Subtract the following complex numbers:
(2 + 2i) - (14+ 16i)

Answer:

-5/3

Step-by-step explanation:

The rate of change of the biking trail is determined using the slope formula. The slope of the line passing through the given coordinates is -5/3.

The rate of change of the biking trail can be determined using the slope formula. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula slope = (y2 - y1) / (x2 - x1).

Using the given coordinates (-3, 14) and (6, -1), we can substitute the values into the formula to find the rate of change of the biking trail.

slope = (-1 - 14) / (6 - (-3)) = -15 / 9 = -5/3

Therefore, the rate of change of the biking trail is -5/3.

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The correct answer is option d) ( y = -x + 2 ).

Let's analyze each option to determine which equation does not represent the line passing through the points (1, 1) and (5, 5).

a) ( y = x ): This equation represents a line with a slope of 1 and passes through the origin. To check if it passes through (1, 1) and (5, 5), we substitute the coordinates into the equation:

- For (1, 1): ( 1 = 1 ) (True)

- For (5, 5): ( 5 = 5 ) (True)

The equation ( y = x ) is consistent with the given points.

b) ( y = 2x - 1 ): This equation represents a line with a slope of 2 and a y-intercept of -1. Checking with the given points:

- For (1, 1): ( 1 = 2(1) - 1 ) (True)

- For (5, 5): ( 5 = 2(5) - 1 ) (True)

The equation ( y = 2x - 1 ) is consistent with the given points.

c) ( 2y = 2x ): This equation can be simplified to ( y = x ), which we have already determined is consistent with the points.

d) ( y = -x + 2 ): Checking with the given points:

- For (1, 1): ( 1 = -1 + 2 ) (True)

- For (5, 5): ( 5 = -5 + 2 ) (False)

The equation ( y = -x + 2 ) does not pass through the point (5, 5).

QUESTION

Which of the following equations does not represent the line passing through the points (1, 1) and (5, 5)?

a) ( y = x )

b) ( y = 2x - 1 )

c) ( 2y = 2x )

d) ( y = -x + 2 )

Final answer:

The correct equation is 3X-3Y = -6, Therefore option A is correct.

Explanation:

To find the correct equation, we can solve the given system of equations. We can do this by using the method of substitution or elimination. Let's use the method of elimination to solve the system.

Multiplying the first equation by 2 and the second equation by 3, we get:

2(x+3y) = 2(-2) ⟶ 2x + 6y = -4

3(2x-6y) = 3(-8) ⟶ 6x - 18y = -24

Adding these two equations together, we eliminate the variable 'x':

(2x + 6y) + (6x - 18y) = -4 + (-24)

8x - 12y = -28

Now, let's compare this equation to the options given. The correct equation is:

3X-3Y = -6

Answer:

A 4955.30

Step-by-step explanation:

A = P ( 1+i) ^ t

where A is the amount in the account

P is the principal

i is the interest rate

and t is the time in years

A = 4000(1+.055)^4

A = 4000(1.055)^4

A = 4955.2986025

Rounding to the nearest cent

A = 4955.30

[tex]x^2+2x+1=(x+1)^2[/tex]

Answer:

(x+1)(x+1)

Step-by-step explanation:

The graph is attached.

To solve the given piecewise function, we need to graph each of the functions that compound the main function with their respective domain restrictions.

So, solving we have:

- First function: Positive slope line (red line).

[tex]f(x)=x+1=y\\\\y=x+1, if x<0[/tex]

Let's find the axis intercepts in order to be able to graph the function.

Finding the x-axis intercept, we need to make "y" equal to 0, so:

[tex]y=x+1\\\\0=x+1\\x=-1[/tex]

So, we have that the x-axis intercept is located at the point (-1,0)

Finding the y-axis intercept, we to mate "x" equal to 0, so:

[tex]y=x+1\\\\y=0+1\\y=1[/tex]

So, we have that the y-axis intercept is located at the point (0,1)

Hence, we have that the function exists from the values of "x" less than 0 to the negative infinite or (-∞,0)

- Second function: Horizontal line (blue line).

