The three consecutive integers are 5, 6, and 7.
What are consecutive integers?
Whole numbers that follow one another without a gap are known as consecutive integers. A few examples of consecutive integers are 15, 16, and 17, 1,2 and 3, and so on.
Finding the Consecutive Integers
Let the three consecutive integers be a, a + 1, and a + 2.
These three consecutive integers are to be such that two times the first integer when added to three times the second integer minus the third integer, it is equal to 21.
⇒ 2a + 3(a+1) - (a+2) = 21
2a + 3a + 3 - a -2 = 21
5a - a + 3 - 2 = 21
4a + 1 = 21
4a = 20
a = 20/4
a = 5
∴ a+1 = 5+1
a+1 = 6
And, a+2 = 5 + 2
a +2 =7
Hence, the three consecutive integers come out to be 5, 6, and 7
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The notation "f(x)" (f of x) is another way of representing y-values in a function
The given statement "The notation "f(x)" (f of x) is another way of representing y-values in a function" is true because it represents the output values.
What is a function?In Mathematics, a function simply refers to a mathematical expression which can be used for defining and showing the relationship that exist between two or more variables in a data set.
This ultimately implies that, a function typically shows the relationship between input values (x-values or domain) and output values (y-values or range) of a data set, as well as showing how the elements in a table are uniquely paired (mapped).
Generally speaking, the output values (y-values or range) of a data set (function) are plotted on the y-coordinate of a graph and they are typically denoted by either the notation f(x) or y.
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Complete Question:
The notation "f(x)" (f of x) is another way of representing y-values in a function. True or False?
I really need help with this question x + 2/3 =9/10
Answer:
x = 7/30
Step-by-step explanation:
x + 2/3 = 9/10
(x + 2/3 = 9/10) * 30 ==> multiply the equation by 30.
30 is the LCM (Least Common Multiple) of 3 and 10.
30x + 2*30/3 = 9*30/10 ==> Now the denominators will be removed,
making the equation much easier to simplify
30x + 60/3 = 270/10 ==> simplify
30x + 20 = 27 ==> solve for x
30x = 7 ==> subtract 20 on both sides
x = 7/30 ==> simplify
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On a negatively skewed curve, which of the following statements is true?
a. The mean, median, and mode is the same.
b. The mode is lower than the mean which is lower than the median.
c. The median is lower than the mode which is lower than the mean.
d. The mean is lower than the mode which is lower than the median.
e. The mean is lower than the median which is lower than the mode.
On a negatively skewed curve The mean is lower than the median which is lower than the mode. The correct answer is E.
Why is a curve negatively skewed?In statistics, a distribution is said to be negatively skewed if more values are concentrated on the right side (tail) of the distribution graph and the left tail is longer.
Positive skew is characterized by a longer or fatter tail on the right side of the distribution, and negative skew is characterized by a longer or fatter tail on the left. These two skews represent the direction or weight of the distribution.
The central tendency of a distribution is defined as its mean, median, and mode. The fact that the mean, median, and mode of the typically skewed data are all equal demonstrates the equality of wealth and income distribution as well as the significance of governmental policies and economic progress.
The distributions have a wide gap because the negative side is so heavily weighted. For instance, the data shows that the distribution of income is unequal and negatively skewed, and the central tendency is as follows:
Mode > Median > Mean.
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Is 904 divisible by 8?
yes. 904 is divisible by 8 and quotient is 113.
Divisibility Rule of 8
If the last three digits of a number are divisible by 8, then the number is completely divisible by 8. Example: Take number 24344. Consider the last two digits i.e. 344. As 344 is divisible by 8, the original number 24344 is also divisible by 8.
What is an arithmetic progression?
"Arithmetic Progression is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value."
Let, there are 'n' terms less than 904 divisible by 3.
Now, the first term divisible by 3 is(a) = 3.
The second term divisible by 3 is = 6.
