Answer: The answer is (B) [tex]47\dfrac{7}{12}[/tex].
Step-by-step explanation: We are given to find the difference between the following two numbers:
[tex]n_1=126\dfrac{1}{4},~~~n_2=78\dfrac{2}{3}.[/tex]
To find the difference, we need to subtract the smaller number from the larger one.
Since, [tex]n_1>n_2[/tex], so the difference is given by
[tex]d\\\\=n_1-n_2\\\\=126\dfrac{1}{4}-78\dfrac{2}{3}\\\\=\dfrac{505}{4}-\dfrac{236}{3}\\\\=\dfrac{505\times3-236\times4}{12}\\\\=\dfrac{1515-944}{12}\\\\=\dfrac{571}{12}\\\\=47\dfrac{7}{12}.[/tex]
Thus, (B) [tex]47\dfrac{7}{12}[/tex] is the correct option.
An amusement park is installing a new roller coaster. The park intends to charge $5 per adult and $4 per child for each ride. It hopes to earn back more than the $650,000 cost of construction in four years. With the best of weather, the park can provide 125,000 adult rides and 50,000 child rides in one season
Answer:
Step-by-step explanation:
5x+ 4y greater than or equal to 650,000
500,000
y greater than or equal to 200,00
Answer is : 5x+4y greater than or equal to 650,000
X less than or equal to 500,000
Y is less than or equal to 200,000
(48.9, -53.3) (84.6, -19.9) (-62.6, 81.7) (-14.4 ,-42.6) (71.2, -84.1) (71.2, 76.8 ) state the domain
A quadratic equation is shown below: 3x2 − 15x + 20 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points) Part B: Solve 3x2 + 5x − 8 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
Answer:
[tex]\text{The roots of }3x^2+5x-8=0\text{ are }x=1,\frac{-8}{3}[/tex]
Step-by-step explanation:
[tex]\text{Part A: Given a quadratic equation }3x^2-15x+20=0[/tex]
[tex]\text{Comparing above equation with }ax^2+bx+c=0[/tex]
a=3, b=-15, c=20
Discriminant can be calculated as
[tex]D=b^2-4ac[/tex]
[tex]D=(-15)^2-4(3)(20)=225-240=-15<[/tex]
The roots are imaginary
The solution is
[tex]x=\frac{-b\pm\sqrt{D}}{2a}[/tex]
[tex]x=\frac{-(-15)\pm \sqrt{-15}}{2(3)}=\frac{15\pm\sqrt{15}i}{6}[/tex]
The roots are not real i.e these are imaginary
[tex]\text{Part B: Given a quadratic equation }3x^2+5x-8=0[/tex]
[tex]\text{Comparing above equation with }ax^2+bx+c=0[/tex]
a=3, b=5, c=-8
Discriminant can be calculated as
[tex]D=b^2-4ac[/tex]
[tex]D=(5)^2-4(3)(-8)=25+96=121>0[/tex]
The roots are real
By quadratic formula method
The solution is
[tex]x=\frac{-b\pm\sqrt{D}}{2a}[/tex]
[tex]x=\frac{-5)\pm \sqrt{121}}{2(3)}=\frac{-5\pm 11}{6}[/tex]
[tex]x=1,\frac{-8}{3}[/tex]
which are required roots.
I choose this method because I can get the solutions directly by substituting the values in formula, and I don't have to guess the possible solutions.
2x+3y=-2 4x+7y=-6 solve for the system of equations
graph the line with the slope 1/3 and y-intercept -2
The graph of the line y = (1/3)x - 2 can be plotted on a graph paper by choosing some arbitrary values of x.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
The given line in terms of the slope-intercept method can be written as,
y = (1/3)x - 2.
Now to plot the graph on graph paper or any digital tool we have to choose some arbitrary values of x that corresponds to some values of y.
Like at x = 0 y = -2 So, the coordinates are (0, -2).
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What is the approximate distance between the points (-5, 1) and (-2, 3) on a coordinate grid ?
You have a cone with a radius of 4 ft and a height of 12 ft. What is the height of the triangle formed by a perpendicular cross-section through the cone’s center?
3tan3x=3
solve please
The sum of the first and third of three consecutive even integers is 136. find the three even integers.
The sum of the first and third even integers is 136. By setting up an equation and solving for x, where x is the first integer, we determine that the consecutive even integers are 66, 68, and 70.
The problem asks us to find three consecutive even integers where the sum of the first and third integer is 136. Let's denote the first integer as x, the second integer as x + 2, and the third integer as x + 4 (since consecutive even numbers have a difference of 2). To solve for the values, we set up the equation x + (x + 4) = 136. Simplifying, we get 2x + 4 = 136. Subtracting 4 from both sides gives us 2x = 132. Dividing both sides by 2, we find out that x = 66. So, the first integer is 66, the second integer is 66 + 2 = 68, and the third integer is 66 + 4 = 70.
Therefore, the three consecutive even integers are 66, 68, and 70.
One number is 2 more than 3 times another. their sum is 22. find the numbers. 8, 14
Kaveri has a total rs 590 as currency notes is the denominations ofrs50 , rs 20 , and rs 10 . the ratio of the number of rs 50 note and rs 2o is 3:5. if she has a total of 25 notes , how many notes of each denomination she has?
A low bal will always cause a hangover
how would you solve it. I know the answer already. my problem working it out.
4b/2 + 3 = 11 + b.
The graph shows the number of paintballs a machine launches, y, in x seconds::
A graph titled Rate of Launch is shown. The x axis label is Time in seconds, and the x axis values are from 0 to 20 in increments of 4 for each grid line. The y axis label is Number of Balls, and the y axis values from 0 to 80 in increments of 16 for each grid line. A line is shown connecting points on ordered pair 4, 16 and 8, 32 and 12, 48 and 16, 64.
Which expression can be used to calculate the rate per second at which the machine launches the balls?
fraction 64 over 4
fraction 4 over 64
fraction 16 over 4
fraction 4 over 16
a fraction should be number of balls over time per second
so it should be 16/4 which is 4 balls per second
Answer: fraction 16 over 4
Step-by-step explanation:
The given graph shows the number of paintballs a machine launches, y, in x seconds.
We know that the rate of change of a line is given by :-
[tex]k=\frac{y_2-y_1}{x_2-x_1}[/tex]
The ordered pairs on the line in graph are (4, 16) and (8, 32) and (12, 48) and (16, 64).
Thus, the rate per second at which the machine launches the balls is given by :-
[tex]k=\frac{32-16}{8-4}=\frac{16}{4}
Use the arc length formula to find the length of the curve y = 5x − 4, −1 ≤ x ≤ 3. check your answer by noting that the curve is a line segment and calculating its length by the distance formula
The arc length is 4√26, which is confirmed by the distance formula for a line segment yielding approximately 20.396 units.
To find the length of the curve y = 5x − 4 over the interval −1 ≤ x ≤ 3, we can use the arc length formula for a function y = f(x). The formula for the arc length L is given as:
L = ∫ab√(1 + (dy/dx)2) dx, where dy/dx is the derivative of y with respect to x.
1. Calculate the derivative dy/dx:
y = 5x − 4, so dy/dx = 5.
2. Substitute the derivative into the arc length formula:
L = ∫-13√(1 + 5²) dx = ∫-13√26 dx.
3. Integrate the function:
L = √26 ∫-13 dx = √26 [x]-13 = √26 (3 − (-1)) = 4√26 ≈ 20.396.
To verify this using the distance formula (since the curve is a straight line), we take the points (−1,−9) and (3,11) from the given curve:
4. Apply the distance formula:
Distance = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) = (-1, -9) and (x2, y2) = (3, 11).
Therefore,
Distance = √((3 - (-1))² + (11 - (-9))²) = √((4)² + (20)²) = √(16 + 400) = √416 = 4√26 ≈ 20.396.
Thus, the arc length calculated using the formula and the distance formula are consistent.
The arc length is 4√26, which is confirmed by the distance formula for a line segment yielding approximately 20.396 units.
I want to make sure of my answer is right?
