The row-reduced form of a system of three linear equations in three variables is given by this matrix. How many solutions does the system have?

Answer:

  x + y = -2

Step-by-step explanation:

When you are given the equation of a line in standard form (or close to it, as here), you can make the equation for a perpendicular line through a given point by ...

Here, if we make the left side of the equation be ...

  x + y =

we have done the first part of the above recipe. For the second part, we put the point values in for the variables:

  x + y = (-1) + (-1) = -2

The equation of the perpendicular line is ...

  x + y = -2

Answer:

A

Step-by-step explanation:

Write each parabola in standard form.

f(x) = x²

f(x) = (x − 0)² + 0

For p(x), complete the square.

p(x) = -50 + 14x − x²

p(x) = -(x² − 14x + 50)

p(x) = -(x² − 14x + 49 + 1)

p(x) = -(x² − 14x + 49) − 1

p(x) = -(x − 7)² − 1

The transformation from f(x) to p(x) includes a reflection about the x-axis, a shift right 7 units, and a shift down 1 unit.

The answer is A.

Answer:

Total = 14,000 * 1 + (.06 / 365) ^365*5

Total = 14,000 * 1.0.000164383561643836^1,825

Total = 14,000 * 1.3498255274

Total = 18,897.56

Step-by-step explanation:

Answer:

The correct answer is option B.  65

Step-by-step explanation:

To find the measure of <VYX

Central angle of arc VW = 44°

Therefore m<VXY = 44/2 = 22°

And central angle of arc XZ = 86° therefore <XVY = 86/2 = 43

To find the mesure of <XYZ

m<XYZ = m<VXY + m<XVY

  = 22 + 43

 = 65°

Therefore the correct answer is option B. 65°

1. For the system of linear equations to have an infinite number of solutions, the two lines must cross over an infinite number of times, ie. they would be the same line.

Now, if they are the same line and we were to write out both equations in the form y = mx + c, this would mean that the m value (the gradient) and the c value (the y-intercept) would be the same. Thus, the first step is to write out both equations in the form y = mx + c.

a) Equation 1:

3x - 9y = -6

3x = -6 + 9y (Add 9y to both sides)

3x + 6 = 9y (Add 6 to both sides)

(1/3)x + 2/3 = y (Divide both sides by 9)

Thus, the first equation may be written as y = (1/3)x + 2/3

b) Equation 2:

(1/2)x - (3/2)y = c

(1/2)x = c + (3/2)y (Add (3/2)y to both sides)

(1/2)x - c = (3/2)y (Subtract c from both sides)

(1/3)x - (2/3)c = y (Multiply both sides by 2/3)

Thus, the second equation may be written as y = (1/3)x - (2/3)c.

2. Now that we have both equations in the form y = mx + c, we can look at their gradients and y-intercepts:

Equation 1: gradient = 1/3, y-intercept = 2/3

Equation 2: gradient = 1/3, y-intercept = -(2/3)c

As we can see above, the gradients of the two lines are the same, however for them to be the same line their y-intercepts must also be equal. Thus, we must equate the two y-intercepts to find c:

2/3 = -(2/3)c

1 = -c (Multiply both sides by 3/2)

-1 = c (Multiply both sides by -1)

Thus, if the system of linear equations has infinitely many solutions, and c is a constant, the value of c is -1 (answer D).

The value of 'c' for the given system of the linear equations with infinitely many solutions is - 1.

"A linear equation is an equation in which the highest power of the variable is always 1."

Given system of linear equations are

1. [tex]3x - 9y=-6[/tex]

⇒ [tex]x - 3y = - 2[/tex]

Therefore, [tex]a_{1} = 1, b_{1} = -3, c_{1} = -2[/tex]

2. [tex]\frac{x}{2}-\frac{3y}{2} =c[/tex]

⇒ [tex]x - 3y = 2c[/tex]

Therefore,    [tex]a_{2} = 1, b_{2} = -3, c_{2} = 2c[/tex]

For the system of the linear equations with infinitely many solutions,

[tex]2c = -2[/tex]

⇒ [tex]c = -1[/tex]

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Verbal expression of w^2 = 32w is:

W to the second power equals 32 with a variable of w.

To the second power means exponent of 2.

Variable is an unknown number represented by a letter. In this case, the variable is "w".

Hope this helps!

- Melanie

Answer:

Step-by-step explanation:

The square of variable w is equal to 32 times that variable.

Answer:

-6/5

Step-by-step explanation:

Slope = (y2 - y1)/(x2 - x1)

Plug in

Slope = (4 + 2)/(-2 - 3)

Slope = -6/5

Answer:

m = -6 / 5

Step-by-step explanation:

If you are given 2 points (x1, y1) and (x2,y2)

the slope is simply

m = (y2-y1) / (x2-x1)

m = (-2 - 4) / [3 - (-2)]

m = -6 / 5

Answer:

  not really

Step-by-step explanation:

The number of friends (x) is expected to be an integer. 6.5 friends does not really make sense.

_____

There are all kinds of ways this might make sense, but none of them are supported by the information given in the problem statement.

No, the solution (6.5,$ 95.25) do not make a sense.

Since, the number of people going for a movie can't be in decimals.

The function h(x) represents the amount of money spent where x is the number of friends at the movies.

The domain of such a function has to be whole numbers.

Because the number of people that go for a movie must exist as a whole they can't exist in decimals.

( i.e. either no one will go.

1 will go.

2 friends will go and so  on)

i.e. the domain is the set of all non-negative integers.

Answer:

303.66 in²

Step-by-step explanation:

The area (A) of a trapezoid is

A = [tex]\frac{1}{2}[/tex] h (a + b)

where h is the perpendicular height and a, b the parallel bases

here h = 12.6, a = 19 and b = 29.2, so

A = 0.5 × 12.6 × (19 + 29.2)

  = 0.5 × 12.6 × 48.2 = 303.66 in²

Answer: THIRD OPTION.

Step-by-step explanation:

The area of a trapezoid can be calculated with this formula:

[tex]A=\frac{h}{2}(B+b)[/tex]

Where "h" is the height, "B" is the long base and "b" is the short base.

You can identify that:

[tex]h=12.6in\\B=29.2in\\b=19in[/tex]

Therefore, you need to substitute these values into the formula  [tex]A=\frac{h}{2}(B+b)[/tex] to calculate the area of that trapezoid. This is:

 [tex]A=\frac{12.6in}{2}(29.2in+19in)\\\\A=303.66in^2[/tex]

This matches with the third option.

For this case we must find the zeros of the following function:

[tex]f (x) = (x-7) (x-3) (x-2)[/tex]

If we equate each term to 0 and we clear the variable "x", we will find the values that make the function equal to zero. So:

Thus, the zeros of the function are:

7,3,2

Answer:

Option C

The zeros of the function f(x) = (x - 7)(x - 3)(x - 2) are 7, 3, 2. The correct option is the third option 7, 3, 2

From the question,

We are to determine the zeros of the given function

The given function is

f(x) = (x - 7)(x - 3)(x - 2)

To determine the zeros of this function, we will set f(x) = 0

That is ,

f(x) = (x - 7)(x - 3)(x - 2)  becomes

0 = (x - 7)(x - 3)(x - 2)

∴ (x - 7)(x - 3)(x - 2) = 0

Then,

We can write that

x -7 = 0 OR x - 3 = 0 OR x - 2 = 0

∴ x = 7    OR    x = 3    OR   x = 2

Hence, the zeros of the function f(x) = (x - 7)(x - 3)(x - 2) are 7, 3, 2. The correct option is the third option 7, 3, 2

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Answer:

  B.  that one thing is equal to another.

Step-by-step explanation:

An equation has a "left side", an "equal sign", and a "right side." It shows the left side is equal to the right side (one thing is equal to another).

___

An equation may or may not involve variables and unknown quantities.

The answer is B.

I tried putting 9 for a and 7 for B. cos(9-7)+cos(9+7) = 2cos(9)cos(7)

[tex]\bf \textit{Product to Sum Identities} \\\\ cos(\alpha)cos(\beta)=\cfrac{1}{2}\left[\cfrac{}{}cos(\alpha-\beta)\quad +\quad cos(\alpha+\beta)\right] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ cos(a)cos(B)=\cfrac{1}{2}\left[\cfrac{}{}cos(a-B)+cos(a-B) \right] \\\\\\ 2cos(a)cos(B)=cos(a-B)+cos(a-B)[/tex]

The answer is:

The range of the function is:

Range: y>2

or

Range: (2,∞+)

To calculate the range of the following function (exponential function) we need to perform the following steps:

First: Find the value of "x"

So, finding "x" we have:

[tex]y=2(5^{x}-1)\\\frac{y}{2}=5^{x}-1\\\\\frac{y}{2}-1=5^{x}\\\\Log_{5}(\frac{y}{2}-1)=Log_5(5^{x})\\\\x=Log_{5}(\frac{y}{2}-1)[/tex]

Second: Interpret the restriction of the function:

Since we are working with logarithms, we know that the only restriction that we found is that the logarithmic functions exist only from 0 to the possitive infinite without considering the number 1.

So, we can see that if the variable "x" is a real number, "y" must be greater than 2 because if it's equal to 2 the expression inside the logarithm will tend to 0, and since the logarithm of 0 does not exist in the real numbers, the variable "x" would not be equal to a real number.

Hence, the range of the function is:

Range: y>2

or

Range: (2,∞+)

Note: I have attached a picture (the graph of the function) for better understanding.

Have a nice day!

Answer:

1.25(w)-12.50=C

Answer:

HL

Step-by-step explanation:

HL (Hypotension-Leg) postulate of congruence : In two right triangles if the hypotenuses are equal and any two corresponding legs are equal in both triangles then the triangles are congruent.

In the given right triangles MAE and TON,

AM = OT,

EM = NT,

Thus, by the HL postulate,

Δ MAE ≅ Δ TON

First option is correct.

Answer:

(x-y)(y-x)

Step-by-step explanation:

because x-y=y-x

Answer:

  width = 13 ft; area = 169 ft^2

Step-by-step explanation:

The equation for the area can be factored as ...

  A = x(26 -x)

This has zeros at x=0 and x=26. The vertex of this downward-opening parabola will be halfway between those, at x=13. Then the area for a width of 13 feet is ...

  A = 13(26 -13) = 13^2 = 169 . . . . ft^2

The maximum area is 169 ft^2, when the width is 13 ft.

_____

You will note that these dimensions make the pen be a square. It can be useful to remember that a square is the rectangle with the largest area for a given perimeter length.

The width that gives the maximum area for the given fencing is 13 feet, and the maximum area is 169 square feet (option B).

The formula given is a quadratic function where x is the width and A is the area. In a quadratic function, the maximum or minimum value occurs at the vertex. The x-coordinate of the vertex can be found using the formula -b/2a where a and b are the coefficients of the quadratic function. Here, a is -1 and b is 26, therefore the x-coordinate of the vertex is -26/-2*-1 = 13. This means that a width of 13 ft will give the maximum area. To find the maximum area, we substitute x = 13 into the function: A = 26*13 - 13^2 = 169 ft2. So, the width that will give the maximum area is 13 feet and the maximum area is 169 square feet.

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Answer:

13.75

Step-by-step explanation:

3b + d = 8.75

2b + 2d = 7.50

(3b + d = 8.75) times 2

(2b + 2d = 7.50) times -3

6b + 2d = 17.5

-6b + (-6d) = -22.5

the b's cancel out, 2d - 6d = -4d and 17.5 - 22.5 = -5

-4d = -5 Divide it and d = 1.25

then plug in 1.25 for d.

