Answer:
1.8
Step-by-step explanation:
6 is 10% of 60, which means 3% of 60 is 1.8.
The number of hours of daylight on a given day in City A is given by the following function, where x is the number of days after January 1.
a. The amplitude of the function y = 4 sin [(2π / 365)(x - 79)] + 12 is 4.
b. The period of the function y = 4 sin [(2π / 365)(x - 79)] + 12 is 365 days.
c. There are approximately 16 hours of daylight on the longest day of the year.
d. There are approximately 8 hours of daylight on the shortest day of the year.
e. The graph for the function is obtained.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The function is given as y = 4 sin [(2π / 365)(x - 79)] + 12.
a. The amplitude of the function is the coefficient of the sine function, which is 4.
Therefore, the amplitude of the function is 4.
b. The period of the function is given by the formula: period = (2π/b), where b is the coefficient of x in the sine function.
In this case, b = (2π/365), so the period is -
period = (2π / (2π/365)) = 365
Therefore, the period value is 365 days.
c. The longest day of the year occurs on the summer solstice, which is around June 21.
On this day, x = 171 (assuming January 1 is x = 1). Plugging x = 171 into the function gives -
y = 4 sin [(2π/365)(171 - 79)] + 12 = 15.998 hours
Therefore, the number of hours for daylight is 16 hours.
d. The shortest day of the year occurs on the winter solstice, which is around December 21.
On this day, x = 355. Plugging x = 355 into the function gives -
y = 4 sin [(2π/365)(355 - 79)] + 12 = 8.002 hours
Therefore, the number of hours for daylight is 8 hours.
e. To graph the function for one period, we need to find the values of y for x ranging from 1 to 365.
We can use a graphing tool or software to plot the function.
The graph is plotted.
The x-axis represents the number of days after January 1, and the y-axis represents the number of hours of daylight.
The function oscillates between 8 and 16 hours of daylight over the course of one year, with the maximum occurring around day 171 and the minimum occurring around day 355.
The graph shows that the function is periodic, with a period of 365 days, as expected.
Therefore, the function is plotted.
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True or False. The point (-1/5, -3/2)
Lies on the graph of f(x).
True; the point (-1/5, -3/2) does lie on the graph of f(x) = 7.5x.
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
f(x) = 7.5x
The point is given as
(x, y) = (-1/5, -3/2)
To determine whether the point (-1/5, -3/2) lies on the graph of f(x) = 7.5x, we can substitute x = -1/5 into the equation and see if it gives us y = -3/2.
f(x) = 7.5x
By substitution, we have
f(-1/5) = 7.5(-1/5)
Evaluate
f(-1/5) = -1.5
Express as fraction
f(-1/5) = -3/2
So, the point (-1/5, -3/2) does lie on the graph of f(x) = 7.5x.
Hence, the statement is false.
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Complete question
True or False. The point (-1/5, -3/2) lies on the graph of f(x).
Where f(x) = 7.5x
Which met represents this solid figure
A. Net 1
B. Net 2
C. Net 3
D. Net 4
Pls help
PLEASE HELP
Using the recursive formula given, find the first five terms of each sequence.
1.) A1 = 12, An=3An-1 -21, n≥2
2.) A1 = 1/2, An = An-1 + 3/2, n≥2
The first five terms of the given sequence are, 12, -9, 30, -51, -72....
What is a sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given is the recursive formula, we need to find the first five terms of the sequence,
1) a₁ = 12, aₙ = 3 and aₙ₋₁-21 :-
a₂ = a₂₋₁ -21
= 12-21
= -9
a₃ = a₃₋₁-21
= -9-21
= -30
a₄ = a₄₋₁-21
= -30-21
= -51
a₅ = a₅₋₁-21
= -51-21
= -72
Hence, the first five terms of the given sequence are, 12, -9, 30, -51, -72....
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Pears cost $3 for a 4 pound bag. If pears cost less per pound than apples but more per pound than peaches, which of the following could be the price per pound of apples and peaches?
Apples are $1.13 per pound and peaches are $1.04 per pound
apples are $1.13 per pound and peaches are $0.63 per pound
apples are $1.13 per pound and peaches are $0.75 per pound
apples are $0.63 perpound and peaches are $1.13 per pound
The price of Apples are $1.13 per pound and peaches are $0.63 per pound Option B
How to find the price per pound of apples and peachesIf pears cost $3 for a 4 pound bag, then the price per pound of pears is:
3/4 = $0.75 per pound
Since pears cost less per pound than apples but more per pound than peaches, we can set up the following inequality:
peaches < pears < apples
Substituting the known price per pound of pears, we get:
peaches < $0.75 < apples
Now, we can check each option to see which satisfies the inequality:
Apples are $1.13 per pound and peaches are $1.04 per pound:
$1.04 < $0.75 < $1.13
This option does not satisfy the inequality.
Apples are $1.13 per pound and peaches are $0.63 per pound:
$0.63 < $0.75 < $1.13
This option satisfies the inequality.
Apples are $1.13 per pound and peaches are $0.75 per pound:
$0.75 < $0.75 < $1.13
This option does not satisfy the inequality.
Apples are $0.63 per pound and peaches are $1.13 per pound:
$1.13 < $0.75 < $0.63
This option does not satisfy the inequality.
Therefore, the price per pound of apples and peaches that could be consistent with the given information is: apples are $1.13 per pound and peaches are $0.63 per pound.
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For f(x) = 4x+ 2 and g( x) =x2 -6 find (f+g) (x)
The value of the function (f+g)(x) = x² + 4x - 4.
What is the difference between function and equation?An output variable and one or more input variables are at least two of the variables that make up a function. A mathematical equation may have any number of variables and says that two expressions are equivalent (none, one, or more). A function is frequently expressed as an equation, however not all equations are functions.
Given that,
f(x) = 4x + 2
g(x) = x² - 6
(f+g)(x) = f(x) + g(x) = 4x + 2 + x² - 6
(f+g)(x) = x² + 4x - 4
Hence, the value of the function (f+g)(x) = x² + 4x - 4.
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Select the equation represented by the fraction strips below. HURRY PLS!
The equation can be written as:
(2 + 1/3) + 3*(1/3)
And the solution, writen as a mixed number, is 3 + 1/3.
Which equation is represented by the diagram?
Here we have a diagram where we can see an addition (its an addition because of the direction of the arrow).
On the leftside we can see two whole squares and a one thid strip.
Then the number is:
2 + 1/3
And to that, we are adding 3 one third strips, then we are adding:
(2 + 1/3) + 3*(1/3)
That should be the equation
We can solve that equation to get:
2 + 1/3 + 3/3
= 2 + 1/3 + 1
= 3 + 1/3
That is the solution written as a mixed number.
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A circle has 24 pi as its circumference. What is the, diameter, radius, and area?
Answer:
See below.
Step-by-step explanation:
We are asked for the diameter, radius, and area of a circle.
We are given the Circumference.
We should know that;
[tex]Circumference = (diameter)\pi[/tex]
[tex]Circumference = 24\pi[/tex] (Exact)
This means that the Diameter is 24.
The Radius is [tex]\frac{1}{2}[/tex] of the Diameter.
This means that the Radius is 12.
The area of a circle is represented as;
[tex]Area = \pi(radius)^2[/tex]
We have the requirements to find the area, with the value of the radius.
Solve for the area;
[tex]Area = \pi(12)^2[/tex]
[tex]Area = 144 \pi[/tex] (Exact)
[tex]Area = about \ 452.39.[/tex] (Approx.)
help help help!! with my math !!!!!!!!!!!!!
Triangle LMO is congruent to NMO because they are reflections of eachother.
Gwen purchased a fruit salad for $12 and two
watermelons to cut up and add to the fruit salad.
The watermelons cost the same amount, and all
the fruit was less than $22 in all. Write an
inequality to represent this situation. Then
complete the sentence.
Answer:27
6574
Step-by-step explanation:
Answer:
2x+12<22
Step-by-step explanation:
Bc I got it correct
Megan puts $200.00 into an account to use for school expenses. The account earns 9% interest, compounded annually. How much will be in the account after 5 years?
Answer:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years)
In this case, we have:
P = $200.00
r = 0.09 (9% expressed as a decimal)
n = 1 (compounded annually)
t = 5 years
Plugging these values into the formula, we get:
A = $200.00(1 + 0.09/1)^(1*5)
A = $200.00(1.09)^5
A = $200.00(1.538624)
A = $307.72
Therefore, after 5 years, Megan will have $307.72 in her account.
Step-by-step explanation:
HELP ASAP, WILL GIVE FIRST ANSWER BRAINLIEST, 50 POINTS!!!
Triangle NMO is drawn with vertices N(−4, −2), M(−1, −1), O(−4 , −5). Determine the image coordinates of N′M′O′ if the preimage is translated 7 units to the left.
N′(3, −2), M′(6, −1), O′(3, −5)
N′(−4, −9), M′(−1, −8), O′(−4, −12)
N′(−4, 5), M′(−1, 6), O′(−4, 2)
N′(−11, −2), M′(−8, −1), O′ (−11, −5)
Answer: Your welcome!
Step-by-step explanation:
N′(−11, −2), M′(−8, −1), O′ (−11, −5)
The image coordinates of N′M′O′ if the preimage is translated 7 units to the left are N′(−11, −2), M′(−8, −1), O′ (−11, −5). This is calculated by subtracting 7 from the x-coordinate of each point in the original triangle NMO. For example, the x-coordinate of point N in the original triangle is -4, so the x-coordinate of point N′ in the translated triangle is -4 - 7 = -11. The y-coordinate of point N does not change, so the y-coordinate of point N′ is also -2.
Answer:
To translate the triangle 7 units to the left, we need to subtract 7 from the x-coordinates of each vertex:
N' = (N_x - 7, N_y) = (-4 - 7, -2) = (-11, -2)
M' = (M_x - 7, M_y) = (-1 - 7, -1) = (-8, -1)
O' = (O_x - 7, O_y) = (-4 - 7, -5) = (-11, -5)
Therefore, the image coordinates of N'M'O' are (-11, -2), (-8, -1), and (-11, -5).
So the answer is N′(−11, −2), M′(−8, −1), O′ (−11, −5).
For each of the questions in this homework, please include an expla
strategies. Also please do not convert any of the fractions to decima
method, or cross multiplication. You may use the fraction tiles
The comparisons of the fractions given above is enumerated below.
What is the rationale for the above response?1) To compare 1/8 and 1/9, I can find a common denominator by multiplying the denominators together. The common denominator is 8 x 9 = 72.
Then, I can convert each fraction to have a denominator of 72 by multiplying the numerator and denominator of each fraction by the appropriate factor. The result is 9/72 and 8/72. Since 9/72 is bigger than 8/72, I know that 1/8 is smaller than 1/9.
2) To compare 7/8 and 8/9, I can find a common numerator by multiplying the numerators together. The common numerator is 56. Then, I can convert each fraction to have a numerator of 56 by multiplying the numerator and denominator of each fraction by the appropriate factor. The result is 49/56 and 64/72. Since 64/72 is bigger than 49/56, I know that 8/9 is bigger than 7/8.
3) To compare 15/38 and 5/13, I can find a common numerator by multiplying the numerators together.
The common numerator is 195. Then, I can convert each fraction to have a numerator of 195 by multiplying the numerator and denominator of each fraction by the appropriate factor.
The result is 75/195 and 75/195. Since the numerators are the same, I can compare the denominators. Since 195 is bigger than 169, I know that 15/38 is smaller than 5/13.
4) To compare 5/9 + 7/12 and 1/2, I can compare each fraction to 1/2 separately.
First, 5/9 is smaller than 1/2 because 9 is bigger than 18, so each ninth is smaller than each half.
Next, 7/12 is also smaller than 1/2 because 12 is bigger than 6, so each twelfth is smaller than each half.
Therefore, both fractions added together (without actually adding them) will be smaller than 1/2.
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Identify the factor pair of ac you could use to rewrite b to factor the trinomial by grouping.
3x²2² +11x-4
The factors of ac are
(Use a comma to separate answers as needed.)
(x+4), (3x-1) are the required factors in the given trinomial solution.
The solution provided below has been developed in a clear step by step manner.
Step: 1
Given polynomial is 3x²2² +11x-4
=3x(x+4)-1(x+4)
=(x+4)(3x-1)
Explanation: Please refer to solution in this step.
Step: 2
(x+4), (3x-1) are the required factors
A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them. Factors can be found using either division or multiplication.
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25 The pyramid P is formed from two parts made of different materials. top bottom The top part of P has a mass of 92.8g and is made from material with a density of 2.9g/cm3 The bottom part of P has a mass of 972.8g The average density of P is 4.7g/cm3 Calculate the volume of the top part of P as a percentage of the total volume of P. Give your answer correct to 1 decimal place. You must show all your working.
The volume of the top part of the pyramid is 13.4% of the total volume.
What is density? How is density calculated?The amount of mass that a material has in relation to its volume is measured by its density. By dividing the substance's mass by volume, it is determined. Density is calculated as follows: density = mass/volume
A fundamental idea in physics, density is utilised in many branches of research and engineering, including the construction of effective engines and turbines, calculating the buoyancy of objects in fluids, and forecasting the behaviour of materials under stress.
Given that, average density of the entire pyramid is 4.7g/cm3 and that the bottom part has a mass of 972.8g.
The density is given as:
density = mass/volume
Substituting the value we have:
4.7g/cm3 = 972.8g/volume
volume = 207.23 cubic cm.
For the top part, density of 2.9g/cm3 and a mass of 92.8g. :
density = mass/volume
2.9g/cm3 = 92.8g/volume
volume = 32 cubic cm.
The percent of the top part with respect to total volume is:
percentage = (volume of top part / total volume) x 100
total volume = volume of top part + volume of bottom part
total volume = 32 cm3 + 207.23 cm3
total volume = 239.23 cm3
percentage = (32 cm3 / 239.23 cm3) x 100
percentage = 13.4%
Therefore, the volume of the top part of the pyramid is 13.4% of the total volume.
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What is the area of this composite figure round to the nearest hundredth
The area of the composite figure is 14.71 square units
What is the area of the composite figure?The area of the composite figure is found by calculating the sum of the areas of the various parts.
The area of the figure = area of sector + area of triangle + area of trapezium
Area of sector = 135/360 * π * 2²
Area of sector = 4.71 square units
Area of triangle = ¹/₂ * 2 * 1
Area of triangle = 1 square unit
Area of trapezium = ¹/₂ (3 + 6) * 2
Area of trapezium = 9 square units
Therefore, area of composite figure = (4.71 + 1 + 9) square units
The area of the composite figure = 14.71 square units
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Rahul plans to invest $25,000 in a retirement account that compounds 6% monthly . He has 25 years left until he retires . How much will he have in the account when he retires?
The total amount that Rahul will have is 108,006.20.
Compound Interest:Compound interest is a type of interest where the interest earned on a principal amount is added to the principal, and the new total amount becomes the basis for calculating interest in the next period.
In other words, the interest is earned not only on the principal amount but also on the accumulated interest.
The formula for compound interest is:
A = P (1 + r/n)^(n*t)Here we have, Rahul's plans to invest $25,000 in a retirement account that compounds 6% monthly.
From the data,
The principal amount, P = 25000
Rate of interest, r = 6% = 6/100 = 0.06
Time period, t = 25 years
Number of compounds, n = 12 [ Since compounded annually ]
By using the formula, A = P (1 + r/n)^(n×t)
A = 25000 [ 1 + 0.6/12]⁽¹²ˣ²⁵⁾
A = 25000 [ 1 + 0.005]⁽³⁰⁰⁾
A = 25000 [1.005]⁽³⁰⁰⁾
A = 108,006.20 (rounded to the nearest cent)
Therefore,
The total amount that Rahul will have is 108,006.20.
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can someone help me with this please?!
Answer:
[tex]x^4-3x^2-x^2-4[/tex]
Step-by-step explanation:
Given information.
P(x) = R(x) - C(x)
[tex]R(x) = 2x^4-3x^3+2x-1[/tex] and [tex]C(x) = 2x^4-x^2+2x+3[/tex]
[tex](2x^4-3x^3+2x-1) - (x^4-x^2+2x+3)[/tex]
Distribute the negative then solve by simplying either add or subtracting.
[tex](2x^4-3x^3+2x-1) +(-x^4+x^2-2x-3)\\[/tex]
[tex](2x^4-x^4)-3x^3-x^2+(2x-2x)+(-1-3)\\\\(x^4) -3x^3-x^2+(0x)-4\\\\x^4 -3x^3-x^2-4[/tex]
i need help with everyone
The growth rate is - 0.17
How to solve for the growth ratea. Growth rate = (38-55)/100 = -0.17
This shows that it is decreasing
ii. Groth rate = 38-12.5)/(100-250)
= -0.17
This shows that it is decreasing as well
b. The relationship is a linear function. This is because rate of change of price and the number of days are equal
c. formula for game price in terms of days would be:
Price = -0.17*d + 55.
d = days
d. when price is 48.20
48.20 = -0.17d + 55
48.20 - 55 = -0.17d
d = 40
40 days after game was released
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Please help!!
Complete the identity
cos^2 θ/2=?
One identity that we can write here is:
cos²(θ/2) = - sin²(θ/2) + 1
How to complete the identity?Here we want to find something that is equal to cos²(θ/2) for every value of theta, that will be an identity.
The general identity for trigonometric functions is:
cos²(θ) + sin²(θ) = 1
So we can rewrite this as:
cos²(θ) = - sin²(θ) + 1
If instead of theta, the argument is theta over two, we could rewrite this as:
cos²(θ/2) = - sin²(θ/2) + 1
That is the identity.
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Express the following expression as a function of an acute angle less than 45°:
cot (-859°)
cot (-859°) can be expressed as cot 41° an acute angle which is less than 45°
What is trigonometry?Trigonometry is used in navigation directions. Estimate the direction you need to place your compass to get a straight line. With the help of a compass and navigation trigonometric functions, it's easy to find a place or find the distance to see the horizon.
What is mathematical expression?A Mathematical Statement which contains numbers and variables.
Angle: The two straight lines meeting at the vertex(a common point)
According to the question:
cot (-859) can be expressed as:
cot (-859 + 360x2)= cot (-859 +720)= cot (139)= cot (180 -139)= cot 41°(or)cot(-859) = cot(-859 + 180°x5)= cot (859 +900)= cot (41)°
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Refer to the sample data for pre-employment drug screening shown below. If one of the subjects is randomly selected, what is the probability that the test result is a false positive? Who would suffer from a false positive result? Why?
Pre-Employment Drug Screening Results
Positive test result
Negative test result
Drug Use Is Indicated
Drug Use Is Not Indicated
Subject Uses Drugs
46
8
Subject Is Not a Drug User
1
30
Question content area bottom
Part 1
The probability of a false positive test result is enter your response here.
(Round to three decimal places as needed.)
The probability of a false positive test result is approximately 0.267 or 0.267 probability units.
What is probability?Probability is the measure of the likelihood or chance that an event will occur, expressed as a number between 0 and 1.
For example, the probability of rolling a six on a fair dice is 1/6 or approximately 0.167. It is a fundamental concept in statistics and plays a crucial role in many real-life applications, such as decision-making, risk analysis, and scientific research.
To find the probability of a false positive test result, we need to calculate the proportion of individuals who test positive but do not use drugs out of the total number of individuals. This is represented by the ratio of the number of false positives to the total number of negative test results, which is:
(false positives) / (negative test results) = 8 / 30 = 0.267
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class 4
66640 divide 31
66640 divided by 31 is approximately equal to 2149.68.
What is division?
Division is a basic arithmetic operation that is used to split a quantity into equal parts or to find out how many times one quantity is contained within another quantity.
When 66640 is divided by 31, the result is:
66640 ÷ 31 =2149.68 (rounded to two decimal places)
Therefore, 66640 divided by 31 is approximately equal to 2149.68.
In general, when we perform division, we are asking the question "how many times does the divisor fit into the dividend?" The dividend is the number being divided, the divisor is the number we are dividing by, and the result is the quotient.,
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some students have a goal of collecting 200 leaves for a science project. what does the 0% mean in this situation?what does 100% mean
0% would indicate that the kids have not gathered any leaves for the scientific project, and 100% would indicate that they have succeeded in collecting 200 leaves.
Why is percentage important?In mathematics, a percentage is a quantity or a ratio that is expressed as a fraction of 100. Calculating a percentage involves multiplying a quantity by 100 and dividing it by the total.
To determine "how much" or "how many," utilise the percentage. Calculating the precise quantity or figure that is being discussed is made easier with the use of a percentage. We compare fractions. determining a percentage rise or fall aids in calculating profit and loss margins.
In this case, 0% would indicate that the kids have not gathered any leaves for the scientific project, and 100% would indicate that they have succeeded in collecting 200 leaves for the project.
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Suppose you know that the radius of one circle is three times the radius of another circle. Explain how you can determine the ratio of the areas of the circles and the ratio of the circumferences of the circles without knowing the actual measurements.
The ratio for the area and the ratio for the circumferences of the circles are 9 : 1 and 6 : 1 respectively.
What is a circle?
A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.
If the radius of one circle is three times the radius of another circle, then we can use this information to determine the ratio of the areas of the circles and the ratio of the circumferences of the circles without knowing their actual measurements.
Let's call the radius of the smaller circle "r" and the radius of the larger circle "3r".
Ratio of areas -
The area of a circle is proportional to the square of its radius, so the ratio of the areas of the two circles is -
= (area of larger circle) / (area of smaller circle)
= (π(3r)²) / (πr²)
= 9r²/r²
= 9/1
Therefore, the ratio of the areas of the two circles is 9:1.
Ratio of circumferences -
The circumference of a circle is proportional to its radius, so the ratio of the circumferences of the two circles is -
= (circumference of larger circle) / (circumference of smaller circle)
= 2π(3r) / 2πr
= 6r/r
= 6/1
Therefore, the ratio of the circumferences of the two circles is 6:1.
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find the x intercept and the y intercept for 6x-3y=-12
The x intercept and the y intercept for 6x - 3y = -12 is x = 0.5y + 2 and y = 2x - 4.
What are intercepts in graphs?The term “intercept” refers to the location where a line or curve crosses a graph's axis. The x-intercept is the point at which the x-axis is crossed. The y-intercept is the point at which the y-axis is crossed.
The line's steepness is measured by its slope (m). It is the difference between the y-coordinate change and the corresponding x-coordinate change. For 6x - 3y = 12, just enter the above coordinates and solve for m to obtain the slope.
To solve for x, we solve the equation so the variable x is by itself on the left side:
6x - 3y = 12
x = 0.5y + 2
To solve for y, we solve the equation so the variable y is by itself on the left side:
6x - 3y = 12
y = 2x - 4
Therefore, the x = 0.5y + 2 and y = 2x - 4.
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write the slope intercept form of the equation of the line described.
through: (5, 0) perp to y= -5/3x
Answer:
y = 3/5x - 3
Step-by-step explanation:
slope (m) of line perpendicular to y = -5/3x is 3/5, the negative reciprocal of -5/3
use the point (5, 0) and the point-slope form to find b, the y-intercept:
y - 0 = 3/5(x - 5)
y = 3/5x - 15/5
y = 3/5x - 3 equation is now in the slope-intercept form
How many solutions does the system of linear equations represented in the graph have? Coordinate plane with one line that passes through the points negative 2 comma negative 3 and 0 comma negative 2 and another line that passes through the points 0 comma 3 and 1 comma 1. One solution at (−1, 2) One solution at (2, −1) No solution Infinitely many solutions
Answer:
One solution at (2, -1)
Step-by-step explanation:
You will want to write the equations for both pairs of points:
(-2,-3) and (0,-2)
The slope is the change in y over the change in x. The first number of the ordered pairs is the x value and the second number in the ordered pair is the y values. Find the change by subtraction
[tex]\frac{-2 - -3}{0 - -2}[/tex] = [tex]\frac{-2+ 3}{0 + 2}[/tex] = [tex]\frac{1}{2}[/tex]
The slope (m) is 1/2.
The y intercept is when x = 0. In the point (0,-2) x is 0, so the y-intercept is -2.
The y-intercept (b) is -2.
y = mx + b Substitute 1/2 for m and -2 for b
y = [tex]\frac{1}{2}[/tex]x - 2
(0,3) and (1,1)
The slope is
[tex]\frac{1-3}{1-0}[/tex] = [tex]\frac{-2}{1}[/tex] = -2
The slope is --2.
The y intercept is 3.
y = mx + b Substitutes -2 for m and 3 for b.
y = -2x + 3
Set the 2 equation equal to each other and solve for x.
-2x + 3 = 1/2 x -2 Multiply all the way through by 2 to clear the fraction.
-4x + 6 = x - 4 Add 4x to both sides
-4x + 4x + 6 = x + 4x -4
6 = 5x -4 Add 4 to both sides
6 + 4 = 5x - 4 + 4
10 = 5x Divide both sides by 5
2 = x
Take either of the two original equations and substitute 2 for x and solve for y
y = -2x + 3
y = -2(2) + 3
y = -4 + 3
y = -1
The solution is (2,-1)
Helping in the name of Jesus.
Solve for x in log3 81 = x.
By answering the above question, we may infer that We may reduce this equation to: Applying the rule that log base an of ab = b 4 = x Hence, x = 4.
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.
The equation may be changed to read:
x = log base 3 of 81.
81 being equivalent to 3 to the power of 4, we get the following:
x Equals log base 3 of 34.
We may reduce this to: Applying the rule that log base an of ab = b
4 = x
Hence, x = 4.
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What is the diffrence between b and 9
Answer: b-8
Step-by-step explanation:
b-9=b-9
b-9+1=b-8