Write the expression in standard form,
(9+2i)(5-3i)

Here we must write and solve a system of equations to find the speed of the boat and the speed of the stream. We will find that the boat's speed is 23km/h and the river's speed is 4km/h.

First, remember the relation:

Distance = Speed*Time.

Now let's define the variables we will be using:

When the boat travels downstream, the total speed of the boat is the speed of the boat plus the speed of the river, and we know that in that case it travels 54km in 2 hours, then:

54km = (B + R)*2h

When the boat travels upstream, we must subtract the speed of the river. In that case, we know that the boat travels 57km in 3 hours, then we have:

57km = (B - R)*3h

Then our system of equations is:

54km = (B + R)*2h

57km = (B - R)*3h

To solve this, first, we need to isolate one of the variables in one of the equations, let's isolate B in the second one:

57km = (B - R)*3h

57km/3h + R = B

19 km/h + R = B

Now we can replace that in the other equation:

54km = (B + R)*2h

54km/2h = B + R

27 km/h = B + R = (19 km/h + R) + R

Now we can solve this for R:

27 km/h = 19km/h + 2*R

27 km/h - 19km/h = 2*R

8 km/h = 2*R

(8km/h)/2 = 4km/h = R

Now that we know the value of R, we can use:

B = 19 km/h + R  = 19 km/h + 4km/h = 23 km/h

So the boat's speed is 23km/h and the river's speed is 4km/h.

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Answer:

(x - 10)(x + 2)

Step-by-step explanation:

We are looking for two things that multiply together to give us

x^2 - 10x - 20

These things are binomials, such as (x+2) or (x-7) or (x+8) or (x-5)

We know the first term in the binomial has to be x, because x times x is x^2.

And then we are looking for two numbers that multiply to -20 but also add up to -8.

-10 and 2 multiply to make -20 and add up to -8 so we pick the answer (x-10)(x+2)

Answer:

Option C

Step-by-step explanation:

x² - 8x - 20

x² - (10x - 2x) - 20

x² - 10x + 2x - 20

x(x - 10) + 2(x - 10)

(x - 10)(x + 2)

Hence

Option C is correct

Answer:

The first one

Step-by-step explanation:

SAS postulate says that if two sides and the included angle of a triangle are equal to two sides and the included angle of another triangle, then the one triangles are said to be congruent.

Answer:

Step-by-step explanation:108 divided by 12 equals 9 so nine feet next to 108 inches.

and nine divided by 3 is 3 so nine yards in the row with 108 inches.

360 divided by 12 which is 30 so 30 feet in the row with 360 inches.

90 feet divided by three so 30 so 30 yards in the row with 360 inches.

24 inches equals 2 feet

double this length is 48 inches or 4 feet

so in all he cut 6 yards and since he only had three yards you will still have  3 yards left over.

Answer:

32

Step-by-step explanation:

180 - 148 = 32

I hope this helps!

Answer:

Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 18 feet by 18 feet by 6 inches for a patio if the concrete costs $42.00 per cubic yard?

Step-by-step explanation:

I HOPE THIS HELPS

2nd X..

I hope that this is correct

Answer:

8690

Step-by-step explanation:

there is no distributive property just multiply using a regular calculator

[tex]-5x -16 = 8x -1\\\\\implies 8x +5x = -16 +1 \\\\\implies 13x = -15\\\\\implies x = -\dfrac{15}{13}[/tex]

Answer:

the answer is B

Step-by-step explanation:

on the Cartesian plane u have to think of the distance from both the positive and negative side

so 3 is 3 units from the origin and -6 is 6 units from the origin

Therefore the total length is 9 (3+6)

And B is the only answer which will give 9

Plotting the graph using geogebra online graphing tool and attaching.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

Let P represent the pressure in pounds and d represent the depth in feet.

Given the equation:

P = 0.455d + 14.3

Plotting the graph using geogebra online graphing tool and attaching.

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Answer:

8 smoothies: 4:6

2 smoothies: 1:1.5, etc.

