Find the slope between the following 2 coordinate points. (-3,6) and (-1,-8)

Answer:

17-i

--------

29

Step-by-step explanation:

To simply fractions with complex numbers, we have to multiply by the complex conjugate of the denominator.

The denominator is 5+2i, so the complex conjuate is 5-2i

3+i         5-2i

------  * ---------------

5+2i     5-2i

Simplifying the numerator

(3+i) * (5-2i) = 3*5 + 5i -3*2i -2i^2 = 15 +5i -6i -2(-1) = 15-i+2 = 17-i

Simplifying the denominator

(5+2i) (5-2i) = 25 -10i + 10i -4i^2 = 25 -4(-1) = 29

17-i

--------

29

Answer:

- [tex]\frac{1}{29}[/tex] i + [tex]\frac{17}{29}[/tex]

Step-by-step explanation:

to simplify the fraction ewe require to rationalise the denominator.

This is done by multiplying the numerator/ denominator by the conjugate of the denominator.

the conjugate of 5 + 2i is 5 - 2i, hence

= [tex]\frac{(3+i)(5-2i)}{(5+2i)(5-2i)}[/tex]

= [tex]\frac{15-i-2i^2}{25-4i^2}[/tex]

[ i² = ([tex]\sqrt{-1}[/tex])² = - 1 ]

= [tex]\frac{-i+17}{29}[/tex] = - [tex]\frac{1}{29}[/tex] i + [tex]\frac{17}{29}[/tex]

Answer:

30 times

Step-by-step explanation:

There's a 50% chance that they will get heads.

60 divided by 2 is 30

50% of 60 is 30

Answer:

We expect 30 heads.

Step-by-step explanation:

There are 2 sides  to a coin, heads and tails.  They are equally likely.  So the probably of getting a heads is 1/2

If we want to know how many times we will get heads, we multiply the number of flips by the probability of getting heads.

number of heads = 60 * 1/2

                              = 30

Answer:

70%

Step-by-step explanation:

We assume, that the number 550 is 100% - because it's the output value of the task.

We assume, that x is the value we are looking for.

If 100% equals 550, so we can write it down as 100%=550.

We know, that x% equals 385 of the output value, so we can write it down as x%=385.

Now we have two simple equations:

1) 100%=550

2) x%=385

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=550/385

Now we just have to solve the simple equation, and we will get the solution we are looking for.

Solution for 385 is what percent of 550

100%/x%=550/385

(100/x)*x=(550/385)*x       - we multiply both sides of the equation by x

100=1.4285714285714*x       - we divide both sides of the equation by (1.4285714285714) to get x

100/1.4285714285714=x

70=x

x=70

Answer:

Average cost per year = 400 + 180/x

Step-by-step explanation:

Using the formula y=mx+b

We know that b is the y intercept or  initial value.  That would be the start up costs

m is the slope on costs each time x increases, that would be 400 per year

Costs = 400x + 180

To find the average cost per year, we need to divide by x

Average cost per year = (400x + 180)/x

                        = 400 + 180/x

Answer:

answer to this question is f(x)  = (180 + 400x)/x

Answer:

$2000 invested in first fund

$1500 invested in second fund

Step-by-step explanation:

An investor invested a total of ​$3,500 in two mutual funds.

Let x be the amount invested in first fund

first fund earned a 4​% profit (4%= 0.04)

So interest is 0.04x for first fund

Let x be the amount invested in first fund

first fund earned a 4​% profit (4%= 0.04)

So interest is 0.04x for first fund

Let y be the amount invested in second fund

second fund earned a =2​% profit (2%= 0.02)

So interest is 0.02y for second fund

An investor invested a total of ​$3,500 in two mutual funds.

So x+y = 3500----> equation 1

y= 3500-x

the​ investor's total profit was ​$110

0.04x + 0.02y = 110----> equation 2

Plug in 3500 -x for y

0.04x + 0.02(3500-x) = 110

0.04x + 70 - 0.02x = 110

0.02x + 70 = 110

Subtract 70 onboth sides

0.02x = 40

Divide both sides by 0.02

x= 2000

y= 3500-x

so y= 3500 - 2000 = 1500

$2000 invested in first fund

$1500 invested in second fund

Answer:

15x^3+26x^2-3x+42

Step-by-step explanation:

The multiplication is 15x³ +26x² - 3x + 42.

Multiplication is the process of adding a number up to a given number.

