For what values of k the vectors are linearly independent?

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We will have a Deficit balance of $30 at the end of the month.

"Unilateral transfer" is the term used to describe the balance of payments deficit's most obvious cause. For instance, Americans who contribute money to another country in the form of foreign aid do not receive anything in return (economically speaking). Few economists would argue that foreign aid-related balance of payment deficits are a "bad thing."

Weekly net income = $380

Monthly net income = $380 * 4 weeks = $1520.

Monthly expenses = $1550

Balance = Monthly income - monthly expenses = $-30.

The negative sign shows a deficit of $30 monthly

Therefore, We will have a Deficit balance of $30 at the end of the month.

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Answer: 4 3/4 OR 4.75

Step-by-step explanation:

Do the operations in the parentheses first.

5 1/2 + 2 3/4 = 8 1/4

Then, subtract.

8 1/4 - 3 1/2 = 4 3/4 OR 4.75

Combining like words, leveraging the sequence of operations, using the distributive principle, and factoring are the methods for simplifying an equation.

Adding or removing phrases with the same variables raised to the same powers is known as combining like words. The order of operations, commonly referred to as PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction), is a set of guidelines that specify the sequence in which mathematical operations must be carried out. By multiplying each phrase inside the parenthesis by the term outside the parentheses, you may apply the distributive principle to multiple a single term as well as the sum or difference of two or more terms. Finding common factors in an expression and separating them out is the process of factoring.

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Answer:

[tex]f(x)=-2(x+2)(x-4)[/tex]

Step-by-step explanation:

In factored form, [tex]f(x)=a(x+2)(x-4)[/tex].

To solve for [tex]a[/tex], use the point [tex](-1,10)[/tex].

[tex]10=a(-1+2)(-1-4) \implies a=-2 \\ \\ \therefore f(x)=-2(x+2)(x-4)[/tex]

For given linear equations the values for following are m= -9, x=2, b=10, w=-4.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

As given linear equations are

4m-5=-41

m= -9

-11=1-6x

x=2

4/5*b+13

b=10

-1/2*w-8=-6

w= -4

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Answer:

The average points received by those students who did not pass the test successfully would be 4 points.

Step-by-step explanation:

Step 1: We know that all students wrote the test and received an average of 6 points.

Step 2: We also know that 60% of those students passed the test successfully and received an average of 8 points.

Step 3: This means that the remaining 40% of students did not pass the test successfully.

Step 4: Since the average points for all students was 6 points and the average points for those who passed the test was 8 points, the average points for those who did not pass the test would be 4 points.

The required volume of the sphere is given as 33.49 cubic centimeters.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
Radius of sphere = 2 cm
The volume of the sphere = 4/3πr³
                                 = 4/3 × 3.14 × 2³
                                 = 33.49 cm³

Thus, the required volume of the sphere is given as 33.49 cubic centimeters.

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The value of x is, 18 and the measure of angle A is 110°.

Parallel lines are those lines that are equidistance from each other and never intersect each other.

We have to given that;

The values of angle A and B are,

⇒ ∠A = 5x + 20

⇒ ∠B = 9x - 92

Now, By figure,

Angles A and B are corresponding angles of parallel lines.

Hence, The sum of angles A and B are 180°.

So, We can formulate;

⇒ ∠A + ∠ B = 180°

⇒ (5x + 20) + (9x - 92) = 180

⇒ 14x - 72 = 180

⇒ 14x = 180 + 72

⇒ 14x = 252

⇒ x = 252 / 14

⇒ x = 18

Hence, The measure of angle A is,

⇒ ∠A = 5x + 20

⇒ ∠A = 5×18 + 20

⇒ ∠A = 90 + 20

⇒ ∠A = 110°

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The complete question is shown in figure.

Answer:

  100.0 feet

Step-by-step explanation:

You want to know the distance to a goalpost when the angle to the top of its 30 ft height is 16°42'.

The tangent relation is ...

  Tan = Opposite/Adjacent

Multiplying by Adjacent/Tan gives ...

  Adjacent = Opposite/Tan

In this problem, the distance to the goal can be modeled by the side "adjacent" to the acute angle 16°42' in a right triangle, and the "opposite" side will be the height of the goal.

  adjacent = 30'/tan(16°42') ≈ 99.995 ft

Rounded to the nearest tenth, the distance to the goalpost is 100.0 feet.

For the triangles that are given, the congruency postulates are;Postulate of ASA Congruency ,the SSS congruency hypothesis,AAS congruency hypothesis, postulate for SAS Congruency,triangles cannot coexist.

Triangle congruency postulates include AAS, ASA, SSS, SAS, and RHS.

