Write and solve an equation to find the value of x.

The augmented matrix, however, is a two-by-four matrix because it also contains the constants.

The augmented matrix will always include one additional column for every additional variable, and the same number of rows as there are equations. An easier technique to write a set of linear equations is to utilize enhanced matrices.

In an augmented matrix, two sides of the matrix are separated by a vertical line that serves as a representation of a succession of equal signs. The collection of linear equations, for instance, would be represented by the matrix. There is only ever one pivot in a column.

For (c): Three rows and four columns make up the augmented matrix of this system. As a result, it only has three pivot points at most. Thus, a pivot column cannot be represented by a single variable.

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Answer:

What is the size of the augmented matrix for the linear system?

B) 2x3

Identify the values for the elements in the augmented matrix:

a11 =  3

a12 =  7

a13 =  20

a21 =  1

a22 =  -4

a23 = 9

Step-by-step explanation:

Answer:

2x=16

/2    /2

x=8

Step-by-step explanation:

just need to isolate the x, by dividing by two on both sides.

hope this helps :)

Answer:

x=8

Step-by-step explanation:

2x=16

Isolate the variable by diving by 2 on both sides

2x=16

÷2 ÷2

so, x=8

The polynomials which, when added to the polynomial 3x²+3x-1, is equivalent to the following expressions: 1, 2x²-3, and x+5 include the following below:

This is referred to as algebraic expressions that consist of variables and coefficients.

For 1; it is calculated as:

3x²+3x-1 + P = 1.

P = 2 - 3x² -3x.

For 2x²-3, it is calculated as:

3x²+3x-1 + P = 2x²-3

P = -2 -x² -3x

For x +5; it is calculated as:

3x²+3x-1 + P = x +5

P = 6 -2x -3x².

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The full question is:

Find a polynomial which, when added to the polynomial 3x^2+3x-1, is equivalent to the following expressions: 1, 2x^2-3, and x+5

On solving the provided question, we can say that the mean that 6 tests including the last test brian took.

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate: Divide by how many digits there are after adding up all the digits. the total divided by the count.

(91n + 98) / (n + 1)  =  92

    91n + 98  =  92(n + 1)

 91n + 98  =  92n + 92

 98  =  n + 92

6  =  n

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The value of a and b are respectively 15 and 17 respectively.

What are trigonometry ratios?

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Given that csc θ = 17/8 and cos θ = a/b.

The reciprocal of sin θ is csc θ.

Therefore,

1/sinθ = 17/8

or, sin θ = 8 /17

Applying the trigonometry identity cos²θ = 1- sin²θ

cos²θ = 1- (8/17)²

cos²θ = 1- 64/289

cos²θ = 225/289

cos θ = 15/17

The value of a is 15 and the value of b is 17.

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Answer:

Step-by-step explanation:

[tex]y=x^2+6x+10\\\\y=x^2+6x+9-9+10\\\\\bold{y=(x+3)^2+1}[/tex]

a = 1 > 0  ← it means the parabla opens up, so, the vertex is minimum

The vertex form is  y = a(x - h)² + k, where (h, k) is the vertex

So, from  y = (x + 3)² + 1   the vertex is:  (-3, 1)

Answer:

1 and 2 is adjacent. 1 and 3 are vertical. 3 and 4 are adjacent. 2 and 4 are vertical angles.

Angles ∠1 and ∠2 as well as angles ∠3 and ∠4 are linear and supplementary angles. And angles ∠2 and ∠4 as well as ∠1 and ∠3 are vertically opposite angles.

Angle is the space between the line or the surface that meets.  And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.

Angles ∠1 and ∠2 are linear and supplementary angles.

Angles ∠1 and ∠3 are vertically opposite angles.

Angles ∠3 and ∠4 are linear and supplementary angles.

Angles ∠2 and ∠4 are vertically opposite angles.

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Answer:c/π=d

Step-by-step explanation: the d and π was multiply with the d and if we want separate with it, we need to use the opposite way to get it.

x+y=10 and ax+0.50y=25 are the system of equations to compute the cost of each mechanical pencil.

Two or more expressions with an Equal sign is called as Equation.

Given that Mr. Spears was purchasing supplies for his math classroom.

He had $25 to spend.

Mechanical pencils and erasers come in bundles of 10

Let x represents the Mechanical pencils

y represents the erasers

x+y=10

y=10-x

Each eraser costs $0.50

ax+0.50y=25

a is the cost of the each mechanical pencil.

Hence, x+y=10 and ax+0.50y=25 are the system of equations to compute the cost of each mechanical pencil.

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The algebraic expression for the sequence 1, 10, 19, is given as a(n) = 1 + (n-1) 9.

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.

For the given sequence the common difference between two consecutive terms is 19 - 10 = 9.

The general form of the nth term of an arithmetic sequence is given as:

a(n) = a + (n-1) d

Since, the value of a = 1 and the common difference d =9, the resulting expression is:

a(n) = 1 + (n - 1) 9

Hence, the algebraic expression for the given sequence is a(n) = 1 + (n - 1) 9.

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Answer:

4.16 in^3

Step-by-step explanation:

Given data

Volume of sphere= 4/3πr^3

Radius=  1 inch radius

Substitute

Volume of sphere= 4/3*3.14*1^3

Volume of sphere= 4/3*3.14*1

Volume of sphere= 4*1.04

Volume of sphere= 4.16 in^3

Answer: 1/4

Step-by-step explanation:

Method 1

this method only works when there is a visual graph, but you can oick 2 points. then go to the point farthest to the left ide of the graph. then count up to be on the same y coordinate as the other point. then count over to be on the same x point, hence 1/4 (up 1 over 4)

Method 2

You can also pick 2 points, and put them into this formula to find slope ([tex]\frac{x2-x1}{y2-y1} }[/tex] then you plug in so the point farthest left would be x1 and y1 and the other point would be y1 and y2 so when you plug in and solve you get 1/4

Answer:

Step-by-step explanation:

rise/run

=1/4

Answer:

x= 55°

y=70°

z= 35°

Step-by-step explanation:

.................

Answer:

x = 45°

y = 70°

z = 25°

Hope this helps!

Answer:

It's A

Step-by-step explanation:

The length of XY, with the area of the rectangular surface of the prism 720 sq.cm, XX' 20 cm and XY : XZ: YZ = 5:3:4, is 12 cm.

Area of the rectangular surface of the prism = 720 sq. cm

XX' = 20 cm

XY : XZ: YZ = 5:3:4

As we know, area of prism = 3 × area of rectangle

⇒720 = 3 × area of rectangle

⇒area of rectangle = 720/3

⇒XY × XX' = 240

⇒XY × 20 = 240

⇒XY = 240/20

⇒XY = 12 cm

Thus, the length of the XY is 12 cm.

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The algebraic solutions are x < -5 and x > 3.

The graph is given below.

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,

x² + 2x > 15

x² + 2x - 15 > 0

x² + (5 - 3)x - 15 > 0

x² + 5x - 3x - 15 > 0

x(x + 5) - 3(x + 5) > 0

(x - 3)(x + 5) > 0

x + 5 > 0 and x - 3 > 0

x < -5 and x > 3

The graph is given below.

Thus,

x < -5 and x > 3 is the solution.

The graph is given below.

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Answer:

x = 6

Step-by-step explanation:

The three angles form a straight line, which is 180 degrees

5x+ (x+54) +90= 180

Combine like terms

6x+144 = 180

Subtract 144 from each side

6x+144-144 =180-144

6x =36

Divide each side by 6

6x/6 = 36/6

x = 6

The amount that Cheryl left with is $ 1.9 or 1 dollar and 90 cents.

1. READ and reread the problem first

2. DRAW an image to illustrate the information. Ask your self Can I infer anything from this information during this step? What could I doodle? Which model will best convey the information? What inferences may I draw from the illustration?

3. WRITE the drawings as a basis for your conclusions. This can be expressed as a mathematical expression, an equation, or a statement.

Given that

Cheryl bought a sandwich for 5 1/2 dollars and a drink for $2. 60  

Here 5 1/2 = 11/2 = 5.5 dollars

Then the total cost of the sandwich and drink = $ 5.5 + $ 2.60 = $ 8.1  

Given that Cheryl gave $ 10

The amount that Cheryl left with = $ 10 - $ 8.1 = $ 1.9

Here is $ 1.9 = 1 dollar and 90 cents

Therefore,

The amount that Cheryl left with is $ 1.9 or 1 dollar and 90 cents.

