A) The integers that make the equation false are {2, 54, 86}
B) We found that by solving the linear equation.
Which integer makes the equation false?
Here we have the following linear equation:
7m - 11 = 5m + 43
And the set of the possible solutions is S: {2, 27, 54, 86}
The simplest way to see which integer makes the equation false, we just need to replace the values of the possible solution sets and see which ones give a false equation.
Another method is to simplify the equation, and i will do that:
7m - 11 = 5m + 43
7m - 5m = 43 + 11
2m = 54
m = 54/2
m = 27
So the equation has a single solution, m = 27.
Then the integers that make the equation false are {2, 54, 86}
B) We determined the only true solution for the linear equation, and thus, all the other possible integers aren't solutions, thus, make the equation false.
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2 √ 3 + 3 √ 3 can you help me solve this equation in simplest form
The simplest form of [tex]2\sqrt{3} + 3\sqrt{3}[/tex] is found to be 8.66025403784 .
What is the simplest form of a equation ?A fraction is in its simplest form when the numerator and the denominator have no common factors besides one.
Reducing equation is a method of rewriting the equation in a simpler form. Certain equations in mathematics are not in the form of linear equations but they can be put in the form of linear equations by performing some mathematical operations on them. After reduction of these equations in linear form they can be solved and the value of unknown can be calculated easily.
Given the equation is;
[tex]2\sqrt{3} + 3\sqrt{3}[/tex]
Now solving it ,
[tex]2\sqrt{3} + 3\sqrt{3}[/tex]
By adding this we get,
[tex]5\sqrt{3}[/tex] (∵ [tex]\sqrt{3}[/tex] is common in both )
= 8.66025403784
The decimal (or) simplified value of [tex]2\sqrt{3} + 3\sqrt{3}[/tex] is 8.66025403784.
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Part A: Given the function g(x) = |x-5 ,describe the graph of the function, including the vertex, dom
Part B: If the parent function f(x) = |x| is transformed to h(x) = |x| + 3, what transformation occurs from
The vertex domain of g(x)=|X-7| is (7,0) (-∞,∞) and (0,∞) and the function f(x)=|x| is vertically shifted.
What is graph of the function?In mathematics, the set of ordered pairs with the (x,y)(x,y) is known as the graph of a function, where f(x)=y. x and f are Cartesian coordinates of points in two-dimensional space, and in the typical scenario where they are real numbers, they constitute a subset of this plane.Instead of the pairs ((x,y),z) and ((x,y),z) as in the definition above, the graph for functions of two variables, i.e. functions whose domain consists of pairs (x,y), (x,y), is typically the set of ordered triples (x,y,z) and (x,y,z) where A surface for a continuous real-valued function of two real variables, this set is a subset of three-dimensional space.Hence, The vertex domain of g(x)=|X-7| is (7,0) (-∞,∞) and (0,∞) and the function f(x)=|x| is vertically shifted.
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a car and a motorcycle leave at noon from the same location, heading in the same direction. the average speed of the car is mph slower than twice the speed of the motorcycle. in two hours, the car is miles ahead of the motorcycle. find the speed of both the car and the motorcycle, in miles per hour.
The speed of car is 50 miles per hour and the speed of the motorcycle is 40 miles per hour.
Let M = speed of the motorcycle.
Hence, speed of the car = 2M - 30.
Distance covered = Time taken x Speed.
Hence in 2 hours,
Distance covered by motorcycle = 2M
Distance covered by car = 2(2M-30).
Given, the car is 20 miles ahead of the motorcycle.
Hence,
2(2M-30) = 2M + 20
4M-60 = 2M + 20
2M = 80
M = 40
2M-30 = 2(40)-30 = 80-30 = 50
Therefore, speed of motorcycle is 40 miles per hour and speed of car is 50 miles per hour.
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A rectangular room has an area of 352 square feet. The length of the room is 6
feet more than the width of the room. Find the length and width of the room, in feet,
and separate them with a comma.
Solving a system of equations we can see that the length is 22 feet and the width is 16 feet.
How to find the length and the width?
For a rectangle of length L and width W, the area is given by the formula:
A = L*W
Here we know that the rectangular room has an area of 352 square feet, and we also know that the length of the room is 6 feet mroe than the width of the room, then we can write a system of equations:
352 = L*W
L = W + 6
To solve that system, we can substitute the second equation in the first one, we will get:
352 = (W + 6)* W
352 = W^2 + 6W
W^2 + 6W - 352 = 0
So we have a quadratic equation, the solutions give:
[tex]W = \frac{-6 \pm \sqrt{6^2 - 4*1*(-352)} }{2} \\\\W = \frac{-6 \pm 38 }{2}[/tex]
We take the positive value as the with, so:
W = (-6 + 38)/2
W = 16
And the length is 6 feet longer than that, so:
L = 16 + 6 = 22
Then the length is 22 feet, and the width is 16 feet.
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3 ^ 21 is how many time as great value of 3 ^ 19
The exponent [tex]3^{21}[/tex] is 9 times greater than the exponent [tex]3^{19}[/tex]
What are Exponents?
Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself.
Solution:
To solve this type of question all we need to know are the Rules of Exponents with their help any question of this type can be solved
Since we are required to find the number of times the value os greater so we will divide the numbers
3^21 / 3^19
By rule of exponents if a^b/a^c then we can write it as a^(b-c)
Similarly 3^21 / 3^19 = 3^(21 - 19) = 3^2 = 9
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write an equation in slope-intercept form for the line that passes through (9,12) and is parallel to y=4
An equation in slope-intercept form for the line that passes through (9,12) and is parallel to y=4 is y= 4x -24.
What is Parallel lines?
Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.
Parallel lines will have the same slope but different y-intercepts so again we can use the coordinates to determine the y intercept of the new equation.
So we know that the slope intercept formula is y=mx + b where m is the slope and b is the y-intercept so we will input the x and y coordinates to solve for b.
12 = 4(9) + b
12 = 36 + b
b = -24
The equation will be y= 4x -24.
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you're selling vegetarian sandwiches for $3 each and turkey sandwiches for $4 each. you sell 25 sandwiches for a total of $85. how many vegetarian and how many turkey sandwiches did you sell
Answer:
You sold 15 vegetarian sandwiches and 10 turkey sandwiches.
Step-by-step explanation:
First, let's call the number of vegetarian sandwiches sold "V" and the number of turkey sandwiches sold "T".
We can set up the following equation: 3V + 4T = 85
Next, we need to find the values of V and T that satisfy this equation. To do this, we can use the fact that V and T must be whole numbers since we cannot sell a fraction of a sandwich.
We can start by trying V = 1 and T = 6. Plugging these values into the equation, we get: 3(1) + 4(6) = 18 + 24 = 42
Since 42 is not equal to 85, this means that V and T cannot both be 1 and 6.
We can try other values of V and T that are whole numbers until we find a combination that satisfies the equation. One way to do this is to use trial and error.
For example, we can try V = 2 and T = 5, which gives us: 3(2) + 4(5) = 6 + 20 = 26 This is still not equal to 85, so we can try other values. We can also use the fact that V + T = 25 (since we sold a total of 25 sandwiches) to help us solve the equation.
If we set V + T = 25, then we can rewrite the original equation as: 3V + 4(25 - V) = 85 Solving for V, we get: 3V + 100 - 4V = 85 Combining like terms, we get: -V = 15 Dividing both sides by -1, we get: V = 15
Since V + T = 25, this means that T = 25 - 15 = 10
Therefore, we sold 15 vegetarian sandwiches and 10 turkey sandwiches.
a saving account earns interest at a rate of 4.8 percent compounded annually. if 100 dollars are initially deposited in this account, no other transactions are made, and interest is paid at the end of the year, what is the least number of years it will take for the value of the account to exceed 300 dollars
explain please
Answer:
24 years
Step-by-step explanation:
You want to know the number of years it will take an account's value to exceed $300, given it was opened with $100 and earns 4.8% interest compounded annually.
Account valueThe value of the account earning compound interest is ...
A = P(1 +r)^t
where principal P is earning interest at rate r for t years.
YearsSolving for t, we get ...
A/P = (1 +r)^t
log(A/P) = t·log(1+r)
t = log(A/P)/log(1 +r) = log(300/100)/log(1 +0.048)
t = log(3)/log(1.048) ≈ 23.433
For the value to exceed $300, it will take 24 years.
<95141404393>
!!30 Points, Pls help ASAP!!
Divide using synthetic division
x^4 – 3x^3 – 7x + 1 ÷ x + 2
The quotient of x⁴ – 3x³ – 7x + 1 ÷ x + 2 is x³ - 5x² + 3x and the remainder is 5
How to perform the synthetic division?From the question, we have the following parameters that can be used in our computation:
x^4 – 3x^3 – 7x + 1 ÷ x + 2
Rewrite as
x⁴ – 3x³ – 7x + 1 ÷ x + 2
This means that
Divisor = x + 2
Dividend = x⁴ – 3x³ – 7x + 1
Using the synthetic division, we have the following setup
-2 | 1 -3 -7 1
Bring down the first factor
-2 | 1 -3 -7 1
1
Multiply by -2
-2 | 1 -3 -7 1
-2
1
Repeat the above steps as follows
So, we have
-2 | 1 -3 -7 1
-2 10 -6
1 -5 3 5
The last number represents the remainder of the division
This means that
Remainder = 5
Quotient = x³ - 5x² + 3x
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Which equation is represented by the graph below
Answer: pls show list of equations
Step-by-step explanation:
What is the equation of a line that passes through (8,-5) and is parallel to the graphed line?
Answer:D. y = 3/4x + 1
Need help and fast please and thank you.
y= 0.141(15) + 0.842 =
y = 2.115 + 0.842
= 2.957
no explanation
A pool has some initial amount of water in it. Then it starts being filled so the water level rises at
a rate of 6 centimeters per minute. After 20 minutes, the water level is 220 centimeters.
Graph the relationship between the pool's water level (in centimeters) and time (in inches minutes).
Answer:
To graph the relationship between the pool's water level and time, we can start by creating a table of values for the water level at different times. Here is an example of such a table:
Time (minutes) Water Level (centimeters)
0 0
1 6
2 12
3 18
4 24
5 30
6 36
7 42
8 48
9 54
10 60
11 66
12 72
13 78
14 84
15 90
16 96
17 102
18 108
19 114
20 120
We can then plot these values on a graph, with the time on the x-axis and the water level on the y-axis. The resulting graph would be a straight line that slopes upwards, starting at the origin (0, 0) and ending at (20, 120).
The graph shows that the water level in the pool increases linearly with time. The slope of the line represents the rate at which the water level is increasing, which in this case is 6 centimeters per minute.
Step-by-step explanation:
A cereal box says that now it contains 20% more originally it came with 18.5 ounces of cereal how much cereal does the box come with now
Answer:
Step-by-step explanation:
Step-by-step explanation: the original weight of a cereals is ounces. Now according to question, new weight of cereals is more of original weight of cereals. Therefore, New weight of cereals will be formulated as Hence, the new weight of cereals is ounces.
Ma Baker's Pies charges $12 for a pumpkin pie and $14 for an apple pie. Last week, they sold a third as many pumpkin pies as apple pies, for a total of $5,400. How many pumpkin pies were sold last week?
20 POINTS!!!!
The Ancient Egyptians were the first to invent a dish close to what we know as a pie today. They had a honey filling covered in a crusty cake made from oats,
Who was the first American author of a recipe for pumpkin pie?This type of pie appears to have been made by some of the early colonists as well—but, by 1796, when Amelia Simmons' American Cookery, the first cookbook written by an American and published in America, appeared, pumpkin pie had evolved into a familiar form that we would recognize today.The cost of one apple pie = $6They stewed pumpkins or filled a hollowed out pumpkin shell with milk, honey and spices, and then baked it in hot ashes. Northeastern Native American tribes grew squash and pumpkins. The Native Americans brought pumpkins as gifts to the first settlers, and taught them the many uses for pumpkin.Types of squashes were first introduced to Europe in the form of Pumpkin seeds brought back from the Americas by Columbus himself. The introduction of pumpkins affected the way food was consumed in Europe. In both Italy and Spain, pumpkins were used in puddings and soups, making food much tastier and more enjoyable.And cost of one pumpkin pie = $8
Let the cost of one apple pie be $x
And cost of one pumpkin pie be $ y.
According to given problem,
For Lisa : sold 8 apple pies and 4 pumpkin pies for a total of $80
8x + 4y = 80 ------------(1)
For Shreya : sold 8 apple pies and 3 pumpkin pies for a total of $72
8x + 3y = 72 ---------------(2)
Solving equation (1) and (2), to get x and y.
Subtract equation (2) from equation (1)
i.e 8x + 4y - (8x +3y) = 80 - 72
or 8x - 8x + 4y - 3y = 8
or y = 8
And x = 6 { 8x + 4×8 = 80 or x = (80 - 32)/8 = 48/8 = 6 }
Hence, the cost of one apple pie = x = $6
And cost of one pumpkin pie = y =$8
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Calculate the surface area of a sphere with a diameter of 28
Answer:
The surface area of a sphere is 2461.76 units.
Step-by-step explanation:
Given;Diameter (d) of a sphere = 28 unitsTo Find;Area of SphereFormula;A = 4 π r²where,
π = 3.14 or 22/7
r = radius of sphere
Here, we know that
radius = diameter ÷ 2 = 28/2 = 14 units
So,
A = 4 π r²
A = 4 × 3.14 × (14)² units
A = 12.56 × 196 units
A = 2461.76 units
Thus, The surface area of a sphere is 2461.76 units.
Answer: the surface area of the sphere of diameter 28cm is 2464 cm²
Step-by-step explanation:
Given, diameter = 28 cm
hence, radius of the sphere = d/2 = 28/2 =14 cm
Therefore, the surface area of a sphere of radius (r) = 4пr²
where п= 22/7= 3.14
= 4×3.14×14×14
= 2464 cm²
suppose the random variable, x, is distributed normal with mean 4 and standard deviation 1.37. suppose the probability that x is less than the value x is equal to 0.8907, that is, p(x0.8907. what is x?
Since the probability is less than equal to 0.8907, then the value of x is 0.9750.
Given, the random variable is from of a normal distribution with
μ = 4 and σ = 1.37
.where, μ is the mean value and σ is the standard deviation.
According to the Question:
P(X≤8.907) = P( X−μ/σ ≤ 0.8907 - 4.00/ 1.37)
= P ( Z ≤ -29196.43)
Using Z-table we get a value of x which is 0.9750
So,
P(X ≤ 0.8907) = 97.50%
According to the calculations, the required value of x is 97.50%.
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Nick has two pet rabbits.His Flemish giant rabbit weighs 5 times as much as his Holland lop rabbit,If nich's Flemish rabbit weighs 12 more pounds than his Holland lop rabbit,how much does his Flemish giant rabbit weight?
Answer:The Flemish giant rabbit weighs 32 pounds.
Step-by-step explanation:
Water is flowing into a tank at a rate of R(t) where t is measured in seconds. Is there ever a time where the R'(t) = 0? If so, what time interval does t occur in? Justify your answer using the Mean Value Theorem. t R(t) 0 70 1 72 2 78 3 80 4 83 5 78 6 82
On solving the provided question, we can say that - by equation, total amount of water removed was = 1.R(0) + 2.R(1) + 3.R(3) = 1(1340) + 2(1190) + 3(950) + 2(740) = 8050 liters
What is equation?An equation is a mathematical formula that expresses equality by joining two expressions together with the equal symbol =. A formula that claims two formulae are equal is the definition of an equation in algebra in its most basic form. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. An equal sign is a part of all mathematical formulas, including equations. Often, algebra is used in equations. In mathematics, algebra is employed when we don't know the precise quantity to calculate.
R'(2) = R(3) - R(1) /3-1 = 950-1190/2 = /120L/hr
total amount of water removed was = 1.R(0) + 2.R(1) + 3.R(3) = 1(1340) + 2(1190) + 3(950) + 2(740) = 8050 liters
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Please help asap ill give brainlest
The solutions to the equation word problems are as follows;
1) Amount jane will have is 50 + 2d
2) Amount Elis will have = 24 + 6d
3) The equation is; 50 + 2d = 24 + 6d
4) Amount each has saved = $63
How to solve Algebra Word Problems?We are given that;
Amount Jane has = $50
Amount Elis has = $24
Amount saved by Jane each day = $2
Amount saved by Elis each day = $6
1) After d days of saving, amount jane will have is;
A = 50 + 2d
2) After d days of saving, amount Elis will have is;
A = 24 + 6d
3) The equation that will be used to show when Joan and Elis would have saved same amount is;
50 + 2d = 24 + 6d
4) 50 + 2d = 24 + 6d
26 = 4d
d = 26/4
d = 6.5 days
Amount each has saved = 50 + 2(6.5) = $63
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yes Are these polygons congruent? 1.5 cm 4 cm 3 cm no 2 cm
Find the value of a if the line line y=-x+4 is tangent to the graph of f(x) = x^2 - 5x +a
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
If the line y=-x+4 is tangent to the graph of f(x) = x^2 - 5x + a, it means that the line and the graph of the function are just touching at a single point, and are not intersecting at any other points.
To find the value of a, we can start by setting the equation for the line and the equation for the function equal to each other:
y = -x + 4
f(x) = x^2 - 5x + a
Then, we can substitute the equation for the function into the equation for the line:
-x + 4 = x^2 - 5x + a
We can then solve this equation for a by moving all the terms to one side:
-x + 4 - x^2 + 5x = a
-x^2 + 6x - 4 = a
We can see that the left-hand side of this equation is a quadratic expression in x, and we know that a quadratic function is tangent to a line when the line is a horizontal tangent. This occurs when the derivative of the function is equal to the slope of the line.
The derivative of f(x) = x^2 - 5x + a is 2x - 5, so we can set this equal to the slope of the line, which is -1:
2x - 5 = -1
2x = -6
x = -3
Now that we know the value of x, we can substitute it back into the equation for the function to find the value of a:
f(-3) = (-3)^2 - 5(-3) + a
f(-3) = 9 + 15 + a
f(-3) = 24 + a
Since the line and the function are just touching at this point, the y-value of the function at x=-3 must be equal to the y-value of the line at x=-3. We can substitute these values into the equation for the line to find the value of a:
y = -(-3) + 4
y = 3 + 4
y = 7
Substituting this back into the equation for the function, we get:
f(-3) = 24 + a = 7
a = 7 - 24
a = -17
Therefore, the value of a is -17.
what do you mean by tangent?
A tangent is a line that touches a curve at a single point, but does not intersect the curve at any other points. In other words, it is a line that is just "skimming" the curve, rather than crossing it.
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Select the equation for the line crossing the points (3,¹/2) and (5,5).
The equation of the line is (b) y = 2.25x - 6.25
How to determine the equation of the lineFrom the question, we have the following parameters that can be used in our computation:
Points = (3, 1/2) and (5, 5)
A linear equation can be represented as
y = mx + c
Substitute the known values in the above equation, so, we have the following representation
1/2 = 3m + c
5 = 5m + c
Subtract the equations
2m = 4.5
Divide by 2
m = 2.25
Substitute m = 2.25 in 5 = 5m + c
5 = 5 * 2.25 + c
So, we have
c = 5 - 5 * 2.25
Evaluate
c = -6.25
Recall that
y = mx + c
So, we have
y = 2.25x - 6.25
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Complete question
Select the equation for the line crossing the points (3,1/2) and (5,5).
(a) y = 5x + 2
(b) y = 2.25x - 6.25
(c) y = 2.25x + 6.25
(d) y = -5x - 2
one number is 431 more than the other, their sum is 679, find the two numbers
Answer:
Step-by-step explanation:
Let's call the two numbers x and y. We can set up the following equation to represent the problem:x + y = 679y = x + 431Substituting the second equation into the first equation, we get:x + (x + 431) = 679Combining like terms, we get:2x + 431 = 679Subtracting 431 from both sides, we get:2x = 248Dividing both sides by 2, we get:x = 124Substituting this value back into the equation y = x + 431, we get:y = 124 + 431 = 555Therefore, the two numbers are 124 and 555.
a tower that is 124 feet tall casts a shadow 138feet long. find the angle of elevation of the sun to the nearest degree.
The angle of the elevation comes to be 41.94 degrees.
What is Angle of Elevation ?The angle of elevation is the angle that is to be formed between the horizontal line and the given line of sight. If the line of sight is upward from the given horizontal line, then the angle formed is an angle of the elevation.
What is Trigonometry ?The most crucial area of mathematics is trigonometry. Combining the Greek "Trigonon" and "Metron," which respectively mean "triangle" and "measure," creates the word "trigonometry." It is the examination of the relationship between a right-angled triangle's sides and angles. By employing formulas and identities based on this relationship, it is thus possible to determine the measure of a right-angled triangle's unknown dimensions.
As in the case of right angled Triangle
From Trigonometry,
tan (α) = [tex]\frac{124}{138}[/tex]
α = arctan( [tex]\frac{124}{138}[/tex] )
α = 41.94 degrees
and in radians = 0.732
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Tommy is flying his kite one afternoon and notices that he has let out
the entire 130 ft of string. The angle his string makes with the ground
is 48°. How high, to the nearest foot, is his kite at this time?
If Tommy is flying his kite one afternoon and notices that he has let out
the entire 130 ft of string. The height , to the nearest foot, is his kite at this time is : 144 ft.
How to find the height?Given data:
String = 130 ft
Angle = 48°
Let h represent the height
Hence,
Tan48° = h/130
h= 130 tan48°
h = 130 (1.11061251483)
h = 144 ft
Therefore we can conclude that the height is 144ft.
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A real estate agent sold three apartment buildings. The first sold for $1,259,300, the second sold for $2,839,750, and the third sold for $1,935,200. What was the total cost for the three buildings?
Answer:
The total cost for the three buildings was $6,034,250.
Step-by-step explanation:
Given,
The first sold for $1,259,300,
the second sold for $2,839,750,
the third sold for $1,935,200.
We add these three sold cost of apartment buildings
$1,259,300 + $2,839,750 + $1,935,200 = $6,034,250.
To calculate the total cost of three things, you will need to add the individual costs of each item together.
1. Determine the cost of each item. Add together the cost of all three items. This total is the cost of the three items.
2. If the items are sold as a package, determine the cost of the package. This is the cost of the three items.
3. If the items are sold at a discounted rate, calculate the total cost of each item after the discount has been applied. Add together the costs of the three items after the discount has been applied. This total is the cost of the three items.
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Given the equation f + 24 = −3, solve for f. NEED HELP ASAAPPPPPPPP I WILL GIVE BRAINLY IF THE QUESTION IS RIGHT!!
−72
−27
−21
8
Answer: -27
Step-by-step explanation:
To solve for x, we have to make f alone.
f+24=-3 [subtract both sides by 24]
f=-27
The answer is -27.
Answer: -27
Step-by-step explanation: f+24+-3 to find f subtract 24 from -3. which equals -27 it might not be the proper way but it works. :)
solve for x. pls helppp
The value of x is 12 .
Given ,
angle DEH as exterior angle and angle E, C, D as interior angles .
What is the relation between interior & exterior angles of a triangle ?
Interior angle refer to all those angles that are inside a shape. On the other hand, the exterior angle is an angle that is made by the side of the shape and a line drawn out from an adjacent side.
Furthermore, the exterior angle is equal to the sum of the non-adjacent interior angles .
Calculations
angle DEH = angle C + angle D
9x + 22 = 5x + 10 + 60
9x - 5x = 70 - 22
4x = 48
x = 12
The value of x is 12 .
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Use arrow notation to describe the translation of point P(–10, 1) to point P′(–16, –1).
Answer: In order to describe a translation using arrow notation, we need to specify the direction and distance of the translation. In the case of the given translation, point P is translated to point P' by moving 6 units to the left and 2 units down. This can be represented using arrow notation as follows:
P' = P ← 6 ↓ 2
Here, the symbol ← represents a leftward movement, and the symbol ↓ represents a downward movement. The numbers 6 and 2 indicate the distance of the movement in the respective directions. This means that point P is translated to point P' by moving 6 units to the left and 2 units down from its original position.
