The length of the larger piece lies in the interval [102.85 , 180) and the length of the smaller piece lies in the interval [0 , 77.15]
What is an interval?In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between.
Given here, that 3 times the larger piece is greater than 4 times the smaller piece. let the length of the larger piece be x and length of the smaller piece be 180-x, then we get the following inequality-
3x > 4(180-x)
3x>720-4x
7x>720
x>102.85
therefore 102.85≤ x <180
Hence, the larger piece lies in the interval [102.85 , 180) and the length of the smaller piece lies in the interval [0 , 77.15]
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Edna brought 4 pies to a party. At the end of the evening 1 and 5/8 pie was left over. How much pie did the guest eat?
Is this the correct way to fill out this deposit slip? (For an assignment) I have yet to put my name and date
Compare 7/8 with 14/16 using (<,>,=)
The required 7/8 is equal to 14/16, or we can write 7/8 = 14/16.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.
Here,
To compare 7/8 and 14/16, we can first convert both fractions to a common denominator. The least common multiple of 8 and 16 is 16, so we can convert 7/8 to 14/16 by multiplying both the numerator and denominator of 7/8 by 2,
7/8 = (7 × 2) / (8 × 2) = 14/16
Now we can see that both fractions have the same denominator, so we can compare their numerators directly:
7/8 = 14/16
Therefore, 7/8 is equal to 14/16, or we can write 7/8 = 14/16.
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An investor wants to complain that the stock market continues to drop. What might they do to the graph shown to try to convince an audience that this is true?
A:) use a smaller range on the vertical scale
B:) use a larger range on the vertical scale
C:) omit numbers on the horizontal scale
Answer:
omit numbers on the horizontal scale
Terry wants to tip 15% to the waiter at a restaurant this means he will multiply the cost by 0.15 if this meal costs 18.10 how much did he tip the waiter
just as the problem states, multiply the cost (18.10) by 0.15
18.10 * 0.15 = 2.72
the tip was $2.72
The metric system is easy to use because it is based on units of ten. how many centimeters are there in 100 meters?
Is this function even, odd, or neither?
What is the area of trapezoid ABCD? Enter your answer as a decimal or whole number in the box. Do not round at any steps
Lakshmi has had a checking account for over twenty years and has always gotten money from her bank by cashing a check. She would like a more convenient method of getting cash, without having to visit the bank each time she needs to withdraw money. What type of card would she get. A. Cash card. B. Credit card. C. Debit card. D. Store gift card
Find quadratic equation from 3 points calculator
To find the quadratic equation from 3 points, use the method of substitution and solve the system of equations. Substituting the given points into the general quadratic equation will result in a system of equations that can be solved for the quadratic equation.
Explanation:To find the quadratic equation from 3 points, we can use the method of substitution. Let's say the three points are (x1, y1), (x2, y2), and (x3, y3). We can substitute these points into the general quadratic equation, y = ax^2 + bx + c, to get three equations. Solving this system of equations will give us the values of a, b, and c, and thus the quadratic equation.
For example, let's say the three points are (1, 3), (2, 6), and (3, 11). Substituting these points into the general quadratic equation, we get the following equations:
3 = a(1^2) + b(1) + c
6 = a(2^2) + b(2) + c
11 = a(3^2) + b(3) + c
Solving this system of equations will give us the values of a, b, and c, and thus the quadratic equation.
Bryan is buying notebooks and pens at an office
supply store. Notebooks cost $3.59 each and pens
cost $1.49 each. Bryan spent a total of $13.
Let x represent the number of notebooks and let y
represent the number of pens.
Write an equation that represents this situation.
How many real solutions does the equation have?
r2 – 94 = 0
The quadratic equation r² – 94 = 0 has two real solutions, as the discriminant is positive when applying the quadratic formula.
Explanation:The question deals with the quadratic equation r2 – 94 = 0. To determine how many real solutions this equation has, we can rearrange it into the standard quadratic form ar2 + br + c = 0, where a = 1, b = 0, and c = -94. The real solutions of a quadratic equation are found using the quadratic formula, which is r = −b ± √(b2 - 4ac) / (2a). In this case, the discriminant (b2 – 4ac) becomes (02 – 4(1)(-94)) which simplifies to 376. This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 1, b = 0, and c = -94. To find the number of real solutions, we need to determine the discriminant, which is given by the formula: discriminant = b² - 4ac. If the discriminant is greater than zero, the equation has two real solutions. If the discriminant is equal to zero, the equation has one real solution. If the discriminant is less than zero, the equation has no real solutions. In this case, the discriminant is: 0 - 4(1)(-94) = 376. Since the discriminant is greater than zero, the equation r² - 94 = 0 has two real solutions. Since the discriminant is positive, this equation has two real solutions.