20 2/7 = 142/7 -20/35
find common denominator ( in this case it is 35)
35/7 =5 , multiply 142*5=710, 7*5 =35
142/7 = 710/35
710/35 - 20/35 = 710-20 = 690
690/35 now simplify that fraction
690/35 = 19.714
19*35 = 665
690-665=25
19 25/35
25/35 can reduce to 5/7
answer = 19 5/7
Part B: Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth
In a store 60 cans of soup are arranged to be this play into equal rows why does the fraction 10 over 60 not represent the situation explain
Oh Plz help - I can't handle this one :)
Sara is 33 years younger than Rolando. The Sum of their ages is 105. Select the system of equations if Sara's age is represented by S and Rolando's age is represented by R.
A. s+r=33
s=r-105
B. s+r=105
r=s-33
C. s+r=105
s=r-105
D. s+r=105
s=r-33
E. None of these
Find the length of a to the nearest tenth.
Walter bought a square plot of land. the perimeter is 544 feet. how wide is the property?
perimeter of a square = is side times 4
so divide 544 by 4
544/4 = 136
the property is 136 feet wide
WILL MARK BRAINIEST!!
e) Isabel’s competition,who sells books and no other products, charges a shipping fee of $1.99 per book plus a fixed fee of $3 for each order. Let x be the number of books purchased and f(x) be the price of shipping one order of books. Write a function that expresses f(x) and explain the value of f(x) for x = 0. (5 points)
f) Graph the function in part e. (10 points)
g) Is your graph discrete or continuous? Explain. (5 points)
Answer:
Isabel’s competition,who sells books and no other products, charges a shipping fee of $1.99 per book plus a fixed fee of $3 for each order. Let x be the number of books purchased and f(x) be the price of shipping one order of books. Write a function that expresses f(x) and explain the value of f(x) for x = 0. (5 points)
The price of the shipping ( f(x)) is equal to the cost of the fixed fee per order (3) plus the product of the number of books ordered (x) and the cost of the fee per book (1.99).
f(x)= 1.99x +3
for f(0) = 1.99(0)+3
f(0) =3
For F(0) there is a order of 0 books. The price is only for the shippping.
Step-by-step explanation:thats it buddy
A function that expresses f(x) is f(x) = 1.99x + 3. Graph is continuous.
What is continuous function?A continuous function is a function that does not have discontinuities that means any unexpected changes in value. A function is continuous if we can ensure arbitrarily small changes by restricting enough minor changes in its input.
For this case we have the following data:
A shipping fee of $ 1.99 is charged for each book sold.
There is a fixed fee of 3 dollars per order.
We must express the total cost by a function of the form .
If x represents the number of books sold, we have an expression of the form:
f(x) = 1.99x + 3
That is, according to the number of books sold, represented by x, a different value will be obtained for the total cost given by function f (x). For example:
If 3 books are sold, we have:
f(x) = 1.99x + 3
f(0) = 1.99(0) + 3
f(0) = 3
Thus, the value of f(x) for x = 0 is f(0) = 3.
The graph is continuous. Continuous is something that can and must be able to be broken down into fractions and decimals. Discrete means something that cannot be broken down into fractions or decimals.
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Angles θ and Φ are supplementary, and theta equals 3pi/7 find the measure of theta
From Plato: Φ =7π/7 or π.
Can someone solve #4 and explain it? I really appreciate it on this problem! Thank you :)
A textile corporation buys equivalent with an initial purchase price of $750000. It is estimated its useful life will be 3 years and at that time it's value will be$75000. The total depreciation is depreciation is divided equally among the three years. What is the total amount of depreciation declared each year?
A jar has 4 balls lettered A, E, D, and G. One ball is drawn from the jar and it's letter is noted. A second ball is also drawn without replacing the first ball and it's letter is noted. List all the possible outcomes and find the probability that the letters on the 2 balls drawn consist of at least 1 vowel, no vowels, and the same letter.
The function h(x) = x2 + 14x + 41 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points)
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points)
Part C: Determine the axis of symmetry for h(x). (2 points)
to anyone who may be a lil' sus, the previous answer is correct.
Wich of the operations ,+,-,x➗are inverse o each other
A pet store has 7 tanks of fish. Each tank has k fish. Using k, write an expression for the total number of fish in the store.
The expression which represents the total number of fish in the store is 7k.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given,
Number of tank = 7
Number of fish in each tank = k
The total number of fish = number of tanks x number of fish in each tank
The total number of fish = 7 x k = 7k
Hence "The expression which represents the total number of fish in the store is 7k".
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