2b + 2(1.25) = 7.50

2b + 2.5 = 7.50

2b = 5

b= 2.5

3(2.5) + 1.25 = 8.75 ? Yes.

2(2.5) + 2(1.25) = 7.50 ? Yes.

4(2.5) + 3(1.25) = 13.75.

Answer:

The correct option is:

a) seasons; "This is the

A semicolon is most commonly used to link (in a single sentence) two independent clauses that are closely related in thought.When a semicolon is used to join two or more ideas (parts) in a sentence, those ideas are then given equal position or rank.

Step-by-step explanation:

Answer:

A.  seasons: "This is the

Step-by-step explanation:

Answer:

6 movies

Step-by-step explanation:  

:Service A

1. $37.92 +&2.18=$40.1

2. $41.1+$2.18=$42.28

3....

4....

5....

6. $48.82+$2.18=$51

Service B

1. $33.25+free movie=$33.25

2. $33.25+$3.55=$36.8

3....

4....

5....

6. $47.45+$3.55=$51

answer is B)

x= 85, y = 100

Answer:

D, x=100 and y=85

Step-by-step explanation:

Hello

In every convex polygon, the sum of the measure of the interior angles is given by the expression SUM = 180 ° (n - 2) where n is the number of sides

the polygon has our sides MN, NO,OP  and PM, the sum of the interior angles is

[tex]sum=180(4-2)\\sum=360 degrees[/tex]

[tex]360= x +y +80+95\\360-80-95= x+y\\x+y=185[/tex]

looking at the graph it is observed that angle  x° is obtuse (more than 90° but less than 180°.) and the angle y is acute (The acute angle is the small angle which is less than 90°)

so

[tex]x>y[/tex]

[tex]x+y=185[/tex]

the response option that meets these two conditions is D, x=100 and y=85

Answer:

No, he did not score 3,

Because, 2 times of 5 is 10 and the sum of 10 and 5 is 15.

Step-by-step explanation:

Let x be the score of Skylar,

Since, Wyatt scored 2 times as many goals as Skylar.

So, Wyatt's score = 2x

Thus, total scores = x + 2x = 3x

According to the question,

3x = 15

x = 5

Hence, Skyler have scored 5 goals.

Because, 2 times of 5 is 10 and the sum of 10 and 5 is 15.

Final answer:

Skylar could have scored 3 goals because, based on the information provided, they scored 5 goals after solving the equation that evaluates the total goals scored by both Skylar and Wyatt.

Explanation:

To determine if Skylar could have scored 3 goals, given that Wyatt scored 2 times as many goals as Skylar and together they scored 15 goals, we can set up a simple algebraic equation. Let's denote the number of goals Skylar scored as S, which means that Wyatt scored 2S goals.

The total number of goals is the sum of the goals scored by both Skylar and Wyatt, which is S + 2S = 15. This simplifies to 3S = 15. By dividing both sides of the equation by 3, we get S = 5.

Therefore, Skylar could have scored 3 goals because the calculations show that Skylar scored 5 goals.

Answer:

  A.  y + 1 = -2(x – 5)

Step-by-step explanation:

For a line with slope m through point (h, k), the equation is ...

  y -k = m(x -h)

Fill in your values of m=-2, h=5, k=-1 and you have ...

  y -(-1) = -2(x -5)

  y +1 = -2(x -5) . . . . . . simplify. Matches selection A.

ANSWER

[tex]S.A = 125 {in}^{2} [/tex]

EXPLANATION

The total surface area of a square pyramid is the area of the 4 triangular faces plus the area of the square base.

This is given by the formula!

[tex]S.A = 4 \times \frac{1}{2} bh + {l}^{2} [/tex]

From the diagram, the base is 5 inches and the height is 10 inches.

