[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies directly with "x"}}{y = k(x)}\hspace{5em}\textit{we also know that} \begin{cases} x=400\\ y=10 \end{cases} \\\\\\ 10=k(400)\implies \cfrac{10}{400}=k\implies \cfrac{1}{40}=k\hspace{5em}\boxed{y=\cfrac{1}{40}x} \\\\\\ \textit{when x = 450, what's "y"?}\qquad y=\cfrac{1}{40}(450)\implies y=\cfrac{45}{4}[/tex]
Diameter of the tin on the picture = ? Height of the tin on the picture = ? Actual weight of coffee = 750 g 1.1 Measure the diameter of the tin in mm and write down the real diameter in mm 1.2 Hence, determine the circumference of the base of the tin in mm. You may us the formula: CС = 2πr Hint: radius = half of diameter MATHEMATICAL LITERACY GRADE 11, 2023 SBA GUIDELINE π = 3,142 Page 2 (3) (3)
Answer: 1.1 The diameter of the tin on the picture is approximately 90 mm.
1.2 The circumference of the base of the tin is approximately 565 mm (2πr = 2π(45) = 565).
Step-by-step explanation: math is stressful fr
We can write the diameter and circumferance of base as -
D = 2√(750ρ/πh)
C = 2π√(750ρ/πh)
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
Given is to find the diameter and height of the tin can.
Assume the density of coffee as {ρ}. We can write the volume of the tin can as -
Volume = mass x density
Volume = 750ρ
We can write -
πr²h = 750ρ
r = √(750ρ/πh)
D = 2r
D = 2√(750ρ/πh)
Now, we can write the circumferance as -
C = 2πr
C = 2π√(750ρ/πh)
Therefore, we can write the diameter and circumferance of base as -
D = 2√(750ρ/πh)
C = 2π√(750ρ/πh)
To learn more on volume click :
brainly.com/question/1578538
#SPJ2
my math teacher hates me sos
Answer:
That sucks
Step-by-step explanation:
Because I said so
If f(x) = 3x +7 and g(x) = x2 - 2x, what is g(f(1)) equal to? Answer: If f(x) = x + 4 and g(x) = 2x + 1, find (g o f)(x). Select one: a. 2x + 9 b. 2x^2 + 9x + 4 c. 2x^2 + 4 d. 2x + 5
Answer:
80 and 2x + 9
Step-by-step explanation:
to evaluate g(f(1)) , evaluate f(1) then substitute the value obtained into g(x)
f(1) = 3(1) + 7 = 3 + 7 = 10 , then
g(10) = 10² - 2(10) = 100 - 20 = 80
------------------------------------------------------
to calculate (g ￮ f)(x) , substitute x = f(x) into g(x)
(g ￮ f)(x)
= g(f(x))
= g(x + 4)
= 2(x + 4) + 1
= 2x + 8 + 1
= 2x + 9
show that T<0,2> (0,1). Is T<0,2> (x,y) = D3 (x,y) a true statement for any point (x,y)? Why or why not.
Answer:
To show that T<0,2> (0,1), we need to evaluate the transformation T at the point (0,1) and check if the result is in the range of T.
T<0,2> (0,1) means that the transformation T takes the point (0,1) in the input space to a point in the output space that has coordinates (0,2).
Let's evaluate T at (0,1):
T<0,2> (0,1) = D3(0,1) + (0,1)
= (0+0, 3+1)
= (0, 4)
The output point (0,4) is not equal to (0,2), which means that T<0,2> (0,1) is false. Therefore, T<0,2> does not map the point (0,1) to (0,2).
To determine if T<0,2> (x,y) = D3 (x,y) is a true statement for any point (x,y), we need to check if the transformation T always equals the function D3.
T<0,2> (x,y) = (x, 3+y)
D3(x,y) = (x,y,3)
Since T and D3 have different ranges (T has a range of R^2 and D3 has a range of R^3), the statement T<0,2> (x,y) = D3(x,y) is not true for any point (x,y).
Therefore, we cannot equate T<0,2> and D3, and the statement T<0,2> (x,y) = D3 (x,y) is false for any point (x,y).
A ferry traveled
1
6
6
1
start fraction, 1, divided by, 6, end fraction of the distance between two ports in
3
7
7
3
start fraction, 3, divided by, 7, end fraction hour. The ferry travels at a constant rate.
At this rate, what fraction of the distance between the two ports can the ferry travel in one hour?
The ferry travels at constant rate is 7/18 miles/hour
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
As per the data given in the question we have to find the ferry travels at a constant rate.
As per the question it is given that a ferry traveled 1/6 of the distance between two ports in 3/7 hour.
Now, Ferry travelled 1/6 miles of distance between two ports in 3/7 hours
Hence, Rate of Ferry is equal to distance travelled over time taken.
Rate of ferry = 1/6 ÷ 3/7
Now we calculate it.
Rate of ferry = 1/6 × 7 / 3 miles/hour
Rate of Ferry = 7/18 miles/hour
Hence, The ferry travels at constant rate is, 7/18 miles/hour.
Learn more about the divide visit:
https://brainly.com/question/28119824
#SPJ3
Solve for the unknown. Round decimals to hundredths and percents to the nearest tenth. 950 increased by 40% =
Answer: We can start by translating the given sentence into an equation:
950 + 0.40(950) = x
where x is the unknown amount after the 40% increase.
To solve for x, we can simplify the right-hand side of the equation:
950 + 0.40(950) = x
950 + 380 = x
1330 = x
Therefore, the unknown amount after the 40% increase is 1330.
Rounding 1330 to the nearest tenth gives 1330.0, and converting to a percent gives 133000%.
Step-by-step explanation:
please help me i need your help. find the value of x
Answer:
122
Step-by-step explanation:
add the 2 angles together and there's your answer.
if you want to check take your answer and subtract from 180.
Answer: 122
Step-by-step explanation:
all triangles add up to 180
54+68=122
180-122=58
58=inner corner
180 (this is the measure of the line) -58 =122
hopefully this helps :))
Allegiant Airlines charges a mean base fare of $89. In addition, the airline charges for making a reservation on its website, checking bags, and inflight beverages. These additional charges average $35 per passenger. Suppose a random sample of 50 passengers is taken to determine the total cost of their flight on Allegiant Airlines. The population standard deviation of total flight cost is known to be $39
If Allegiant Airlines charges a mean base fare of $89. The population mean cost per flight is $128.
How to find the population mean cost per flight?As given in the problem, the population mean base fare is $89 and the population mean additional fare per person is $39.
To find the population mean cost per flight, we need to add the population mean base fare to the population mean additional fare per person,
Population mean cost per flight = (Population mean base fare + Population mean additional fare per person)
Population mean cost per flight = ($89 + $39)
Population mean cost per flight = 128
Therefore the population mean cost per flight is $128.
Learn more about population mean cost per flight here:https://brainly.com/question/15556079
#SPJ1
The complete question is:
Allegiant Airlines charges a mean base fare of $89. In addition, the airline charges for making a reservation on its website, checking bags, and inflight beverages. These additional charges average $39 per passenger (Bloomberg Businessweek, October 8 � 14, 2012). Suppose a random sample of 60 passengers is taken to determine the total cost of their flight on Allegiant Airlines. The population standard deviation of total flight cost is known to be $40.
Allegiant Airline reports a population mean base fare of $89 and a population mean additional fare of $39 per person. What is the population mean cost per flight?
Triangle ABC has vertices A (-1, 2), B (5, 2), and C (5,-3) and triangle XYZ has vertices X(-0.5, 1), Y(2.5, 1), and 2(2.5, "-1.5)." What is the scale factor of the dilation that maps Triangle ABC onto triangle XYZ. ((PLS HELP ITS DUE TOMORROW))
The solution is, the scale factor of the dilation that maps Triangle ABC onto triangle XYZ is √2.
What is scale factor?A scale factor is when you enlarge a shape and each side is multiplied by the same number. This number is called the scale factor. Maps use scale factors to represent the distance between two places accurately.
here, we have,
given that,
Triangle ABC has vertices A (-1, 2), B (5, 2), and C (5,-3)
and triangle XYZ has vertices X(-0.5, 1), Y(2.5, 1), and 2(2.5, "-1.5)."
now, we now that,
distance formula:
d=√(x2−x1)^2+(y2−y1)^2
so, we get,
length of AB = 3√2
and, length of XY = 3
so, scale factor = AB/XY
=3√2/3
=√2
Hence, The solution is, the scale factor of the dilation that maps Triangle ABC onto triangle XYZ is √2.
To learn more on distance click:
brainly.com/question/7942332
#SPJ1
Describe the translation that maps figure ABCD onto figure EFGH
The translation that maps figure ABCD onto figure EFGH is described as follows: Translate figure ABCD 7 units right to form figure EFGH..
What is a translation?Translation transformation is a type of geometric transformation that moves every point of an object or shape in a straight line without changing its orientation or size.
A translation happens when either a figure or a function are moved horizontally or vertically.
How to determine the translation ruleIf we look at the corresponding vertices on each figure, we have that:
7 was added to the x-coordinate of each vertex.The y-coordinate of each vertex remains constant.Hence: Translate figure ABCD 7 units right to form figure EFGH.
More can be learned about translation at
https://brainly.com/question/30926188
#SPJ1
what are the domain and range of the function f(x)=2^x+1
The domain of a function is the set of all possible input values (x) for which the function is defined.
The range of a function is the set of all possible output values (f(x)) that the function can produce.
For the given function f(x) = 2^(x+1), the domain includes all real numbers because we can substitute any real number for x and obtain a valid output.
To find the range, we can examine the behavior of the function as x approaches positive and negative infinity. As x approaches negative infinity, the exponent (x+1) becomes very large negative number, and 2^(x+1) approaches zero. As x approaches positive infinity, the exponent (x+1) becomes very large positive number, and 2^(x+1) approaches infinity. Therefore, the range of the function is (0, infinity).
So, the domain is (-infinity, infinity) and the range is (0, infinity).
THE 14 BUSINESSES IN A SHOPPING CENTER ELETRICITY BILL. THIS MONT THEY USED 2,996 KILOWATT HOURS OF ELECRICITY HOW MANY KILOWATT HOURS MUST EACH BUSINESSES PAY FOR
Therefore , the solution of the given problem of fraction comes out to be 214 kilowatt hours of electricity for the month.
A fraction is what?Any combination of equal portions or fractions can be combined to represent a whole. In standard English, the quantity of a certain size is defined as a fraction. 8, 3/4. Wholes also include fractions. The ratio of numerator to ratio is a mathematical symbol for integers. All of these number fractions are simple fractions. There is a fraction inside of the fraction but rather remainder in a difficult fraction. because the values, numerators, and numerators of real fractions vary
Here,
We must divide the total amount of electricity used by the number of businesses in order to calculate how many kilowatt hours each business is responsible for paying for:
=> 14, 14 businesses x 2,996 kilowatt hours = 214 kilowatt hours per company
As a result, each company is required to pay for roughly 214 kilowatt hours of energy per month.
To know more about fraction visit:
https://brainly.com/question/10354322
#SPJ1
You need to spend exactly $1 and buy 40 stamps. There are 3
kinds of stamps that cost 1, 4, and 12 cents respectively. How many
stamps do you need to buy of each kind (if you have at least one of
each
You need to buy 1 stamp that costs 12 cents, 3 stamps that cost 4 cents each, and 8 stamps that cost 1 cent each, to have a total of 40 stamps and spend exactly $1.
The reasoning is as follows:
If you were to buy only 1 cent stamps, you would need to purchase 100 of them to spend $1, which would exceed the required 40 stamps. On the other hand, if you were to buy only 12 cent stamps, you would only be able to purchase 8 stamps, which would fall short of the required 40 stamps. Therefore, a combination of all three types of stamps is necessary.
Starting with the most expensive stamp, one 12 cent stamp leaves you with 88 cents. Then, 3 stamps of 4 cents each will cost you 12 cents, leaving you with 76 cents. Finally, 8 stamps of 1 cent each will cost you 8 cents, which adds up to $1 and gives you a total of 40 stamps.
For more questions like Combinations visit the link below:
https://brainly.com/question/29156801
#SPJ11
The diagram shows two squares overlapping.
Work out the size of the angle marked z.
The measure of the angle ∠Z will be 88°.
What is geometry?Geometry is the study of two-dimensional and three-dimensional figures such as quadrilaterals, triangles, circles, their sides, and angles. Symmetry is defined as if the object is cut by its centre line the two cut parts should be the mirror image of each other so that we can call them symmetric to each other.
Given that the two angles are (9p + 20)° and (7p + 32 )°. The value of angle z is calculated as,
9p + 20 + 7p + 32 = 180
16p = 180 - 20 - 32
16p = 128
p = 8
The measure of the angle ∠Z will be,
9p + 20 + ∠Z= 180
72 + 20 + ∠Z= 180
∠Z = 180 - 72 - 20
∠Z = 88°
Therefore, the angle ∠Z is 88°.
To know more about geometry follow
https://brainly.com/question/26518383
#SPJ1
For the following situation, do the following but do not solve.
1. Define variables x and y.
2. Give a complete list of constraint inequalities.
3. Give a target (objective) equation (concerning profit).
Suppose a coffee company makes two blends, Columbian Supreme and Columbian Treat. Columbian Supreme takes 12 ounces of premium beans and 4 ounces of bargain beans per bag of coffee. Columbian Treat takes 7 ounces of premium beans and 9 ounces of bargain beans per bag of coffee. Suppose that 1600 ounces of premium beans and 800 ounces of bargain beans are available. If the company profits $4 per pound of Columbian Supreme and $3.25 per pound of Columbian Treat, then how can they maximize their profit? What is the maximum profit?
equation is 4x + 3.25y
To maximize their profit, the coffee company needs to define the variables x and y, which represent the number of pounds of Columbian Supreme and Columbian Treat respectively. Then, the complete list of constraint inequalities can be written as:
Finally, the target (objective) equation is 4x + 3.25y, which represents the total profit from selling x pounds of Columbian Supreme and y pounds of Columbian Treat.
Learn more about Columbian Treat
brainly.com/question/27069010
#SPJ11
Let A = and B a matrix of type (2,3). We assume that the second line of
B^tA^t is [1 − 2]. Calculate the second column of B. You must
justify your answer.
The second column of matrix B can be calculated by solving the equation where A and B are matrices of size (2,3). The second column of B is
[tex][b_21, b_22] = [(1 - a_11b_11 - a_13b_31)/a_12, (-2 - a_11b_12 - a_13b_32)/a_12][/tex]
First, we must transpose both A and B:
[tex]A^t[/tex]= [tex][a_11, a_12, a_13][a_21, a_22, a_23][/tex]
[tex]B^t[/tex] = [tex][b_11, b_21][b_12, b_22][b_13, b_23][/tex]
The second column of B.
[tex]B^tA^t[/tex] = [tex][a_11b_11 + a_12b_21 + a_13b_31, a_11b_12 + a_12b_22 + a_13b_32][/tex]
[1, -2] = [tex][a_11b_11 + a_12b_21 + a_13b_31, a_11b_12 + a_12b_22 + a_13b_32][/tex]
Since we have two equations and two unknowns, we can solve for the elements of the second column of B.
Solving for [tex]b_21[/tex]:
[tex][a_11b_11 + a_12b_21 + a_13b_31, a_11b_12 + a_12b_22 + a_13b_32][/tex]
Solving for [tex]b_22[/tex]:
[tex]-2 = a_11b_12 + a_12b_22 + a_13b_32b_22 = (-2 - a_11b_12 - a_13b_32)/a_12[/tex]
Therefore, the second column of B is:
[tex][b_21, b_22] = [(1 - a_11b_11 - a_13b_31)/a_12, (-2 - a_11b_12 - a_13b_32)/a_12][/tex]
To know more about matrix here:
https://brainly.com/question/28180105
#SPJ11
Evaluating Trigonometric Functions In Exercises 15-30, find the exact values of the sine, cosine, and tangent of the angle.
