Answer:
[tex]a_1=1\\a_n=a_{n-1}+6[/tex]
Step-by-step explanation:
So to define a recursive equation, you need to find how much each term is increasing or decreasing by. You also need to find the first term. To find the first term you can simply plug in 1 into x: [tex]a_1=6(1)-5 = 6-5 = 1[/tex]. And as you can see the slope is 6, so each term is increasing by 6. So you get the recursive function: [tex]a_1=1\\a_n=a_{n-1}+6[/tex]
which of these ratios are equivalent ratio
1:4 2:8 3:6 7:28
Answer:
1:4
2:8
7:28
Step-by-step explanation:
1:42:8 , 1:47:28, 1:4This container is composed of a right circular cylinder and a right circular cone.
k
Which is closest to the surface area of the container?
C
1243 ft²
1696 ft²
754 ft²
490 ft²
24 ft-
13 ft
10 ft
The closest surface area of the container is: 1,696 ft².
What is the Volume of a Cone and a Cylinder?Curved surface area of a cone = πrl
Surface of a cylinder = 2πr(h + r)
Surface area of the container = Curved surface area of a cone + Surface of a cylinder - area of circular base
= πrl + 2πr(h + r) - πr²
r = 24/2 = 12 ft
l = 13 ft
h = 10 ft
Plug in the values
Surface area of the container = π(12)(13) + 2π×12(10 + 12) - π(12²) = 1,696.5 ft².
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Which of the following number lines represents the solution set of x/-1 >or= -4?
The number line that shows that x ≥ -4 is; Option B
How to Interpret Number Lines?
We want to find the number line that represents x ≥ -4
Now, for greater than sign, the number line would point to the right while for less than sign the number line would point to the left.
Now, for greater than or equal to sign the dot would be shaded and as such looking at the correct number line would be that in Option B.
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PLEASE PASS IF YOU DON'T KNOW. find the 6th derivative of cot²3x. WILL MARK BRAINLIEST FOR THE RIGHT ANSWER
Answer:
Find the derivative using the chain and power rules.
-6csc^(2 )(x^(3)-2x^(2))(3x^(2)-4x)
Step-by-step explanation:
Find sin 0
a. 8/15
b. 15/8
c. 15/17
D 8/17
Answer:
C
Step-by-step explanation:
first you need to memorize
SOH CAH TOA
IT means
Sine =opposite/hipotenuse
Cosine = adjecent/hipotenuse
tangent = opposite/adjecent
in this case, we need to find sine
so it's SOH
opposite of theta Θ is 15
and it's hipotenuse , we don't know yet. so need to find it by using Pythagorean theorem
let it be x
x =√ 15²+ 8²
=√ 225+ 64
=√289
= 17
so the answer is 15/17
Class A has 30 pupils and class B has 26 pupils.
Both classes sit the same maths test.
The mean score for class A is 70.
The mean score for both classes is 76.
What is the mean score (rounded to 2 DP) in the maths test for class B?
The mean score of class B is 82. 92
How to determine the mean scoreClass A = 30 pupils
Class B = 26 pupils
Mean score for class A = 70
Mean score of class B = unknown
Total mean score = 76
We have, [tex]\frac{(76 *( 30 + 26) - 70 *30) }{26}[/tex]
Then simply,
Calculate the sum or difference between the classes = [tex]\frac{76 * 56 - 70 * 30}{26}[/tex]
Calculate the product or quotient of the classes = [tex]\frac{4256 - 70 * 30}{26}[/tex]
= [tex]\frac{4256 - 2100}{26}[/tex]
= [tex]\frac{2156}{26}[/tex]
= [tex]\frac{1078}{13}[/tex]
= [tex]82. 92[/tex]
Thus, the mean score of class B is 82. 92
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Please help me answer all of these questions. Its a chance to get 100 points please help me. Whoever does all of them I will mark brainlest. :) Please help.
Answer:
Step-by-step explanation:
Well since the questions are related to geometric series I'm assuming the reasoning for 0.99999.... = 1, is going to be a geometric series in this instance. All though there are other ways to prove this.
1.
a. So if you think about it, 0.999 can be represented as: [tex]\frac{9}{10} + \frac{9}{100} + \frac{9}{1000}....[/tex] and so on. This is a geometric series. The geometric sequence explicit equation can be determined by realizing each term is the previous term multiplied by 1/10, since the numerator is staying the same, but the denominator is being multiplied by 1/10. So the explicit equation for the sequence is: [tex]a_n=\frac{9}{10}*(\frac{1}{10})^{n-1}[/tex]. The sum of an infinite series can be defined as: [tex]S_\infty=\frac{a_1}{1-r}[/tex] when |r| <1 , which in this case it is. So plugging the values into the equation you get: [tex]S_\infty=\frac{\frac{9}{10}}{1-0.10}=\frac{\frac{9}{10}}{\frac{9}{10}} = 1[/tex]. So the sum of this infinite series that represents [tex]0.\overline{9}[/tex] is equal to 1.
b. Another repeating decimal can easily be determined using the repeating decimal 0.9. If you multiply both sides by 10, you'll get: [tex]9.\overline9 = 10[/tex].
