What is the midline of the function graphed below?

1


2


3


4


5

The ordered pair solutions for the system of equations are:

(4, 5) and (-1, 0).

We have,

To find the ordered pair solutions for the system of equations, we need to solve the equations simultaneously.

The given equations are:

f(x) = x² - 2x - 3

f(x) = x + 1

Since both equations are equal to f(x), we can set them equal to each other:

x² - 2x - 3 = x + 1

Now, let's solve this quadratic equation:

x² - 2x - 3 - x - 1 = 0

x² - 3x - 4 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula.

Let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation,

a = 1, b = -3, and c = -4.

Substituting these values into the quadratic formula:

x = (-(-3) ± √((-3)² - 4(1)(-4))) / (2(1))

x = (3 ± √(9 + 16)) / 2

x = (3 ± √25) / 2

x = (3 ± 5) / 2

We have two possible solutions:

When x = (3 + 5) / 2 = 8 / 2 = 4

When x = (3 - 5) / 2 = -2 / 2 = -1

Therefore, the ordered pair solutions for the system of equations are:

(4, f(4)) and (-1, f(-1))

Now, let's substitute these values into either equation to find the corresponding y-values (f(x)):

For x = 4:

f(4) = 4 + 1 = 5

So, one solution is (4, 5).

For x = -1:

f(-1) = -1 + 1 = 0

So, another solution is (-1, 0).

Therefore,

The ordered pair solutions for the system of equations are:

(4, 5) and (-1, 0).

Learn more about solutions of equations here:

https://brainly.com/question/545403

#SPJ1

Answer:

IF the answer is 344 then I can help u with this question

The parent function of the transformed function is y = f ( x ) = x

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) is

The transformed function is represented as y

where y = 2 ( x - 5 )

On simplifying , we get

y = 2( x - 10 )

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

The function is shifted horizontally left by 10 units and multiplied by a scale factor of 2 units.

Hence , the parent function is f ( x ) = x

To learn more about transformation of functions click :

https://brainly.com/question/26896273

#SPJ1

Step-by-step explanation:

Simple, she found the sum of the interior angles not exterior angles.

The exterior angles of any polygon add up to 360 degrees.

What Cindy did was found the total interior angle measure of a hexagon which is 720

The total of the players' scores is: -3700

We are given the scores of the players named as:

Joseph 500

Sarah –1,500

Malachi –2,200

Tyson 400

Shaun –600

Summer –300

Thus, to get the total of the players scores, we will add up all the scores to get the following:

500 + (-1500) + (-2200) + 400 + (-600) + (-300) = -3700

This would be the sum total of the players' scores.

Read more about Total Score at: https://brainly.com/question/23276479

#SPJ1

The measurement of a crayon and half a pencil dreambox will depend on the specific dimensions of the dreambox. As there is no information provided about the exact size or shape of the dreambox.

To measure the crayon and half pencil dreambox, you would typically need a measuring tool such as a ruler or tape measure. Here are the steps to measure it:

1. Determine the length measurement: Place the dreambox on a flat surface and measure the length from one end to the other using the measuring tool. Make sure to align the measuring tool properly to get an accurate measurement.

2. Measure the width: Measure the width of the dreambox by placing the measuring tool perpendicular to the length measurement. Again, ensure that the measuring tool is aligned correctly to obtain an accurate width measurement.

3. Measure the height: Measure the height of the dreambox by placing the measuring tool vertically from the bottom to the top of the dreambox. Ensure that the measuring tool is aligned properly for an accurate height measurement.

By following these steps and using a measuring tool, you can obtain the measurements of the crayon and half pencil dreambox accurately.

For more such questions on dimensions, click on:

https://brainly.com/question/29755536

#SPJ8

Answer:

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

Let the radius be r.

Use circumference formula and find the value of r:

Find the area using the circle area formula:

The matching choice is (B).

Answer:

Step-by-step explanation:

Answer:

D) 210 degrees

Step-by-step explanation:

The angle 210 degrees is equal to 7π/6 radians.

This is a coterminal angle of 31π/6, because it is the same angle, just measured from a different starting point.

You would need 36 gallons of pure methane and 84 gallons of water to obtain a mixture of 120 gallons with 70% methane.

To determine the quantities of pure methane and water needed to obtain a mixture of 120 gallons with 70% methane, we can set up a simple equation based on the conservation of mass.

Let's assume that the 70% methane refers to the methane content by volume in the final mixture.

This means that 70% of the total volume of the mixture will be methane, while the remaining 30% will be water.

Let's represent the volume of pure methane as "x" gallons.

Therefore, the volume of water will be (120 - x) gallons since the total mixture volume is 120 gallons.

Since methane represents 70% of the total volume, the methane volume in gallons will be 0.7 × 120 = 84 gallons.

Setting up the equation based on the volume of methane:

x = 84

Now we can solve for x:

x + (120 - x) = 84

120 - x = 84

x = 120 - 84

x = 36

So, you would need 36 gallons of pure methane and (120 - 36) = 84 gallons of water to obtain a mixture of 120 gallons with 70% methane.

Learn more about Equations click;

https://brainly.com/question/29657983

#SPJ1

The missing value 'x' in the two-way relative frequency table is 0.36.

To convert the two-way table to a two-way relative frequency table, we need to calculate the relative frequencies for each category. Relative frequency is calculated by dividing the frequency of a particular category by the total count in that row or column.

Let's denote the missing value as 'x'. To find the value of 'x', we need to ensure that the sum of the relative frequencies in each row and each column adds up to 1.

First, let's calculate the relative frequencies for each category:

Likes hockey: The total count in this row is 12 + 18 = 30.

Relative frequency of "Likes hockey" = 12/30 = 0.4

Relative frequency of "Doesn't like hockey" = 18/30 = 0.6

Likes baseball: The total count in this column is 12 + 14 = 26.

Relative frequency of "Likes baseball" = 12/26 ≈ 0.4615

Relative frequency of "Doesn't like baseball" = 14/26 ≈ 0.5385

To ensure that the relative frequencies add up to 1, we can set up the following equations:

0.4 + x = 1 (sum of relative frequencies in the "Likes hockey" row)

0.4615 + 0.5385 + x = 1 (sum of relative frequencies in the "Likes baseball" column)

Simplifying the equations, we have:

x = 0.6 (1 - 0.4) = 0.6 * 0.6 = 0.36

For more such questions on relative frequency

https://brainly.com/question/27562468

#SPJ8

The total number of people in the population is 2940.To find the total number of people, we need to determine the ratio of big spenders to the total population.

Given that the ratio of big spenders to tightwads is 5 to 2, we can consider it as 5x to 2x, where x is a common factor.

We are told that there are 2100 big spenders, which represents the 5x portion of the ratio. So we can set up the equation:

5x = 2100

To solve for x, we divide both sides of the equation by 5:

x = 2100 / 5

x = 420

Now that we know the value of x, we can find the total population by adding the big spenders (5x) and the tightwads (2x):

Total population = [tex]5x + 2x = 7x[/tex]

Substituting the value of x:

Total population [tex]= 7 * 420 = 2940[/tex]

For more such questions on ratio

https://brainly.com/question/12024093

#SPJ8

Answer:

0.7 Radians

Step-by-step explanation:

0.7 radians is equal to 40.107°. Therefore, 0.7 radians is greater than 40°.

Hello!

7/8 - 2/3

= 7*3/8*3 - 2*8/3*8

= 21/24 - 16/24

= 5/24

The laptop computer will be worth $700 or less after 6 years.

To determine the number of years it takes for the laptop computer to be worth $700 or less, we can set up an equation based on the given information.

Let's denote the initial value of the laptop as V0 = $2900. Each subsequent year, its value will be 70% of its value the previous year.

So, the value of the laptop after one year would be V1 = 0.7 * V0 = 0.7 * $2900 = $2030.

In general, the value of the laptop after n years can be represented as Vn = [tex]0.7^n[/tex] * V0.

We want to find the value of n when Vn ≤ $700. Thus, we can set up the following inequality:

[tex]0.7^n[/tex] * V0 ≤ $700

Substituting the value of V0, we get:

[tex]0.7^n[/tex] * $2900 ≤ $700

Dividing both sides of the inequality by $2900, we have:

[tex]0.7^n[/tex] ≤ $700 / $2900

[tex]0.7^n[/tex] ≤ 0.2414

To solve for n, we can take the logarithm (base 0.7) of both sides:

n ≤ log0.7(0.2414)

Using logarithmic properties, we can rewrite this as:

n ≤ log(0.2414) / log(0.7)

Using a calculator, we find:

n ≤ 6.54 (rounded to two decimal places)

Since n represents the number of years, it must be a whole number.

For more such questions on computer,click on

https://brainly.com/question/24540334

#SPJ8  

The shape that is generated when a two-dimensional object is rotated about an axis is a cylinder.

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases connected by a curved surface. The bases are congruent and lie in parallel planes, and the curved surface is formed by connecting corresponding points on the two bases with straight lines.

The axis of a cylinder is a line passing through the center of both bases. The volume of a cylinder can be calculated by multiplying the area of the base by the height, and the surface area can be calculated by summing the areas of the two bases and the curved surface.

Learn more about cylinders at: https://brainly.com/question/24159177

#SPJ1

Answer:

1900

Step-by-step explanation:

Use a proportion:

16 is to 950 as 32 is to x.

16/950 = 32/x

32/16 = x/950

x/950 = 2

x = 1900

Answer: 1900

The range of the absolute value function y = |x| is all non-negative numbers, which can be expressed as [0, ∞).

The absolute value function is a type of mathematical function that measures the distance between a given number and zero. It is denoted by two vertical bars surrounding the number or expression.

The range of the absolute value function is the set of all non-negative numbers. This is because the absolute value of any number is always a positive number or zero.

For example, the absolute value of 3 is 3, and the absolute value of -3 is also 3.This means that the output of the function can never be negative and can range from zero to infinity.

To learn more about : range

https://brainly.com/question/30389189

#SPJ8

The range of the absolute value function below is C. f(x) < 1.

The domain and range of a function are the components of a function. The domain is the set of all the input values of a function and range is the possible output given by the function. Domain→ Function →Range.

The range of a function is the set of all its outputs. Example: Let us consider the function f: A→ B, where f(x) = 2x and each of A and B = {set of natural numbers}.

The function y=|ax+b| is defined for all real numbers. So, the domain of the absolute value function is the set of all real numbers. The absolute value of a number always results in a non-negative value.

Learn more about range on

https://brainly.com/question/4106049

#SPJ1

What is the range of the absolute value function below?

f(x) > -4

f(x) > -1

f(x) < 1

f(x) < 4

The inequality that describes the situation is x ≤ 16

From the question, we have the following parameters that can be used in our computation:

There must be no more than 16 people on the field at the same time.

Represent the number of people with x

So, we have

There must be no more than 16 x

No more than means

Less than or equal to

So, we have

x ≤ 16

Hence, the inequality that describes the situation is x ≤ 16

Read more about inequality at

https://brainly.com/question/32124899

#SPJ1

Hello!

perimeter = 2(l + L)

perimeter = 40ft

2(12 + L) = 40

2*12 + 2*L = 40

24 + 2L = 40

2L = 40 - 24

2L = 16

L = 16/2

L = 8

Hello!

[tex]\sf the~ fourth ~number ~=~ x\\\\\\\Large \underline{\textbf{Equation:}}\\\\\\\dfrac{5+7+7+x}{4} = 7\\\\\\\Large \underline{\textbf{Solve the equation:}}\\\\\\\dfrac{5+7+7+x}{4} = 7\\\\\\\dfrac{19+x}{4} = 7\\\\\\\dfrac{19+x}{4} \times~4~= ~7~\times~4\\\\\\19+x~= ~28\\\\\\x = 28 - 19\\\\\boxed{ \textbf{\sf x = 9}}[/tex]

Answer:

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

106+37+x= 180( being sum of angle of triangle)

143+x= 180

x= 180-143

= 37

•°•x= 37°

Answer:

37

Step-by-step explanation:

106+37+x-180

x-180-143

x+-37

The angle of the sector with an area of 30 cm² and a radius of 12 cm is approximately 46.94°.

To find the angle of a sector, we can use the formula:

Angle = (Area of Sector / Area of Circle) * 360°

Given that the area of the sector is 30 cm² and the radius is 12 cm, we can calculate the area of the circle using the formula for the area of a circle:

Area of Circle = π * r²

Substituting the given radius into the formula, we have:

Area of Circle = π * (12 cm)²

To find the angle, we can now substitute the known values into the formula for the angle of a sector:

Angle = (30 cm² / (π * (12 cm)²)) * 360°

Simplifying the equation:

Angle = (30 cm² / (144π cm²)) * 360°

Angle = (30 / 144π) * 360°

Calculating the value using a calculator:

Angle ≈ 46.94°

Therefore, the angle of the sector with an area of 30 cm² and a radius of 12 cm is approximately 46.94°.

For more such questions on radius

https://brainly.com/question/27696929

#SPJ8

The resulting matrix B - A is [ 0/4 - 1/1 - 3/4 - 1 - 1/3 - undefined ].

To find the matrix B - A, we subtract the corresponding elements of matrix A from matrix B.