We substitute the values to get:

[tex]S.A = 4 \times \frac{1}{2} \times 5 \times 10 + {5}^{2} [/tex]

This simplifies to;

[tex]S.A = 100 + 25[/tex]

[tex]S.A = 125 {in}^{2} [/tex]

The lower end of the digestive tract that gathers and expels solid waste from the body is called the rectum. The process involves the colon, where digestion occurs, water is reabsorbed, and waste is turned into feces, which is then eliminated through the anus.

The thick, lower end of the digestive tract where solid waste is gathered and leaves the body is called the rectum. After digested food passes through the small intestine, it enters the large intestine, or colon, where it undergoes further digestion and water reabsorption. The colon is home to a diverse microbiota that aids in digestion. The waste material, now known as feces, is then moved to the rectum. The rectum stores the feces until it triggers neural signals that lead to the urge to eliminate this waste through the anus.

Answer: B. 548

Step-by-step explanation:

You know that the exponential regression equation [tex]y = 14.08* 2.08^x[/tex] models the number of fish in a lake.

You know that the variable "x" represents the year. Therefore, ir order to predict the number of fish in year 5, you need to substitute [tex]x=5[/tex] into the given exponential regression equation.

Then, you get:

[tex]y = 14.08* 2.08^x\\\\y = 14.08* 2.08^5\\\\y=548.17[/tex]

Rounded to the nearest whole number:

[tex]y=548[/tex]

Answer:

The correct answer option is C. 548.

Step-by-step explanation:

We are given that the number of fish in a lake can be modeled by the following exponential regression equation:

[tex] y = 1 4 . 0 8 \times 2 . 0 8 ^ x [/tex]

where [tex]x[/tex] represents the number of year.

We are to determine whether which of the given answer options best predict the number of fish in year 5.

[tex] y = 1 4 . 0 8 \times 2.08^5[/tex]

[tex]y = 548.17[/tex] ≈ 548

Answer:

Step-by-step explanation:

The distributive property lets you multiply each term inside parentheses by a factor outside parentheses. Here, we've gone from 4(x -1) to 4x -4.

The commutative property lets you change the order of elements of a sum or product. Here, we've gone from 3 + ( ) to ( ) + 3.

The associative property lets you move the parentheses from one group of elements of a sum or product to a different group of elements of the same sum or product. Here, we moved the parentheses from the first two terms to the last two terms of the sum.

_____

Comment on these properties in relation to the Order of Operations

The order of operations for evaluating an expression virtually ignores all of these properties, with the possible exception of the distributive property.

For evaluation of numerical expressions, any sum inside parentheses is evaluated to a single number before the multiplication implied by the parentheses is done. Hence the distributive property is not needed. (The distributive property must be used to remove parentheses when literal or mixed expressions are being evaluated.)

Likewise, the associative and commutative properties are ignored, because operations of addition or multiplication are always carried out left-to-right according to the order of operations. In actual practice, the associative and commutative properties can be used to simplify the evaluation of expressions, provided they are used properly and the meaning of the expression is not altered.

Answer:

64 people/m^2

Step-by-step explanation:

The population density can be found by diving the number of people by the amount of area

I assume that the answer should be in metre squares or the area should be 1.95 million km^2

124000000/(1.95*1000000)

=63.5897...

=64 people/m^2

Answer:

64M people/km^2

Step-by-step explanation:

To calculate the density of population you just have to divide the population by the area of the country or region that you are calculation, in this case it wouldbe like this:

Density of population= [tex]\frac{124 M}{1.95 km^{2}  }[/tex]

D= [tex]\frac{124 M}{1.95 km^{2}  }[/tex]= 63,58 M[tex]\frac{M}{km^{2} }[/tex]

So rounded to the neares whoel number would be 64 M people per squared kilometer.

Answer: x=243

Step-by-step explanation:

Answer:$2,000

Step-by-step explanation: