Please quickly help me will give 100 points and brainliest!
A shipping box has dimensions as shown in the diagram. The red, dashed line represents the longest length of item that will fit inside the box. What is the length of the longest item that will fit inside the shipping box?

Enter the correct answer in the box by replacing the values of m and n.

since i don't see the graph ill go with... B The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.

-24/6 = -4

Step-by-step explanation:

The slope of the line can be found using the formula:

slope = (change in y) / (change in x)

In this case, we can use the two given points on the line: (0, 24) and (6, 0).

Change in y = 0 - 24 = -24

Change in x = 6 - 0 = 6

Therefore, slope = -24/6 = -4

This means that for every minute that passes, the swimmer completes four laps. The swimmer's pace is steady and consistent throughout the race, gradually decreasing the number of laps remaining until they finish at 0 after six minutes.

Answer:

The slope of the line represents the rate of change in the number of laps remaining per unit of time (in this case, per minute). In other words, it tells us how quickly the swimmer is completing laps.

Since the slope of the line is -4, this means that the swimmer is completing 4 laps every minute. This could be interpreted as the swimmer's pace or speed in the race. The negative sign indicates that the number of laps remaining is decreasing over time, which is expected as the swimmer completes more and more laps.

It's worth noting that the slope is constant throughout the race, meaning that the swimmer is maintaining a consistent pace. This information could be useful for the swimmer and their coach in terms of planning and pacing the race.

Answer:

We can use the formula for compound interest to find the future value (FV) of Natalie's investment:

FV = P * (1 + r/n)^(n*t)

Where:

P is the principal amount (the initial investment), which is $2,000 in this case

r is the annual interest rate as a decimal, which is 11% or 0.11

n is the number of times the interest is compounded per year, which is 12 since interest is compounded monthly

t is the number of years, which is 20

Substituting the values into the formula, we get:

FV =

2

,

000

∗

(

1

+

0.11

/

12

)

(

12

∗

20

)

�

�

=

2,000 * (1.00917)^240

FV = $18,255.74

Therefore, after 20 years of compounded monthly interest at a rate of 11%, Natalie's investment of 2,000 will be worth approximately 18,256.

Answer:

$17,870

Step-by-step explanation:

You must use the formula for compound interest.

A = P(1 + r/n)^nt

I suggest you look it up at some point so that you can do these more easily in the future!

Answer:

1/4 cup of flour and 1/8 cup of sugar. (i am estimating)

Step-by-step explanation:

Answer:

$11,170

Step-by-step explanation:

First you convert the percentage to decimal form out of 100 (which you divide)

3.9%/100 =  0.039

A = P(1 + rt)

A = 10000(1 + 0.039 * 3)     ( * = multiplication)

I = $11,170 - 10,000 = $1,170

Which you should get $1,170.00 or $1,170 (which is pretty much the same thing)

Hope this helps!

The given parallelogram is not a rectangle.

One of the tests for a rectangle is if a right angled triangle can be created by diagonally dividing the rectangle .

The test for a right - angled triangle is the Pythagorean Theorem which is :

Side ² + Side ² = Hypotenuse ²

Using, the dimensions, check to see if there is a right triangle :

7. 2 ² + 9. 1 ² = 12 ²

134. 65 ≠ 144

There is no right angled triangle so this is a parallelogram that is not a rectangle .

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Answer:

  116

Step-by-step explanation:

Given the ratio 1.2 : 29, you want x in the equivalent ratio 4.8 : x.

Equivalent ratios can be written as a proportion:

  1.2/29 = 4.8/x

Multiplying by 29x, we have ...

  1.2x = 29(4.8)

Dividing by 1.2 gives ...

  x = 29(4.8/1.2) = 29(4) = 116

The ratio is the same as 4.8 to 116.

__

Additional comment

A proportion like this can be written 4 ways. The solution takes only one step if the unknown is in the numerator.