[tex]y=2,if0\leq x\leq 1[/tex]

Since there is not variable, we know that it's a horizontal line that passes through y equal to 2.

Hence, we have that the function exists between the values of "x" from  0 to 1 or  [0,1]

- Third function: Positive slope line (green line).

[tex]y=x,ifx>0[/tex]

Let's find the axis intercepts in order to be able to graph the function.

Finding the x-axis intercept, we need to make "y" equal to 0, so:

[tex]0=x+\\\\0=x+\\x=0[/tex]

So, we have that the x-axis intercept is located at the point (0,0)

Finding the y-axis intercept, we to make "x" equal to 0, so:

[tex]y=x\\\\y=0\\y=0[/tex]

We have that the function only pass through the point (0,0) or origin.

Hence, we have that the function exists from the values of "x" greater than 2.

So, the graph of the given function is attached.

Have a nice day!

Answer:

the answer is 30

Step-by-step explanation:

because it is an equilateral triangle all sides are the same so if you set 3x+15 equal to 7x-5 and solve for x you get 4x=20 and x= 5

when you plug 5 in to each equation you get 30 for both sides and so it proves that the answer is 30

For this case we must find the value of n of the following equation:

[tex]n + \frac {1} {5} n = 24[/tex]

Taking common factor "n" from the left side of the equation we have:

[tex]n (1+ \frac {1} {5}) = 24\\n \frac {6} {5} = 24[/tex]

Multiplying by 5 on both sides of the equation:

[tex]6n = 120[/tex]

Dividing between 6 on both sides of the equation:

[tex]n = 20[/tex]

Thus, the value of n is 20.

Answer:

[tex]n = 20[/tex]

Answer: Second Option

[tex]n = 20[/tex]

Step-by-step explanation:

Let's call n the number searched.

Then one fifth of this number is written as

[tex]\frac{1}{5}n[/tex]

Then at 1 / 5n the number n is added.

So, we have

[tex]n + \frac{1}{5}n[/tex]

Now we know that the result of this sum is equal to 24. Then we write the equation:

[tex]n + \frac{1}{5}n = 24[/tex].

Now we solve the equation:

[tex]\frac{6}{5}n = 24[/tex]

Muple both sides of equality by [tex]\frac{5}{6}[/tex]

[tex]\frac{5}{6} * \frac{6}{5}n = 24*\frac{5}{6}[/tex]

[tex]n = 20[/tex]

Answer:

1/24

Step-by-step explanation:

Step-by-step explanation:

-1 7/8+1 11/12

=-15/8+23/12 by taking Lcm as 24 we get:

=-45+46/24=1/24

Answer:

    -9/7

Step-by-step explanation:

To find the slope given 2 points, we use the formula

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

 where (x1,y2) and (x2,y2) are the two points

m = (-3-6)/(5--2)

m = (-3-6)/(5+2)

   = -9/7

Answer:

y=-1.3x+3.4

Step-by-step explanation:

Answer:

In the account that paid 3% Ramon put [tex]\$800[/tex]

In the account that paid 6% Ramon put [tex]\$1,600[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

[tex]P(rt)=Pa(rat)+Pb(rbt)[/tex]

in this problem we have

[tex]t=t\ years\\ P=\$2,400\\ Pa=\$x\\ Pb=\$(2,400-x)\\r=0.05\\ra=0.03\\rb=0.06[/tex]

substitute

[tex]2,400(0.05t)=x(0.03t)+(2,400-x)(0.06t)[/tex]

solver for x

Simplify

[tex]2,400(0.05)=x(0.03)+(2,400-x)(0.06)[/tex]

[tex]120=0.03x+144-0.06x[/tex]

[tex]0.03x=24[/tex]

[tex]x=\$800[/tex]

therefore

In the account that paid 3% Ramon put [tex]\$800[/tex]

In the account that paid 6% Ramon put [tex]\$2,400-\$800=\$1,600[/tex]

To solve this problem, we set up an equation representing the total interest earned from the two different bank accounts. After doing a bit of algebra, we find that Ramon put $1200 into each account.

This question falls into the category of the linear system in mathematics which deals with simple interest calculations. The total amount invested by Ramon is $2400 and we don't know how it was distributed into the two accounts, so we can name the amount in the account with 3% interest x and the other with the 6% interest 2400-x, as the total should be $2400.

We know the total interest earned was 5% of the whole sum, so we can set up the equation:

0.03x + 0.06(2400 - x) = 2400 * 0.05.

Solving the equation, we find that x, the amount in the first account, is $1200 and therefore, $1200 must have been put into the second account.

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Answer:

4

Step-by-step explanation:

hdhfy+_-_+4-_+_6+_-$(64&4

Answer:

Step-by-step explanation:

Area of a triangle is A=(1/2)*base*height

A = (1/2)*(4.4)*(3.3) = 0.726 cm2

Answer:

A. [tex]y\le2x^2-8x+3[/tex]

Step-by-step explanation:

The given parabola has vertex at (2,-5).

The equation of this parabola in vertex form is given by:

[tex]y=a(x-h)^2+k[/tex], where (h,k)=(2,-5) is the vertex  of the parabola.

We substitute the values to get:

[tex]y=a(x-2)^2-5[/tex]

The graph passes through; (0,3).

[tex]3=a(0-2)^2-5[/tex]

[tex]\implies 3+5=4a[/tex]

[tex]\implies 8=4a[/tex]

[tex]\implies a=2[/tex]

Hence the equation of the parabola is

[tex]y=2(x-2)^2-5[/tex]

We expand this to get:

[tex]y=2x^2-8x+8-5[/tex]

[tex]y=2x^2-8x+3[/tex]

Since the outward region was shaded, the corresponding inequality is

[tex]y\le2x^2-8x+3[/tex]

The correct answer is A

Answer:

Step-by-step explanation:

Formula

Number of students voting = (ratio of those voting / total) * total students.

Givens

ratio: those voting = 4

ratio: total number = 5

total students = 825

Solution

Voting students = (4/5)*825

voting students = 0.8 * 825

voting students = 660            

Answer:

To maximize the income should be 28 buses and 160 cars

Step-by-step explanation:

Let

x-----> the number of cars

y ----> the number of bus

we know that

[tex]5x+32y\leq1,710[/tex] ------> inequality A

[tex]x+y\leq 189[/tex] ----> inequality B

The function of the cost to maximize is equal to

[tex]C=2x+6y[/tex]

Solve the system of inequalities by graphing

The solution is the shaded area

see the attached figure

The vertices of the solution are

(0,0),(0,53),(160,28),(189,0)

Verify

(0,53)

[tex]C=2(0)+6(53)=\$318[/tex]

(160,28)

[tex]C=2(160)+6(28)=\$488[/tex]

therefore

To maximize the income should be 28 buses and 160 cars

Answer:

There should be 30 buses in the lot to max out income

Step-by-step explanation:

Answer:

2767550

Step-by-step explanation:

looking at the number 2767545

reading number from right to left

the most right number is 0 there that is the ones digit

next right number is 4 that is the tens digit (that is what we are rounding to. we use the one right of the ten's digit to decide to round up or not. You round up if is 5 or more. So since the ones digit is 5, that is 5 or more. so we round the 4 in the ten's to a 5 and make one's 0.

---

If someone side round to nearest hundreds: it would be 2767500 because the digit directly to the right of it was a 4

Answer:

2767550.

Step-by-step explanation:

Th ten's digit is 4 and as the units digit is 5 we round up. That gives us

2767550.

Answer:

see explanation

Step-by-step explanation:

The error is in Step 1, by not adding 2 on the left side, that is

Given

7.7 = w - 2 ( add 2 to both sides )

7.7 + 2 = w - 2 + 2

9.7 = w

[tex]\dfrac{2n}{3n}=\dfrac{2\cdot \not n}{3\cdot\not n}=\dfrac{2}{3}[/tex]

The x-intercepts of the parabola are [tex]\(x = -3 + \sqrt{\frac{14}{3}}\) and \(x = -3 - \sqrt{\frac{14}{3}}\).[/tex]

To find the x-intercepts of the parabola, we need to set y=0 in the equation of the parabola and solve for x.

