The solution of the system of equations is (4, 3)
How to solve the system of equations?Here we want to solve the system below:
8x+2y=38
2x-4y=-4
If we add 2 times the first equation and the second equation we will get:
2*(8x + 2y) + (2x - 4y) = 2*38 - 4
16x + 4y + 2x - 4y = 72
18x = 72
x = 72/18 = 4
And the vale of y is given by inputing x = 4 in one of the two equations.
2*4 - 4y = -4
8 - 4y = -4
-4y = -4 - 8
y = -12/-4 = 3
The solution is (4, 3)
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If f is differentiable at a, must f be continuous at a? A. No, if f is differentiable at a and does not have a corner at a, then f is continuous at a B. No, if f is differentiable at a and does not have a vertical tangent at a, then f is continuous at а. C. No, if f is differentiable at a and positive at a, then f is continuous at a. D. Yes, iff is differentiable at a, then fis continuous at a.
The correct statement regarding the continuity of differentiable functions is given as follows:
D. Yes, if f is differentiable at a, then f is continuous at a.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
For a function to be classified as differentiable, the function must be continuous, plus the first derivative of the function must also be continuous.
This means that all differentiable functions are continuous, and thus the correct option is given by option D.
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find x, please show the work
Paul, Maria, Stephanie, and Andy have a total of $56 to spend at the amusement park. Admission will cost them $5 each for a total of $20. They can spend the rest on food and rides. They plan to spend twice as much on rides as on food. How much do they plan to spend on rides?
Answer:
They plan to spend $24 on rides.
Step-by-step explanation:
Let the amount they spend on food be x.
ride : 2x
amount left= $56-$20
= $36
2x+x= 36
x=12
2x= 2(12)
= 24
Mateo currently has $100 in his bank account and plans on saving $20 per week in order to save for soccer camp over the summer. Write an equation to represent the amount of money saved, S, with respect to the number of weeks that have passed, w.
S = _ w + _
The equation that represents the amount of money saved is S = $100 + $20w
What is the equation that represents the amount of money saved?The equation that represents the amount of money saved is a linear equation . A linear equation is an equation that has a single variable raised to the power of 1.
The form of the linear equation is:
Total money saved = amount in the bank + (amount that would be saved each week x number of weeks)
S = $100 + ($20 x w)
S = $100 + $20w
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A car dealership increased the price of a certain car by 14% The original price was 32,600
Answer: 37164
Step-by-step explanation:
14% of 32,600 is 4564
-To find the new value of the car, you must add the 14% of the original value and the original value together
-4,564 + 32,600 = 37164
any " Which of the following numbers have a remainder of I when divided by 2? (There is more than one answer) A) 327 B) 400 C) 751 D) 148 E) 1,356
A. 327 and C.751 have a remainder of 1 when divided by 2
What is an Even Number?Even Numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2. They are numbers that are a multiple of 2. Examples are: 2, 4, 6, 8, 10, and so on are even numbers.
How to determine this,
By dividing each words by 2
327 divided by 2 = 163 remainder 1
So, this is not an even number when divided by 2
400 divided by 2 = 200 remainder 0
This is an even number
751 divided by 2 = 375 remainder 1
This is not an even number
148 divided by 2 = 74 remainder 0
This is an even number
1356 divided by 2 = 678 remainder 0
So, this is an even number
Therefore, only 327 and 751 have a remainder of 1 when divisible by 2.
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The table below represents a linear function for the cost of a gym membership based on the number of months of membership.
What is the slope and y-intercept of the linear function.
The equation of line is y = 30x + 75 , where the slope is m = 30 and the y intercept is 75
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 1 , 105 )
Let the second point be Q ( 3 , 165 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 165 - 105 ) / ( 3 - 1 )
Slope m = ( 60 / 2 )
Slope m = 30
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 105 = 30 ( x - 1 )
On simplifying the equation , we get
y - 105 = 30x - 30
Adding 105 on both sides of the equation , we get
y = 30x + 75
Hence , the equation of line is y = 30x + 75
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Select all of the expressions that have a positive value based on the positions of a and b.
(Select all that apply.)
1. -b
2. a+b
3.a-b
4. a*b
5. -b/a
The expressions that have a positive value based on the positions of a and b are a + b and a×b. options 2 and 4
What are algebraic expressions?Algebraic expressions are defined as expressions that are made up of terms, variables, factors and constants.
These expressions are also composed of mathematical operations such as;
SubtractionBracketParenthesesMultiplicationAdditionDivisionFloor divisionGiven the expressions;
a+ b and a×b.
They have the variables both positive
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Which number is a factor of 24 but not a multiple of 12
What is the connection string for SQL Server using Windows Authentication?
The connection string for SQL Server using Windows Authentication is as follows:
Server=myServerAddress;Database=myDataBase;Trusted_Connection=True;
Specify the server address in the format "Server=myServerAddress". Replace "myServerAddress" with the name or IP address of the SQL Server instance you want to connect to.
Specify the name of the database you want to connect to in the format "Database=myDataBase". Replace "myDataBase" with the name of the database.
Use Windows Authentication by setting "Trusted_Connection=True". This means that the user running the application is authenticated using their Windows credentials, rather than a SQL Server login.
Use semicolons (;) to separate the different parts of the connection string.
Using Windows Authentication is a more secure and convenient way to connect to a SQL Server database, as it eliminates the need to store and manage login credentials in the application.
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Find the value of each variable
The triangle on the left is a 45 45 90 triangle and the triangle on the right is a 30 60 90 triangle.
In a 45 45 90 triangle, the length of the hypotenuse is equal to the length of either one of the legs times the square root of 2. So that means that a and c are both 18.
In a 30 60 90 triangle, the length of the hypotenuse is twice that of the leg opposite the 30 degree angle. So that means that b is 36. The length of the leg opposite the 60 degree angle is the length of the other leg times the sq root of 3. So that would give you d = 18 sq root 3.
What is the average increase in pennies for Daisy's piggy bank over the first 2 days (starting with day 0)?
The average increase in first 2 days is 1.5 pennies/day.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Given is a tabular data about Daisy's piggy bank.
The average increase in first 2 days -
{a} = (7 - 4)/(2 - 0)
{a} = 3/2
{a} = 1.5
Therefore, the average increase in first 2 days is 1.5 pennies/day.
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A family went on a cross-country road trip for their summer vacation. The following table shows the number of days and the total amount of miles their car had driven.
Number of Days 2 5 6 8 12
Miles Driven 425 967 1,253 1,253 2,648
Which of the following graphs is most appropriate to construct for the data given in the table to observe how the miles change over a certain number of days? Explain.
A scatter plot, because it would show the association, or relationship, between the two variables
A scatter plot, because it would show how a variable changes over time between each individual data point
A line graph, because it would show the association, or relationship, between the two variables
A line graph, because it would show how a variable changes over time between each individual data point
Thus, a line graph would be more appropriate for this particular data set to observe the changes in the miles driven over a certain number of days.
What is data?Data refers to any collection of facts, figures, or information that can be processed, analyzed, and interpreted to gain insights and knowledge. It can be in various forms such as text, images, audio, video, or numerical values, and can be collected from various sources such as surveys, sensors, social media, or transactions.
Given by the question: -
The most appropriate graph to construct for the given data is a line graph because it would show how the miles driven change over time between each individual data point. A line graph is useful for showing trends or changes over time, and it allows us to see the progression of the miles driven during the trip. This graph would have days on the x-axis and miles driven on the y-axis, with a line connecting the data points. This would help to visualize any patterns or trends in how the miles driven change over time during the trip.
On the other hand, a scatter plot would show the relationship between the two variables, but it would not show the changes over time. While scatter plots are useful for showing relationships between variables, they do not show the order or progression of the data points over time.
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What is the result of multiplying the first equation by 2 and adding to the second equation?
6x − y = 7
2x + y = 5
A. 14x + 3y = 19
B.14x + y = 19
C.14x - y = 19
Isabella scored 76% on her first math test this quarter. Her next two scores were 80%
and 84%. If she continues to improve at this rate,
A. What would be her score on the fifth (and final) test for the quarter?
B. Assuming each test is worth 100 points, what is Isabella's percentage for tests?
Answer:
your welcome
Step-by-step explanation:
A. she scored 89 %
B. 89 points
How many nets are there for a triangular pyramid?
The net of a triangular pyramid consist of a total of 4 triangles. it has 4 faces with the base being one of them which is also in the shape of a triangle.
A net of the triangular pyramid is the pattern formed when the surface of it is laid out flat showing each triangular face of the figure, therefore we know that the net of a triangular pyramid consist of a total of 4 triangles.
Triangular pyramid is a pyramid which has a triangular base. In geometry, vertices are essentially corners. All triangular-based pyramids, either regular or irregular, have four vertices.
It has 6 edges, 4 faces, 4 vertices.
A regular triangular pyramid has equilateral triangles all four faces
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Find the number of sides (n) of the polygons with the angle values shown in the items below.
a) The sum of the interior angles is 10,440∘
b) The value of each interior angle is 171∘
As per the concept of polygon,
a) The sum of the interior angles is 10,440° then the number of sides is 58
b) The value of each interior angle is 171°, then the number of sides is 36
A polygon is a two-dimensional geometric shape made up of straight lines and angles. The number of sides a polygon has is directly related to the sum of its interior angles.
a), we can use the formula for the sum of the interior angles of a polygon, which is (n-2) times 180 degrees, where n is the number of sides. To find n, we can rearrange the formula to
=> n = (sum of interior angles / 180) + 2.
Plugging in the value of 10,440 degrees for the sum of interior angles, we get
=> n = (10440 / 180) + 2 = 58.
Therefore, the polygon in item a) has 58 sides.
For item b), we can use the formula for the value of each interior angle of a regular polygon, we get
=> n = (180(n-2)) / 171 = (180n - 360) / 171.
Solving for n, we find that the polygon in item b) has 36 sides.
In conclusion, polygons with the angle values shown in items a) and b) have 58 and 36 sides respectively. These formulas can be applied to any polygon to find the number of sides based on its interior angle values.
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100 points help i will mark branilyest
Answer:
[tex]\frac{2}{11}[/tex]
Step-by-step explanation:
[tex]\frac{6}{11} * \frac{1}{3}[/tex]
since 6 and 3 are opposite of each other in this multiplication problem, you can divide them by 3 since they are both divisible by 3
[tex]\frac{2}{11} * \frac{1}{1} = \frac{2}{11}[/tex]
Patrick ran from his home to a shop 400m away at an average speed of 2 m per second he walked back to his home at an average speed of 1 m per second find the average speed for the whole journey if he did not stop at the shop
The average speed that Patrick used to run from his home to a shop and walk back to his home is 1.33 m per second.
What is the average speed?The average speed is the total distance divided by the total time.
The average or mean is the quotient of the total value and the total time or number of items in a data set.
The distance from Patrick's home to a shop = 400 m
Running speed from home to the shop = 2 m per second
The total time used in running to the shop = 200 seconds (400/2)
The distance from the shop to Patrick's home = 400 m
Walking speed from shop to the home = 1 m per second
The total time used in walking back to the home = 400 seconds (400/1)
The total distance to and from shop = 800 m (400 x 2)
The total time used to run to and walk from the shop = 600 seconds (200 + 400)
The average speed for the whole journey = Total Distance/Total Time
= 800/600 = 1.33 m per second
Thus, for covering a total distance of 800 m in 600 seconds, Patrick's average speed was 1.33 m per second.
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The picture has a side of 7 inches.
What is the area of the picture?
Answer:
Step-by-step explanation:
So here is what I did. If the picture is square then you would multiply Length times the Width to get 49 square inches. But if it’s not a square then you would still multiply Length by Width.
f(x)=x² +16x-24 and
g(x)=x²-5x-17, find (ƒ + g)(x).
If functions f(x)=x² +16x-24 and g(x)=x²-5x-17 then (f+g)(x) is 2x² +11x-41.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given functions are f(x)=x² +16x-24 and g(x)=x²-5x-17.
We need to find (ƒ + g)(x).
From properties we have (ƒ + g)(x)=f(x)+g(x)
(ƒ + g)(x)=x² +16x-24+x²-5x-17.
Add the like terms
(f+g)(x)=2x² +11x-41
Hence, if functions f(x)=x² +16x-24 and g(x)=x²-5x-17 then (f+g)(x) is 2x² +11x-41.
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Points A, B, C and D are collinear, with B between A and C, and C between B and D. What is the measure of CD, if AB = 4x-1, BC= 6x-2, BD = 11x + 5, and AD = 64?
A. 15 units
B. 22 units
C. 25 units
D. 27 units
E. 33 units
Answer:
D. 27 units.
Step-by-step explanation:
See my attachments.
I need a answer and explaination.
Answer:
x = 33°
Step-by-step explanation:
Vertically opposite angles:Vertically opposite angles are congruent.
∠AOB = ∠DOC
4x - 6 = 2x + 60
Add 6 to both sides,
4x = 2x + 60 + 6
4x = 2x + 66
Subtract 2x from both sides,
4x - 2x = 66
2x = 66
Divide both sides by 2
x = 66 ÷ 2
[tex]\boxed{x = 33}[/tex]
∠AOB = 4x - 6
= 4*33 -6
= 132 - 6
∠AOB = 126°
∠DOC = 126°
Karen and Bill collect coins. Karen has x coins. Bill has 9 coins fewer than two times the number of coins Karen has. Write and simplify an expression for the total number of coins Karen and Bill have.
Answer: Let's call the total number of coins Karen and Bill have "t".
We can start by writing an expression for the number of coins Bill has:
2x - 9 = 9 + 2x
So the total number of coins Karen and Bill have is:
t = x + (2x - 9)
Simplifying the expression for t:
t = 3x - 9
So the total number of coins Karen and Bill have is equal to 3 times the number of coins Karen has minus 9.
