The sandwich's price is represented by the variable s , 2 is the coefficient of s and 2.97 represents both the cost of a big drink and a constant
What is Algebraic Expression?
An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. For instance, the algebraic formula 3x2 2xy + c
The cost of Andrew's lunch is written as the algebraic expression
2s + 2.79 as a given. He bought a huge drink and two sandwiches.
In the algebraic expression given;
2s + 2.79
Here, 2 stand in for the coefficients of s, which stands for the quantity of sandwiches he purchased.
The sandwich's price is represented by the variable s, which is a function of the coefficient.
And 2.97 represents both the cost of a big drink and a constant since no further letters have been added.
Hence, sandwich's price is represented by the variable s , 2 is the coefficient of s and 2.97 represents both the cost of a big drink and a constant
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the greatest common divisor of two integers is $(x 2)$ and their least common multiple is $x(x 2)$, where $x$ is a positive integer. if one of the integers is 24, what is the smallest possible value of the other one?
The greatest common divisor (24,6) is 6 and the least common multiple (24,6) is 24.
As per the question statement, the greatest common divisor of two integers is (x+2) and the least common multiple x(x+2). It is given that one of the integers is 24.
Let us assume that "b" is the value of other one.
greatest common divisor(24,b) = (x+2)
least common multiple(24,b) = x(x+2)
Formula:
greatest common divisor(24,b)*least common multiple(24,b) = 24*b
24*b = (x+2)*x(x+2)
[tex]b = \frac{x(x+2)^{2} }{24} \\[/tex]
Hence, the smallest possible value of the other one is "6" and x = 4.
Hence, the greatest common divisor (24,6) is 6 and the least common multiple (24,6) is 24.
Common divisor: A number or expression that evenly divides two or more other numbers or phrases.Common multiple: A number into which every number in a particular collection may be split equally.To learn more about common divisor and common multiple, click on the link given below:
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The cost of gasoline is $2.45 per gallon. The price per gallon increased an average of 2% per hour over the period of a day. This can be modeled by the function G(t) = 2.45(1.02)t, where t is the number of hours since midnight. What would be the most appropriate
Answer:
The average cost for a gallon of gasoline in 2006 was $2.45. In 2007, the average cost of a gallon of gasoline was $3.29.
5. Realizar las siguientes operaciones y simplificar el resultado:
a. 3(x3 − x2 + 5) − 8(x3 − 4x2 + 7x)
b. 7x2 + 2x + 5 + x(x + 7)
c. 10 (t3 − 4t2 + 1) − t(2t + 6) + 8(t3 − t − 5)
d. (x − 1)(x + 2)(x − 3)
e. (3a − 2b2)(3a + 2b2) − 3(4a − b2)2 + 2(−2a − b2)(2a − b2)
Answer:
a. -5x³ + 29x² - 56x + 15
b. 8x² + 9x + 5
c. 18t³ - 42t² - 14t - 30
d. x³ - 2x² - 5x + 6
e. -2b⁴ + a² + 6b² - 24a
Step-by-step explanation:
a. 3(x³ − x² + 5) − 8(x³ − 4x² + 7x)
3x³ - 3x² + 15 - 8x³ + 32x² - 56x
-5x³ + 29x² - 56x + 15
b. 7x² + 2x + 5 + x(x + 7)
7x² + 2x + 5 + x² + 7x
8x² + 9x + 5
c. 10(t³ − 4t² + 1) − t(2t + 6) + 8(t³ − t − 5)
10t³ - 40t² + 10 - 2t² - 6t + 8t³ - 8t - 40
18t³ - 42t² - 14t - 30
d. (x − 1)(x + 2)(x − 3)
(x - 1)(x + 2)
x(x + 2) - 1(x + 2)
x² + 2x - x - 2
x² + x - 2(x - 3)
x(x² + x - 2) - 3(x² + x - 2)
x³ + x² - 2x - 3x² - 3x + 6
x³ - 2x² - 5x + 6
e. (3a − 2b²)(3a + 2b²) − 3(4a − b²)2 + 2(−2a − b²)(2a − b²)
3a(3a - 2b²) + 2b²(3a - 2b²)
9a² - 6ab² + 6ab² - 4b⁴ - 3(4a − b²)2 + 2(−2a − b²)(2a − b²)
9a² - 4b⁴ - 24a + 6b² + 2(−2a − b²)(2a − b²)
(−2a − b²)(2a − b²)
-2a(2a - b²) - b²(2a - b²)
-4a² + 2ab² - 2ab² + b⁴
-4a² + b⁴
2(-4a² + b⁴)
-8a² + 2b⁴
9a² - 4b⁴ - 24a + 6b² - 8a² + 2b⁴
-2b⁴ + a² + 6b² - 24a
Find the difference between 2.5 and 7.5 and the sum of 2.75 and 9.55
⇒To get the difference we subtract.
[tex]2.5-7.5=-5\\[/tex]
⇒To get the sum we add.
[tex]2.75+9.55=12.3[/tex]
Goodluck!!
A) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over times, x measured in seconds. During what interval(s) of the domain is the water balloon's height staying the same?
A.0 ≤ x ≤ 2
B.2 ≤ x ≤ 5
C.5 ≤ x ≤ 6
D.6 ≤ x ≤ 8
B) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. During what interval(s) of the domain is the water balloon's height increasing?
A.0 ≤ x ≤ 2
B.40 ≤ y ≤ 70
C.5 ≤ x ≤ 8
D.40 ≤ y ≤ 10
C) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. During what interval(s) of the domain is the water balloon's height decreasing the fastest?
A.5 ≤ x ≤ 9.5
B.8 ≤ x ≤ 9.5
C.6 ≤ x ≤ 8
D.5 ≤ x ≤ 6
D) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. Justify your answer from Part C.
A.5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing.
B.8 ≤ x ≤ 9.5 is the interval where the slope is the steepest.
C.6 ≤ x ≤ 8 is the interval where the balloon's height decreases the most.
D.5 ≤ x ≤ 6 is the interval where the slope is the steepest.
Please help as fast as possible <3
As shown in the reference graph attached hereby with the question statement, if the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds, then,
(A) During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.
(B) During (0 ≤ x ≤ 2) seconds, the height of the water balloon is increasing.
(C) During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.
(D) From Part (C), it can be justified that 5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing, and, (5 ≤ x ≤ 6) is the interval where the slope is the steepest.
As per the question statement and the reference graph attached alongside, the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds.
We are required to determine the correct time domains for four different situations, by observing the plotted graph.
Part (A) is to determine the correct time domain where the water balloon's height remains the same.
From the graph, it is clear that, the height remains constant at (y = 70), parallel to the x-axis from the 2nd second to the 5th second. Hence, During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.
Part (B) is to determine the correct time domain where the height of the water balloon is increasing.
From the graph, it is clear that, the slope of the concerned graph rises only from [(y = 40) to (y = 70)], starring from the 0th second until the 2nd second. Hence, During (0 ≤ x ≤ 2) seconds in the time domain, , the height of the water balloon is increasing.
Part (C) is to determine the correct time domain where the height of the water balloon decreases the fastest.
From the graph, it is clear that, the graph decreases thrice, first from [(y = 70) to (y = 40)], starting at the 5th second uptil the 6th second, then from [(y = 40) to (y = 10)], starting at the 6th second uptil the 9th second and lastly, from [(y = 10) to (y = 0)], starting at the 9th second till the 9.5th second. Here, we can easily calculate that, the balloon dropped 30ft in 1 sec at the first instance, 30ft in 3 seconds at the second instance and, 10ft in 0.5 seconds.
Since, [(30/1) > (10/0.5) > (30/3)],
Or, [30 > 20 > 10],
Thus, During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.
Part (D) is to determine the correct statement mentioned under it's options, with judgement based on Part (C).
Option (i) states that [(5 ≤ x ≤ 9.5) is the interval where the balloon's height is decreasing] which is true, as we can observe from the graph that the slope is decreasing during the time interval of 5 to 9.5th seconds, although at different rates at different intervals.
Option (ii) states that [(8 ≤ x ≤ 9.5) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is false, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.
Option (iii) states that, [(6 ≤ x ≤ 8) is the interval where the balloon's height decreases the most] which is false, as balloons height falls the farthest by 30fts in two separate intervals, between (5 ≤ x ≤ 6) seconds and (6 ≤ x ≤ 9) seconds.
Finally, Option (iv) states that [(5 ≤ x ≤ 6) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is true, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the maximum in the shortest time period.
Time Domain: Time domain refers to the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to the time interval over which, the function occurs.To learn more about Time Domain, click on the link below.
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3) Graph the solution set to y - 2x = -5 on the
coordinate plane.
Answer:
y=2x-5
Step-by-step explanation:
y - 2x = -5
add 2x to both sides.
y=-5+2x
Answer:
y = 2x - 5 is a line. determine the two points that this line intersects with the axes then connect these points to graph it.
Step-by-step explanation:
Given y = 2x -5 set y = 0 then solve for the abscissa
y = 2x - 5
0 =2x - 5
2x=5
x = 5/2
we now have the point (5/2,0)
set now x = 0 then solve for ordinate
y = 2x - 5
y = 2(0) - 5
y = -5
we now have the point (0, - 5)
we now simply draw a line passing thru the two points ( 5/2, 0) and (0, - 5)
kindly see the graph of y = 2x - 5 with points (5/2, 0) and (0, - 5)
Hope this helps
Label the rotated image PQR. Let P represent A'. Q represent B', and R represent C.
help meeeeeeeeeeee pleaseeeeeeeeeeeeee!!
Answer:
use a calculator or try math app
The value of [tex]\sqrt{6}[/tex] is not -4 because ______.
The solution of the value is mathematically given as
√6 =2.449
This is further explained below.
What is square Root?Generally, In mathematics, the term "square root" refers to a component of a number that, when multiplied by itself, results in the same value as the original number.
As an example, both 3 and –3 are square roots of the number 9.
A number y is said to have a square that is equal to a given number x if and only if it satisfies the following condition: y2 = x.
Another way to express this is to say that the number y has the same value as its own square. For example, the square roots of 16 are 4 and -4, since 42 divided by 2 is 16.
In conclusion,
√6 is not -4
because
√6 =2.449
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Geometry homework
-foundation’s of geometry-
I need help
Answer:
m<2=m<5=50
m<4=85
m<6=45
Step-by-step explanation:
Answer:
1:85 2:50 3:45 4:85 5:50 6:45
Step-by-step explanation:
pls give brainliest
1 should be like 4 and 3 should be like 6.
Like 6+1 is 130 so 2 is 50
The value of y is directly proportional to the value of x. When x=3.5, the value of y is 14. What is the value of y when x = 28? Record your answer
For x = 28, the value of [y] such that [x] is directly proportional to [y] will be 112.
What is direct proportionality?Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. Mathematically, direct proportionality is represented by a straight line and it equation is of the form -
y = kx
k = y/x
where [k] is the constant
Given is the value of [y], which is directly proportional to the value of [x], and when [x] = 3.5, the value of [y] is 14.
We have the following data -
[y] = 14 at [x] = 3.5
Now, since [y] is directly proportional to [x], we cam write -
y = kx
k = y/x
k = 14/3.5. [1]
Now, for x = 28, we can write the relation as -
y/x = k
k = y/28 [2]
Now, equating equation [1] and [2], we get -
14/3.5 = y/28
y = (14 x 28)/3.5
y = (140 x 28)/35
y = (140 x 4)/5
y = 28 x 4
y = 112
Therefore, for x = 28, the value of [y] such that [x] is directly proportional to [y] will be 112.
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Solve for p
1.5m+3p=18
please show steps
Answer:
Step-by-step explanation:
Answer: p= 6-0.5
solve 1.5m + 3p=18
p= 6-0.5m
write an equation in slope intercept form for a horizontal line through (15,21)
Slope-intercept form is y = 21.
What is a equation of line?The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).
Given that,
The line is horizontal. It means slope of this line is zero. We can use the point-slope form for a linear equation since we know the slope and the point (15, 21).
Point-slope form: [tex](y-y_{1}) = m(x-x_{1})[/tex]
Where,
m = slope and [tex](x_{1}, y_{1})[/tex] is the points.
Then,
[tex](y-y_{1}) = m(x-x_{1})[/tex]
[tex](y-21) = 0(x-15)[/tex]
[tex]y-21 = 0\\y=21[/tex]
Hence, the Slope-intercept form is y = 21.
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Find the value of x in each case:
The angle x has a measure of 37
What are angles?Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines
How to determine the value of x?The given parameter is the figure
On the figure, we have the following angle measures
2x, 79, 32 and 5x
The sum of angles in a quadrilateral is 360 degrees
So, we have the following equation
2x + 79 + 32 + 360 - 5x = 360
Evaluate the like terms in the above equation
So, we have the following equation
-3x + 79 + 32 = 0
Evaluate the like terms in the above equation
So, we have the following equation
-3x = -111
Divide both sides of the equation by 3
x = 37
Hence, the value of x is 37
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Put the following equation of a line into slope-intercept form, simplifying all fractions. 3y-2x= -9
y=2/3x-3 that is the slope intercept form
Daniel and Paul have saved $37 to buy their mother a present Daniel saved $8 less than paul how much money did Paul save a ) 14.75b) 18.50c)20.00d)22.50
Answer:
D. 22.50
Step-by-step explanation:
22.5 - 8 = 14.5
14.5 + 22.5 = 37
there are two aircraft carriers, a and b, and carrier a is longer in length than the carrier b. the total length of these two carriers is feet, while the difference of their lengths is only feet.
there are two aircraft carriers, a and b, and carrier a is longer in length than the carrier b. then Carrier A is 2,104 feet and Carrier B is 2,094 feet.
Since there are two aircraft carriers, A and B, and carrier A is longer in length than the carrier B, and the total length of these two carriers is 4198 feet, while the difference of their lengths is only 10 feet, to determine the length of each aircraft carrier, the following calculation must be performed:
(4,198 - 10) / 2 = X
4.188 / 2 = X
2,094 = X
2,094 + 10 = 2,104
2,094 + 2,104 = 4,198
Therefore, Carrier A is 2,104 feet and Carrier B is 2,094 feet.
the complete question is
There are two aircraft carriers, A and B, and carrier A is longer in length than the carrier B. The total length of these two carriers is 4198 feet, while the difference of their lengths is only 10 feet.
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The table shows values of f(x). What is the value of f(2)? Enter your answer in the box. f(2)=
X: 0 1 2 3 4
f(x): 4 2 3 9 1
According to the table, the value of the function f(2) is 3
What are functions?Functions are equations, ordered pairs, tables and graphs that are used to represent a relation
How to evaluate the function?From the question, the function is represented by the table of values given as
X: 0 1 2 3 4
f(x): 4 2 3 9 1
From the question, the function to calculate is given as
f(2)
This means that we calculate the value of the function, when x = 2
i.e.
We calculate f(x), when x = 2
So, we look at the table of values for this function value
From the table of values, we have
When x = 2, f(x) = 3
This means that
f(2) = 3
So, we can conclude that the value of the function f(2) based on the given table when x =2 is 3
Hence, the function f(2) has a value of 3
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-7/8 is at most the difference of twice a number m and 5/4
Answer:
Step-by-step explanation:
The given inequality can be written as 2m - 5/4 ≤ -7/8.
An inequality -7/8 is at most the difference of twice a number m and 5/4 which is 2m - 5/4 ≤ -7/8.
Difference of twice a number 'm' and 5/4 is 2m - 5/4 and this is at most -7/8 means less than or equal to.
∴ The given statement can be written as 2m - 5/4 ≤ -7/8
Answer:
2m - 5/4 ≤ -7/8
Step-by-step explanation:
hope this helps
a restaurant offers three desserts, and exactly twice as many appetizers as main courses. a dinner consists of an appetizer, a main course, and a dessert. what is the least number of main courses that the restaurant should offer so that a customer could have a different dinner each night in the year 2003?
The least number of main courses that the restaurant should offer is 8.
What is linear inequality ?The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
Calculationslet m be the number of main courses restaurant serves
so, 2m is the number of appetizers
then the number of dinner combination is = 2m x m x 3 = 6m^2
since the customer wants to eat a different dinner in all 365 days of 2003,
we must have ,
[tex]6m^{2}[/tex] ≥ 365
[tex]m^{2}[/tex] ≥ 60.83.....
also the 2003 is not a leap year
because 2003 / 4 is not equal to an integer
the smallest integer value satisfies this is 8 .
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PLEASE HELP !! Write the equation of the line that passes through the points(4,7) and(5,−7). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
// ignore, made mistake//
Answer:
(4.7) and (5.-7)
Step-by-step explanation:
find the gradient using the formula:
y2-y1 (divide this by the bottom)
x2-x1
-7-7
5-4
=-14/1
-14 is the answer
then you will say y-y1= m(x-x1)
you can choose to sub any point
I will use (4;7)
therefore...
y-7=-14(x-4)
y= -14x+56+7
y= -14x+63
The equation P=3s represents the perimeter P of an equilateral triangle with side length s. is there a proportional relationship between the perimeter and the side length of an equilateral triangle? Explain.
The constant of proportionality (K ) we will write
Perimeter = 3 ( side) where K = 3
Perimeter of any polygon is defined as the sum of all sides of polygon.
Given polygon is a triangle. A triangle is any polygon which has three sides.
And as the sides of a polygon increases the perimeter also increases.
One can say that perimeter and side of a polygon has a direct relationship.
That is when we write it mathematically we write it like:
Perimeter ( P ) ∝ Sides of polygon
However given is an equilateral triangle
this means that all sides of the triangle are equal
so let us consider the side of the triangle as "s"
Thus we get that perimeter will be 3 times s
which when mathematically written will be:
Perimeter ∝ ( side)
to remove the constant of proportionality (K ) we will write
Perimeter = 3 ( side) where K = 3
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please help !! if anyone knows
Answer:
Answer down below!
