A swimming pool is in the shape of a rectangular prism. The pool is 30 feet long, 16 feet wide, and 6 feet deep. James stretched a hose straight from a top corner of the pool to the bottom corner farthest away. What is the length of the hose from the top corner to the bottom corner farthest away? ​

Answer: x2−6x−119

Step-by-step explanation:

provided in the screenshot below

Answer:

8 student tickets and 6 adult tickets

Step-by-step explanation:

We know Mika paid $68, and we know he bought 14 movie tickets.

We also know the cost for both adult and student tickets. To find how many of each he bought, we can write the following equation:

6a + 4s = 68

(a means amount of adult tickets and s means amount of student tickets)

Since we don't know the amount of either adult or student tickets, we can guess the values and plug them into the equation.

Let's try 10 student tickets and 4 adult tickets

6(4) + 4(10) = 64

Okay, the total value isn't 64, but it's close. Let's try something close to that.

Let's try 8 student tickets and 6 adult tickets

6(6) + 4(8) = 68

We used guessing and a bit of logic to get the answer

graph{2x^2-8x-10 [-40, 40, -20, 20]} [Ans]

Answer:

x+3/5=2

or,x+0.6=2

or,x=2-0.6

x=1.4

Answer:

Refer to step-by-step

Step-by-step explanation:

Prove the following, \(\lim_{x \to \ 2} 2^{x}=4\), \(\lim_{z \to \ -1} 3^{x}=\frac{1}{3}\), and \(\lim_{x \to \ 1} e^{x-1} = 1\).

For part f:

Plug in the value of the limit, 2,

\((2)^{2} =4\)

Thus we proved the limit.

For part g:

Plug in the value of the limit, -1,

\(3^{(-1)}\)=>\(3^{-1}\)=>\(\frac{1}{3^{1} }=\frac{1}{3}\)

Thus we proved the limit.

For part h:

Plug in the value of the limit, 1,

\(e^{(1)-1}\)=>\(e^{1-1}\)=>\(e^{0}=1\)

Thus we proved the limit.

Answer:

Interest = $63

Balance = $2,063

Step-by-step explanation:

Compound Interest Formula

\(\boxed{\sf I=P\left(1+\frac{r}{n}\right)^{nt} -P}\)

where:

Given:

Substitute the given values into the formula and solve for I:

\(\implies \sf I=9000\left(1+\dfrac{0.014}{2}\right)^{2 \times 0.5}-9000\)

\(\implies \sf I=9000\left(1+0.007\right)^{1}-9000\)

\(\implies \sf I=9000\left(1.007\right)-9000\)

\(\implies \sf I=9063-9000\)

\(\implies \sf I=63\)

Therefore, the account earns $63 interest in the first six months.

The balance after six months is $2,063.

The line slants downward from left to right, indicating that as x increases, y decreases.

The given linear equation is -x = 2y + 1. To represent this equation graphically, we need to rearrange it into the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.Rearranging the given equation, we get:2y = -x - 1

Dividing both sides by 2:y = (-1/2)x - 1/2

The slope of the line is -1/2, which means that for every unit increase in x, y decreases by 1/2 unit. The y-intercept is -1/2, indicating that the line intersects the y-axis at (0, -1/2).

Based on this information, the best graph that represents the linear equation y = (-1/2)x - 1/2 is a straight line with a negative slope of -1/2, starting at the point (0, -1/2) and extending infinitely in both directions.

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Answer:

B

Step-by-step explanation:

y-y1=m(x-x1)

y-1=4(x-4)

Conniving these points and connecting them, we get a V- shaped graph that's reflected vertically and shifted 4 units to the left wing.

       To graph the function g( x) = - f( x 4), we need to start with the graph of the function f( x) = | x| and  also apply the given  metamorphoses.  The function f( x) = | x| represents the absolute value function, which is a V- shaped graph symmetric with respect to the y- axis.  

First, we shift the graph of f( x) = | x| horizontally by 4 units to the left by replacing x with( x 4). This results in f( x 4).  Next, we multiply the entire function by-1, which reflects the graph vertically. This gives us- f( x 4).  Combining these  metamorphoses, we've the function g( x) = - f( x 4). To graph g( x), we can  compass a many points and  also draw the graph by connecting them.

Let's start with the original graph of f( x) = | x| and apply the  metamorphoses

For f( x)  x = -3,-2,-1, 0, 1, 2, 3  

f( x) =  3, 2, 1, 0, 1, 2, 3  For

g( x) = - f( x 4)  x = -7,-6,-5,-4,-3,-2,-1  

g( x) = -3,-2,-1, 0,-1,-2,-3

conniving these points and connecting them, we get a V- shaped graph that's reflected vertically and shifted 4 units to the left wing.

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Both the length and width of Reagan's garden, based on the area of the square garden is 5 ft.

Reagan is said to be making a square garden in her backyard. The area of this square garden is predicted to be 25 ft².

Seeing as this is a square, it means that all sides of the garden will be the same. The length and the width will also be the same.

When given the area of a square, you can find the length and the width by the formula:
= √ area

= √ 25 ft²

= 5 ft

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Answer:

3 6/10, 5 2/5, 5 2/6, 3 3/9, 4 2/7, 6 6/8

Step-by-step explanation:

divide numerator by denominator

The length of the diameter of the sphere is 30 cm.

The surface area of a sphere is given by the formula:

\(A = 4\pi r^2\)

where A is the surface area and r is the radius of the sphere.

We are given that the surface area of the sphere is 900π cubic cm. Therefore:

\(A = 4\pi r^2 = 900\pi\)

Dividing both sides by 4π, we get:

\(r^2 = 225\)

Taking the square root of both sides, we get:

r = 15

The diameter of the sphere is twice the radius, so:

d = 2r = 30

Therefore, the length of the diameter of the sphere is 30 cm.

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Answer:

2/10*4/10=2/25 aka 0.08 aka rounded is 0.1

Step-by-step explanation:

hope this helps plz give brainliest

The two equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p include the following:

B. 2.3p – 10.1 = 6.49p – 4

C. 230p – 1010 = 650p – 400 – p

From the information provided, we have the following equation:

2.3p – 10.1 = 6.5p – 4 – 0.01p

Next, we would simplify the given equation by collecting like terms as follows;

2.3p - 10.1 = 6.5p - 0.01p - 4 = 6.49p - 4

2.3p - 10.1 = 6.49p - 4

In Mathematics, the multiplication property of equality states that both sides of an equation will remain the same and equal, when both sides of the equations are multiplied by the same number.

By multiplying both sides of the given equation by 100, we have;

100 × (2.3p - 10.1) = 100 × (6.5p - 4 - 0.01p)

230p - 1010 = 650p - 400 - p

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Using p for price and q for quantity, the demand function is; q = -3/2p + 1590

Given that at;

The monthly demand at a price of $900 = 240

The monthly demand at a price of $850 = 315

We are told that the system is a linear function. Therefore demand function would be in the form of slope intercept form as;

q = mp + c

Where;

q = quantity demanded

p = price

m = slope

c = y-intercept

At a price of $900 with a monthly demand of 240 gives the equation;

240 = 900m + c  ---(1)

At a price of $850 with a monthly demand of 315 gives the equation;

315 = 850m+ c  ------(2)

Subtracting eqn 2 from 1 gives;

-75 = 50m

m = -75/50

m = -3/2

Substituting m = -3/2 into equation 1;

240= -3/2(900) + c

c = 240 + 3/2(900)

c = 1590

Therefore the demand function can be given as; substituting m and c into equation 5, we have; q = -3/2p + 1590

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Given:

A function

Required:

Divide f(x) by 2x + 1.

Explanation:

The dividend is

and the divisor is 2x+1.

Find the remainder by substituting

in f(x).

The remainder is 0.

Final Answer:

Option B is the correct answer.

Answer:

325 mph and 420 mph

Step-by-step explanation:

If the speed of the slower plane is x, then the speed of the faster plane is x + 95.

The distance traveled by the slower plane is 3x.

The distance traveled by the faster plane is 3(x + 95).

The total distance is 2235 miles.

3x + 3(x + 95) = 2235

3x + 3x + 285 = 2235

6x = 1950

x = 325

x + 95 = 420

The speed of the planes is 325 mph and 420 mph.

Answer:

¹/₄ hr or 0.25 hrs

⁷/₆ hr or 70 mins

He will make it in time (justification below)

4.

a. False

b. True

c. False

Step-by-step explanation:

The questions are all in relation to the equation:

speed (km/hr) = distance (km)/time (hr)

It may be worth learning about how formula triangles work because I think you would find them helpful, there are videos online on this

The first question is asking about times;

Rearranging the equation/formula above, time = distance/speed;

So, we just plug in the information for each distance travelled;

The first 30 km is covered at 120 km/hr;

So, the time taken will be:

t = ³⁰/₁₂₀

This simplifies to:

t = ¹/₄ = 0.25

So, it will take ¹/₄ hr or 0.25 hrs to cover 30 km at 120 km/hr;

¹/₄ hr is the same as 15 mins

The next 56 km is covered at 48 km/hr;

So:

t = ⁵⁶/₄₈

This simplifies to:

t = ⁷/₆

So, it will take ⁷/₆ hr or 70 mins

The second question requires us to know the time taken to cover 16 km at 100 km/hr;

t = ¹⁶/₁₀₀

This simplifies to:

t = ⁴/₂₅ = 0.16

So, ⁴/₂₅ hr or 9.6 mins

If he has 15 mins to make it to school and we've just calculated it will taken 9.6 mins, then he will make it in time

4.

a.

False

Jason runs 5 km in 30 mins, which means he could run 10 km in 60 mins;

Donna runs 9 km in 60 mins, so Jason runs at a faster speed since he would cover 10 km in 60 mins

b.

True

Rachel covers 10 km in 10 mins;

Speed will be:

10/10 = 1

So, her speed is 1 km/min

An hour is 60 mins so, her speed in km/hr will be:

60 × 1 = 60

60 km/hr

This is greater than the limit 50 km/hr

c.

False

The 2 runners run the same track, this means they run the same distance;

If James takes longer, then this is because he is running slower or, in other words, Paula is running faster

d.

Can't see the full question

We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.

What is banquet?

A banquet is a large formal meal that usually involves multiple courses and is served to a group of people on special occasions such as weddings, awards ceremonies, or fundraising events. Banquets often include speeches, presentations, and entertainment, and are typically held in a large venue such as a hotel ballroom, banquet hall, or conference center. Banquets can be hosted for a variety of purposes, such as to honor a special guest, celebrate an achievement, or raise money for a charitable cause.

To create a graph showing the solution region of the system of inequalities representing the constraints of the situation, we can use custom relationships to define the variables and constraints.

Let's define the variables:

Let x be the number of adult guests.

Let y be the number of student guests.

Now, let's write the system of inequalities representing the constraints of the situation:

The total number of guests cannot exceed 125: x + y ≤ 125

The cost of hosting the banquet cannot exceed $3375: 45x + 15y ≤ 3375

To graph this system of inequalities, we can plot the boundary lines of each inequality and shade the region that satisfies all the constraints.

The boundary lines of each inequality are:

x + y = 125 (the line that connects the points (0, 125) and (125, 0))

45x + 15y = 3375 (the line that connects the points (0, 225) and (75, 0))

To find the viable combinations of guests that satisfy all the constraints, we need to shade the region that is below the line x + y = 125 and to the left of the line 45x + 15y = 3375.

The resulting graph should look like this:

The point where the two lines intersect, (75, 50), represents the maximum number of adult guests (75) and the maximum number of student guests (50) that can be invited to the banquet while staying within the budget and venue capacity. Any point within the shaded region represents a viable combination of guests.

We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.

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The following elements were included in the response: labeling x-axis as age, labeling y-axis as texting speed, plotting points according to age and texting speed, and identifying a relationship between texting speed and age.

In the response, the following elements were included:

1. Labeling the x-axis as the input variable, age: This is important to indicate the independent variable being plotted.

2. Labeling the y-axis as the output variable, texting speed: This is crucial to indicate the dependent variable being represented.

3  Plotting the points according to age and texting speed: This involves placing the ordered pairs (age, texting speed) on the coordinate plane, with age values on the x-axis and texting speed values on the y-axis.

4. Identifying a relationship between the change in texting speed as age increases: By analyzing the plotted points and examining the pattern or trend, one can determine if there is a relationship between age and texting speed. For example, if the texting speed generally increases as age increases or if there is a linear or nonlinear relationship between the two variables.

Including all of these elements allows for a comprehensive analysis of the relationship between age and texting speed, providing a visual representation and enabling the identification of any patterns or trends.

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Answer:

x = 2

Step-by-step explanation:

10x -3x + 2 +6 = 22

7x + 8 = 22

7x = 22 - 8

7x = 14

x = 14/7

x = 2

Answer:

x = 2

Step-by-step explanation:

The value of n(AUB) i.e. union of A and B is 53.

What are Intersections and Unions in Probablity?

The union of two sets results in a new set that contains all of the items from both sets. The union is abbreviated as A∪B or "A or B." The intersection of two sets yields a new set containing all of the members from both sets. The junction is denoted by the letters A∩B or "A and B."

Solution:

Given that,

n(A) = 14

n(B) = 51

n(A∩B) = 12

We know that thee formula is n(AUB) = n(A) + n(B) - n(A∩B)

Putting the values,

n(AUB) = 14 + 51 - 12 = 53

So, the answer for the value of n(AUB) = 53

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Given:

Quadrilateral STUV is a Rhombus.

Required:

The value of y.

Explanation:

The diagonals of the Rhombus are perpendicular bisectors of each other.

Therefore.

Substituting the value in the above equation, we get

Answer:

Thus the required value of y is 3.

Answer:

Step-by-step explanation: a mouse

For this problem, we are given the attendance graph of three sports centers in the span of 7 months. We need to identify which of the three centers had the largest increase in attendance during this time.

To solve the problem, we need to compare the attendance of each sports center in month 7 with their attendance in month 1.

The Coors field seems to have a growth in attendance of 2.5 horizontal bars, the Petco Park seems to have a growth in attendance of 4.8 bars and the Turner field seems to have a growth in attendance of 3.9 bars. With thi,s we conclude that Petco Park saw the highest growth in attendance.

The answer is Petco Park.

Use Pythagorean theorem:

According to question

base = 13

perpendicular = 13

So the hypotenuse is 18.38 inches

The average rate of change for the interval from x =  7 to x =  8 is 35.  

To calculate the average rate of change for the interval from x =  7 to x =  8, we need to find the difference in y- values and divide it by the difference inx-values within that interval.

Let's calculate it step by step using the given table  

For the interval from x =  7 to x =  8  x1 =  7, y1 = -37  x2 =  8, y2 = -2   Difference in y- values Δy =  y2- y1 = -2-(- 37) =  35  

Difference inx-values Δx =  x2- x1 =  8- 7 =  1  

Average rate of change =  Δy/ Δx =  35/ 1 =  35  

Thus, the average rate of change for the interval from x =  7 to x =  8 is 35.   Note: It's important to mention that the values calculated then are grounded solely on the given data. Please  insure you  corroborate the  delicacy of the  handed data and  environment before using the answer in any important or critical  operations.

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Hi there!

\(\large\boxed{\text{ P = 31ft, A = 35ft}^2}\)

Perimeter: Add up all the side lengths.

14 + 10 + 7 = 31 ft.

Area: Use the following formula:

A = 1/2(bh) where:

b = bass

h = height

Thus:

A = 1/2(10 · 7) = 35 ft²

Answer:

27.3

Step-by-step explanation:

27.3

Answer:

Plays a musical instrument

Top left

Plays a sport: 0.46

Plays a musical instrument

Top right

Does not Play a sport: 0.54

Does not play a musical instrument

Bottom Left

Plays a sport: 0.73

Does not play a musical instrument

Bottom right

Does not Play a sport: 0.27

Step-by-step explanation:

I hope this helps you! :D