Matrix A:

[ 0/0 1/1 -1/0 ]

Matrix B:

[ 0/4 -3/-4 1/3 ]  

Subtracting the corresponding elements, we get:

[ 0/4 - 0/0 -3/-4 - 1/1 1/3 - (-1/0) ]

Simplifying each fraction:

[ 0/4 - 0 3/4 - 1 1/3 + 1/0 ]

Since division by zero is illogical, we must be careful with the final fraction.

Since it is impossible to divide by zero, the fraction 1/0 is undefinable.

As a result, the matrix B - A is as follows: [0/4 -3 3/4 - 1 undefined]

The division by zero results in the last member of the resulting matrix having an undefined value.

This means that for that particular element, the operation is either not defined or not possible.

Please be aware that division by zero is undefinable in mathematics and produces uncertain outcomes or undefinable values.

The final member of the resulting matrix in this instance has an undefined value.

For similar question on resulting matrix.  

https://brainly.com/question/29143452  

#SPJ8

Mario Ramirez's monthly disability benefit is approximately $118.32.

To calculate Mario Ramirez's monthly disability benefit, we need to consider his years of service, final average salary, and the benefits rate.

First, let's determine the number of years of service he had. Mario worked for 21 years in the Western State University system.

Next, we can calculate his annual disability benefit by multiplying his final average salary by the benefits rate.

Annual disability benefit = Final average salary x Benefits rate

= $74,820 x 0.019

= $1,419.78

Finally, to find the monthly disability benefit, we divide the annual disability benefit by 12:

Monthly disability benefit = Annual disability benefit / 12

= $1,419.78 / 12

≈ $118.32

Therefore, Mario Ramirez's monthly disability benefit is approximately $118.32.

Learn more about disability benefit click;

https://brainly.com/question/30704484

#SPJ1

Answer:

[tex]\Huge \boxed{\boxed{ x = 1}}[/tex]

Step-by-step explanation:

Isolate the variable on one side of the equation before trying to solve it. It means that you should only have constants (numbers) on the other side of the equal sign and the variable alone on the one side.

To do this, you can add, subtract, multiply, divide, or use any other operation to both sides of the equation as long as you do the same thing on both sides.

Your final step depends on the equation and how you've simplified it. In general, you want to figure out how you arrived at the final equation by working backwards from it. You'll isolate the variable in the last action you took.

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

Step1: Subtract [tex]\bold{2x}[/tex] from both sides

Step 2: Subtract 3 from both sides

Step 3: Divide both sides of the equation by 6

So the solution to the equation [tex]\bold{8x + 3 = 2x + 9}[/tex] is [tex]\bold{x = 1}[/tex].

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

The measure of angle d in the given triangle is 30 degree.

From the given figure,

95°+c=180° (Sum of two adjacent angles is 180°)

c=180°-95°

c=85°

Now, consider triangle with three angles 65°, c and d.

Here, 65°+c+d=180° (Sum of interior angle of triangle is 180°)

65°+85°+d=180°

150°+d=180°

d=180°-150°

d=30°

Therefore, the measure of angle d in the given triangle is 30 degree.

To learn more about the angle sum property of a triangle visit:

https://brainly.com/question/8492819.

#SPJ1

The mistake that Katie made in the stem and leaf diagram, was that she D. Missed a length.

Looking at the stem and leaf diagram, we see that there are 14 leaves. This means that there are 14 lengths of caterpillars. However, there are 15 lengths shown on the table.

This means that there is a length missing that Katie failed to account for. Upon close inspection of the stem and leaf plot, we find that the missing length is a second value of 70 because there are two lengths that are 70 but this is shown only once on the stem and leaf plot.

Find out more on stem and leaf plots at https://brainly.com/question/27683035

#SPJ1

The correct transformation that describes why rectangles ABCD and A′B′C′D′ are similar is Rectangle ABCD was dilated by a scale factor of 5 to form rectangle A′B′C′D′.

Dilation is a transformation that changes the size of an object while maintaining its shape. In this case, the coordinates of rectangle ABCD were multiplied by a scale factor of 5 to obtain the coordinates of rectangle A′B′C′D′.

This means that each side length of rectangle ABCD was multiplied by 5 to get the corresponding side length of rectangle A′B′C′D′.

The reflection across the y-axis and the rotation of 90° counterclockwise would result in different shapes and orientations, not maintaining the similarity between the two rectangles.

The dilation by a scale factor of 15 or 1/5 would also change the proportions and not result in a similar rectangle.

For more such questions on dilated,click on

https://brainly.com/question/30240987

#SPJ8  

Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

Know more about triangle,

https://brainly.com/question/13677972

#SPJ1