Answer:

y=3x+4

Step-by-step explanation:

y-y1=m(x-x1)

y-(-5)=3(x-(-3))

y+5=3(x+3)

y=3x+9-5

y=3x+4

Answer:

(1) x+6

Step-by-step explanation:

Possible rational zeroes include ±1, ±2, ±3, ±4, ±6, ±12

Check each answer choice with synthetic division:

1 | 1 9 16 -12

 __1_10_26

    1 10 26 | 14

-2 | 1  9   16 -12

   __-2_-14_-4

      1  7   2  | -16

-6 | 1 9     16 -12

    __-6_-18_12

      1  3   -2  | 0

Therefore, x+6 is a factor of the polynomial

Answer:

(1) x+6

Step-by-step explanation:

Answer:

zero point zero three six

Answer:

if it's only translated left 3, then it should be A (-5, -1) B (-1, -1) and C (-1, 2)

Answer:

y = 2x - 7

Step-by-step explanation:

lmk if you want an explanation

Answer:20.75 after sale

Step-by-step explanation:

25/100 of 83 is 2075

2075/100 = 20.75

Answer:

C.24

Step-by-step explanation:

First multiply 8 by 24 this is so you know how much 24 adults would be. You will get 192 so next you need to subtract 192 from the total money 272 to get 80 and 80 should be how much all of the kids cost now to check and make sure there are 40 people divide 80 by 5 to get 16 which is the total number of kids no just add 16 and 24 together to get 40

Answer:

13,586400000000001 per time  

Step-by-step explanation:

Answer: equation: y = 2.5x + 46

slope: 2.5

y intercept: 46

she will be 8 months old by the time she is 66 cm

Step-by-step explanation: the eqation is written in y= mx+b format, where m is the slope and b is the y intercept. You can solve the last part of the problem by using this equation and subbing 66 in for y.

y = 2.5x + 46

66 = 2.5x + 46

20 = 2.5x

8 = x

Answer:

[tex]g(x)=x+8[/tex]

Step-by-step explanation:

Translating a function up is very simple, all you need to do here is add 8.

If you want to think of it logically,

[tex]f(x)=x[/tex]

the whole right side of the function here can be our output. If x is 8, then the output, or height, is also 8. if you wanted to translate that up to 10, you'd simply need to add 2 to it, meaning [tex]x+2[/tex]. Then, at any given point on the function, it'd be 2 higher than it would be otherwise.

Hey there!

(5 * 6) * 4

= 30 * 4

= 120

So you’re basically looking for something that’s equivalent to 120

CHOICE A.

5 * (5 * 6)

= 5 * 30

= 150

So, Choice A is probably NOT the answer you’re looking for!

CHOICE B.

4 * (5 * 6)

= 4 * 30

= 120

Choice B. is probably the answer you’re probably looking for.

So, I recommend you to color it apricot. :)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

[tex] \frac{(7 {x}^{2} {y}^{4} ) ^{2} }{49 {x}^{6} {y}^{5} } \\ = \frac{ {7}^{2} {x}^{2 \times 2} {y}^{4 \times 2} }{49 {x}^{6} {y}^{5} } \\ = \frac{49{x}^{4} {y}^{8} } {49 {x}^{6} {y}^{5}} \\ = {x}^{4 - 6} {y}^{8 - 5} \\ = {x}^{ - 2} {y}^{3} \\ = \frac{y ^{3} }{ {x}^{2} } [/tex]

Answer:

[tex] \frac{y ^{3} }{ {x}^{2} } [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

There are two stationary points

Note that 1/2 = 0.5

==========================================================

How to get those answers:

Stationary points occur when the derivative is zero, when the graph is neither increasing nor decreasing (i.e. it's staying still at that snapshot in time).

Apply the derivative to get:

f(x) = 4x^3 - 3x + 3

f ' (x) = 12x^2 - 3

Then set it equal to zero and solve for x.

f ' (x) = 0

12x^2 - 3 = 0

12x^2 = 3

x^2 = 3/12

x^2 = 1/4

x = sqrt(1/4) or x = -sqrt(1/4)

x = 1/2 or x = -1/2

x = 0.5 or x = -0.5

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

Let's do the first derivative test to help determine if we have local mins, local maxes, or neither.

Set up a sign chart as shown below. Note the three distinct regions A,B,C

The values -0.5 and 0.5 are not in any of the three regions. They are the boundaries.

The reason why I split things into regions like this is to test each region individually. We'll plug in a representative x value into the f ' (x) function.