The multiplication (3x + 7)(5x²-3x+6) is as shown:

(3x + 7)(5x²-3x+6)

= 15x³ - 9x² + 18x +35x²- 21x +42

= 15x³ +26x² - 3x + 42

Hence, the multiplication is 15x³ +26x² - 3x + 42.

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Answer:

49 inches

Step-by-step explanation:

Write and solve an equation of ratios, as follows:

7 inches               x

-------------- = -----------------

8 inches        56 inches

Then (8 ")x = (7 ")(56 "), and

x = 392/8 inches = 49 inches.

The actual width of the helicopter is 49 inches.

The actual width is found to be 49 inches, which corresponds to answer choice B.

The question is asking us to determine the actual width of a helicopter given its scale model dimensions and the actual length. To solve the problem, we use the concept of ratios or proportions. The scale model is 8 inches long and 7 inches wide, and the actual helicopter is 56 inches long.

We set up a proportion to find the actual width:

To solve for x, we cross multiply:

8 * x = 56 * 7

x = (56 * 7) / 8

x = 392 / 8

x = 49 inches

Therefore, the correct answer is B: 49 inches, which is the actual width of the real helicopter.

Answer:

Cost of 5 camera cases is $85.

Step-by-step explanation:

First we need to determine what type of function we're dealing with, is it linear, quadratic or exponential?  We can determine this by calculating the first difference.

We can translate the number of cameras to correspond to the x axis and cost to the y axis.  By doing this we can come up with the ordered pairs of (2,25), (4,59),(10,305).  Let's get the first two ordered pairs and calculate the first difference:

[tex]\frac{59-25}{4-2}=17[/tex]

And now the second and third value:

[tex]\frac{305-59}{10-4}=41[/tex]

Notice how these values do not match, this means that this function is not increasing at a constant rate meaning that this function is not linear.  Now let's calculate the second difference:

[tex]\frac{41-17}{10-2}=3[/tex]

This means our function is quadratic with a=3.  Remember that generally speaking a quadratic function is such that:

[tex]y=ax^2+bx+c[/tex]

Where a,b,c are coefficients and in this case a=3.  Now, let's solve for b and c values by using the coordinates given.  Let's use the coordinates (2,25) where x=2 and y=25 and so:

[tex]f(x)=ax^2+bx+c\\\\25=3(2)^2+b(2)+c\\25=3(4)+2b+c\\25=12+2b+c\\13=2b+c\\\\b=\frac{13-c}{2}[/tex]

Now let's solve for "c" by using different coordinates (4,59) where x=4 and y=59 and also use the "b" value that we calculated above and so:

[tex]f(x)=ax^2+bx+c\\\\59=3(4)^2+(\frac{13-c}{2})(4)+c\\59=48+\frac{52-4c}{2}+c\\11=\frac{52-4c+2c}{2}\\11=26-2c+c\\-15=-c\\\\c=15[/tex]

Now that we know the value of "c" we can use the equation for b to solve for b and so:

[tex]b=\frac{13-c}{2}=\frac{13-15}{2}\\\\b=-1[/tex]

So this means in the quadratic equation a=3, b=-1 and c=15 therefore by using the general equation of a quadratic function we obtain or final equation:

[tex]f(x)=ax^2+bx+c\\\\f(x)=3x^2-x+15[/tex]

Since we want to find the total cost of producing 5 camera cases x=5 and so:

[tex]f(x)=3x^2-x+15\\\\f(5)=3(5)^2-(5)+15\\f(5)=75-5+15\\\\f(5)=85[/tex]

And so the cost of 5 camera cases is $85.

Answer:

b=2 or b=-2.5

Step-by-step explanation:

We solve absolute value equations the same as any other equation using inverse operations. However, the inverse operation for absolute value requires one special condition. Since absolute values change a number to a positive regardless if it has a negative sign, we have two possible answers. When we have the absolute value operation isolated, we will set it equal to both the negative and positive option.  

[tex]-10-|1+4b|=-19\\-10+10-|1+4b|=-19+10\\-|1+4b|=-9\\\frac{-|1+4b|}{-1} =\frac{-9}{-1} \\|1+4b|=9[/tex]

We now have the absolute value isolated. We will set it equal to both 9 and -9.

