The width of a rectangle measures (7r - 2s) centimeters, and its length measures
(r-5s) centimeters. Which expression represents the perimeter, in centimeters, of
the rectangle?
Answers
The perimeter of the given rectangle is 16r-14s centimeters.
Let width be represented by=w
Let length be represented by=l
Let perimeter be represented by=p
Then,
l=(r-5s)centimeters (Given in the question)
while w=(7r-2s)centimeters (Given in the question)
The formula for the perimeter of a rectangle= 2(l+b)
where l is the length while b is the breadth of the rectangle.
On putting values in the equation:
p=2(l+b)
p=2(l+w)
p=2[(7r-2s)+(r-5s)]
on opening the bracket 2 is multiplied by both terms.
p=2(7r-2s)+2(r-5s)
p=(2x7r-2x2s)+(2xr-2x5s)
p=(14r-4s)+(2r-10s)
p=14r-4s+2r-10s
p=14r+2r-4s-10s
p=14r+2r-(4s+10s)
p=14r+2r-(14s)
p=16r-(14s)
Thus,
p=16r-14s centimeters
The perimeter of the given rectangle is 16r-14s centimeters.
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Related Questions
Mia is deciding between two truck rental companies. Company A charges an initial fee of $30 for the rental plus $3 per mile driven. Company B charges an initial fee of $85 for the rental plus $2 per mile driven. Let AA represent the amount Company A would charge if Mia drives xx miles, and let BB represent the amount Company B would charge if Mia drives xx miles. Write an equation for each situation, in terms of x,x, and determine which company would be cheaper if Mia needs to drive 80 miles with the rented truck.
Answers
Answer:
(a.): Company A: 3x + 30; Company B: 2x+85
(b.) Company B is cheaper as it would cost $245 for Mia to drive 80 miles
Step-by-step explanation:
The equations we need are linear and we can think of them as such. x represents the slope (cost per mile) and the initial fee represents our y-intercept or constant (amount paid before Mia ever drives)
(a.): Thus, for company A, we have y = 3x + 30 and for company B we have y = 2x + 85.
(b.) Since we know that Mia needs to drive 80 miles, we plug this into x for both companies and find which one is lower
Company A: 3(80) + 30 = $270
Company B: 2(80) + 85 = $245
Company B's price would be lower for Mia's needs.
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An inequality is shown.
-2x+12<18
What is the solution to the inequality?
0x<3
x>3
Answers
Answer:
-3 < x
Step-by-step explanation:
first of all get the positive x on one side, so we have
12 < 18 + 2x ( positive x is easier to work with)
then, get only x on one side
-6 < 2x
simplify
-3 < x
Which table shows a function that is decreasing only over the interval (-1, infinity)
Answers
The last table shows the function that is decreasing only over the interval [tex](-1, \infty)[/tex].
From given tables we clearly see that in below table, the functions are decreasing as 'x' increases
x f(x)
-3 -5
-1 -1
-1 -1
0 0
1 -4
2 -8
We need to find interval [tex](-1, \infty)[/tex].
In first table,f(x)=-5,-2,-1,2. Here the functions are in increasing order
In second table, f(x)=-7,-6,1,-1. Here the functions does not follow a specific order
in third table, f(x)=-1,2,1,-6, Here also the functions does not follow a specific order.
In fourth table, f(x)=1,0,-4,-8. Here the functions are in decreasing order.
Hence, the fourth table shows the function that deceases over interval [tex](-1, \infty)[/tex].
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Which fraction is equivalent to 80%? (in simplest fraction form)
Answers
Answer:
4/5 or four fifths
Step-by-step explanation:
First you make 80% the fraction 80/100
Next you find the greatest common factor (GCF) which in each of them is 20
Finally you divide 80 and 100 by 20 and you get 4 and five now make them a fraction and you get 4/5
Suppose your math teacher was running for Governor. In a pre-election poll of 750 people, the estimate (called a point estimate) was 40%, meaning that 40% of the people would vote for your math teacher. Suppose there was a 4% margin of error. How many people (out of 750) said they would vote for your math teacher? Show your work. Write the answer as a complete sentence.
Answers
Solution
- 40% of peole would vote for the mMath teacher out f the 750 people. This implies that the number of people tahat would vote for him is
[tex]\begin{gathered} 40\%\times750 \\ \frac{40}{100}\times750=300\text{ people} \end{gathered}[/tex]- We are also told that there is a margin of error of 4%. This implies that the number of people that vote for the math teacher is either 4% more or 4% less than the 300 people
- 4% margin of error can be gotten as follows:
[tex]\frac{4}{100}\times750=30[/tex]- Thus, the number of people that vote for him is 300 give or take 30 people
number 8 State how you know each pair of triangles are congruent
Answers
trianglesPairs of congruent triangles
Triangles A is congruent since UV = WX
Triangle Δ KLJ = Δ MNO and are congruents
Triangle Δ UGI ≠ Δ MNO ≠ ΔKLJ is congruent
One third times the difference of thirty and a variable is three fourths. one third times the quantity 30 minus y equals three fourths one third times the quantity y minus 30 equals three fourths one third times 30 minus y equals three fourths one third times y minus 30 equals three fourths
Answers
The original statement is same as third statment and value of y is 27.
Writing the equation form for each statement -
Let the variable be represented as y.
One third times the difference of thirty and a variable is three fourths1/3(30 - y) = 3/4
one third times the quantity 30 minus y equals three fourths1/3×30 - y = 3/4
one third times the quantity y minus 30 equals three fourths1/3×y - 30 = 3/4
one third times 30 minus y equals three fourths1/3(30 - y) = 3/4
one third times y minus 30 equals three fourths1/3(y - 30) = 3/4
Based on the interpretation of all the sentences in equation form, we find the statement 3 to be same as original statement. Solving the equation to get the value of y.
1/3(30 - y) = 3/4
10 - y/3 = 3/4
10 = 3/4 + y/3
10 = (3×4 + y×4)/12
10×12 = 12 + 4y
4y + 12 = 120
4y = 120 - 12
4y = 108
y = 27
Hence, the value of y is 27.
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Answer:
the answer is A.
1 over 3 (30 - y) = 3 over 4
Write an equation of the line in point-slope form that passes through the given points in the table. Then write the equation in slope-interceptform.x1520253035HHHу160200240280320An equation of the line in point-slope form is
Answers
Point slope form: y - 160 = 8(x-15)
Slope intercept form: y = 8x + 40
Explanation:
To write an equation of the line in point-slope form that passes through the given points in the table, we need to pick any two of the points in the table for x and y axis and find the changes of x and y
Points chosen: (20, 200) and (15, 160)
m = slope = (change in y)/ (change in x)
[tex]\begin{gathered} m\text{ = }\frac{200-160}{20-15}\text{ = }\frac{40}{5} \\ m\text{ = 8} \end{gathered}[/tex]Point-slope form:
[tex]\begin{gathered} y-y_1=m(x-x_1)\text{ then we would pick any of the points used earlier} \\ U\sin g\text{ (15, 160)} \\ y\text{ - 160 = 8( x - 15)} \\ y\text{ - 160 = 8x -120} \\ y\text{ =}8x\text{ + 40} \end{gathered}[/tex]The equation in the slope intercept form:
[tex]\begin{gathered} y\text{ = mx + b} \\ y\text{ = 8x + 40} \\ \text{where m = 8 b = intercept = 40} \end{gathered}[/tex]Hence, Point slope form: y - 160 = 8(x-15)
Slope intercept form: y = 8x + 40
How do you decide how well data represent
a population?
Use examples to explain.
Answers
The data that represent a population is helpful when we have to find the information only about one field.
In the given question we have decide how well data represent a population.
The total group you want to make judgments about is referred to as a population. Data is a set of quantitive data which refers the population only in numbers. So the data is only helpful when we have to find the only in small amount and only one field.
Data collection from a large population is typically only simple when the population is small, approachable, and cooperative.
Example: Gathering information from a population
A high school administrator is looking for trends in the final exam results of all graduating seniors. They use the entire population dataset since they are only interested in applying their findings to the graduating seniors in this high school. So the data is useful.
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there is a step missing from the solution. Which equation is the missing step?
Answers
To determine the next step, we need to slove the expression.
divide both sides by -1:
[tex]\begin{gathered} \frac{8}{-1}=\frac{-\sqrt[]{0.025x+7}}{-1} \\ -8=\sqrt{0.025x +7} \end{gathered}[/tex]Square both sides of the equation:
[tex]\begin{gathered} 8^2=(\sqrt{0.025x +7})^2 \\ 64\text{ = 0.025x + 7 } \\ 64\text{ - 7 = 0.025x } \\ 57\text{ = 0.025x } \\ Hence,\text{the missing step: }64\text{ = 0.025x + 7 (option B)} \end{gathered}[/tex]help meeeeeeeeee pleasee
Answers
Answer: 2.5, 5.3
Step-by-step explanation:
[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3[/tex]
Tim buys a torch and a battery
The torch costs eleven times as much as the battery
Tim pays with a £10 note and gets £4.84 change
How much does the battery cost?
Answers
The cost of battery is £0.43.
Given,
In the question:
Tim buys a torch and a battery
The torch costs eleven times as much as the battery and
Tim pays with a £10 note and gets £4.84 change.
To find the how much does the battery cost?
Now, According to the question:
Let cost of battery = £ x
So, Cost of torch = £ 11x
Based on the given conditions :
=> x + 11x = £ 10 - £ 4.84
=> 12x = £ 5.16
=> x = £ 5.16/ 12
=> x = £ 0.43
Hence, The cost of battery is £0.43.
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Simplify the equation 10x - 8x +2 + 10
Answers
And then add 2 and 10 =12
Steps
10x-8x=2x
2+10=12
2x+12
According to the rules of significant figures:1.25 × 200 = 300True orFalse
Answers
According to the rules of significant figures:
1.25 × 200 = 300
the answer is
TRue
Attendance at october fest was 15% more than last year. this year's attendance was 1785 people. find the number of people who attended the festival last year. rounded to the nearest person
Answers
Using the concept of equations, 1552 people attended the festival last year.
What are algebraic equations?Two algebraic expressions are combined to create an algebraic equation using the equals (=) sign. Algebraic equations are also known as polynomial equations since they contain polynomials on both sides of the equal sign. An algebraic equation consists of variables, coefficients, constants, and algebraic operations including addition, subtraction, multiplication, division, and exponentiation.
An integer or set of integers that satisfy the condition in the equation are the roots or solutions of an algebraic equation.
Let the number of people who attended the festival last year =x
Then, we can write an equation as
1785=1.15 × x
x = 1785/1.15
=1552 people
So, last year's attendance = 1552
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write and equation in slope-intercept form to represent each table x-3,6,9,12 y-5, -1, -7, -13
Answers
The equation that represents the table, in slope-intercept form, is: y = -2x + 11.
How to Write the Equation of a Line in Slope-intercept Form?The slope-intercept form of an equation that represents a line is expressed as y = mx + b, where:
m = slope = change in y / change in x.b = y-interceptUsing two pairs of values from the table, (6, -1) and (9, -7):
Slope (m) = (-7 -(-1)) / (9 - 6)
Slope (m) = -6/3
Slope (m) = -2.
Find the y-intercept, b, by substituting m = -2 and (x, y) = (6, -1) into y = mx + b:
-1 = -2(6) + b
-1 = -12 + b
-1 + 12 = b
b = 11
To write the equation, substitute m = -2 and b = 11 into y = mx + b:
y = -2x + 11
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?
Find the Area of the figure below, composed of a rectangle and a semicircle. The
radius of the circle is shown. Round to the nearest tenths place.
Area of Irregular Shapes
Nov 03, 2-44:03 PM
Answer:
9
3
20 POINTS PLEASE HELP !!!!!
Answers
Area of irregular shape is 41.13m².
Define area.The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat.
Given,
Area of irregular shape = Area of rectangle + Area of semicircle
Area of rectangle = Length × Breadth
Area of rectangle = 9 × 3
Area of rectangle = 27 m²
Area of semicircle:
1/2πr²
1/2 × 3.14 × 3²
14.13 m²
Area of irregular shape = 27 + 14.13
Area of irregular shape = 41.13
Area of irregular shape is 41.13m².
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What are the missing parts that correctly complete the proof? given: point m is on the bisector of angle j k l. prove: point m is equidistant from the sides of angle j k l. art: three rays k j, k m, and k l point in rightward direction sharing a common endpoint at k. ray k m is horizontal and bisects angle j k l equally. the perpendicular from point m to ray k j is made by a dotted line. the perpendicular cuts ray k j at x. angle k x m is labeled a right angle. the perpendicular from point m to ray k l is made by another dotted line. the perpendicular cuts ray k l at y. angle k y m is labeled a right angle. drag the answers into the boxes to correctly complete the proof.
Answers
The missing parts of proof are:
∠JKM≅∠LKMMK≅MKAAS Congruence PostulateCorresponding parts of congruent triangle are equalDefinition of equidistantExplain property of anglesIn geometry, a line that divides an angle into two equal angles is referred to as an angle bisector. By definition, a bisector is something that divides an object or a shape into two equal parts. A ray is said to be an angle bisector if it divides an angle into two equal portions of the same measure.
Angle Bisector's Qualities:
All of the angle bisector's points are equally spaced from both of the angle's arms.Any angle, including acute, obtuse, and right angles, can have an angle bisector drawn to it.The ratio by which the angle bisector splits the opposite side of a triangle is the same as the ratio by which the other two sides are divided.Given,
KM is the bisector of ∠JKL
1. As per the definition of bisector, ∠JKM≅∠LKM
Given,
∠KXM and ∠KYM are right angles
∠KXM≅∠KYM because all right angles are congruent
2. Because of Reflexive Property of congruence, MK≅MK
3. Given △KXM≅△KYM, AAS congruence postulate
4. Given MX≅MY, this is according to CPCTE property
5. Given, Point M is equidistant from the sides of ∠JKL, as per the definition of equidistant
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HELP QUICK 30 POINTS!!!!
What equation is graphed in this figure?
A. y−4=−2/3(x+2)
B. y+2=−3/2(x−2)
C. y+1=−2/3(x−3)
D. y−3=3/2(x+1)
Answers
Answer:
B is correct. The slope is -3/2.
Answer:D
Step-by-step explanation:
what is evaluate 5-(6/3)
Answers
Torren deposits $4500 in an account earning 2% interest, compounded annually. The equation that represents this situation is:A(n) = 4500(1 + 0.02) - 1How much will he have in the account at the beginning of year 8? Round youranswer to the nearest dollar.A. $5169B. $32,130C. $16,124D. $5272
Answers
Torren will have $5169 in the account at the beginning of year 8. Option A is correct.
The following formula can be used to calculate the compound interest.
[tex]A(n) = P(1 + r)^{(t- 1)}[/tex]
where,
A(n) denotes the final sum.
P stands for the initial deposit.
r denotes the interest rate (in decimal).
t denotes the time (in year).
The compound interest will be C.I = A - P in this case.
We are given in the question;
The account's initial deposit is $4500, and the term is 8 years.
As a result,
A = 4500 and
t = 8
As we all know, interest is compounded once a year.
We shall divide the interest rate in percentage form by 100 to convert it to decimal form.
r = 2% = 2/100
⇒r = 0.02
The given equation is
[tex]A(n) = 4500(1 + 0.02)^{(n- 1)}[/tex]
Substituting the given values in the above equation, we will get,
[tex]A(n) = 4500(1 + 0.02)^{(8- 1)}[/tex]
[tex]A(n) = 4500(1 + 0.02)^{7}[/tex]
[tex]A(n) = 4500 \times 1.14868[/tex]
[tex]A(n) = 5169.06[/tex]
[tex]A(n) = 5169[/tex]
Thus, Torren will have $5169 in the account at the beginning of year 8. Option A is correct.
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3 times x increased by 20 as a algebraic expression
Answers
Answer:
3x+20
Step-by-step explanation:
“3 times x” means 3x
and “increased by 20” means to add 20 to the equation.
if you were to solve this equation, the answer to the first step would be 6.666!
divide each side by 3. 3/3 is 1, and 20/3 is 6.666! therefore, the 1 cancels out and you get this number, which is the value of x.
now, for the second step, you would get 39.998, which is your overall answer! all you have to do is replace x with the answer from the previous step (6.666)
i hope this helped!!
Solve for x: 6x + 3 = 5x - 8
О -11
О 11
о
О -5
0
О 5
F
Answers
Answer:
6x+3=5x-8
6x-5x= -8-3(match the like terms)
x= -11
which value represents between 11% and 17%?
Answers
0.159 - A
It is between 11% and 17%
A lawnmower designer wants to build a lawnmower that measures
8 feet in height, 3 feet width, and 7 feet in length. She needs to construct a three dimensional model of the lawnmower. First, determine
the width for the scale model given a height of 10 inches?
Answers
The width of the scale model given a height of 10 inches as in the task content is; 3.75 inches.
What is width of the scale model given a height of 10 inches?It follows from the task content that the width of the scale model is to be determined given a height of 10 inches.
According to the design, the lawnmower measures; 8 feet in height, 3 feet width, and 7 feet in length.
Hence, since 8 feet in height corresponds to 10 inches on the scale, the width on the scale can be determined by proportion as;
8/10 = 3/x
x = ( 10 × 3 ) / 8
x = 30/8
x = 3.75 inches.
Therefore, the width on the scale as required is; 3.75 inches.
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24. Find fl-1).For questions 24-27, use the graph below.25. Find f(4).26. Find f(-3).27. If f(x) = 9, find x.
Answers
Let's start by calculating the value for f(-1).
For this we go to the graph and count the number of squares to the left of the axis to be at -1. In this case f(-1) would be 5.
Now let's calculate f(4)
For this case the value of f(4) would be 0.
Similarly we calculate f(-3). As you can see in the graph it would be 6.
The last scenario would be for when f(x) = 9, we look for that value on the curve and realize that it corresponds to x = 1.
I need help evaluating/answering this!
Answers
The value of the expression is equal to 6.
What is an expression?
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is [3(6-14)]/(-4). The value of the expression will be calculated below,
E = [3(6-14)]/(-4).
Simply the expression by using mathematical operations,
E = [3( -8)]/(-4).
E = 3 x 2
E = 6
Therefore, the value of the expression is equal to 6.
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Vivian has $535 in her stavings account and she has to pay $5.00 each month for her cell phone Reza has $145 and he saves $25 each month for his job walking the dogs at this rate when will they had the same amount of money and how much will they have
Answers
Answer: $456
Step-by-step explanation: They will both have the same amount of money at 7 months
What is the reciprocal of 1 1/8 ?
Answers
Answer:
0.8 repeated
Step-by-step explanation:
Because it is
jaylens snow cone stand went thourgh 10 bags of ice in the first hour it was open and 8 1/6 simplify your answer and write it as a fraction or as a whole or mixed number
Answers
The fraction form of 8 1/6 is 49/8 as the definition of fraction says, "An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided".
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. A fraction merely informs us of the number of parts that make up the whole. The slash that is written between the two numbers identifies a fraction. The numerator is the highest number, and the denominator is the lowest number. 1/2, for instance, is a fraction.
Here,
8 1/6=(6*8+1)/8
=49/8
According to the definition of a fraction, which states that it is "a number represented mathematically as a quotient, where the numerator and denominator are divided," the fraction form of 8 1/6 is 49/8.
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