Given that the vertex of the parabola is [tex]\((-3, -14)\),[/tex] the equation of the parabola can be expressed in the form [tex]\(y = a(x - h)^2 + k\)[/tex], where [tex]\((h, k)\)[/tex]represents the vertex and a is the coefficient determining the direction and width of the parabola.

Using the vertex form, we have:

[tex]\[ y = a(x + 3)^2 - 14 \][/tex]

We know that the y-intercept is (0,13) so when x=0, y=13:

[tex]\[ 13 = a(0 + 3)^2 - 14 \]\[ 13 = a(9) - 14 \]\[ 13 = 9a - 14 \]\[ 9a = 13 + 14 \][/tex]

[tex]\[ 9a = 27 \]\[ a = \frac{27}{9} \]\[ a = 3 \][/tex]

So, the equation of the parabola is:

[tex]\[ y = 3(x + 3)^2 - 14 \][/tex]

Now, to find the x-intercepts, we set y=0:

[tex]\[ 0 = 3(x + 3)^2 - 14 \]\[ 3(x + 3)^2 = 14 \]\[ (x + 3)^2 = \frac{14}{3} \][/tex]

Now, we take the square root of both sides:

[tex]\[ x + 3 = \pm \sqrt{\frac{14}{3}} \][/tex]

Hello There!

The Answer Would Be 0.25

This is because you have to multiply your original number 5.8 by 0.25 to get the new dilation.

The scale factor is 0.25

Answer:

-3 degrees at 8 pm.

Step-by-step explanation:

That would be  12 - 15

= -3 degrees.

Answer:

-3

Step-by-step explanation:

The answer would be -3, because if it were to go down 15 degrees from when it was 2 PM. The equation you would have to do is 12 - 15. Which answsering that would be -3

Answer:

5/18

Step-by-step explanation:

speed = distance / time

s = (2/9 miles) / (4/5 hours)

To divide by a fraction, multiply by the reciprocal:

s = (2/9) × (5/4)

s = 10/36

s = 5/18

So the snake's speed is 5/18 miles per hour.

Final answer:

To calculate the snake's speed, you divide the distance (2/9 miles) by the time (4/5 hours), resulting in a speed of 5/18 miles per hour.

Explanation:

To calculate the snake's speed in miles per hour, we divide the distance traveled by the time taken. The snake slithers 2/9 miles in 4/5 hours, which can be written as a rate equation:

Speed = Distance ÷ Time

Plugging in the numbers, we calculate:

Speed = (2/9) miles ÷ (4/5) hours

To find the speed in miles per hour, we solve the equation:

Speed = (2/9) ÷ (4/5)

To divide one fraction by another, we multiply by the reciprocal of the divisor:

Speed = (2/9) × (5/4)

Speed = (2×5) ÷ (9×4)

Speed = 10/36

When this fraction is simplified, it equals 5/18 miles per hour.

If we want to relate it to units of m/s as the reference information suggests, we can use an online unit converter or unit analysis, considering that 1 mile per hour is approximately equal to 0.44704 meters per second.

If you cut the wire in half and pass 24 volts through it, you would measure 400 milliamps of current.

Ohm's law states that the current (I) through a wire is directly proportional to the voltage (V) and inversely proportional to the resistance (R). The formula is given by:

[tex]\[ I = \frac{V}{R} \][/tex]

If you double the voltage (V) and cut the wire in half, the length of the wire (which affects resistance) is also halved. Let's denote the original resistance as [tex]\( R_1 \)[/tex] and the halved resistance as [tex]\( R_2 \)[/tex]. The new equation becomes:

[tex]\[ I_2 = \frac{V_2}{R_2} \][/tex]

Now, since resistance is directly proportional to the length of the wire, we can write:

[tex]\[ R_2 = \frac{1}{2} \cdot R_1 \][/tex]

Substitute this into the previous equation:

[tex]\[ I_2 = \frac{V_2}{\frac{1}{2} \cdot R_1} \][/tex]

Now, let's use the information given. Initially, [tex]\( V_1 = 12 \)[/tex] volts and [tex]\( I_1 = 100 \)[/tex] milliamps. We can find [tex]\( R_1 \)[/tex] using Ohm's law:

[tex]\[ R_1 = \frac{V_1}{I_1} \][/tex]

Substitute the values:

[tex]\[ R_1 = \frac{12 \, \text{volts}}{100 \, \text{milliamps}} = 120 \, \text{ohms} \][/tex]

Now, substitute [tex]\( R_1 \)[/tex] into the equation for [tex]\( I_2 \)[/tex]:

[tex]\[ I_2 = \frac{24 \, \text{volts}}{\frac{1}{2} \cdot 120 \, \text{ohms}} \][/tex]

Simplify:

[tex]\[ I_2 = \frac{24 \, \text{volts}}{60 \, \text{ohms}} \][/tex]

[tex]\[ I_2 = 0.4 \, \text{amps} \][/tex]

To convert amps to milliamps, multiply by 1000:

[tex]\[ I_2 = 0.4 \, \text{amps} \times 1000 = 400 \, \text{milliamps} \][/tex]

Therefore, if you cut the wire in half and pass 24 volts through it, you would measure 400 milliamps of current.

By applying Ohm's law, the new current measured after cutting the wire in half and applying 24 volts is calculated to be 400 milliamps.

According to Ohm's law, the current (I) through a resistor is directly proportional to the voltage (V) and inversely proportional to the resistance (R), as described by the equation I = V / R. Given the initial conditions of 12 volts and 100 milliamps of current, we can calculate the resistance of the wire using R = V / I. The resistance (R) would then be 120 ohms.

When the wire is cut in half, the resistance is halved because resistance is directly proportional to the length of the wire. Now, with a resistance of 60 ohms and applying 24 volts across it, the new current can be calculated with Ohm's law by I = V / R, which gives us I = 24 V / 60 Ω = 0.4 A, or 400 milliamps of current.

Answer:

-5

Step-by-step explanation:

On the number line, the arrow is from -2 (opens) to the left; that means solutions will be any values less than -2

So

-5 < -2 : YES ( solutions will be any values less than -2)

-2 = -2 : NO  (solutions will be any values less than -2)

0 > -2 : NO  (solutions will be any values less than -2)

3 > -2 : NO  (solutions will be any values less than -2)

Answer

- 5

Answer:

-5

Step-by-step explanation:

First

(open circle) means < or >

 (closed circle) means < or >

SInce the arrow is pointing to the left the answer would be to the left.

So -3, -4, -5, -6, -7, -8, -9, -10etc

so -5 is one of them so thats ur answer

D ! :)

Got it wrong, and it showed me the correct answer. IT IS NOT B.

A school assembly has 179 students in it. Nine teachers escort k number of students out of the assembly, until there are 26 students remaining

The equation for the situation is given as;

26 = 179 - 9k

From the equation above, 26 is the result of the difference between "179" and "9k".

Thus, the situtation that bets represent the equation is, a school assembly has 179 students in it. Nine teachers escort k number of students out of the assembly, until there are 26 students remaining.

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Answer:

slope = - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

y = 2x + 5 is in this form with slope m = 2

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]

Answer:

Slope [tex]m_{2} = \frac{-1}{2}[/tex].

Step-by-step explanation:

Given  :  equation is y = 2x+5.

To find : What is the slope of a line perpendicular to the line.

Solution : We have given y = 2x+5.

On comparing by the slope form of line is

y = mx + b

where, m = slope , b = y-inercept.

So , [tex]m_{1}[/tex] = 2 .

When the two line are perpendicular to each other then thier slope is

[tex]m_{2} = \frac{-1}{m_{1}}[/tex].

Then plug the value of  [tex]m_{1}[/tex] = 2 .

[tex]m_{2} = \frac{-1}{2}[/tex].

[tex]m_{2} = \frac{-1}{2} [/tex].

Therefore, Slope [tex]m_{2} = \frac{-1}{2}[/tex].

-4x = -60

  x = -60 / -4

  x = 15

The answer is

x = 15