Answer:B
Step-by-step explanation:
It takes Ross traveling at 36 miles per hour 10 minutes longer to go a certain distance than it takes Maria traveling at 45 miles per hour find the distance traveled
On solving the provided question, we can say that the equation will be distance = distance 36t + 18 = 63t distance = 63t = 63(2/3) = 42 miles
What is equation?A mathematical equatiοn is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is known as an equation in algebra. Fοr instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relatiοnship between the two sentences οn either side of a letter is described by a mathematical fοrmula. Often, there is οnly one variable, which also serves as the symbοl. for instance, 2x – 4 = 2.
the equatiοn will be
distance = distance
36t + 18 = 63t
27t = 18
t = 18/27 = 2/3 hr
distance = 63t = 63(2/3) = 42 miles
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3. Mrs. Doyle asks Lowell to create a verbal
representation for the equation y = x - 25. Did
Lowell complete the task correctly? Justify
your answer.
A $25 charge is added for
rush delivery
Lowell's verbal representation of the equation y = x - 25 is "y is equal to x minus 25".
This verbal representation accurately describes the equation. In the equation, y is the dependent variable and x is the independent variable. The equation says that y is equal to x minus 25, which means that for every value of x, there is a corresponding value of y that is x minus 25.
So, Lowell has completed the task correctly.
A right rectangular prism has a square base with sides 1/2 in. Long. The volume of the prism is 3/8 in to the third power. What is the prism?
Answer:
If the base of the right rectangular prism is a square with sides that are 1/2 inch long, then the area of the base is (1/2)^2 = 1/4 square inches.
Since the volume of the prism is given as 3/8 cubic inches, we can use the formula for volume of a right rectangular prism (V = Bh) to solve for the height of the prism:
V = Bh
3/8 = (1/4)h
Multiplying both sides by 4, we get:
3 = h
So the height of the prism is 3 inches.
Therefore, the right rectangular prism has a square base with sides 1/2 inch long and a height of 3 inches, making it a 1/2 x 1/2 x 3 inch rectangular prism.
Points A, B, and C are colinear in that order. Find xusing the segment addtion postulate method
AC = 3X +3
AB = -1 + 2X
BC=11
Using the segment addition postulate approach, the valve of x is 7.
What purposes do postulates serve?A postulate is a claim that is accepted as true in the lack of supporting data. Postulates serve as a basis for the verification of succeeding propositions and serve the dual purpose of defining concepts that are not yet specified. Two points determine a line segment. A line segment can go on for ever along a line.
The segment addition postulate states that if three points A, B, and C are parallel to one another in that sequence, then the lengths of AB and BC added together equal the length of AC.
AC = AB + BC
Substituting the given values, we get:
3x+3 = (-1 + 2x)+11
When the right side of the equation is simplified, we obtain:
3x + 3 = 2x + 10
Subtracting 2x from both sides, we get:
x + 3 = 10
Subtracting 3 from both sides, we get:
x = 7
Therefore, x = 7.
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An older person is 5 years older than four times the age of a younger person.
The sum of their ages is 30. Find their ages.
Their ages are _____
(Use a comma to separate answers as needed.)
Their ages are 5 years, 25 years
How to find their ages?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Let L and Y represent the age of the older person and younger person respectively.
Using the given information, we can write:
L = 4Y + 5 --- (1)
L + Y = 30 --- (2)
From (2):
L = 30 - Y --- (3)
Put (3) in (1):
L = 4Y + 5
30 - Y = 4Y + 5
4Y + Y = 30 - 5
5Y = 25
Y = 25/5
Y = 5 years
Put Y = 5 into (3):
L = 30 - Y
L = 30 - 5
L = 25 years
Their ages are 5 years, 25 years
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NEED PLS THANK YOU DUE TODAY
Now , to find the area
Total area of figure = Area of first Triangle + Area of second triangle
The area of the triangle = ( 1/2 ) x Length x Base
Total area of figure = ( 1/2 ) x ( 36 x 15 ) + ( 1/2 ) x ( 15 x 8 )
= ( 1/2 ) x 540 + ( 1/2 ) x 120
= 270 + 60
= 330 inches²
Therefore , the value is 330 inches²
Hence , The area of the figure is 330 inches²
our jobs are to be done on four different machines. The cost in rupees of
producing ith on the jth machine is given below. Assign the jobs to different machines
so as to minimise the total cost.
