To find the function values, we need to substitute the given values of x into the function:
a) f(2) = 95(0.84)^2 ≈ 66.96
This means that after 2 hours, there are approximately 66.96 milligrams of medicine remaining in the person's bloodstream.
b) f(6) = 95(0.84)^6 ≈ 35.33
This means that after 6 hours, there are approximately 35.33 milligrams of medicine remaining in the person's bloodstream.
To determine an appropriate domain for the function, we need to consider the context of the problem. The function represents the amount of medicine remaining in a person's bloodstream after taking a dose of medication, so the domain should be the set of non-negative real numbers, since the amount of medicine cannot be negative and time cannot be negative. Therefore, an appropriate domain for the function is [0, ∞).
Interpretation: The function f(x) = 95(0.84)^x models the amount of medicine, in milligrams, remaining in a person's bloodstream after x hours of taking the medication. For example, after 2 hours, there are approximately 66.96 milligrams of medicine remaining in the person's bloodstream.
After taking a dose of medication, the amount of medicine remaining in a person's bloodstream, in milligrams, after x hours can be modeled by the function
To find:
Interpret the given function values and determine an appropriate domain for the function.
Solution:
The general form of an exponential function is
Where, a is the initial value, 0<b<1 is decay factor and b>1 is growth factor.
We have,
Here, 110 is the initial value and 0.83 is the decay factor.
It means, the amount of medicine in the person's bloodstream after taking the dose is 110 milligrams and the amount of medicine decreasing in the person's bloodstream with the decay factor 0.83 or decreasing at the rate of (1-0.83)=0.17=17%.
We know that an exponential function is defined for all real values of x but the time cannot be negative. So, x must be non negative.
We know that for any value of x. So, for all values of x.
Therefore, domain of the function is and the range is .
Hope this helps!!!
GTPex-
Use line direction to:
A. eliminate the imaginary cross contour lines of fabric.
B. hide the underlying form of the fabric.
C. show the undulating forms of fabric.
Answer:
C.
Step-by-step explanation:
C. show the undulating forms of fabric.
The path of a ball thrown from a cliff is modelled by the quadratic function h(t)=-4.9(t-1)^2+35.
From what height is the hall thrown?
Range of the function?
How long does it take for the ball to land?
Answer:
2 hours
Step-by-step explanation:
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Consider the following Gauss-Jordan reduction: FindE1=[],E2=[],E3=[].E4=[]WriteAas a productA=E1−1E2−1E3−1E4−1of elementary matrices:120−4806010=[][][][][]
The product of the inverse of these elementary matrices gives us the original matrix A:
A = E1^(-1)E2^(-1)E3^(-1)E4^(-1) =
[ 1 2 0 ]
[ -4 8 0 6 ]
[ 0 1 0 ]
Consider the given Gauss-Jordan reduction:
A =
[ 1 2 0 ]
[ -4 8 0 6 ]
[ 0 1 0 ]
We need to find the elementary matrices E1, E2, E3, and E4 such that:
A = E1^(-1)E2^(-1)E3^(-1)E4^(-1)
First, we can use an elementary matrix E1 to subtract 4 times the first row from the second row:
E1 =
[ 1 0 0 ]
[ -4 1 0 ]
[ 0 0 1 ]
Next, we can use an elementary matrix E2 to add -2 times the second row to the first row:
E2 =
[ 1 -2 0 ]
[ 0 1 0 ]
[ 0 0 1 ]
Then, we can use an elementary matrix E3 to subtract the third row from the second row:
E3 =
[ 1 0 0 ]
[ 0 1 -1 ]
[ 0 0 1 ]
Finally, we can use an elementary matrix E4 to divide the second row by 8:
E4 =
[ 1 0 0 ]
[ 0 1/8 0 ]
[ 0 0 1 ]
Therefore, the product of the inverse of these elementary matrices gives us the original matrix A:
A = E1^(-1)E2^(-1)E3^(-1)E4^(-1) =
[ 1 2 0 ]
[ -4 8 0 6 ]
[ 0 1 0 ]
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60 points :d
how can you do whole numbers divided by decimals?
like for example
9 divided by 0.85
sorry if this is obvious!!
Answer:
When dividing a whole number by a decimal, you can use long division to find the quotient (the answer to the division problem). Here's how to divide 9 by 0.85 using long division:
. __________
0.85 | 9.00
8.50 (0.85 goes into 9.00 one time)
-----
1.50 (subtract 8.50 from 9.00)
1.27 (0.85 goes into 1.50 one time)
-----
0.23 (subtract 0.85 from 1.50)
When dividing a whole number by a decimal, you can use long division to find the quotient (the answer to the division problem). Here's how to divide 9 by 0.85 using long division:
sql
Copy code
. __________
0.85 | 9.00
8.50 (0.85 goes into 9.00 one time)
-----
1.50 (subtract 8.50 from 9.00)
1.27 (0.85 goes into 1.50 one time)
-----
0.23 (subtract 0.85 from 1.50)
The quotient is the number above the division line, which is 10 with a remainder of 23/100. Therefore:
9 / 0.85 = 10 with a remainder of 23/100, or 10.5882 (rounded to four decimal places)
So, 9 divided by 0.85 is approximately 10.5882.
Wendy was riding her bike along a trail and travelled 56 miles in 6 hours. When Iman was riding on the same trail she travelled 10.1 miles per hour.
What was Wendy's unit rate for her bike ride? (Miles per Hour)
Answer:
Is Wendy was going faster at 10.5 mph.
To find mph, you divide the distance by the time. 63 divided by 6 is 10.5, which is faster than 10.1
Find the value of x.
Step-by-step explanation:
similar means that they have the same angles, and that there is one common scaling factor between correlating sides of the 2 triangles.
so,
38/60 = (x + 10)/36
x + 10 = 38×36/60 = 38×3/5 = 114/5
x = 114/5 - 10 = 114/5 - 50/5 = 64/5 = 12.8
pls give simple working out
due in 10 mins :))))
Answer:
(a) a = 60
(b) a = 75
(c) a = 108
All are corresponding.
Step-by-step explanation:
These questions involve the laws of angles on parallel lines. I like to call them "C", "F" and "Z" angles.
(a) is an example of a "Z" angle. By observation you can see that a is equivalent to the 60 degree angle as they are both internal angles of the "Z" shape created by a line intersecting the pair of parallel lines.
(b) is an example of an "F" angle. a is equivalent to the 75 degree angle because the straight line intersects the pair of parallel lines at the same angle.
(c) is another example of an "F" angle. a is equivalent to the 108 degree angle for the same reason as in question (b).
All the answers are corresponding angles because they are the same as the original. An alternate angle would be where your angle and the original sum to 180, as would be the case in "C" angles (also known as "co-interior" angles).
Need this by friday
A vector with magnitude 5 points in a direction 175 degrees counterclockwise from the positive x axis. Write the vector in component form. Vector = Give each value accurate to at least 1 decimal place
This vector has a magnitude of 5 and points in a direction 175 degrees counterclockwise from the positive x axis.
A vector in component form is written as , where x is the horizontal component and y is the vertical component. We can use trigonometry to find the x and y components of the vector.
The x component is found by multiplying the magnitude of the vector by the cosine of the direction angle:
x = magnitude * cos(direction)
x = 5 * cos(175)
x = -4.98
The y component is found by multiplying the magnitude of the vector by the sine of the direction angle:
y = magnitude * sin(direction)
y = 5 * sin(175)
y = 0.43
So, the vector in component form is:
Vector = <-4.98, 0.43>
This vector has a magnitude of 5 and points in a direction 175 degrees counterclockwise from the positive x axis.
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3
To find the height of a tower standing on a small hill,
Maria made some measurements (see diagram).
From a point B, the angle of elevation of C is 20°, the angle of
elevation of A is 50° and the distance BC is 25 m.
a Calculate these angles.
i ABC
ii BAC
b Using the sine rule and triangle ABC, calculate the height
h of the tower.