The equation has two real solutions.
Explanation:This expression is a quadratic equation of the form where the constants are To find the number of real solutions, we can use the discriminant, which is given by . If Δ > 0, there are two real solutions. If Δ = 0, there is one real solution. If Δ < 0, there are no real solutions. Let's calculate the discriminant:
Δ = 0² - 4(1)(-94) = 376
Since Δ > 0, the equation has
what is 13n-6p-11n=2p solve for n
What is the vertex form of f(x)=x^2+24x+138
Answer:
(x +12)^2 - 6
Step-by-step explanation:
d/dx x^2 + 24x + 138 = 2x + 24
when 2x + 24 = 0, the gradient = 0
x = -12
f(-12) = -6
therefore we have (x +12)^2 - 6.
The 24 students in Mr. Brown’s homeroom sold 72 magazine subscriptions. The 28 students in Mrs. Garcia‘s homeroom sold 98 magazine subscriptions. Whose homeroom sold more magazine subscriptions per student? Explain your reasoning.
What method would you choose to solve the equation 2x^2-7=9
1. A recipe calls for cups of flour, cup of white sugar, and cup of brown sugar. The recipe makes 6 servings.
(a) How many cups of flour are there per serving? Show your work.
(b) How many total cups of sugar (white and brown) are there per serving? Show your work.
(c) Suppose you modify the recipe so that it makes 9 servings. How much more flour do you need for the modified recipe than you need for the original recipe? Show your work.
2. Your bank account has in it. You deposit $5 per day.
(a) How much money is in your account after 5 days? Show your work.
(b) After you have made all of your deposits, you withdraw $2 a day until your account balance is $0. How many days will you withdraw $2? Show your work.
3. A scuba diver was exploring a reef 32.12 m below sea level. The diver ascended to the surface at a rate of 8.8 m/min.
(a) Write an equation to model the situation. Use the formula d = RT.
(b) Explain why it is reasonable to write the distance, d, as a positive number.
(c) How long did it take the diver to reach the surface?
Need the answer A.S.A.P!
1. This problem lacks given values, where are the numbers? Just fill-in the numbers I will variables in this case.
Let us say that:
x = number of cups of flour
y = number of cups of white sugar
z = number of cups of brown sugar
(a) Just divide x by 6 to get cups of flour per serving
x / 6
(b) Simply add y and z and divide the sum by 6
(y + z)/6
(c) From (a) we know that there are x / 6 flours per serving, so simply multiply that by 9 then subtract the original x to know how much more you need:
[(x / 6) * 9] – x
2.
(a) We know that we deposit $5 per day, so after 5 days we got:
total deposit = ($5 / day) * 5 days = $25
(b) The total deposit is 25 dollars, so removing $2 a day we need:
25 / 2 = 12.5 days
3.
(a) d is distance, R is rate, T is time
32.12 = 8.8 T
(b) It is rightful to write distance d as a positive number since the scuba diver was ascending towards the surface. If this is to be plotted on a Cartesian plane, we are moving towards the positive y axis
(c) solving for T:
32.12 = 8.8 T
T = 32.12 / 8.8
T = 3.65 minutes
With nothing but nick and pennies in his pocket , Rupert can afford 77 cents worth of candy. If he has 21 coins in his pocket how many coins does he have of each type
Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted. the students kept track of many lifestyle variables including how many hours of sleep obtained on a typical day. researchers found that visually impaired students averaged 8.14 hours of sleep, with a standard deviation of 1.78 hours. assume that the number of hours of sleep for these visually impaired students is normally distributed.
Sports a pennant for the sports teams at lincoln high school is in the shape of an isosceles triangle. if the measure of the vertex angle is 18, find the measure of each base angle.
The measure of each base angle is 81.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given,
Sports a pennant for the sports teams at lincoln high school is in the shape of an isosceles triangle.
An isosceles triangle is a triangle in which two sides are equal.
Given that the measure of the vertex angle is 18
We need to find the measure of each base angle.
By angle sum property the sum of three angles is 180 degrees.
x+x+18=180
2x+18=180
Subtract 18 from both sides
2x=180-18
2x=162
Divide both sides by 2
x=81
Hence, the measure of each base angle is 81.
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After 2 1/4 h, a chainsaw has used 2 13/16 gal of fuel. How many gallons of fuel did the chainsaw use each hour? Enter your answer as a mixed number in simplest form in the box.