[tex]1+4b=9\\1-1+4b=9-1\\4b=8\\b=2[/tex]

and

[tex]1+4b=-9\\1-1+4b=-9-1\\4b=-10\\b=\frac{-10}{4}=\frac{-5}{2}=  -2.5[/tex]

Answer: 1.996666666666667

Step-by-step explanation:

3ounces divided by 5.99

Answer:If you round 5.99 it would be 6.00 and then dived 3 and 6.00 its going to be 1.5 because you have to split it up

Step-by-step explanation:

Answer: 19.04 divided by 5.6 is 3.4

Step-by-step explanation:

Answer:

B. 2x^2 − x

Step-by-step explanation:

3x^2 + x − x^2 − 2x

We need to combine like terms

3x^2 -x^2+ x − 2x

2x^2 -x

The expression 3x² + x - x² - 2x simplifies to 2x² - x, which is Choice B.

To simplify the expression 3x² + x - x² - 2x, you can combine like terms. The equation has two terms involving x squared (x²) and two terms involving x to the first power.

Combine the x² terms: 3x² - x² = 2x².

Next, combine the x terms: x - 2x = -x.

Putting them together, the simplified expression is 2x² - x.

Therefore, the answer is Choice B: 2x² - x. This step-by-step process demonstrates the importance of combining like terms and simplifying expressions to arrive at the correct solution.

Answer:

Twenty Pounds

Step-by-step explanation:

Equation #1:

30lbs x Mix Price = (Lollipop Lbs  x 0.95)  + (Caramel Lbs X 1.10)

Equation #2:

Lollipops Lbs + Caramel Lbs = 30 Lbs

Rearrange expressions to solve for different variables

EQ1:   Caramel Lbs = (30 - .95 Lollipop Lbs)/ 1.10      NOTE: (mix price = 1.00)

EQ2:  Lollipop Lbs = 30 - Caramel Lbs

Substitute formula 1 into formula 2

Lollipop Lbs = 30 - [(30 - .95 Lollipop Lbs)/1.10]

Distribute divisor

Lollipop Lbs  = 30 - 27.2727 + .8636 Lollipop Lbs

Collect terms

Lollipop Lbs  =  2.7273 + .8636 Lollipop Lbs

Remove .8336 Lollipops from both sides of the equation

.1364 Lollipop Lbs = 2.7273

Divide both sides by .1364   (Answer is  19.9949 which rounds to 20)

Lollipop Lbs =  20

PROOF:

30 = (20 x 0.95) + (10 x 1.10)

30 = 19 + 11

30 = 30   TRUE!

To determine the number of pounds of lollipops in the mixture, we can set up an equation with the total weight of the mixture and the weight of the lollipops. Solving the equation, we find that there are 15 pounds of lollipops in the mixture.

To solve this problem, we can set up an equation using the given information.

Let x represent the number of pounds of lollipops in the mixture.

Since Rachel has a total of 30 pounds of the mixture, we can write the equation: x + (30 - x) = 30

Simplifying the equation, we have: 2x = 30

Dividing both sides by 2, we find that x = 15.

Therefore, there are 15 pounds of lollipops in the mixture.

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Answer:

It would be 1 and 2/5 or 1.4 per minute.

Step-by-step explanation:

Answer:

31/40

Step-by-step explanation:

LCD = 40

Multiplying numerators and denominators to get the LCD in all fraction denominators

Then rewriting the equation with the equivalent fractions

With like denominators we can operate on just the numerators

Answer:

31/40

Step-by-step explanation:

3/8+2/5

First make them both have same denominator:

3/8  8 x 5= 40 3 x 5=15/40

2/5  5 x 8=40 2x8=16 16/40

15/40+16/40=31/40

Answer:

sqrt(x)

Step-by-step explanation:

1/ ( x^(-3/6))

We can simplify the fraction

1/ ( x^(-1/2))

A negative exponent means that since it is in the denominator, it goes to the numerator.  It still keeps the exponent.

x^ (1/2)

sqrt(x)

Answer:

x = - 3, x = 2

Step-by-step explanation:

Since x = 1 is a zero then (x - 1) is a factor of the polynomial

dividing x³ - 7x + 6 ÷ (x - 1)

= (x - 1)(x² + x - 6)

= (x - 1)(x + 3)(x - 2)

equating (x + 3)(x - 2) = 0 gives the other zeros

equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 2 = 0 ⇒ x = 2

Hey there!

"Which quantity is proportional to [tex]\frac{35}{80}[/tex]?"

The easier way, I figured out how to solve  this particular problem is simplify the fraction to decimal

[tex]\frac{35}{80}[/tex] [tex]= 0.4375[/tex]

[tex]\boxed{Answer: \frac{21}{48} AND \frac{7}{16}}[/tex]

Good luck on  your assignment and enjoy your day!

