Identify m∠MNP. PLEASE HELP!!!!

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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Answer:

B.

Step-by-step explanation:

First thing to determine is how this parabola opens.  Up or down? Or left or right?  

*We see that the axis of symmetry is a line parallel to the y-axis; therefore, the axis of symmetry is an x =    line, making this an up or down parabola.  Now we need to determine how everything else all fits in.

The standard form of this type of parabola is

[tex]4p(y-k)=-(x-h)^2[/tex]

where p is the distance between the vertex and the focus.  If the vertex has a y coordinate of 3, and the focus has a y coordinate of -3, the vertical distance between those 2 numbers is 6.  Therefore, p = 6.  Filling in then:

[tex]4(6)(y-3)=-(x-4)^2[/tex]

and [tex]24(y-3)=-(x-4)^2[/tex]

Dividing both sides by 24 gives you what you are looking for:

[tex]y-3=-\frac{1}{24}(x-4)^2[/tex]

The equation of the parabola is:

⇒ y - 3 = -(1/24)(x - 4)²

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line, which is known as the directrix.

We can use the standard form of the equation of a parabola with vertex (h, k) and axis of symmetry parallel to the y-axis, which is given by:

(x - h)² = 4p(y - k)

where (h, k) is the vertex and p is the distance between the vertex and the focus.

In this case, the vertex is (4, 3) and the focus is (4, -3).

Therefore, We get;

p = 3 - (-3)

p = 6.

Substituting the values of h, k, and p, we get:

(x - 4)² = 4(6)(y - 3)

Simplifying, we get:

(x - 4)² = 24(y - 3)

Now, we can simplify the equation to match it with the given options:

(x - 4)² = 24y - 72

(x - 4)² + 72 = 24y

y = (1/24)(x - 4)² + 3

Therefore, the equation of the parabola is:

B.) y - 3 = -(1/24)(x - 4)²

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Final answer:

The graph of an equation reveals all possible solutions, and a system of equations can be solved graphically by finding the intersection points of their lines. Changing the slope or intercept allows manipulation of these lines, and growth rates show the rate of increase as perce

Explanation:

The graph of an equation illustrates the relationship between two variables and reveals the set of all possible solutions that satisfy the equation. When graphing a line, the slope dictates the direction and steepness of the line, while the intercept indicates where the line crosses the y-axis. To manipulate a line on a graph, you can change the slope or the intercept, altering its position and angle.

To solve a system of equations using graphs, plot each equation on the same set of axes. The point where the lines intersect represents the solution to the system, which is the set of values that satisfies all equations simultaneously. If using tables, input different values for one variable and solve for the other to find ordered pairs. When the pairs from different equations match, you've found an approximate solution. A growth rate can be determined by calculating the percentage change and can be interpreted as the rate at which a quantity increases over time.

Learning how to read and manipulate a graph is critical to interpret and express equations visually. Graphs not only convey solutions but also the behavior of equations, such as trends and growth rates, which are essential in understanding and communicating mathematical concepts effectively.

Answer:

a) Let b represent the number of blue marbles placed in the second jar. Then 34-b is the number of yellow marbles in the second jar, and 25 - (34-b) is the number of yellow marbles remaining in the first jar. That value simplifies to b-9. The positive difference between b and (b-9) is 9.  

b) Let n, d, p represent the numbers of nickels, dimes, and pennies, respectively.  

.. (5n + 10d + p)/(n + d + p) = 7 ... the average value of the collection is 7 cents per coin  

.. (5(n-1) + 10d + (p+5))/((n-1) + d + (p+5)) = 6 ... replacing one nickel with pennies changes the average to 6 cents per coin  

Multiplying by the denominator and subtracting the right side of each resulting equation gives  

.. 10d + 5n + p = 7d + 7n + 7p  

.. 10d + 5n + p = 6d + 6n + 6p + 24  

Subtracting the second equation from the first gives  

.. 0 = d + n + p - 24 ... tells us the total number of coins is 24. This tells us the total value is $1.68 = 24*$0.07.  

This sum will consist of at least 3 pennies. If that is all the pennies, then the remaining 21 nickels and dimes must add to $1.65. If all were nickels, the value of the 21 coins would be $1.05. We have $0.60 more than that. For each nickel traded for a dime, we gain $.05, so 12 of the 21 nickels must be traded for dimes to raise the total coin value to $1.65.  

Alternatively, you can write two equations in the two unknowns:  

.. d + n = 21  

.. 10d + 5n = 165  

Subtracting 5 times the first equation from the second gives  

.. 5d = 60 ... which gives the same answer as reasoned above.  

There are 3 pennies, 9 nickels, 12 dimes. (If there are 8 pennies to start, then the number of nickels is zero, so it is impossible to trade one for 5 pennies. The solution shown is the only one.)