1) The congruency rule in this case is the ASA Congruency postulate because we have two corresponding angles and a congruent side included.

2) Since both triangles are furnished with three corresponding congruent sides, we can argue that the triangle congruence postulate in this case is the SSS congruency postulate.

3)In this case, the AAS Congruency postulate serves as the congruency rule because we are provided two related angles and the non-included congruent side.

4) The congruency rule in this case is the SAS Congruency postulate because we are given two congruent sides and an angle that also includes a congruent side.

5) The triangles are not congruent since we are provided three congruent angles but no information about any congruent sides.

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Considering the figure in the problem the longest side is

In a triangle, the longest side is located opposite from the largest angle, while the shortest side is located across from the smallest angle.

Triangle inequity: Any triangle in which the total of any two sides is greater than the length of the third side is a proper way a to form a triangle

According to the figure, the largest angle is 74 degrees.

The side opposite the largest angle is GH which is in the option A

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13 units is the distance from the given point (-12, 5) to the origin.

Both statistical and qualitative methods can be used to determine how far apart two things or points are.

The word "distance" in physics can refer to an actual length or, more frequently, to an estimate based on a range of other factors.

The length of the line segment that connects any two points on a plane provides the distance between those spots.

To calculate the distance between two points, one commonly uses the equation d=((((x2 - x1)2 + (y2 - y1)2).

So, the given point is:

(-12, 5)

Assume that O (0, 0) is the origin and that M (-12, 5) is the provided location.

The distance between M and O is:

= √(−12−0)2+(5−0)2

= √(−12)2+(5)2

= √144+25

= √169

= √13×13

= 13 units

Therefore, 13 units is the distance from the given point (-12, 5) to the origin.

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Answer:

f(10) = 340

Step-by-step explanation:

to find f(10) substitute x = 10 into f(x) , that is

f(10)

= 4(10)² - 4(10) - 20

= 4(100) - 40 - 20

= 400 - 60

= 340

Answer: 2.1

Step-by-step explanation: 5.88 divided by 2.80 = 2.1

Answer:

Step-by-step explanation:

3.08

The probability that these two spins added together would equal 7 is 1/25.

The probability that each spin will land on a specific number is 1/5. Since the spins are independent, we can multiply the probability of each spin landing on the desired number to find the probability of both spins landing on the desired numbers.

To get the sum 7, Charlie's spinner needs to land on 4, which is (1/5) and Libby's spinner needs to land on 3 which is also (1/5).

The probability of both spins landing on the desired numbers is (1/5) * (1/5) = 1/25.

It is important to note that the probability is low because the spins are independent events, meaning that the outcome of one spin does not affect the outcome of the other spin.

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Answer:

are know :D Hello, what are you doing

ordered pair is in the solution set of the system of inequalities shown in the graph will be (1, 5)

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

Set of such values is called solution set to the considered equation or inequality.

The shaded portion will be consider as the dashed line joining points

The portion affected by the two shadings would be the portion common to the right of the dashed line joining points

The ordered pair is in the solution set of the system of inequalities shown in the graph will be (1, 5)

Hence, ordered pair is in the solution set of the system of inequalities shown in the graph will be (1, 5)

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Triangle ABC is first mirrored over the x-axis, then across the y-axis, to form triangle A'B'C.

The Complete Question.

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The speed of Mr. Black to his friend's house is 60 miles per hour.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Speed = Distance travelled / Time taken

Let x be the speed of Mr. Black to his friend's house.

Let d be the distance in miles that Mr. Black travelled to reach friend's house.

Time taken to reach friend's house = 2 hours

x = d / 2 ⇒ d = 2x

Speed of Mr. Black during return is 20 mph slower.

Speed during return = x - 20

The trip back took 1 hour longer.

Time = 2 + 1 = 3 hours

x - 20 = d / 3

Substituting d = 2x in the above equation,

x - 20 = 2x / 3

3 (x - 20) = 2x

3x - 60 = 2x

x = 60

Hence the speed is 60 mph to his friend's house.

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Answer:

x = 2, y = 2

x = 4, y = 4

x = , y = 0

x = 4, y = 4

Step-by-step explanation:

Therefore , the solution of the given problem of trigonometry comes out to be  - (√2-+√6 ) / 4.

The connection between trigonometric and square spline The field is believed to have been founded in the late 1700s, but it really began in the third-century BC when the mathematical and astronomy sciences were combined. Numerous geometric equations can be solved or the results of calculations using them can be computed using precise mathematical methods. Trigonometry is the study of the six basic trigonometric operations.

Here,

Given :

cos(x + y)

cos(x) cos(y) -  sin(x) sin(y)  by the cosine addition identity.

We receive:

If we look just at unit circle, we should notice that cos(x) = √2/2 instead than sin(x) = √2/2.