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Answer:

-131

Step-by-step explanation:

2×2×3×4-15×2×2×3+-1

48-179

=-131

The equation of the line in the attached graph in slope intercept form is written as

The slope, m of the linear function is calculated using the points on the graph (1, -4) and  (2, -10)

m = (y₀ - y₁) / (x₀ - x₁)

plugging in the values and evaluating

m = (-10 + 4) / (2 - 1)

m = (-6) / (1)

m = -6

equation passing through point (2, -10), using the point slope formula

(y - y₁) = m (x - x₁)

y - (-10) = -6(x - 2)

y + 10 = -6x + 12

rearranging the equation

y = -6x + 12 - 10

y = -6x + 2

The equation of the line in slope intercept form is written as y = -6x + 2

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Answer:

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

hope it helps..

have a great day!!

Answer:

[tex]f(x) = 0.5(x+3)(x-1)[/tex]

Step-by-step explanation:

GIVEN :-

A quadratic function is represented by the graph in which :-

TO FIND :-

GENERAL CONCEPT USED IN THIS QUESTION :-

A quadratic function has 2 forms :-

SOLUTION :-

The quadratic function in the graph intersects x-axis at two points (-3 , 0) & (1 , 0). But there are infinite parabolas which also intersect the same two points. And those parabolas have their unique quadratic function.

To find the unique quadratic function , you need to use three points on the

curve so that you can form 3 equations & solve them.

Using the General form of quadratic function , substitute the known values for x & y.

Let the three points be -

Substitute (-3 , 0) in general form of function -

[tex]0 = a(-3)^2 + b(-3) + c[/tex]

[tex]=> 9a-3b+c = 0[/tex]  (eqn.1)

Substitute (1 , 0) in general form of function -

[tex]0 = a(1)^2 + b(1) + c[/tex]

[tex]=> a + b +c =0[/tex]  (eqn.2)

Substitute (0 , -1.5) in general form of function -

[tex]-1.5 = a(0)^2 + b(0) + c[/tex]

[tex]=> c = -1.5[/tex]

Substitute c = -1.5 in -

1) eqn.1 → [tex]9a - 3b - 1.5 = 0[/tex]

[tex]=> 9a - 3b = 1.5[/tex]  

[tex]=> 3(3a-b) = 1.5[/tex]

[tex]=> 3a-b = 0.5[/tex]  (eqn.4)

2) eqn.2 → [tex]a+b-1.5=0[/tex]

[tex]=> a+b=1.5[/tex] (eqn.5)

Add eqn.4 & eqn.5 to get the value of 'a'.

[tex](3a-b)+(a+b) = 0.5+1.5[/tex]

[tex]=> 4a = 2[/tex]

[tex]=> a = \frac{2}{4} = \frac{1}{2} = 0.5[/tex]

Substitute a = 0.5 in eqn.5 -

[tex]0.5 + b = 1.5[/tex]

[tex]=> b = 1.5 - 0.5 = 1[/tex]

Now, rewrite the function in general form by putting the values of 'a' , 'b' & 'c'.

[tex]f(x) = (0.5)x^2 + (1)x - 1.5[/tex]

[tex]=> f(x) = 0.5(x^2 + 2x - 3)[/tex]

Factorise the quadratic polynomial.

[tex]=> f(x) = 0.5(x^2 + 3x - x - 3)[/tex]

[tex]=> f(x) = 0.5[x(x+3)-1(x+3)][/tex]

∴  [tex]f(x) = 0.5(x+3)(x-1)[/tex]

Another way to find the function is by taking any point on the curve & using the vertex of the parabola ; substitute the known values for x , y , h & k in  the Standard form of the function.

Let that point on the curve be (-3 , 0)

Vertex = (-1 , -2)

Substitute the values of x , y , h & k in Standard form of function.

[tex]0 = a[-3 - (-1)]^2 + (-2)[/tex]

[tex]=> 0 = 4a-2[/tex]

[tex]=> 4a = 2[/tex]

[tex]=> a = \frac{2}{4} = 0.5[/tex]

Now rewrite the Standard form of the function by putting the values of h , k & a.

[tex]f(x) = 0.5(x+1)^2-2[/tex]

Expand it.

[tex]=> f(x) = 0.5(x^2+2x+1)-2[/tex]

[tex]=> f(x) = 0.5x^2+x+0.5-2[/tex]

[tex]=>f(x) = 0.5x^2 + x- 1.5[/tex]

[tex]=>f(x) = 0.5(x^2 + 2x - 3)[/tex]

Factorising it will give the final answer.

∴  [tex]f(x) = 0.5(x+3)(x-1)[/tex]

Answer:

A. parallel

Step-by-step explanation:

when the slopes are the same it's parallel

when slopes are multiplied and they equal -1 it's perpendicular

The inverse of the logarithmic function f x log9x is f-1(x)=9^x.

The inverse of a logarithmic function is the exponential function. To find the inverse of the logarithmic function f x log9x, we can use the following equation: f-1(x)=9^x. This equation states that the inverse of the logarithmic function f x log9x is the exponential function f-1(x)=9^x.

The inverse of the logarithmic function f x log9x is f-1(x)=9^x, which is the exponential function.This means that for any value of x, the inverse of the logarithmic function f x log9x is equal to 9 raised to the power of x. For example, if x=2, then the inverse of the logarithmic function f x log9x is 9^2, or 81. Similarly, if x=3, then the inverse of the logarithmic function f x log9x is 9^3, or 729. In general, the inverse of the logarithmic function f x log9x is 9 raised to the power of x, for any value of x.

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Answer: f –1(x) = 9x

Step-by-step explanation:

Answer:

The third from the top does not belong with the others.

Step-by-step explanation:

With the exception of the 3rd quotient, the expressions all involve powers of the same base.  There is an exponent property that can be used in such a situation:

[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]

but the base, a, must be the same in both parts of the quotient!

Answer:

just ask your teacher

Step-by-step explanation:

maybe she can help lol

(a) Since cosθ = 7/12 and sinθ < 0, we can find the other four trigonometric functions as follows:

sinθ = √(1 - cos²θ) = √(1 - (7/12)²) = √(1 - 49/144) = -√(95/144)

tanθ = sinθ / cosθ = (-√(95/144)) / (7/12) = -4√(5/18)

cotθ = 1 / tanθ = -1 / (-4√(5/18)) = 1/(4√(5/18))

secθ = 1 / cosθ = 1 / (7/12) = 12/7

cscθ = 1 / sinθ = -1 / (-√(95/144)) = √(95/144)

(b) Since tanθ = 4/3 and θ is in Quadrant III, we can find the other five trigonometric functions as follows:

cosθ = √(1 / (tan²θ + 1)) = √(1 / (16/9 + 1)) = √(9 / 25) = 3/5

sinθ = cosθ * tanθ = (3/5) * (4/3) = 4/5

cotθ = 1 / tanθ = 1 / (4/3) = 3/4

secθ = 1 / cosθ = 1 / (3/5) = 5/3

cscθ = 1 / sinθ = 1 / (4/5) = 5/4

Trigonometric functions are a set of functions that relate the angles of a right triangle to the ratios of the sides of the triangle. The six most commonly used trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

The sine function, represented by sin, gives the ratio of the side opposite the angle to the hypotenuse. The cosine function, represented by cos, gives the ratio of the adjacent side to the hypotenuse. The tangent function, represented by tan, gives the ratio of the opposite side to the adjacent side.

The cotangent function, represented by cot, gives the ratio of the adjacent side to the opposite side. The secant function, represented by sec, gives the ratio of the hypotenuse to the adjacent side, and the cosecant function, represented by csc, gives the ratio of the hypotenuse to the opposite side.

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There is one way to implement a function in Python that takes in an array of integers and returns the smallest positive integer that does not occur in the array.

def smallest_missing_positive(a):

   #Create a set to store the unique elements in the array

   unique_set = set(a)

   #Iterate through the positive integers starting from 1

   for i in range(1, len(a) + 2):

       #If the current integer is not in the set, return it

       if i not in unique_set:

           return i

This function first converts the input array into a set, which removes any duplicate elements. It then iterates through the positive integers starting from 1 up to the length of the array plus 2. For each integer, it checks whether it is in the set of unique elements from the input array. If it is not, the function returns that integer as it is the smallest positive integer that does not occur in the array.

For example, when the function is called with the input array [1, 3, 6, 4, 1, 2], it will return 5 as it is the first missing positive number.

You can also use a set and difference() method of set to check the missing elements from 1 to maximum element of array+1 and find the missing first one, this method is more efficient than the above one when the array is large.

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