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Answer:

(-infinity,-1)U(-1,infinity)

Step-by-step explanation:

plug in the number where the piecewise function changes which is -1 and 1

(-1)^2-(-1)-2 =0

(-1)=-1

These aren't equal so the function  is discontinuous at x = -1 because of a jump

(1) = 1

-2(1) + 3 = 1

These are equal so the function is continuous at x = 1

So from negative infinity to -1 the function is continuous and from -1 to infinity

(-infinity,-1)U(-1,infinity)

The amount invested in savings with annual interest rate of 6% and 10% is $398200 and $199100.

Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows Rs. 5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years.

Let S be his savings.

He divided S into x that goes at 6% and y at 10%

As he put twice as much at the lower-yielding one, x = 2y.....(1)

Simple interest is given by: Amount x interest x time

Thus,

SI₁ = x . 0.06 . 1 = 0.06x

S I₂ = y. 0.10 . 1 = 0.10y

As x = 2y, I₁ = = 0.06 . 2y = 0.12y

As we know that the annual interest was $3982

SI₁ + SI₂ = 3982

0.12y + 0.10y = 3982

0.22y = 3982

y = 3982/0.22

y = 18100

As x = 2y, x = 36200

Hence, the amount invested is $36200 and $18100.

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Answer:

1:20

Step-by-step explanation:

Let's review the ratio of meters:centimeters

1:100 (1 meter to 100 centimeters)

Thus, our answer will be in meters:centimeters

Let's plug this in

5:100

Let's simplify by dividing both sides by 5, now!

5 / 5 = 1

100 / 5 = 20

So, our final ratio is 1:20

Answer:

y= -(x)-2

Step-by-step explanation:

if you want to find  an equation passing through the point that is perpendicular to an y=mx +c type equation. all you have to do is to change sign of the gradient. it's simple.

Sorry for the inconvenience.

The equation that represents the total amount the fan paid is

32 x (P + 25) = 3,232.

The amount spent by the friend is $909.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

Amount spend for 32 tickets = $3,232

Cost of parking = $25

Let p represent the amount the fan paid for each ticket.

The cost of each ticket.

32 x (P + 25) = 3,232

Solve for P.

32 x (P + 25) = 3,232

P + 25 = 3,232/32

P = 101 - 25

P = $76

Now,

The amount spent by the friend.

= 9 x (76 + 25)

= 9 x 101

= $909

Thus,

32 x (P + 25) = 3,232 represents the total amount the fan paid is

The amount spent by the friend is $909.

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Answer:

(x - 6)² + y² = 36 and x2 + (y + 6)2 = 36.

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r is given by:

(x - h)² + (y - k)² = r².

So, for a circle with a diameter of 12 units, the radius is 6 units.

For the center of the circle to lie on the y-axis, the x-coordinate, h, is 0.

So, the equation for a circle with center (0, k) and radius 6 units is:

(x - 0)² + (y - k)² = 6²

x² + (y - k)² = 36

Two possible values for the y-coordinate of the center, k, that would give us two different circles are k = 6 and k = -6.

So, the two equations are:

x² + (y - 6)² = 36

and

x² + (y + 6)² = 36.

Answer:

11,209

Step-by-step explanation:

1 x 10,000 is 10,000, 1 x 1,000 is 1,000 100 x 200 is 200, 0 x 10 = 0, 9 x 1 = 9. 10,000 + 1,000 + 200 + 0 + 9 = 11209

Answer:

Step-by-step explanation:

yes

Answer:

yes

Step-by-step explanation:

each 'x-value' maps to a unique 'y-value'

Answer:

c(3a) = 2(3a)^2 - 4(3a) + 3 = 18a^2 - 12a + 3.

Step-by-step explanation:

c(3a) = 18a^2 - 12a + 3

Note: this is the simplified form of the expression.

The current asset is $10,150, the total long term asset is $13108, the total current liabilities is $985, the long term liabilities is $9982 and the total equity is $12273

The company has $10,150 in current assets, which are made up of $8,250 in cash, $1,225 in inventory, and $675 in accounts receivable.

The company has $985 in current liabilities, which are made up of $485 payable to suppliers and a $500 loan that must be repaid in the following six months.

The owner's equity is equal to the $12,000 initial investment plus the $1,291 in earnings retained less the $2,018 in long-term loan repayment plus the $1,000 set aside for long-term investment, for a total of $12,273.

The value of the company's assets (land, buildings, and equipment) plus the owner's equity, or $12,273 + $8,878 + $4,230, equals the net worth of the business, or $25,381.

a) The current assets of the company are:

$8,250 in cash

$1,225 in inventory

$675 in accounts receivable

The current assets total $10,150.

b) The long-term assets of the company are:

Land and building worth $8,878

Equipment worth $4,230

The total long-term assets of the company are $8,878 + $4,230 = $13,108.

c)The current liabilities of the company are:

$485 owed to suppliers

$500 loan to be paid off in the next six months

The total current liabilities of the company are $485 + $500 = $985.

d)The long-term liability of the company is the five-year loan of $12,000, of which $2,018 has been paid back, leaving a remaining balance of

= $12,000 - $2,018 = $9,982.

e) The total equity of Company X

= $12,000 (initial investment) + $1,291 (retained earnings) - $2,018 (repaid long-term loan) + $1,000 (long-term investment)

= $12,273.

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Answer: [tex]8[/tex] and [tex]8[/tex]

Step-by-step explanation:

Let the numbers be [tex]x[/tex] and [tex]y[/tex].

[tex]x+y=16 \implies y=16-x\\\\xy=64 \longrightarrow x(16-x)=64\\\\16x-x^2 =64\\\\x^2 -16x+64=0\\\\(x-8)^2=0\\\\x=8 \implies y=8[/tex]

Answer:

  (a)  y = x/3 -1

Step-by-step explanation:

You want the equation of the line graphed showing points (3, 0) and (6, 1).

The slope of the line is its "rise" divided by its "run." Here, the points are 3 units apart horizontally, and 1 unit vertically, with the line going up to the right. That means ...

  slope = rise/run = +1/+3 = 1/3

The slope-intercept form of the equation for a line is ...

  y = mx +b . . . . line with slope m and y-intercept b

The slope of 1/3 means the coefficient of x will be 1/3. There is only one answer choice like that:

  y = x/3 -1

Therefore , the solution of the given problem of speed comes out to be

speed of freight train is 10 mi/h.

We can determine how fast that anything is traveling by looking at it from a distance. The amount of distance an object can go in a given length of time depends on its speed. Velocity is calculated using the formula velocity = distance/time. The three most used units of speed are meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) (mph).

Here,

Given :

passenger train covers a distance of 175 mi.

freight train covers a distance of 125 mi.

Speed of passenger train is 14 mi /h

Using formula of time -distance,

=> 175/14 = 12.5 hour

So, speed of freight train is :

=> speed = 125/12.5 = 10 mi/h

Therefore , the solution of the given problem of speed comes out to be

speed of freight train is 10 mi/h.

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The Angle C is 83.2°

The Law of Cosines, also known as the Cosine Formula, is a mathematical relationship that relates the lengths of the sides of a triangle to the cosine of one of its angles. The law states that in a triangle ABC with sides a, b, and c opposite to angles A, B, and C, respectively, the following equation holds:

c^2 = a^2 + b^2 - 2ab cos(C)

where "cos" represents the cosine function. The Law of Cosines can be used to find missing sides or angles in a triangle when given sufficient information. It is widely used in geometry, trigonometry, and engineering. The Law of Cosines is an extension of the Pythagorean theorem and can be used when the triangle is not a right triangle. It is a powerful tool for solving a variety of problems in a wide range of fields.

To find the angle C in triangle ABC, you can use the Law of Cosines. The Law of Cosines states that in a triangle ABC with sides a, b, and c and opposite angles A, B, and C, the following equation holds:

c² = a² + b² - 2abcos(C)

In this case, a = 20 cm, b = 29 cm, and c = 24 cm, and we are given that angle BAC = 82 degrees. Using this information, we can calculate cos(C) as follows:

cos(C) = (a² + b² - c²)/(2ab) = (20² + 29² - 24²)/(2×20×29) = 0.2618

Finally, we can use the inverse cosine function (arccos) to find angle C:

C = arccos(cos(C)) = arccos(0.2618) = 83.2 degrees (rounded to one decimal place).

So, angle C in triangle ABC is approximately 83.2 degrees.

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Answer:

The inequality to compare the number of pictures taken during school to the number of pictures taken after school is: 19 < 24.

Step-by-step explanation:

Here's a step-by-step explanation of the inequality comparison:

Start with the two values being compared: 19 pictures taken during school and 24 pictures taken after school.

Use the inequality symbol (<) to compare the two values: 19 < 24.

Read the inequality as "19 is less than 24". This means that there were fewer pictures taken during school (19) than after school (24).

So the inequality comparison between the number of pictures taken during school and after school is: 19 < 24.

The solution to the equation -1/5 = -2y + 8/5 is y = 9/10

Given the equation in the question;

-1/5 = -2y + 8/5

First, rewrite the equation as;

-2y + 8/5 = -1/5

Move all terms not containing y to the right side of the equation

-2y + 8/5 - 8/5 = -1/5 - 8/5

-2y = -1/5 - 8/5

Add  -1/5 and -8/5

-2y = ( -1 - 8) / 5

-2y = -9 / 5

Divide both sides by -2

-2y / -2 = -9/5 ÷ -2

y = -9/5 × -1/2

y = 9/10

Therefore, the value of y is 9/10.

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There are 4 kilograms of type B in one bag of the blend.

What is a linear equation in one variable?

A linear equation in one variable is an equation that can be written in the form ax + b = 0, where a and b are constants and x is the variable. This equation represents a straight line in a coordinate plane and the solution to the equation corresponds to the x-coordinate of the point where the line intersects the x-axis.

Let's call the amount of type B in one bag of the blend "x".

Since one bag of the blend is 4 kilograms of type A, we know that one bag is 4 + x kilograms of coffee.

And since 6 bags of the blend is a total of 48 kilograms, we can write an equation:

6 * (4 + x) = 48

Expanding the left-side of the equation:

24 + 6x = 48

Subtracting 24 from both sides:

6x = 24

Dividing both sides by 6:

x = 4

Hence, there are 4 kilograms of type B in one bag of the blend.

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On solving the provided question, we cans ay that by unitary method, for 875 miles = car will take 0.04*875 = 35 gallons

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

by unitary method,

Sera drove 450 miles

car used 18 gallons of gas

for 1 mile, car take = 18/450 = 0.04gallons

for 875 miles = car will take 0.04*875 = 35 gallons

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By solving a system of equations, wewill see that they sold 325hamburgers.

Let's define the variables:

h = number of hamburgers.

c = number of cheeseburgers.

We know that the total combined number is 588, then we can write:

h +c = 588

And there were 62 fewer cheeseburers than hamburgers, then:

c = h - 62

Now we have a system of equations:

h +c = 588

c = h - 62

c is already isolated on the second equation, so we can replace that on the first equation to get:

h + (h - 62) = 588

2h = 588 + 62

2h = 650

h = 650/2 = 325

They sold 325 hamburgers.

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A wheelchair ramp is too steep, it may be difficult to use so we need to choose correct slope to design wheel chair.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

Slope is also important to people who use wheelchairs. If a wheelchair ramp is too steep, it may be difficult to use. Constructing a ramp with the right slope is especially important for people who use manual wheelchairs instead of power wheelchairs. If a ramp is too steep, the user may not have the upper arm strength necessary to power a manual chair up the ramp.

Therefore, a wheelchair ramp is too steep, it may be difficult to use so we need to choose correct slope to design wheel chair.

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[tex]\displaystyle \lim_{x\to 16} ~~ \cfrac{4-\sqrt{x}}{16x-x^2} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{4-\sqrt{x}}{16x-x^2}\implies \cfrac{4-\sqrt{x}}{x(16-x)}\implies \cfrac{4-\sqrt{x}}{x( ~~ 4^2-(\sqrt{x})^2 ~~ )} \\\\\\ \cfrac{4-\sqrt{x}}{x( ~~ [4-(\sqrt{x})][4+(\sqrt{x})] ~~ )}\implies \cfrac{1}{x( ~~ 4+\sqrt{x} ~~ )} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_{x\to 16} ~~ \cfrac{1}{x( ~~ 4+\sqrt{x} ~~ )}\implies \cfrac{1}{16( ~~ 4+\sqrt{16} ~~ )}\implies \cfrac{1}{16(4+4)}\implies \cfrac{1}{128}[/tex]

Answer: To find the limit as x approaches 16, we can substitute x = 16 into the expression:

lim (4-√X)/16X-X² = (4 - √16)/16 * 16 - 16^2 = (4 - 4)/16 * 16 - 256 = 0/256 - 256 = -256.

So the limit as x approaches 16 is -256.

Step-by-step explanation:

The system of equations that models the situation is given as follows:

The system of equations is constructed by linear functions in slope-intercept format, which are explained as follows:

y = mx + b.

In which:

Hence the two functions are given as follows:

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Answer:

Step-by-step explanation:

The place value of the 5 in the number 2.35 x 104 is ten thousand.

In scientific notation, the number 2.35 x 104 represents 2.35 times 10 to the power of 4. The number 10 to the power of 4 is 10,000, so the digit 5 is in the ten thousand place. The ten thousand place has a value of 10,000, so the 5 in 2.35 x 104 has a place value of 10,000.

So, the place value of the 5 in 2.35 x 104 is ten thousand.

Answer:

(x - 1)² + (y - 1)² = 25

Step-by-step explanation:

the distance from the center of the circle to any point on the edge (or arc) of the circle is the radius of the circle.

per the distance formula (= Pythagoras for the right-angled triangle of the coordinate differences between the 2 points) we know

AB² = (xb - xa)² + (yb - ya)² = (5 - 1)² + (4 - 1)² =

= 4² + 3² = 16 + 9 = 25

AB = radius = 5

the standard form of a circle is

(x - h)² + (y - k)² = r²

(h, k) being the coordinates of the center of the circle, r being the radius.

(x - 1)² + (y - 1)² = 25

is the correct equation.

It took 3 hours to travel 150 miles with a speed of 50 miles per hour.

The speed of an object tells how fast or slow an object will cover a distance in the time period. The speed of an object is directly proportional to the distance covered by the object and will be inversely proportional to time.

Here we have

A drive of 50 miles per hour between Seattle and Portland
which are 150 miles apart  

Given speed = 50 miles per hour

Distance covered = 150 miles  

The time is taken to travel the distance, Time = Distance / Speed  

= (150/50) =  3 hrs

Therefore,

It took 3 hours to travel 150 miles with a speed of 50 miles per hour.  

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Answer: 2 1/2 or 2.5

Step-by-step explanation: 3/1 * 5/6= 15/6

divide 15/6 which equals 2.5 or 2 1/2

Answer: second blank for x= 2, fifth blank for x= 9. First blank for y= 0, third blank for y= 4, fourth blank for y= 36.

Step-by-step explanation:

plug in x and y values to equation and solve.

The solution to the equations are as follows:

1. X^2 + 6X + 3 = 0, the solution is (-3,-1).

2. 52726 - 6 = 52,720

3. 12 - 8 + (-5) = -1

4. X^2 + 8X + 20 = 0, the solution is (-5, -4).

5. x⁻¹+4x⁻²=0

X^2 + 6X + 3 = 0, can be solved by the quadratic formula: X = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = 6, and c = 3.

X = (-6 ± √(6^2 - 4 * 1 * 3)) / 2 * 1

X = (-6 ± √(36 - 12)) / 2

X = (-6 ± √(24)) / 2

X = (-6 ± 2√6) / 2

X = (-3 ± √6), (-3 - √6)

52726 - 6 = 52720

12 - 8 + (-5) = -1

X^2 + 8X + 20 = 0, can be solved by the quadratic formula: X = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = 8, and c = 20.

X = (-8 ± √(8^2 - 4 * 1 * 20)) / 2 * 1

X = (-8 ± √(64 - 80)) / 2

X = (-8 ± √(-16)) / 2

Since the square root of a negative number is not defined in real numbers, there are no real solutions to this equation.

x⁻¹ + 4x⁻² = 0

Dividing both sides by x⁻², we get x + 4 = 0

Subtracting 4 from both sides, we get x = -4.

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The complete question goes thus:

Solve:

1.X2 +6x +3=0

2.52726-6=0

3.12-8+-5:0

4.X(X+8)=-20

5.x⁻¹+4x⁻²=0

The total commission the realtor earns is given by the equation A = $ 9375

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total commission amount the realtor earns be represented as A

Now , the equation will be

The percentage of commission = 1.25 %

The total amount for the 2 homes = $ 750,000

So , the amount of commission A = percentage of commission x total amount for the 2 homes

Substituting the values in the equation , we get

The amount of commission A = ( 1.25 / 100 ) x 750,000

On simplifying the equation , we get

The amount of commission A = 0.0125 x 750,000

The amount of commission A = $ 9375

Hence , the amount of commission is $ 9375

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