Answer:

The best function represented by the scatter plot is f(x) = -5 + 0.5 x ⇒ 1st answer

Step-by-step explanation:

* Lets talk about the scatter plot

- Scatter plots are similar to line graphs in that they use horizontal and

 vertical axes to plot data points

- Scatter plots show how much one variable is affected by another.

- The relationship between two variables is called their correlation

- There are three types of correlation:

  positive: one variable increases so the other increase

  negative: as one variable increases, the other decreases

  no correlation:  there is no clear relationship between the variables

* Lets solve the problem

- The scatter plot shows the relationship between the leaf length (x)

  and leaf width f(x)

- Some leaves of a tree are ordered pairs:

# (11 , 0.5) , (12 , 1) , (13 , 1.5) , (14 , 2) , (15 , 2.5) , (16 , 3) , (17 , 3.5) ,

  (18 , 4) , (19 , 4.5) , (20 , 5) , (21 , 5.5) , (22 , 6)

∵ The scatter plot is similar to the line graph

- Lets find the equation which represents the relation between

 x and f(x)

∵ The form of the linear equation is y = mx + c, where m is the slope

  of the line and c is the y-intercept

- The rule of the slope of the line which passes through points (x1 , y1)

 and (x2 , y2) is: [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

- Chose any two points to find the slope of the line

∵ (12 , 1) and (14 , 2) are two points on the line

∴ [tex]m=\frac{2-1}{14-12}=\frac{1}{2}=0.5[/tex]

- Substitute the value of m in the equation

∴ y = 0.5 x + c

- To find c use any point from above and substitute x and y by its

  coordinates

∵ Point (16 , 3) lies on the line

∴ 3 = 0.5(16) + c ⇒ simplify

∴ 3 = 8 + c ⇒ subtract 8 from both sides

∴ 3 - 8 = c

∴ c = -5  

- Substitute the value of c in the equation

∴ y = 0.5 x - 5

* The best function represented by the scatter plot is f(x) = -5 + 0.5 x

Answer:

The function in choice

A) [tex]h(t) = -16(t - 3)^{2} + 34[/tex]

could possibly represent this relationship.

Step-by-step explanation:

Consider the vertex form of parabolas with a local extrema at [tex](x_{0}, y_{0})[/tex].

[tex]y = a(x - x_{0})^{2} + y_0[/tex].

Note the minus sign in front of [tex]x_0[/tex] in this expression.

The coefficient [tex]a[/tex] cannot be zero. The value of [tex]a[/tex] depends on the direction and width of the parabola's opening:

For this parabola,

Among the four functions, only the function in A) meets the requirements.

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: First option.

Step-by-step explanation:

Knowing that the transformation T maps triangle XYZ onto triangle X'Y'Z', you can identifyfrom the figure that the triangle XYZ is the preimage, because it is the original shape and the triangle X'Y'Z' is the image, because is the shape obtained after the transformation.

You can observe in the figure that the image of the vertex X is the vertex X', the image of the vertex Y is the vertex Y' and the image of the vertex Z is the vertex Z'.

Therefore, the conclusion is: The image of Y is Y'.

Answer:

50m.

Step-by-step explanation:

When 2 chords  of a circle intersect the following products are equal:

15 * 15 = 5 * (TW - 5)

5TW = 225 + 25 = 250

TW = 250/5 = 50 m

Option c 50m

When a line passes through the center of the circle to the chord then the line is perpendicular bisector of the same chord which means it divide the chord in equal parts and makes an angle of 90 degrees with the chord.

Pythagoras theorem is the theorem used to calculate the hypotenuse in a right-angled triangle from the two legs of the triangle.

hypotenuse² = base²+height².

Let the center (the point in bold be C) and the point of intersection between QE and TW be R, So CQ is the radius, CR = radius-5.

Let the radius be 'r' so In Triangle CQR using the Pythagoras theorem

r² = (r-5)²+15²

r²-(r-5)²=225

(r-(r-5))(r+r-5) = 225

5.(2r-5)=225

(2r-5)=45

2r - 5 =45

2r=50

r = 25 and diameter is equal to 2*r and hence the diamter is 50.

The diameter in the figure is 50m

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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:

let's take a peek at the graph.

the graph of the equation touches the x-axis at 1, 2 and 3, at 1 it crosses it, at 2 it crosses it, at 3 is doesn't cross it, it simply bounces off of it.

on the roots/solutions the graph crosses the x-axis, they have ODD multiplicity, on the solutions it bounces off of it, they have EVEN multiplicity, so then.

x = 1 => x - 1 = 0  <------ one  factor

x = 2 => x - 2 = 0 <------ another factor

x = 3 => x - 3 = 0  <------ another factor, BUT with even multiplicity

(x-1)¹(x-2)¹(x-3)² = f(x)

(x-1)(x-2)(x-3)² = f(x).

