subtract equation (4) by equation (3), we get,

8x = 5.60

x = 0.7

Now put this value of x in (1),

we get,

5(0.7) + 4y = 35.5

3.5 + 4y = 35.5

subtracting both sides by 3.5, we get

4y = 32

by dividing both sides by 4, we have

y = 8

Therefore, cost per kg of clay is $0.7

and cost per kg of wood is $ 8.

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The solution that works for both the equations is (-4, 5) and the two lines intersect at this point.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

The given equation are:

y = -1/2x + 3

y = 5

Substitute the value of y in first equation:

5 = -1/2x + 3

5 = -x + 6 / 2

10 = -x + 6

10 - 6 = -x

x = -4

The solution that works for both the equations is (-4, 5) and the two lines intersect at this point.

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As stated in the preceding statement When 4 points are given in one method for calculating grade point averages (GPA), the resulting mean grade rating is 3.41.

Average While calculating the arithmetic mean, a group of integers is added, their count is divided, and the result is then taken. For instance, the average of 2, 3, 5, 7, and 10 is 5, this is the result of 30 reduced by 6.

The quality points by each grade every course must first be calculated before being added together to determine the GPA.

3 credit hours times 4 points for A equals 12 quality points.

B - ( 3 points x 2 credit hours ) x 2 (because there are 2 courses) = 18 quality points

C - 2 points x 4 credits = 8 quality points

D - 1 point x 3 credits = 3 quality points

Now add up all the quality points = 12 + 18 + 8 + 3 = 41

Add the credit hours as well = 3 + 2 + 4 + 3 = 12

Divide the total kit by total semester credit to calculate the GPA = 41/12 = 3.41

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To find out how much Quadra spent, we can use this equation:

Fitting the numbers into the equation would look like this:

We multiply by 0.75 because it is equivalent to 3/4.

If we now know that Quadra spent £90, we can subtract that from her total amount of money to get the amount of money she saved.

Therefore, Quadra saved £30.

The length of the line segment after the dilation with a scale factor of 2 is given by the equation A' = L ( 2 ) , where L is the length of the segment

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the length of the line segment be represented as L

Now , the dilation factor is represented as d = 2

And , the dilation centered at the origin

So , the length of the line segment after the dilation is A'

On simplifying the equation , we get

The length of the line segment after the dilation A' = L x ( dilation factor )

The length of the line segment after the dilation A' = L ( 2 )

Hence , the dilation A' = 2L

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The value of the x is 19.9.

A planar triangle's side's square is equal to the sum of the squares of the other sides minus the product of those sides and the cosine of the angle between them, divided by two.

Given:

The angle C is 98°.

Applying law of cosines:

c² = a² + b² -2ab cosC.

Substituting the values,

c² = (17)² + (13)² -2(17)(13) cos98°.

c² = 458 -  (-0.13917)442

c² = 396.48686

c = 19.9

Hence, x = 19.9.

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The value of the last one is 18.

The solution of the diagram can be modelled with an equation. Therefore, let's find the last value.

we will use variable to represent the fruit names.

Hence,

yellow fruit = x

red fruit = y

green fruit = z

Therefore,

x + y + z = 29

2y + z = 26

2z + y = 25

Using substitution,

y = 25 - 2z

2(25 - 2z) + z = 26

50 - 4z + z = 26

50 - 3z = 26

-3z = 26 - 50

-3z = -24

z = 8

y = 25 - 2(8)

y = 25 - 16

y = 9

Therefore,

x + 9 + 8 = 29

x = 29 - 17

x = 12

Finally,

x + 1 / 2x  = 12 + 1 / 2(12) = 12 + 6 = 18

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The steps that an accountant generally follows to prepare a bank reconciliation statement will be:

A company's prepared bank reconciliation statement demonstrates that the balance of its recorded bank account matches the balance the bank lists.

This report comprises every transaction from a specific time period, including deposits and withdrawals.

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The value of 1 unit = 11/8

The value of 5 units = 11/8 × 5 = 55/8

The value of 5 units as a mixed fraction= 6 7/8

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. This is not a ratio of two like units, such as shirts. This is a ratio of two unlike units: cents and ounces.

If 8 units = 11

therefore 1 unit will be ;

8 units/8 = 11/8

1 units = 11/8

Therefore 5 units = 11/8 × 5 = 55/8

5 units in improper fraction is 55/8

= 6 7/8

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Δ BAD and Δ CAD are congruent by SAS rule.

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Given that, in a Δ BAC, AD bisects ∠ BAC, AB = AC,

We need to prove, BD = DC

         STATEMENT                                                     REASON

1) AD bisects ∠ BAC                                                      given

2) ∠ 1 = ∠ 2                                                           definition of angle bisector

3) AB = AC                                                                      given

4) AD = AD                                                             Reflexive property

5) Δ BAD ≅ Δ CAD                                                       SAS rule

Hence, Δ BAD and Δ CAD are congruent by SAS rule.

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Answer: First, let's calculate Jason's weekly earnings:

Jason's weekly tips = $2100 * 18% = $378

Jason's total weekly earnings = $2100 + $378 = $2478

Next, let's calculate David's weekly earnings:

David's weekly commission = $3500 * 6% = $210

David's total weekly earnings = $185 + $210 = $395

To find the monthly earnings, we need to multiply their weekly earnings by 4 (since there are 4 weeks in a month):

Jason's monthly earnings = $2478 * 4 = $9912

David's monthly earnings = $395 * 4 = $1580

So, Jason makes more money in one month, earning approximately $9912, compared to David's $1580.

Step-by-step explanation:

The individual who makes more money in a month between Jason and David is David.

Jason's weekly tips = 18% of $2100

= $378

David weekly salary= $185

David's weekly tips = 6% of $3400

= $210

Total weekly salary of David = $185 + $210

= $395

Total monthly salary of Jason= $378 × 4

= $1,512

Total monthly salary of David= $395 × 4

= $1,580

Therefore, David makes more money than Jason in a week.

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The value of t for a t-distribution with 15 degrees of freedom is -2.131.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values.

Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

Given:

Degree of freedom df = 15

and area to the left of t = 0.025

Hence, area right of t = 1-0.025 = 0.975

From the table of t-distribution for the area left of t = 0.025 and 15 degrees of freedom, the corresponding value of t is -2.131.

Hence, t = -2.131

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