The required three consecutive odd numbers that sum up 57 are 17, 19 and 21.
What are consecutive numbers ?
Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.
Since, we know that any odd number is always of the form (2k +1). We express an odd number in this form because we know that an odd number is not divisible by 2.
Now, the next odd number after (2k+1) will be (2k+3) because if we take (2k+2) then we can see that it is clearly divisible by 2.
So, we can say that the difference between any two consecutive odd numbers is:
= 2k+3 – (2k+1)
=2k+3-2k-1
=2
So, for every two consecutive odd numbers there is a difference of 2.
Now, let us take ‘n’ to be an odd number.
So, an odd number just before n will be (n-2).
And also an odd number just after n will be (n+2).
Since, it is given that the sum of these three consecutive odd numbers is 57. So, we can write the following equation:
n-2+n+n+2=57
3n=57
So, n = 19
The odd number before n will be = n -2 = 19-2 = 17
And the odd number after n will be = n+2 = 19 + 2 = 21
Therefore, The required three consecutive odd numbers that sum up 57 are 17, 19 and 21.
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maths question on triangles
Answer:
The height (AE) is 20 cm
Step-by-step explanation:
Volume = 1/3(area of the base) height
600 = 1/3(18 x 5)h
600 = 30h Divide both sides by 30
[tex]\frac{600}{30}[/tex] = [tex]\frac{30h}{30}[/tex]
20 = h
Evaluate x/y for x=1/6 and y=1/3.
1/18
1/2
1/9
9
Answer:
soln:
x/y=1/6/1/3
=1/6×3/1
=1/2
Therefore x/y = 1/2
How do you find the total from 1 to 100?
The total number from 1 to 100 is found by addition
What is addition in math ?
Combining things and counting them as one big group is done through addition.
In math, addition is the process of adding two or more integers together.
Addends are the numbers that are added, and the outcome of the operation, or the final response, is referred to as the sum.
In the problem the addends are the numbers 1 2 3 4 5 6 .......97 98 99 100
The applying the addition operation the sum is calculated to be 5050. calculator will make the operation easier
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Snooty had to solve the following
equation for x:
x² = 64
Someone told Snooty there are actually
2 solutions! This confused Snooty. Can
you explain to Snooty why there are 2
solutions for x in this equation?
Type a response
0.
Answer:
8, -8
Step-by-step explanation:
There are 2 answers for the solution because x² = 64 can equal 8, and -8. It can equal 8 because 8 x 8 = 64. It can also equal -8 because -8 x -8 is a positive 64.
What is the equation of the line of symmetry for the parabola represented by the equation y = −2x^2 − 16x − 27?
Enter your answer as the correct equation, like this: x = 42
Answer: x=-4
Step-by-step explanation:
You can find this algebraically by either solving for the y-value of the vertex or by adding the two zeros and dividing by two.
In this case: (-5.581, 0) and (-2.419)
-5.581 + -2.419
= -8
-8/2 = -4
Look at this table:
13
15
19
-19
-9
Is this relation a function?
yes
no
Yes, the given Relation is a Function.
How do you figure out if a relation is a function?Relation: It belongs to the Cartesian product's subgroup. Or just a lot of points (ordered pairs). In other words, the ordered pair collection, where the ordered pair is made up of an object from each set, is used to define the relationship between the two sets.
To Analyze a relationship between two values to see if it can be classified as a function:
1)Choose the input values.
2)Determine the results.
3)Consider the connection to be a function if each input value results in just one output value. Do not classify the relationship as a function if any input value results in two or more outputs.
In the given table all ordered pairs have unique x values so the given relation is a function.
Yes, the given Relation is a Function.
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Which congruence theorem can be used to prove △ ABC ≅ △ DEF?
The ASA criterion might be the most appropriate, as it states that two triangles are congruent if two angles and the included side are congruent.
