Answer:
To solve 2^x = 32, we need to find the value of x that satisfies the equation.
We can rewrite 32 as a power of 2 by noting that 2^5 = 32. Therefore, we have:
2^x = 2^5
Since the bases of the powers are equal, we can equate the exponents:
x = 5
So the solution to 2^x = 32 is x = 5.
To rewrite this equation in a logarithmic form, we can use the definition of logarithms:
log(base 2)32 = x
Here, the logarithm with base 2 of 32 is equal to x.
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Diana has watched 13 out of 25 episodes of a television series. What decimal represents the part of the series she has NOT watched yet?
Answer:
Step-by-step explanation:
Can a triangle with angle measures of 45-45-90 have the side lengths 30, 30 and 60?
(Geometry/Trig)
Step-by-step explanation:
No, the ratio in a 30-60-90 triangle is
::
[tex]1:1:\sqrt{2} [/tex]
not
1:1:2
If x^2-x-6=0 then x is
, then x is
Question 1 options:
-2 or 3
-1 or 6
1 or 6
2 or -3
Answer:
-2 and 3 is the required answer
Answer: The answer is: -2 or 3
Step-by-step explanation:
x^2 -x -6 = 0
x^2 -3x +2x -6 = 0
x(x-3) + 2(x-3) = 0
(x-3)(x+2) = 0
So x-3 = 0 :: x = 3
or x+2 = 0 :: x=-2
If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, where will B' be?
Reflection over the y-axis, rotation 90° clockwise, and translation (x + 2, y - 1)
If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, B' would be located at B' (3, -4).
What is a translation?In Mathematics, a translation is a type of rigid transformation which is used in moving every point of an object in the same direction, as well as for the same distance.
By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:
Coordinate B = (-3, 1) → Coordinate B' = (-(-3), 1) = (3, 1).
Next, we would apply a rotation of 90° clockwise as follows;
(x, y) → (y, -x)
Coordinate B' = (3, 1) → Coordinate B' = (1, (-3)) = (1, -3)
Lastly, we would apply a translation (x + 2, y - 1) as follows:
Coordinate B' = (1, -3) → (1 + 2, -3 - 1) = B' (3, -4).
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A, B, and C started a business with Rs 60,000. Amount invested by 'A' and 'C' together is twice that of 'B', while the amount invested by 'A' and 'B' together is thrice that of 'C'. 'A' invested for 6 months, 'B' for 9 months, and 'C' for a year. Find the share of 'B' (in Rs) out of the total profit of Rs 3400.
Answer:
Step-by-step explanation:
Let the amount invested by A, B, and C be denoted by a, b, and c respectively.
From the given information,
a + b + c = 60000 ---(1)
a + c = 2b ---(2)
a + b = 3c ---(3)
Multiplying equation (2) by 3 and equation (3) by 2, we get:
3a + 3c = 6b
2a + 2b = 6c
Adding these two equations, we get:
5a + 5b + 5c = 0
a + b + c = 0
This is not possible as the sum of the investments cannot be zero. Therefore, there must be an error in the problem statement.
Without further information or correction, it is not possible to find the share of B in the profit.
john put three gallons into his truck
A town has a population of 1900
people at time t=0 In each of the following cases, write a formula for the population P, of the town as a function of year t
(a) The population increases by 60
people per year.
P= X people x=?
Answer:
The formula for the population P, of the town as a function of year t, if the population increases by 60 people per year, is:
P(t) = 1900 + 60t
where t is the number of years elapsed since t=0.
The formula for the population P, of the town as a function of year t is
P = 1900 + 60t
We have,
If the population increases by 60 people per year, then we can use the following formula to find the population P as a function of time t (in years):
P = 1900 + 60t
Here, the initial population at t=0 is 1900 people, and the population increases by 60 people per year,
So we add 60t to the initial population to get the population at time t.
For example,
If we want to find the population after 5 years, we can substitute t=5 into the formula:
P = 1900 + 60(5) = 2200
So the population after 5 years would be 2200 people.
Thus,
The formula for the population P, of the town as a function of year t is
P = 1900 + 60t
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compare 9\10 and 3\2 on number line
Comparing the numerator 9 < 15 thus, 9/10 is less than 3/2.
What is common denominator?A multiple of the denominators of two or more fractions can be used as a common denominator to add, subtract, or compare the fractions. As fractions with dissimilar denominators cannot be added together or directly compared, they must be changed into comparable fractions with the same denominator. We must determine the least common multiple (LCM) of the fraction denominators in order to determine a common denominator. The lowest number that is a multiple of both denominators is known as the LCM. Once we have the common denominator, we may multiply the numerator and denominator by the same factor to change each fraction to an equal fraction with the same denominator.
The two values are 9/10 and 3/2.
Taking the LCM we have:
9/ 10 and 15/10
Now comparing the numerator 9 < 15 thus, 9/10 is less than 3/2.
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On number line we can compare 9/10 and 3/2 as 9/10 < 3/2.
What is number line?
A number line is a visual representation of numbers in order, usually shown horizontally. It is a line with a starting point and an endpoint that represent the smallest and largest numbers, respectively.
To compare 9/10 and 3/2 on a number line, we need to first convert them to the same denominator. The least common multiple of 10 and 2 is 10, so we can convert 3/2 to 15/10:
9/10 = 0.9
3/2 = 15/10 = 1.5
Now, we can plot these two numbers on a number line:
We can see that 9/10 is to the left of 3/2 on the number line.
Therefore we can compare 9/10 and 3/2 as 9/10 < 3/2.
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Graphical Misrepresentations of Data – Warning!
Graph can be misleading! Distorting the truth unfortunately does happen within the field of Statistics through distorting data. Some graphs are misleading and other deceive! The misrepresentation may be intentional or purely innocent on the behalf of the researcher/statistician.
When reviewing graphs, it is important to have an eye for characteristics that may manipulate the facts and in turn the data. For example, incorrect depiction of size of graphics.
Please review a few graphs from a local newspaper, magazine or professional journal. Please describe the graph, provide the source and why you chose this particular one.
Please provide 3 to 4 characteristics of a good graph.
Your statements should be:
Substantive and clearly articulated
Professionally written
Demonstrate knowledge of the content
Contribute to the discussion (possibly with a question) to further increase and deepen the understanding of the topics being discussed
You may use supporting articles, textbook references, and even personal experience (as long as it relevant and empirical in nature).
On the graph we have to ensure that the data points are seen, the text and design on the graph are meaningful along with keeping the alignment on a common scale.
What is a graph?The graph only presents the facts in an organised manner. It facilitates our understanding of the facts. The numerical information gleaned via observation is referred to as data.
For the given question,
In a graph the data should be shown clearly.
Now, displaying the data clearly entails making sure the data points are visible while also including relevant language on the graph itself.
Designing of the graph should be in a simple manner.
The alignment to be used has to be on a common scale.
The visual encoding has to be transparent.
Use of standard-forms are welcomed.
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A box contains four apples, six oranges, and a pear. Preston reaches into the box and selects two of the 11 fruits uniformly at random without replacement. Let m/n be the probability that he selects an apple and an orange, where m and n are relatively prime positive integers. Find m+n.
the answer is m + n = 24 + 55 = 79.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
There are two ways this can happen: either he selects an apple first and then an orange, or he selects an orange first and then an apple. We can compute the probability of each of these events separately and then add them together.
First, let's consider the probability that Preston selects an apple first and then an orange. The probability of selecting an apple first is 4/11, and then the probability of selecting an orange from the remaining 10 fruits (which includes 3 apples and 6 oranges) is 6/10. So the probability of this event is (4/11) * (6/10) = 24/110.
This can be simplified by dividing the numerator and denominator by 2:
48/110 = 24/55
So the probability that Preston selects an apple and an orange is 24/55. Therefore, the answer is m + n = 24 + 55 = 79.
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The point (7,8) in the coordinates plane represents a ratio. Adela claims that you can find an equivalent ratio by adding the same number to both coordinates of the point. Is Adela correct?
Answer:
It depends on the context of the problem and the interpretation of the ratio represented by the point (7, 8).
If we interpret the point (7, 8) as representing the ratio 7:8, then Adela's claim is incorrect. Adding the same number to both coordinates of the point would change the value of the ratio. For example, adding 1 to both coordinates would give the point (8, 9), which represents the ratio 8:9, which is not equivalent to 7:8.
However, if we interpret the point (7, 8) as representing a different type of ratio, such as the ratio of the distances from the point to two fixed points or the ratio of the areas of two shapes, then it may be possible to find an equivalent ratio by adding the same number to both coordinates of the point. In this case, Adela's claim could be correct.
Without more information about the context and interpretation of the ratio represented by the point (7, 8), it is difficult to determine the correctness of Adela's claim.
QUESTIONS 1. Lizzy a level 300 students at UEW calls her father to send her money to buy Milo which cost $4 each and books which cost $8 each. The father sent her 20 pairs of shoes and 20 pairs of new jeans trousers which she can freely see on the market for $ 20 each and $ 40 each respectively. a. Write down the equation of Lizzy's budget line and interpret the results.
b. Carefully sketch the budget line
c. If Lizzy discovers that substituting two (2) tins of milo for three (3) will not change her level of satisfaction, what must be the lowest price of books before she will substitute milo for books given that the price of milo remains $4.
a.The equation of Lizzy's budget line can be written as:
4M + 8B + 20(20)S + 20(40)J = I.
b.To sketch the budget line, we can plot the points (0, I/8), (I/4, 0), and (5I/16, 3I/16) on a graph.
c.The lowest price of books that Lizzy will substitute for Milo is $6.
What is budget line?A budget line is a graphical representation of all possible combinations of two goods that can be purchased with a limited amount of income or resources. It shows the various combinations of two goods that a consumer can afford to buy with a given income and the prices of the two goods.
In the given question,
a. The equation of Lizzy's budget line can be written as:
4M + 8B + 20(20)S + 20(40)J = I
where M is the number of tins of Milo, B is the number of books, S is the number of pairs of shoes, J is the number of pairs of jeans, and I is the total income or budget.
Interpretation: This equation represents all the possible combinations of Milo, books, shoes, and jeans that Lizzy can buy with her given income. It shows that she has to choose between buying more of one good and less of the other goods depending on their prices and her budget.
b. To sketch the budget line, we need to solve the equation for one of the variables. Let's solve for B:
4M + 8B = I - 20(20)S - 20(40)J
B = (1/2)I - 40S - 40J - 2M
This equation shows that the maximum number of books that Lizzy can buy depends on her income (I), the prices of shoes (S) and jeans (J), and the number of tins of Milo (M) she buys. The slope of the budget line is -4, which means that for every 1 unit increase in the number of books, Lizzy has to give up 4 units of Milo.To sketch the budget line, we can plot the points (0, I/8), (I/4, 0), and (5I/16, 3I/16) on a graph, where the x-axis represents the number of tins of Milo (M) and the y-axis represents the number of books (B). Then, we can draw a straight line connecting these points to represent Lizzy's budget line.c. Let's assume that the lowest price of books that Lizzy will substitute for Milo is P dollars. Then, the new budget line can be written as:
4M + P(2/3)B + 20(20)S + 20(40)J = I
To find the lowest price of books that Lizzy will substitute for Milo, we need to solve for P. We can do this by setting the coefficients of M and B in the new budget line equal to those in the original budget line:
4 = (2/3)P
P = (3/2) * 4
P = 6
Therefore, the lowest price of books that Lizzy will substitute for Milo is $6.
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A.The equation of Lizzy's budget line can be written as:
4M + 8B + 20(20)S + 20(40)J = I.
B.To sketch the budget line, we can plot the points (0, I/8), (I/4, 0), and (5I/16, 3I/16) on a graph.
C.The lowest price of books that Lizzy will substitute for Milo is $6.
What is budget line?
A budget line is a graphical representation of the limits of a consumer's purchasing power, given their income and the prices of goods and services. It shows all the possible combinations of two goods that a consumer can purchase with a given income, while spending all of their available resources.
According to given information:a. The equation of Lizzy's budget line can be written as:
4M + 8B + 20(20)S + 20(40)J = I
where M is the number of tins of Milo, B is the number of books, S is the number of pairs of shoes, J is the number of pairs of jeans, and I is the total income or budget.
Interpretation: This equation represents all the possible combinations of Milo, books, shoes, and jeans that Lizzy can buy with her given income. It shows that she has to choose between buying more of one good and less of the other goods depending on their prices and her budget.
b. To sketch the budget line, we need to solve the equation for one of the variables. Let's solve for B:
4M + 8B = I - 20(20)S - 20(40)J
B = (1/2)I - 40S - 40J - 2M
This equation shows that the maximum number of books that Lizzy can buy depends on her income (I), the prices of shoes (S) and jeans (J), and the number of tins of Milo (M) she buys. The slope of the budget line is -4, which means that for every 1 unit increase in the number of books, Lizzy has to give up 4 units of Milo.
To sketch the budget line, we can plot the points (0, I/8), (I/4, 0), and (5I/16, 3I/16) on a graph, where the x-axis represents the number of tins of Milo (M) and the y-axis represents the number of books (B). Then, we can draw a straight line connecting these points to represent Lizzy's budget line.
c. Let's assume that the lowest price of books that Lizzy will substitute for Milo is P dollars. Then, the new budget line can be written as:
4M + P(2/3)B + 20(20)S + 20(40)J = I
To find the lowest price of books that Lizzy will substitute for Milo, we need to solve for P. We can do this by setting the coefficients of M and B in the new budget line equal to those in the original budget line:
4 = (2/3)P
P = (3/2) * 4
P = 6
Therefore, the lowest price of books that Lizzy will substitute for Milo is $6.
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Tiffany's mom is renting a car for their upcoming vacation. She wants to spend no more than $17 per day for the car. Which of the following car rental companies will fit into her budget? Select ALL that apply.
Car Rental Company Amount Charged
A $33 for 2 days
B $50 for 3 days
C $72 for 4 days
D $89 for 5 days
A
Car Rental Company A
B
Car Rental Company B
C
Car Rental Company C
D
Car Rental Company D
Answer: i think its A and B
Step-by-step explanation: 33 divided by 2 is 16.5
50 divided by 3 is 16.6667
72 divided by 4 is 18 so that would be to much
89 divided by 5 is 17.8 which is also to much
a rocket is launched from the top of a 30 foot cliff with an initial velocity of 170 feet per second. the height, h, of the rocket after t seconds is given by the equation h=-16t^2+170t+30. How long after the rocket is launched will it be 20 feet from the ground?
However, we need to choose the positive value for t, since time cannot equation be negative in this case. Therefore, the rocket will be 20 feet from the ground approximately 1.411 seconds after it is launched.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
So we have:
[tex]-16t^2 + 170t + 30 = 20\\-16t^2 + 170t + 10 = 0\\8t^2 - 85t - 5 = 0\\t = (-b + \sqrt(b^2 - 4ac)) / 2a\\t = (-(-85) + \sqrt((-85)^2 - 4(8)(-5))) / 2(8)\\t = (85 + \sqrt(7225 + 160)) / 16\\t = (85 + \sqrt(7385)) / 16[/tex]
However, we need to choose the positive value for t, since time cannot be negative in this case. Therefore, the rocket will be 20 feet from the ground approximately 1.411 seconds after it is launched.
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What are the first three terms of the sequence defined by the following equation? a_n= 7 + (n - 1) 5
7, 2, -3
7, 12, 17
7, 35, 175
12, 17, 22
Answer:
7, 12, 17 which is the second choice
Step-by-step explanation:
The given sequence is expressed by the equation
[tex]a_n = 7 + (n - 1)5\\\\(n - 1)5 = 5n - 5\\\\a_n = 7 + (n - 1)5= 7 + 5n - 5\\\\= 2 + 5n\\\\a_n = 5 + 2n\\\\a_1 = 2 + 5(1) = 2 + 5 = 7\\\\a_2 = 2 + 5(2) = 2 + 10 = 12\\\\a_3 = 2 + 5(3) = 2 + 15 = 17\\\\[/tex]
So the first three terms are
7, 12, 17 which is the second choice
PLS HELP!!! DUE TOMORROW!! 50 POINTS!! show work pls!!
The right triangle BCD have the following solution:
a). The opposite side to the angle D is BC and the adjacent side is DC
b). sin D = 0.55
c). D = 33°
d). B = 57°
How to evaluate for the solutions of the right triangle BCD.Considering the angle D for right triangle BCD, the side opposite the angle D is BD which is also equal to 11 cm, and the side adjacent to the angle D is DC.
sin D = 11/20 {opposite/hypotenuse}
sin D = 0.55 to the nearest tenth
D = sin⁻¹(0.55)
D = 33.3670
D = 33 to the nearest degree
angle B = 180 - (90 + 33) {sum of interior angles of a triangle}
angle B = 57°.
Therefore, the right triangle BCD have the following solution:
a). The opposite side to the angle D is BC and the adjacent side is DC
b). sin D = 0.55
c). D = 33°
d). B = 57°
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find the areas of the sectors formed by angleDFE. Round your answers to the nearest hundredth
The area of the sector formed by angle DFE is approximately 3.29 square feet.
What is area of the sector?
To find the area of a sector of a circle, we need to know the central angle that defines the sector and the radius of the circle. We can then use the formula:
Area of sector = (central angle / 360 degrees) x π x (radius)²
In this case, we are given that the radius of the circle is 4 feet and the central angle that defines the sector is 75 degrees. Therefore, the area of the sector can be calculated as:
Area of sector = (75 / 360) x π x (4)²
= (0.2083) x π x 16
= 3.29 square feet (rounded to the nearest hundredth)
Therefore, the area of the sector formed by angle DFE is approximately 3.29 square feet.
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which is more 7,000 milliliters or 7 liters?
Answer:
It’s the same
Step-by-step explanation:
There equal
7 liters = 7000 milliliters
Helppppp me please!!!! I'm in algebra 2 high school.
[tex]f(-x)[/tex] is not equal to f(x), the function [tex]f(x) = 5x^3 + x[/tex] is neither even nor odd.
What type of function have both an odd and even value?If a function meets the requirements for both odd and even, then the answer is yes. The function is both even and odd if [tex]f(-x) = f(x)[/tex] and [tex]f(-x) = -f(x)[/tex] for every x in the domain of f.
These functions are known as the zero function or identically zero function because they imply that f(x) = 0 for all x in the domain of f.
The given function is [tex]f(x) = 5x³ + x.[/tex]
To know that a function f(x) is even if f(-x) = f(x) for all x in the domain of f.
A function f(x) is odd if f(-x) = -f(x) for all x in the domain of f.
Thus,
[tex]f(-x) = 5(-x)³ + (-x) = -5x³ - x[/tex]
[tex]f(x) = 5x³ + x[/tex]
Comparing f(-x) with f(x), we get:
[tex]f(-x) = -5x³ - x[/tex]
[tex]f(x) = 5x³ + x[/tex]
Since f(-x) is not equal to f(x), the function f(x) = 5x^3 + x is neither even nor odd.
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Which of the following expressions are equivalent to 18x - 24y? Select all that apply.
3(6x-8y)
O2(9x+12y)
6(3x-4y)
6(18x-4y)
(6x-24y)3
O-2(-9x+12y)
Write 4/8 in lowest terms
Answer:
4/8 in lowest terms is 1/2.
Step-by-step explanation:
Answer: 1/2
4/8 is equivalent to 1/2
Of the 40 learners in the class, 12 walks to school, twice the number who walk, come by car or taxi and the remainder cycle to school. What fraction does not cycle to school? Answer must be simplest form.
The fraction of learners who do not cycle to school is equal to 9/10.
How to evaluate for the fraction of learners.Given that the total number of learners is 40, 12 of which walk to school and twice of the number of learners who walk, come to school by car or taxi, then the remainder of learners who cycle to school is calculated as;
40 - [12 +2(12)] = 4
The number of learners who do not cycle to school is;
12 + 2(12) = 36
fraction of learners who do not cycle to school = 36/40
by simplification;
fraction of learners who do not cycle to school = 9/10.
Therefore, the fraction of learners who do not cycle to school is equal to 9/10.
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An appliance store decreases the price of a 19-in. television set 28% to a sale price of $435.60.What was the original price?
Answer:
Step-by-step explanation:
Let x be the original price of the television set.
The sale price is 28% off the original price, which means that the sale price is equal to 100% - 28% = 72% of the original price.
So we can write an equation based on this information:
0.72x = 435.60
Solving for x, we get:
x = 435.60 / 0.72
x ≈ $605
Therefore, the original price of the television set was approximately $605.
Write the equation of the line
Answer:
Below
Step-by-step explanation:
Pick two convenient integer coordinate sets on the line
like 0,0 and 10,4
find slope, m = ( y1-y2) / (x1-x) = ( 4-0) / ( 10-0) = 4/10 = 2/5
b = y axis intercept = 0
Slope - intercept equation of a line is of the form : y = mx + b
substitute in the m and b values found above to get
y = 2/5 x + 0
or just y = 2/5 x
Find the perimeter of a rectangle with w=5 and l=9
Answer:
28 units
Step-by-step explanation:
The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width.
Substituting l = 9 and w = 5, we get:
P = 2(9 + 5) = 2(14) = 28
Therefore, the perimeter of the rectangle is 28 units.
pls answer fast
Eric is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 5 km/h. After three hours, the velocity of the runner is 3 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the runner at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equation obtained in Part A for the first 5 hours? (5 points)
(10 points)
Answer:
Step-by-step explanation:
Part A:
Let's assume that the velocity of the runner changes linearly over time. We can use the slope-intercept form of a linear equation, y = mx + b, to describe the velocity of the runner at different times. In this case, the y-axis represents the velocity in km/h and the x-axis represents time in hours. We can define:
y = velocity of the runner in km/h
x = time in hours
The velocity of the runner changes by -2/3 km/h for every hour that passes. This gives us a slope of -2/3. We can use the point-slope form of a linear equation to find the equation of the line:
y - 5 = -2/3(x - 1)
Simplifying this equation, we get:
3y - 15 = -2x + 2
Rearranging to standard form, we get:
2x + 3y = 17
So the equation in two variables in standard form that can be used to describe the velocity of the runner at different times is 2x + 3y = 17.
Part B:
To graph the equation obtained in Part A for the first 5 hours, we can simply plot points for different values of x and y. For example, we can use x = 0, 1, 2, 3, 4, and 5 to find the corresponding values of y using the equation 2x + 3y = 17. Then we can plot these points on a graph and connect them with a straight line.
Here are the values of y for different values of x:
x = 0, y = 17/3
x = 1, y = 5
x = 2, y = 13/3
x = 3, y = 3
x = 4, y = 7/3
x = 5, y = 1
Plotting these points and connecting them with a straight line, we get the graph of the equation 2x + 3y = 17 for the first 5 hours:
|
6.0 -| .
| .
5.5 -| .
| .
5.0 -| .
|.
4.5 -|
|
4.0 -| .
| .
3.5 -| .
| .
3.0 -| .
|.
2.5 -|
|
2.0 -| .
| .
1.5 -| .
| .
1.0 -|.
|
0.5 -|
|
--------------
0 1 2 3 4 5
The y-intercept of the line is 17/3, which represents the initial velocity of the runner at time 0. The slope of the line is -2/3, which represents the rate of change of the velocity over time.
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Part A:
Let v be the velocity of the runner in km/h and let t be the time elapsed in hours. We can use the two given data points to form a system of two equations:
v = 5 when t = 1
v = 3 when t = 3
To find the equation in standard form, we can first use point-slope form:
v - 5 = m(t - 1) (using the point (1, 5))
v - 3 = m(t - 3) (using the point (3, 3))
Simplifying both equations:
v - 5 = m(t - 1)
v - 3 = m(t - 3)
v = mt + (5 - m)
v = mt + (3m - 3)
Setting the right-hand sides equal to each other:
mt + (5 - m) = mt + (3m - 3)
Simplifying and rearranging:
-m = -2
m = 2
Substituting m = 2 into one of the equations above:
v = 2t + 3
This is the equation in two variables in standard form that describes the velocity of the runner at different times.
Part B:
To graph the equation v = 2t + 3 for the first 5 hours, we can plot points for different values of t and then connect them with a line. For example:
When t = 0, v = 3, so the point (0, 3) is on the line.
When t = 1, v = 5, so the point (1, 5) is on the line.
When t = 2, v = 7, so the point (2, 7) is on the line.
When t = 3, v = 9, so the point (3, 9) is on the line.
When t = 4, v = 11, so the point (4, 11) is on the line.
When t = 5, v = 13, so the point (5, 13) is on the line.
Plotting these points on a coordinate plane and connecting them with a line, we get the graph of the equation v = 2t + 3 for the first 5 hours:
|
15 +-------*
| |
13 + *
| |
11 + *
| |
9 + *
| |
7 + *
| |
5 + *
| |
3 +---------------*-----------*
0 1 2 3 4 5 6 7
The x-axis represents time (t) in hours, and the y-axis represents velocity (v) in km/h. The line starts at (0, 3) and has a slope of 2, indicating that the velocity is increasing by 2 km/h for every hour that passes.
Step-by-step explanation:
3/10=
19/50=
5/10=
1/5=
14/25=
3/25=
Answer:
3/10 = 0.3
19/50 = 0.38
5/10 = 0.5
1/5 = 0.2
14/25 = 0.56
3/25 = 0.12
The perimeter of a movie screen is 70 meters it is 23 meters wide how tall is it
Answer:
height = 12 m
Step-by-step explanation:
We can assume from the problem that the movie screen is rectangular and the formula for perimeter (P) of a rectangle is
P = 2h + 2w, where l is the length and w is the width.
Thus, we can plug in 70 for P and 23 for w and solve for h:
[tex]70=2h+(2*23)\\70=2h+46\\24=2h\\12=h[/tex]
Rewrite the following equations in the form (x−p)2=q 0=x^2-18x+1 and the equation x^2+26x+167.5=0
For the first equation, we can complete the square to find its vertex form. Here's how we do it:
0 = x^2 - 18x + 1
0 = (x - 9)^2 - 80
So we have (x - 9)^2 = 80. This is in the form (x - p)^2 = q, where p = 9 and q = 80.
For the second equation, we can complete the square in a similar way:
x^2 + 26x + 167.5 = 0
x^2 + 26x = -167.5
x^2 + 26x + (26/2)^2 = -167.5 + (26/2)^2
(x + 13)^2 = 9.25
So we have (x + 13)^2 = 9.25. This is in the form (x - p)^2 = q, where p = -13 and q = 9.25.
I hope that helps!
5. Andrew needs to choose a captain creature and a partner creature for his
expedition to a mysterious dungeon. Each creature belongs to the grass,
fire, or water group, and each group has 6 creatures. If the captain and
partner creatures cannot be from the same group, how many ways can
Andrew choose a captain creature and a partner creature?
Andrew needs to choose a captain creature and a partner creature for his expedition to a mysterious dungeon. Each creature belongs to the grass, fire, or water group, and each group has 6 creatures, hence there are 216 ways
If the captain and partner creatures cannot be from the same group, how many ways can Andrew choose a captain creature and a partner creature?" by using combinatorial techniques.
Since Andrew cannot choose a captain and partner creature from the same group, there are 3 choices for the captain creature and 2 choices for the partner creature.
Therefore, the number of ways that Andrew can choose a captain and partner creature is: 3 * 2 * 6 * 6 = 216
Therefore, there are 216 ways that Andrew can choose a captain creature and a partner creature for his expedition to the mysterious dungeon
Find out more about such combination on:https://brainly.com/question/30646507
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