15. 105 deg = 60 deg + 45 deg
17. 195 deg = 225 deg - 30 deg
19. (11pi)/12 = (3pi)/4 + pi/6
12 21. - pi/12 = pi/6 - pi/4
23. 75°
25.-285°
27. (13pi)/12
222 29. - (7pi)/12
16. 165 deg = 135 deg + 30 deg
18. 255 deg = 300 deg - 45 deg
20. (17pi)/12 = (7pi)/6 + pi/4
22. - (19Y)/12 = (2pi)/3 - (9pi)/4
24. 15°
26.-165°
28. (5pi)/12
30. - (13pi)/12
For 15:
Sine: √2/2
Cosine: √2/2
Tangent: 1
For 17:
Sine: -1/2
Cosine: √3/2
Tangent: -1/√3
For 19:
Sine: (1+√3)/2
Cosine: (1-√3)/2
Tangent: √3
For 21:
Sine: -1/2
Cosine: -√3/2
Tangent: 1/√3
For 23:
Sine: √3/2
Cosine: 1/2
Tangent: √3
For 25:
Sine: -√2/2
Cosine: -√2/2
Tangent: -1
For 27:
Sine: (1-√3)/2
Cosine: (1+√3)/2
Tangent: -√3
For 29:
Sine: -(√3-1)/2
Cosine: (1+√3)/2
Tangent: -√3
For 16:
Sine: √3/2
Cosine: -1/2
Tangent: -√3
For 18:
Sine: -√2/2
Cosine: √2/2
Tangent: -1
For 20:
Sine: (√3-1)/2
Cosine: (1+√3)/2
Tangent: √3
For 22:
Sine: -(1+√3)/2
Cosine: (√3-1)/2
Tangent: -1/√3
For 24:
Sine: 1/2
Cosine: √3/2
Tangent: 1/√3
For 26:
Sine: √2/2
Cosine: -√2/2
Tangent: 1
For 28:
Sine: (√3+1)/2
Cosine: (1-√3)/2
Tangent: -1/√3
For 30:
Sine: -(1-√3)/2
Cosine: (√3+1)/2
Tangent: √3
Learn more about Trigonometric Functions
brainly.com/question/6904750
#SPJ11
Tamera Purchased 31 Cases of tile to use on her bathroom floors. She used 17 cases in her upstairs bathroom and the rest in her downstairs bathroom, whic equation expresses how many cases. She used in her downstairs bathroom?
The equation that expresses how many cases Tamera used in her downstairs bathroom is: Downstairs cases = Total cases - Upstairs cases
We know that Tamera purchased a total of 31 cases of tile, and used 17 cases in her upstairs bathroom. Therefore, the number of cases she used in her downstairs bathroom can be found by subtracting the number of cases used in her upstairs bathroom from the total number of cases:
Downstairs cases = Total cases - Upstairs cases
Downstairs cases = 31 - 17
Downstairs cases = 14
Therefore, Tamera used 14 cases of tile in her downstairs bathroom.
To learn more about downstairs follow the link: https://brainly.com/question/29243261
#SPJ4
In this caee there are no restricoions onb1b2, andbnso the zystern has the uniquex1=−40b1+16b2+9bj,x1=1b1−5b2−3b3+x1=5b2−2b2−bjfor all values ofb1,b2, andb3. Exercise set 1,6 7.−1x1+5x1=band using Theorm i.6. 2x1+2x2=b11.xk+x2=25x3+6x2=9 2. 4x1−5x3=−12x1−5x2=9the bri natue ike aviten 3.x1+3x2+x1=42x1+2x4+x1=−12x5+2x1+x4=4.4x3+3x2+2r5a 4 asind matrar fa tindu3xx+3xz+2xy=2xz+xn=5Q.x1−4x1=4x1+2x2+x2+x1L.B4=t1by=is.x+y+z=5 6. −x−2y−3z=0x+y−4z=10(y+x+4y+4z=7−4x+y+8=04.3x+7y+9z=4−ay−2x−4y−4tan 14. −x1+4x1+f1=x1+9x2+2x1=dx1+2r1=1r11b3=a1d2=1. Thue Iatsa Eneriaes.
It seems like the question is asking about a system of equations with no restrictions on the variables b1, b2, and b3. However, the question is filled with typos and formatting errors that make it difficult to understand the exact problem and provide an accurate answer. It would be best to ask the student to clarify the question and provide a properly formatted version of the problem before attempting to answer.
Learn more about system of equations
brainly.com/question/12895249
#SPJ11
Find two numbers a and b such that the following system of linear equations is inconsistent. ax-3y=2 -4x+5y=b
The values of a and b that will result in an inconsistent system are a = 12/5 and b = 20x - 5y.
To find two numbers a and b such that the system of linear equations is inconsistent, we need to make sure that the two equations have the same slope but different y-intercepts. This will result in the two equations being parallel to each other and never intersecting, making the system inconsistent.
The first equation is: ax - 3y = 2. We can rearrange this equation to solve for y and find the slope:
3y = ax - 2
y = (a/3)x - (2/3)
The slope of this equation is a/3.
The second equation is: -4x + 5y = b. We can rearrange this equation to solve for y and find the slope:
5y = 4x + b
y = (4/5)x + (b/5)
The slope of this equation is 4/5.
For the system to be inconsistent, the slopes need to be equal. So we can set a/3 = 4/5 and solve for a:
a/3 = 4/5
a = 12/5
Now we need to find a value for b that will result in a different y-intercept. We can do this by plugging in the value of a into one of the equations and choosing a different value for the y-intercept:
y = (12/5)(1/3)x - (2/3)
y = 4x - (2/3)
If we choose a different value for the y-intercept, such as -1, we can solve for b:
y = 4x - 1
5y = 20x - 5
b = 20x - 5y
So the values of a and b that will result in an inconsistent system are a = 12/5 and b = 20x - 5y.
For more about linear equations:
https://brainly.com/question/11897796
#SPJ11
please help, i will give brainliest! please also explain how you got the answer!
Answer: 7.59
Step-by-step explanation: I added all of the miles he traveled up together. ( don't overthink questions like this)
Given the function, f(x) = 3x4- 7x3 - 6x2+ 12x + 8
a) Determine the number of turning points.
b) Describe the End Behavior
c) List the potential (possible) real zeros.
d) Use Descartes' Rule of Signs to determine the number of positive real zeros and number ofnegative real zeros.
e) Find all rational zeros.f) Graph the function.Make sure that you label each category.
a) The number of turning points of the function is 3.
b) The end behavior of the function is that as x approaches positive infinity.
c) The potential real zeros of the function are the factors of the constant term, 8. These are ±1, ±2, ±4, and ±8.
d) Using Descartes' Rule of Signs, there are 3 sign changes in the polynomial, so there can be 3 or 1 positive real zeros.
e) Using synthetic division and the potential real zeros, we can find that the rational zeros are -2 and 4.
f) The graph of the function is shown below with the turning points and zeros labeled.
The number of turning points of the function is 3. because the degree of the polynomial is 4 and the number of turning points is one less than the degree.
f(x) approaches positive infinity and as x approaches negative infinity, f(x) approaches negative infinity. This is because the leading coefficient is positive and the degree is even.
There are 2 sign changes in the polynomial with the x values replaced with -x, so there can be 2 or 0 negative real zeros.
To know more about synthetic division click on below link:
https://brainly.com/question/28824872#
#SPJ11
How can you show that a 20% off coupon and a 10% off coupon is not the same as a 30% off coupon?
Answer:
If applying the 20% off coupon and the 10% coupon it would be separate. This would be different than a 30% coupon
Step-by-step explanation:
Let's say you are taking 20% off of $100, doing that would reduce the price to $80 because you took off $20, after this you would apply the 10% off coupon to the $80, your total would be 72 now because 10% of 80 is 8. The 20% Coupon and the 10% coupon stacked would bring your total to $72. If you flat out took 30% out of 100 dollars you would be left with $70 compared to the $72 that you got with the 20% coupon and the 10% coupon.
20% + 10% would remove less than a 30% coupon because after applying the 20% coupon, your 10% coupon would remove less because of the lower number being subtracted. Hope this helps
Let the statements p and q be defined as follows:
p = "You mowed the lawn."
q = "You left the room a mess."
Translate the following symbolic statement into words:
Its means that either statement p is false or statement q is true
The symbolic statement that needs to be translated into words is not provided in the question. However, I will provide an example of how to translate a symbolic statement involving the statements p and q into words.
Example: p ∧ q
This symbolic statement can be translated into words as follows: "You mowed the lawn and you left the room a mess." The symbol ∧ represents the logical conjunction "and", which means that both statements p and q are true.
Another example: ¬p ∨ q
This symbolic statement can be translated into words as follows: "You did not mow the lawn or you left the room a mess." The symbol ¬ represents the logical negation "not", and the symbol ∨ represents the logical disjunction "or", which means that either statement p is false or statement q is true.
I hope this helps! If you have a specific symbolic statement that you need help translating, please provide it in the question and I will be happy to help.
Learn more about disjunction
brainly.com/question/24661758
#SPJ11
Find the similarity ratio and the ratio of the perimeters of two regular octagons with areas of 48cm2 and 147cm2
The Simple ratio and the ratio of the perimeters of two regular octagons are approximately 1.472
The formula for the area of the regular polygon is:
Area = (2 + 2[tex]\sqrt{2}[/tex]) × [tex]s^{2}[/tex]
Where, s = length of the side of a polygon
consider two equations for the two octagons,
48 = (2 + 2[tex]\sqrt{2}[/tex]) × [tex](s1)^{2}[/tex]
147 = (2 + 2[tex]\sqrt{2}[/tex]) × [tex](s2)^{2}[/tex]
The length of each polygon is
s1 = [tex]\sqrt{\frac{48}{(2 + 2\sqrt{2} )} }[/tex] ≈ 3.079cm
s2 = [tex]\sqrt{\frac{147}{(2 + 2\sqrt{2} )} } }[/tex] ≈ 4.532cm
The similarity ratio is,
s2 ÷ s1 ≈ 1.472
The ratio of perimeters is,
8s2 ÷ 8s1 = s2 ÷ s1 ≈ 1.472
Therefore, the similarity ratio and the ratio of the perimeters are both approximately 1.472.
To learn more about, Ratios
https://brainly.com/question/12101336
https://brainly.com/question/15604456
A line / is said to be tangent to a circle Cat a point P if and only if I meets Cat P and at no other point besides P. Given a circle centered at a point O, a point P on the circle, and a line / passing through P, show that lis tangent to the circle at P if and only if /is perpendicular to the line OP.
Yes, a line / is said to be tangent to a circle at a point P if and only if it meets the circle at P and at no other point besides P. Given a circle centered at a point O, a point P on the circle, and a line / passing through P, we can show that / is tangent to the circle at P if and only if it is perpendicular to the line OP.
To show this, first consider a line / that is perpendicular to the line OP. Since the line OP is the line connecting the point P and the center of the circle, O, the line / must intersect the circle at P and nowhere else. This means that / is tangent to the circle at P.
Now, consider a line / that is not perpendicular to the line OP. Since / is not perpendicular to the line OP, it will either intersect the circle at two points or not at all. Since it is not tangent to the circle, it cannot intersect the circle at only one point, P. Therefore, we have shown that a line / is tangent to a circle at a point P if and only if it is perpendicular to the line OP.
You can learn more about tangent at: brainly.com/question/19424752
#SPJ11
45 minutes of 2 1/2 hours as a percentage
show method
Answer:
30%
Step-by-step explanation:
First, I added up the number of minutes in 2 1/2 hours. 2 hours is 120 minutes, and 1/2 hour is 30 minutes. 120 + 30 = 150.
Next, divide 45 (which is the number out of 150 we are determining the percentage for) by 150 (which is the total number of minutes). Multiply that number by 100 to get 30. The answer is 30%.
If h(x)=f(x)g(x)+f(x)/g(x), then find the value of h’(5)
According to the solving the value of given function h’(5) h’(5) = [2f’(5)g(5)] / g(5)² + f(5) / g(5)²
What exactly is a function?A function is described as a relationship between a group of inputs with one output each. A function is, to put it simply, a relationship between inputs in which each input is connected to exactly one output. Every function has a domain and a codomain, or range. A function is typically represented by the notation f(x), where x represents the input.
According to the given information:To find the value of h’(5), we need to find the derivative of h(x) first. We can use the product rule and the quotient rule to do that:
h(x) = f(x)g(x) + f(x)/g(x)
h’(x) = f’(x)g(x) + f(x)g’(x) + [g(x)f’(x) – f(x)g’(x)] / g(x)² (by the quotient rule)
h’(x) = [f’(x)g(x) + g(x)f’(x)] / g(x)² + [f(x)g’(x) – f(x)g’(x)] / g(x)² + f(x) / g(x)²
h’(x) = [2f’(x)g(x)] / g(x)² + f(x) / g(x)²
Now we can find h’(5) by plugging in x = 5:
h’(5) = [2f’(5)g(5)] / g(5)² + f(5) / g(5)²
To know more about functions visit:
brainly.com/question/22340031
#SPJ1
It! Add and Subtract Polynomials idd or subtract the polynomials. ((2)/(5)a^(4)-6a^(3)-(5)/(6)a^(2)+(a)/(2)+1)+((9)/(4)a^(3)+(2a^(2))/(3)+(5)/(3)a-(8)/(5)) (2a^(2)b^(2)+3ab^(2)-5a^(2)b)-(3a^(2)b^(2)-9
The polynomial that need to be added is
(2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 5a^(2)b^(2) - 3ab^(2) + 5a^(2)b + 9
To add or subtract polynomials, we need to combine like terms. Like terms are terms that have the same variable and the same exponent.
First, let's add the first two polynomials:
((2)/(5)a^(4)-6a^(3)-(5)/(6)a^(2)+(a)/(2)+1)+((9)/(4)a^(3)+(2a^(2))/(3)+(5)/(3)a-(8)/(5))
= (2/5)a^(4) + (-6 + 9/4)a^(3) + (-5/6 + 2/3)a^(2) + (1/2 + 5/3)a + 1 - 8/5
= (2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5
Now, let's subtract the third polynomial from this result:
(2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - (2a^(2)b^(2)+3ab^(2)-5a^(2)b)
= (2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 2a^(2)b^(2) - 3ab^(2) + 5a^(2)b
Finally, let's subtract the last term from this result:
(2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 2a^(2)b^(2) - 3ab^(2) + 5a^(2)b - (3a^(2)b^(2)-9)
= (2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 5a^(2)b^(2) - 3ab^(2) + 5a^(2)b + 9
To know more about like terms click on below link:
https://brainly.com/question/29169167#
#SPJ11
Suppose an object has a height of 0 feet after 10seconds. This same object has maximum height of 200 feet at 0 seconds. 1. Find H(T)=A(T−h)2+k where H(T) is the height of the object in feet after T seconds. Answers in Exact Form 2. When will the object have a height of 100 feet? Answers in Exact Form and round 3 decimals.
The object will have a height of 100 feet after 100 seconds.
The equation for the height of the object in feet after T seconds is H(T) = A(T - h)2 + k, where A and h are constants. Given that the object has a height of 0 feet after 10 seconds, and a maximum height of 200 feet at 0 seconds, we can solve for A and h.
We know that H(0) = 200, so k = 200.
We also know that H(10) = 0, so A(10 - h)2 + 200 = 0. Solving for A, we get A = -(h2 + 200) / 102.
Now we have an equation with two unknowns, A and h, so we can use substitution to solve for h. We can substitute -(h2 + 200) / 102 for A in our original equation, and solve for h. This gives us h = 10.
We now know A = -(102 + 200) / 102 = -20.
So, our equation for the height of the object in feet after T seconds is H(T) = -20(T - 10)2 + 200.
To find the height of the object after 100 seconds, substitute 100 for T in the equation. This gives us H(100) = -20(100 - 10)2 + 200 = 100.
Learn more about substitution
brainly.com/question/10423146
#SPJ11