  \(\dfrac{1.2}{29}=\dfrac{4.8}{x},\quad\dfrac{29}{1.2}=\dfrac{x}{4.8},\quad\dfrac{1.2}{4.8}=\dfrac{29}{x},\quad\dfrac{4.8}{1.2}=\dfrac{x}{29}\)

Answer:

98

Step-by-step explanation:

Answer:

$3

Step-by-step explanation:

Step-by-step explanation:

To solve the problem, we'll use the information given to find the values of A and k in the equation T = 20 + Ae^(-kt), where T is the temperature in degrees Celsius at time t.

a. Finding the value of A:

We're given that the initial temperature of the tea was 70℃. Substituting this into the equation, we get:

70 = 20 + Ae^(0) (since e^0 = 1)

70 - 20 = A

A = 50

So the value of A is 50.

b. Finding the value of k:

We're told that it takes 4 minutes for the tea to decrease in temperature from 70℃ to 50℃. We can use this information to set up an equation and solve for k.

Substituting T = 70 and t = 4 into the equation, we have:

70 = 20 + 50e^(-4k)

Subtracting 20 from both sides:

50 = 50e^(-4k)

Dividing both sides by 50:

1 = e^(-4k)

Taking the natural logarithm (ln) of both sides:

ln(1) = ln(e^(-4k))

0 = -4k

Dividing both sides by -4:

0 = k

However, we need to check if this solution satisfies the condition for the tea to decrease in temperature from 70℃ to 50℃ in 4 minutes.

Substituting T = 50 and t = 4 into the equation, we have:

50 = 20 + 50e^(-4(0))

50 = 20 + 50e^0

50 = 20 + 50(1)

50 = 20 + 50

50 = 70

Since 50 is not equal to 70, the value of k = 0 does not satisfy the given condition.

Let's try another approach:

Substituting T = 50 and t = 4 into the equation, we have:

50 = 20 + 50e^(-4k)

Subtracting 20 from both sides:

30 = 50e^(-4k)

Dividing both sides by 50:

0.6 = e^(-4k)

Taking the natural logarithm (ln) of both sides:

ln(0.6) = ln(e^(-4k))

ln(0.6) = -4k ln(e)

ln(0.6) = -4k(1)

ln(0.6) = -4k

Simplifying further:

k = ln(0.6) / -4

Using a calculator or computer to evaluate ln(3/5) / -4, we get approximately:

k = ln(5/3) / 4

To recap:

a. The value of A is 50.

b. The value of k is approximately k = ln(5/3) / 4

.

Note: The calculations provided are based on the given information and assumptions. If there are any additional details or specific conditions provided, please let me know, and I'll be happy to assist you further.

1. We can see that the number in the bottom box is: 13.5yd.

2. The number in the top box is: 7.5yd.

3. The area of the table = 78.75yd²

A trapezoid, also known as a trapezium in some countries, is a quadrilateral shape that has only one pair of parallel sides. The parallel sides of a trapezoid are called the bases of the trapezoid, and the non-parallel sides are called the legs.

We see here that in order to get the number in the bottom box, we discover that the number in the top box is a square which means that all the sides are equal to 7.5yd.

Thus, the number in the bottom box = 3 + 7.5 + 3 = 13.5yd.

Thus, the area of the table, a trapezoid = 1/2(a + b)h

Where a = 7.5yd

b = 13.5yd

height, h = 7.5yd.

Thus, A = 1/2(7.5 + 13.5) 7.5 = 157.5/2 = 78.75

∴ Area of the table, A = 78.75yd²

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The the length of each side of the triangle are: 5 units, 8.7 units and 10 units respective

A triangle is a polygon with three sides, three angles, three vertices and sum of angles equal to 180 degrees

From the triangle, Using the trigonometric ratio of sine

Sin C = opposite/Hypothenuse

Sin30 = 5/H

Making h the subject of the relation we have

h= 5/sin30

h=5/0.5

Therefore the value of h=10 units

To find the third side use Pythagoras theorem

10² = 5²+p²

100-25 = p²

75 = p²

Taking the square of both sides

p=√75

p=8.7 units

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Answer:

Step-by-step explanation:

slope intercept: y = mx + b

where m is the slope and b is the y-intercept

Equation: y = -3x + 4

Since y-intercept is given, then we have the first point of the line as (0,4)

Let's find the value of x when y is 0

y = -3x + 4

0 = -3x + 4

3x = 4

x = 4/3

(4/3,0) ---second point

Since there are two points/coordinates already then we can now plot/graph.