Therefore, the common difference between terms divisible by 3 is(d)
The last term that is less than 904 and divisible by 3 is() 903.
Now, if we compare it with arithmetic progression, then:
The required number is 301.
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Are the following expressions equivalent? How do you know?
-2(x-1)+3(x+2) and x+8
Yes, these expressions are equivalent.
What are equivalent expressions?Expressions that are equivalent do the same thing even when they have distinct appearances.
When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
We may be given equations with algebraic expressions on both sides in some situations.
The two expressions on either side of the equation must be comparable in order for the equation to hold true for all values of the variable. F
According to our question-
-2(x-1)+3(x+2)
further solving gives;
x+8
Hence, Yes, these expressions are equivalent.
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Taub is a high school basketball player. In a particular game, she made some three point shots and some two point shots. Taub made a total of 11 shots altogether and scored a total of 30 points. Graphically solve a system of equations in order to determine the number of three point shots made, x, and the number of two point shots made, y.
In ΔMNO, o = 8 inches, m m∠O=48° and m m∠M=28°.
The length of side m is, 5.08 inches.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In ΔMNO,
⇒ o = 8 inches, m ∠M = 28° and m ∠O = 48°.
Now, Let the length of side m = x
So, By sine rule, we get;
⇒ sin M / m = Sin O / o
Substitute all the values, we get;
⇒ sin28°/ x = sin 48° / 8
⇒ 0.47 / x = 0.74 / 8
⇒ x = 0.47 × 8 / 0.74
⇒ x = 5.08 inches
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PLEASE PLEASE HELP ME!!! Question
Let f(x)=8x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 7 units down.
What is the equation for g(x)?
Enter your answer by filling in the box.
g(x)=
the equation for g(x)= 32x-7
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
EXPLANATION
We want to find the equation for g(x).
First, the function is stretched vertically by a factor of 4. This means that the function changes as follows:
f(x)→4f(x)
Therefore, the function becomes:
4(8x)
=32x
Then, it is translated 7 units down. This means that the function changes as follows:
f(x)→f(x)-7
Therefore, the equation for g(x) is:
g(x)=32x-7
Hence, the equation for g(x)= 32x-7.
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Which of Newton's Laws explain why the table moves at 0.25 m/s/s when you push on it
Answer:
First Newton's Law of motion
Step-by-step explanation:
a body will remain in it's constant motion or at rest unless acted upon by an external force.
How do you find the end behavior of a graph with Asymptotes?
To find the equation of an asymptote from a graph, look for the line that the graph approaches but never touches. Then calculate the slope of the line and the y-intercept. This will give you the equation of the asymptote.
How to find an asymptote?To find the equation of an asymptote from a graph, look for the line that the graph approaches but never touches. Asymptotes usually run parallel to the x-axis or the y-axis, so look for a straight line that is horizontal or vertical.
Once you have identified the line, calculate the slope of the line and the y-intercept. The slope of the line is the ratio of the change in the y-values to the change in the x-values.
Once you have found the slope and the y-intercept, you can use the slope-intercept form of a line to find the equation of the asymptote: y = mx + b, where m is the slope and b is the y-intercept. This will give you the equation of the asymptote.
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What is the answer of X² 6x 16?
The solution of (x^2 + 6x - 16) is ( x+8 )( x−2 ).
Lets solve the equation (x^2 + 6x - 16) in order to find its solution:
The equation is ( x^2 + 6x − 16 )
Now factorizing it
= ( x^2 + 8x − 2x − 16)
Taking x common from the first two terms and -2 common from the last two terms:
= [x (x+8) −2 (x+8) ]
Now,
= [ (x+8) (x−2) ]
Therefore, it is shown that the solution of the equation "(x^2 + 6x - 16)" is (x+8)(x−2) which is obtained through factorization.
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The circumference of a circle is 5piem. What is the area, in square meters? Express your answer in terms of pie
The area of circle with circumference 5πm is 6.25π square meters.
What is circumference and area of a circle?
The measurement of the circle's perimeter, also known as the circle's boundary, is called its circumference.
Circumference of circle(C)= 2πr
The area of a circle is the space encircled or encompassed by its circumference. It has a square unit of measurement.
Area of circle(A)= πr^2
We are given the circumference of circle(C)= 5π
This implies that 2πr= 5π because C= 2πr
On solving the equation,
2πr= 5π
r=5/2
=2.5
Now, area of circle(A)= πr^2
So, A= π (2.5)^2
A= 6.25π square meters
Hence, The area of circle with circumference 5πm is 6.25π square meters.
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Lat Friday Scott had $26. Over the weekend he received ome money for babyitting. He now ha $39. How much money did he receive?
Scott receive 39-26= 13 dollar when Lat Friday Scott had $26. Over the weekend he received ome money for babyitting. He now ha $39.
Money is defined as something that serves as a medium of exchange.
Money has three functions that distinguish it from the rest of the assets: 1) It is a means of change; 2) It is a unit of account; and 3) It is a store of value.
1.- MEANS OF PAYMENT OR CHANGE: basically, it consists of the use of money to make any type of transaction, thus facilitating the exchange of goods, products and services. Deliver one thing for another.
2.- ACCOUNT UNIT: this fulfills the function of determining the units of value, or prices, that the goods, products and services have. It is related to the prices.
3.- DEPOSIT OF VALUE: it consists of being able to buy something in the future. Money has the capacity to remain stable over time, which allows a person who has a capital today to invest it in the following months, or even years
Lat Friday Scott had $26.
Over the weekend he received ome money for babyitting.
He now ha $39.
Scott receive 39-26= 13 dollar
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Question
Isabella and Penelope are both draining their backyard swimming pools. Isabella’s pool holds 1,700 gallons and she is draining the water at a rate of 2.4 gallons per minute. Penelope’s pool holds 1,350 gallons and she is draining the water at a rate of 1.6 gallons per minute. How long will it take to have the same amount of water in both pools?
how many minutes?
How do you know if a set of ordered pairs is a function?
The set of ordered pair (x,y) is a function If each value of x has exactly only one corresponding value of y .
What are Function ?
The Function is defined as a relation that associates each element 'a' from a non empty set A to at least a single element 'b' from another non-empty set B.
For Example : Consider the ordered pairs , F = [tex][(0,4) , (2,3)][/tex] ;
the element 0 has the image as 4 , and the element 2 has the image as 3 .
So , we can see that , the each value of x has exactly only one corresponding value of y .
Therefore , the given ordered pair can be considered as a function .
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How to find the average of 20,30,20,10,10,10
Answer: 4.16
Step-by-step explanation:
How many congruent triangles can be made by joining the midpoints of the sides of triangle?
It is proved that a triangle is divided into four congruent triangles by the line segments connecting the middle points of its sides.
What are triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices.
The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.
This characteristic is known as the triangle's angle sum property.
If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.
In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.
A closed, two-dimensional shape is a triangle. It is a polygon with three sides. Straight lines make up all of the sides.
The vertex is the intersection of two straight lines. The triangle therefore has three vertices.
Hence, It is proved that a triangle is divided into four congruent triangles by the line segments connecting the middle points of its sides.
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plssss i’ll give points?
d
d
d
d
d
d
d
d
dd
d
d
d
d
Answer:
d
Step-by-step explanation:
A hore walk 4224 feet in 12 minute at thi rate how many yard doe a hore walk in twelve minute
1408 yards in 12 minutes doe a horse walk in twelve minute.
The term measurement in math is defined as the process of associating numbers with physical quantities and phenomena.
Here we have given that a horse can walk 4224 feet in 12 minutes.
As we all know that One yard is equal to three feet.
Therefore, if you want to get the yard equivalent, then we have to divide the feet term by 3.
Here we know that the horse walking distance in 12 minutes is 4224 feet.
Then the yard equivalent value is calculated as,
=> 4224/3
=> 1408
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rewrite (-4)^2/7 in radical form
The expression (-4)^2/7 can be written as seventh root 16
What are radicals?The √ symbol that is used to denote square root or nth roots. A radical expression is an expression containing a square root. Radicand is a number or expression inside the radical symbol. Radical equation is an equation containing radical expressions with variables in the radicands.
For example, x^2/3, 3 is the root while 2 is the power of x . therefore the x^2/3 can be written as cube root of x squared.
Similarly in (-4)^2/7 2 is the power of (-4), this means (-4)² = 16
7 is the root of (-4)²
Therefore (-4)^2/7 can be written in radical for seventh root 16.
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bro how does 90 go into 30 explain
Step-by-step explanation:
division so like it would go in 3 times I think
The interactions of snakes and mice make up which ecological unit?
A. species
B. community
C. biome
D. population
Answer:
The interactions of snakes and mice make up which ecological unit?
A. species
B. community
C. biome
D. population
Step-by-step explanation:
The best answer here is community. Please see the explanation below.
Ecological UnitsA species is frequently defined in biology as the biggest group of creatures in which any two individuals of the appropriate sexes or mating types may create viable offspring, usually by sexual reproduction. Ex: "A rattlesnake and a cobra are two different species of a snake." OR "The male and female cows we found are the same species."A community, also known as a biological community, is a group or association of populations of two or more distinct species that occupy the same geographical region at the same time. Ex: "There are snakes, mice, and trees in the forest community."A biome is a community of plants and animals that live naturally in a certain region and have common traits. Ex: "The continent of Africa has rich biological diversity because it contains nine biomes."A population is the whole number of inhabitants occupying an area of the same species. Ex: "Ecologists are studying the decline of the red panda population in relation to ecotourism and zoos."Please let me know if this helped!!!
Write and solve an equation to find the value of x below.
Answer:
Equation:
[tex]7x + 10 = 150[/tex]
Value of x:
[tex]x = 20[/tex]
Step-by-step explanation:
In the figure, we are given 2 angles, 150° and (7x+10)°.
These 2 angles are vertical angles because they are directly opposite of each other and formed by intersecting lines.
Vertical angles are congruent, which means the same.
Thus, to make an equation to solve for x, we need to set the angles equal to each other.
Equation: [tex]7x + 10 = 150[/tex]
Solving for x:
[tex]7x + 10 = 150[/tex]
⇒ [tex]7x = 140[/tex] . . . . . . . . . subtract 10 from both sides of the equation
⇒ ∴ [tex]x = 20[/tex] . . . . . . . . . divide both sides by 7 to isolate x
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Answer:
Step-by-step explanation:
Using VAT:
Angles opposite each other are consider equal.
Therefore : 7x+10 = 150
Solve for x: 7x= 150-10
x= 140/7
x= 20
To check : 7x+10 = 150
7(20)+10=150
140+10=150
150=150 (correct)
Brianna i getting material for a chemitry experiment. Her teacher give her a container that ha 0. 85 liter of a liquid in it. Brianna need to ue 0. 2 of thi liquid for the experiment. How much liquid will Brianna ue?
Brianna will use 0.17 liters of the liquid
We know that an equation in which two ratios are set equal to each other is called as proportion.
Here, Brianna has a container which has 0.85 L of liquid in it.
Brianna needs to use 0.2 of this liquid.
Assume that 0.85 L represents the 100% of the liquid.
Then 0.2 represents 0.2 × 100 = 20% of the liquid .
Let Brianna will use x liters of liquid.
Consider a proportion.
[tex]\frac{0.85}{100} =\frac{x}{20}[/tex]
0.0085 = x/20
x = 0.0085 × 20
x = 0.17 liters
so, she will use 0.17 liters of liquid.
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What are the 7 steps to solve a math problem?