Additionally, we are told that cos(y)= -1/2,

but if we look at the unit circle, we should find that sin(y)=√3/2.

Use both of them to the following: cos(x + y).

cos(x) sin - cos(y) (x) sin(y) via the cosine addition identity.

=> √2/2 - 1/2 - √2/2*√3/2

=> -√2/4   - √6/4

=> -√2- √6 / 4

=> - (√2-+√6 ) / 4

Therefore , the solution of the given problem of trigonometry comes out to be  - (√2-+√6 ) / 4.

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To find the acute angle of a right triangle with side lengths divide the length of side "a" by the length of the hypotenuse, side "c."

A right triangle is a kind of triangle with a right, or 90-degree, angle. Since the sum of the angles in a triangle must be 180 degrees, the remaining two angles are acute, which implies they are less than 90 degrees.

Orient the triangle in such a way one leg of the 90-degree angle will be vertical. Mark this leg as "a." The other leg of the 90-degree angle will be horizontal. Mark that leg "b." Mark the third side, the hypotenuse, "c."

Measure the length of the three sides. In some applications, you will only be able to calculate sides "a" and "b." In this case, use the Pythagorean Theorem to calculate side "c."

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Answer: 1 5/8 is indeed greater than 1.6. 5/8 equals to decimal form 0.625 add the one and we get 1.625. Which is only a bit bigger than 1.6 hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

1 5/8 (1.625) is greater than 1.6 

1.625 > 1.6

1) A  perpendicular bisector in kite ABCD is; BD

2) An isosceles triangle in kite ABCD is; ΔABC

3) A right triangle in kite ABCD is; ΔABM

In geometry, a kite is defined as a quadrilateral with reflection symmetry across a diagonal.

1) A perpendicular bisector is defined as a line segment which bisects another line segment at 90 degrees.

Looking at the diagram, Line BD bisects Line AC and as such BD is the perpendicular bisector.

2) An Isosceles triangle is defined as a a triangle in which two sides have the same length.

In this case, in Triangle ABC, AB and BC have the same length and as such Triangle ABC is the Isosceles Triangle.

3) A right triangle is defined as a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.

In this case if Mis the intersection of BD and AC, then the right angle triangle is ABM

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

What approach to solving a system of linear equations is the simplest?

Graphing. One of the most straightforward methods for resolving a set of linear equations is to use a graph.

                 You only need to graph each equation as a line and identify the point or points where the lines converge. Since these equations are already expressed in slope-intercept form, graphing them is simple.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

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Answer:

Step-by-step explanation:

Here, 4 teams given. Each teams has played every other teams 4 times.

so here we will name each team

team a = bulls

team b = lakers

team c = knickers

team c = warriors

So to find total number of games, we know that Bulls played with the other 3 teams by 4 times that is (4×3) = 12, Lakers played with the other two teams by 4 times that is (4×2) = 8, Knicks played with Warriors 4 times.

Therefore, total number of games = .

Total points given, for Bulls = 22, for Lakers = 19, for Knickers = 14, for Warriors = 12.

So sum of total points =

For a win a team earned 3 points and for a tie two teams win 1 point.

That means for tie total point = 1+1 = 2.

Let's take total number of game which ended as win played be x and total number of game which ended as a tie be y.

We have got total number of games is 24.

So we can write the equations as,

.......Equation 1

And also we have got total number of points is 67. So the equation is,

.......Equation 2

From equation 1, if we move x to the right side we will get,

Now let's substitute this value in equation 2, to get the value of x. By substituting the value we will get,

We will expand 2 now.

We will move 48 to the other side by subtracting it from both sides. We will get,

So the number of games which ended as a win = 19

The number of games which ended as a tie = 24 -19 =5  

So we have got the required answers.

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The composite number between 71, 81, 41 and 61 is 71.

A composite number is a positive integer that can be divided by at least one positive integer other than itself and one. It is the opposite of a prime number, which can only be divided by itself and one. Composite numbers are also referred to as composite integers, composite numbers, or simply composites. Examples of composite numbers include 4, 6, 8, 9, 10, 12, 14, 15, and 16.

A composite number is a positive integer that has more than two factors. 71 is a composite number because it has the factors 1, 71, and itself. It also has the factors 11, 7, and 7. Thus, 71 is the composite number between 71, 81, 41, and 61.

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The house must have 13 bedrooms.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

let the number of bedrooms be x.

As, the maximum number of people allowed is twice the number of bedrooms plus one .

So, max people ≤ 2x + 1

Now, we have number of people = 1 + 1 + 4 = 6

Then, the maximum bedrooms have

= 2 (6)+ 1

= 13

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