The equation to represent the function is y = 6x + 10 where y is the height of the drone in meters and x is the time in seconds. so the drone rises 6 meters per second.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
Let us find the rate of change, we can divide the total change in the height of the drone by the time taken for the change.
rate of change = (change in height) / (time taken)
(40 m - 10 m/ (5 s - 0 s)= 30 m/5 s=6m/s
The drone rises 18 m every 3 s
rise per second = 18 m / 3 s = 6 m/s
This means that the initial height of the drone is 10 meters, since it takes 3 seconds for the drone to rise to a height of 28 meters
Therefore, the equation to represent the function is:
y = 6x + 10
where y is the height of the drone in meters and x is the time in seconds.
Therefore, the drone rises 6 meters per second.
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The sales tax rate is 4.5%. How much sales tax will you pay on a $125 purchase?
Work Shown:
4.5% of 125 = 0.045*125 = 5.625
That rounds to 5.63
Answer:
5.625
Step-by-step explanation:
If joes shoes cost 44 dollars and 20 cents and joe has 10
dollars and 68 cents. How much money does joe need?
Answer: 44.20-10.68=33.52
He need 33.52$
Step-by-step explanation:
A candle is burning. It starts out 12 inches long. After 1 hour, it is 10 inches long. After 3 hours, it is 5.5 inches
1. Explain one reason why it might be reasonable to model the relationship between time and height of the candle with a linear function.
2. Explain one reason it might NOT be reasonable to model this relationship with a linear relationship
The reasons for (1) and (2) are added below
Why it is reasonable to use a linear functionOne reason why it might be reasonable to model the relationship between time and height of the candle with a linear function is that the rate of change of the candle's height appears to be constant over time.
Why it is unreasonableOne reason why it might NOT be reasonable to model this relationship with a linear function is that the candle's height cannot continue to decrease indefinitely.
This means that the candle's height is bounded and cannot continue to decrease linearly forever.
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sum of 2nd term of an infinite geometric series is -1/2 and the third term is 1/4 find the sum of series
Answer:
2
Step-by-step explanation:
1 plus 1 due to the characterisation of the number 1 increasing by 1 gives you 2
cos(y) = sin(0)
what is the value of 0?
mr ramirez bought a watermelon that weighs 12 pounds for a picnic he cuts it into pieces that each weigh 1.5 pounds. how many pieces of water melon can mr ramiez cut?
Equivalence means to be same, whether it be value, temperature, size, etc.
Let's make an equation to solve this problem. We first would need to take the total (12 pounds) and divide that total by the amount each slice must weigh (1.5 pounds) to get an equal number of slices.
12 ÷ 1.5 = 8To check our work, we can take number of slices (8), and multiply that by the weight of each slice (1.5 pounds) to get the original weight of the watermelon.
8 × 1.5 = 12Now, we know for sure that Mr. Ramirez can make 8 watermelon slices each weighing 1.5 pounds if he has a 12-pound watermelon.
CJ has three more pet pigs than Jacqui has. Let’s write an expression to represent how many pigs CJ has. To do that, we follow these steps:
Identify the constants and the variables.
There is one known number or constant here: it is 3. CJ has 3 more pigs than Jacqui. That number, 3, won’t change. The variable is the number of pets Jacqui has. Let’s call that j.
Identify the operations.
The phrase “more than” tells us we need to add. There are no other operations in this expression.
Rewrite the phrase as an expression.
“Three more pet pigs than Jacqui has” is 3 + j.
Last year, Shailyn read four fewer books than Oswaldo. Which expression shows how many books Shailyn read last year?
Answer: Let's follow the same steps as in the previous example:
Identify the constants and the variables.
The known constant here is 4. Shailyn read 4 fewer books than Oswaldo. Let's call the number of books Oswaldo read "o".
Identify the operations.
The phrase "four fewer" tells us we need to subtract.
Rewrite the phrase as an expression.
"Four fewer books than Oswaldo" is o - 4.
So, the expression that shows how many books Shailyn read last year is o - 4.
