The counterexample for the conjecture If the perimeter of a rectangle is 40 units, the area must be at least 1 square unit is: A rectangle with length 19.99 units and width 0.01 unit has a perimeter of 40 units and an area of 0.1999 square unit.
What is counterexample?The term counterexample refers to an instance or example that makes the statement false. This is used in logic to check if a statement is true or not. Counter example tend to counter the statement being discussed with valid points.
The question wants to show the relationship that may exist between perimeter and area of a rectangle.
The counterexample provided the dimensions that gave the perimeter which is 40 but failed to give area of 1 square unit
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Ron is renting an apartment and his landlord just raised his rent.he now pays 1500 and his rent will go up 10%.what will be the new payment
Answer:
it would be 150 more, so 1650
Step-by-step explanation:
divide 1500 by 10 to get 10%
In Exercises 1-6, describe the transformation of f(x) = x² represented by g.
Then graph each function.
1. g(x) = x² - 2
G=
h=
M=
2. g(x) = (x - 5)²
3. g(x) = (x + 1)² + 3
The graph of the function after transformation is attached below.
The connection between several systems is defined by coordinate transformations, which offer formulas for the coordinates in one system in terms of the coordinates in another system.
The coordinate transformation from polar to Cartesian coordinates is given by the formulas x = r cos and y = r sin, for example, if the polar axis is the positive x axis on the plane and the origins of the Cartesian coordinates (x, y) and polar coordinates (r) are the same.Every bijection from the space to itself can be related to two coordinate transformations.The formulas for the new coordinates of each point's image are constructed in a way that the old coordinates of the original point's image are maintained.In particular, the change of algebraic equations, it is a typical kind of algebraic problem.The graph of the transformed function is attached below. The red graph indicates the parent function f(x) = x² and the blue graph indicated the graph of transformation g(x) = x² - 2
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help me im having trouble solving this
Step-by-step explanation:
[tex]sa = 2\pi \: r {}^{2} + 2\pi \: rh \\ = 2 \times 3.14 \times 3 { }^{2} + 2 \times 3.14 \times 11[/tex]
elizabeth gives a walking tour of a popular tourist city to one person for to increase her business, she would lower the price by $2 per person for each additional person. write the cost per person c as a function of the number of people n on the tour. how much does she make for a tour with people?
Thus cost per person c as a function of the number of people n is
c(n) = 43 + (n-1)(43-(n-1)2) and amount she makes is $229
In the problem it is given that Elizabeth gives a walking tour of a popular tourist city to one person for 43 to increase her business, she would lower the price by $2 per person for each additional person. we have to find the cost per person c as a function of the number of people n on the tour. Also the amount she makes for a tour with 7 people.
So we can write it as
c(1) = 43
c(2) = 43 + 41
c(3) = 43 + 2(43-2*2)
c(4) = 43 + 3(43-3*2)
c(n) = 43 + (n-1)(43-(n-1)2)
To find the amount she makes we write c as a function of n where n=7
c(7) = 43 + 6(43-6^2) = 43 + 6*31 = 43 + 186 = $229
Thus cost per person c as a function of the number of people n is c(n) = 43 + (n-1)(43-(n-1)2) and amount she makes is $229.
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Expressed as a product of its prime factors in index form, a number N is
N = 3 x 5² x x³
Express 5N² as a product of prime factors in index form.
Give your answer in terms of x.
5N² is expressed as a product of prime factors in index form as [tex]5^{5} * 3^{2} * x^{10}[/tex] .
What are prime factors index form?In the expression of a number as the product of its prime factors, known as prime factor index form, each prime factor is only mentioned once, either as itself or, if necessary, to a required power.
Given:
N is a number that is expressed as a product of its prime factors in index form.
N = [tex]3x * 5x^{2} * x^{3}[/tex]
We have to express 5N² as a product of prime factors in index form.
5N² = 5([tex]3x * 5x^{2} * x^{3}[/tex])²
= [tex]5 * 9x^{2} *5^{4} x^{2} *x^{6}[/tex]
= [tex]5 * (5^{2}x)^{2}* (3x )^{2} *x^{6}[/tex]
( using exponential properties [tex]a^{m} *a^{n} = a^{m+n} and (a^{m} )^{n} = a^{mn}[/tex])
= [tex]5^{5} * 3^{2} * x^{10}[/tex]
The prime factors of 5N² are 5,3 and x respectively.
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Lacy earned $900 last week before taxes, if she paid 19 % in taxes;
a) How much did she pay in taxes?
b) What is her net pay?
Answer: a) $171 b) $729
Step-by-step explanation:
a) 0.19 * $900 = $171
b) net pay = the money one earns after all deductions
$900 (what she earned) - $171 (taxes she had to pay) = $729
Find the midpoint of points (-4,3) and (4,-3)
Find the measure of the missing angles.
Answer:
B = 95°C = 85°
Step-by-step explanation:
the angle C is the opposite angle to that of 85 degrees, therefore congruent, we subtract 85 x 2 ° from the sum of the angles (360 °, is a round angle) and find the sum of the other two angles, always opposite and increasing, divide by two and we have the value of the angle B
C = 85°
B = [360 - (85 * 2)] : 2
B = (360 - 170) : 2
B = 190 : 2
B = 95°
-----------------
check
85 + 85 + 95 + 95 = 360°
the answer is good
Use this table to answer the following questions.If the number of gallons of gas is known, can you find the number of gallons consumed? Explain how this value would be calculated.
The table of values indicates a proportional relationship between the number of gallons of gas and the number of miles driven, therefore;
The number of miles driven, f(x) can be found from the number of gallons of gas consumed, x, using the equation; f(x) = 31•xWhat is a proportional relationship?A proportional relationship is one in which one variable, y, can be obtained from another variable, x, by multiplying x by a factor.
Please find attached a table showing the number of gallons of gas and the miles driven obtained from a similar question online
Let x represent the number of gallons of gas and let f(x) represent the number of miles driven
The difference between the consecutive terms of the first three values in the number of gallons and miles driven are each equal to 2 and 62 respectively
4 - 2 = 2 - 0 = 2
124 - 62 = 62 - 0 = 62
Therefore, given that the first difference is constant, the first three points have a linear relation, which gives;
Slope of the line = 62/2 = 31
Intercept = 0
Therefore;
f(x) = 31•x
Checking the fourth point, gives;
x = 10
f(10) = 31 × 10 = 310
The relationship between the miles driven, f(x), and the number of gallons is therefore a proportional relationship, which is presented as follows;
f(x) = 31•x
Therefore, if the number of gallons of gas, x, is known, the number of miles driven, f(x), can be found using the equation;
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What value is equivalent to 2 × 3 + 4 − 62?
Answer:
-52
Step-by-step explanation:
I hope this helps!
Answer: -52
Step-by-step explanation: Using PEMDAS
(2x3)+4-62
6+4-62
10-62
= -52
Solve the inequality. (NESTED absolute value inequality)
[tex]||x-5| -4| \leq 1[/tex]
The result of the Nested absolute inequality when resolved gives:
x = -10, 0. See the solution below.
It is to be noted that when one absolute-value expression is inside another one, this is called a "nested" expression. Absolute expressions are expressions that values that can NEVER be negative.
The solution hence is given as follows:
Given: ||x-5|4|≤1
One absolute-value expression is stacked inside another in this equation. I'll work from the outside in, sorting items into their respective cases. Assume the argument of the outer bars is negative (do the "minus" case):
Step 1 - first splitting:
|x-5| -4 ≤ -1
|x-5| ≤ 3
I have to stop here since the last statement above states that an absolute value equals a negative number. Absolute values, on the other hand, are never negative! As a result, this step is invalid; it yields no viable solutions to the original problem.
Now I'll look at the scenario where the argument of the outside bars is positive (the "plus" case):
|x-5| -4 ≤ 1
|x-5| ≤ 1 + 4
Recall that absolute values are never negative. This equation is correct, and I've isolated the leftover absolute value, so I'll go over the two situations again.
Step 2 - First, consider the "minus" case:
x+5 ≤ -5
x ≤ -5-5
x≤ -10
The variable can have a "minus" value; the sole constraint is that an absolute-value expression cannot have a "minus" value. Now consider the "plus" case:
⇒ x + 5 ≤ 5 again recall that this is an absolute expression hence the laws of polarity while cross the inequality sign is suspended.
x ≤ 5-5
x≤0
Hence the answer which is complete is:
x = -10, 0
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find the slope of the line that goes through the points (-4,1) and (8,-5)
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-4)}}} \implies \cfrac{-6}{8 +4}\implies {\Large \begin{array}{llll} -\cfrac{1}{2} \end{array}}[/tex]
you are given two reports estimating the mean increase in monthly household spending on gasoline over the past six months: report 1: based on a simple random sample of 14 households, we are 98% confident that the mean increase in monthly household spending on gasoline over the past six months is between $64.35 and $83.59. report 2: based on a simple random sample of 53 households, we are 95% confident that the mean increase in monthly household spending on gasoline over the past six months is between $58.37 and $71.93 determine which report you find most convincing, and explain your reasoning why.
In my opinion, Report 1 is more persuasive than Report 2 due to the fact that the margin of error in Report 1 is narrower than in Report 2.
This is further explained below.
What is the margin of error.?Generally, we consider report one and report two
For Report
at 98% confidence interval = $64.35 to $83.59
Therefore, the Margin of error
M.E= $83.59 - $64.35
M.E = $19.24
For Report 2:
95% confidence interval = $58.37 to $71.93
Margin of error
M.E= $71.93 - $58.37
M.E= $13.56
Since Report 1 has a smaller margin of error than Report 2, I find Report 1 to be more convincing.
In conclusion, A report with a lower margin of error, in my opinion, is often more credible than one with a bigger one.
This is because more exact data indicates a report with a reduced margin of error.
To put it another way, information in a report with a lower margin of error is more likely to be correct than information in a report with a higher margin of error.
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Name the property used in the given expression −33/ 57 × −7/ 28 = −7/ 28 × −33/ 57
Answer:
Communitive Property
Step-by-step explanation:
a * b = b * a
In your case,
(-a / b) * (-c / d) = (-c / d) * (-a / b)
brainly pls :)
Answer:
Answer:
Communitive Property
Step-by-step explanation:
a * b = b * a
In your case,
(-a / b) * (-c / d) = (-c / d) * (-a / b)
Step-by-step explanation:
A. Use the cartesian plate on the right to plot all the points.
Pt. A (-4, 3) pt. D (0, -3)
Pt. B (2, 5) pt. E (-5, -2)
Pt. C (5, -1)
[tex]__________________________[/tex]
Refer to the attachment for the answer
PLEASE HELP ME
Solve for x. Show each step of the solution.
2.54-x+12=21-42.5x+7
The solution of the equation 2.54-x+12= 21-42.5x+7 is x = 0.324
The equation is
2.54-x+12 = 21-42.5x+7
Rearrange the terms are do the suitable arithmetic operation in the equation
2.54-x+12= 21-42.5x+7
-x+12+2.54 = -42.5x+7+21
Add the like terms together
-x+14.54 = -42.5x+28
Here we have to rearrange the term and make the all the like terms in each sides
Move 14.54 to the right hand side and move -42.5x to the left hand side
Then the equation will become
-x+42.5x = 28-14.54
41.5x = 13.46
x = 13.46/41.5
x = 0.324
Hence, the solution of the equation 2.54-x+12= 21-42.5x+7 is x = 0.324
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Jack mails 10 packages that each weigh the same amount. If the combined weigh of all 10 package is 67 1/2 pounds, how much does one package weigh? Show your work.
One package weighs 6.75 pounds.
In this question, we have been given Jack mails 10 packages that each weigh the same amount.
We need to find the weight of one packet.
Let each package weighs m pounds.
The combined weigh of all 10 package is 67 1/2 pounds.
So, we get an equation,
10m = 67.5
We solve above equation.
m = 67.5 / 10
m = 6.75 pounds
Therefore, one package weighs 6.75 pounds.
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Randy planted a small pine tree in his yard. When he bought the tree it was 6 inches tall and grew at a rate of 2 inches weekly. Write a function of height, h, in terms of weeks, w.Using the equation from problem #1 What will the height of the tree be in 13 weeks?
Answer:6+2w=h
The height of the tree will be 32 inches on week 13
Step-by-step explanation:
ok
a²-ab-ac+bc / a² +ab-ac-bc Simplying Algebraic fractions by factorizing
Answer:
(a - b)/(a + b).
Step-by-step explanation:
a²-ab-ac+bc / a² +ab-ac-bc
= a(a - b) - c(a - b) / a(a + b) - c(a + b)
= (a - c)(a - b) / (a - c)(a + b)
The (a - c) is common to top and bottom, so
= (a - b)/(a + b).
Please help me with my trig
Question 28&29
The expressions related to the roots of each quadratic equation are listed below:
Case 1 - x² + 3 · x - 9 = 0
Roots: α = - 3 / 2 - 3√5 / 2, β = - 3 / 2 + 3√5 / 2
a) α + β = - 3
b) α² + β² = 27
c) α³ + β³ = - 108
Case 2 - x² + 4 · x - 2 = 0
Roots: α = - 2 - √6, β = - 2 + √6
a) α + β = - 4
b) α² + β² = 20
c) α³ + β³ = - 88
How to determine the roots of quadratic equations and calculate the values of equations based on these roots
This question consists in two parts, find the roots by factoring the quadratic equations by algebra properties and determine the expressions based on the two roots of each expression. A root is a value of x such that the polynomial is equal to zero.
Case 1
x² + 3 · x - 9 = 0
x² + 3 · x = 9
x² + 3 · x + 9 / 4 = 9 + 9 / 4
(x + 3 / 2)² = 45 / 4
x + 3 / 2 = ± 3√5 / 2
x = - 3 / 2 ± 3√5 / 2
The roots are α = - 3 / 2 - 3√5 / 2 and β = - 3 / 2 + 3√5 / 2 and the following expressions are evaluated:
a) α + β = - 3
b) α² + β² = (- 3 / 2 - 3√5 / 2)² + (- 3 / 2 + 3√5 / 2)² = 27
c) α³ + β³ = (- 3 / 2 - 3√5 / 2)³ + (- 3 / 2 + 3√5 / 2)³ = - 108
Case 2
x² + 4 · x - 2 = 0
x² + 4 · x + 4 = 6
(x + 2)² = 6
x + 2 = ± √6
x = - 2 ± √6
The roots are α = - 2 - √6 and β = - 2 + √6 and the following expressions are evaluated:
a) α + β = - 4
b) α² + β² = (- 2 - √6)² + (- 2 + √6)² = 20
c) α³ + β³ = (- 2 - √6)³ + (- 2 + √6)³ = - 88
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Diego and Stacy can paint a doghouse in 5 hours when working together. Diego works twice as fast as Stacy. Let x be the number of hours it would take Diego to paint the doghouse and y be the number
of hours it would take Stacy to paint the doghouse. How long would it take Stacy
to paint the doghouse if she was working alone? How long would it take Diego to paint the doghouse if he was working alone?
Please show steps!
If Stacy works alone, it will take her 11 hours 40 minutes to paint the doghouse.
If Diego works alone, it will take him 5 hours 40 minutes to paint the doghouse.
How to find how long would it take Stacy and Diego to paint the doghouse while working alonegiven data
Diego and Stacy can paint a doghouse in 5 hours
Diego works twice as fast as Stacy
Let x be the number of hours it would take Diego to paint the doghouse and y be the number
Putting the given information mathematically
Diego and Stacy can paint a doghouse in 5 hours
x + y = 5hoursDiego works twice as fast as Stacy
x = 2yx + y = 5hours
Since x = 2y
2y + y = 5
3y = 5
y = 5/3
y = 1 1/3
from x = 2y
x = 2 * 5/3
x = 10/3
x = 3 1/3
1/3 hours is a fraction of hours. we convert it to minutes by multiplying by 60
= 1/3 * 60
= 20 minutes
Therefore it will take Diego 3 hours 20 minutes and Stacy 1 hour 20 minutes for them to complete a 5 hours work
If Diego works alone
Diego alone = 5 hours + Stacy's hours * 1/2
since Diego is twice faster than Stacy then Stacy's time will be halved
Diego alone = 5 hours + 80 minutes * 1/2
Diego alone = 5 hours + 40 minutes
Diego alone = 5 hours 40 minutes
if Stacy works alone
Stacy alone = 5 hours + Diego's hours * 2
Stacy alone = 5 hours + 3 hours 20 minutes * 2
Stacy alone = 5 hours + 6 hours 40 minutes
Stacy alone = 11 hours 40 minutes
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Simplify each expression. Which expression is not equivalent to the other two?
A. 15j + 30
B. 5(3j - 6)
C. 3(5j - 10)
Answer: A is not equivalent to the other 2
Step-by-step explanation:
A. 15j+30
B. 5(3j-6) = 15j-30
C 3(5j-10) = 15j-30
multiply the stuff inside paranthesis for the last 2
So a is the outsider
For a party, Bert gets 4 different kinds of soda. He buys a 6-pack of each kind. At home, he divides the sodas evenly among 3 coolers. How many sodas are in each cooler?
The number of sodas that can fit in inside each cooler is 8
How to determine the number of sodas in each cooler?From the question, the given parameters are:
Number of packs = 6
Kinds of soda = 4
Number of cooler = 3
The number of sodas in each cooler is calculated as
Sodas = Number of packs x Kinds of soda/Number of cooler
Substitute the known values in the above equation
So, we have
Sodas = 6 x 4/3
Evaluate
Sodas = 8
Hence, there are 8 sodas in each cooler
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will give 15 points if the question is answered
The surface area of a cylinder is equal to 208π square units.How to calculate the surface area of right cylinder?The surface area is the sum of the areas of all faces of the solid. In the case of a right cylinder, the surface area is the sum of the two areas of the circular base and the lateral area (A), in square units, whose formula is described below:A = 2π · r² + 2π · r · h (1)Where:r - Base radiush - HeightIf we know that r = 8 and h = 5, then the surface area of the right cylinder is:A = 2π · 8² + 2π · 8 · 5A = 208πThe surface area of a cylinder is equal to 208π square units.
domain and range puzzle answers
1. What is the equation of an ellipse with center, (h, k) that is elongated in the x-direction?
The equation of an ellipse with center, (h, k) that is elongated in the x-direction is: (x - h)²/a² + (y - k)²/b² = 1.
What is defined as the ellipse?In aspects of locus, an ellipse is the collection of every point on an XY-plane with whom the distance from 2 fixed points (called foci) adds up to the a constant value.
Ellipse does have two focal points, which are also known as foci.A fixed distance is referred to as a directrix.The eccentricity of an ellipse ranges from 0 to 1.The total sum of every distance from an ellipse's locus to its two focal points is constant.Ellipse contains a single major and one minor axis, as well as a center.The standard form of equation of ellipse with centres (h, k) that is elongated in the x-direction is given as;
(x - h)²/a² + (y - k)²/b² = 1
Now, when the centre of the ellipse coincides with the origin of coordinates axis, the becomes;
x²/a² + y²/b² = 1
Thus, the equation of ellipse of obtained.
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for a certain company, a train coming from new york to washington dc takes 3 hours to travel 228 miles. a new train company is able to complete the same journey in only 2.5 hours. how much faster is the new company’s train in terms of miles per hour?
A.) 7.5
B.) 11.7
C.) 15.2
D.) 17.3
E.) 21.4
Answer:
The new company’s train is C. 15.2 miles faster.
Step-by-step explanation:
Train A: 228/3 = 76 miles per hour
Train B: 228/2.5 = 91.2 miles per hour
91.2 - 76 = 15.2
Which expression is equivalent to −3(b − 7)?
Answer:
- 3b + 21
Step-by-step explanation:
- 3(b - 7) ← multiply each term in the parenthesis by - 3
= - 3b + 21
Answer:
-3(b-7) = -3b + 21
pls help i rlly need this
The slope of the line is 2 , the correct option is (A).
Slope of the line is defined as the change in y coordinate with respect to the change in x coordinate of the line , the slope of the line is denoted by "m" .
The slope of the line passing through the two points (a,b) and (c,d) is given by m = (d-b)/(c-a) .
In the question ,
a line is given
let us name the points as M and N ,
the named graphed is shown below,
Assuming the cube in the graph be of 1 unit each.
So , the coordinates of M and N from the graph is
M = (1,1) and N= (-1,-3),
So the slope of the line passing through the points (1,1) and (-1,-3) is
slope = (-3-1)/(-1-1)
= -4/-2
= 2.
Therefore , the slope of the line is 2 , the correct option is (A).
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The perimeter of an equilateral triangle is 17 inches more than the perimeter of a square, and the side of the triangle is 8 inches longer than the side of the square. Find the side of the triangle ( Hint: An equilateral triangle has three sides the same length.)
The side of the triangle is 15 inches.
How to find the perimeter of a triangle and square?The perimeter of an equilateral triangle is 17 inches more than the perimeter of a square, and the side of the triangle is 8 inches longer than the side of the square.
Hence,
let
perimeter of the square = x inches
perimeter of an equilateral triangle = x + 17
Let
side of the square = y
side of the triangle = 8 + y
Therefore,
Perimeter of the square
x = y + y + y + y
x = 4y
Perimeter of the triangle
x + 17 = 8 + y + 8 + y + 8 + y
x + 17 = 24 + 3y
x - 3y = 7
Combine the equation,
x = 4y
x - 3y = 7
Therefore,
4y - 3y = 7
y = 7
x = 4(7)
x = 28
Therefore,
side of the triangle = 8 + y = 8 + 7 = 15 inches
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