Step-by-step explanation:
Give the circumference and the area of a circle with diameter 4yd use the value of 3.14 for pi
Answer:
Circumference = 12.56 yd
Area = 12.56 yd²
Step-by-step explanation:
Equations we need to know:
Circumference of circle - 2πr
Area of circle - πr²
1) Circumference
2 x 3.14 x 2 = 12.56
2) Area
3.14 x 2² = 12.56
We have to make sure the we are using the radius and not the diameter otherwise our answer would be wrong
Hope this helps, have a lovely day! :)
Answer:
Area=12.56yd^2, Circumfrence=12.56yd
Step-by-step explanation:
the formula for the area of a circle is pi*r^2 and since pi is 3.14 and r is 2 so r^2 is 4 and 4*3.14 is 12.56 (r is the radius)
the formula for the circumference of a circle os 2*pi*r and r is 2 so its 2*3.14*2 multiplying all these terms again gives us 12.56 but be careful with the units as with the area comes yd^2 and with the circumference comes yd only
Choose the best answer.
A statement in which a conclusion is true if the conditions of a particular hypothesis are true is called a
A statement in which a conclusion is true if the conditions of a particular hypothesis are true is called a conditional statement.
What is the conditional statement?A conditional statement is one that has the form "If P then Q," where P and Q are sentences. P is referred to as the hypothesis in this conditional statement, and Q is referred to as the conclusion. "If P then Q" implies that Q must be true sometimes when P is true.
The type of conditional statements are as follows:
General truth: I feel better all day if I eat breakfast.Future event - I will investigate tonight if I have a scan tomorrow.Assumption: If I had a million dollars, I would purchase an airplane!Hypothetical outcome - I might have been offered the position if I had geared up for the interview.A statement in which a conclusion is true if the conditions of a particular hypothesis are true is called a conditional statement.
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the sum of 3 consecutive multiples of 8 is 888 find the multiples
[tex]\fbox{\textbf{288, 296, and 304}}
[/tex]
Step-by-step explanation:Let's assume the first multiple of 8 is x, then the second multiple is x+8, and the third multiple is x+16.According to the problem statement, the sum of these three multiples is 888:x + (x+8) + (x+16) = 888Simplifying the left side:3x + 24 = 888Subtracting 24 from both sides:3x = 864Dividing both sides by 3:x = 288Therefore, the first multiple of 8 is 288, the second is x+8 = 296, and the third is x+16 = 304.So, the three consecutive multiples of 8 that add up to 888 are 288, 296, and 304Find the equation of the straight lines Parallel to the line y + 8 = 0 and passes through (2; 1).
Answer:
[tex]y = 1[/tex]
Step-by-step explanation:
Rearranging the equation:
[tex]y = -8[/tex]
Three points to be considered:
1. Above is a horizontal line cutting through the y-axis at y value of [tex]-8[/tex].
2. A horizontal line has a slope (or gradient) of 0.
3. Parallel lines have the same slope (or gradient)
∴The straight line passing through (2, 1) will also have a zero slope. In addition, this is a horizontal line, which cuts the y-axis at y value of 1.
The equation of straight line:
y = 1
Select all the equations that are equivalent.
52 = 8n + 4
4(2n + 1) = 52
4 = 52 – 8n
4n = 48
n = 6
The equivalent equations are 52 = 8n + 4, 4(2n + 1) = 52 and 4 = 52 – 8n.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
To determine which equations are equivalent to each other, we can simplify and manipulate each equation to see if they have the same solution(s).
52 = 8n + 4 can be simplified by subtracting 4 from both sides:
48 = 8n
n=6
Now 4(2n + 1) = 52
8n+4=52
8n=48
n=6
So the 52 = 8n + 4 and 4(2n + 1) = 52 are equivalent equations.
Now 4 = 52 – 8n
8n=52-4 is also equivalent equation.
4n=48 and n=6 are also equal but they are not in the same form as above equations.
Hence, 52 = 8n + 4, 4(2n + 1) = 52 and 4 = 52 – 8n are equivalent equations.
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How do you write Euler's number in Symbolab?
To write Euler's number in Symbolab, you can simply use the notation "e". For example, if you want to evaluate the exponential function with a base of e raised to the power of 2, you can enter "e^2" in Symbolab.
Euler's number, denoted as "e", is a mathematical constant that is approximately equal to 2.71828. To write Euler's number in Symbolab, you can simply use the letter "e" in lowercase. For example, to evaluate the exponential function with a base of e raised to the power of 2, you can enter "e^2" in Symbolab.
Alternatively, if you want to use the built-in function for Euler's number in Symbolab, you can use the "exp(x)" notation, where x is the exponent. For example, to evaluate e raised to the power of 2, you can enter "exp(2)" in Symbolab. Symbolab supports various mathematical functions and constants, including trigonometric functions, logarithmic functions, and mathematical constants, which can be used to solve various mathematical problems.
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