The distance between any two point is 5 unit.
What is distance?
The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common language can refer to a physical length or an assumption based on other factors.
As per the question
Triangle xyz is translated = 4units
And triangle xyz left to yield=3 unit
The distance between the corresponding is hypotenuse of the triangle is-
Buy applying Pythagorus theorem we can get C^2=a^2+b^2
As we know a,b=legs
c=hypotenus
C^2=a^2+b^2C^2
=3^2+4^2
=9+16
=25C =√25 =5 unit
Therefore, the distance between any two point is 5 unit.
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Simplify to create an equivalent expression.
\qquad{2(3y+6)-3(-4-y)}2(3y+6)−3(−4−y)2, left parenthesis, 3, y, plus, 6, right parenthesis, minus, 3, left parenthesis, minus, 4, minus, y, right parenthesis
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
9y9y9, y
(Choice B)
B
5y+245y+245, y, plus, 24
(Choice C)
C
9y-249y−249, y, minus, 24
(Choice D)
D
9y+249y+24
The generated equivalent expression is 9y + 24. So, the correct answer is option D.
What is an expression?
An expression can be defined as the combination of variables and constants with two or more operations applied on it. The operation can be addition, subtraction, multiplication and division.
Simplifying to generate an equivalent expression
The given expression is 2(3y + 6) - 3(- 4 - y)
= 2(3y + 6) + 3(4 + y)
= 6y + 12 + 12 + 3y
= 6y + 3y + 24
= 9y + 24
Hence, the generated equivalent expression is 9y + 24.
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A student showed their work when dividing fractions. Explain their errors and find the correct solution!
6 \ 3/4=6/1x3/4
=18/4
4 2/4 or 4 1/2
The correct solution of division fractions is 18/4.
What is division?Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. The primary objective of division is to count the number of equal groups that are created or the number of individuals in each group after a fair distribution.
When describing how much of anything is left over, a fraction is used. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator
Given that,
The division fraction is 6× 3/4
So, the fraction is 6/1×3/4
Therefore, the division fraction is 4×2/4 or 18/4
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If l = √m-5 and m = 4n²-3, what is l when n = 2? What is n when l = 4?
what of disibility rules?
If f(x) is a decreasing function, which of the following statements must be true? Select all that apply.
(Assume that f(x) is always decreasing.)
a) f(5)−f(1) / 5−1 > 0
b) f(5)−f(1) / 5−1 < 0
c) For some value of x≠5, f(x)=f(5)
d) f(5) < f(1)
e) f(5) > f(1)
The two true statements are:
b) (f(5)−f(1)) / (5−1) < 0
d) f(5) < f(1)
Which of the following statements must be true?
We know that f(x) is a decreasing function, this means that, as x increases, the value of f(x) decreases.
So, if there are two values in the domain a and b, such that a < b, we will have that:
f(a) > f(b).
Then the statement:
[ f(5) - f(1)]/(5 - 1) < 0
Is true, because f(1) is larger than f(5).
Which means that statement d ( f(5) < f(1)) is also true.
Then the two correct options are b and d.
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11. Find the solution of the following system of equations using substitution:
2x + 7y = 5
y = x + 2
Answer:
(x,y) = (-1,1)
Step-by-step explanation:
step 1
subsitute the given value of y into the equation
2x+7(x+2)=5
step 2
solve for x
x= -1
step 3
subsitute the value of x in to the second equation
y= -1+2
step 4
solve for y
y=1
step 5
check if there true by putting the value of x and y back in to the equation.
then configure x and y into an ordered pair.
(x,y)=(-1,1)
I hope this helped!
Identify all the pairs of parallel sides of each figure.
Answer:
2 on the 1st, 1 on the second, 3 on the third, 1 on the fourth
What is this number sequence called?
7, 22, 11, 34, 17, 52, 26, 13 and so on.
The numbers 7, 22, 11, 34, 17, 52, 26, 13 and so on represent hailstone sequence.
What is a hailstone sequence?These patterns are referred to as hailstone sequences because the values frequently rise and fall, resembling a hailstone inside a cloud.
It should be noted that such numbers can either rise or fall.
Therefore, the numbers 7, 22, 11, 34, 17, 52, 26, 13 and so ob represent hailstone sequence.
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Write as a
14/11
as a decimal.
0 0.36
0.36
0.036
O 0.36
Answer:
Step-by-step explanation:
divide 14 by 11
which is 0.36
A jewelry maker incurs costs for a necklace according to the equation shown below.
C(x) = 30x + 1692
The revenue function for the necklaces is given below.
R(x) = 77x
How many necklaces must be sold to break even?
necklaces
1. Which of the following is a linear inequality in two variables? A. 3a-2b = 6 C. 3x ≤ 10 B. 3c+16 < -10 D. 3x + 4y ≥ 10
Answer:
D
Step-by-step explanation:
a linear expression in two variables has the form ax + by
an inequality uses the symbols < , > , ≤ , ≥
the only expression in this form is
3x + 4y ≥ 10
Between what two integers does square root of -80 lies
Answer: 8 and 9
Step-by-step explanation:
square root of - 80 is 8.94427191 so 8 and 9 is the integers around it.
11. Represent and Connect After a recycling
awareness program, the number of tons of
recyclable material taken to the landfill is
reduced by 13 tons per month. Represent
the total change in the tons of recyclable
material taken to the landfill after
10
7 months resulting from the awareness
program. Show your work.
The total change in the tons of recyclable material taken to the landfill after 10 7 months resulting from the awareness program = (x - 95.9) tons, where x is the initial amount.
In this question, we have been given after a recycling awareness program, the number of tons of recyclable material taken to the landfill is reduced by 13 tons per month.
We need to represent the total change in the tons of recyclable material taken to the landfill after 10 7 months resulting from the awareness program.
Given that reduction in materials = 13 7/10 tons per month
We rewrite the improper fraction 13 7/10 as a proper fraction.
13 7/10 = 137/10
Monthly reduction = 137/10 tons
After 7 months : (7 × 137/10)
= 959/10 tons
= 95.9 tons
Change in amount of material taken to the land fill:
Initial amount - amount after 7 months
If initial amount be x, then the change in amount = (x - 95.9) tons
So, we get an expression (x - 95.9)
Therefore, the total change in the tons of recyclable material taken to the landfill after 10 7 months resulting from the awareness program = (x - 95.9) tons, where x is the initial amount.
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Which of the following best represents the
rate of change of this function?
A -1/2
B 1/2
C 2
D -2
Answer:
Step-by-step explanation:
Need more clarification! Which function?
What is the difference between -5 and 3 on a number line
Answer:
8
Step-by-step explanation:
-5 is 5 units left of zero.
3 is 3 units right of zero.
The difference is 8.
Simplify.
(y^5)^3
Write your answer without parentheses.
Answer:
[tex]\boxed{\sf y^{15}}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sf (\:y^5\:)^3[/tex]When any expression is given in the format [tex]\sf (\ a^b \ )^c[/tex] then [tex]\sf a^{bc}[/tex].
[tex]\sf \rightarrow y^{5(3)}[/tex]simplify
[tex]\sf \rightarrow y^{15}[/tex]PLEASE HELP ME FIGURE THIS OUT
Cycling.
The graph below shows the ages of the top five male finishers in the Mt. Washington Auto Road Bicycle Hillclimb each year from 2017 through 2021.
1. Write the relation of this situation as a set of ordered pairs in terms of (age, finishing place).
2. Identify the domain and range of the relation.
3. Do the ordered pairs represent a function? Explain.
Answer:From the given table, we have that:
1. The relation of the situation is: (20,2), (22.5, 5), (25,4), (27.5, 4), (29,4), (29,5), (30,1), (30,2), (30,3), (30,4), (30,5), (32.5, 1), (32.5, 3), (35,4), (40,2), (42.5, 3).
2. The domain is {20, 22.5, 25, 27.5, 29, 30, 32.5, 35, 40, 42.5} and the range is {1, 2, 3, 4, 5}.
3. There are inputs such as 25, 29, 30 and 32.5 that are mapped to multiple outputs, hence the relation does not represent a function.
What is the relation of this situation?
To build the relation, we look at the graph, and write all pairs of (Age, Finishing Place), as follows:
(20,2), (22.5, 5), (25,4), (27.5, 4), (29,4), (29,5), (30,1), (30,2), (30,3), (30,4), (30,5), (32.5, 1), (32.5, 3), (35,4), (40,2), (42.5, 3).
What are the domain and the range?
The domain of a relation is the set that contains all possible input values for the values, that is, the values of x.
The range of a relation is the set that contains all possible output values for the values, that is, the values of y.
Hence, for the given relation:
The domain is {20, 22.5, 25, 27.5, 29, 30, 32.5, 35, 40, 42.5} and the range is {1, 2, 3, 4, 5}.
When does a relation represents a function?
A relation represents a function if each value of the input is mapped to only one value of the output.
For this problem, we have that:
There are inputs such as 25, 29, 30 and 32.5 that are mapped to multiple outputs, hence the relation does not represent a function.
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Step-by-step explanation:
what’s the answer to this question
find the coordinates of pint P along the directed line segment AB so that AP to PB is the give ratio 2 to 6
Coordinates of P is 8
Since 3+2 = 5, we are dividing line segment AB into 5 congruent parts with point P 3/5 of the way from A to B.
x-coordinate of P = x-coordinate of A + (3/5)(change in x from A to B) = -4 + (3/5)(20) = 8
y-coordinate of P = y-coordinate of A + (3/5)(change in y from A to B) = 8 + (3/5)(-10) = 2
P = (8,2)
In each axis, find the distance from A to B, apply the ratio to get the distance from A to P, and add that value to A.
Note the ratio: We are given the ratio of AP to PB as 3/2. This means that the ratio of AP to AB is 3/5
Here is is for the X-axis:
AB = 20
AP = 20 *3/5 = 12
So P = -4 + 12 = 8
It is one of the branches of geometry where the position of a point is defined using coordinates.
Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.
A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
It is used to divide any line into two parts, in m:n ratio
The number line which is also known as a Cartesian plane is divided into four quadrants by two axes perpendicular to each other, labelled as the x-axis (horizontal line) and the y-axis(vertical line).
The four quadrants along with their respective values are represented in the graph below-
Quadrant 1 : (+x, +y)
Quadrant 2 : (-x, +y)
Quadrant 3 : (-x, -y)
Quadrant 4 : (+x, -y)
The point at which the axes intersect is known as the origin. The location of any point on a plane is expressed by a pair of values (x, y) and these pairs are known as the coordinates.
How To Find Coordinates of a Point on Graph With Examples
A set of values that shows the exact position of a point in a two-dimensional coordinate plane are called the coordinates. These represent the exact location of a point on a coordinate graph having both x, y axes. You can check the definition of coordinates, step by step detailed procedure to find the coordinates of a point with solved examples.
Coordinates Definition
A pair of numbers that describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines called the coordinates. Usually represented by (x, y) the x value and y value of the point on a graph. Every point or an ordered pair contains two coordinates. The first one is the x coordinate or abscissa and the second is the y coordinate or ordinate. The values of the coordinates of a point can be any positive or negative real number.
The other types of coordinates are map coordinates (north/south, east/west), three-dimensional coordinates, polar coordinates (distance, angle), etc. Detailed information about x coordinate, y coordinate of a point follows:
x‐coordinate (Abscissa): The first number or the number which is located to the left side of a comma in the point is the x coordinate of the ordered pair. It represents the amount of movement along the x-axis from the origin. The movement is to the right side if the number is positive and to the left side of the origin if the number is negative.
y‐coordinate (Ordinate): The number which is located to the right side of the comma in the ordered pair or the second number is known as the y coordinate of the ordered pair. This ordinate indicates the amount of movement along the y-axis. If the number is positive, then the movement is above the origin and the movement is below the origin if the number is negative.
Point on x-axis: A point on the x-axis means its movement along the horizontal line is always zero and the y-coordinate of all points on the x-axis is zero. Therefore, the coordinates of a point on the x-axis are of the form (x, 0).
Point on y-axis: A point on the y-axis means the distance from the y-axis is zero and the x coordinate of every point on the y-axis is zero. Hence, the coordinates of a point on the y-axis are (0, y).
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Find x
A. 2.6
B 3.1
C 2.9
D 4
Answer:x=
Step-by-step explanation:
() Which number is closest to √5?
1.7
2.2
3.4
3.1
Answer:
Step-by-step explanation:
A factory bottles 360 bottles of juice in 5 minutes. Find the factory’s unit rate of bottles per minute.
Answer:
72
Step-by-step explanation:
let's begin by restating what we already know,
360 bottles of juice in 5 minutes
for goodness's sake let's abbreviate this
360 boj in 5 mins
RATIO TIME!
360 : 5
pay attention how I put the BOJ (bottles of juice) first and the time last
now to find how many boj per min. we will say
[tex]\frac{1}{5} (360: 5)[/tex]
72:1
so, we now know that the factory of juice produces 72 bottles of juices per minute ( that's ALOT of juices per minute imo)
^_^ hope this helps, happy learning
need the domain and range!
Answer: Domain: [-1, 1]
Range: [-2, 3]
Step-by-step explanation:
Domain: The x-values go from -1 to 1 with x=-1 and x=1 included.
Range: The range starts at the vertex of the function which is y=-2 and goes up to y=3 where the graph is cut off by 2 points on y=3.
please answer as soon as possible
Three angles add up to 180 degrees, angle one has a measure of 4x+8, angle two has a measure of 8x+3 and angle three has a measure of 9x+3.
Given that the sum of the angles is 180 degrees, what is the measure of angle one? Round your answer to the hundredths place IE 79.50.
Answer:
39.60°
Step-by-step explanation:
The sum of three angles is 180 degrees.
Show this as equation and solve for x:
4x + 8 + 8x + 3 + 9x + 3 = 18021x + 14 = 18021x = 166x = 166/21x = 7.90 (rounded)Angle one is:
4*7.90 + 8 = 39.605. Estimate:
$53
X 4
+what do I add
Math
The phone company Ringular has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 500 minutes, the monthly cost will be $132. If the customer uses 700 minutes, the monthly cost will be $172.
A) Find an equation in the form
y=mx+b
where
x
is the number of monthly minutes used and
y
is the total monthly of the Ringular plan.
The equation in the form y = mx + b is as follows:
y = 1 / 5 x + 32
How to represent a linear equation?The customer uses 500 minutes, the monthly cost will be $132. If the customer uses 700 minutes, the monthly cost will be $172.
Using linear equation in slope intercept form,
y = mx + b
where
m = slopeb = y-interceptHence,
x = the number of monthly minutes used
y = the total monthly of the Ringular plan
Therefore, the equation in slope intercept form can be represented as follows:
(500, 132)(700, 172)
let's find the slope,
m = 172 - 132 / 700 - 500
m = 40 / 200
m = 4 / 20
m = 1 / 5
Hence,
y = 1 / 5x + b
using (500, 132) let's find the y-intercept
132 = 1 / 5 (500) + b
132 = 100 + b
b = 132 - 100
b = 32
Therefore, the equation in the form y = mx + b is as follows:
y = 1 / 5 x + 32
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Use Order of Operations
mot to solve.
14+7 x 54 ÷6-7
10=7-m
Do I minus by 10 on each side or do I add minus by 7?
Answer:
[tex] \sf \large{m=−3}[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
10=7−m
Step 1: Simplify both sides of the equation.
10=7−m
10=7+−m
10=−m+7
Step 2: Flip the equation.
−m+7=10
Step 3: Subtract 7 from both sides.
−m+7−7=10−7
−m=3
Step 4: Divide both sides by -1.
−m/−1= 3/−1
m=−3
given g(x) is ...............
Answer:
-40
Step-by-step explanation:
It states with g(-2) that x = -2, so we can plug -2 for x.
g(x) = 3x^3 - 2x^2 + 4x
g(x) = 3(-2)^3 - 2(-2)^2 + 4(-2)
g(x) = 3(-8) - 2(4) + 4(-2)
g(x) = -24 - 8 - 8
g(x) = -40
How many times larger is (1.064 x 101) than (7 x 10−1)?
0.152
15.2
6.58
7.448
Answer:
is 15.2
Step-by-step explanation:
Bill is buying several bottles of pop for a party. They each cost the same amount.
If Bill can buy 4 bottles for $7.16, how many bottles could he buy for $10.74?
Answer:
6
Step-by-step explanation:
First, divide 7.16 by 4 to find the price of one bottle, which is 1.79. Then, divide 10.74 by 1.79 to get 6.