Answers
Answer:
<8, <1, <4 are all 96
<6,<7,<3, <2 are all 84
Step-by-step explanation:
Related Questions
Matt's bus ride to school is 3 minutes more than 1/4 the time of Rick's bus ride. Write an equation to model this situation and graph it
Answers
An equation that models the relationship between the amount of time taken by Rick's bus ride and Matt's bus ride is M = t/3 + 3, which is shown in the graph attached below.
How to write an equation to model this situation?In order to write this equation, we would assign variables to the amount of time taken by Matt's bus ride and Rick's bus ride to school respectively, and then translate the word problem into algebraic equation as follows:
Let the M indicate the amount of time taken by Matt's bus ride.Let the t indicate the amount of time taken by Rick's bus ride.Next, we would translate the word problem into an algebraic equation as follows;
Matt's bus ride Time = 3 minutes more than 1/4 the time of Rick's bus ride
M = (1/4 × t) + 3
M = t/3 + 3
Based on the graph shown in the image attached below that models the relationship between the amount of time taken by Rick's bus ride and Matt's bus ride, we can reasonably and logically deduce that the y-intercept is equal to 3 and the slope of the graph is equal to 1/4.
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How do you solve this problem?
Given the ordered pairs A(1,4) and B(0,-4), create a sine and cosine equation
Answers
The sine and cosine functions with the ordered pairs A(1,4) and B(0,-4) are given as follows:
Sine: f(x) = 4sin(π(x + π/2)).Cosine: g(x) = -4cos(πx).What is the definition of the trigonometric functions?Both the sine and the cosine functions have similar definitions, given as follows:
f(x) = asin(b(x+c))+d.g(x) = acos(b(x+c))+d.The meaning of the coefficients of the functions are presented as follows:
a is the amplitude of the trigonometric function.b: The period of the trigonometric function is of 2π/b.c is the phase shift of the trigonometric function.d is the vertical shift of the trigonometric function.The functions vary between -4 and 4, hence the amplitude is given as follows:
a = 4.
This is the standard oscillation for a trigonometric function with amplitude 4, between -4 and 4, hence the vertical shift is of:
d = 0.
The difference between the x-coordinates of the maximum and the minimum value is half the period, hence the period is of 2 x 1 = 2, and the coefficient b is:
2π/b = 2
b = π.
The cosine function has no phase shift, it just is inverted, as it should assume a value of 4 at x = 0, hence the definition is:
g(x) = -4cos(πx).
The sine function has a phase shift, as it should assume a value of -4 at -π/2, not π/2, hence it is shifted shift π/2 units, hence the definition is:
f(x) = 4sin(π(x + π/2)).
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A solution to a system of linear equations in two variables is an ordered pair that.
Answers
The solution to a system of linear equations is the ordered pair (or pairs) that satisfies all equations in the system.
What ordered pair is a solution to the system of linear equations?
An equation is said to linear when it is in ax+ by = c form where a , b and c are real numbers . System of linear equation consist of a set of two or more equation with same variables. such as ,
a₁ x + b₁ y = c₁
a₂ x + b₂ y = c₂
A solution to a linear system is an ordered pair (x ,y) that solves both the equations .
To check that an ordered pair is a solution ,we have to substitute the corresponding values of our variables (x ,y) into our equations and see if they satisfy both the equations.
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when the lengths of two opposite sides of a square garden were increased by x meters each and the lengths of the other two sides were decreased by x meters each, the area of the new garden was 64 square meters. what was the area of the original square garden?
Answers
the area of the original square garden is 80 square meters.
Let the side of the original square be a. We are given that the area of the new garden was (a - x)(a + x) = a² - x² = 64.
We want to find the area of the original square, so the value of a².
(1) The area of the new garden was 80 percent of the area of the original square garden --> 64 = 0.8a² --> a² = 80. Sufficient.