Step-by-step explanation:
simplify 3-2(b-2)=2-7b solve for b
The required value of the given expression which satisfy it is b = 3/5.
What is Simplification?To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
According to question:We have,
3 - 2(b - 2) = 2 - 7b
= 3 - 2b - 4 = 2 - 7b
= 5b = 3
= b = 3/5
Thus, required value of the b for the given function is b = 3/5.
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If the scale factor of figure A to figure B is 3:8 find x
Sets A and B are subsets of the universal set U.
These sets are defined as follows.
U= {f, k, m, q, x,y}
A={f, k, m, y}
B = {f, m,q}
Find the following sets.
Write your answer in roster form or as Ø.
(a) AUB' =
(b) A' B' =
(a) The union set is AUB'={f, k, m, x, y}.
(b) The union set is A'UB'={q,k, x, y}.
What is the union of two sets?The union of two sets is also a set. This set contains all the elements of both two sets.
The universal set is U= {f, k, m, q, x,y} and two subsets are A={f, k, m, y} and B = {f, m,q}.
(a)
B' is the complementary set of B. So, find the elements of B'=U-B.
B'= {f, k, m, q, x,y}-{f, m,q}
={k, x,y}
Now, find the union set AUB'.
AUB' ={f, k, m, y}U{k, x,y}
={f, k, m, x, y}
Therefore, the required answer is AUB'={f, k, m, x, y}.
(b)
Also, A' is the complementary set of A. So, find the elements of A'=A-B.
A'= {f, k, m, q, x,y}-{f, k,m, y}
={q,x}
Now, find the union set A'UB'.
A'UB' ={q,x}U{k, x,y}
={q,k, x, y}
Therefore, the required answer is A'UB'={q,k, x, y}.
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tell how the communative and associative properties of adddition can help you evsaluate the expression using mental math? 8+(-8-5)
Using commutative and associative properties of addition, the solution for given expression is -5.
What is commutative and associative property?
The associative and commutative characteristics are universal principles that apply to addition and multiplication. The associative property states that rearranging the numbers will get the same result, while the commutative property states that rearranging the numbers will yield the same result.
These properties tell that one can add in any order, the result will always be the same.
We are given an expression as 8+(-8-5).
So, in this instead of adding from left to right, we can see that the 8 + (-8) will be zero and only -5 will be left as an answer.
Hence, the solution for given expression is -5.
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estimate the population in the year 2040
well, in 2007 it was 12000, so initially that's what it was, and in 2019 it went to 23000, so that's 12 years later, and in 2040, that'll be 33 years later.
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 23000\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &12\\ \end{cases} \\\\\\ 23000 = 12000(1 + \frac{r}{100})^{12}\implies \cfrac{23000}{12000} =\left(1+ \cfrac{r}{100} \right)^{12} \\\\\\ \cfrac{23}{12}=\left(\cfrac{100+r}{100} \right)^{12}\implies \sqrt[12]{\cfrac{23}{12}}=\cfrac{100+r}{100}[/tex]
[tex]100\sqrt[12]{\cfrac{23}{12}}=100+r\implies 100\sqrt[12]{\cfrac{23}{12}}-100=r\implies \boxed{5.57\approx r} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to 5.57\%\to \frac{5.57}{100}\dotfill &0.0557\\ t=years\dotfill &\stackrel{year~2040 }{33}\\ \end{cases} \\\\\\ A \approx 12000(1 + 0.0557)^{33} \implies \boxed{A \approx 71782}[/tex]
What are the zeros of this function?
A. -1, 3
B. 3, 1
C. 0, 1.5
D. 1, 2
Answer:
B
Step-by-step explanation:
the zeros are the values of x on the x- axis where the graph crosses
the graph crosses the x- axis at 1 and 3
then the zeros are x = 1 , x = 3
Find
(M.
f(x)=√√√x²-1
g(x)=√√√x-1
a. √√x+1
b. √√x-1
C.
d.
-X+1
1
X+1
The function operation (f/g)(x) in the functions f(x) = √( x² - 1 ) and g(x) = √( x - 1 ) is √( x + 1).
What is the function operation (f/g)(x) in the function?A function is simply a relationship that maps one input to one output.
Given the functions in the question;
f(x) = √( x² - 1 )g(x) = √( x - 1 )(f/g)(x) = ?To evaluate (f/g), replace the function designators in f/g with the actual functions.
(f/g)(x) = f(x) / g(x)
(f/g)(x) = ( √( x² - 1 ) ) / ( √( x - 1 ) )
Now, rewrite 1 as 1²
(f/g)(x) = ( √( x² - 1² ) ) / ( √( x - 1 ) )
Factor using difference of square
(f/g)(x) = ( √( (x - 1)(x + 1 ) ) / ( √( x - 1 ) )
Combine into a single radical
(f/g)(x) = √( ( (x - 1)(x + 1) ) / ( x - 1 ) )
Now, cancel out the common factors (x-1)
(f/g)(x) = √( (x + 1) / 1 )
(f/g)(x) = √( x + 1)
Therefore, the function operation (f/g)(x) is √( x + 1).
Option A) √( x + 1) is the correct answer.
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In ΔGHI, i = 800 cm, m m∠G=26° and m m∠H=122°. Find the length of h, to the nearest 10th of a centimeter.
Answer:
For the nearest 10th of a centimeter, the value of h is 460 cm
Step-by-step explanation:
To find length of h we can use Law of Sines . The Law states that for a triangle with sides a, b, and c and angles A, B, and C opposite to those sides, the following equation holds:
a/sin A = b/sin B = c/sin C
In ΔGHI, let h be the length of the side opposite angle H, and let i be the length of the side opposite angle I.
Now:
h/sin 122° = i/sin 26°
We can find h by cross multiplying:
h = i * sin 122° / sin 26°
=459.9
Here,
h = 459.9 cm
By taking approximation we get 460 cm
Answer:
This answer is actually 1280.3
Step-by-step explanation:
Find the value of X
Please help! Asap
Answer:
Step-by-step explanation:
Determine whether the statement is true or false. 1. A census is a count of part of a population.. O True O False
The statement regarding the census in this problem is classified as a True statement.
What are the concepts of population and sample?Population: Collection or set of individuals or objects or events whose properties will be studied.
Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.
A Census is when a group of the population is chosen, that is, a sample is chosen, hence the statement for this problem is true.
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Can someone please help me do this
The vertices of the image of triangle ABC are A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4) and C''(x, y) = (- 4, 4).
How to determine the image of a triangle set on Cartesian plane
Any triangle can be generated by three points that are not collinear, in this problem we need to determine the image of a triangle, which is the result of two rigid transformations: (i) Reflection over the y-axis, (ii) Dilation centered at the origin with a scale factor of 2, whose definitions are shown below:
Reflection over the y-axis:
(x, y) → (- x, y)
Dilation centered at the origin with a scale factor of 2:
(x, y) → (2 · x, 2 · y)
If we know that A(x, y) = (3, 4), B(x, y) = (4, 2), C(x, y) = (2, 2), then the image of the vertices are determined below:
Reflection over the y-axis
A'(x, y) = (- 3, 4), B'(x, y) = (- 4, 2), C'(x, y) = (- 2, 2)
Dilation centered at the origin with a scale factor of 2
A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4), C''(x, y) = (- 4, 4)
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Calculate the area of the triangle
find the length of the x
a^2 + b^2 = c^2
12x^2 + b^2 = 13^2
144 + b^2 = 169
b^2 = 25
b = 25; x = 5
use the formula
a = (1/2)(24)(5)
a = (1/2)(120)
area = 60
A car travels 55 mph and passes a truck travelling 50 mph. How long will it take the car to be
more than 23 mi ahead?
Answer:you never asked for like in what minutes or hours?
Step-by-step explanation:
The car, traveling at a speed 5 mph faster than the truck, will take more than 4.6 hours to be more than 23 miles ahead.
Explanation:This question pertains to relative speed. When the car is traveling at 55 mph and the truck at 50 mph, the car is effectively moving away from the truck at (55 mph - 50 mph) = 5 mph. To calculate the time it will take for the car to be more than 23 miles ahead, we can use the formula: Time = Distance/Speed. So the time it would take is Time = 23 miles / 5 mph = 4.6 hours. Therefore, it will take the car more than 4.6 hours to be more than 23 miles ahead.
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An electric clock is stopped by a power failure. What is the probability that the second hand is stopped between the 4 and the 9?
Answer: the answer is 5/12
Y = -6x + 2
Y = -6x - 8
Answer:
Flase, no real numbers (2+-8)
Step-by-step explanation:
First, you conjoined the equations (-6x+2=-6x-8). Then you conjoined the variables first, (-6x+6x=0). Now you have 2=-8, which is not true.
Graph the following points on the coordinate plane. Find the measure of ∠ACB
to the nearest tenth.
A (-3, 2), B (0, 0), C (2, 3)
The measure of angle ∠ACB is 45 degrees
How to find the measure of ∠ACBFrom the question, we have the following parameters that can be used in our computation:
A (-3, 2), B (0, 0), C (2, 3)
The graph is attached
The lines AB and BC are perpendicular lines
This means that
∠B = 90 degrees
Calculate the length AB and BC using
distance = √[(x2 - x1)² + (y2 - y1)²]
So, we have
AB = √[(-3 - 0)² + (2 - 0)²] = √13
BC = √[(0 - 2)² + (0 - 3)²] = √13
The angle C is then calculated as
tan(C) = AB/BC
tan(C) = √13/√13
tan(C) = 1
Take the arctan of both sides
C = 45
Hence, the measure of ∠ACB is 45 degrees
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If 3250 was increased by 46%, the result would be
How many numbers of the form x15y are divisible by 15
Find the lengths of the sides of a triangle if two of the sides are equal, the third side is 1 1/3 cm longer than the others, and its perimeter is 5 2/5 cm. The two equal sides of the triangle are (blank)cm. The third side is (blank) cm.
Answer:
Step-by-step explanation:
Here's a step by step solution with more details:
Let's call the length of the two equal sides of the triangle as x.
The third side, which is 1 1/3 cm longer, will have a length of x + 1 1/3 cm.
The perimeter of the triangle is 5 2/5 cm, so we can write an equation using the lengths of the sides:
x + x + (x + 1 1/3) = 5 2/5
Simplifying the equation:
2x + 1 1/3 = 5 2/5
Subtracting 1 1/3 from both sides:
2x = 4 1/5
Dividing both sides by 2:
x = 2 2/5
So the two equal sides of the triangle are 2 2/5 cm and the third side is 2 2/5 + 1 1/3 = 3 7/15 cm.
Answer:
One equal side = [tex]1\frac{16}{45}[/tex]cm and third side is [tex]2\frac{31}{45}[/tex]cm
Step-by-step explanation:
This is describing an isosceles triangle
1[tex]\frac{1}{3}[/tex] = [tex]\frac{4}{3}[/tex]
5[tex]\frac{2}{5}[/tex] = [tex]\frac{27}{5}[/tex]
Let
x = one of the two equal sides of the triangle
∴ Third side of triangle = [tex]\frac{4}{3} + x[/tex]
Perimeter of a triangle = Sum of all three sides:
[tex]\frac{27}{5}[/tex] [tex]= x + x + (\frac{4}{3} + x)[/tex]
Expand the parenthesis using the Distributive Law and bring all the like terms together:
[tex]=\frac{27}{5} = 2x + \frac{4}{3} + x[/tex]
[tex]= \frac{27}{5} = 3x + \frac{4}{3}[/tex]
[tex]= \frac{27}{5} -\frac{4}{3} = 3x[/tex]
The two denominators of the two fractions have to be manipulated to be made the same:
[tex]= (\frac{3}{3})(\frac{27}{5}) - (\frac{5}{5})(\frac{4}{3}) = 3x[/tex]
[tex]= \frac{81}{15} - \frac{20}{15} = 3x[/tex]
[tex]= \frac{81 - 20}{15} = 3x[/tex]
[tex]= \frac{61}{15} = 3x[/tex]
Cross-multiplication is added:
[tex]= (61)(1) = (15)(3x)[/tex]
[tex]= 61 = 45x[/tex]
Isolate x and make it the subject of the formula:
x = [tex]\frac{61}{45}[/tex]
x = One of the two equal sides = [tex]1\frac{16}{45}[/tex]cm
∴Third side:
= [tex]\frac{61}{45} + \frac{4}{3}[/tex]
= [tex]\frac{61}{45} + (\frac{15}{15})(\frac{4}{3})[/tex]
= [tex]\frac{61}{45} + \frac{60}{45}[/tex]
= [tex]\frac{61 + 60}{45}[/tex]
= [tex]\frac{121}{45}[/tex]
= [tex]2\frac{31}{45}[/tex]cm
Find the average rate of change
Please helppppp
Step-by-step explanation:
please review the attachment. That's the answer.
A positive integer is twice another. The difference of the reciprocals of the two positive integers is frac(1,10). Find the two integers.
The two integers are 5 and 10.
What do you mean by Integers?
An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.
Integer is a Latin word which means 'whole' or 'intact'. This means integers do not include fractions or decimals.
A number is positive if it is greater than zero, so it said to be positive integers
A number is negative if it is less than zero, so it said to be negative integers.
A number line is a visual representation of numbers on a straight line. This line is used for the comparison of numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally.
Given:
Let x be the positive number
2x be the other positive number
Find the first integer
[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]
[tex]\frac{2x - x}{2x^2} = \frac{1}{10}[/tex]
[tex]\frac{x}{2x^2} = \frac{1}{10}[/tex]
[tex]\frac{1}{2x} = \frac{1}{10}[/tex]
2x = 10
x = 5
Therefore, the first positive integer is 5.
Find the other integer
2x = 2(5) = 10
Therefore, the other integer is 10.
To check:
[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]
[tex]\frac{1}{5} - \frac{1}{10} = \frac{1}{10}[/tex]
[tex]\frac{2}{10} - \frac{1}{10} = \frac{1}{10}[/tex]
[tex]\frac{1}{10} = \frac{1}{10}[/tex]
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5x-4>12 or 12x+5<-4
The solution is the union of the solutions from both inequalities. That is, x is either greater than 3.2 or less than -0.75. So, the final solution is: -0.75 < x < 3.2.
What is inequalities?
An inequality is a mathematical statement that represents a comparison between two values, and indicates the relationship of one value being greater than, less than, or equal to the other. It is usually represented using symbols such as ">" (greater than), "<" (less than), ">=" (greater than or equal to), "<=" (less than or equal to), and "≠" (not equal to). For example, the inequality "2x + 3 > 7" expresses that the value of the expression "2x + 3" is greater than 7 for some values of x.
Inequalities are used to describe a range of values that satisfy a certain condition. The solution to an inequality is a set of values that make the inequality true.
To solve the inequality "5x - 4 > 12 or 12x + 5 < -4", we can start by solving each inequality separately and then combining the solutions to find the final solution.
Solving the first inequality: 5x - 4 > 12Adding 4 to both sides, we get 5x > 16
Dividing both sides by 5, we get x > 3.2
So, the solution to this inequality is x > 3.2
Solving the second inequality: 12x + 5 < -4Subtracting 5 from both sides, we get 12x < -9
Dividing both sides by 12, we get x < -0.75
So, the solution to this inequality is x < -0.75
Final solution: Combining the solutions from both inequalities:
Since "or" is used in the inequality, the solution is the union of the solutions from both inequalities. That is, x is either greater than 3.2 or less than -0.75. So, the final solution is: -0.75 < x < 3.2.
So the solution to the inequality "5x - 4 > 12 or 12x + 5 < -4" is -0.75 < x < 3.2.
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cathy invest $3,700 into an account with a 3.75% annual interest rate, making no other deposits or withdrawals.
a) what with cathy’s balance be after 6 years if the interest rate is compounded quarterly?
b) how much more (or less) money would be in cathy’s account if the interest is compounded continuously?
Answer: no
Step-by-step explanation:
