the concept of a sequence of transformations is a fundamental one in many different fields, as it allows us to understand how complex systems or objects can be broken down into smaller, more manageable parts that can be manipulated or analyzed in a systematic way.
What is a sequence?
The sequence is an ordered list of elements or events that follow a particular pattern or rule. In mathematics, a sequence typically refers to a set of numbers that are arranged in a specific order, with each element in the sequence being defined by a mathematical formula or recurrence relation.
A sequence of transformations refers to a series of steps or operations that are performed in a specific order to change or manipulate a given object or system. These transformations can take many different forms, depending on the context in which they are used.
For example, in mathematics, a sequence of transformations might refer to a series of algebraic manipulations that are used to simplify or solve an equation. In computer science, a sequence of transformations might refer to a series of functions or algorithms that are applied to data in order to transform it into a different format or structure.
In other fields, such as physics or chemistry, a sequence of transformations might refer to a series of physical or chemical changes that occur in a system over time. These transformations could include changes in temperature, pressure, or chemical composition, among other factors.
Therefore , the concept of a sequence of transformations is a fundamental one in many different fields, as it allows us to understand how complex systems or objects can be broken down into smaller, more manageable parts that can be manipulated or analyzed in a systematic way.
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1. It is 5/6 of a mile from Chloe's house to the library. Chloe has
biked 1/6 of a mile so far. How much further does Chloe need
to go to reach the library? Show your work
Simon bought a pack of butter for baking. The pack has 8 sticks of butter that are each 1/2 of a cup. Simon used 1 1/4 of butter to make brownies , 3/4 cup of butter to make a cake , and 1 1/4 cup of butter to make cookies . how much butter does Simon have left ?
The amount of butter that Simon has left is given as follows:
0.75 cups.
How to obtain the amount of butter?The amount of butter that Simon has left is obtained applying the proportions in the context of the problem.
The pack has 8 sticks of butter that are each 1/2 of a cup, hence the number of cups purchased is given as follows:
8 x 1/2 = 4 cups.
Simon used 1 1/4 of butter to make brownies , 3/4 cup of butter to make a cake , and 1 1/4 cup of butter to make cookies, hence the number of cups used is given as follows:
1.25 + 0.75 + 1.25 = 3.25.
Hence the amount of butter that Simon has left is given as follows:
4 - 3.25 = 0.75 cups.
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Alyssa filled her car tank with 16.8 gallons of gas. If gas costs $2.85 per gallon, how much did she pay? Round to the nearest cent.
Show your work!!
16.8 gallons
2.85 dollars/gallons
[tex]16.8 \times \frac{2.85 \: dollars}{gallons} = 47.88 \\ [/tex]
Alyssa paid a total of $47.88 for 16.8 gallons of gas when each gallon costs $2.85
Explanation:The subject of this question is mathematics. Let's start by identifying what we know. We know that Alyssa filled her tank with 16.8 gallons of gas and that the cost of gas is $2.85 per gallon.
To find out how much Alyssa paid in total, we need to multiply the number of gallons by the cost per gallon:
16.8 gallons * $2.85/gallon = $47.88Now, we are asked to round to the nearest cent. Rounding $47.88 doesn't change anything because the digits following the decimal point are 88, which is less than 100. So, the total amount Alyssa paid is $47.88.
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what is the proverb which says we must make our plan fit the circumstances
Is the relationship shown by the data linear? If so, model the data with an equation.
The relationship is not linear.
Is the relationship shown by the data linear? If so, model the data with an equation.
The relationship is not linear.
The relationship shown on the table is such that C. The relationship is not linear.
How to find the model equation ?To determine if the relationship is linear, we can check if the differences in the y-values are constant for equal differences in the x-values.
Calculate the differences between the x-values and the y-values:
Δx1 = 7 - 1 = 6
Δy1 = -7 - (-4) = -3
Δx2 = 13 - 7 = 6
Δy2 = 10 - (-7) = 17
Δx3 = 19 - 13 = 6
Δy3 = -13 - 10 = -23
The differences in x-values are constant (Δx1 = Δx2 = Δx3 = 6), but the differences in y-values are not (Δy1 ≠ Δy2 ≠ Δy3). Therefore, the relationship is not linear.
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A parabola opening up or down has vertex (-5, -5) and passes through (-19, 29/4).
Write its equation in vertex form.
Simplify any fractions.
Answer:
y = [tex]\frac{1}{16}[/tex] ( x + 5 )² - 5
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k , (h, k) are coordinates of the vertex.
If a parabola passes through the point A ( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) , then
[tex]y_{1}[/tex] = a( [tex]x_{1}[/tex] - h )² + k
a = [tex]\frac{y_{1} -k }{ (x_{1} -h)^2}[/tex]
~~~~~~~~~~~~~~~~~~
Vertex at ( - 5, - 5 )
A( - 19, [tex]\frac{29}{4}[/tex] )
a = [ [tex]\frac{29}{4}[/tex] - ( - 5)] ÷ [ - 19 - ( - 5)]² = ( [tex]\frac{29}{4}[/tex] + 5 ) ÷ ( - 14 )² = 0.0625 = [tex]\frac{1}{16}[/tex]
y = [tex]\frac{1}{16}[/tex] ( x + 5 )² - 5
The heights of five-year-olds are Normally distributed with a mean of 42.5 inches and a standard deviation of 2.5
inches. A random sample of 16 five-year-olds is taken and the mean height is recorded. What would be the mean of
the sampling distribution of all possible samples of size 16?
O 2.66
O 10.63
O 17
O 42.5
The mean of the sampling distribution of all possible samples of size 16 will be 42.5, the correct option is D.
Normal distribution with mean μ = 42.5 inches and standard deviation σ = 2.5 inches. Let x₁, x₂, ..., xₙ be a random sample of size n = 16 from X, and let x be the sample mean
The sampling distribution of the mean x is also Normal, with mean μ and standard deviation σ/√n.
f(x) = (1/√(2π) × (σ/√n)) × exp[-(x - μ)² ÷ (2 × (σ/√n)²)]
we integrate
Mean of x = ∫(-∞ to ∞) x × f(x) dx
Mean of x = 2 × ∫(μ to ∞) x × f(x) dx
Next, we substitute
u = (x - μ) / (σ/√n):
Mean of x = 2 × ∫(0 to ∞) (u × (σ/√n) + μ) × (1/√(2π) × (σ/√n)) × exp(-u² / 2) du
Simplifying this expression gives:
Mean of x = μ
Therefore, the mean of the sampling distribution of all possible samples of size 16 is equal to the population mean μ, which is 42.5 inches.
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The complete questions is :
The heights of five-year-olds are Normally distributed with a mean of 42.5 inches and a standard deviation of 2.5 inches. A random sample of 16 five-year-olds is taken and the mean height is recorded. What would be the mean of the sampling distribution of all possible samples of size 16?
A 2.66
B 10.63
C 17
D 42.5
Miss x baked 286 loaves of bread on Saturday. She baked 78 fewer loaves of bread on Saturday that Sunday.How many loaves of bread did she bake on both days?
Miss x baked 286 loaves of bread on Saturday and 208 loaves of bread on Sunday. To calculate the total loaves of bread baked on both days, we can subtract 78 from 286 to get the number of loaves of bread baked on Sunday.
Miss x baked 286 loaves of bread on Saturday. We know that she baked 78 fewer loaves of bread on Sunday than Saturday. To calculate the total loaves of bread baked on both days, we can subtract 78 from 286 to get the number of loaves of bread baked on Sunday. This gives us 208 loaves of bread baked on Sunday. Adding this to the 286 loaves of bread baked on Saturday, we get a total of 494 loaves of bread baked on both days. Therefore, Miss x baked 286 loaves of bread on Saturday and 208 loaves of bread on Sunday.
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Helpppppp
The fox population in a certain region has a continuous growth rate of 5 percent per year. It is estimated that the population in the year 2000 was 12500.
(a) Find a function that models the population t years after 2000 (t=0 for 2000).
Your answer is p(t)=-----------
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer must be an integer)----------------
The estimated fox population in the year 2008 is 19498.
What is a function?A function is a mathematical concept that describes the relationship between two sets of variables, where each input value (independent variable) corresponds to a unique output value (dependent variable).
According to question:(a) The continuous growth rate of 5% per year means that the fox population is increasing at a rate proportional to its current size. Let P(t) be the fox population t years after 2000. Then, we can model the population using the differential equation:
dP/dt = kP
where k is the constant of proportionality. To solve this differential equation, we can separate the variables and integrate:
dP/P = k dt
ln|P| = kt + C
where C is the constant of integration. To find the value of C, we use the initial condition that the population in the year 2000 (t=0) was 12500:
ln|12500| = 0 + C
C = ln|12500|
Therefore, the solution to the differential equation is:
ln|P| = kt + ln|12500|
Simplifying, we get:
P(t) = [tex]e^(kt + ln|12500|)[/tex]
P(t) = 12500 [tex]e^(kt)[/tex]
where P(t) is the fox population t years after 2000.
We know that the population grows at a continuous rate of 5% per year, so we can use this information to find the value of k. Since the continuous growth rate is given by r = 0.05, we have:
k = ln(1 + r) = ln(1.05)
As a result, the following function represents the fox population t years after 2000:
p(t) = 12500 [tex]e^(0.05t)[/tex]
(b) Since t is the number of years after 2000, we must determine the value of p(8) in order to calculate the fox population in 2008. We have the following using the function from section (a):
p(8) = 12500 [tex]e^(0.05(8))[/tex]
= 19498
Therefore, the estimated fox population in the year 2008 is 19498.
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Decompose the composite figure to find its total area.
The area of the composite figure using area formula is 45unit².
Option b is the correct option.
What are composite figures?The space that any composite shape occupies is referred to as the area of composite shapes. In order to create the desired shape, a few polygons are connected to create a composite shape. These figures or forms can be constructed using a variety of geometrical elements, including triangles, squares, quadrilaterals, and others.
To determine the area of a composite object, divide it into simple shapes like a square, triangle, rectangle, or hexagon. In essence, a composite shape is a combination of fundamental shapes. It goes by the name's "composite" or "complex" shapes.
In the question, we can see that the composite figure comprises of a triangle and a rectangle.
Now, length of the rectangle as per the vertices is, l = 6 units.
Breadth of the rectangle as per the vertices is, b = 6 units.
As the length and breadth of the rectangle as per the vertices are equal it's a square with side a = 6 units
Area of square = a²
= 6²
=36unit².
Now in the triangle,
Base, b = 6 units
Height, h = 3 units.
Area = 1/2 × b × h
= 1/2 × 6 × 3
= 9unit².
Therefore, the total area of the figure is 36 + 9 = 45unit².
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Create a set of four lengths so that: • Each length is different. • Each length is a whole number (in inches). • No matter which three you choose, you will always be able to make a triangle. Explain how you know that your set of lengths meet all the requirements.
One possible set of four lengths that meets the given requirements is:
3 inches, 4 inches, 5 inches, 7 inches
To show that this set of lengths meets all the requirements, we need to demonstrate that:
Each length is different: We can see that all four lengths are different.
Each length is a whole number: We can see that all four lengths are whole numbers.
No matter which three you choose, you will always be able to make a triangle: To show this, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
For example, if we choose the lengths 3, 4, and 5, we can see that 3 + 4 = 7, which is greater than 5. Therefore, we can make a triangle with sides of length 3, 4, and 5. Similarly, if we choose the lengths 3, 4, and 7, we can see that 3 + 4 = 7, which is still greater than 7. Therefore, we can make a triangle with sides of length 3, 4, and 7.
We can repeat this process with any combination of three lengths from the set, and we will always find that we can make a triangle. Therefore, we have shown that the set of lengths {3 inches, 4 inches, 5 inches, 7 inches} meets all the requirements.
Find the compound interest on Rs 16000 at 20% per annum for 9 months compound quarterly
To calculate the compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly, we need first to calculate the quarterly interest rate and the number of compounding periods.
Quarterly interest rate = Annual interest rate / 4
= 20% / 4
= 5%
Number of compounding periods = (Time in months) / (Number of months per compounding period)
= 9 / 3
= 3
Using the formula for compound interest:
A = P(1 + r/n)^(nt)
where,
A = final amount
P = principal amount
r = annual interest rate
n = number of compounding periods per year
t = time in years
Plugging in the values, we get:
A = 16000(1 + 0.05/4)^(4*3/12)
A = 16000(1 + 0.0125)^1
A = 16000(1.0125)
A = 16180
Therefore, the compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly is Rs 1800 (i.e., A - P = 16180 - 16000).
What is the meaning of "[tex]r_{i} \circ r_{j} =r_{i+j}[/tex] for all [tex]i[/tex] and [tex]j[/tex]"?
The expression "[tex]r_i \ o \ r_j = r_{i+j},[/tex]for all i and j" represents a mathematical relationship involving a binary operation "o" and a sequence of elements denoted by "[tex]r_i[/tex]", where "i" and "j" are integers.
What is the meaning of "[tex]r_i \ or \ r_j = r_{i \ + j}[/tex] for all i and j"?
The expression states that for any two integers "i" and "j", the result of applying the binary operation "o" to the elements "r_i" and "r_j" is equal to the element "[tex]r_{i+j}[/tex]" in the sequence that is the sum of the indices "i" and "j".
In other words, if we have a sequence of elements "r_1, r_2, r_3, ..." and a binary operation "o", then this expression tells us that the result of applying the operation "o" to any two elements in the sequence is equal to the element in the sequence whose index is the sum of the indices of the two original elements.
For example, as given in the polygon, a sequence of numbers {1, 2, 3, 4, ...} and the binary operation is addition (+), then the expression "[tex]r_i \ o \ r_j = r_{i+j}[/tex], for all i and j" tells us that the sum of any two numbers in the sequence is equal to the number whose index is the sum of the indices of the two original numbers.
For instance, 1 + 2 = 3, which is the same as r_1 o r_2 = r_{1+2} = r_3.
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Please help me! I give brainly and points
Answer:
3.5
Step-by-step explanation:
Answer: 3.5
Step-by-step explanation: In this scenario, the vertex would be the peak of the baseball throw. We can find the x value of the vertex by using -b/2a. With your equation of 112x-16x^2 we need to change the x^2 value to the front to make it -16x^+112x so that it is in standard form. Now take your b value (112), make it negative (-112), and divide that by 2 times -16. to get 3.5.
I should also include that the x value of the vertex is equal to t which is seconds.
Which of the following is not a line segment in the drawing? Answers.
JL
MN
JK
NK
1) the JK does not form the line segment.
2) NL line segment is different from other three options.
What is line segment?It is a part of line having two ends points.
The simplest definition of a line is an arrangement of points that extends in opposite directions to infinity, while a ray is a section of a line that has one endpoint and extends continuously in one direction, while a segment of a line is a section of a line between two endpoints.
1) Like a line can be expressed in liner form such as y=mx+c where as, a line segment will consist of two coordinates such as A(x₁,y₁) and B(x₂,y₂).
Here, the JK does not form the line segment as there is no connecting line between them.
2) Here, NL line segment is different from other three options as is formed the line JL.
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Tamie collected 340 milliliters of rain water on Monday. She collected1.5 liter of rain water on Tuesday .how many total milliliters of rain did tamie collect on Monday and Tuesday
Step-by-step explanation:
on Monday:340ML
on Tuesday:1.5L
total millilitres?so we have to get the to get the total of water in Millilitres (ML)
step 2:we have to convert the 1.5L to ML
we know 1L=1000ML
and 1000ML=1ML
so 1.5L =1500ml
Step 3
340 +1500=1840ML
Richard has a credit card that allows him to defer credit card payments for 1 year if he becomes unemployed. The interest on the card debt continues to accrue, but there are no late payment penalties. Suppose Richard has $1,597.57 in credit card debt, and the annual interest rate is 23.5% compounded monthly. How much will Richard owe (in dollars) after 1 year if he takes advantage of this option? Assume he makes no other purchases with the card. (Round your answer to the nearest cent.)
Thus, the amount of money Richard owe (in dollars) after 1 year on his credit card is $2,016.19.
Define about the term compounded monthly:Compounding interest on both the principal and the accrued interest is expressed by the term "monthly compound interest," which refers to interest that is compounded over month. The principal amount times one plus the interest rate divided by a number of periods, raised to the power of such number of periods, is how monthly compounding is computed.
Formula for amount after compounding:
A = P[tex](1 + r/n)^{nt}[/tex]
A = amount after compounding
P is principal (=$1,597.57)
r is rate of interest (23.5%)
n is the number of times compounded (= 12)
t is time in years (1 year)
A = 1597.57* [tex](1 + 0.235/12)^{12*1}[/tex]
A = 1597.57* 1.26
A = 2,016.19
Thus, the amount of money Richard owe (in dollars) after 1 year on his credit card is $2,016.19.
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12) A carpenter wants to make a sofa like a doll's sofa that is 27 inches long. The scale is 9/2
inches to 1 foot. What is the length of the carpenter's sofa?
Answer the following questions in your work book; 1. Three resistors in parallel carry electric current. One resistor carries 1/5 and another carries ½% of the current: a. What fraction of total current is carried by the tow resistors b. What fraction of total current is carried by the third resistor c. If the total current is 8A what current is carried by the third resistor
The measure οf the equal sides οf the triangle is 8√3 cm and the perimeter οf the triangle is apprοximately 49.9 cm.
The current carried by the third resistοr is 2.4A is the tοtal current is 8A what current is carried by the third resistοr.
What is a fractiοn?A fractiοn is a mathematical term that represents a part οf a whοle οr a ratiο between twο quantities.
a. Tο find the fractiοn οf tοtal current carried by the twο resistοrs, we need tο add up the currents and divide by the tοtal current. Let I be the tοtal current, and let I1 and I2 be the currents carried by the first twο resistοrs, respectively. Then we have:
I1 = 1/5I
I2 = 1/2I
The tοtal current is:
I = I1 + I2 = (1/5 + 1/2)I = 7/10I
Therefοre, the fractiοn οf tοtal current carried by the twο resistοrs is:
(I1 + I2)/I = (1/5I + 1/2I)/I = (7/10I)/I = 7/10
b. Let I3 be the current carried by the third resistοr. Then we have:
I3 = I - (I1 + I2) = I - 7/10I = 3/10I
Therefοre, the fractiοn οf tοtal current carried by the third resistοr is:
I3/I = (3/10I)/I = 3/10
c. If the tοtal current is 8A, then we have:
I = 8A
The current carried by the third resistοr is:
I3 = 3/10I = 3/10 x 8A = 2.4A
Therefοre, the current carried by the third resistοr is 2.4A.
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A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the scoops of ice cream the college will need?
The college will have about 480 students who prefer ice cream.
The college will have about 640 students who prefer ice cream.
The college will have about 1,280 students who prefer ice cream.
The college will have about 1,440 students who prefer ice cream.
In the percentage , the statement is the best prediction about the scoops of ice cream the college will need is D)The college will have about 1,440 students who prefer ice cream.
What is percentage?
percentage. Divide the A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a number by the total and multiply by 100 to find the percent of a given number. Therefore, the percentage refers to a portion per hundred. Per 100 is what the word percentage signifies. The letter "%" stands for it.
Here then given, Total number of students = 4000
Sample number of students = 225.
In 225 students 81 students prefer ice cream.
Now to find percentage then,
=> [tex]\frac{81}{225}\times100[/tex]
=> 0.36*100
=> 36%.
Now Number of students who prefer ice cream = 36% of 4000
=> 36/100 * 4000
=> 1440.
Hence the correct option is D)The college will have about 1,440 students who prefer ice cream.
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describe a sequence of transformations that will take figure M onto its congruent image figure N
οther valid transfοrmatiοn sequences cοuld Sequences achieve the same result, and the specific sequence used wοuld depend οn the specific shapes and οrientatiοns οf figures M and N.
What is Sequences?A sequence is an οrdered list οf elements in mathematics. Numbers, functiοns, and οther mathematical οbjects can be used as elements. A series is frequently denοted by stating its terms in parenthesis, separated by cοmmas. The series οf natural numbers, fοr example, can be denοted as: (1, 2, 3, 4, 5, ...) Similarly, the series οf even numbers is denοted as fοllοws: (2, 4, 6, 8, 10, ...) Depending οn whether it has a finite οr infinite number οf terms, a sequence might be finite οr infinite.
Here's an example transfοrmatiοn sequence that cοuld pοtentially cοnvert figure M intο its cοngruent image figure N:
Figure M shοuld be mοved tο a new lοcatiοn in space sο that it aligns with the cοrrespοnding pοrtiοn οf figure N.
Figure M shοuld be rοtated abοut a pοint until it aligns with the οrientatiοn οf figure N.
Figure M shοuld be mirrοred acrοss a line οf symmetry tο match the mirrοr image οf figure N.
Figure M shοuld be translated tο its final lοcatiοn sο that it exactly cοincides with figure N.
It shοuld be nοted that many οther valid transfοrmatiοn sequences cοuld achieve the same result, and the specific sequence used wοuld depend οn the specific shapes and οrientatiοns οf figures M and N.
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what is the synynom of oil
Step-by-step explanation:
oil change. palm trees oil
Helppppp
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
In the exponential decay, A) r = -0.0839 , B) r = -8.39% , C) Value=$11,800.
What is exponential decay?
The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.
To find the annual rate of change between 1992 and 2006, we can use the formula:
r = [tex](V_2/V_1)^{1/n}-1[/tex]
where V1 is the initial value, V2 is the final value, and n is the number of years between the two values.
=>r = -0.0839
Therefore, the rate of change between 1992 and 2006 is -0.0839.
To express the rate of change in percentage form, we can multiply the result from part A by 100:
=>r = -0.0839 x 100
=> r = -8.39%
Therefore, the rate of change between 1992 and 2006 is a decrease of 8.39%.
To find the value of the car in the year 2009, we can assume that the value continues to drop at the same percentage rate as calculated in part A.
From 2006 to 2009, there are 3 years. So, using the formula for exponential decay, we have:
where V0 is the value in 2006, r is the rate of decrease, and n is the number of years between 2006 and 2009.
=>V = 11792.51
Therefore, the value of the car in the year 2009 would be approximately $11,800 (rounded to the nearest $50).
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The sum of two numbers is 261. Their difference is 175. Write a system of equations and solve to find the two numbers.
The value of the two numbers are 43 and 218
How to determine the valueFrom the information given, we have;
Let the numbers be x and y
Then,
The difference between the numbers = x - y
The sum of the numbers = x + y
Substitute the values
x + y = 261
x - y = 175
Let's solve the simultaneous equations
Make 'x' the subject from 1
x = 261 - y
Substitute the value in 2
261 - y - y= 175
collect the like terms
-2y = - 86
y = 43
Substitute to determine the value of x
x = 261 - y = 261 - 43 = 218
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In a class of 30 students, 13 of them are boys.
What percentage of the class are girls?
Give your answer to 1 decimal place.
Answer:
56.7%
Step-by-step explanation:
Total number of students = 30
Number of boys in the class = 13
Number of girls in the class = 30 - 13 = 17
Now we have to find the percent of girls of the class
Therefore
[tex]\dfrac{\text{Number of girls}}{\text{Total students}} \times100[/tex]
[tex]=\dfrac{17}{30}\times100=56.67\%[/tex]
[tex]56.67\implies56.7\%[/tex]
Hence, girls are 56.7% of the class.
Select the correct answer. A diagonal curve declines through (negative 2, 5), (negative 1, 3), (0, 1), (1, negative 1), (2, negative 3), and (3, negative 5) on the x y coordinate plane. The area below the curve is shaded. Which of the following inequalities is graphed on the coordinate plane? A. y ≤ − 2 x + 1 B. y ≥ − 2 x + 1 C. y < − 2 x + 1 D.
To determine the correct inequality that represents the shaded area below the diagonal curve, we need to identify the equation of the line that passes through the two endpoints of the curve, which are (-2, 5) and (3, -5).
First, we need to find the slope of the line:
slope = (change in y) / (change in x)
slope = (-5 - 5) / (3 - (-2))
slope = -10 / 5
slope = -2
Next, we can use the point-slope form of the equation of a line to find the equation of the line:
y - y1 = m(x - x1), where m is the slope and (x1, y1) is one of the points on the line.
Using the point (-2, 5), we have:
y - 5 = -2(x - (-2))
y - 5 = -2(x + 2)
y - 5 = -2x - 4
y = -2x + 1
So the equation of the line passing through the endpoints of the curve is y = -2x + 1.
To determine which inequality represents the shaded area below the curve, we can test a point that is not on the line, such as (0, 1).
Plugging in (0, 1) into the equation of the line, we get:
1 = -2(0) + 1
1 = 1
Since 1 is equal to 1, the point (0, 1) is on the line. Therefore, the inequality that represents the shaded area below the curve is y < -2x + 1, since the points below the line satisfy this inequality.
So the correct answer is C. y < -2x + 1.
A student started a project using a pencil with a length of 7 1/2 inches. After the student completed the project, the pencil had a length of 5 7/8 inches. How much shorter, in inches, was the pencil after the student completed the project than when the student started the project? 4 A 1 4/8 B 1 5/8 C 2 3/8 D 2 6/8. also subscribe to my friends channel it's called your local kirby guy.
the answer is 1 5/8 inches shorter. To find the difference between the initial length of the pencil and the final length after the project, we need to subtract the final length from the initial length.
Initial length of the pencil = 7 1/2 inches
Final length of the pencil = 5 7/8 inches
To subtract these two values, we need to convert the mixed numbers to improper fractions.
7 1/2 = 15/2
5 7/8 = 47/8
Now we can subtract:
15/2 - 47/8
To subtract these fractions, we need to find a common denominator. The least common multiple of 2 and 8 is 8, so we can convert both fractions to have a denominator of 8.
15/2 = 60/8
47/8 = 47/8
Now we can subtract:
60/8 - 47/8 = 13/8
So the pencil is 13/8 inches shorter after the project. To write this as a mixed number, we divide the numerator by the denominator:
13 ÷ 8 = 1 with a remainder of 5
So the answer is 1 5/8 inches shorter.
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I need help with this.
The total cost of the metal which will be used to construct the metal tank would be = $82.5
How to calculate the area of the metal tank?To calculate the area of the metal tank, the formula for the area of the cylinder is used which would be;
= 2πr (h+r)
Where
R = 12/2 = 6 ft
h = 4ft
π = 3.14
area = 2×3.14×6(4+6)
= 37.68×10
= 3.75 ft²
But 1ft² = $22
3.75ft² = X
make X the subject of formula;
X = 22× 3.75 = $82.5
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what is the area of each triangle 24 ft 20 ft
The area of triangle ABC is 249.36 sq ft while the area of ΔACD and ΔBCD is 124.68 sq ft
What is the area of a triangle?The area of a triangle can be calculated using the formula:
Area = (1/2) x base x height
where "base" is the length of the base of the triangle and "height" is the perpendicular distance from the base to the opposite vertex.
Lets find altitude with with Pythagoras formula:
[tex]\rm a^2 + b^2 = c^2[/tex]
[tex]\rm a^2 + 12^2 = 24^2[/tex]
[tex]\rm a^2 = 24^2 -12^2[/tex]
[tex]\rm a^2 = 576 - 144[/tex]
[tex]\rm a^2 = 432[/tex]
a = √432
a =
a = 20.78
To find the area of a triangle, we use the formula A = 1/2 × base × height.
In this case, the base of the triangle is 24 ft and the height is 20.78 ft.
Therefore,
A = 1/2 × 24 ft × 20.78 ft
A = 249.36 sq ft
Hence, The area of each triangle is 249.36 square feet.
Now, Both tringles are 1/2 of the area as base = 12 = 1/2 × 24
ΔACD = 1/2 × 249.36
ΔACD = 124.68 sq ft
ΔBCD = 1/2 × 249.36
ΔBCD = 124.68 sq ft
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Complete question:
What is the area of each triangle Base = 24 ft 20 ft
SOMEONE PLS! GRAPH THIS ! 40 POINTS!! AND BRAINLIEST IF CORRECT!!!!
SLOPE: -3/4
Y -intercept (0,5)
The equation with SLOPE: -3/4 and Y-intercept (0,5) is Y = (-3/4)x + 5 and graphed below.
What is intercept?The pοint οn a line's graph where it crοsses the x-axis is knοwn as the x-intercept.
The pοint where a line's graph crοsses the y-axis is knοwn as the y-intercept.
On any graph, the x and y -intercepts are crucial lοcatiοns. The graphs οf linear equatiοns will be the main tοpic οf this chapter. Hοwever, at this pοint, we may utilize these cοncepts tο identify nοnlinear graph intercepts. Always keep in mind that intercepts are οrdered pairs that shοw where the graph and axes cοnnect.
The fοrmula οf slοpe-intercept is y=mx+b.
By using this fοrmula
Y=(-3/4)x+b
Using the given pοint we get,
5=(-3/4)0+b
Or, b=5
The answer is Y=(-3/4) x+5
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