To use a congruence criterion in the given situation, you will need to determine which criterion is most appropriate based on the information provided. There are several congruence criteria that can be used to determine whether two triangles are congruent, including the Side-Side-Side (SSS) criterion, the Side-Angle-Side (SAS) criterion, the Angle-Side-Angle (ASA) criterion, and the Angle-Angle-Side (AAS) criterion.
In this case, the ASA criterion might be the most appropriate, as it states that two triangles are congruent if two angles and the included side are congruent. Given that ∠A=∠C=90∘ and AE=CB, you can use the ASA criterion to conclude that triangles AEB and CED are congruent.
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The question is -
Which congruence theorem can be used to prove EB = BD, AE = CB, ∠ A = ∠ C = 90°?
How to teach area Grade 5?
On the basis of their sides, we may similarly determine the areas of various shapes like rectangles, parallelograms, triangles, and any polygon.
The space the thing occupies is known as the area. Any shape can call this area home. We solely take into account the side's length when calculating the square's area. A square's area is equal to the sum of its squared sides since all of its sides are equal.
Similar to triangles, we can determine the area of any polygon based on its sides, as well as the areas of other forms like rectangles, parallelograms, and triangles. The radius of the surface, or the separation of the outer line from the axis for curved surface objects, is used to compute the area of the surface.
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Make a sketch if you need to and solve this problem using similar triangles. A telephone pole has a shadow of 16 ft. When a person 5 ft. Tall has a shadow of 6 ft. How tall is the pole? write answer as a fraction. X = ft.
The height of the poll is 40/3 and 13.3ft.
Let us assume that the Height of an object is h.
Let us assume that the shadow of an object is y.
(As the shadow is always proportional to height .)
Thus y∝h
y = kh
As given
when a person 5 ft. tall has a shadow of 6 ft.
h = 5 ft and y = 6 ft
Put in y = kh
6 = 5k
[tex]k=\frac{6}{5}[/tex]
As given
A telephone pole has a shadow of 16 ft.
Let us assume that the height of the pole is x.
h = x and y = 16 ft
16 = hk compare the value of k
[tex]k=\frac{16}{x} \\\\\frac{6}{5} =\frac{16}{x} \\\\x=\frac{16*5}{6} \\\\x=\frac{80}{6} \\\\x=\frac{40}{3} ft[/tex]
0r
x=13.3ft
Therefore, The height of the poll is 13.3ft
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Will mark brainliest the first answer with explanation!!!
Consider a game in which each play costs one nickel (5¢). During each play, the game dispenses a coin to the player to keep. The game machine contains equal numbers of pennies (1¢), nickels, dimes (10¢), and quarters (25¢). The nickels that the player inserts do not go into the same pool of "reward" coins. What is the expected profit, in cents, for a player who plays five games in a row?
The expected profit, in cents, for a player who plays five games in a row, is given as follows:
26.25 cents.
How to obtain the expected profit?The distribution that models the profit of a player for a single game is given as follows:
P(X = -4 cents) = 0.25. -> pays 5 cents, wins 1 cent, loses 4 cents.P(X = 0 cents) = 0.25. -> pays 5 cents, wins 5 cents.P(X = 5 cents) = 0.25. -> pays 5 cents, wins 10 cents.P(X = 20 cents) = 0.25. -> pays 5 cents, wins 25 cents.The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability, hence:
E(X) = -4 x 0.25 + 0 x 0.25 + 5 x 0.25 + 20 x 0.25 = 5.25 cents.
For five games, the expected value is obtained as the multiplication of the expected value of a single game by five, hence:
5E(X) = 5 x 5.25 = 26.25 cents.
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Is it true a 0 or 1?
Therefore, In the binary number 0 comes out to be false and 1 comes out to be true.
Describe a binary number.Binary code, the foundation of everything binary utilised in computing systems, provides a numbering system in which there are only two potential values for each digit: 0 or 1.
Here,
In this case, binary logic has two states: false and true. "binary" – It's critical that there be two of them.
If you want to, you can refer to them as 0 and 1, yes and no, or off and on if you're an electrical engineer. They function as intended.
Therefore, In the binary number 0 comes out to be false and 1 comes out to be true.
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When two angles and a non-included side of one triangle are congruent to the corresponding pieces of another triangle?
The correct answer is option b) AAS
What is meant by triangle ?A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point.Polygons of the form with three sides and three vertices are called triangles. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. Tri-, which means "three," and angulus, which means "angle or corner," are the roots of the Latin word triangulus, which means "three-cornered" or "having three angles."According to the AAS congruence theorem, if two angles and the non-included side of one triangle are congruent with the corresponding components of another triangle, then the two triangles are congruent.
Therefore, option B is the correct answer.
"AAS congruence" theorem an be used to prove that the triangles are congruent .
The complete question is:
Two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle. Which congruence theorem can be used to prove that the triangles are congruent?
a) SSS
b) AAS
c) SAS
d) HL
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What is an example of perpendicular equations?
An example of perpendicular equations are:
f(x)=2x+4
g(x)=[tex]\frac{-1}{2}\\[/tex]x+2
A straight line passing through a point is called a perpendicular line. It forms a 90-degree angle with a specific place where the line passes. The need for determining the perpendicular line is coordinates and a line equation.
Think about a line with the equation ax + by + c = 0 and the coordinates (x1, y1). The slope should be a/b. Let m1 and m2 represent the slopes of two lines; their product will be -1 if the lines are perpendicular to one another.
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
m = Δy/Δx = dy/dx = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
A line's slope often indicates the steepness and direction of the line.
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Think about a line with the equation ax + by + c = 0 and the coordinates (x1, y1). The slope should be a/b. Let m1 and m2 represent the slopes of two lines; their product will be -1 if the lines are perpendicular to one another.
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
m = Δy/Δx = dy/dx = change in y/change in x
where "m" represents a line's slope.
If g(x) = - 4x^2 - 3x + 2, determine g(-2).
Show your work.
Answer:
g(-2) = -8
Step-by-step explanation:
If [tex]g(x) = - 4 x^2 - 3x +2[/tex], determine g(-2):
[tex]g(-2) = - 4 (-2)^2 - 3(-2) +2\\g(-2) = - 4 (4) - (-6)+2\\g(-2) = -16 + 6 + 2 \\[/tex]
g(-2) = -8
find and sketch the domain of the function. f(x, y, z) = ln(144 − 9x2 − 16y2 − z2)
The domain of the function f(x, y, z) = ln(144 − 9x² − 16y² − z²) is x ∈ (-4, 4), y ∈ (-3, 3) and z ∈ (-12, 12). It forms an ellipsoid.
Domain of a function is the set of all values possible for the input parameters for real output parameter or output parameter in given range.
f(x, y, z) = ln(144 − 9x² − 16y² − z²)
For f(x, y, z) to be real, 144 − 9x² − 16y² − z² should be greater than 0. So,
144 − 9x² − 16y² − z² > 0
9x² + 16y² + z² < 144
x²/ 4² + y²/ 3² + z²/ 12² < 1
So the domain is an ellipsoid.
Therefore x ∈ (-4, 4)
y ∈ (-3, 3)
z ∈ (-12, 12)
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find an equation of the tangent line to the curve at the given point. y = 4ex cos(x), (0, 4)
The equation of the tangent line to the curve at the given point, y = 4ex cos(x), (0, 4) as calculated is y' = 0.
In order to find the equation we will have to differentiate y = 4ex cos(x)
On differentiating we get the differential as ,
y' = - 4eˣsin(x)
given the value of x as 0 and y as 4
y' = -4e⁰sin(0)
= 0 because sin( 0 ) = 0
Therefore ,the required equation is , y' = 0.
Differentiation is a technique which is used to find the derivative of a function . Differentiation is a mathematical procedure it determines the rate of change of a function based on one of its variables.
Other than differentiation calculus also has a branch known as integration.
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How many solutions does quadratic equation 2x² 7x 5 0 have?
Step-by-step explanation:
I cannot read what equation you wrote.
but it does not matter.
a quadratic equation has always 2 solutions.
as a cubic equation has always 3 solutions.
and so on.
sometimes they can be identical like for 0 = x² (with 0 as solution 2 times).
and sometimes they can be imaginary like in -1 = x².
but there always are 2 solutions for a quadratic equation.
for example with normal numbers :
1 = x²
the solutions are sqrt(1) = ±1 = +1 and -1.
Why does AAS congruence work?
Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle. AAS congruence may be demonstrated with a few simple methods.
When two triangles in geometry are the same size and shape, they are said to be congruent. The Angle-Angle-Side (AAS) congruence theorem is one of several approaches to demonstrate that two triangles are congruent.
According to the AAS congruence theorem, triangles are congruent if two angles and the side that connects them in one triangle are congruent with two angles and the side that connects them in another triangle. This is how this theorem is expressed:
If ∠A = ∠E, ∠B = ∠F, and AB = EF, then ∆ABC ≅ ∆DEF
In other terms, triangles ABC and DEF are congruent if two angles and the side between them in triangle ABC are equivalent to two angles and the side between them in triangle DEF.
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What are the 2 formulas for volume?
Answer:
length x width x height or probably like area x height
Step-by-step explanation:
Is cleaning the measuring instrument not necessary?
It is necessary to clean the measuring instrument the moving parts of the measuring device may be harmed if airborne dust or dirt gets inside of it. Additionally, if any foreign objects are present between the measurement target and the measuring device, precise measurements may be affected.
what is measuring instrument?A measuring instrument is a tool used to quantify anything tangible. The act of obtaining and comparing physical amounts of actual objects and occurrences is known as measuring in the physical sciences, quality control, and engineering. Vernier calipers, micrometers, dial gauges, gauges of various types, bubble levels, protractors, and rulers are some of the primary goods that fall under the category of measurement instruments. These equipment are employed in the production process and for quality assurance.
It is necessary to clean the measuring instrument the moving parts of the measuring device may be harmed if airborne dust or dirt gets inside of it.
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ralph records the time it takes for each of his classmates to run around the track one time. as he analyzes the data on the graph, he locates the mean and median time. which component of data analysis is ralph utilizing?
The component of data analysis that Ralph is utilizing is the overall spread of the data. That is option D.
What is data analysis?Data analysis is defined as the method a researcher uses to collect, clean, sort, and process raw data in a way that it's representation can be understood by the reader.
The mean of a data set is defined as the addition of all the data set which is then divided by the number of the data set.
The median of a data set is the number that falls at the middle of the set after being arranged in an ascending or descending order.
Therefore, to find the mean and median of a data set will depend on the spread out of the data.
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Complete question:
Ralph records the time it takes for each of his classmates to run around the track one time. As he analyzes the data on the graph, he notices very little variation between his classmates' times.
Which component of data analysis is Ralph observing?
A. An outlier in the data set
B. The overall shape of the data
C. The center of the data set
D. The overall spread of the data
Answer:
The overall spread of the data.
Step-by-step explanation:
Got it right on the test.
27) An amusement park ride, the Demon Drop, includes a drop of close to 100 feet. Use the given equation to
approximate the time (seconds) that it takes the dropped object to fall a distance of about feet. Solve for "t" to
the nearest tenth.
A canoe travels 4 miles per hour downstream and 2 miles per hour upstream.
Let x represent the canoe's speed with no water current (still water) and y
represent the speed of the water current, in miles per hour. Then the situation
can be represented by this system of equations:
Choose the two correct options.