1. y = 5x + 15.

2. y = total cost

x = number of calendar

m = cost per calendar = slope = 5

b = initial value/y-intercept = 15

3. $1,015.

4. The equation in slope-intercept form is: y = 5x + 15

5. Slope (m) = 5

6. y-intercept (b) = 15; x-intercept = -3.

7. See attachment below for the graph.

Using the information given, we can create an equation in slope-intercept form y = mx + b, where m would be the slope and b would be the y-intercept of the linear equation.

Let,

1. To create an equation that models the situation, substitute m = 5 and b = 15 into y = mx + b:

y = 5x + 15.

2. The variables and numbers in the equation are:

y = total cost

x = number of calendar

m = cost per calendar = slope = 5

b = initial value/y-intercept = 15

3. Substitute x = 200 into y = 5x + 15

y = 5(200) + 15

y = 1,015

Total cost = $1,015.

4. The equation in slope-intercept form is: y = 5x + 15

5. The slope (m) = 5

6. The y-intercept (b) = 15

To find the x-intercept, substitute y = 0 into y = 5x + 15

0 = 5x + 15

-5x = 15

x = 15/-5

x = -3

The x-intercept = -3.

7. See attachment below for the graph.

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Answer:

x + 80 =180 (Being sum of 180 degree)

or,x=180 -80

= 100

The total number of pieces of candy is 234.

The number of bags are 9

The number of candy in each bag can be determined as,

The total pieces of candy in 5 bags can be determined as,

Thus, option (b) is the correct answer.

The experimental probability that the card selected was a K or 6 is 17/100 or 0.17.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that it is certain. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In other words, it is the ratio of the number of desired outcomes to the total number of outcomes.

The frequency of card 6 is 7 and the frequency of card K is 12. However, the card K is also counted in the total count for JQK, so we need to subtract 2 from the frequency of K to get the actual count of K.

Actual count of K = 12 - 2 = 10

Total count of 6 and K = 7 + 10 = 17

The experimental probability of drawing a K or 6 is the frequency of drawing K or 6 divided by the total number of draws:

Experimental probability = (frequency of K or 6) / (total number of draws)

Experimental probability = 17 / 100

Therefore, the experimental probability that the card selected was a K or 6 is 17/100 or 0.17.

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The number 842 is the number whose digit 4 is ten times larger than in the number 384

To solve the problem, we need to find a number in which the digit 4 is ten times larger than in the number 384.

In the number 384, the digit 4 is in the ones place, which means that its value is 4.

To find a number in which the digit 4 is ten times larger, we need to find a number in which the digit 4 is in the tens place and its value is 10 times larger than 4, which is 40.

The only answer option that fits this description is 842. In this number, the digit 4 is in the tens place and its value is 40, which is ten times larger than its value in the number 384.

Therefore, the correct answer is 842.

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Answer:

200 cans.

Step-by-step explanation:

f(c)=10r + 120

Put t=8 into it

T(c) = 10 x 8 + 120

=200 cans

(Use substitution method)

To solve the system of equation graphically we need to plot each equation on the plane. First we notice that both equation are linear, which means that their graphs are lines; this also means that to graph them we just need two points for each equation. Let's graph the equations.

First equation: y=x-2

As we said we just need two points on the line, to get them we just need to give values to x (any values we want) and plug them in the equation to get y.

If x=0, then we have:

hence the line passes through the point (0,-2)

If x=1, then we have:

hence the line passes through the point (1,-1)

With this we conclude that the line passes through the points (0,-2) and (1,-1). Plotting this points on the plane and joining them with a straight line we have the graph of the first equation:

Second equation: y=-2x-5:

We follow the same procedure as with the first equation.