Answer:
1 1/4 or 5/4 gallon per hour.
Step-by-step explanation:
Fuel used in 2 1/4 hour = 2 13/16 gallon
Fuel used in 9/4 hour = 45 / 16 gallon
Fuel used in one hour = [tex]\frac{\frac{45}{16}}{\frac{9}{4}}[/tex]
= 5 / 4 gallon per hour = 1 1 /4 gallon per hour
Thus, teh fuel used in each hour is 1 1/4 gallon or 5 / 4 gallon.
Your classmate is unsure about how to use side lengths to determine the type of triangle. How would you explain this to your classmate?
Answer:
First, look at the side lengths a, b, and c, where c is the longest. Then take the sum of a squared and b squared and compare it to c squared. If they are equal, the triangle is a right triangle. If c squared is less than a squared plus b squared, the triangle is acute. If c squared is greater than a squared plus b squared, the triangle is obtuse.
What is the solution of the system? Use elimination.
-12x - y = 6
17x + y = 4
A. (-30, 2)
B. (-2, 30)
C. (2, -30)
D. (30, -2)
Answer:
C: (2, -30)
Step-by-step explanation:
55.25 divided by 0.85
What is the measure of angle a
Answer:
m∠A = 70°
Step-by-step explanation:
The given figure is nothing but parallel lines cut by a transversal.
We use property of transversal to find the value of angle A.
Here ∠A and 110° are pair of interior angles on the same side.
The pair of interior angles on the same side add upto 180 degrees.
Therefore, ∠A + 110 = 180
Subtract 110 from both sides, we get
∠A + 110 - 110 = 180 -110
∠A = 70°
m∠A = 70°
Kirk traded New Zealand dollars for Mexican pesos at an exchange rate of 1 New Zealand dollar = 8.8352 Mexican pesos. He gave the exchanger a total of 2600 New Zealand dollars and was charged a flat fee of 65 New Zealand dollars. Approximately how many Mexican pesos does Kirk have?
Answer: 22,397.23
Step-by-step explanation:
confirmed
Haresh is writing a coordinate proof involving an isosceles triangle. Haresh places his triangle on the coordinate plane such that the base of the triangle lies along the x-axis.
What coordinates should he assign to this third vertex of the isoceles triangle?
(2a, b)
(a/2, b/2)
(a/2, b)
(b, 2b)
Answer:- (a/2, b) is coordinates should he assign to the third vertex of the isosceles triangle.
Explanation:-
As the given triangle is isosceles then the median of the triangle divides it into two equal triangles such that the base of the new triangles becomes half of the original triangle[tex]=\frac{1}{2}a[/tex]
[where a is the base of the original isosceles triangle]
Since the median of the given triangle join the third vertex and the mid point of the base thus the x coordinate of the points remains same[tex]=\frac{1}{2}a[/tex] and from the graph it is clear that y coordinate of third point is b .
Thus the coordinates for the third vertex must be [tex](\frac{a}{2},b)[/tex].
If the temperature is 64.4 degrees Fahrenheit, what is the temperature in degrees Celsius?
18
3.8
53.6
58.3
Answer:
[tex]18^{\circ}C[/tex]
Step-by-step explanation:
Given :The temperature is 64.4 degrees Fahrenheit
To Find : What is the temperature in degrees Celsius?
Solution:
The temperature is 64.4 degrees Fahrenheit
To convert in into Celsius
Formula : [tex]T(^{\circ}C) =(T(^{\circ}F)-32) \times \frac{5}{9}[/tex]
Substitute the vale
[tex]T(^{\circ}C) =(64.4-32) \times \frac{5}{9}[/tex]
[tex]T(^{\circ}C) =(32.4) \times \frac{5}{9}[/tex]
[tex]T(^{\circ}C) =18^{\circ}C[/tex]
So, Option A is true
Hence the temperature in degrees Celsius is [tex]18^{\circ}C[/tex]
Generally speaking, using a ______ year's history of cash receipts and disbursements will be a satisfactory basis for projecting the future. Part of a year or full year
Generally speaking, using a FULL year's history of cash receipts and disbursements will be a satisfactory basis for projecting the future.
Explanation:
Though a rough projection can be made in half year's data as well, but a good and solid projection can be made using full year's data. Almost all business run for a full year, so its good to project on an yearly basis. Like in this particular year the profits are this much, so we can project that in the next year we can see a higher profit.
The sides of a triangular lot are represented by x, 3x, and 3x + 2. Find each side if the perimeter is 632 feet.