A tour boat left the dock and traveled west at an average speed of 10 mph. A smaller fishing boat left some time later traveling in the same direction but at an average speed of 12 mph. After traveling for 10 hours, the fishing boat caught up to the tour boat. The tour boat left _______ hours earlier than the fishing boat.

Answer:

The correct answer is A. Aimee's graph is correct because the ratio [tex]\frac{2}{3} :1[/tex] is equal to 2:3, which her graph shows in each point.

Step-by-step explanation:

We are given that Aimee noticed her plant grew 2/3 of an inch every week since it sprouted and a graph is drawn to show the plant growth.

We are to determine whether which of the given statements is correct.

The ratio [tex]\frac{2}{3} :1[/tex] is basically equal to 2:3. Therefore, the graph is correct as it shows the same ratio at each point.

For the points (6, 4) and (3, 2) = [tex]\frac{4-2}{6-3} =\frac{2}{3}[/tex]

Answer:

[tex]y-5=\frac{-1}{2}(x+2)[/tex] point-slope form

[tex]y=\frac{-1}{2}x+4[/tex]  slope-intercept form

Step-by-step explanation:

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

The slopes of perpendicular lines are opposite reciprocals.

The slope of y=2x-5 is 2.

So we are looking for a line perpendicular to y=2x-5 which means we first to the take the opposite reciprocal of it's slope giving us:

opposite reciprocal of (2) is opposite (1/2)=-1/2.

So the slope of the line we are looking for is -1/2.

This means are equation for our line is in this form:

[tex]y=\frac{-1}{2}x+b[/tex]

To find b we will use a point (x,y) that is on our line.

We are given a point (x,y)=(-2,5).

Plug this into our equation:

[tex]5=\frac{-1}{2}(-2)+b[/tex]

[tex]5=1+b[/tex]

Subtract 1 on both sides:

[tex]4=b[/tex]

So the equation for our line that we are looking for is:

[tex]y=\frac{-1}{2}x+4[/tex]  (slope-intercept form).

You could also go for point-slope form [tex]y-y_1=m(x-x_1)[/tex] where m is the slope and [tex](x_1,y_1)[/tex] is a point on the line.

We have m=-1/2 and (x1,y1)=(-2,5) so our equation in point slope-form is:

 [tex]y-5=\frac{-1}{2}(x-(-2))[/tex]

Simplifying just a hair:

[tex]y-5=\frac{-1}{2}(x+2)[/tex].

Answer:

(2x-7) units

Step-by-step explanation:

[tex]\tt length=\cfrac{area}{width}\\\\\\ length=\cfrac{24x^3-76x^2-28x}{12x^2+4x}=\cfrac{4x(6x^2-19x-7)}{4x(3x+1)}=\\\\\\=\cfrac{6x^2+2x-21x-7}{3x+1}=\cfrac{2x(3x+1)-7(3x+1)}{3x+1}=\\\\\\=\cfrac{(3x+1)(2x-7)}{3x+1}=2x-7[/tex]

The length of the rectangle can be found by dividing the area given as (24x³-76x²-28x) by the width given as (12x²+4x). This simplifies to 2x - 7 units which is the expression for the length of this rectangle.

In mathematics, to find the length of a rectangle when given the area and the width, you have to divide the area by the width. The area A is given as 24x³-76x²-28x square units, and the width w is given as (12x²+4x) units. Following the formula A = lw, where l is length and w is width, the length can be found by rearranging this formula to l = A/w.

Applying this to the given values: l = (24x³-76x²-28x) / (12x²+4x) simplifies to l = 2x - 7 units. Therefore, the expression for the length of the rectangle is 2x - 7 units.

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Answer:

Option A 0.496

Step-by-step explanation:

we know that

The approximate average rate of change is equal to

[tex]\frac{f(8)-f(3)}{8-3}[/tex]

[tex]\frac{f(8)-f(3)}{5}[/tex]

we have

[tex]f(x)=0.01(2^{x})[/tex]

Find f(8)

For x=8

[tex]f(8)=0.01(2^{8})=2.56[/tex]

Find f(3)

For x=3

[tex]f(8)=0.01(2^{3})=0.08[/tex]

Find the approximate average rate of change

[tex]\frac{f(8)-f(3)}{5}[/tex]

substitute

[tex]\frac{2.56-0.08}{5}=0.496[/tex]

Answer: A, 0.496

Step-by-step explanation:

To find the difference, you need to raise the base, 2, to each number since x represents the days.

Raise 2 to the power of 3:

2^3 = 8

multiply by 0.01

0.01 * 8 = 0.08

That is the growth of day three.

Now do the same with the 8

Raise 2 to the power of 8

2^8 = 256

Now multiply that by 0.01

0.01 * 256 = 2.56

Now use this formula: f(b) - f(a)/b - a

2.56 - 0.08/8 - 3

Subtract 0.08 from 2.56

2.56 - 0.08 = 2.48

Subtract 3 from 8

8 - 3 = 5

Now divide: 2.48/5 = 0.496

0.496 is the average rate of change between day 3 and day 8. Also I got 100 on the test so I know the answer :))

Answer:

Step-by-step explanation:

Unit vector is a vector with mangnitue 1 and we can find out the magnitude of the vector [tex]u = (x , y)[/tex] with the following formula

[tex]magnitude = \sqrt{x^{2}+y^{2}}[/tex]

So in the given options whichever vector has magnitude 1 it will be a unit vector.

So if we put the values in the above mentioned formula

1.Magnitude of option A is not 1 so it is not a unit vector

2.Magnitude of option B is  1 so it is a unit vector

3.Magnitude of option C is  1 so it is a unit vector

4.Magnitude of option D is not 1 so it is not a unit vector

A unit vector is of length 1 and is used to represent the positive direction on an axis in a Cartesian system. In mathematics, the i, j, and k unit vectors denote the positive directions on the X, Y, and Z axes, respectively. The magnitudes of all unit vectors are one, and they are crucial in representing directions in space.

In mathematics, a unit vector is a vector of length 1. The unit vectors in a Cartesian system are typically denoted as i, j, and k. Unit vector i signifies the positive direction on the X-axis, while unit vector j represents the positive direction on the Y-axis. In three-dimensional space, unit vector k denotes the positive direction on the Z-axis.

For example, Consider any vector A in a Cartesian coordinate system (figure 2.16). The scalar x-component of vector A is its dot product with the unit vector i, while the scalar y-component of that vector is its dot product with the unit vector j. This approach effectively expresses A in terms of the unit vectors of the axes. By their very definition, these unit vectors are dimensionless, such as their direction allows precise representations of vectors in space.

In summary, unit vectors essentially establish the directions for the system of coordinates in question. These vectors assist in expressing the direction of physical entities, such as the projection of vector A onto the x-axis or the y-axis. The magnitudes of these unit vectors are always one, so their principal significance comes from the directions they represent.

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Answer:

[tex]RS\ 8,748[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

step 1

Find the rate of interest

in this problem we have

[tex]t=8\ years\\ P=RS\ 3,560\\ A=RS\ 4,272\\r=?[/tex]

substitute in the formula above

[tex]4,272=3,560(1+8r)[/tex]

solve for r

[tex]8r=(4,272/3,560)-1[/tex]

[tex]r=[(4,272/3,560)-1]/8[/tex]

[tex]r=0.025[/tex]

convert to percentage

[tex]r=0.025*100=2.5\%[/tex]

step 2

What will be the simple interest on Rs 6480 in 14 years at the same rate of interest?

we have

[tex]t=14\ years\\ P=RS\ 6,480\\ A=?\\r=0.025[/tex]

substitute in the formula above

[tex]A=6,480(1+0.025*14)[/tex]

[tex]A=6,480(1+0.35)[/tex]

[tex]A=RS\ 8,748[/tex]

Answer: Answer should be 882.

Step-by-step explanation:

5% =0.05

840*0.05=42

840+42=882

We will have a total of 882 employees.

The percentage is defined as a ratio expressed as a fraction of 100.

For example, If Misha obtained a score of 67% on her exam, that corresponds to 67 out of 100. It is expressed as 67/100 in fractional form and as 67:100 in ratio form.

Last year at this time we had 840 employees.

Since that time our staff has increased by 5%.

We have to determine the employees will we have in total

The total employees = 840 + 5% of 840

The total employees = 840 + 0.05 × 840

The total employees = 840 + 42

The total employees = 882

Hence, there are 882 employees will we have in total.

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1 MILLIliter, namely one thousandth of a liter, meaning there are 1000 mLs in one liter.

the spoon holds 5 mL, how many are there in 1 liter? namely how many times is 5 in 1000?  simply 1000 ÷ 5 = 200.

The number of spoon that will hold 1 litre of liquid is 200 spoons.

Measurement is use to show the amount of something.

The small measuring spoon holds 5 millilitres . Therefore, the number of spoon that can hold 1 litres  can be calculated as follows;

Let's convert

1000 ml = 1 l

5 ml = 1 spoon

1000 ml = ?

number of spoon = 1000 / 5

number of spoon = 200

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Answer:

40

Step-by-step explanation:

There are 3 red bars

It states we have 24 red notebooks

24/3 = 8

Each bar represents 8 notebooks

We have 5 gold  bars

5*8 = 40

We have 40 gold notebooks

Answer:

40

Step-by-step explanation:

There are 5 gold books for every 3 red books.

You are trying to find the ratio of "x" gold books to 24 red books.

First, divide 24 with 3:

24/3 = 8

The questioner multiply 8 to the ratio's denominator. To solve completely, what you do to the denominator of the fraction, you must do to the numerator. Multiply:

5 x 8 = 40

40 gold notebooks is your answer, making the ratio 40 gold : 24 red.

~

Answer:

[tex](6,17)[/tex]

Step-by-step explanation:

we know that

In this problem

The gate hinges must be placed at the mid-point of the fence.

The formula to calculate the midpoint between two points is

[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

we have

[tex]A(4,12),B(8,22)[/tex]

substitute the values in the formula

[tex]M(\frac{4+8}{2},\frac{12+22}{2})[/tex]

[tex]M(6,17)[/tex]

Answer: (6,17)

Step-by-step explanation: Plato and Edmentum

Answer:

-7 + a = 37

Step-by-step explanation:

The value of 'a' is 44 and the equation for the statement "The sum of -7 and a is equal to 37" is -7 + a = 37

Let's start by writing the equation for the given statement:

-7 + a = 37

To find the value of 'a', we need to isolate 'a' on one side of the equation. We can do this by performing inverse operations. The inverse of subtracting 7 is adding 7. So, we will add 7 to both sides of the equation:

-7 + a + 7 = 37 + 7

On the left side, the -7 and +7 cancel out, leaving us with:

a = 44

Therefore, the value of 'a' that satisfies the given equation is 44.

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Answer:

-1.9, -1.8, and -1.7 (answers will vary)

Step-by-step explanation:

Since you have to pick a rational number that is between -2 and -1 there is an infinite options you can choose from. A rational number is a number that can be written as a fraction so you could choose a number like -1.0000000000000000000000001 and 1.999999999999999999999999.

Answer:

Option A) y=1000(1.15)^6   2313 bacteria

Step-by-step explanation:

The initial value is 1,000 and the growth factor would be the the 15%.

15% can be rewritten to .15, but you have to have to add 1 for the start to make the equation easier. Thus making the growth factor 1.15

After multiplying 1000(1.15)^6 you will get 2313.06076562 which is simplified to 2,313 bacteria.

Hope this is helpful. :)

The population of the culture 6 days after inoculation is y = 1,000(1.15) 2,313 bacteria.

According to the given statement, a growth medium exists inoculated with 1,000 bacteria.

Bacteria grow at a rate of 15% = 0.15

Add 1 to create it easier = 0.15 + 1 = 1.15

We have to estimate the population of the culture 6 days after inoculation.

[tex]= 1000(1.15)^6[/tex]

= 1000(2.313)

= 2313 bacteria

The population of the culture 6 days after inoculation = 2313 bacteria

Therefore the correct answer is y = 1,000(1.15) 2,313 bacteria.

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Answer:

Step-by-step explanation:

[tex]\begin{array}{c|c}x&f(x)\\-7&\boxed{-3}\\-3&5\\2&-4\\4&-8\end{array}[/tex]

From the table we have f(-7) = -3

Answer:

f(-7) = -3

Step-by-step explanation:

System of equations have infinitely many solution for x and y.

We have to given that,

System of equation are,

3x + 2y = 12

12x + 8y = 48

We can use the elimination method to solve,

System of equation are,

3x + 2y = 12  .. (i)

12x + 8y = 48  .. (ii)

Multiply by 4 in (i) and subtract from (ii);

12x + 8y - 12x - 8y  = 48 - 48

0 = 0

Hence, System of equations have infinitely many solution for x and y.

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Answer:

c = 6t + 19.60

Step-by-step explanation:

   Let t = the time in hours for which Beth rented the bike. Then  

       6t = the rental cost for the bike and

$19.60 = the up-front cost

The expression for the total cost (c) is

c = 6t + 19.60

The expression for the total cost is C = 19.60 + 6t. According to the given statements, time t is the variable term.

An expression is the combination of variables, coefficients, and constants. These are separated by operators like addition or subtraction. Each combination is called a term.

Given that,

Beth rented a bike from Julia's Bikes.

It cost $19.60 plus $6 per hour.

So, here the variable is time because as the time increases the cost also increases.

Consider time = t and the total cost = C

Then, the expression that represents the given statements is

C = 19.60 + 6t

∴ The expression is C = 19.60 + 6t.

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Answer: A. 47

Step-by-step explanation: The answer would be 47 degrees because the 47 degree angle has one mark, and so does x and y. This means that these angles are the same.

Answer:

he would have 10 roses left

Step-by-step explanation:

12-5=7-2=5

5+9=14-4=10

Answer:

C)

Step-by-step explanation:

To find area, You use the equation (Length × Width). If you need to find the perimeter By using the Area, You need to Divide one of the Equal Sides, since it is a square you can use either length or width, So Since it is a square, You Can also use the Square Root method. Square root is basically Dividing the number by the number it was multiplied by.

EX:

9 × 9 = 81

because

81 ÷ 9 = 9

So, If both the Length and width are 9, You add them together to get eighteen. Though since it's a square, You Can't only Count The Half of the Shape, So you multiply that by two, Leaving you with 36

Answer: C) 36 ft

To solve this equation, we need to fin out how long each side is. To do this, find the square root of 81, since it is a perfect square.

[tex]\sqrt{81 ft} = 9 ft[/tex]

So now we know that each side is 9 feet, we need to find the perimeter of the square using these dimensions.

9 ft · 4 sides = 36 ft of fencing

Therefore, Ariel needs 36 ft of fencing for her garden.

Lindsey purchased 72 coss.

Let's break down the problem:

1. Lindsey needs to buy exactly 2 pillets, and each pillet costs $1. So, she spends $2 on pillets.

2. She has $20 in total, and she spent $2 on pillets, leaving her with $20 - $2 = $18.

3. She spends the remaining $18 on coss, and 4 coss cost $1.

To find out how many coss she can buy with $18, we divide $18 by the cost of 4 coss:

$18 ÷ $1 = 18 coss × 4 coss/$1 = 72 coss

So, Lindsey purchases D. 72 coss with the remaining $18.

Complete Question:

0.5 pillets = 1 dollar

4 coss = 1 dollar

Lindsey has $20 to spend. She needs to buy exactly 2 pillets. She spends the remaining amount buying coss. How many coss does Lindsey purchase?

A. 4

В. 5

С. 64

D. 72

5a+8

Answer is NOT 5a+8

5(a+3) Multiply the bracket by 5

5(a)+5(3)

5a+15

Correct answer is supposed to be: 5a+15

Answer:

9

Step-by-step explanation:

hundreds   tens  ones  .  tenths  hundredths  thousandths  ten thousandths

9                   7       2      .    6               5                 8                       0

The 9 is in the hundreds place    

Answer:

-[tex]\sqrt{5}[/tex]

Step-by-step explanation:

A root with square root or under root is only obtained when we take the square root of both sides. Remember that when we take a square root, there are two possible answers:

For example, for the equation:

[tex]x^{2}=3[/tex]

If we take the square root of both sides, the answers will be:

[tex]x=\sqrt{3} \text{ or } x= -\sqrt{3}[/tex]

Only getting one solution with square root is not possible. Solutions with square root always occur in pairs.

For given case, the roots are 6 and [tex]\sqrt{5}[/tex]. Therefore, the 3rd root of the polynomial function f(x) had to be -[tex]\sqrt{5}[/tex]

It seems you made error while writing option B, it should be - square root of 5.

Answer:

B

Step-by-step explanation:

Answer:

The red point (-4 , -6)

Step-by-step explanation:

* Lets revise the complex number

- The complex number z = a + bi, where a is the real part and b is the

  imaginary part

- The real part represented by the x-axis and the imaginary part

  represented by the y-axis

- The value of i is √(-1)

- The complex conjugate of a complex number is the number with an

 equal real part and an imaginary part equal in magnitude but opposite

 in sign

- Ex: the conjugate of a + bi is a - bi

* Lets solve the problem

∵ A is an complex number

∵ The x-coordinate of A is -4 and the y-coordinate of it is 6

∵ The x-axis is the real axis and y-axis is the imaginary axis

∴ A = -4 + 6i

∵ The conjugate numbers are equal in real part and the imaginary

  part equal in magnitude and different in sign

∴ The conjugate of A = -4 - 6i

- From the graph The red point (-4 , -6) represents the complex

 conjugate of point A

Answer:

D. y> 1

The shaded area on the graph is y>1 but since the line is solid it is also equal to 1.

Answer:

y ≥ 1

Step-by-step explanation:

The given line is a horizontal line.

The equation of a horizontal line is y = a, where "a" is a constant.

Here the horizontal drawn at y = 1.

Therefore, the equation of line is y = 1

The solution is shaded above the line, therefore, it is y > 1

The line is a solid, therefore, the inequality that represents the solution is y ≥ 1

Answer: D) y ≥ 1

Are you sure that one of the variables is v and not y?

v+4= -2(x-1)

Since you posted v, I will use v in place of y.

v + 4 = -2x + 2

v = -2x + 2 - 4

v = -2x - 2

Done!

Answer:

The slope is 14/1, meaning you rise 14, then run 1. This is a steep slope.

Step-by-step explanation:

The slope equation is y=mx+b. The "m" in the equation is equal to the slope. In your case, 14 takes the place of the "m", making it the slope.

The slope of the equation y = 14x + 10 is 14, which means the line has a positive slope, indicating a rise of 14 units in y for each unit increase in x. The y-intercept of the line is 10.

The equation given is y = 14x + 10. To understand the slope of this linear equation, we can refer to the formula y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the number 14 is the coefficient of x, which means the slope of the line is 14. This indicates that for each unit increase in x, the value of y will increase by 14 units. Therefore, the line represented by this equation has a positive slope, which tells us that as x increases, y also increases at a constant rate. The slope is important in many fields, including economics, as it measures the relationship between two variables.

The y-intercept is the point where the line crosses the y-axis, which occurs when x equals 0. In our equation, the y-intercept is 10, indicating that the line crosses the y-axis at the point (0, 10).

Answer:

34.24 cm²

Step-by-step explanation:

You first need to find the area of the circle.

4 is radius. r*r*3.14=50.24

Now the triangle is 4*4=16.

50.24-16= 34.24

Answer:

B.

Step-by-step explanation:

The area of the shaded region will be the area of the circle minus the area of the triangle inside the circle. Then:

The circle has radius 4 cm (distance from the center to the edge of the circle), so the area of the circle is

[tex]A=\pi r^2 = 3.14(4cm)^2 = 3.14(16cm^2) = 50.24 cm^2.[/tex]

Now, the area of the triangle is

[tex]A_2 = \frac{b*h}{2}[/tex].

The base of the triangle is the diameter of the circle (as you can see in the image) and the height is the radius of the circle. Then the are of the triangle is

[tex]A_2 = \frac{8*4}{2} = \frac{32}{2} = 16cm^2[/tex].

Finally, the shaded area is [tex]A-A_2 = 50.24-16 = 34.24 cm^2[/tex].