Answer: No, x^2 and 2x are not like terms. Like terms are terms that have the same variable raised to the same exponent. In this case, x^2 and 2x have the same variable, but they are raised to different exponents, so they are not like terms.
Terms can be added or subtracted together, but terms that are not like terms cannot be combined.
For example:
5x^2 and 2x^2 are like terms, so they can be added together (5x^2 + 2x^2 = 7x^2)
5x and 2x are like terms, so they can be added together (5x + 2x = 7x)
On the other hand:
5x^2 and 2x are not like terms, so they cannot be added together.
Step-by-step explanation:
 What property is used to do…
-2y + 15 = -23
Answer:
-2y= -23-15
-2y=-38
-y= -38/2
-y=19 proved
Which is the graph of a logarithmic function?
The domain and range of the graph of a logarithmic function are;
Domain; 0 < x < +∞Range; The set of real numbers.How can the graph that correctly represents a logarithmic function be selected?The basic equation of a logarithmic function can be presented in the form;
[tex]y = log_{b}(x) [/tex]
Where;
b > 0, and b ≠ 1, given that we have;
[tex]y = log_{1}(x)[/tex]
[tex] {1}^{y} = 1[/tex]
The inverse of the logarithmic function is the exponential function presented as follows;
[tex]x = {b}^{y} [/tex]
Given that b > 0, we have;
[tex] {b}^{y} = x > 0[/tex]
Therefore, the graph of a logarithmic function has only positive x-values
The graph of a logarithmic function is one with a domain and range defined as follows;
Domain; 0 < x < +∞
Range; -∞ < y < +∞, which is the set of real numbers.
The correct option therefore has a domain as x > 0 and range as the set of all real numbers.
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Answer:
3 or C
Step-by-step explanation:
The answer above is correct.
Read the excerpt from The Land.
"I'm ready to start getting to know him," I answered. "Not ready to mount him yet."
"Now, what you mean by that? Get on that horse."
"No, sir, I can't. You need to give me some time with him first."
"Well, I don't have none of that."
"It's important. Now, I said I'd ride your horse, Mister Sutcliffe, but I've got my own way of dealing with horses. You want me to win, then I've got to deal with this grey my way."
Based on this dialogue, which word best describes Paul’s approach to riding a new horse?
overbearing
carefree
methodical
informal
From the conversation it can be inferred that Paul's approach to getting on the horse is methodical (option c).
What is methodical behavior?A methodical attitude or behavior refers to the preference of people to use an organized method and sequences to perform an activity correctly.
According to the above, it can be inferred that Paul behaves in a methodical manner because he prefers to relate to the horse slowly and in a controlled manner before proceeding to mount it.
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The question is about unit circle in screenshot
The complete sentence for the unit circle is:
When t = 0, AP = 0, so sin t will begin at a value of 0. As t increases from 0 to π/2, sin t increases. Eventually, when t = π/2, OP will be 0, so sin t = AP will be 1.
How to complete a sentence with concepts from trigonometry
In this problem we have sentence to be completed by direct observation to the variables seen in a unit circle, a form used to teach trigonometric functions in a graphic manner. Now we proceed to present the complete sentence below:
When t = 0, AP = 0, so sin t will begin at a value of 0. As t increases from 0 to π/2, sin t increases. Eventually, when t = π/2, OP will be 0, so sin t = AP will be 1.
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WILL MAKE BRAINLIEST!!
Complete the congruence statement for the figure below.
What number is represented by the question mark?
111= 0, 3213=0, 7756= 1,7662= 2, 6855= 3, 8096= 5,6666=4 . 8193= 3,9313= 1,8639= 4,1234=0, 2581 = 2,7186= 3, 2679=?
The number that is represented by the question mark in the sequence is 2
What are sequence?Sequence are set of numbers that follow a predefined and predetermined patterns guided by a rule
How to determine the number represented by the question mark?The sequence of numbers is given as:
111= 0, 3213=0,
7756= 1, 7662= 2,
6855= 3, 8096= 5,
6666=4 8193= 3,
9313= 1, 8639= 4,
1234=0, 2581 = 2,
7186= 3, 2(6)7(9)=
From the complete question, the values of the sequence are determined by the count of numbers that are circled or in brackets
In the 2(6)7(9), two numbers are circled.
The numbers are 6 and 9
This means that the value of 2679 is 2
i.e. 2(6)7(9)= 2
Hence, the number that is represented by the question mark in the sequence is 2
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The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.15 gallons. A previous study found that for an average family the variance is 3.61 gallons and the mean is 19.4 gallons per day. If they are using a 95% level of confidence, how large of a sample is required to estimate the mean usage of water
The minimum sample size required to estimate the mean usage of water = 2225.07
What is Standard deviation?
In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.
We can find the minimum sample size required to estimate the mean usage of water as shown below:
Standard deviation [tex]\sigma =3.61[/tex]
Margin of error E=0.15
Critical value for 95% confidence interval = 1.96
Required minimum sample size: [tex]n=(\frac{Z_{\frac{\alpha}{2}}.\sigma }{E} )^2[/tex]
[tex]=(\frac{1.96\times 3.61}{0.15} )^2[/tex]
=2225.07
Hence, the minimum sample size required to estimate the mean usage of water = 2225.07
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The projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s2.
An object is launched at an initial velocity of 19.6 meters per second from an initial height of 24.5 meters. Which equation can be used to find the number of seconds it takes the object to hit the ground?
A. 0 = –4.9t2 + 19.6t + 24.5
B 0 = –4.9t2 + 24.5t + 19.6
C. 19.6 = –4.9t2 + 24.5t
D. 24.5 = –4.9t2 + 19.6t
Answer: 0=-4.9t²+19.6t+24.5
Step-by-step explanation:
[tex]s(t)=gt^2+v_0t+s_0\\v_0=19,6\ \frac{m}{s} \ \ \ \ s_0=24,5\ m\ \ \ \ g=-4,9\ \frac{m}{s^2} \ \ \ \ S(t)=0\ (the\ object \ hitts\ the \ ground)\ \Rightarrow\\0=-4,9t^2+19,6t+24,5.[/tex]
A scientist observes the bacteria’s growth. In the first observation, there were 12 bacteria, 24 in the second observation, 48 in the third and so on. How many bacteria will be there in the 8th observation? Use the explicit formula.
1,536
28
126
27
Answer:
Step-by-step explanation:96 in the fourth since they are adding the answer itself two times before you get the other like 12 bacteria and then 24 so that means 12 + 12 is 24 and the third one 48 so 24 +24 =48
fourth 48 + 48=96
fifth 96+96=192
sixth 192+192=384
seventh 384+384=768
last but not least 768+768 = 1536
so your answer is 1,536
is flipped ten times, and he is asked to predict in advance the outcome. Our individual gets seven out of ten correct. What is the probability he would have done at least this well if he had no ESP
The required probability is 0.171.
What is probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
We can find required Probability as shown:
From 10 coins we choose 7 he guessed correct with probability of each 1/2. For three remaining coins he failed to predict the outcomes of the flip with the probability of 1/2 for each. Similarly for 8,9 or 10 successive trials. Let X denote number of successive trials
[tex]P(X\geq 7)= \tbinom{10}{7}.\frac{1}{2^{10}}+\tbinom{10}{8}.\frac{1}{2^{10}} +\tbinom{10}{9}.\frac{1}{2^{10}}+\tbinom{10}{10}.\frac{1}{2^{10}}[/tex]
[tex]=120.\frac{1}{2^{10}} +45.\frac{1}{2^{10}} +10.\frac{1}{2^{10}} +.\frac{1}{2^{10}}[/tex]
[tex]=\frac{120+45+10+1}{2^{10}}[/tex]
[tex]=\frac{176}{1024}[/tex]
=0.171
Hence, the required probability is 0.171.
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Given question is incomplete. This is complete question:
A man claims to have extrasensory perception. As a test, a fair coin is flipped 10 times and the man is asked to predict the outcome in advance. He gets 7 out of 10 correct. What is the probability that he would have done at least this well if he had no ESP?
Work out the area of the triangle.
Answer:
555.75m²Step-by-step explanation:
Triangle Area = 1/2b*h
1/2 57 * 19.5 =
28.5 * 19.5 =
555.75m²
a. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity. -1/1.06
The required answers are:
a. The linear approximating polynomial at a = 1: P₁(x) = x - 2
b. The quadratic approximating polynomial at a = 1: P₂(x) = -3 + 3x - x²
c. Appromating the given quantity -1/1.06 for P₁(x) and P₂(x): -3.06 and -7.30 respectively.
Using Taylor polynomial series, the required approximating polynomials are calculated.
What is the Taylor polynomial series?The Taylor polynomial series is
Pₙ(x) = ∑ [tex]\frac{f^n(a)}{n!}[/tex](x - a)ⁿ; limits from 0 to n
Where fⁿ(a) is the nth derivation of f(x) at a
The first order(linear) Taylor polynomial series is
P₁(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a)¹
The second order(quadratic) Taylor polynomial series is
P₂(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a) + [tex]\frac{f''(a)}{2!}[/tex](x - a)²
Calculation:The given function is f(x) = -1/x at a = 1
f(a) = f(1) = -1
f'(x) = -(-1/x²) = 1/x²; f'(a) = f'(1) = 1
f''(x) = -2/x³; f''(a) = f''(1) = -2
a. Linear approximating polynomial:
From the Taylor series, we have
P₁(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a)¹
On substituting,
P₁(x) = -1 + (1/1!)(x - 1)¹
= -1 + (x - 1)
= x - 2
b. Quadratic approximating polynomial:
From the Taylor series, we have
P₂(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a) + [tex]\frac{f''(a)}{2!}[/tex](x - a)²
On substituting,
P₂(x) = f(1) + (1/1!)(x - 1) + (-2/2!)(x - 1)²
= -1 + (x - 1) - (x - 1)²
= -1 + x - 1 - (x² - 2x + 1)
= x - 2 - x² + 2x - 1
= -3 + 3x - x²
c. Approximating the given quantity -1/1.06:
Substituting x = -1.06 in P₁(x) and P₂(x),
P₁(x) = x - 2
⇒ P₁(-1.06) = (-1.06) - 2 = -3.06
P₂(x) = -3 + 3x - x²
⇒ P₂(-1.06) = -3 + 3(-1.06) - (-1.06)² = -7.30
Therefore, the approximating polynomials are calculated by using Taylor polynomial series.
Disclaimer: The given question is incomplete. Here is the complete question.
Question:
a. Find the linear approximating polynomial for the following function centered at the given point a.
b. Find the quadratic approximating polynomial for the following function centered at the given point a.
c. Use the polynomials obtained in parts a. and b. to approximate the given quantity.
f(x) = -1/x , a = 1; approximate -1/1.06
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Last year, nicholas started babysitting to earn extra spending money. over the summer, he tracked how much money he earned at each babysitting job. this box plot shows the results.
The percent of the time Nicholas earned is the percent of the time 25%
The 5 values of the given box plot are;
The minimum fee = 20
In the first quartile, the 25th percentile point, Q₁ = 25
In the median or second quartile, the fiftieth percentile factor, Q₂ = 30
The 1/3 quartile, the 75th percentile point, Q₃ = 40
The maximum value = 55
The range = The most value - The minimal fee
The range = 55 - 20 = 35
We are aware that Nicholas earned $25 or less from the minimum value up to the first quartile, Q₁, which is the 25th percentile point, in which we've got 25 percent of the statistics points.
Consequently, the percentage of the time Nicholas earned $25 or much less is 25 percent of the time.
In mathematics, a percentage is a variety of ratios that can be expressed as a fraction of 100. If we have to calculate the percent of various, divide the wide variety by way of the whole and multiply by way of a hundred. For this reason, the shared approach is a component in line with a hundred. The phrase according to cent means in keeping with one hundred.
A relative cost indicates the hundredth component of any amount. One percent (symbolized 1%) is the hundredth part; for this reason, a hundred percent represents the whole lot and two hundred percent specifies two times the given amount.
Multiply the entire number amount through the decimal equal to the proportion. The end result is the share portion quantity. (consequently, this answers the question “How a whole lot is 24 percentage of 500,” you examine that 24 percent of 500 is a hundred and twenty).
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Two friends are planning for a gathering. The food budget is modeled by 1/2(x-120)=10,where x is the amount spent on food. What are the least and greatest amounts that the two friends could spend on food
The least and greatest amounts that the two friends could spend on food are 100 and 140 respectively
Functions and values
Functions are expressions written in terms of letters known as variables. Given the equation that represents the food budget of two friends as shown;
1/2(x-120)=10
where x is the amount spent on food.
In order to determine the least and greatest amounts that the two friends could spend on food,
For the least amount
-(x-120) = 20
-x+120 = 20
x = 100
For the greatest amount
(x-120) = 20
x = 140
Hence the least and greatest amounts that the two friends could spend on food are 100 and 140 respectively
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A bookshelf is 4-3/4 feet wide. how many 3-inch-wide books will fit on the shelf?
19 books can fit into a bookshelf that has a width of 19/4 feet
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
The bookshelf is 4 3/4 feet wide = 19/4 feet
1 ft = 12 in, hence:
19/4 feet = 19/4 feet * 12 in per feet = 57 inches
Number of books = 57 inches / 3 in = 19
19 books can fit into a bookshelf that has a width of 19/4 feet
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If you apply the changes below to the quadratic parent function, f(x) = x²
what is the equation of the new function?
• Shift 3 units right.
• Vertically stretch by a factor of 4.
• Reflect over the x-axis.
A. g(x) = -4(x+3)²
B. g(x) = -4(x-3)²
C. g(x) = (-4x - 3)²
D. g(x) = 4x²+3
The equation of the unique function exists g(x) = -4(x-3)².
What is a quadratic equation?The polynomial of degree two exists named a quadratic polynomial and the equation corresponding to a quadratic polynomial P(x) exists named a quadratic equation.
Given: F(x) = x²
The vertical stretch by a factor of 4 exists can be satisfied by (b)
if we use a vertical stretch, it transforms the y-values which causes it to seem skinnier when graphed.
Multiply 4 by f(x) which provides 4x².
As the reflection over the x-axis, so multiply it by -1 to f(x), which results in -4x².
Shift the graph right 3 which exists by moving it right, so by adjusting the x values indicating use f(x-3), to obtain this subtract the value from x when you move right, and add the value to x when you move left.
Hence, the unique graph would be g(x) = -4(x-3)²
Therefore, the correct answer is option B. g(x) = -4(x-3)².
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Diamond went to lunch with her friends. The total bill came to $32.20. If Diamond tipped 19%, how much tip did she leave?
$6.12
Step-by-step explanation:A percentage is some portion of a whole number. Multiple methods can be used to find percentages.
Multiplication to Find Percentages
One of the easiest ways to find percentages is to multiply the original number by a decimal. To do this, one first needs to turn the percentage into a decimal.
For example,
19% = 0.19To convert a percentage to a decimal, just move the decimal point 2 places to the left.
Then, multiply this decimal by the whole number, and the answer, in this case, will be the tip.
19% of $32.20
Now, to solve we can just multiply.
0.19 * 32.20 = 6.118The exact answer is 6.118. However, since we are using money, we are going to round to the nearest hundredth place. This gives the final answer of $6.12.
Determine the unknown length or angle measurement. Round each answer to the nearest whole number
(a) The value of the unknown length, a, is 18 cm
(b) The value of the unknown angle measurement, θ, is 39°
From the question, we are to determine the unknown length and angle measurement
(a)
A + B + C = 180° (Sum of angles in a triangle)
A = 180° - (B + C)
A = 180° -(68° + 59°)
A = 53°
Using the law of sines
[tex]\frac{a}{sin A}=\frac{c}{sin C}[/tex]
[tex]\frac{a}{sin 53^\circ}=\frac{19.5}{sin 59^\circ}[/tex]
[tex]a=\frac{19.5 \times sin 53^\circ}{sin 59^\circ}[/tex]
[tex]a= 18.168[/tex]
[tex]a \approx 18 cm[/tex]
(b)
[tex]\frac{sin A}{a}=\frac{sin B}{b}[/tex]
[tex]\frac{sin \theta}{15}=\frac{sin 57^\circ}{20}[/tex]
[tex]sin \theta=\frac{15 \times sin 57^\circ}{20}[/tex]
[tex]sin \theta=0.6290[/tex]
[tex]\theta=sin ^{-1} (0.6290)[/tex]
[tex]\theta=38.976 ^\circ[/tex]
[tex]\theta \approx 39^\circ[/tex]
Hence, the value of the unknown length, a, is 18 cm
The value of the unknown angle measurement, θ, is 39°
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You have fifteen blankets that each take up 557 cubic inches of space. How many blankets could you pack into a 14-inch moving box
You have fifteen blankets that each take up 557 cubic inches of space. In a 14-inch moving box, we can pack approximately 5 blankets.
The Volume that can take up by single blanket is 557 cubic inches.
The dimension of the moving box = 14 × 14 × 14
Hence, the volume of the moving box = 2744 cubic inches
The total number of blankets that can be packed in the given moving box = 2744/557 = 4.92 ≅ 5
Therefore, in a 14-inch moving box, there can be 15 blankets with 557 cubic inches of space of each can be packed.
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There are 26 prize tickets in a bowl, labeled A to Z. What is the probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen? Does this represent an independent or dependent event? Explain.
Using it's concept, there is a 0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For the first ticket, since 5 out of 26 letters are vogal, the probability is:
5/26.
For the second ticket, since there is no replacement, the probability is:
4/25.
The probability of both tickets is:
[tex]p = \frac{5}{26} \times \frac{4}{25} = 0.0308[/tex]
0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.
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You have 1 blue suit, 2 black suits, and 1 brown suit, You also have 2 blue ties, 3 red ties, and 3 pink ties. What is the probability that you pick a striped shirt AND a blue suit AND a pink tie
The probability that you pick a striped shirt AND a blue suit is 1/4 AND a pink tie is 3/8.
According to the statement
Number of blue suit = 1
Number of black suit = 2
Number of brown suit = 1
Number of blue ties = 2
Number of red ties = 3
Number of pink ties = 3
Now we find the probability by its formula
Probability that picked suit is blue = blue suits/ total number of suits
Probability = 1/4
Now,
Probability that picked tie is pink = Pink tie / total number of ties
Probability = 3/8
So, The probability that you pick a striped shirt AND a blue suit is 1/4 AND a pink tie is 3/8.
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The measure of one angle of an octagon is twice the measure of one of the other seven congruent angles. What is the measure of each angle?
Each one of the smaller angles x = 120 degrees and the larger angle = 2x = 2 × 120 = 240 degrees
How to find the angle of octagon?The angle of an octagon can be found as follows;
An octagon is a polygon that has 8 sides.
The sum of angles in an octagon is 1080 degrees.
Therefore,
x + x + x + x + x + x + x + 2x = 1080
Hence,
9x = 1080
divide both sides by 9
x = 1080 / 9
x = 120
Therefore, each one of the smaller angles x = 120 degrees and the larger angle = 2x = 2 × 120 = 240 degrees
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The figure shows lines r, n, and p intersecting to form angles numbered 1, 2, 3, 4, 5, and 6. All three lines lie in the same plane.
not to scale
Based on the figure, which of the individual statements would provide enough information to conclude that line r is perpendicular to line
p?
Select all that apply.
A m2 3 = m/6
OB. m2 3+m/4= 90°
Answer:
B.
Step-by-step explanation:
If the measures of angles 3 and 4 add to 90, then lines r and p meet at right angles making them perpendicular.
Answer: B.
Answer:
Step-by-step explanation:
A procedure for using sample data to find the estimated regression equation is _____. Group of answer choices point estimation interval estimation the least squares method extrapolation
c. the least squares method.
Regression equation:
In simple linear regression, the predicted value of the dependent variable is given by the equation = b0 + b1x. The values of b0 and b1 are calculated from the data so that the line = b0 + b1X minimizes the total sum of squared errors (error is the difference between the predicted value and the actual value of y).
Least squares method:
The least squares method is a statistical procedure to find the best fit for a set of data points by minimizing the sum of the offsets or residuals of points from the plotted curve.
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What's the difference between sampling with replacement and sampling without replacement? How should you account for this
using TI-84's or the "hat method"?
When sampling with replacement is used, an element that has already been chosen is put back into the sample frame and given the chance to be chosen again.
In the case of sampling without replacement, an element is eliminated from the sample frame after it has been chosen.
In this question, we are supposed to state the differences between sampling with replacement and sampling without replacement.
Generally speaking, sampling without replacement is more effective than producing representative samples using replacement sampling. It prevents the inclusion of the same population element in the sample several times.
By "drawing from a hat" or by using a computer program that simulates the same process, you select the sample at random using the lottery method.
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rewrite each expression without using absolute value notation |7m-56| if m<8
Considering the definition of the absolute value function, the expression is written as -7m + 56.
What is the definition of the absolute value function?The absolute value function is defined as follows:
[tex]|x| = x, x \geq 0[/tex].[tex]|x| = -x, x < 0[/tex]That is, where the expression is negative, it is multiplied by -1, while where it is not negative the expression is kept.
In this problem, the expression is:
|7m - 56|
For m < 8, we have that one example is m = 0:
7(0) - 56 = -56.
The expression is negative, hence the signal is changed, that is:
|7m - 56| = -(7m - 56) = -7m + 56.
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A doctor asked a patient to reduce his medication by a regular number of tablets per week. The reduction plan begins one week after the visit to the doctor. If 10 weeks after the visit to the doctor the person is taking 40 tablets and 20 weeks after the visit the person is taking 30. Find the weekly reduction in his consumption of tablets.
1 tablet weekly reduction in his consumption of tablets.
What is an algebraic expression?Algebraic expression is a set of variable, constant and algebraic operations like addition, subtraction, multiplication and division. for example 3x^2+2x+3=0
Tablet after 10 week of doctor visit = 40 tablet
Tablet after 20 week of doctor visit= 30
In 10 week there is a difference of (40-30) 10 tablets.
in 10 week there is reduction of 10 tablets its mean there is reduction of 1 tablet per week
so, the weekly reduction of 1 tablet per week.
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x: -1/2
-6(x-2):
por favor necesito una respuesta
The value of the expression if x = -1/2 is 15
Function and valuesGiven the expression below shown;
f(x) = -6(x - 2)
If the value of x is -1/2, hence;
f(-1/2) = -6(-1/2 - 2)
Simplify
f(-1/2) = -6(-5/2)
f(-1/2) = 6 * 5/2
f(-1/2) = 3 * 5 = 15
Hence the value of the expression if x = -1/2 is 15
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What is the image point of (-8, 3) after the transformation R2700 0 T-2,-1?
The transformation of the coordinate (-8, -3) R 270° and T-2,-1 is (-5, -9)
What is transformation?Transformation is the change of the coordinates of a shape either by rotation, reflection or translation.
Analysis:
When coordinates (x, y) rotate 270° the resulting coordinates become (-y, x)
so coordinates (-8, -3) after 270° rotation becomes ( 3, -8)
When it is translated 2 units to the left and 1 unit down, that is -3 + -2 = -5 and -8 + -1 = -9
Therefore the transformed coordinate becomes (-5, -9)
Learn more about transformation: brainly.com/question/4289712
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If someone can help with this that would be great
Answer:
p ≈ 7.3 m
Step-by-step explanation:
using the Sine Rule in the triangle
[tex]\frac{p}{sinP}[/tex] = [tex]\frac{r}{sinR}[/tex] ( substitute values )
[tex]\frac{p}{sin40}[/tex] = [tex]\frac{10}{sin62}[/tex] ( cross- multiply )
p × sin62° = 10 × sin40° ( divide both sides by sin62° )
p = [tex]\frac{10sin40}{sin62}[/tex] ≈ 7.3 m ( to the nearest tenth )
Answer:
[tex]\fbox {p = 7.3 m}[/tex]
Step-by-step explanation:
Applying the Law of Sines :
[tex]\boxed {\frac{sin R}{PS} = \frac{sin P}{RS}}[/tex]
Substitute the values :
sin 62° / 10 = sin 40° / pp = sin 40° × 10 / sin 62°p = 0.64278761 × 10 / 0.882947593p = 7.3 m (nearest tenth)