To start off, we'll check region A. Let's try something like x = -2

f ' (x) = 12x^2 - 3

f ' (-2) = 12(-2)^2 - 3

f ' (-2) = 45

The actual result doesn't matter. All we care about is whether if its positive or negative. In this case, f ' (x) > 0 when we're in region A. This tells us f(x) is increasing on the interval [tex]-\infty < x < -0.5[/tex]

Let's check region B. I'll try x = 0.

f ' (x) = 12x^2 - 3

f ' (0) = 12(0) - 3

f ' (0) = -3

The result is negative, so f ' (x) < 0 when [tex]-0.5 < x < 0.5[/tex]. The f(x) curve is decreasing on this interval.

The change from increasing to decreasing as we pass through x = -0.5 indicates that we have a local max here.

Plug x = -0.5 into the original function to find its paired y coordinate.

f(x) = 4x^3 - 3x + 3

f(-0.5) = 4(-0.5)^3 - 3(-0.5) + 3

f(-0.5) = 4

The point (-0.5, 4) is a stationary point. More specifically, it's a local max.

Side note: This is the same as the point (-1/2, 4) when written in fraction form.

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

Let's check region C

I'll try x = 2

f ' (x) = 12x^2 - 3

f ' (2) = 12(2)^2 - 3

f ' (2) = 45

The positive outcome tells us that any number from region C does the same, and f ' (x) > 0 when [tex]0.5 < x < \infty[/tex]. The function f(x) is increasing on this interval.

Region B decreases while C increases. The change from decreasing to increasing indicates we have a local min when x = 0.5

Plug this x value into the original equation

f(x) = 4x^3 - 3x + 3

f(0.5) = 4(0.5)^3 - 3(0.5) + 3

f(0.5) = 2

The local min is located at (0.5, 2) which is the other stationary point.

The graph and sign chart are shown below.

The local min is located at (0.5, 2) which is the other stationary point.

Stationary points occur when the derivative is zero, when the graph is neither increasing nor decreasing.

Apply the derivative to get:

f(x) = 4x^3 - 3x + 3

f ' (x) = 12x^2 - 3

Then set it equal to zero and solve for x.

f ' (x) = 0

12x^2 - 3 = 0

12x^2 = 3

x^2 = 3/12

x^2 = 1/4

x = 1/2 or x = -1/2

x = 0.5 or x = -0.5

The first derivative test to help determine if we have local mins, local maxes, or neither.

A = numbers to the left of -0.5

B = numbers between -0.5 and 0.5 excluding both endpoints

C = numbers to the right of 0.5

Thus, The values -0.5 and 0.5 are not in any of the three regions. They are the boundaries.

Let's try something like x = -2

f ' (x) = 12x^2 - 3

f ' (-2) = 12(-2)^2 - 3

f ' (-2) = 45

In this case, f ' (x) > 0 when we're in region A.

Let's check region B x = 0.

f ' (x) = 12x^2 - 3

f ' (0) = 12(0) - 3

f ' (0) = -3

The result is negative, so f ' (x) < 0 when f(x) curve is decreasing on this interval.

The change from increasing to decreasing as we pass through x = -0.5 indicates that we have a local max here.

Substitute x = -0.5 into the original function to find its paired y coordinate.

f(x) = 4x^3 - 3x + 3

f(-0.5) = 4(-0.5)^3 - 3(-0.5) + 3

f(-0.5) = 4

The point (-0.5, 4) is a stationary point, it's a local max.

Let's check region C x = 2

f ' (x) = 12x^2 - 3

f ' (2) = 12(2)^2 - 3

f ' (2) = 45

The positive outcome tells us that any number from region C does the same, and f ' (x) > 0 when The function f(x) is increasing on this interval.

Susbtitute this x value into the original equation

f(x) = 4x^3 - 3x + 3

f(0.5) = 4(0.5)^3 - 3(0.5) + 3

f(0.5) = 2

Hence, The local min is located at (0.5, 2) which is the other stationary point.

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Answer:

The roses are sold individualy for $5.00.

Step-by-step explanation:

To find the answer, you divide 90 (the total amount) by 18 (the number of roses). Because we are doing division, you forget about the dollar sign (for now) and do the division. 90➗18=5. Since it is money, it would be $5.00

Answer:

You know that 1 mile = 5280 feet and 1 foot = 12 inches, so using these conversion factors you can go from one to the other.

I hope this answered you question!

Step-by-step explanation: