Therefore , the solution of the given problem of function comes out to be [-3√x + 3√(x + h)] / h / √x√(x + h).
What is function?Every subject will be covered, including created and real locations as well as algebraic variable design, in the midterm test questions. a schematic illustrating the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input.
Here,
A function's difference quotient, f(x), is provided by:
=> [f(x+ h) - f(x)] / h
where h denotes a slight modification to the x-value.
The difference quotient for the function f(x) = -3/x can be calculated as follows:
=> [f(x + h) - f(x)] / h
=> [-3/√(x + h) + 3/√x] / h (substituting x + h for x in the function)
=> [-3√x + 3√(x + h)] / [h√x√(x + h)] (finding a common denominator and combining the terms)
=> [-3√x + 3√(x + h)] / h / √x√(x + h) (dividing by the denominator)
Therefore, the difference quotient of f(x) is:
=> [-3√x + 3√(x + h)] / h / √x√(x + h)
The difference fraction of f(x) is thus:
=> [-3√x + 3√(x + h)] / h / √x√(x + h)
To know more about function visit:
https://brainly.com/question/28193995
#SPJ1
Find the diameter. Round to the nearest whole number.
Answer : 14
Explanation : Divide The Circumference By π, Or 3.14 For The Answer.
Answer: 14
Step-by-step explanation:
To find the diameter, divide your circumference by pi "3.14".
43.9/3.14 = 13.9808917197
Rounded to the nearest whole number is: 14
Have a good day!
One side of a parallelogram is 30cm, and its area is 540cm². Find the height corresponding to the given side.
The height corresponding to the given side is 18cm
How to determine the heightSome of the properties of a parallelogram are given below as;
The opposite sides of a parallelogram are equal.The opposite angles of a parallelogram are congruent or equal.The measure of the sum of the interior angles are 360 degrees.The interior alternating angles are supplementary, that is, their sum is 180 degrees.The formula for calculating the area of a parallelogram is expressed as;
Area = bh
Given that;
b is the base side of the parallelogram and h is the height
Substitute the values
540 = 30h
Divide by the coefficient of h
h = 18 cm
Learn about parallelograms at: https://brainly.com/question/10744696
#SPJ1
can someone help me with this
The other leg measures 4 centimetres in length.
The right triangle in the illustration has a hypotenuse that is 5 cm long and a leg that is 3 cm long. The length of the other leg must be determined.
Applying the Pythagorean theorem, which asserts that the square of the hypotenuse's length is equal to the sum of the squares of the two legs of a right triangle, we may write:
[tex]a^2 + 3^2 = 5^2[/tex]
When we simplify this equation, we obtain:
[tex]a^2[/tex] + 9 = 25
By taking 9 away from both sides, we arrive at:
[tex]a^2[/tex] = 16
By multiplying both sides by their square roots and keeping in mind that a must be positive, we arrive at:
a = 4
Hence, the other leg is 4 cm long.
To know more about Length visit:
brainly.com/question/30100801
#SPJ9
If C(x, y) = 500 − 5xy + 12x2y, find
∂C
∂x
and
∂C
∂y
.
If
q =
6p1 + 4p2
p1 + p2
,
find
∂q
∂p1
and
∂q
∂p2
.
The answers are, For C(x, y) = 500−5xy + 12x2y, ∂C/∂x = -5y + 24xy and ∂C/∂y = -5x + 12x².
For q = 6p₁ + 4p₂ / (p₁ + p₂), ∂q/∂p₁ = -2(p₁ - p₂)/(p₁ + p₂)² and ∂q/∂p₂ = 2(p₁ - p₂)/(p₁ + p₂)².
What is functions?A function is a mathematical object that accepts one or more inputs, processes those inputs according to a predetermined procedure, and then generates an output.
The domain and range of a function are its inputs and outputs, respectively.
An equation, a graph, or a table can all be used to depict a function.
To find ∂C/∂x and ∂C/∂y for C(x, y) = 500 − 5xy + 12x²y, we differentiate C with respect to x and y, respectively, while treating the other variable as a constant:
∂C/∂x = -5y + 24xy
∂C/∂y = -5x + 12x²
To find ∂q/∂p₁ and ∂q/∂p₂ for q = 6p₁ + 4p₂ / (p₁ + p₂), we differentiate q with respect to p₁ and p₂, respectively, while treating the other variable as a constant:
∂q/∂p₁ = (4p₂ - 2p₁ - 4p₂) / (p₁ + p₂)² = -2(p₁ - p₂)/(p₁ + p₂)²
∂q/∂p₂ = (6 - 2p₁/(p₁ + p₂)) / (p₁ + p₂) - (6p₁ + 4p₂)/(p₁ + p₂)²
= 2(p₁ - p₂)/(p₁ + p₂)²
To know more about domain and range visit:
brainly.com/question/29452843
#SPJ1
Which value must be added to the expression x^2 + 12x to make it a perfect-squared trinormal?
hii
what is meant by corrosion
Answer:
Corrosion is a natural process which converts refined metal to their more stable oxide.It is the gradual destruction of materials {usually metals} by chemical reaction with their environment.In the most common use of the world, this means electrochemical oxidation of metals in reaction with an oxidant such as oxygen.
A more clear view of the graph.
Answer:
Hi! The slope is -3/2
Y intercept 2.5
(0,2.5)
Step-by-step explanation:
I hope this helps!
Answer:
The slope is [tex]\frac{-3}{2}[/tex]
The y - intercept is 2 1/2
The y-intercept point is (0, 2 1/2)
Step-by-step explanation:
If you start at the point on the left to get to the lower point on the right, you need to go down 3 units and to the right 2 units. This is the slope. Going down represents a negative number and going right represents a positive number. The slope is [tex]\frac{-3}{2}[/tex]
The y -intercpet is where the graph is cross the y axis. It looks like it is crossing between 2 and 3. So, 2 1/2 is a good estimate. Actually, I did calculate the y-intercept and it is in fact 2 1/2.
The point of the y-intercept is when x = 0
(0, 2 1/2)
Helping in the name of Jesus.
If the product of two numbers is 23 and the sum of the reciprocals is 2, what is the sum of these numbers?
Answer:
Let the two numbers be x and y. We know that:
xy = 23
We also know that:
1/x + 1/y = 2
Multiplying both sides of the second equation by xy, we get:
y + x = 2xy
Substituting the value of xy from the first equation, we get:
y + x = 2(23)
y + x = 46
Therefore, the sum of the two numbers is 46.
Step-by-step explanation:
Members of a charity organization are interested in finding ways to make it easier for individuals to donate money to their cause.
They analyze the data from their last fiscal year of donations and find that 75% of their money came from online sources. Of the 60% of donations that came from regular donors (repeat donors), approximately 95% were submitted through the organization’s website.
Is the method of donation (online vs. not online) independent from the type of donor (regular vs. new) in this sample?
We cannot determine whether the method of donation is independent from the type of donor in this sample based on the information given in the question.
Define the term statistical analysis?Statistical analysis is the process of collecting, cleaning, analyzing, and interpreting data using statistical methods and techniques. It involves summarizing and describing data, identifying patterns and relationships, testing hypotheses, and making predictions based on the data.
We cannot determine whether the method of donation (online vs. not online) is independent from the type of donor (regular vs. new) in this sample based on the information given in the question.
To determine whether two categorical variables (in this case, method of donation and type of donor) are independent, we would need to conduct a chi-square test of independence. This would involve comparing the observed frequencies of each combination of the two variables to the expected frequencies if the two variables were independent.
However, the question only provides information on the percentage of donations from online sources and the percentage of donations from regular donors that were submitted through the organization's website. It does not provide information on the percentage of donations from new donors that were submitted through the website, or the percentage of donations from regular donors that were not submitted through the website. Therefore, we cannot determine whether the method of donation is independent from the type of donor in this sample.
To know more about statistical methods, visit:
https://brainly.com/question/15525560
#SPJ1
Julia Bourne obtained an installment loan of $3,800.00 to purchase a lawn and garden tractor. She agreed to repay the loan in 24 monthly payments of $167.15. What is the APR?
The APR for the loan given is $105.8
What is APR?APR also called Annual Percentage Rate is the cost of your mortgage credit as a yearly rate.
To get the APR , we have to calculate the total amount paid in 24 months.
The total amount paid in 24 months = 24 × 167.15
= $4011.6
The principal is $3800, therefore the total interest paid in the two years is
I = A-P
I = 4011.6-3800
I = $211.6
Since APR is annual , then we need to calculate the interest for a year
yearly interest = 211.6/2
= $105.8
learn more about APR from
https://brainly.com/question/24703884
#SPJ1
Any help would be much appreciated!!
In AJKL, JK II MN. Given that MJ = 10, NK = 25, and LN = 20, find LM.
M
K
LM = 0
Answer:
please mark as brainliest
Answer:
LM = 8Step-by-step explanation:
To find:-
The value of LM .Answer:-
We are here given that JK is parallel to MN , and the values of MJ is 10 , NK = 25 and LN is 20 . We are interested in finding out the value of LM .
We can use Thale's Theorem here , according to which;
Thale's Theorem:-
If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.So here we have;
[tex]\longrightarrow \dfrac{LM}{MJ}=\dfrac{LN}{NK} \\[/tex]
On substituting the respective values, we have;
[tex]\longrightarrow \dfrac{LM}{10}=\dfrac{20}{25}\\[/tex]
[tex]\longrightarrow LM = 10\times \dfrac{20}{25}\\[/tex]
[tex]\longrightarrow\large \pmb{\underline{\boxed{ LM = 8 }}} \\[/tex]
Therefore the value of LM is 8 .
The formula to work out the distance a train travels is distance = speed x time.
A train travels at a speed of 100 km per hour for 3 hours.
How far does it travel?
help pls now i mark brainlest and 5 sta its timed
Answer:
I think its the third option
Step-by-step explanation:
because its matches both of the evidence provided
Marissa and Lauren are traveling to Niagara Falls in Canada. When they arrive at the hotel, they notice there is a $20 per day parking fee if you park your car or a $5 charge each time the valet gets your car for you. If Marissa and Lauren plan on walking everywhere except for when they visit a museum, which parking option should they choose and why?
Marissa and Lauren should choose the $5 charge each time the valet gets their car for them.
What is car?A car, also known as an automobile, is a wheeled motor vehicle used for transportation. Most definitions of cars say that they run primarily on roads, seat one to eight people, have four tires, and mainly transport people rather than goods. Cars are equipped with controls used for driving, parking, passenger comfort, and controlling a variety of lights. Over the decades, additional features and controls have been added to vehicles, making them progressively more complex.
Since they are planning on walking everywhere except for when they visit a museum, they will not need to use their car frequently, so the $20 per day parking fee would be an unnecessary expense. The $5 charge each time the valet gets their car for them will be much more cost-effective and will also save them time, as the valet will have their car ready when they need it.
To learn more about car
https://brainly.com/question/23423168
#SPJ1
Use the data in the given table to fill in the missing coefficients. Round your answers to 3 decimal places.
x y
2 8.18
6.5 12.816
11 16.768
15.5 21.222
20 26.462
24.5 31.36
29 34.584
y
=
x
+
By using the data in the given table, the missing coefficients should be filled as followed;
y = x + 6.128.
How to construct and plot the data in a scatter plot?In this scenario, the x-values would be plotted on the x-axis (x-coordinate) of the scatter plot while the y-values would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the x-values and y-values, a linear equation for the line of best fit is given by
y = x + 6.128
In conclusion, we can reasonably infer and logically deduce that the scatter plot most likely indicates a linear relationship between the x-values and y-values.
Read more on scatter plot here: brainly.com/question/28605735
#SPJ1
what percentage is more than 40%but less than 80%
Answer: 32%
Step-by-step explanation:
Find the Area of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place.
The area of the figure is 88.3 square units
How to determine the area of the figureFrom the question, we have the following parameters that can be used in our computation:
a rectangle and a semicircle
The area of the figure is calculated as
Area = Sum of areas of rectangle and semicircle.
From the figure, we have
Dimension of rectangle = 10 by 6
Semicircle = Diameter of 6
Using the above as a guide, we have the following:
Area = 10 * 6 + 3.142 * (6/2)^2
Evaluate
Area = 88.278
Approximate
Area = 88.3
Hence, the area is 88.3 square units
Read more about area at
https://brainly.com/question/22972014
#SPJ1
The function f is given by f(x) = [tex]\int\limits^x_1 {\sqrt{t^3+2} } \, dx[/tex]. What is the average rate of change of f over the interval [0,3]?
Therefore , the solution of the given problem of function comes out to be f's average rate of change over the range [0, 3] is roughly 3.862.
What is function?All of the subjects, including real and fictitious locations as well as arithmetic variable design, will be covered in the midterm exam questions. a schematic illustrating the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input.
Here,
f(b) – f(a) = average rate of change (b - a)
Since a = 0 and b = 3 in this instance, we get:
typical rate of change is equal to f(3) - f(0) /. (3 - 0)
We must assess the integral with x = 3 substituted before we can determine f(3):
From x=0 to x=3, compute f(3) = t3 + 2 dx.
By substituting u = t³ + 2, du = 3t² dt, we can assess this integral:
=> f(3) = ∫√(t³ + 2) dt evaluated from t=0 to t=3
=> (1/3) * ∫√u du evaluated from u=2 to u=29
=> (1/3) * [(2/3) * (29^(3/2) - 2^(3/2))]
=> 11.585
Simply enter x = 0 into the integral and assess it to obtain f(0):
Evaluation of f(0) = t³ + 2 dx from x=0 to x=3 = 0
Therefore, the average rate of change of f over the range [0, 3]
Average rate of change is
=> (11.585 - 0) / 3 - (f(3) - f(0))
=> 3.862
Therefore, f's average rate of change over the range [0, 3] is roughly 3.862.
To know more about function visit:
https://brainly.com/question/28193995
#SPJ1
The list below shows the scores for each of Sarah’s homework assignments.
100, 95, 47, 83, 87, 89, 89
If the score 47 is removed from the list, which of the following statements is true?
Group of answer choices
The mean will decrease.
The mean will increase by about 6.
The mean will increase by 47.
The mean will remain the same.
Answer:
i think it will decrease
Step-by-step explanation:
The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown:
Constraint Television Radio Online
Audience per advertisement 140,000 18,000 30,000
Cost per advertisement $1,500 $200 $550
Maximum media usage 15 19 12
To ensure a balanced use of advertising media, radio advertisements must not exceed 45% of the total number of advertisements authorized. In addition, television should account for at least 15% of the total number of advertisements authorized.
(a) If the promotional budget is limited to $24,100, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter “0”
8 TV advertisements, 9 radiο advertisements, and 12 οnline advertisements shοuld be run tο maximize tοtal audience cοntact.
Let x be the number οf TV advertisements, y be the number οf radiο advertisements, and z be the number οf οnline advertisements.
The οbjective is tο maximize the tοtal audience, which is given by:
Tοtal audience = 140,000x + 18,000y + 30,000z
The cοnstraints are:
Cοst cοnstraint: 1500x + 200y + 550z ≤ 24,100
TV cοnstraint: x ≥ 0.15(x + y + z)
Radiο cοnstraint: y ≤ 0.45(x + y + z)
Maximum media usage cοnstraint: x ≤ 15, y ≤ 19, z ≤ 12
Nοn-negative cοnstraint: x ≥ 0, y ≥ 0, z ≥ 0
Using a sοlver, we get the fοllοwing οptimal sοlutiοn:
x = 8, y = 9, z = 12
Therefοre, 8 TV advertisements, 9 radiο advertisements, and 12 οnline advertisements shοuld be run tο maximize tοtal audience cοntact.
Learn more about advertisements
https://brainly.com/question/29564877
#SPJ1
I WILL MARK BRAINLIEST IF ANSWERED IMMEDIATELY!
PROBLEMS SHOWN ON IMAGE :)
All three questions have to be answered like shown examples of similar problems, if you could right it out it and answer them would be even better!!
question 4)
2x^5+4x^3-6x^2-12
question 5)
3x^7-8x^6-9x^5+24x^4
question 6)
-5x^3+10x^2-3x+6
Sure hope this helps you
please help me.....................
The simplest fοrm οf the given expressiοn is A. −4(2x+1) and B. 8x + 6y − 36
What is pοlynοmials?Using variables and cοefficients, pοlynοmials are algebraic expressiοns. The term "indeterminates" is sοmetimes used tο describe variables. The terms Pοly and Nοminal, which tοgether signify "many" and "terms," make up the wοrd pοlynοmial.
When expοnents, cοnstants, and variables are cοmbined using mathematical οperatiοns like additiοn, subtractiοn, multiplicatiοn, and divisiοn, the result is a pοlynοmial (Nο divisiοn οperatiοn by a variable). The expressiοn is categοrized as a mοnοmial, binοmial, οr trinοmial based οn the number οf terms it cοntains.
A. 8(-x - 1/2)
Using distributive property
- 8x - 4
−4(2x+1)
B. -8(-x -3/4y + 9/2)
Using distributive property
8x + 6y − 36
Hence the simplest fοrm οf the given expressiοn is −4(2x+1) and 8x + 6y − 36
Learn more about polynomials, by the following link.
https://brainly.com/question/2833285
#SPJ1
what should be added to 6x²+9x-8 to obtain 4x²-8x+6 ?
Hence, in answering the stated questiοn, we may say that As a result, we equatiοn must add (2x - 1)2 + 5 tο 6x² + 9x - 8 tο get 4x² - 8x + 6.
What is equatiοn?A algebraic equatiοn is a strategy fοr linking twο prοpοsitiοns and expressing equivalence using the equals symbοl (=). A mathematical sentence that shοws the equivalency οf twο fοrmulas is knοwn as an equatiοn in algebra. In the calculatiοn 3x + 5 = 14, fοr example, the equal sign puts a space between the values 3x + 5 and 14. Tο describe the relatiοnship between the twο sentences printed alοng either side οf a letter, a mathematical fοrmula can be utilised. Usually, the insignia and the prοgramme are the same. 2x - 4 = 2, fοr example.
Tο identify what shοuld be added tο 6x² + 9x - 8 tο create 4x² - 8x + 6, we need tο undertake a methοd called "cοmpleting the square".
We can cοnclude frοm cοmparing the twο fοrmulas that a = 4, b = -8, and c = 6.
Sο we must "finish the square" by adding and remοving a term equal tο (b/2a)2. In this instance, we have:
(b/2a)² = (-8/2(4))
a² = 1
4x² - 8x + 6 + 1 - 1
(4x² - 8x + 1) + (6 - 1) (6 - 1)
(4x² - 8x + 1) is a perfect square trinοmial, which may be factοred as (2x - 1)².
As a result, the ultimate sοlutiοn is:
6x² + 9x - 8 + 1 - 1 + (2x - 1) (2x - 1)
a² + 5
As a result, we must add (2x - 1)² + 5 tο 6x² + 9x - 8 tο get 4x² - 8x + 6.
To know more about equation visit:
brainly.com/question/649785
#SPJ1
Confused about what inflection points will be on this graph:
In response to the question, we may say that The function therefore has graphs a single inflection point at x = -1.
What is graphs?Graphs are used by mathematicians to rationally represent or chart facts or values. Often, a graph point will show a connection between two or more objects. A graph is a type of non-linear data structure that is made up of nodes, or vertices, and edges. affix the nodes, also referred as as vertices. This graph includes edges E=1, 2, 1, 3, 2, 4, and (2.5) and vertices V=1, 2, 3, 5. (3.5). (4.5). graphs of exponential growth in the form of statistical charts (bar charts, pie charts, line charts, etc.). the form of a triangle-shaped logarithmic graph.
According to the graph you gave, there are two crucial spots, one at x = -1 and the other at x = 2, where the first derivative is 0 or undefined. The x-axis is divided into three intervals by these key points: (-infinity, -1), (-1, 2), and (2, infinity).
The function is rising and concave down, which means that it is curving downwards at a slower pace, on the range (-1, 2). As a result, when x = -1, there is an inflection point.
The function is rising and concave up, indicating that it is curving upwards at an increasing pace, on the interval (2, infinite). As a result, this interval lacks an inflection point.
The function therefore has a single inflection point at x = -1.
To know more about graphs visit:
https://brainly.com/question/11950136
#SPJ1
Can l get some help please
The probability of obtaining at least 1 six in 5 throws of the die is 1 - (1-p)⁵.
What is the probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen.
The probability of obtaining a six on one throw of the die is given as a fraction, say p.
We are not given the value of p, but we know that the die is biased so that the probability of obtaining a six is greater than 1/6.
The probability of not obtaining a six on one throw of the die is (1-p), since the sum of the probabilities of all possible outcomes must be 1.
To find the probability of obtaining at least 1 six in 5 throws of the die, we can use the complement rule.
This states that the probability of an event happening is equal to 1 minus the probability of the event not happening.
So, the probability of not obtaining any sixes in 5 throws of the die is:
(1-p)⁵
The probability of obtaining at least 1 six in 5 throws of the die is therefore:
1 - (1-p)⁵
This formula gives the probability of obtaining at least one six in any 5 throws of the die, regardless of the order in which the throws occur.
Note that we cannot determine the exact value of the probability without knowing the value of p, but we can use the given information that the die is biased so that the probability of obtaining a six is greater than 1/6 to conclude that the probability of obtaining at least one six in 5 throws of the die is also greater than 1/6.
Therefore, The probability of obtaining at least 1 six in 5 throws of the die is 1 - (1-p)⁵.
To learn more about the probability visit:
https://brainly.com/question/25839839
#SPJ1
Raju & akash is given to solve a mathematical problem. the probabitlity that they will solve this problem is 1/3 & 3/4 respectively. Then, find the probability that both Raju & AKAsh will solve any random problem given to them after sufficient time
Answer:
Step-by-step exp4/12lanation:
CAN SOMEONE HELPP WITH THIS QUESTION?✨
The angle of elevation represented by θ is equal to 1.13186 in radian approximately to 5 decimal place.
How to calculate for the angle of elevation θ in degreeThe angle of elevation is the angle θ between the horizontal line given as 2000 feet and the line of sight which is above the horizontal line.
The angle θ in degree is calculated, and then converted to radian as follows:
since the camera and the rocket is 4255 feet apart, then;
θ = tan⁻¹(4255/2000)
θ = 64.82482°
To convert 64.82482° to radian, we multiply by π/180
θ' = 64.82482° × π/180
θ' = 1.13186 approximately to 5 decimal place.
Therefore, the angle of elevation represented by θ is equal to 1.13186 in radian approximately to 5 decimal place.
Know more about angle of elevation here:https://brainly.com/question/25748640
#SPJ1
The teacher was correcting some math work and noticed there seemed to be a mistake. Rewrite the product below with the decimal point correctly placed. 28.7x5.29=1518.23
Answer:
151.823
Step-by-step explanation:
Answer:
Step-by-step explanation:
28.7x5.29=151.823
There are 3 numbers after the decimal points on the left of the calculation so there must be 3 numbers after thge decimal point on the right side.
The road from A to E and the road from C and D are perpendicular and intersect at point F. Theresa's house is at C, 500 feet from the intersection. Ray's house is at D, 750 feet from the intersection. Ivy's house is at E, 750 feet from the intersection.
Zanas house is at A, 500 feet from the intersection, and Tan's house is at B, 750 feet from F. Which distance is longer, the distance from Zana's house to Tan's house or the distance from Theresa's house to Is house? Show how you know.
Step-by-step explanation:
what is meant by "distance" ?
ground distance (using the roads to get there), or air distance (line of sight) ?
I have to assume we mean air distance, as the ground distance is the same in both cases (500 ft + 750 ft = 1250 ft).
for the air distance we need to use Pythagoras
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), and a and b being the legs.
Zana to Tan = AB
FB² = FA² + AB²
750² = 500² + AB²
562,500 = 250,000 + AB²
312,500 = AB²
AB = 559.0169944... ft
Theresa to Ivy = CE
CE² = CF² + FE²
CE² = 500² + 750² = 250,000 + 562,500 =
= 812,500
CE = 901.3878189...
so, the distance from Theresa to Ivy is longer.
Gertrude is making a punch for the holiday party. For every one cup of orange juice, she uses 3 cups of fruit punch. If she uses 15 cups of fruit punch, how many cups of orange juice will she be using?