Answer:

D

Step-by-step explanation:

you need to get the x alone so to do that, you need to add 7y so you do it on both sides and it gives you x=7y+8

The value of the expression  x − 7y = 8 will be x = 7y + 8. The correct option is D.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given expression is  x − 7y = 8. The value of x will be calculated as below:-

x − 7y = 8

x = 7y +  8

Therefore, the value of the expression  x − 7y = 8 will be x = 7y + 8. The correct option is D.

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Answer:172

Step-by-step explanation:

24.5 times 6 is 157

Plus 15 for the paint is 172 for the TOTAL for ALL she spent

Answer:

Step-by-step explanation

[tex]\bf \begin{array}{ccll} miles&hours\\ \cline{1-2} 48&1\\ 30&x \end{array}\implies \cfrac{48}{30}=\cfrac{1}{x}\implies \cfrac{8}{5}=\cfrac{1}{x}\implies 8x=5 \\\\\\ x=\cfrac{5}{8}\qquad \textit{37 minutes and 30 seconds}[/tex]

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 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:

  1/8 ft³

Step-by-step explanation:

Apparently cubic blocks that are 1/5 of 2 1/2 ft on a side are used to fill the cube that is 2 1/2 ft on a side. Then each edge of the block is ...

  (1/5) × (5/2 ft) = 1/2 ft

The volume of the block is the cube of that:

  (1/2 ft)³ = 1/8 ft³

Answer:

A

Step-by-step explanation:

The equation will be in the form

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (2.5, 0) ← 2 points on the line

m = [tex]\frac{0-5}{2.5-0}[/tex] = - 2

The line crosses the y- axis at (0, 5) ⇒ c = 5

y = - 2x + 5 or

y = 5 - 2x → A

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: x=243

Step-by-step explanation:

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:

A. (-6, 5, 5)

Step-by-step explanation:

A suitable calculator can reduce the augmented matrix for the system.

Answer:

$.80 and 1.25

Step-by-step explanation:

hope this helps

Answer:

y = 1.383x - 1.526

Step-by-step explanation:

Intercept-    -1.526

Slope-  1.383

Line of best fit- y = 1.383x - 1.526

Answer:

[tex]y=1.383x-1.526[/tex]

Step-by-step explanation:

The given data table is

x :        4       7       10       12       13

y :        5       7       12       14       18

We need to find the equation of the best fit line.

The general form of a best fit line is

[tex]y=mx+b[/tex]         .... (1)

where, m is slope and b is y-intercept.

[tex]m=\frac{\sum_{i=1}^nx_iy_i-n\overline{x}\overline{y}}{\sum_{i=1}^nx_i^2-n\overline{x}^2}[/tex]

[tex]b=\overline{y}-b\overline{x}[/tex]

Using the graphing calculator we get

[tex]m=1.38321\approx 1.383[/tex]

[tex]b=-1.52555\approx -1.526[/tex]

Substitute m=1.383 and b=-1.526 in equation (1).

[tex]y=1.383x-1.526[/tex]

Therefore, the equation of best fit line is [tex]y=1.383x-1.526[/tex].

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:

  (x, y) = (2, 10)

Step-by-step explanation:

Adding the two equations will eliminate the y-variable:

  (-4x -y) +(-7x +y) = (-18) +(-4)

  -11x = -22 . . . . . simplify

  x = 2 . . . . . . . . . divide by -11

__

Put this into the first equation to find y:

  -4·2 -y = -18

  -8 +18 = y = 10 . . . . . add 18+y

The solution is (x, y) = (2, 10).

Answer:

x = 2 and y = 10

Step-by-step explanation:

It is given that,

-4x - y = -18 ---(1)

-7x + y= -4   ---(2)

To find the solution of equations

Step 1:  Add eq(1) + eq(2)

-4x - y = -18 ---(1)

-7x + y=  -4   ---(2)

-11x + 0 = -22

11x = 22

x = 22/11 = 2

Step 2: Substitute the value of x in eq (2)

-7x + y= -4   ---(2)

-7*2 + y = -4

-14 + y = -4

y = -4 + 14 = 10

Therefore x = 2 and y = 10

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: x=3

Step-by-step explanation: First we do distributive property in the parentheses. Next we subtract both sides by 6. Lastly we divide both sides by 3. Algebraic Rules!!!

Work:

3(x+2)=15

3x+6=15

3x+6-6=15-6

3x=9

3x/3=9/3

x=3

Multiply the bracket by 3

3x+6=15

3x+6-6=15-6

3x=9

divide by 3 for 3x and 9

3x/3=9/3

x=3

Check answer by using substitution method

3(x+2)=15

3(3+2)= 15

Multiply the bracket by 3

9+6= 15

15= 15

Answer is x= 3

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The sculptures of great baseball sluggers are found in famous places of the city.

Here,

The sculptures of any famous personalities are installed in the places that are frequently visited by the public , so that the it will gain traction.

Thus,

The sculptures of famous baseball players will be available in city malls , museums , parks or baseball stadium.

The players coming to play baseball will be motivated by seeing their idols.

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Answer:

1.25(w)-12.50=C