acellus algebra 2. piece wised functions.
find f(-2) for the piece wised function

In conclusion the discount amount is Rs. 1250.

Why it is?

Let's start by using algebra to represent the problem:

Let's assume the market price of the article is "M".

The shopkeeper offers a 20% discount, so the selling price (SP) would be:

SP = M - 0.20M

SP = 0.80M

Then, a 10% VAT is levied on the selling price, so the final price (FP) would be:

FP = SP + 0.10SP

FP = 1.10SP

FP = 1.10(0.80M)

FP = 0.88M

We know that the customer paid Rs. 500 for VAT, so:

0.10SP = 500

Substituting SP = 0.80M, we get:

0.10(0.80M) = 500

Solving for M, we get:

M = 6250

So, the market price of the article is Rs. 6250.

Now, to find the discount amount, we can subtract the selling price from the market price:

Discount amount = Market price - Selling price

Discount amount = Rs. 6250 - 0.80 x Rs. 6250

Discount amount = Rs. 1250

Therefore, the discount amount is Rs. 1250.

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Answer:

c. [tex]p^2+2p-24[/tex]

Step-by-step explanation:

[tex](p + 6)(p - 4)\\\\= (p)(p) + (6)(p) + (-4)(p) + (6)(-4)\\\\= p^2+6p-4p-24\\\\=p^2+2p-24[/tex]

Thus, the radius of circle KM for the given value of tangent is found as: MK = 6 mm.

A tangent is really the line that follows the curve's slope at a specific location. It is the line that contacts the curve at any specific point and follows the curve in that location.

Given:

MK ⊥ NM (property of tangent drawn to any circle)

Using the Pythagorean theorem in right triangle NMK

NK² = MK² + NM²

MK² = NK² -  NM²

MK² = 10² + 8²

MK² = 100 - 64

MK = 6 mm

Thus, the radius of the circle KM for the given value of tangent is found as: MK = 6 mm.

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The length of the entire trip is equal to the time required to travel [tex]22 km[/tex], the boat's average speed on calm water is [tex]3.24 km/h[/tex]

In mathematics, an equation is a statement that all equations are the same.

A variable is a symbol that represents an unknowable value or a value that is subject to vary within a given range, and an equation may contain one or more of these symbols.

Mathematics can be used to identify hidden quantities in problems and to express interactions between variables.

As an example, the equations [tex]2x+5= 13[/tex] contain the response variable, which stands for an indeterminate value.

To determine the value of[tex]x[/tex] that makes the equation remain true, this equation can be solved.

Since [tex]2(4)+5=13[/tex], the solution in this case is [tex]x=4[/tex] Equations come in a variety of different forms, such as linear equations, quadratic equations, and systems of equations.

Given

We can create another equation since the duration of the full journey is equal to the duration needed to travel [tex]22 km[/tex] along the lake:

The sum of the times against and with the current is the total time.

By simplifying and substituting the formula

[tex]15/(b-2) +6/(b+2) = 22/b[/tex]

After multiplying both sides by [tex]b(b-2)(b+2)[/tex] we get

[tex]22(b-2)(b+2) = 15b(b+2) +6b(b-2)[/tex]

Adding and subtracting

[tex]15b^{2} +30b +6b^{2} - 12b =22(b^{2} -4)\\21b^{2} +42b -22b^{2} +88 = 0\\-b^{2} +2b+4[/tex]

The boat speed cannot be negative so we considered positive value

[tex]3.24 km/h for b =1+\sqrt{5}[/tex]

Therefore the length of the entire trip is equal to the time required to travel [tex]22 km[/tex], the boat's average speed on calm water is [tex]3.24 km/h[/tex]

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If the representative fraction scale is 1:48000, then the verbal scale from inches to feet is  1 inch represents 0.00025 feet.

We have to find the verbal (written) scale from inches to feet that represents a map with a representative-fraction (RF) scale of 1:48,000,

We use the formula:

⇒ Verbal scale = RF × Inches per foot,

We know that the RF scale is 1:48,000, which means that one unit on the map represents 48,000 units in the real world.

There are 12 inches in a foot,

So, we can convert the verbal scale to inches-per-foot by dividing by 12:

⇒ Inches per foot = (Verbal scale)/(12),

⇒ Inches per foot = (1/48000) × (12/1) = 0.00025

Therefore, the verbal scale from inches to feet is : 1 inch represents 0.00025 feet.

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Answer: 3,64

Step-by-step explanation:

1. Let's call the first number "x" and the second number "y". We know that:

x = 4 + 2y (equation 1)

x - y = 27 (equation 2)

We can use equation 1 to substitute x in equation 2:

(4 + 2y) - y = 27

Simplifying the equation:

3y = 23

So the second number is:

y = 23/3

Using equation 1, we can find the first number:

x = 4 + 2(23/3) = 50/3

Therefore, the numbers are 50/3 and 23/3.

2. Let's call the length of the equal sides of the triangle "x" and the length of the third side "y". We know that:

y = x + 10 (equation 1)

2x + y = 100 (equation 2)

We can use equation 1 to substitute y in equation 2:

2x + (x + 10) = 100

Simplifying the equation:

3x = 90

So the length of the equal sides is:

x = 30

Using equation 1, we can find the length of the third side:

y = 30 + 10 = 40

Therefore, the lengths of the sides are 30, 30, and 40.

The correct option:D. x = -10. The value of 'x' for the given linear equation in one variable is found as -10.

If the degree n with in equation is equal to 1, then a linear equation only contains ONE variable. The highest exponent a single variable can have is referred to as the equation's degree.

Given equation:

10 = −4x + 3x

Adding the variable'x' with sign, the coefficient will be added and the sign with the larger value will be taken.

10 = −1x

10 = -x

Divide both side by -1.

x = -10.

Thus,  the value of 'x' for the given linear equation in one variable is found as -10.

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Correct question:

Solve 10 = −4x + 3x

Option:

A. x = 2

B. x = 10

C. x = -6

D. x = -10

Answer:

A) The slope is negative.  It is -30

B)The slope is positive.  It is 2.5

Step-by-step explanation:

Graph A:

I selected two points on the graph.

(1, 220) and (7, 40)

The slope is the change in y over the change in x.  The y values are 40 and 220.  The x values are 7 and 1.  You find the change by subtracting.

[tex]\frac{40 - 220}{7-1}[/tex] = [tex]\frac{-180}{6}[/tex] = -30

Graph B:

This graph is proportional because it is a straight line and it goes through the original.  This means that the slope can be found with any ordered pair in the form [tex]\frac{y}{x}[/tex].  I am going to use the point (2, 5).  [tex]\frac{5}{2}[/tex] = 2.5

Helping in the name of Jesus.

In the given problem, we find that Luis is wrong because the probability of getting a Yahtzee in one roll of the dice is 1/6^5.

Luis is wrong because the probability of getting a Yahtzee in one roll of the dice is 1/6^5. This is approximately 0.00077 or 0.077%.

A Yahtzee is a combination of five dice with the same number on each dice. The probability of rolling any specific combination of five dice is 1/6^5 and this is because each dice has a 1/6 probability of showing the required number.

The probability of rolling a Yahtzee in one roll of the dice is 6 times the probability of rolling any specific combination, which is 6 x 1/6^5 or 1/6^4  since there are only six possible combinations of a Yahtzee (one for each number on the dice). Therefore, the correct probability of getting a Yahtzee in one roll of the dice is 1/6^5 and not 1/6b5 as Luis had stated.

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When 7 is divided by 70.85, the quotient is 0.0988.

The quotient is the result of a division operation.

A division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.

A division operation involves the dividend (in this situation, 7) divided by the divisor (70.85) to get 0.0988 (the quotient).

7 ÷ 70.85 = 0.0988

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The domain, ranges and piecewise functions are;

10. D = (-∞, 3], R = [-2, ∞)

11. D = (-∞, -1), R = (-∞, 3)

12. [tex]f(x) =\begin{cases}\frac{2}{5}\cdot x + 4 & \text{ if } x\leq 0 \\x-5 & \text{ if } x > 0 \end{cases}[/tex]

13. [tex]f(x) =\begin{cases}-x-2 & \text{ if } x < -1 \\5 & \text{ if } -1 < x < 3\\ -2\cdot x + 5& \text{ if } 3 \leq x < \infty\end{cases}[/tex]

14. [tex]f(x) = \begin{cases}-2 & \text{ if } x < 4 \\\frac{1}{2} \cdot x + 4 & \text{ if } -4 < x \leq 2 \\-x& \text{ if} 2 < x < \infty\end{cases}[/tex]

A piecewise function comprises of two or more functions that set the definition or rule of the function based on the specified interval.

10. The piecewise function indicates;

p(x) = -3·x + 7 if x ≤ 3

When x = 3,  p(x) = -3 × 3 + 7 = -2

When x approaches -∞, p(x) → ∞

The domain and range in the interval x ≤ 3 are;

Domain = (-∞, 3]

Range = [-2, ∞)

P(x)  = x if 3 < x < 5

The domain and range in the interval 3 < x < 5 are;

Domain; (3, 5)

Range; (3, 5)

P(x) = -1 if x ≥ 5

The domain and range in the interval x ≥ 5 are;

Domain; [5, ∞)

Range; -1

Therefore;

D = (-∞, ∞)

R = [-2, ∞)

11. k(x) = x + 4 if x < -1

k(x) = 5 if -1 < x < 2

k(x) = -(1/2)·x + 1 if x ≥ 2

The domain and range in the interval x < -1 are;

Domain; (-∞, -1)

Range; (-∞, 3)

The domain and range in the interval -1 < x < 2 are;

Domain; (-1, 2)

Range; 5

The domain and range in the interval x ≥ 2 are;

Domain; [2, ∞)

Range; (-∞, 0]

The function is undefined for x = -1

The domain and range of the piecewise function is therefore;

D; (-∞, -1) ∪ (-1, ∞)

R; (-∞, 3) ∪ [5, 5]

12. The points on the graph where x ≤ 0 are; (0, 2), and (-5, 0)

The slope is; 2/5

The y-intercept is; (0, 4)

The equation is therefore; y = (2/5)·x + 4

Therefore; f(x) = (2/5)·x + 4 if x ≤ 0

The points on the graph when x > 0 are; (0, -5), and (5, 0)

The slope is; 5/5 = 1, the y-intercept is; (0, -5)

The equation is therefore; y = x - 5

Therefore; f(x) = x - 5 if x > 0

The piecewise function is therefore;

[tex]f(x) =\begin{cases} \frac{2}{5}\cdot x +4 & \text{ if } x\leq 0 \\x -5 & \text{ if } x > 0 \end{cases}[/tex]

13. The points on the graph when x < -1 are; (-1, -1), and (-2, 0)

The slope is; 1/-1 = -1

The equation is; y - 0 = -1×(x - (-2)) = -x - 2

y = -x - 2

Therefore, f(x) = -x - 2 if x < -1

The points on the graph when -1 < x < 3 are; (-1, 5), and (3, 5)

The slope is; 0, the equation is; y = 5

Therefore; f(x) = 5 if -1 < x < 3

The points on the graph when 3 ≤ x < ∞ are; (3, -1), and (5, -5)

The slope is; -4/2 = -2

The equation is; y - (-1) = -2×(x - 3) = -2·x + 6

y = -2·x + 6 - 1 = -2·x + 5

y = -2·x + 5

Therefore; f(x) = -2·x + 5 if 3 ≤ x < ∞

The piecewise function is therefore;

[tex]f(x) =\begin{cases} -x -2 & \text{ if } x < -1 \\5 & \text{ if } -1 < x < 3\\-2\cdot x + 5 & \text{ if } 3 \leq x < \infty \end{cases}[/tex]

14. The functions in the piecewise function graph are;

f(x) = -2 if x < -4

The points in the interval -4 < x ≤ 2 are; (-4, 2), (0, 4)and (2, 5)

The slope is; 3/6 = 1/2

The y-intercept is; (0, 4)

The function is therefore; f(x) = (1/2)·x + 4

The points in the interval 2 < x < ∞ are; (2, -2), and (4, -5)

The slope is; -3/2 = -1.5

The equation is; y - (-2) = (-3/2) × (x - 2) = -x + 2

y = -x + 2 - 2 = -x

y = -x

The function is therefore; f(x) = -x

The piecewise function is therefore;

[tex]f(x) =\begin{cases} -2 & \text{ if } x < -4 \\\frac{1}{2}\cdot x + 4 & \text{ if } -4 < x \leq 2\\-x & \text{ if } 2 < x < \infty \end{cases}[/tex]

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To find the circle and radius of equation x2 + y2 +12x +6y +20=0, we need to complete the square for both x and y terms.

First, we can simplify the equation by rearranging the constant term to the right-hand side:

x^2 + y^2 + 12x + 6y = -20

Next, we can complete the square for the x-terms by adding (12/2)^2 = 36 to both sides of the equation:

x^2 + 12x + 36 + y^2 + 6y = -20 + 36

Simplifying further:

(x + 6)^2 + (y + 3)^2 = 13

This is now in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

So the center of the circle is (-6, -3) and the radius is the square root of 13. Therefore, the equation x^2 + y^2 + 12x + 6y + 20 = 0 represents a circle with center (-6, -3) and radius sqrt(13).

Answer:

A, D, and E

Hope this helps<3

It will take approximately 3.33 hours for both persons working together to complete the job.

What is distance?

Distance is the measure of how far apart two objects or locations are from each other. It is usually measured in units such as meters, kilometers, miles, or feet.

To solve this problem, we can use the following formula:

1 / T = 1 / t1 + 1 / t2

Where T is the time it takes for both persons working together to complete the job, t1 is the time it takes for the first person to complete the job alone, and t2 is the time it takes for the second person to complete the job alone.

Plugging in the given values, we get:

1 / T = 1 / 5 + 1 / 10

Simplifying the right side, we get:

1 / T = 3 / 10

Multiplying both sides by 10T, we get:

10 = 3T

Dividing both sides by 3, we get:

T = 10 / 3 = 3.33 hours

Therefore, it will take approximately 3.33 hours for both persons working together to complete the job.

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The swimming pool's actual measurements are[tex]1500m^{2}[/tex], which solves the area issue that was presented.

By calculating how much space would be needed to fully enclose its exterior, its overall size can be calculated. The surrounding region is considered when selecting a comparable product for the rectangular design.

We know, [tex]area = length *breadth[/tex] of a rectangle

[tex]length(l) = 10[/tex] squares and [tex]breadth (b) = 6[/tex] squares

Given [tex]1 cm = 5 m[/tex]

∴ length = [tex]5 *10 = 50 m[/tex], breadth = [tex]6*5 = 30 m[/tex]

    =[tex]50*30= 1500m^{2}[/tex]

Therefore area of the pool is [tex]1500m^{2}[/tex]

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Answer:

892 m squared

Step-by-step explanation:

Answer:14.54

Step-by-step explanation: CALCULATOR

According to the information, the actual width of the item is 21.6 yards.

We can use the scale factor to find the actual width of the item from its model width. The scale factor is 1:12, which means that every 1 unit on the model represents 12 units in actual size. The model width is given in feet, so we need to convert it to yards before we can use the scale factor.

Now we can use the scale factor to find the actual width:

So,

To solve for x, we can cross-multiply:

Therefore, the actual width of the item is 21.6 yards.

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The angle A and D will be equal by the help of side angle side theorm.

What is side angle side theorem?

The Side-Angle-Side (SAS) theorem is a concept in geometry that states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In other words, if two triangles have the same length of two sides and the angle between those sides is also the same, then the two triangles are identical in shape and size. The SAS theorem is one of the several postulates that can be used to prove congruence between two triangles.

The angle ABC is equal to angle DBE by vertical opposite angle

AC  is equal to DE

and CB is equal to EB

therefore angle A and angle D

Congruent triangles are triangles that have the same shape and size. When two triangles are congruent, it means that they have the same angles and side lengths. In other words, they are identical in every way, and one can be superimposed onto the other by rotating, reflecting or translating.

There are several ways to prove that two triangles are congruent, including:

Side-Side-Side (SSS) theorem: if all three sides of one triangle are congruent to the corresponding sides of another triangle, then the two triangles are congruent.

Side-Angle-Side (SAS) theorem: if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Angle-Side-Angle (ASA) theorem: if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

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Answer:

7

Step-by-step explanation:

Since Nancy has 4 pencils, we know Byron has 3 times that amount

4 groups of 3 is equivalent to 12.

We know that is how many pencils Byron has. Mac has 5 less.

So, 12-5 = 7.

Answer: Given that MNOP is a trapezium with MN parallel to OP and A is the midpoint of NO.

To prove that the area of triangle MAP is half the area of trapezium MNOP, we need to use the following theorem:

Theorem: If a line segment joins the midpoint of one side of a triangle to a vertex opposite to that side, then the segment divides the triangle into two equal areas.

Proof:

Since A is the midpoint of NO, we can draw a line segment AP from vertex P to point A on NO as shown in the figure below:

      M _______N

       |\      |

       |  \    |

       |    \  |

       |      \|

      O--------P

            A

We can see that triangle MAP is formed by the line segment AP and side MP of the trapezium.

Also, we can see that triangle MAN is congruent to triangle NOP because they are both right triangles with corresponding sides parallel. Therefore, they have the same area.

Since MNOP is a trapezium, the area of trapezium is given by:

Area of trapezium MNOP = (1/2)(MN+OP) × height

Since MN is parallel to OP, the height of the trapezium is the same as the height of triangle MAN and NOP.

Therefore, the area of trapezium MNOP can be written as:

Area of trapezium MNOP = (1/2)(MN+OP) × height

= (1/2)(MA+AP+OP) × height

= (1/2)(MA+MP) × height (Since AP = NO/2 = height)

So, we have proved that:

Area of trapezium MNOP = (1/2)(MA+MP) × height

Using the theorem, we know that AP divides triangle MAP into two equal areas. Therefore,

Area of triangle MAP = (1/2) × Area of triangle MAP

Substituting the above in the expression for the area of trapezium, we get:

Area of trapezium MNOP = Area of triangle MAP + (1/2) × Area of triangle MAP

= (3/2) × Area of triangle MAP

Therefore, we have:

Area of triangle MAP = (1/2) × Area of trapezium MNOP

Thus, we have proved that the area of triangle MAP is half the area of trapezium MNOP.

Answer:

256ft²

Step-by-step explanation:

White squares=

2 (8x8) =

2 (64) = 256

Whole Rectangle=

8 + 8 = 16

A = bh = 16 x 32 = 512

512 - 256 = 256

Answer:c

Step-by-step explanation:

Step-by-step explanation:

For the number to be even, it needs to end in an even number ,,,,there are no even numbers that are primes ( because the number would be divisible by 2)

Answer:

12a-b

Step-by-step explanation:

Given expression = 12a -b

The factored form for the given expression, cannot be determined because the given expression is a simplified expression its factor cannot be possible.

Answer: 1 (12a-b)

Step-by-step explanation: You would do distributive property to solve this, and 1 * 12 equals 12, so that works. 1 * b equals b, because multiplying it by 1 doesn't change its value. Hope this helps

 Other methods that may be used to collect data on this topic include observation or self-report measures, but these may be less accurate than standardized measures.

When using terms in your answer, it is important to ensure that they are used correctly and in the appropriate context. This will help to provide clear and accurate information to the student asking the question.

The best way for a researcher to collect quantitative data about how much emergency department nurses use touch to comfort patients would be to use a standardized measure such as the Touch Questionnaire.

This measure assesses the frequency and nature of touch behaviors used by healthcare providers during interactions with patients, including comforting touches.

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The perimeter of ΔJKL = KJ + JL + KL = 35 + 43.986 + 37.5 = 116.5

What is perimeter?

To find the perimeter of ΔJKL, we first need to find the length of JL. We can use the law of cosines to do this:

cos(J) = (KJ² + JL² - KL²) / (2KJJL)

cos(57) = ((35)² + x² - (37.5)²) / (235x)

x² - 23537.5*cos(57)*x + ((35)² - (37.5)²) = 0

Using the quadratic formula, we get:

x = [23537.5cos(57) ± √((23537.5cos(57))² - 4*((35)²-(37.5)²))]/2

x = [23537.5cos(57) ± √((435)²(37.5)²cos(57)² + 4*(37.5)²)]/2

x = 43.986 or x = 10.402

Since x represents the length of a side of a triangle, we know that the value of x we're looking for is the larger one, so x = 43.986.

Now we can find the perimeter of ΔJKL:

Perimeter = KJ + JL + KL = 35 + 43.986 + 37.5 = 116.486

Rounding to the nearest tenth, we get a final answer of 116.5.

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Complete question is: The perimeter of ΔJKL = KJ + JL + KL = 35 + 43.986 + 37.5 = 116.5

Answer:

70 days

Step-by-step explanation:

1 week = 7days

10 weeks = ? days

We Take

10 x 7 = 70 days

So, 10 weeks equal 70 days.

Adele has walked 7 1/20 miles so far this week.

To find out how many miles Adele has walked so far this week, we need to add the miles she walked on Monday, Tuesday, and Wednesday.
Step 1: Convert the mixed numbers into improper fractions.
- Monday: 2 3/5 = (2 × 5 + 3)/5 = 13/5
- Tuesday: 1 3/4 = (1 × 4 + 3)/4 = 7/4
- Wednesday: 2 7/10 = (2 × 10 + 7)/10 = 27/10
Step 2: Find a common denominator and add the fractions.
- Common denominator: 20 (least common multiple of 5, 4, and 10)
- Convert the fractions: 13/5 = 52/20,

7/4 = 35/20,

27/10 = 54/20
- Add the fractions:

52/20 + 35/20 + 54/20

= (52 + 35 + 54)/20

= 141/20
Step 3: Convert the improper fraction back to a mixed number.
- 141/20 = 7 + 1/20

= 7 1/20.

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27/2 or 13.5 pieces.

To find the quotient, we need to divide the length of the sub sandwich by the length of each piece she wants to cut it into:

9 ÷ (2/3)

We can simplify this by multiplying the numerator by the reciprocal of the denominator:

9 ÷ (2/3) = 9 × (3/2)

Multiplying straight across:

9 × (3/2) = 27/2

So Jenny will be able to cut the sub sandwich into 27/2 or 13.5 pieces.

Step-by-step explanation:

Cutting a 9 inch sub into 2/3 inch pieces ?

9 inch / 2/3 inch / piece = 9 * 3/2= 27/2 = 13.5 pieces ~ 13 with a bit left over