~[tex]LoveYourselfFirst:)[/tex]

Answer:

3/5 no

14/36 no

26/52 no

21/48 yes

7/16 yes

Step-by-step explanation:

For the 1st question, the answer is A) Distributive Property:

The reason why Step 1 is A) Distributive Property is because you're distributing 2 to the #'s that are in the parenthesis().

For the 2nd question, it's either A) Reflexive Property or C) Symmetric Property...

Y = 3x

Y = x+2

set the two y's equal to each other

3x=x+2

Isolate the x

2x=2

divide

ANSWER: x=1 y=3 or (1,3)

Answer:the anwser is  (3,9)

Step-by-step explanation:I orgainly thought 1,3

Answer:

4 people voted for hot dogs

Step-by-step explanation:

20-6-10=4

Answer:

Not sure what your exact question is, but I'll make an assumption that you are asking for the percentages of each statistic. It's going to be:

30% pizza

50% chicken

20% hot dogs

Step-by-step explanation:

Because you have 20 members, to get a total percentage, I divided by 2 to get to 10, which is going to make it easier to determine the percentages.

Next, because you divided the total players by 2, you have to do the same for each of the votes as well. Six becomes three, 10 becomes 5, and the rest (which is four) becomes two.

Now, you need to multiply by 10 to get the exact percentage. 10 becomes 100%, and the same for all the other numbers.

Hope this helps!

Answer:

20% tip

Step-by-step explanation:

Dinner:  $48.00

Tax:  0.05($48.00) = $2.40

Total (final) bill before tip:  $50.40

Tip:  $10.08

Percentage tip was then $10.08 (100%) / $50.40 = 20%

The family left a 20% tip.

Answer:

15/100

Step-by-step explanation:

If the the number as a decimal is in the hundredths place you put the number over 100

Answer:

it's 1/3

Step-by-step explanation:

5/6+(-1/2)

5/6-1/2

LCM= 6

(5-3)/6

2/6

1/3

Answer:

the original price is $28.57

Step-by-step explanation:

If the discount is 30% then the amount paid is 70% of the original price. Sally paid $20, it is the discounted price, equivalent to 70%.

We need to divide $20 by 70% to get the original price or the 100%.

$20 / 70% = $28.57 original price.

Since the handbag was has discount of 30%, we multiply the original price with the 30% to get the discount value.

$28.57 * 30% = $8.57 discount

To check: deduct the discount from the original price to get the discounted price.

$28.57 - $8.57 = $20

Answer:

2 x^2 (2 x - 3) (x^2 + 1)

Step-by-step explanation:

Factor the following:

4 x^5 - 6 x^4 + 4 x^3 - 6 x^2

Factor 2 x^2 out of 4 x^5 - 6 x^4 + 4 x^3 - 6 x^2:

2 x^2 (2 x^3 - 3 x^2 + 2 x - 3)

Factor terms by grouping. 2 x^3 - 3 x^2 + 2 x - 3 = (2 x^3 - 3 x^2) + (2 x - 3) = x^2 (2 x - 3) + (2 x - 3):

2 x^2 x^2 (2 x - 3) + (2 x - 3)

Factor 2 x - 3 from x^2 (2 x - 3) + (2 x - 3):

Answer:  2 x^2 (2 x - 3) (x^2 + 1)

Answer:

[tex]2x^{2} (2x-3)(x^{2} +1)[/tex]

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

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

  = (-5--5)/ (9--8)

 = (-5+5)/(9+8)

 = 0/17

=0

The slope it 0

This is a horizontal line because the y value doesn't change.  If the y value doesn't change, the slope it zero.

Answer:

[tex]y=-2cos (2(x+\pi ))-1[/tex]

Step-by-step explanation:

From the graph, we can see that y = -3 when x  = 0.

So to check whether which of the given options is the equation of the given graph, we will set our calculator to the radian mode and then plug the value of x as 0.

1. y = -2 cos (4(x + pi)) - 1 = -2 cos (4(0 + pi)) - 1  = 3

2. y = 2 cos(x + pi) = 2 cos(0 + pi) = -1

3. y = -2 cos (2(x + pi)) - 1 = -2 cos (2(x + pi)) - 1 = -3

Therefore, the equation of this graph is  y = -2 cos (2(x + pi)) - 1.