A boat travels 33 miles downstream in 4 hours. The return trip takes the boat 7 hours. Find the speed of the boat in still water.

Answer:

[tex]x^2-x-1+\frac{-9}{x-3}[/tex]

Step-by-step explanation:

I prefer to use synthetic division when possible.  Here it is possible since we are dividing by a linear factor.

Since we are dividing by x-3, 3 goes on the outside.

If we were dividing by x+3, -3 goes on the outside.

3|  1    -4      2     -6

|         3      -3     -3

_______________

   1     -1       -1      -9

So the quotient is 1x^2-1x-1    +  (-9)/(x-3).

Let's simplify this and also put in the pretty math code:

[tex]x^2-x-1+\frac{-9}{x-3}[/tex]

Answer:

B there were 4 ducks living in Anoops pond when he first built it

Step-by-step explanation:

The equation is in the form

y = a b^x

The a  is the initial value at time x =0

The b is the growth rate

x is the time

So

4 * 3^t

4 is the initial amount of ducks

3 is the growth rate, or the duck population increase by a factor of 3 each time period

t is the time period in years

Answer:

[tex]x=\frac{k}{8} -\frac{c}{8} \\[/tex]

The Solution of x in the given equation [tex]8x+ c = k[/tex]  is [tex]x =\frac{k-c}{8}[/tex]

An equation with two polynomial sides or a set of polynomial equations is known as an algebraic equation or a polynomial equation. They are further divided into levels: linear formula for level one. degrees 2 quadratic equation.

Given that [tex]8x+ c = k[/tex]

[tex]8x = k-c[/tex]

[tex]x =\frac{k-c}{8}[/tex]

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Answer:

-10x+18

Step-by-step explanation:

combine like terms.

The expression 8−4x+10−6x can be simplified by adding and subtracting similar terms. Add 8+10 which gets 18. Subtract -4x - 6x which gets -10x. So, the simplified expression is 18 - 10x.

The expression given is 8−4x+10−6x. In this expression, similar terms are grouped together to simplify it. By similar terms, we mean terms that involve the same variable raised to the same power. In this case, the similar terms are -4x and -6x (the 'x' terms) and 8 and 10 (the constant terms). So let's add and subtract these similar terms.

First, add 8 and 10 to get 18.

Secondly, subtract -4x - 6x. This gives you -10x.

So, the simplified form of your expression (8−4x+10−6x) is 18 - 10x.

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Answer:

-12

Step-by-step explanation:

Slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

We are given m=-7 and a point (x,y)=(-1,-5) in on the line.

Entering this information into y=mx+b, we will be allowed enough information to find the y-intercept, b.

y =mx+b with m=-7 and (x,y)=(-1,-5):

-5=-7(-1)+b

-5=7+b

Subtract 7 on both sides:

-5-7=b

-12=b

So the y-intercept is -12.

Answer:

(x-5)

Step-by-step explanation:

factor the equation and the sign is x-5 because the equation has to be negative at the 25.

The width of the rectangle is found by dividing the area by the length, which simplifies to x - 5.

The area of a rectangle is given by the product of its length and width. Given the area is x² - 25 and the length is x + 5, you can find the width by dividing the area by the length.

So, the width = area / length = (x² - 25) / (x + 5).

Factoring the numerator gives us (x + 5) (x - 5), therefore, the width = [(x + 5) (x - 5)] / (x + 5). As you can see, (x + 5) is a common factor in the numerator and denominator so we can cancel them out.

The resulting expression for the width is x - 5.

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Answer: First Option

[tex]\frac{x(x-4)(x-1)}{2(x+4)}[/tex]

Step-by-step explanation:

We have the following expression

[tex]\frac{x^2-16}{2x+8}*\frac{x^3-2x^2+x}{x^2+3x-4}[/tex]

First factorize the denominators:

[tex]\frac{x^2-16}{2(x+4)}*\frac{x^3-2x^2+x}{(x+4)(x-1)}[/tex]

Now we factor the numerators

[tex]\frac{(x-4)(x+4)}{2(x+4)}*\frac{x(x^2-2x+1)}{(x+4)(x-1)}[/tex]

[tex]\frac{(x-4)(x+4)}{2(x+4)}*\frac{x(x-1)^2}{(x+4)(x-1)}[/tex]

now we simplify the expression

[tex]\frac{(x-4)}{2}*\frac{x(x-1)}{(x+4)}[/tex]

[tex]\frac{x(x-4)(x-1)}{2(x+4)}[/tex]

The answer  is the first option

Answer:

A on Edge

Step-by-step explanation:

Good Luck!

The table of values consists of a grouped data representing the function. The corresponding vaues of x if y is 4,2, and 9 are 16, 8 and 36

The table of values consists of a grouped data representing the function.

Given the equation y = x/4

If y = 4

4 = x/4

x = 16

If y = 2

2 = x/4

x = 8

If y = 9

9 = x/4

x = 36

Hence the corresponding vaues of x if y is 4,2, and 9 are 16, 8 and 36

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Answer:

4 integers

Step-by-step explanation:

We are given with two fractions

3/2 = 1.5  and 21/4 = 5.25

Let us draw a number line first and then we plot these two numbers on them.

Please refer to the picture attached. Here we see the number line in black line , where the integers are starting with 0. We have plotted the numbers 1.5  and 5.25  in red.

We are asked to determine the number of integers that lies between 1.5 and 5.25.

The definition of integer says , the whole numbers which be negative also including 0.

Hence we can see that there are 4 whole numbers between 1.5 and 5.25 ,

2,3,4,5

Hence our answer is 4 integer

Answer:

315 ft^2

Step-by-step explanation:

Answer: [tex]315\ ft^2[/tex]

Step-by-step explanation:

In order to calculate the area of a rectangle, you can use the following formula:

[tex]A=lw[/tex]

Where "l" is the lenght of the rectangle and "w" is the width.

In this case you know that this rectangle has a length of 21 feet and a width of 15 feet. Then:

[tex]l=21\ ft\\w=15\ ft[/tex]

Therefore, you can substitute these values into the formula, getting that the area of this rectangle is:

[tex]A=(21\ ft)(15\ ft)\\\\A=315\ ft^2[/tex]

Answer:

2 2/3 or

2.666667 inches rainfall or

8/3 inches of rainfall.

Step-by-step explanation:

Set up a proportion. Since you are going to be looking for inches of rainfall, it should go in the numerator.

2 in rainfall/9 hours = x / 12 inches.               Multiply both sides by 12

2*12 /9 = x

8/3 inches = x

2 2/3 inches should fall in 12 hours.

Answer:

2.67 in

Step-by-step explanation:

∵ In 9 hours amount of rainfall = 2 in

∴ In 1 hours amount of rainfall = 2/9 in

∴ in 12 hours amount of rainfall = (2/9) × 12

                                                  =  [tex]\frac{24}{9}[/tex] =  [tex]\frac{8}{3}[/tex]

                                                 ≈  [tex]2\frac{2}{3}[/tex] in or 2.67 in.

In 12 hours 2.67 in. rain fell.

Answer:

[tex]\pi-\bold{pi}\\\\\pi\ \text{it's the ratio of a circle's circumference to its diameter}\\\\\pi=\dfrac{\text{circumference of a circle}}{\text{circle diameter}}\\\\\pi\ \text{it's irrarional number}\\\\\pi=3.14159265358979323846264338327...\\\\\text{Approximation of}\ \pi:\\\\\pi\approx3.14\\\\\pi\approx\dfrac{22}{7}\\\\\pi\approx\dfrac{355}{113}[/tex]

The number pi occurs when calculating the surface area or volume of the rotational solids.

Cylinder:

[tex]S.A.=2\pi r^2+2\pi rH\\\\V=\pi r^2H[/tex]

Cone:

[tex]S.A.=\pi r^2+\pi rl\\\\V=\dfrac{1}{3}\pi r^2H[/tex]

Sphere:

[tex]S.A.=4\pi R^2\\\\V=\dfrac{4}{3}\pi R^3[/tex]

The number pi occurs when calculating the area and the circumference of a circle.

[tex]C=\pi d=2\pi r\\\\A=\pi r^2[/tex]

It is also used to convert angle measure in degrees to radians.

[tex]x^o=\dfrac{x\pi}{180}\ rad[/tex]

The meaning of pi is when you calculate the volume for cylinders, cone, and spheres. A cone volume shows [tex]\frac{1}{3}[/tex][tex]\pi[/tex][tex]r^2h[/tex]. You see, it shows pi. Also, pi means 3.14 in approximation, but if it was not in approximation, it would have been 3.141592654. Pi is a irrational number, since it goes on forever. For the circumference to the diameter (of a circle) formula would be [tex]\pi[/tex] = C/D. And there more about the definition of pi, it is also the sixteenth letter of the Greek alphabet, considering to be the letter P.

Hope this helped!

Nate

Answer:

D. 2

Step-by-step explanation:

Since midpoints will be involved, use multiples of 2 to name the coordinates for M and N.

Let

Then the midpoint P coordinates are

[tex]P\left(\dfrac{2a+0}{2},\dfrac{0+2b}{2}\right)\Rightarrow P(a,b)[/tex]

Use distance formula to find OP and MN:

[tex]OP=\sqrt{(a-0)^2+(b-0)^2}=\sqrt{a^2+b^2}\\ \\MN=\sqrt{(2a-0)^2+(2b-0)^2}=\sqrt{4a^2+4b^2}=2\sqrt{a^2+b^2}[/tex]

So,

MN=2OP

or

OP=1/2 MN

Answer:

The correct option is D.

Step-by-step explanation:

Given: ΔMNO is a right angled triangle with right angle ∠MON, P is midpoint of MN.

To prove: [tex]OP=\frac{1}{2}MN[/tex]

Since midpoints will be involved, use multiples of _2_ to name the coordinates for M and N.

Let the coordinates for M and N are (0,2m) and (2n,0) receptively.

Midpoint formula:

[tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

The coordinates of P are

[tex]Midpoint=(\frac{2n+0}{2},\frac{2m+0}{2})[/tex]

[tex]Midpoint=(n,m)[/tex]

The coordinates of P are (n,m).

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using distance formula, the distance between O(0,0) and P(n,m) is

[tex]OP=\sqrt{(n-0)^2+(m-0)^2}=\sqrt{n^2+m^2}[/tex]

Using distance formula, the distance between M(0,2m) and N(2n,0) is

[tex]MN=\sqrt{(2n-0)^2+(0-2m)^2}[/tex]

[tex]MN=\sqrt{4n^2+4m^2}[/tex]

On further simplification we get

[tex]MN=\sqrt{4(n^2+m^2)}[/tex]

[tex]MN=2\sqrt{(n^2+m^2)}[/tex]

[tex]MN=2(OP)[/tex]

Divide both sides by 2.

[tex]\frac{1}{2}MN=OP[/tex]

Interchange the sides.

[tex]OP=\frac{1}{2}MN[/tex]

Hence proved.

Therefore, the correct option is D.

For this case we have by definition, the GFC of two numbers is given by the largest factor that divides both numbers without leaving residue.

We have the following expression:

[tex]3p ^ 4[/tex] and [tex]4p[/tex]

So, we look for the factors of 3 and 4:

3: 1.3

4: 1, 2, 4

Thus, the GFC of both numbers is "1".

The GFC of both expressions is: [tex]1p = p[/tex]

Answer:

p

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

Explanation:

If Jack were to get really lucky and draw either

* 8 red balls in a row

* 8 green balls in a row, or,

* 8 white balls in a  row

then the answer would be 8. However, this event of drawing the same color ball 8 times in a row is fairly unlikely. What is more likely is that there will be multiple colors involved (because we have roughly the same number for each color mors or less). So consider the scenario in the next section below.

----------

If Jack were to draw a red ball first, then a green ball second, and then a white ball third, then so far has selected 3 balls from the drawer. None of the colors match up. This is leading to the worst case scenario in terms of the number of balls to select. In other words, Jack is really unlucky to not get any colors match up so far. When aiming for a guarantee like this, it is wise to think of the worst case scenario.

If we repeat the pattern (red, green, white) then so far we have 2 balls of each color. In total we have selected 6 overall. Note how 3*2 = 6.

Repeat this a third time, then we'll select 9 balls total (3*3 = 9)

The fourth iteration of this pattern has 3*4 = 12 balls overall picked out, and so on.

If we continue the pattern, then we'll see that we will need to select 3*8 = 24 balls to guarantee that we have at least 8 of the same color (eg: 8 red balls). Chances are that we'll have 8 of the same color before we hit the 24 ball mark, but we wont have a 100% guarantee of such. Reaching 24 balls is the only way to guarantee the claim is true.

So to summarize: I pictured the worst case scenario (red,green,white) and extended out the pattern so that it led to 24 as the final answer.

He would have 8 balls of one color and 7 of each of the other two colors, making a total of 23 balls, which is less than the total number of balls available.

In this problem, we have a dark room with a total of 15 red balls, 10 green balls, and 9 white balls. Jack wants to take the minimum number of balls such that he has at least 8 balls of the same color. We'll find out how many balls he needs to achieve this goal.

Let's assume Jack takes "x" balls. To find the minimum number of balls he needs to have at least 8 of the same color, we can apply the Pigeonhole Principle. This principle states that if there are "n" pigeonholes and "m" items to be placed in them, and if "m" is greater than "n," then there must be at least one pigeonhole with more than one item.

In our problem, the colors of the balls represent the pigeonholes, and the balls that Jack takes represent the items to be placed in those pigeonholes. To guarantee that at least 8 balls have the same color, we need to find the minimum value of "x" such that at least one color has 8 balls.

The worst-case scenario for the minimum number of balls needed is when Jack takes 7 balls of each color. In this case, he would have 7 red balls, 7 green balls, and 7 white balls, making a total of 21 balls. However, this is more than the total number of balls available (15 + 10 + 9 = 34).

Thus, Jack can take 8 balls to ensure that he has at least 8 balls of the same color. In the worst-case scenario, he would have 8 balls of one color and 7 of each of the other two colors, making a total of 23 balls, which is less than the total number of balls available.

So, the minimum number of balls Jack needs to take is 8.

Let "R," "G," and "W" represent the sets of red, green, and white balls, respectively.

Given:

|R| = 15, |G| = 10, |W| = 9

Let "x" be the number of balls Jack takes.

We need to find the minimum "x" such that:

max(|R∩x|, |G∩x|, |W∩x|) ≥ 8

The worst-case scenario is when Jack takes 7 balls of each color, so:

|R∩x| ≤ 7, |G∩x| ≤ 7, |W∩x| ≤ 7

Total balls available in the worst-case scenario:

Total = |R∩x| + |G∩x| + |W∩x| ≤ 7 + 7 + 7 = 21

However, Total < |R| + |G| + |W|, so Jack can take 8 balls (x = 8) to guarantee that he has at least 8 balls of the same color, and the worst-case scenario would result in a total of 23 balls, which is less than the total number of balls available.

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Answer:

A

Step-by-step explanation:

The angle adjacent to 133 and 133 form a straight angle and are supplementary, hence

adjacent angle = 180° - 133° = 47°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles. The angle 90 is an exterior angle, thus

p + 47 = 90 ( subtract 47 from both sides )

p = 43° → A

A box has six sides.

Using the dimensions of the box:

2 sides are 5 x 7

2 sides are 7 x 3

2 sides are 5 x 3

Now calculate the total area:

2 x 5 x 7 = 70

2 x 7 x 3 = 42

2 x 5 x 3 = 30

Total area = 70 + 42 + 30 = 142 square inches.

Answer:

The answer is 142 square inches.

Step-by-step explanation:

Let length be = 5

Let the width be = 7

Let the height be = 3

The gift box is a 3 D box with 6 faces.

So, we get three possible combinations, and each combination is multiplied by 2 for a parallel face.

Hence, we get;

[tex](5)(7)(2)=70[/tex] square inches

[tex](5)(3)(2)=30[/tex] square inches

[tex](7)(3)(2)=42 [tex] square inches

Therefore, the amount of gift wrap needed will be:

[tex]70+30+42=142[/tex] square inches.

Answer:

24 units

Step-by-step explanation:

As we can see in the attached picture. The area will be given by the sum of the area of the rectangle and the area of the triangle in the bottom.

The rectangle has a base of 6 units and a height of 3 units. Therefore:

A1 = bh = 6*3 = 18 units.

The triangle has a base of 6 units and a height of 2 units. Therefore:

A2 = (1/2)bh = (6*2)/ 2 = 6 units

Then, the total area is:

A = A1 + A2 = 6 + 18 = 24 units

Answer:

B = 60°; c = 30; b = 25.98

Step-by-step explanation:

1. Calculate ∠B

 ∠A + ∠B + ∠C =180°

30° + ∠B + 90° = 180°

       ∠B + 120° = 180°

                  ∠B = 60°

2. Calculate c

  sinA = a/c

sin30° = 15/c

      ½ = 15/c

       c = 2 × 15 = 30

3 .Calculate b

   sinB = b/c

sin60° = b/30

 √3/2 = b/30

       b = (30√3)/2 = 15√3 = 25.98

Answer:

189ish

Step-by-step explanation:

use a calculator

and I think that this is right...

Answer:

7/12

Step-by-step explanation:

If the probability of winning a race is 5/12, the odds in favor of winning the race is 7/12.

Probability of winning a race: 5/12 or a 5 out of 12 chance.

12 - 5 = 7

Numerator = 7

The denominator would stay 12.

Denominator = 12

Therefore, the odds of winning the race is 7/12.

Answer:

Explanation:

The exponential parent function is the most basic form of the exponential form, which is:

That is so because other expnential functions, named daughter functions, can be obtained as a stretching, compression, or translation of such parent function.

Let's see every option:

That is true: the end behavior of the function is y approaches zero from above, when x goes to negative infinite, never getting the zero value, and y increases indefintely as x goes to positive infinite, then y is always positive.

This is false: the origin is the point (0,0). When you make x = 0, you get y = a⁰ , which is 1. So instead of the origin it goes through (0, 1).

This is true: the function is defined for all the values of x, from negative infinity to positive infinity. which is all real numbers.

This is true as shown above.

Although exponential parent functions have characteristics such as a horizontal asymptote at y=0, positivity, and either exponential growth or decay, they do not have a constant slope or rate of change. This is unlike linear functions which maintain a consistent slope.

The characteristics of an exponential parent function, depicted in mathematical terms as f(x) = a*b^x, generally include several properties. Such properties include a horizontal asymptote at y=0, the function being always positive since it's above the x-axis, and it showing exponential growth if b is greater than 1, or exponential decay if b is between 0 and 1.

However, one feature that is not characteristic of an exponential parent function is having a constant slope or rate of change. The rate of change in exponential functions varies across the graph, which is contrary to linear functions that maintain a constant slope.

As an example: the function y = 2^x is an exponential one. The slope between any two points is not consistent. For instance, between x=0 and x=1, the slope would be 2, while between x=1 and x=2, the slope is 2, indicating that the rate is not constant.

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Answer:

Option D, 34.5 cm

Step-by-step explanation:

Length of arc is represented by (rθ)

Where r = radius and θ = angle at the center formed by arc in radians.

length of arc = [tex]33\times (\frac{\Theta}{180})\pi[/tex]

                     = [tex]33\times (\frac{60\pi}{180})[/tex]

                      = (33 × π/3)

                      = (11π)

                      = 11 × 3.14

                      = 34.5 cm

Option D, 34.5 cm is the answer.

Answer:

7 worms

Step-by-step explanation:

Let each can have x worms, so we can say

Luis has 4x worms

Diego has 3x + 2 worms

Cecil has 2x worms

Since, in total they have 65 worms, we can write and equation and solve:

4x + 3x + 2 + 2x = 65

9x + 2 = 65

9x = 63

x = 63/9

x = 7

There are 7 worms in each can.

Answer:

7

Step-by-step explanation:

Answer:

(4,5)

Step-by-step explanation:

The vertex is written in vertex form.

y = a(x - b)^2 + c

Vertex: (b,c)  Notice the sign change on b.

So for your equation, you get (4,5) No sign change on the 5.

Answer: (4, 5)

Proof of validity is shown below.

Answer:

2

Step-by-step explanation:

i got it right on the quiz

Points with opposite x-coordinates and the same y-coordinate are symmetrically placed with respect to the y-axis. Their distance from the y-axis is the absolute value of their x-coordinate.

If points A and B have opposite x-coordinates but the same y-coordinates, we can deduce that they are positioned symmetrically with respect to the y-axis. The distance of each point from the y-axis is equal to the absolute value of their x-coordinate. This is because the y-axis serves as a reference line where the x-coordinate is zero.

For example, if point A has coordinates (-5, 3) and point B has coordinates (5, 3), then both points are 5 units away from the y-axis. The only difference between their positions is the direction relative to the y-axis; point A is on the left side and B is on the right side.

So, the general rule is that no matter the y-coordinate, the distance of a point from the y-axis is simply the absolute value of its x-coordinate.

Answer:

James=x=15 points

Matt=4x=4×15=60 points

Emily=4x+20= (4×15)+20= 60+20=80points

Step-by-step explanation:

You should breakdown the question by writing an expression to represent the points for each person

Lets assume James had x points

So Matt had 4 times as many points as James= 4x points

Emily had 20 points more than Matt= 4x+20 points

Total number of points all together was =155

Write an expression for the total number of points all together

[tex]x+4x+4x+20=155[/tex]

Solve for x in the equation

[tex]x+4x+4x+20=155\\\\9x+20=155\\\\\\9x=155-20\\\\\\9x=135\\\\\\x=15[/tex]

Substitute values in expressions

James=x=15 points

Matt=4x=4×15=60 points

Emily=4x+20= (4×15)+20= 60+20=80points

Answer:

[tex]4,320\pi\ ft^{3}[/tex]  or  [tex]13,564.8\ ft^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the cylinder (well) is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]h=30\ ft[/tex]

[tex]r=24/2=12\ ft[/tex]

substitute

[tex]V=\pi (12)^{2}(30)[/tex]

[tex]V=4,320\pi\ ft^{3}[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]V=4,320(3.14)=13,564.8\ ft^{3}[/tex]

Answer:

Option B

Step-by-step explanation:

Given:

As per the contract "Notification of the Buyer’s intent to do so must be made by written letter or phone call to the phone number and address listed below within one business week of delinquency.”

So,buyer needs to only notify the bank about the monthly payments in case of delinquency and not about if payment is going to be late or not.

Option B is correct

Notify the bank if a payment is going to be late !

The buyer is not responsible for paying an additional $75.00 for payments made after the 15th of the month it was due; this is not specified in the contract's provided clauses.

According to the contract, the responsibility that is not a part of the buyer's obligations is option (c): Pay an additional $75.00 with a payment made after the 15th day of the month it was due. The contract stipulates that the buyer should pay the monthly payment on time (a), notify the bank if a payment is going to be late (b), and notify the bank of his or her intent to split a late payment into three partial payments (d) in the event of delinquency. However, there is no mention within the provided excerpt of the contract that indicates an additional fee of $75.00 is imposed for late payments. It is important for individuals facing financial difficulties, such as inability to make timely payments, to communicate effectively with their lenders to find potential solutions and avoid the repercussions of default.