Jobs
M1
M2
M3
M4
J1
15
11
13
15
J2
17
12
12
13
J3
14
15
10
14
J4
16
13
11
17
Find the dimensions for which the enclosed area is 1600 square feet. (View image)
Answer:
perimeter of rectangle = 2(length +breadth)
=2(20+80) m
=200 m
∴perimeter of rectangle is 200 m
complete the remainder of the table for the given function rule: y=2x/3+4
The table of values is
X |f(x)
0 | 4
2 | 5.33
4 | 6.67
6 | 8
How to complete the table of valuesFrom the question, we have the following parameters that can be used in our computation:
y = 2x/3 + 4
We have the x values to be
x = 0, 2 4 and 6
Substitute the known values in the above equation, so, we have the following representation
y = 2 * 0/3 + 4 = 4
y = 2 * 2/3 + 4 = 5.33
y = 2 * 4/3 + 4 = 6.67
y = 2 * 6/3 + 4 = 8
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A 10-ft board is cut into 2 pieces so that one piece is 6 ft longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces
The length of the both pieces are 1ft and 9ft respectively. Option C
How to determine the lengthsWe have from the information given that;
The shorter side = xThe longer side = 6 + 3xThe total length = 10ftNow, substitute the values, we get
x + 6 + 3x =10
Collect the like terms
x + 3x = 10 -6
Add the like terms
4x = 10 - 6
Substract the like terms
4x = 4
Make 'x' the subject of formula by dividing both sides by 4, we get;
x = 4/4
divide the values
x = 1
Thus, the values are 1ft and 9ft
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A chef bought 3 bags of beans. Each bag contains kilograms of beans. How
many kilograms of beans did she buy?
The chef bought a total of 4 1/5 kilograms of beans.
How many kilograms of beans did she buy?Number of bags of beans the chef bought= 3
Quantity of beans in each bag = 1 2/5 kilograms
Total kilograms of beans bought by the chef= Number of bags of beans the chef bought × Quantity of beans in each bag
= 3 × 1 2/5
= 3 × 7/5
= 21/5
= 4 1/5 kilograms of beans
Ultimately, the chef bought 4 1/5 kilograms of beans.
Complete question:
a chef bought 3 bags of beans. Each bag contains 1 2/5 kilogram of beans. How many kilograms of beans did she buy?
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Please help me ASPA find the value of X
Answer:
9
Step-by-step explanation:
set up a ratio
20 is to 3x-2 as ( 20 + 28) is to 7x -3
20 / ( 3x-2) = ( 20 + 28) / (7x-3 ) cross multiply to get
140x - 60 = 144x - 96
36 = 4x
x = 9
How many solutions does the system have? { � = 5 � + 1 � = − 2 � − 8 ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ y=5x+1 y=−2x−8
The given system of linear equations has a unique solution.
What are linear equations?A linear equation is an algebraic equation in which each term has an exponent of 1 and when graphed, the result is always a straight line.
Given that, a system of linear equations, y = 5x+1 and y = -2x-8, we are asked to find how many solutions do they have,
The rule for a system of linear equations, a₁x+b₁y+c₁ = 0 and a₂x+b₂y+c₂ = 0 are :-
When the system has a unique solution :-a₁ / a₂ ≠ b₁ / b₂, and the lines intersect at one only point.
When the system has a no solution :-a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂, and the lines are parallel.
When the system has infinite solution :-a₁ / a₂ = b₁ / b₂ = c₁ / c₂, and the lines overlaps.
Checking for the given equations,
y = 5x+1 and y = -2x-8
Converting into standard form of the linear equations,
5x-y +1 = 0 and 2x+y+8 = 0
5/2 ≠ -1
The equation is following the rule of unique solution, also the graph is intersecting at one point, [graph is attached]
Hence, the given system of linear equations has a unique solution.
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Answer:
One solution
Step-by-step explanation:
Grayson is going to invest in an account paying an interest rate of 4% compounded
continuously. How much would Grayson need to invest, to the nearest dollar, for the
value of the account to reach $15,000 in 5 years?
Grayson would need to invest approximately $10,994 to the nearest dollar for the value of the account to reach $15,000 in 5 years.
What is continuously compounded interest?
Continuous compounded interest indicates that an account balance is constantly earning interest and reinvesting that money so that it, too, earns interest.
The formula for continuous compounding is given by:
[tex]A = Pe^{rt}[/tex]
where A is the amount in the account after t years, P is the principal amount (the amount invested), r is the annual interest rate, and e is the base of the natural logarithm.
We want to find P when A = $15,000, r = 0.04, and t = 5 years.
Substituting these values into the formula, we get:
[tex]15000 =Pe^{0.04*5}[/tex]
Simplifying the right-hand side, we get:
[tex]15000 =Pe^{0.2}[/tex]
Dividing both sides by e^(0.2), we get:
[tex]P= \frac{15000}{e^{0.2}}[/tex]
Using a calculator, we get:
P ≈ $10,994
Therefore, Grayson would need to invest approximately $10,994 to the nearest dollar for the value of the account to reach $15,000 in 5 years.