(2) x = 4 --> a² - 4² = 64 --> a² = 80. Sufficient.
the area is the quantity that expresses the quantity of a location on the aircraft or on a curved surface. The place of an aircraft region or plane vicinity refers back to the location of a form or planar lamina, at the same time as floor area refers to the place of an open surface or the boundary of a 3-dimensional object. location may be understood as the quantity of fabric with a given thickness that might be vital to style a model of the form, or the amount of paint necessary to cowl the surface with an unmarried coat. it's by far the two-dimensional analog of the duration of a curve (a one-dimensional idea) or the volume of a strong (a three-dimensional concept).
place plays a vital position in current mathematics. further to its apparent importance in geometry and calculus, the place is associated with the definition of determinants in linear algebra and is a simple asset of surfaces in differential geometry. In analysis, the vicinity of a subset of the plane has defined the use of the Lebesgue measure, though no longer every subset is measurable. In the trendy, region in better mathematics is visible as a unique case of quantity for two-dimensional regions.
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Rewrite the expression 12x + 8 to find an equivalent expression
. Show three possible expressions what do the rewritten expression tell you about the relesginship among the quantities
Answers
Three Expression equivalent to 12x + 8 are,
4 ( 3x+2 ) , 12 (x + 2/3) , 8 (2x/3 + 1)
Equivalent expressions:
Equivalent expressions are expressions that work the same even though they look different.
If two or more algebraic expressions are equivalent, then all expressions will give the same value if we put different value of variable.
Here,
given expression is " 12x + 8 "
we have to write three equivalent expression to 12x + 8
a.
If we take 4 common we will get,
12x + 8 = 4 ( 3x+2 )
so,
one of the expression equivalent to 12x + 8 is 4 ( 3x+2 )
b.
If we take 12 common then,
12x + 8 = 12 (x + 8/12)
= 12 (x + 2/3)
one of the expression equivalent to 12x + 8 is 12 (x + 2/3)
c.
If we take 8 common then,
12x + 8 = 8 ( 12x/8 + 1)
= 8 (2x/3 + 1)
one of the expression equivalent to 12x + 8 is 8 (2x/3 + 1)
Hence,
Three Expression equivalent to 12x + 8 are,
4 ( 3x+2 ) , 12 (x + 2/3) , 8 (2x/3 + 1)
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The area of a triangle i 247 inche. If the width i 19 inche find the height of the triangle
Answers
[tex]\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh ~~ \begin{cases} b=\stackrel{width}{base}\\ h=height\\[-0.5em] \hrulefill\\ A=247\\ b=19 \end{cases}\implies 247=\cfrac{1}{2}(19)h \\\\\\ 494=19h\implies \cfrac{494}{19}=h\implies 26=h[/tex]
Therefore:
x= height
19*x=247*2
19x=494
x=26
The height of the triangle is 26 inch
(26*19)/2=area=247
Help me find terms and like terms please
Answers
The like terms in the expression are -8x^2,-10x,14 and -6. The like terms are 14 and -6
What are terms in algebraic expression?A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms. For example, in the expression 5x + y, the two terms are 5x and y.
In the expression 14-8x^2-6-10x, there are 4 terms in it: 14, -8x^2, - 6, - 10x.
out of the four terms only two are alike because of they are both constant. This like terms are -6 and 14.
10x and -8x^2 are unlike terms because x^2 is a different term from 10x.
Therefore the like terms are -6 and 14
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PLEASE HELP 15 POINTS!!
AND WILL MARK BRAINLIEST
The data in the table describes the preferred type of exercise of student athletes.
Cycling. Running Row Totals
Male 0.22 0.32 0.54
Female. 0.15 0.31 0.46
Column Totals 0.37 0.63. 1.00
What is the conditional relative frequency that a male prefers cycling? Round your answer to two decimal places.
0.41
0.58
0.59
0.62
Answers
Step-by-step explanation:
you take the specific number (males prefer cycling = 0.22) and the fitting total.
note there are 2 possibilities for that total :
all males
all people preferring cycling
the way it was phrased I would say the reference is all males.
the conditional relative frequency is then
0.22 / 0.54 = 0.407407407... ≈ 0.41
but if the meaning would be rather about how many of all people preferring cycling are male, then we would have
0.22 / 0.37 = 0.594594595... ≈ 0.59
both results are in your answer options.
I think the intended result is 0.41, because I understand the problem that way :
find the conditional relative frequency that a student athlete surveyed prefers cycling, given that the student is male.
the other should be phrased like
find the conditional relative frequency that a student athlete surveyed is male, given that the student prefers cycling.
• 3 pages are edited every 5 minutes.
• 5 pages are edited every 3 minutes.
• 6/10 of a page is edited per minute.
• 1 2/3 of a page is edited per minute.
a) 1 and 2
b) 1 and 3
c) 3 and 4
d) None of the above
Answers
Answer:
1 and 3
Step-by-step explanation:
where the dots on the graph are, you can read that in 5 minutes, 3 pages are edited. in 10 minutes, 6 pages.
so statement 1 is correct.
when every 10 minutes 6 pages are edited, divide both by 10 to get what is edited per minute. -> 6/10 pages are edited per minute.
In triangle XYZ, m∠Y = 62.45° and m∠Z = 41.8°. Determine the measure of the exterior angle to ∠X.
Answers
Answer:
m∠X=75.75
Step-by-step explanation:
A triangle's angles combine to 180 degrees. Subtract 62.45+41.8 from 180.
The measure of the exterior angle of the triangle is given by ∠A = 104.25°
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the triangle be represented as ΔXYZ
Let the measure of the exterior angle be m∠A
Now , the measures of the angles of the triangle are
The measure of angle ∠Y = 62.45°
The measure of angle ∠Z = 41.8°
The measure of angle ∠X = m∠X
Now , for a triangle , the sum of the interior angles = 180°
So ,
m∠X + m∠Y + m∠Z = 180°
Substituting the values in the equation , we get
m∠X + 62.45° + 41.8° = 180°
Subtracting 104.25 on both sides of the equation , we get
m∠X = 75.75°
Now , the measure of angle exterior to m∠X be ∠A = 180° - m∠X
The measure of m∠A = 180° - 75.75°
The measure of m∠A = 104.25°
Therefore , the measure of ∠A = 104.25°
Hence , the exterior angle of the triangle is ∠A = 104.25°
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in rational expression what is the answer of 7n-7 divide n-1
Answers
7 is the answer.
Greg and Max left Ottawa for Toronto in their old jalopy to see the Grey Cup football game
The mileage gauge on the car was not working but the speedometer was. Their jalopy
averaged 40 mph from Ottawa to Toronto and 35 mph on the return trip. The total
traveling time for the round trip was 15 hours. Being good mathematics students, Greg and
Max were able to determine the distance between the two cities. What is this distance?
Answers
The distance between the two cities, Ottawa and Toronto, as determined by Greg and Max is 280.37 miles.
What is a Speedometer?
The instrument on a car that measures and shows speed is called a speedometer, and it is crucial for safety on roads and highways all over the world.By instantly sensing the speed on the ground, the speedometer on a car, truck, or motorbike can instantly notify the driver how fast the vehicle is travelling at any given moment.The instrument currently appears in many forms as a motorcycle speedometer or a bike speedometer and is digital in many modern automobiles.What is Distance?
The measurement of the distance between two objects or locations 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. The term is also frequently used metaphorically to denote a measurement of the degree of separation or difference between two related objects.A metric space is a mathematical concept that is used to define the majority of these conceptions of distance, both literal and figurative.How is Distance Calculated?
The distance between two locations can be calculated using the formula,
d = s x t,------ (1)
where [tex]d[/tex] is the distance travelled, [tex]s[/tex] is the average speed, and [tex]t[/tex] is the total time.
In the given question, it is given that Greg and Max travel from Ottawa to Toronto with an average speed of 40 mph and 30 mph for the return trip.
So, [tex]s_{1}=40 mph[/tex] and [tex]s_{2}=35mph[/tex].
The total travelling time for the round trip, T = 15h ------(2)
Let the distance from Ottawa to Toronto be x.
From (1), we get that, the formula for the time taken is,
[tex]t=\frac{d}{s}[/tex]
So, the time taken to travel from Ottawa to Toronto,
[tex]t_{1} =\frac{d}{s_{1} } \\\implies t_{1} =\frac{x}{40}[/tex] ------- (3)
And, the time taken for the return trip (back from Toronto to Ottawa),
[tex]t_{2} =\frac{d}{s_{2} } \\\implies t_{2} =\frac{x}{35}[/tex] --------(4)
Here, the total time travelled from the round trip is equal to the sum of the time taken to travel from Ottawa to Toronto and back from Toronto to Ottawa.
T = t_1 + t_2------(5)
Substituting the values of (2), (3), and (4) in (5), we get
15 = x/40 + x/35
--> 15 = 0.0535x
Simplifying,
x = 15/0.0535
--> x = 280.37 miles
Therefore, the distance between the two cities as determined by Greg and Max is equal to 280.37 miles.
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Change the subject of the formula y = g√x + h to x.
Answers
Answer:
[tex]x=\frac{(y-h)^{2} }{g^{2} }[/tex]
Step-by-step explanation:
[tex]y=g\sqrt{x} +h\\\\[/tex]
[tex]-g\sqrt{x} =h-y[/tex]
[tex]\sqrt{x} = -\frac{h-y}{g}[/tex]
[tex]\sqrt{x} =\frac{y-h}{g}[/tex]
∴ [tex]x=\frac{(y-h)^{2} }{g^{2} }[/tex]
HELP and please explain it
Answers
Answer:
SAS, ASA, SSS, ASA, Yes
Step-by-step explanation:
Makayla rents a kayak. She pays a rental fee of $12.99 plus $3.75 for each hour that he spends in the water. How much did Makayla spend if he was on the river for 4 1/2 hours? Round to the nearest hundredth.
Answers
Makayla spend $29.87 if he was in the river for 4(1/2) hours.
Given, Makayla rents a kayak.
She pays a rental fee of $12.99 plus $3.75 for each hour that he spends in the water.
Now, we have to find that how much did she pay if she was in the river for 4(1/2) hours.
Let the no. of hours in the water be, x
So, Rental fee = 12.99 + 3.75x
As, she was in the water for 4(1/2) hours i.e. 9/2 hours
the rent will be = 12.99 + 3.75(9/2)
Rent = 12.99 + 1.875(9)
Rent = $29.865
Hence, Makayla spend $29.87 if he was in the river for 4(1/2) hours.
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Between which two integers does √84 lie?
Answers
Answer:
Step-by-step explanation:
Between 9 and 10.
Why?
Because sq of 9 is 81 and sq of 10 is 100 which gives us the gesture that sq.rt of 84 is between 9&10.
Hence, Two integers are 9 and 10.
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Find the range of the functio
h(x) = -x^2; {-2,-1,3}
Answers
Answer:
in the picture
Step-by-step explanation:
hope it helped
How to solve and find derivative of y at 1
Answers
After differentiation of function with respect to y, the value of y'(1) is 0.225.
In the given question we have to find the value of derivative of y at 1.
The given function is [tex]\frac{x^2}{36}+\frac{y^2}{64}=1[/tex]
To find the derivative of y at 1 we have to firstly derivate the given function with respect to y.
Now writing the given function in the y form
[tex]\frac{x^2}{36}+\frac{y^2}{64}=1[/tex]
Subtract x^2/36 on both side, we get
[tex]\frac{y^2}{64}=1-\frac{x^2}{36}[/tex]
Multiply by 64 on both side, we get
[tex]y^2=64-64\times\frac{x^2}{36}[/tex]
[tex]y^2=64-\frac{16x^2}{9}[/tex]
Differentiating with respect to y on both side
[tex]2y\frac{dy}{dx}=0-\frac{16\times2x}{9}[/tex]
[tex]2y\frac{dy}{dx}=\frac{32x}{9}[/tex]
Simplifying
dy/dx = 16x/9y
We can write dy/dx as y' so
y' = 16x/9y
We have to find the value of y'(1).
Since the y is the function of x so we put x=1 and we know y(1)=7.89, so
y'(1) = 16*1/9*7.89
y'(1) = 16/71.01
y'(1) = 0.225
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Which postulate should be used to show that the
triangles are congruent?
Answers
SSS should be used to show that the triangles are congruent.
What is the congruent triangle?
Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them. Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.
From the given images of the triangles, it is clear that the the legs of the triangles are equal to each other.
If two legs of two triangles are equal, then the bases are equal to each other.
Thus to prove that the triangles are congruent to each other, apply SSS postulate.
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The area of a parallelogram i 12 quare unit. One ide of the parallelogram i 18 unit long. The other ide i 6 unit long. Determine whether each dimenion could be the height of the parallelogram. Pick all correct. A. 2/3 unit
B. 3/2 unit
C. 2 unit
D. 3 unit
Answers
The possible heights of the parallelogram are 2/3 and 3
So, the correct option is A and C
The given expression:
area of a parallelogram, A = 12 square unit
a side of the parallelogram, = 18 units
another side of the parallelogram = 6 units
let,
the height of the parallelogram, h
The area of a parallelogram is given as;
Area = base (b) x height (h)
height (h) = Area/base(b)
From the given sides, the possible heights of the parallelogram are calculated as follows;
if the base, b = 18 units
height(h) = 12/18
= 2/3
Also, if the base, b = 6 units
height(h) = 12/6
= 2
Therefore, the possible heights of the parallelogram are 2/3 and 2
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(PLEASE HELP FAST) A 9-member team plans to run a 4-mile relay race. Distance markers are placed on the racecourse every 0.25 mile. a. Place an X on the number line at the approximate locations where the relay exchanges will take place. b. Will any of the relay exchanges take place at any of the 0.25-mile markers? If so, which one(s)? List the locations of all of the exchanges in decimal form.
Answers
Answer:
D or C
Step-by-step explanation:
The parent function f(x) = log4x has been transformed by reflecting it over the x-axis, stretching it vertically by a factor of two and shifting it up five units. Which function is representative of this transformation?
a. g(x) = log4(2x) + 5
b. g(x) = 2log4(x) - 5
c. g(x) = -2log4(x) + 5
d. g(x) = log4(-2x) - 5
Answers
The function which is representative of the transformation of the parent function f(x) = log4x by reflecting it over the x-axis, stretching it vertically by a factor of two, and shifting it up five units is g(x) = -2log4(x) + 5. Option C is correct.
The reflection over the x-axis is given by the transformation:
f₁(x) = - f(x)
Therefore, the first step we get is:
f₁(x) = - log(4x)
Stretching by a factor n along the y-axis is given by the transformation:
f₂(x) = n · f₁(x)
Therefore, we will get:
f₂(x) = -2 · log(4x)
Shifting a function up of a quantity n is given by:
f₃(x) = f₂(x) + n
Therefore, we will get:
f₃(x) = -2 · log(4x) + 5
So,
g(x) = -2 log4(x) + 5
Thus, the function which is representative of the transformation of the parent function f(x) = log4x by reflecting it over the x-axis, stretching it vertically by a factor of two, and shifting it up five units is g(x) = -2log4(x) + 5. Option C is correct.
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Find the measures of the exterior angles of the polygon. 75°
x°
90°
90°
Answers
The measure of the exterior angle x of the polygon is x = 105° .
In the question ,
it is given that ,
in the figure, the measure of external angles are 75° , 90° , 90° and x .
we know that By Polygon Exterior Angle Sum Theorem states that the sum of measure of all exterior angle of a polygon is 360° ,
So , 75° + 90° + 90° + x = 360°
75° + 180° + x = 360°
255° + x = 360°
Subtracting 255 from both the sides , we get
x = 360° - 255°
x = 105°
Therefore , The measure of the exterior angle x of the polygon is x = 105° .
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twenty tiles are numbered through and are placed into box . twenty other tiles numbered through are placed into box . one tile is randomly drawn from each box. what is the probability that the tile from box is less than and the tile from box is either even or greater than ? express your answer as a common fraction.
Answers
The probability of first tile is less than 15, is 70% and the second tile is even or greater than 25, is 60%.
In the given question we have to find the probability of first tile is less than 15 and the second tile is even or greater than 25.
Tiles numbered 1 through 20 are placed in a box.
Tiles numbered 11 through 30 are placed in a second box.
One tile is randomly drawn from each box.
Now finding the probability of first tile is less than 15.
Since in first box tile is numbered as 1 to 20.
So the outcomes of less than 15 = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
So favourable outcome = 14
Total number of tile = 20
So the probability = 14/20 = 70%
Now finding the probability of second tile is even or greater than 25.
Since in second box tile is numbered as 11 to 30.
So the outcomes of even or greater than 25 = 12, 14, 16, 18, 20, 22, 24, 26, 27, 28, 29, 30
So favourable outcome = 12
Total number of tile = 20
So the probability = 12/20 = 60%
Hence, the probability of first tile is less than 15, is 70% and the second tile is even or greater than 25, is 60%.
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The right question
"Tiles numbered 1 through 20 are placed in a box. Tiles numbered 11 through 30 are placed in a second box. One tile is randomly drawn from each box. Find each probability. The first tile is less than 15 and the second tile is even or greater than 25."
A manatee can swim an average of 10 miles every 2 hours. Assume the distance y in miles is proportional to the number of hours x the manatee swam.
Answers
The distance Manatee will swim in 5 hours is 25 miles.
What is distance?Distance can be defined as the length between two points.
To calculate the distance manatee can swim in 16 hours, we use the equation below
y₁/x₁ = y₂/x₂............ Equation 1Make y₂ the subject of the equation
y₂ = (y₁×x₂)/x₁............ Equation 2Where:
y₁ = 10 milesx₁ = 2 hoursx₂ = 5 hoursSubstitute these values into equation 2
y₂ = (10×5)/2y₂ = 25 mile.Hence, manatee can swim a distance of 25 miles.
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Complete question: A manatee can swim an average of 10 miles every 2 hours how far can it swim in 5 hours. Assume the distance y in miles is proportional to the number of hours x the manatee swam.
Find the slope between these two points. *
(17,8), (17, 24)
O 0
undefined
1
1/2
c
Answers
The slope between points (17,8) and (17,24) is (B) undefined.
We know that the slope of a line passing through two points (a,b) and (c,d) is given by,
m = (d-b)/(c-a)
So here given points are (17,8) and (17,24)
Then, a=17, b=8, c=17, d=24
Now the slope between these two points is given by,
m = (24-8)/(17-17) = 16/0
So the slope value does not exist or infinity.
Hence the slope between the points (17,8) and (17,24) is Infinity or undefined.
Thus, the correct option is (B).
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Solve five and five-sixths minus three and three-fourths plus two and one-half equals blank line.
Answers
Step-by-step explanation:
55/12
hope this helps:)
Find the circumcenter of the triangle formed by the vertices (4 2) (3 3) and (2 2)
Answers
Coordinate of circumcenter of the given triangle = (3, 2)
What is circumcenter of a triangle?
Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.
Let the coordinate of circumcenter be (x , y)
Distance of Circumcenter from (4,2) =
[tex]\sqrt{(x - 4)^2 + (y-2)^2[/tex]
Distance of Circumcenter from (3, 3) =
[tex]\sqrt{(x - 3)^2 + (y-3)^2[/tex]
Distance of Circumcenter from (2,2) =
[tex]\sqrt{(x - 2)^2 + (y-2)^2[/tex]
By the problem,
[tex]\sqrt{(x - 2)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 2)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 4x + 4 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\6x - 4x +6y -4y = 18-8\\2x +2y = 10\\x+ y = 5\\[/tex]..... (1)
Again,
[tex]\sqrt{(x - 4)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 4)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 8x + 16 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\8x - 6x +4y -6y = 20-18\\2x -2y = 2\\x- y = 1\\[/tex]...... (2)
Adding (1) and (2)
[tex]2x = 6\\x = \frac{6}{2}\\x = 3[/tex]
Putting the value of x in (1),
3 + y = 5
y = 5 - 3
y = 2
Coordinate of circumcenter = (3, 2)
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Callie ha a rope that i 14. 7 inche long. She cut the rope into 3 piece. If each piece i the ame length, how long i each piece of rope?
Answers
the length of each rope would be 4.9 inches.
One of the four fundamental operations in mathematics is division; the other three are addition, subtraction, and multiplication. Simply put, division is the process of dividing a large group into smaller ones so that each group has the same number of items. In mathematics, it is a procedure for equal sharing and grouping.
Callies has a rope of length = 14.7 inches,
she cut the rope into pieces = 3
let 'x' be the length of each rope,
if each piece is of the same length, the length of the original rope would be 3x.
this implies, 3x = 14.7 inches,
x = 4.9 inches.
therefore, the length of each rope would be 4.9 inches.
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(complete question)
Callie has a rope that is 14.7 inches long. She cut the rope into 3 pieces. If each piece is the same length, how long is each piece of rope?
Rafi has $6,629 in an account that earns 10% interest compounded annually. To the nearest cent, how much interest will he earn in 4 years?
Answers
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6629\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]A=6629\left(1+\frac{0.1}{1}\right)^{1\cdot 4} \implies A \approx 9705.52~\hfill \underset{earned~interest}{\stackrel{9705.52~~ - ~~6629}{\approx\text{\LARGE 3076.52 }}}[/tex]