x + y = 4
x - y = 2
A. The speed of the water current is 1 mile per hour.
B. The speed of the canoe in still water is 3 miles per hour.
C. The speed of the canoe in still water is 1 mile per hour.
D. The speed of the water current is 3 miles per hour.
Answer:
A, B
Step-by-step explanation:
Given the system of equations, we should first solve for x and y so we can answer this question:
equation 1: x + y = 4, equation 2: x - y = 2 ⇒ add both equations together
x + y + x - y = 4 + 2 ⇒ combine like terms
2x + 0y = 6 ⇒ divide both sides by 2
x = 3 ⇒ plug into the x + y = 4 equation to solve for y
3 + y = 4 ⇒ subtract 3 from both sides
y = 4 - 3 = 1
Since we know y is the speed of the water current and x is the canoe's still water speed, we know that the water current's speed is 1 mph and the canoe's still water speed is 3 mph
This corresponds with choices A and B
Write an equation for the line in slope-intercept form
Answer: y=2/5x +5
Step-by-step explanation: slope is 2/5 y intercept is 5
What does it mean to apply a function?
Function application is the process of applying a function to a domain-specific argument in order to get the relevant value from the function's range.
What does a function mean?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). Apply is a function in mathematics and computer science that applies arguments to a function.An example of a rule is a function, which produces one output for a single input.
Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x. I submitted written applications to a number of businesses. For this position, a high school graduation is required. Teenage dropouts are not required to apply. Apply a second coat of paint to the wall once the first one has dried and been thinly applied.
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How do you write 9 more than a number?
9 more than a number in mathematical expression is written as n+9.
Any two integers can be compared using the greater than and less than symbols. Greater than and less than symbols are used to indicate whether one number is greater than or less than another. The greater than sign (>) is used when the first number exceeds the second number. The less than sign (<) is used when the first number is less than the second number.
The quantity on the left of the > sign is the greater quantity. It could be a variable or expression [like 10x-2 > 50].
Let the number be n,
More than signifies addition. Therefore, the expression would be n+9.
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bramdpm owns nearly 2 times as many cds as ingrid.brandon owns 56 cds.write an equation and use it to estimate the number n of cds ingrid owns.
The number of CDs that Ingrid owns will be 28.
What is the equation's answer?
A direct consequence is the distribution of weights to the significant variables that result in the calculation's optimal.
Nearly twice as many CD promotions are in Brandon's possession than they are in Ingrid's. Brandon says he has 56 CDs.
Let 'x' represent Ingrid's CD collection. Then Brandon will have twice as many CDs.
The equation is then presented as,
Then the equation is given as,
2x = 56
Simplify the equation, then we have
2x = 56
x = 56 / 2
x = 28
The number of CDs that Ingrid owns will be 28.
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What are 2 examples of arithmetic sequences in real life?
Stacking chairs and sitting around table are examples of arithmetic sequence in real life
What is simple arithmetic?
The foundational subject in mathematics is arithmetic, which covers operations with numbers. These include multiplication, division, addition, and subtraction. One of the key areas of mathematics, arithmetic serves as the cornerstone for students studying the topic of mathematics.
How is arithmetic sequence used in daily life?
There are numerous applications for arithmetic sequences in daily life. The clock, for instance, demonstrates properties of an arithmetic sequence. The standard deviation of a clock's time is 1. Other examples of arithmetic sequences can be seen in daily life, such as our age.
Among these there are many other examples of arithmetic sequence is real life like fencing and perimeter examples.
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Could you please find X and show me how
Answer:
[tex]x=13\cos 25^{\circ}[/tex]
Step-by-step explanation:
[tex]\cos 25^{\circ}=\frac{x}{13} \\ \\ x=13 \cos 25^{\circ}[/tex]
How many solutions does the pair of equations y 0 and y =- 5 have class 10?
If there were two equation, one on top of the other, there would be infinitely many solutions. but here no solution
If there were two lines that intersected at one point, there would be one solution.
y=0 and y=-5 don't have any solutions. When you ask if a pair of equations have a solution, that means there is an intersection of the equations. The 2 equations will meet somewhere, and that is the solution. To find the solution, you set the equations equal to each other.
0≠-5
It is obvious that 0 and -5 are not equal to each other. Therefore, there is no solution. Also, y=0 and y=-5 are horizontal lines that are parallel to each other. They will never meet, which means there will be no intersection. No intersection means no solutions
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