Answer:
sometimes there are more, sometimes there are less
Step-by-step explanation:
for example 1+1 only requires 1 step
hope this helps
Answer:
STEP 1: The Right Problem to Solve
STEP 2: Analyse the Problem
STEP 3: Define the Problem
STEP 4: Develop Opportunities (Possible Solutions)
STEP 5: Select the Best Solution
STEP 6: Implement the Solution
STEP 7: Evaluate and Learn
Step-by-step explanation:
Hope It Helps!
Determine whether quadrilateral ABCD is a rhombus, a rectangle, a square, or none. Select all that apply. Explain. A(−9, 1), B(2, 3), C(12, −2), D(1, −4)
The quadrilateral ABCD indicates that it is a rhombus.
What is rhombus?A quadrilateral with four equal-length sides is known as a rhombus in plane Euclidean geometry (plural rhombi or rhombuses). Another name for this object is an equilateral quadrilateral because all of its sides are equal in length.
The rhombus is frequently referred to as a "diamond" after the diamonds suit in playing cards, which resembles the projection of an octahedral diamond, or as a "lozenge," though the former term is occasionally used to refer specifically to a rhombus with a 60° angle which some authors refer to as a calisson after the French sweet , and the latter term is occasionally used to refer specifically
Lets mark the given points onto a graph
As you can see in the graph,
The points given for quadrilateral ABCD indicates that its is a rhombus
As, All sides are equal
opposites sides are parallel
Thus, The quadrilateral ABCD indicates that it is a rhombus.
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(r^4-3r^3+6r-18)/(r-3) Synthetic Division
The solution of (r⁴ - 3r³ + 6r - 18) / (r - 3) using synthetic division is r³ + 6.
What is the solution of (r⁴ - 3r³ + 6r - 18) / (r - 3) using synthetic division?The solution of (r⁴ - 3r³ + 6r - 18) / (r - 3) using synthetic division is given below:
(r⁴ - 3r³ + 6r - 18) / (r - 3)
The divisor is +3
The coefficients are:
1 -3 6 -18
Using synthetic division
the first coefficient is 1
the second coefficient = 1 * 3 + -3
the second coefficient = 0
the third coefficient = 0 * 3 + 6
the third coefficient = 6
the fourth coefficient = 6 * 3 + (-18)
the fourth coefficient = 0
Therefore, the solution = 1(r⁴/r) + 0(r³/r) + 6(r/r) + 0
the solution = r³ + 6
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Which of these numbers lies between 8885 and 9885?
a}8875
b}8895
c} 9895
d}9975
Answer:
b
Step-by-step explanation:
Need the answer to the problem below.
((5 * 7) ^ 7) ^ 5 =
Answer:
Here is your answer
((5 * 7) ^ 7) ^ 5 =
(35 ^ 7) ^ 5 =
64339296875 ^ 5 = 1102507499354148695951786433413508348166942596435546875
Step-by-step explanation:
please help me with this question thank you
Answer:
2): x - $31 = $69
Step-by-step explanation:
See attached worksheet. The derivation of the answer, x - $69 = $31 (then x = $100) is shown. Convert the written question into an equation: If x is the amount given the cashier, then once $69 is subracted, Lemon receives $31:
x - $69 = $31
This can be rearranged to: x - $31 = $69, the second answer option. Other options have errors, noted by the red circles. There are no reasons that inequalities are involved, and seemingly random values of $61 and $30 have no relationship to the problem.
Answer:
B) Let x = amount paid to cashier
x - $31 = $69
x = $100
Step-by-step explanation:
We want to determine the amount Lemon paid the cashier. Therefore, the unknown variable is:
Let x = the amount he paid the cashier.If Lemon received $31 in change, then the amount he paid the cashier less the change is equal to the cost of the walnuts:
x - $31 = $69To solve the equation, add $31 to both sides:
x - $31 + $31 = $69 + $31x = $100Therefore, the amount Lemon paid the cashier was $100.