If x=0 we have:

Hence the line passes through (0,-5)

If x=1 we have:

Hence the line passes through (1,-7)

Plotting this points and joining then with a line we have the graph for the second equation:

Finally, we plot both lines in the same plane. The solution of the system will be the point of intersection of the lines. The graph of the system is shown below:

From it we notice that the lines intersect at (-1,-3).

Therefore, the solution of the system is the point (-1,-3) which means that x=-1 and y=-3.

Answer:

Subtract

31

31

from both sides of the equation.

x

2

+

y

2

−

4

x

−

12

y

=

−

31

x2+y2-4x-12y=-31

Complete the square for

x

2

−

4

x

x2-4x

.

Tap for more steps...

(

x

−

2

)

2

−

4

(x-2)2-4

Substitute

(

x

−

2

)

2

−

4

(x-2)2-4

for

x

2

−

4

x

x2-4x

in the equation

x

2

+

y

2

−

4

x

−

12

y

=

−

31

x2+y2-4x-12y=-31

.

(

x

−

2

)

2

−

4

+

y

2

−

12

y

=

−

31

(x-2)2-4+y2-12y=-31

Move

−

4

-4

to the right side of the equation by adding

4

4

to both sides.

(

x

−

2

)

2

+

y

2

−

12

y

=

−

31

+

4

(x-2)2+y2-12y=-31+4

Complete the square for

y

2

−

12

y

y2-12y

.

Tap for more steps...

(

y

−

6

)

2

−

36

(y-6)2-36

Substitute

(

y

−

6

)

2

−

36

(y-6)2-36

for

y

2

−

12

y

y2-12y

in the equation

x

2

+

y

2

−

4

x

−

12

y

=

−

31

x2+y2-4x-12y=-31

.

(

x

−

2

)

2

+

(

y

−

6

)

2

−

36

=

−

31

+

4

(x-2)2+(y-6)2-36=-31+4

Move

−

36

-36

to the right side of the equation by adding

36

36

to both sides.

(

x

−

2

)

2

+

(

y

−

6

)

2

=

−

31

+

4

+

36

(x-2)2+(y-6)2=-31+4+36

Simplify

−

31

+

4

+

36

-31+4+36

.

(

x

−

2

)

2

+

(

y

−

6

)

2

=

9

(x-2)2+(y-6)2=9

This is the form of a circle. Use this form to determine the center and radius of the circle.

(

x

−

h

)

2

+

(

y

−

k

)

2

=

r

2

(x-h)2+(y-k)2=r2

Match the values in this circle to those of the standard form. The variable

r

r

represents the radius of the circle,

h

h

represents the x-offset from the origin, and

k

k

represents the y-offset from origin.

r

=

3

r=3

h

=

2

h=2

k

=

6

k=6

The center of the circle is found at

(

h

,

k

)

(h,k)

.

Center:

(

2

,

6

)

(2,6)

These values represent the important values for graphing and analyzing a circle.

Center:

(

2

,

6

)

(2,6)

Radius:

3

3

Answer:

center: (2,-6)

radius: 8

Step-by-step explanation:

trust me i checked khan academy

The table that identifies points on a line with a slope of -3 and y-intercept of -10 is:

x | y

2 | -4

4 | 2

6 | 8

8 | 14

The equation is written as y = -3x + 10

for x = -2, -3(-2) - 10 = -4

for x = -4, -3(-4) - 10 =- 2

for x = 6, -3(-6) - 10 = 8

for x = 8, -3(-8) - 10 = 14

In this table,  the x-values are given in the left column and the corresponding y-values are given in the right column.

The points (-2, -4), (-4, 2), (-6, 8) and (-8, 14) lie on the line with a slope of -3 and a y-intercept of -10.

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Answer:

8.

Step-by-step explanation:

Constant = Constant

Answer:

Step-by-step explanation:

15+5x=20x

   -5x  -5x  => Subtract 5x from each side

You get

15 = 15x

Divide both sides by 15

1=x

The features related to vectors are listed below:

Case A: u' = (- 4√41 / 41, - 5√41/ 41)

Case B: Tip coordinantes of vector v: (x, y) = (10, 10)

Case C: r = 11.402

In this question we must determine three features related to vectors: (a) unit vector, (b) the definition of a vector based on the coordinates of its base and its tip, (c) The magnitude of a resulting vector.

Case A - Unit vector

Unit vectors are vectors with magnitude 1, for the case of vector u we have the following definition:

u' = u / ||u||

Where:

Please notice that the magnitude of the vector is determined by Pythagorean theorem:

r = √[(Δx)² + (Δy)²]

Where:

Thus, the unit vector of u is:

u' = (- 4, - 5) / √[(- 4)² + (- 5)²]

u' = (- 4, - 5) / √41

u' = (- 4 / √41, - 5 / √41)

u' = (- 4√41 / 41, - 5√41/ 41)

Case B - Definition of a vector

This can be found easily by vector subtraction:

v = Tip coordinates - Base coordinates

(3, 4) = (x, y) - (7, 6)

(x, y) = (3, 4) + (7, 6)

(x, y) = (10, 10)

Case C - Magnitude of a vector

The magnitude is found by means of Pyhtagorean theorem:

r = √[(- 4 - 3)² + (- 5 - 4)²]

r = √[(- 7)² + (- 9)²]

r = 11.402

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The area of the label needed to cover the face of the box is 144 in².

To find the Area if Face we need to find the length and breadth of the rectangular faces first.

using distance formula the distance between (-6,5) & (6,5) is 12

and distance between (-6,-4) & (6,-4) is also 12.

Hence this is a rectangular box with both length and breadths as 12.

Area of the face = Length × Breadth

Area= 12×12

Area = 144 in²

What is Distance Formula?

The distance formula can be used to calculate the separation between two points on the xy-plane. The co-ordinate of a point is represented as an ordered pair (x, y), where the x-coordinate (or abscissa) is the distance from the x-axis and the y-coordinate (or ordinate) is the distance from the y-axis.

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Answer:

144 in2

Step-by-step explanation:

Answer:

27.84?

Step-by-step explanation:

17.4*1.6

If  a player hits a ball while a bird is flying across the field. The intersection points of the equations represent: C the time when the height of the ball and the bird are the same.

Intersection points  can be defined as the points in which two parallel lines meet each other.

Given data:

Height of the baseball over time = h = –16t² + 65t

Height of a bird over time = h = 8t + 20

Where:

t = time in seconds

h = height in feet

–16t² + 65t =  8t + 20

-16t² +57t -20 =0

So,

t = -57 ±√57² -4×(-16) × (-20) / 2× (-16)

t = -57±√3249  -1280/ -32

t = -57 ±√1969 /-32

t = -57 + 44.373 / -32

t =  -12.627 /-32

t =.395

And

t = -57 - 44.373 / -32

t =  -101.373 /-32

t =3.168

Based on the above of the height of both the baseball and the bird, the time when the height of the ball and the bird are the same  are the points were the two lines intersect.

Therefore the correct option is C.

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The maximum volume of the cylinder is approximately 1257 cubic centimeters.

The volume V of a right circular cylinder with radius r and height h is given by:

V = πr²h

Substituting the given expressions for the radius and height of the cylinder, we get:

V = πx²(800/πx - x)

Simplifying the expression, we get:

V = 800x - πx³

To find the maximum value of V, we need to find the value of x that maximizes V. We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

dV/dx = 800 - 3πx² = 0

3πx² = 800

x² = 800/3π

x ≈ 6.43

Substituting this value of x back into the expression for V, we get:

V ≈ 1257

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Answer:12

Step-by-step explanation: multiply the second fraction by 3 on the top and bottom to equalize the tow fractions denominators