Given the system x + 2z = -2
x + y + kz = 2
3x + ky - 2z = 2
(a) Give the augmented matrix for the system. (b) For which values of k (if any) does the system have a unique solution? (c) For which values of k (if any) does the system have a infinitely many solutions? (d) For which values of k (if any) does the system have a no solution?

Dilation is neither horizontal nor vertical. Dilation is a transformation that changes the size of a shape but does not change its orientation.

It can be represented by a formula in coordinate geometry: (x, y) → (kx, ky), where k is a scale factor (greater than 0). The scale factor determines the amount of scaling that is applied to the shape. For example, if k = 2, then the coordinates of the original point (x, y) would be multiplied by 2, resulting in a new point (2x, 2y). This would result in the shape being twice as big as the original. Similarly, if k = 0.5, then the coordinates of the original point (x, y) would be divided by 2, resulting in a new point (0.5x, 0.5y). This would result in the shape being half as big as the original. Therefore, dilation can be used to scale shapes both up and down in size, but it does not alter their orientation.

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The reduced form of 14/10 is 7/5. The answer is obtained using the method of simplifying fractions.

What is meant by simplifying fractions?

Making a fraction as simple as possible is referred to as simplifying (or reducing) a fraction.

To do this, we divide the denominator and numerator by the biggest number that can be divided exactly into both numbers. In other words, we choose the biggest common number between the top and bottom and divide it by that.

In a fraction, the numerator and denominator are referred to as the "terms." Thus, when we simplify a fraction, we cast it in its most basic mathematical form.

Now, to reduce 14/10, we will find the highest common factor of 14 and 10.

The highest common factor is 2 i.e. both numerator and denominator are divisible by 2.

So, on dividing both the terms by 2, we get

(14÷2)/(10÷2)= 7/5

Hence, the reduced form of 14/10 is 7/5.

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Answer:

Equation:

[tex]7x + 10 = 150[/tex]

Value of x:

[tex]x = 20[/tex]

Step-by-step explanation:

In the figure, we are given 2 angles, 150° and (7x+10)°.

These 2 angles are vertical angles because they are directly opposite of each other and formed by intersecting lines.

Vertical angles are congruent, which means the same.

Thus, to make an equation to solve for x, we need to set the angles equal to each other.

Equation: [tex]7x + 10 = 150[/tex]

Solving for x:

[tex]7x + 10 = 150[/tex]

⇒ [tex]7x = 140[/tex] . . . . . . . . . subtract 10 from both sides of the equation

⇒ ∴ [tex]x = 20[/tex] . . . . . . . . . divide both sides by 7 to isolate x

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Answer:

Step-by-step explanation:

Using VAT:

Angles opposite each other are consider equal.

Therefore : 7x+10 = 150

Solve for x: 7x= 150-10

                    x= 140/7

                    x= 20

To check : 7x+10 = 150

                 7(20)+10=150

                 140+10=150

                 150=150 (correct)

Answer: multiplying by denominators

Step-by-step explanation: not sure if this is the right answer in this context but i hope it helps

technically cross multiplying basically is multiplying by denominators, but depending on the math level they are sometimes considered different methods

again, this may not be correct so if you want a more clear answer could you provide a bit of context? sorry, hope it helps anyway though.

The total number of books that Jarrod packed into boxes can be represented by 84 + x*12.

The total number of books that Jarrod packed into boxes can be found by multiplying the number of boxes he packed with the number of books per box.

In this case, Jarrod packed 6 boxes of science textbooks with 14 books per box, so the number of books in the science boxes is 614 = 84. He also packed math textbooks with 12 books per box, so the number of books in the math boxes can be represented by x*12, where x represents the total number of boxes he packed.

So the total number of books that Jarrod packed into boxes can be represented by 84 + x*12.

Therefore, the equation that can be used to find the total number of books that Jarrod packed into boxes is: 84 + x*12 = Total number of books.

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Depending on the patient and the strength of the eye drop, eye dilation caused by eye drops used for eye examinations typically lasts between 4 and 24 hours.

What is eyes dilation?

There are causes of dilated pupils besides underlying disease. Examples include a pitch-black room, sleep, fear, or adverse drug reactions.

When you get your eyes dilated, your doctor uses special drops to open your pupils wide.

This let them get a look at your whole eye, including all the nerves and blood vessels at the back, to check for signs of diseases

When dilated, the pupil is unable to get smaller, and thus block out light in bright areas. This causes glare in your vision so you can't see things clearly.

The drops also make it difficult to focus on things up close, but usually don't affect distance vision.

So, Your eyesight will be impaired, so some experts say you should play it safe and not get behind the wheel will leads to affecting your driving

Hence, depending on the patient and the strength of the eye drop, eye dilation caused by eye drops used for eye examinations typically lasts between 4 and 24 hours.

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Answer:

It is called the perimeter

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Solutions are where the graphs intersect....they are equal at these points

(2,-3)  and (4,-1)  

There is likely one more point of intersection down and to the left which is not shown on the graph

The measure of four angles of quadrilateral is 360°.

What is quadrilateral?

A closed quadrilateral has four sides, four vertices, and four angles.

It is a type of polygon.

In order to create it, four non-collinear points are joined.

Quadrilaterals always have a total interior angle of 360 degrees.

A polygon with four sides, four angles, and four vertices is called a quadrilateral.

The Latin words quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral.

A quadrilateral is shown in the above image as an example.

A quadrilateral is a polygon with four vertices and four sides that each contain four angles, the sum of which is 360 degrees.

Two triangles are created when we draw a diagonal to a quadrilateral. These two triangles have a 180° angle sum.

As a result, the quadrilateral's total angle sum is 360°.

Hence, the measure of four angles of quadrilateral is 360°.

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Answer: To make 20 oz of hair dye, the hairstylist needs to use 1 and 1/8 oz of red tone, 3/4 oz of gray tone and 5/8 oz of brown tone.

We can use proportionality to figure out how much of each dye color is needed.

Let's call the amount of red dye needed x, the amount of gray dye needed y and the amount of brown dye needed z.

According to the proportionality, we can write the following equation:

(1 + 1/8)x + (3/4)y + (5/8)z = 20

To find the amount of each dye color needed, we can solve this equation for x, y and z.

First, we can clear the fractions by multiplying all terms by 8:

(8 + 1)x + (6)y + (5)z = 160

Now we can solve for x:

9x + 6y + 5z = 160

x = (160 - 6y - 5z)/9

Similarly, we can solve for y and z:

y = (160 - 9x - 5z)/6

z = (160 - 9x - 6y)/5

Now we can substitute the desired amount of 20 oz into the equation and solve for x, y and z

Step-by-step explanation:

Answer:U: 1.98 V: 1.4 And also the other side, square root symbol: 1.4

Step-by-step explanation:

I hope this helps man, i havnt done this stuff in a while...

XY is the diameter because the diameter is the entire side to side while radius is from the middle to the side.

The diameter is the entire side to side while radius is from the middle to the side.

The diameter of a circle is represented by the letter d.

here O is the center of the circle

radius of the circle is OX and YO

diameter of the circle is 2×radius

then here diameter of the circle is XY

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The percentage of the tip that she leaves will be 20.02%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Mrs. Peterson had lunch at Lunchee's. She paid $12.99 for her meal. She left a tip of 2.60.

Then the percentage is given as,

P = [2.6 / 12.99] x 100

P = 0.2002 x 100

P = 20.02%

The percentage of the tip that she leaves will be 20.02%.

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Answer:

sometimes there are more, sometimes there are less

Step-by-step explanation:

for example 1+1 only requires 1 step

hope this helps

Answer:

STEP 1: The Right Problem to Solve

STEP 2: Analyse the Problem

STEP 3: Define the Problem

STEP 4: Develop Opportunities (Possible Solutions)

STEP 5: Select the Best Solution

STEP 6: Implement the Solution

STEP 7: Evaluate and Learn

Step-by-step explanation:

Hope It Helps!

Completing a square is a method for transforming a quadratic equation’s form so that its LHS becomes a perfect square, commonly known as vertex form. This is accomplished by rearranging the phrase.

X2 is x multiplied by itself, which is symbolized by and may be expressed as xx or x(x) as an algebraic term. 2 is an exponent in. It denotes that x has been multiplied by itself twice. x 2 = x .

heres the answer is, X squared is a helpful notation that we use in math. It can be used in different kinds of algebraic expressions. It simplifies our calculations and allows us to develop formulas to solve problems quicker!

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Answer:

Since, 6x -4 and 14 both are values of f(X)then,

6x-4=14

or,6x=14+4

or,X=18/6

:.X=3

*mark me brainliest

Answer: X=3 :)

Step-by-step explanation:

f(x)= 6x-4 and f(x)=14

6x-4=14

6x=4+14

6x=18

Divide both by 6

x=3

The length of rectangle :10 feet

               The width of rectangle :  4 feet

       Given

        perimeter of the rectangle :28 feet

       let  width of the rectangle be :x

         and  length  of the rectangle be :  6+x   (as per given condition)

      therefore  

                      perimeter = 2(length +width)

                               28 = 2(6+x+x)

                               28 = 2(6+2x)

                               28 = 12+4x

                               28-12 = 4x

                                16  = 4x

                                 x = 4

  as width of rectangle  is : 4

similarly  length : 6+x

                            6+4

                            :10

The dimensions of the rectangle are : length =10

                                                               width = 4

verification :

perimeter =2(l+w)

28 = 2(10+4)

28 = 28

What we can conclude by the given triangle about similarity is;

ΔPQR ∼ ΔPST

Similar triangles are defined as triangles that have the same shape, but their sizes may vary. Thus, if two triangles are similar, then it means that their corresponding angles are congruent and corresponding sides are in equal proportion.

Now, there are three types of similarity theorems for triangles namely;

Angle Angle(AA) Similarity

Side Angle Side(SAS) Similarity

Side Side Side(SSS) Similarity

We see that both triangles PQR and PST have equal angle R and angle T which are both 36 degrees. Thus, they are both similar by the AA Similarity theorem

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The formula for the area of a square is A = s², where A is the area of the square and s is the length of one of its sides.

To calculate the area of a square, multiply the length of one side by itself. For example, if the side of a square is 5 meters, the area of the square would be 25 square meters (5² = 25). If the side of a square is 8 feet, the area of the square would be 64 square feet (8² = 64). The area of a square is always equal to the length of one side multiplied by itself.

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Mina will receive $13.33 after converting her 18 Pounds GBP to Dollars USD

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. When a conversion is necessary, the appropriate conversion factor to an equal value must be used

To change 18GBP to USD at the current exchange rate of 1.35GBP to 1 USD

Divide the Amount being converted by the exchange rate

that is, 18GBP/1.35

=13.33USD

Hence, 13.33USD is the amount that Mina will receive after converting her 18 GBP

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The length of side m is, 5.08 inches.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In ΔMNO,

⇒ o = 8 inches, m ∠M = 28° and m ∠O = 48°.

Now, Let the length of side m = x

So, By sine rule, we get;

⇒ sin M / m = Sin O / o

Substitute all the values, we get;

⇒ sin28°/  x = sin 48° / 8

⇒ 0.47 / x  = 0.74 / 8

⇒ x = 0.47 × 8 / 0.74

⇒ x = 5.08 inches

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On solving the provided question we can say that when each teacher is matched with 30 students, t is not a function.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

When each teacher is matched with 30 students, t is not a function.

This is true since it demonstrates a one-to-many link.

Therefore, this is the case because it shows a many-to-one relationship and multiple weights can have the same cost.

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The nearest whole number to which the new height of the image is enlarged is 9cm.

By scaling, we can create a drawing of an object that corresponds to the object's true size. In geometry, scaling refers to either growing or reducing figures in order to preserve their fundamental shape. Similar figures are what we call scaled figures.

Given that the original size was in the ratio 4: 3.

When the image is enlarged the enlarged image will be in the similar ratio to the original size.

Hence, the ratio in which the enlarged image will be increased is 4x : 3x.

The new width is given as 12,

The value of 4x = 12

x = 3

Then the new height of the image is:

3 (3) = 9cm.

Hence, the new height of the image is 9cm.

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The solution of (x^2 +  6x - 16) is ( x+8 )( x−2 ).

Lets solve the equation (x^2 +  6x - 16) in order to find its solution:

The equation is ( x^2 + 6x − 16 )

Now factorizing it

= ( x^2 + 8x − 2x − 16)

Taking x common from the first two terms and -2 common from the last two terms:

= [x (x+8) −2 (x+8) ]

Now,

= [ (x+8) (x−2) ]

Therefore, it is shown that the solution of the equation "(x^2 +  6x - 16)" is (x+8)(x−2) which is obtained through factorization.

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All exponential functions pass through (0, 1)

We know that the exponential function f with base b is defined as:

f(x) = b^x

where b > 0 and b is not equal to 1

and x is any real number.

For x = 0,

f(0) = b^0

f(0) = 1

This means, the graph of function f(x) passes through (0, 1)

For example consider an exponential function f(x) = 2^x

For x = 0,

f(0) = 2^0

f(0) = 1

the graph of f(x) = 2^x passes through (0, 1)

so, the characteristics of the graphs of all exponential functions:

The graphs contain the point (0, 1).

The x-axis is an asymptote.

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Aira should must score a total of 179 combined in her next two quizzes in order to make the average of all the marks of the quizzes as 83.

Aira has got 76, 85, 81 and 77 marks in her 4 quizzes.

I have to give two more quizzes and the marks obtained in those two quizzes should be such that the average of all the quizzes should be 83.

We know that we can find the average of the data by taking the sum of all the given values and dividing that particular value by the number of data given to us.

Here in this case let assume that she obtained X marks in her next to test combined. Now this way total number of observation are 6.

Now, we can simply apply the formula to find the average of the data.

Average = (76 + 85 + 81 + 77 + X)/6

83 = (76 + 85 + 81 + 77 + X)/6

X = 179

So, Aira should obtain 179 marks in her next to quizzes in order to make the average of all the score equal to 83.

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The formula for a sector's area is: 1. A = (sector angle / 360 ) * (pi *r2)

2. A = (sector angle / (2*pi)) * (pi * r2) 3. A = (fraction of the circle) * (pi * r2)

The ratio used to find the area of the sector is that of how to know what fraction of the circle is the sector.

Ratio = (θ/360°)

θ is the angle subtended at the center of the circle by the arc, measured in degrees.

For this question,

θ = 60°

Ratio = (θ/360°) = (60°/360°) = (1/6)

Area of a circle is given as

Area of a circle = πr²

where

π = pi

r = radius of the circle = 8

Area of the circle = πr²

Area of the circle = π (8²) = 64π square units

Area of the sector is given as

Area of the sector = (Ratio) × (Area of the circle)

Ratio = (1/6)

Area of the circle = 64π square units

Area of the sector = (Ratio) × (Area of the circle)

Area of the sector = (1/6) × (64π) = (64π/6) = (32π/3) square units

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