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A 10-ft board is cut into 2 pieces so that one piece of 6 feet longer than 3 times the shorter piece. If the shorter piece is x feet long find the lengths of both pieces
The lengths of the pieces are 1ft and 9ft
How to determine the length of sides
From the information given, we have that;
The shorter side = x
The longer side of the board = 6 +3x
The total length = 10
Substitute the values, we have;
x + 6 + 3x = 10
collect the like terms
x + 3x = 10 -6
Add or substract the like terms, we have;
4x = 4
Now, make 'x' the subject of formula by dividing by 4, we get;
4x/4 = 4/4
x = 1 ft
The longer side = 9ft
Hence, the values are 1 and 9
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Please help me I need help with algebra 2
Answer:If (x + 1) is a factor of the polynomial p(x), then p(x) can be written as:
p(x) = (x + 1) q(x)
for some polynomial q(x). By substituting x = -1 into this expression, we can find the value of c:
p(-1) = (-1 + 1) q(-1) = 0 q(-1) = 0
So,
0 = 5(-1)^4 + 7(-1)^3 - 2(-1)^2 - 3(-1) + c
= -5 + 7 - 2 + 3 + c
= c = 3
So, the value of c that makes (x + 1) a factor of the polynomial p(x) = 5x^4 + 7x^3 - 2x^2 - 3x + c is c = 3.
In a running race, you covered 3000 m. The ratio of distance covered by walking to running is 2:13. How many meters did you walk?
Answer:
400 m walking
Step-by-step explanation:
sum the parts of the ratio , 2 + 13 = 15 parts
divide the distance covered by 15 to find the value of one part of the ratio.
3000 m ÷ 15 = 200 m
then
2 parts = 2 × 200m 400 m
400 m covered by walking
whats the missing of the angle 104, 30?
Answer:46
Step-by-step explanation:
180=104+30+x
134+x=180
x=46
F(x)=|x| is transformed to g(x)=|x|+4 what transformation happens from f(x) to g(x)
Step-by-step explanation:
The transformation from the function f(x) = |x| to the function g(x) = |x| + 4 can be thought of as a vertical shift upward by 4 units. The shape of the absolute value function remains unchanged, but the entire graph is shifted upward along the y-axis by 4 units. This can be visualized by observing that for any value of x, g(x) = f(x) + 4.
So, the transformation of f(x) to g(x) is a vertical shift upward by 4 units
The average rate of change of a function
f(x) = x2
between
x = 4
and
x = 6
is
average rate of change =
`
6 − 4
=
On solving the provided question we can say that The average rate of change between x₁ and x₂ and a function f(x), is 10.
What is function?The subject of mathematics includes quantities and their variatiοns, equations and related structures, shapes and their locations, and places where they can be fοund. The term "functiοn" refers to the relationship between a set of inputs, each of which has an assοciated output.
A connectiοn between inputs and οutputs in which each input leads tο a single, distinct result is known as a function. Each functiοn is given a domain and a codοmain, or scope. Usually, f is used to denοte functions (x). input is an x. There are fοur main types of functiοns accessible. based οn the following factors: on functiοns, one-to-one functiοns, many-to-one functions, inside functiοns, and on functions.
The average rate of change between x=x and a function f(x)
F(x₂) - F(x₁)/(x₂) - x₁
so,
f(x) = x²
average rate = f(6) - f(4) / 6-4 = 36-16 / 2 = 20/2 = 10
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I’m stuck on this one question help
Answer:
E is a major arc
C is a minor sector
A is a major segment
Major segment is the portion (or part) of the circular region enclosed between a chord and the corresponding major arc.
Major arc is the longer arc connecting two endpoints on a circle.
A sector with a central angle less than 180° is called a minor sector.
For every 3 lemons you buy at a farm stand, the total cost increases by $1.80.
The constant of proportionality is
An equation that relates the total cost y and the number of lemons x is y=____x
Use the equation you wrote to complete the table.
The constant of proportionality is 0.60
The equation is y = $0.60x.
Here is the completed table
Number of lemons Total cost
4 $2.40
7 $4.20
15 $9
18 $10.80
What is the total cost of lemons?Direct variation is when two variables move in the same direction. As the number of lemons bought increases, the total cost increases.
The equation that represents direct variation is:
y = kx
Where:
y = total cost k = constant of proportionality x = number of lemons$1.80 = 3k
k = $1.80 / 3
k = $0.60
y = $0.60x
Total cost of 4 lemons= $0.60 x 4 = $2.40
Total cost of 18 lemons= $0.60 x 18 = $10.80
Number of lemons that cost $4.20 : 4.20 / 0.6 = 7
Number of lemons that cost $9 : 9 / 0.60 = 15
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A certain antihistamine is often prescribed for allergies. A typical dose for a 100-pound person is 19 mg every six hours. Complete parts (a) and (b) below. a. Following this dosage, how many 13.2 mg chewable tablets would be taken in a week? b. This antihistamine also comes in a liquid form with a concentration of 13.2 mg/ 10mL. Following the prescribed dosage, how much liquid antihistamine should a 100-pound person take in a week?
A 100-pound person could take mL in a week? this is the question i need answered the most...thank you
Answer: First, let's find out how many times a 100-pound person would take the antihistamine in a week:
Every 6 hours * 24 hours/day = 4 times a day
4 times a day * 7 days/week = 28 times a week
Next, let's find the number of 13.2 mg chewable tablets taken in a week:
A typical dose of 19 mg * 28 doses/week = 532 mg
532 mg / 13.2 mg/tablet = 40 tablets
So, a 100-pound person would take 40 chewable tablets in a week following the prescribed dosage.
Now, let's find the amount of liquid antihistamine to be taken in a week:
A typical dose of 19 mg * 28 doses/week = 532 mg
532 mg / 13.2 mg/10 mL = 40.15 mL
So, a 100-pound person would take 40.15 mL of liquid antihistamine in a week following the prescribed dosage.
Step-by-step explanation:
10. How much would you need to deposit in an account now in order to have $20,000 in the account in 4 years? Assume the account earns 5% interest.
Answer:
20000*4*5/100=4000
Step-by-step explanation:
Hope this helps!
Find the volume of the solid that results when the region enclosed by the given curves is revolved about the x-axis. Round the answer to at least two decimal places.
[tex]y=e^{x}, y=0,x=0,x=ln(3)[/tex]
Answer:
Step-by-step explanation:
Algebra: let f(x)= 3x+7 f^-1 (x)=
Answer:
Step-by-step explanation:
To find the inverse of a function, we need to switch the x and y values and solve for y (or x, depending on how the original function is written). The inverse of the function f(x) = 3x + 7 is written as f^-1(x). To find f^-1(x), we can follow these steps:
Replace the function f(x) with y to make it easier to manipulate: y = 3x + 7.
Swap the x and y variables: x = 3y + 7.
Solve for y:
Subtract 7 from both sides to get x - 7 = 3y.
Divide both sides by 3 to get (x - 7) / 3 = y.
Write the inverse function using f^-1(x) instead of y:
f^-1(x) = (x - 7) / 3
So, the inverse of the function f(x) = 3x + 7 is f^-1(x) = (x - 7) / 3.
If the x-values are equal for two points, then the two points are on a ____ line
If the x-values are equal for two points, then the two points are on a vertical line.
When will x - values for two points be equal ?When there is a vertical line, then it will cross the x - axis at only a single point. This point will be such that all the x - values on the line would be - values because the line stands on only one point on the x - axis.
The same applies to the y - axis for horizontal lines. This is because the horizontal line would cross the y - axis at a single point. For instance, all the points on y = 2, would have a y - value of 2.
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what’s the equation of the line graphed below i’ll give you brainlist pls help
y=3/2x+4
y=2/3x+4
y=2/3x-6
y=3/2x-6
Answer:
y = 2/3x + 4
Step-by-step explanation:
y-intercept (b) is 4
Use points (-6, 0) and (0, 4) to find the slope (m) = (4-0)/(0--6) = 4/6 = 2/3
y = mx + b = 2/3x + 4
Please Help Me Answer!
The probability that a randomly chosen college student exercises in the morning or afternoon is B. 0. 39.
How to find the probability ?The probability that a college student chosen at random will either exercise in the morning or afternoon can be found by the formula :
= Probability that student exercises in the morning + Probability that student exercises in the afternoon
Probability that student exercises in the morning = 0. 25
Probability that student exercises in the afternoon = 0. 14
The probability would therefore be:
= 0. 25 + 0. 14
= 0. 39
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1/4x
10. Last night, 4 friends went out to dinner at a restaurant. They split the bill evenly. Each friend paid $12.75 for his or her meal and each left the same amount for a tip, t. The total dinner bill including the tip was $61. What equation could you use to describe the situation?
Answer:
Step-by-step explanation:
Let's call the number of friends "f". Since each friend paid $12.75 for their meal, the cost of the meals can be represented as f * 12.75. And since each friend left the same amount for a tip, the cost of the tips can be represented as t * f.
The total cost of the dinner including the tip was $61, so we can write the following equation:
f * 12.75 + t * f = 61
Expanding the left side of the equation:
12.75f + t * f = 61
Combining like terms:
13.75f + t = 61
Solving for t:
t = 61 - 13.75f
So, the equation that describes the situation is t = 61 - 13.75f.