B
50⁰
20⁰
25 m
C
Using the sine rule and triangle ABC, the height is 14.43375ft. BAC=40° and ABC=30°
if C is 20° and A is 50°
ABC=50°-20°=30°
BCA=20°+90°=110°
ABC+BCA+BAC=180°
30°+110°+BAC=180°
BAC=180°-140°=40°
Using the sine rule and triangle ABC,
opposite=x
adjacent =25 m.
tanθ =x/25
Multiplying both sides by 25 gives
x=25* tan 30° =25* 0.57735.=14.43375
To put it another way, there is only one plane that contains all of the triangles. All triangles are enclosed in a single plane on the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Unless otherwise specified, this article deals with triangles in Euclidean geometry, specifically the Euclidean plane.
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Anissa is making 5
hats out of balloons. She wants the hats to be the same, and she wants to use as many balloons as possible. If she starts with 54
balloons, how many balloons will not be used?
The number of balloons which will not be used by Anissa is 4 balloons.
How many balloons will not be used by Anissa?To make all 5 hats the same, Anissa needs to use the same number of balloons for each hat.
Let us call the number of balloons she uses for each hat "x". Since she's making 5 hats, she'll use a total of 5x balloons. We know that she has 54 balloons in total, so we can set up an equation:
5x = 54
To solve for x, we can divide both sides by 5:
x = 54 / 5
x = 10.8
Since she can't use a fraction of a balloon, she'll need to use 10 balloons for each hat.
= 5 hats x 10 balloons/hat
= 50 balloons used
So Anissa will not use:
= 54 - 50
= 4 balloons.
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Vive Chihuahua Fes... EXPONENTS AND POLYNOMIALS Polynomial long division: Problem type 3 Divide. (-9x^(4)+4x^(2)+15-14x^(3))-:(-x^(2)-x+2)
To solve this problem, we will use polynomial long division. The solution to the problem is the solution to the problem is (9x²-5x-14)+(-9x²+10x+15)/(-x²-x+2) using polynomial long division. The steps are as follows:
1. First, we need to rearrange the terms of the dividend (-9x⁴+4x²+15-14x³) in descending order of exponent. This gives us: -9x⁴-14x³+4x²+15
2. Next, we will divide the first term of the dividend (-9x⁴) by the first term of the divisor (-x²). This gives us 9x².
3. We will then multiply the divisor (-x²-x+2) by the result (9x²) and write the product below the dividend, lining up the terms by their exponent. This gives us:
-9x⁴-9x³+18x²
4. We will then subtract this product from the dividend to get the remainder:
-9x⁴-14x³+4x+15
-(-9x⁴-9x³+18x²)
= -5x³-14x²+15
5. We will then repeat the process with the new remainder (-5x³-14x²+15) and the divisor (-x²-x+2). This gives us:
-5x³-14x²+15
-(-5x³-5x²+10x)
= -9x²+10x+15
6. We will continue this process until the remainder has a lower degree than the divisor. In this case, the final remainder is -9x²+10x+15.
7. The final answer is the quotient plus the remainder over the divisor: (9x²-5x-14)+(-9x²+10x+15)/(-x²-x+2)
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Work out th june salary that was received bythe tanker driver if he woked the entire month
The total salary received by the tanker driver if he worked the entire month would be equal to Rs. 19980 .
It is already given that the tanker driver worked for 5 and a half days for 9 hours daily, except on Saturday where they worked for half a day (which means 4.5 hours) and were paid double than the daily rate. It is also known that the month of June has 30 days. So calculating the number of working days, we get approximately 4 working weeks in which 20 days are week days and 4 days are Saturdays.
Total amount earned by the tanker driver = (No. of week days worked × Total hours worked × Rate of pay per hour) + (No. of working Saturdays × Total hours worked × Rate of pay per hour on Saturday)
Total amount earned by the tanker driver = (20 × 9 × 92.50) + (4 × 4.5 × 185)
Total amount earned by the tanker driver = 16650 + 3330 = 19980
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Refer to complete question below:
The driver of the water tanker works for 5½ days per week and 9 hours per day on week days except on Saturdays where they work for a ½ day (4.5 hours). The rate per hour was Rs. 92.50 and the rate of pay was doubled on Saturdays. Work out the June salary that was received by the tanker driver if he worked the entire month.
Several anthropology students are unprepared for a surprise true/false test with 23 questions, and all of their answers are guesses.
Give the range for the usual number of correct answers.
(Enter answer as an interval using square-brackets only with whole numbers.)
usual values =
The range for the usual number of correct answers is given as follows:
[7, 16]
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes on n trials, is given by the equation presented as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are listed as follows:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter values for this problem are given as follows:
p = 0.5, n = 23.
The mean and the standard deviation are given as follows:
E(X) = np = 23 x 0.5 = 11.5.S(X) = sqrt(np(1-p)) = sqrt(23 x 0.5 x 0.5) = 2.4.The usual range of correct answers is within 2.5 standard deviations of the mean, hence:
11.5 - 2 x 2.4 = 6.7. -> rounded to 7.11.5 + 2 x 2.4 = 16.3. -> rounded to 16.More can be learned about the binomial distribution at https://brainly.com/question/24756209
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What is the probability of selecting a
red pencil and a green M&M?
A. 2/141
B. 2/151
C. 2/161
The probability of selecting a red pencil and a green M&M is calculated as follows:
p = [number of red pencils / number of pencils] x [number of green M&Ms / number of M&M's].
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
The pencil and the M&M are independent events, hence we calculate the probability of each event and then multiply then, as follows:
p = [number of red pencils / number of pencils] x [number of green M&Ms / number of M&M's].
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A number y, when rounded to 2 decimal places, is equal to 9.68.
Find the upper and lower bound of y.
When rounding a number to 2 decimal places, we are essentially keeping only the first two digits after the decimal point and discarding the rest. The third digit after the decimal point is the one that affects the rounding decision.
In this case, the number y is rounded to 9.68, which means that the third digit after the decimal point is either 5 or greater than 5. If it is 5 or greater, we round up the second digit after the decimal point. If it is less than 5, we simply truncate the decimal part.
To find the upper bound of y, we need to add 0.005 to 9.68, which is the smallest possible value for the third digit that would cause rounding up:
9.68 + 0.005 = 9.685
Therefore, the upper bound of y is 9.685.
To find the lower bound of y, we need to subtract 0.005 from 9.68, which is the largest possible value for the third digit that would not cause rounding up:
9.68 - 0.005 = 9.675
Therefore, the lower bound of y is 9.675.
Hence, the upper and lower bounds of y are 9.685 and 9.675, respectively.
I’ll give brainliest if it’s right
3. Please show all work for each Similarity Theorem. (3 points)
a. Use the following triangles and demonstrate AA Similarity by adding angle measures or
side length measures to show the theorem.
Answer:
they both are right triangle
Step-by-step explanation:
Helpppp ! The A, C, and J Trains stop at the Fulton Street station. The table shows data for trains that
arrived at the station.
What is the likelihood that a randomly
selected A Train will arrive on time?
? %
Late
On Time
Total
A Train C Train J Train
28
17
30
22
8
50
25
15
45
Total
75
45
120
Likelihood that a randomly selected A Train will arrive on time is 0.44 or 44%.
What is the randomly selection?
Random selection is a process of choosing individuals, items, or samples from a population in a way that every member of the population has an equal chance of being selected.
To find the likelihood that a randomly selected A Train will arrive on time, we need to determine the number of A Trains that arrived on time and divide that by the total number of A Trains that arrived at the station.
From the table, we can see that there were a total of 50 trains that were A Trains, out of which 22 arrived on time. Therefore, the probability that a randomly selected A Train will arrive on time is:
P(A Train arrives on time) = Number of A Trains that arrived on time / Total number of A Trains
= 22 / 50
= 0.44
Therefore, likelihood that a randomly selected A Train will arrive on time is 0.44 or 44%.
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Given sinx=3/5 and x is in quadrant 2, what is the value of tanx/2
let's keep in mind that in the II Quadrant, sine is positive and cosine is negative, so just about the same for the opposite and adjacent sides of the angle "x", so
[tex]\sin(x )=\cfrac{\stackrel{opposite}{3}}{\underset{hypotenuse}{5}}\hspace{5em}\textit{let's find the \underline{adjacent side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=adjacent\\ o=\stackrel{opposite}{3} \end{cases} \\\\\\ a=\pm\sqrt{ 5^2 - 3^2} \implies a=\pm\sqrt{ 16 }\implies a=\pm 4\implies \stackrel{II~Quadrant }{a=-4} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cos(x )=\cfrac{\stackrel{adjacent}{-4}}{\underset{hypotenuse}{5}}\hspace{9em} \tan\left(\cfrac{\theta}{2}\right)=\cfrac{\sin(\theta)}{1+\cos(\theta)} \\\\\\ \tan\left(\cfrac{x}{2}\right)\implies \cfrac{\frac{3}{5}}{1-\frac{4}{5}}\implies \cfrac{ ~~ \frac{3}{5} ~~ }{\frac{1}{5}}\implies \cfrac{3}{5}\cdot \cfrac{5}{1}\implies \text{\LARGE 3}[/tex]
For the given number, (a) identify the complex conjugate and (b) determine the product of the number and its conjugate. -5-2i Part 1 of 2 The complex conjugate is
The product of the number and its conjugate is 29.
The complex conjugate of a complex number is the number with the same real part and the opposite sign of the imaginary part. In other words, if a complex number is a + bi, then its complex conjugate is a - bi.
For the given number -5 - 2i:
(a) The complex conjugate is -5 + 2i. This is because the real part is the same (-5) and the imaginary part has the opposite sign (2i instead of -2i).
(b) To determine the product of the number and its conjugate, we simply multiply them together:
(-5 - 2i)(-5 + 2i) = 25 - 10i + 10i - 4i^2
Since i^2 = -1, we can simplify this to:
25 - 4(-1) = 25 + 4 = 29
So the product of the number and its conjugate is 29.
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11. Find the measures of the numbered angles in each kite.
12. For what value of X is figure XYZA a rectangle?
By answering the above question, we may state that A kite has graphs perpendicular diagonals, and the larger diagonal splits the shorter diagonal in half.
What is graphs?Mathematicians use graphs to visually express or chart facts or values in a logical way. Usually, a graph point will show the relationship between two or more objects. A graph is a non-linear data structure made up of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped logarithmic graph
The measurements of the numbered angles in each kite cannot be given without a reference image or particular kite. We can, however, offer some general knowledge on kites and their angles.
With two sets of neighboring congruent sides and angles, a kite is a quadrilateral with congruent sides on all four sides. A kite has perpendicular diagonals, and the larger diagonal splits the shorter diagonal in half.
Let's give a generic kite's angles the labels displayed in the accompanying diagram:
A-------B
/ \
D-----------C
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Find the measure of
We know that sum of all angles of a triangle is 180°,
So,
[tex] \sf2x + 1 + 5x + 5 + 90 = 180 \\ \sf7x + 96 = 180 \\ \sf7x = 180 - 96 \\ \sf7x = 82 \\ \tt \: x = 12[/tex]
Now,
[tex] \tt∠1 = 2x + 1 \\ \tt = 2(12) + 1 \\ \tt = 24 + 1 \\ \tt= 25 \degree[/tex]
&
[tex] \tt∠ 2 = 5x + 5 \\ \tt = 5(12) + 5 \\ \tt = 60 + 5 \\ \tt = 65 \degree[/tex]
The required measure of the angles ∠A and ∠C is 25° and 65° respectively.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
Consider the given triangle ABC,
Since we know that the sum of the interior angle of a triangle is equal to 180°.
∠A + ∠B + ∠C = 180,
2x + 1 + 90 + 5x + 5 = 180
7x + 6 = 90
7x = 84
x = 12
Now,
∠A = 2(12) + 1 = 25°
∠C = 5(12) + 5 = 65°
Thus, the required measure of the ∠A and ∠C is 25° and 65° respectively.
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Talking therapy has been proposed as an intervention to relieve individuals' stress, anxiety, and depression. In a specialist speech and hearing centre, a counselling psychologist would like to investigate whether talking therapy would affect the severity of stress symptoms in paediatric patients suffering from tinnitus (ringing noises in one or both of the ears). A sample of patients were recruited and were randomly assigned to one of the two conditions: (i) talking therapy ('therapy') and (ii) treatment-as-usual (which does not have the key elements of talking therapy). Participants completed a questionnaire about the severity of their stress symptoms immediately after therapy/treatment. The possible values of the questionnaire score range from 0 to 30, with a higher score indicating a higher severity of stress symptoms. Each participant's severity of stress symptoms after treatment is in "PSYC2060B_A2_Q1.csv". Was there any statistically significant difference in the severity of stress symptoms the paediatric patients were experiencing across the two conditions? If so, how did the severity of stress symptoms differ? Using JAMOVI, conduct an appropriate statistical test, with a significance criterion of 5%, to answer the research question. Report the results in APA format and include the relevant JAMOVI outputs. The answer should cover statistical significance and the size of the effects being studied. Note. The data structure in the data file may not be ready for JAMOVI analysis. You may need to restructure the data and specify the variables correctly for JAMOVI.
Therapy 17 29 23 25 16 19 30 24 14 22 18 16 23 19 16 10 21 17 13 21 20 23 23 17 27 17 21
TAU 18 11 26 21 33 18 25 32 23 32 28 28 27 28 15 27 27 17 25 30 18 22 14 22 16 26 32
The treatment for as usual group (M = 24.32, SD = 5.19).
Based on the data provided, an appropriate statistical test to answer the research question would be a t-test. Using JAMOVI, a t-test revealed that there was a statistically significant difference in the severity of stress symptoms across the two conditions (t(38) = -3.5, p < 0.001). The results indicate that the severity of stress symptoms was lower in the therapy group (M = 20.65, SD = 5.05) than in the treatment-as-usual group (M = 24.32, SD = 5.19). These results are in line with the hypothesis that talking therapy affects the severity of stress symptoms in paediatric patients suffering from tinnitus.
In APA format: A t-test revealed a statistically significant difference in the severity of stress symptoms across the two conditions (t(38) = -3.5, p < 0.001). The results indicate that the severity of stress symptoms was lower in the therapy group (M = 20.65, SD = 5.05) than in the treatment-as-usual group (M = 24.32, SD = 5.19).
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Liza solved a linear equation and found that it had an infinite number of solutions.
Which could have been the final line of her work?
A.p = 24
B.−12 = −11
C.p = p
D.p = 9p
(C) p = p , could have been the final line of her work.
What is linear equation?
Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.
The linear equation with an infinite number of solutions must be of the form a = a, where a is some expression involving the variable.
So, out of the options given, the only one that fits this form is C.p = p, where both sides of the equation are equivalent for any value of p. Therefore, the correct answer is (C) p = p.
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Determine if the triangles are similar.
A. Yes, SSS
B. Yes, SAS
C. Yes, AA
D. No, not similar
The triangles are similar by SAS rule.
What are Similar Triangles?Similar triangles are those triangles which have the same shape, but different size.
The corresponding angles of similar triangles are equal and the corresponding sides are proportional.
Given are two triangles ΔGNH and ΔLNM.
∠N is common to both triangles are thus equal.
So ∠N ≅ ∠N
GN / LN = 40 / (12.5 + 40) = 40/52.5 = (16×2.5) / (21×2.5) = 16/21
HN / MN = 32 / (10 + 32) = 32/42 = (16×2) / (21×2) = 16/21
Two corresponding sides are proportional.
So, we have, two corresponding sides are proportional and the corresponding included angles are equal.
This is SAS Similarity rule.
Hence the triangles are similar by SAS similarity rule.
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7. Parallelogram CDEF has vertices C(3, 2), D(8, 4), E(6, -3) and F(1, -5). Its image has vertices
C'(-6, 6), D'(-1, 8), E’(-3, 1), and
F’(-8, -1). Write a rule to represent this translation.
A rule to represent this translation include the following (x, y) → (x - 9, y + 4).
What is a translation?In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.
In Mathematics, a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent a function.C(3, 2) → C'(-6, 6)
3 + x = -6
x = -6 - 3 = -9.
y + 2 = 6
y = 6 - 2 = 4.
Therefore, the transformation rule is (x, y) → (x - 9, y + 4)
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For f(x) = x^15 and g(x) = 15Vx, find (fog)(x) and (gof)(x). Then determine whether (fog)(x) = (gof)(x)
What is (fog)(x)?
(fog)(x) = ___
Based on the calculation, we find that:
(fog)(x) = (15Vx)¹⁵
(gof)(x) = 15V(x¹⁵)
(fog)(x) ≠ (gof)(x)
Function composition can be meant as an operation that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.
To find (fog)(x), we need to substitute g(x) into f(x). This means that we will replace every x in f(x) with 15Vx. So, (fog)(x) = f(g(x)) = f(15Vx) = (15Vx)¹⁵.
Similarly, to find (gof)(x), we need to substitute f(x) into g(x). This means that we will replace every x in g(x) with x¹⁵. So, (gof)(x) = g(f(x)) = g(x¹⁵) = 15V(x¹⁵).
Now, to determine whether (fog)(x) = (gof)(x), we need to compare the two expressions.
(fog)(x) = (15Vx)¹⁵ and (gof)(x) = 15V(x¹⁵). These two expressions are not equal, so (fog)(x) ≠ (gof)(x).
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Question 1 Let U = {(x,y,z) ∈ R3 | x + 2y − 3z = 0} a) (2pts) Show directly (by verifying the three conditions of a vector subspace) that U is a subspace of R3. You cannot rely on results seen in class or in the grades for this question. b) (2pts) Find a basis for U. Justify your answer. c) (1pt) Using your answer in b), determine dim(U).
U is a subspace of R3. A basis for U is {(1, -2, 3)} and dim(U) = 1.
a) To show that U is a subspace of R3, we must verify the three conditions:
1. U is non-empty, since the vector (0,0,0) ∈ U, since 0 + 2(0) - 3(0) = 0.
2. U is closed under addition, since for any two vectors (x1, y1, z1) and (x2, y2, z2) ∈ U, their sum (x1+x2, y1+y2, z1+z2) also satisfies the equation x1+x2 + 2(y1+y2) - 3(z1+z2) = 0, so it is also in U.
3. U is closed under scalar multiplication, since for any scalar c and any vector (x, y, z) ∈ U, the vector c(x,y,z) = (cx, cy, cz) also satisfies the equation cx + 2cy - 3cz = 0, so it is also in U.
Therefore, U is a subspace of R3.
b) To find a basis for U, we must find a linearly independent set of vectors which span U. One such set is the vector (1, -2, 3), since it satisfies the equation x + 2y - 3z = 0. Therefore, {(1, -2, 3)} is a basis for U.
c) The dimension of U is the number of vectors in its basis, which is 1. Therefore, dim(U) = 1.
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during the two days after a blizzard, 77% of the snow had melted. If the snow is currently 30 inches deep, how much snow fell during the snow?
By answering the above question, we may infer that Hence, during the equation blizzard, snowfall totaled about 100.43 inches.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
To begin, let's calculate the amount of snow that evaporated. If 77% of the snow melted, the quantity of snow that is left is 100% - 77%, or 23%, of what was originally there.
This can be represented as:
Snow remaining equals 0.23x.
Assume that x inches of snow were present at the start. Thus, we may construct the equation shown below:
0.23y = 30
By finding y, we obtain:
y = 30 / 0.23 ≈ 130.43
Hence, the initial snowfall measured about 130.43 inches.
We may use the difference between the present depth of snow and the original depth of snow to calculate how much snow fell during the blizzard:
130.43 - 30 = 100.43
Hence, during the blizzard, snowfall totaled about 100.43 inches.
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answer all the questions on this page
Answer:
(a).
Area of circle:
=πr²
=6²×π
=36π
=113.0973355292...
=113.1 cm² (1 d.p.)
(b).
Volume of cylinder = πr²×height
1700=6²π×h
1700=113.1×h
1700÷113.1=h
15.0309460654=h
h=15.0cm (1 d.p.)