Step-by-step explanation:
We can tell from ABC and A'B'C' that they are similar, but not alike
Segment AC = 6 and segment A'C' =4
They just subtracted two from the 6
Let's do the same thing for segment BC!
If BC = 3, then we know that B'C' = 1
PLEASE HURRY I NEED HELP RIGHT NOW!!
What is the length of BC?
Answer:
31cm
Step-by-step explanation:
Add AC and BC together to get AB.
AC = 2x - 13 and
BC = 3x + 4 and
AB = 36 (this is all the given information)
The two smaller pieces can be combined to equal the whole segment.
AC + BC = AB
2x - 13 + 3x + 4 = 36
combine like terms.
5x - 9 = 36
Add 9
5x = 45
Divide by 5.
x = 9
But you're not done because they asked for BC.
BC = 3x + 4
substitute 9 for x.
BC = 3(9) + 4
BC = 27 + 4
BC = 31
BC is 31 cm.
Jonathan has 3982 stickers in his sticker collection. Jessie has 2825 stickers in his collection. How many stickers do Jonathan and Jessie have altogether?
plsssssss helppppp meee with this
Answer:
Step-by-step explanation:
Answer:
..........
Step-by-step explanation:
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..
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A total of 77 tornadoes have been documented in tuscaloosa county in the period beginning on january 1, 1950 and ending on december 31, 2020. What is the recurrence interval for tornadoes in tuscaloosa county?.
The number of tornadoes is 77
total time for occurrence is 70 years
using these
= ( 77/70)
= ( 1.1 )
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help me please if you can:)
In the polygon, The triangles are not similar
What is similar triangles ?The term similar triangles refers to triangles that the ratio of the sides are equal.
In the problem, the sides of the triangles are given as
In DQRS: QR = 4 RS = 15, and < DR = 36In DUVT: VT = 8 TU = 32, and < DT = 36The ratio of the sides
In DQRS: QR / RS = 4/15 = 0.27
In DUVT: VT / TU = 8/32 = 0.25
0.27 ≠ 0.25
since the ratio of the sides are not equal the two triangles are not similar
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The Transverse Tire Company produces all types of tires at its factory. Due to fixed costs associated with the running of
the factory, the company starts with a loss of $200,000, or a profit of -$200,000, at the beginning of each month. The
first major hurdle the company faces each month is to break even, or reach a the point at which the profit is zero. The
company sells tires in batches of 1000. it earns $40,000 for each batch of tires it manufactures and sells.
1. Identify the two quantities that are changing in this situation.
2. identify the independent and dependent variables for these quantities.
3. Write an equation to represent the profit the company will make when they manufacture and sell batches of tires.
4. Use your equation to complete the table for this situation:
5. What is the unit rate of change in this problem?
please help i need to submit but today
The solutions for each statement are given below.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
The initial amount of the company = -$200,000
Earnings for selling one batch = $40,000
Now,
1.
The two quantities that are changing in this situation are:
The number of batches.
The amount of profit.
2.
The independent variable is the number of batches.
The dependent variable is the profit.
3
The number of batches = x
The amount of profit = y
The equation for the profit.
P = -200,000 + B x 40,000
Where B is the number of batches.
4.
Batches of tires Profits
B P
0 -200,000
1 -160,000
2 -120,000
3 -80,000
4 -40,000
5 0
5.
The unit rate of change.
= (-120,000 + 160,000) / (2 - 1)
= 40,000
Thus,
The statements are given above.
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Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Lou's car had 16.2 gallons in the 15 gallons in the -gallon tank on the coldest day of the year.
Lou filled the tank with gas that cost $ 3.50 per gallon. How much did Lou spend on gas?
From the given parameter, the total amount that Lou spent on the gas is; $30.8
How to solve Algebra Word Problems?We are told that Lou's car had 6.2 gallons in the 15 gallons in the -gallon tank on the coldest day of the year.
Now, Lou filled the tank with gas that cost $ 3.50 per gallon.
Thus;
Amount of gas that Lou bought = 15 - 6.2
Amount of gas that Lou bought = 8.8 gallons
Since he bought these gallons at the cost of $3.50 per gallon, then it means that;
Total amount he spent = 8.8 * 3.5
Total amount he spent = $30.8
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Complete question is;
Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Lou's car had 6.2 gallons in the 15 gallons in the -gallon tank on the coldest day of the year.
Lou filled the tank with gas that cost $ 3.50 per gallon. How much did Lou spend on gas?