2.
a. So this is an arithmetic sequence and it appears to be increasing by 5, with the first term being 3. So an explicit formula can be written using these two values: [tex]a_n=3+5(n-1)[/tex] which can also be simplified by distributing the 5, to get: [tex]a_n=3+5n-5=5n-2[/tex]. A recursive rule can also be easily defined using these two values, it's simply: [tex]a_n=a_{n-1}+5\\a_1=3[/tex]
b. The 1000th term can be evaluated using the explicit formula by plugging in 1000 in as n: [tex]a_{1000} =5(1000)-2=5000-2=4998[/tex]
c. The explicit formula, since it's much easier to evaluate values, by simply plugging in 1000 as n
d. The issue with a recursive rule, is you need to know all previous values, to determine [tex]a_n[/tex], because it's doing some operation on the previous value, except to know that previous value, you need the previous previous value, and so on. This is an issue with much larger numbers, which is why the explicit formula is generally more better.
Riddle-if you solve it i will delete your answer and you have to post the riddle. Riddle-you enter a room. 2 dogs, 4 horses, 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground?.
Answer:
10
Step-by-step explanation:
2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.
The total number of legs in the room would be 10.
How to identify how many legs are on the floor of the room?From the given information, it can be inferred that none of the legs of the animals is on the floor of the room.
It is given that 2 dogs, 4 horses, 1 giraffe, and a duck are lying on the bed. 3 chickens are flying over a chair.
The legs of the bed and the chair do.
So we can say that the chair and the bed each have four legs.
so that would be two more legs.
In total we have:
4 + 4 + 2 = 10.
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The following three shapes are based only on squares, semicircles, and quarter circles.
Find the perimeter and the area of each shaded part.
The perimeter of the shaded part is: 25.1 cm.
The area of the shaded part is: 36.6 cm².
How to Find the Perimeter and Area of the Shaded Part?Area = Area of square - 2(area of square - area of quarter circle) = s² - 2(s² - 1/4πr²).
Parameters given are:
s = 8 cmr = 8 cmPlug in the values into the equation
Area = 8² - 2(8² - 1/4π(8²)).
Area = 64 - 2(64 - 50.3)
Area = 36.6 cm²
Perimeter = 2(perimeter of quarter circle) = 2(1/4(2πr)) = 2(1/4(2π8)) = 25.1 cm
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For the following exercises, determine whether the relation is a function.
1. {(a, b), (c, d), (e, d)}
Answer:
The given relation [tex]$\{(a, b),(c, d),(e, d)\}$[/tex] is a function.
Step-by-step explanation:
A relation [tex]$\{(a, b),(c, d),(e, d)\}$[/tex] is given.
It is required to determine whether the given relation is a function.
To determine whether the given function is a relation, identify the domain and range and then check whether the given relation is a function.
Step 1 of 1
The given relation is {(a, b),(c, d),(e, d)}.
The set of the first components of each ordered pair is called the domain.
From the relation, the domain is {a, c, e}.
The set of the second components of each ordered the range.
From the relation, the range is {b, d, d}.
The given relation is a function. But it is not a one-to-one function.
How many real solutions does this system of equations have? x² + y² = 25 and x-3y=15
[tex]x - 3y = 15 \\ x = 15 + 3y[/tex]
[tex](15 + 3y) {}^{2} + y {}^{2} = 25[/tex]
[tex]225 + 90y + 9y {}^{2} + y {}^{2} = 25[/tex]
[tex]10y {}^{2} + 90y + 200 = 0[/tex]
[tex]y {}^{2} + 9y + 20 = 0[/tex]
[tex](y + 4)(y + 5) = 0[/tex]
[tex]y = - 4 \: \: \: \: \: \: y = - 5[/tex]
[tex]for \: y= - 4 \\ x = 15 + 3( - 4) = 15 - 12 = 3[/tex]
[tex]for \: y = - 5 \\ x = 15 + 3( - 5) = 15 - 15 = 0[/tex]
104, 137, 154, 131, x; mean= 130
Hello!
The mean is the average of the terms.
⇒ Mean = Sum of terms / Number of terms
⇒ 130 = 104 + 137 + 154 + 131 + x / 5
⇒ x + 526 = 650
⇒ x = 124
∴ The missing number is 124.
Help me to solve this question
Answer:
[tex]\left \{ {{\theta_1=\frac{\pi }{4} } \atop {\theta_2=\frac{3\pi }{4} }} \right. .[/tex]
Step-by-step explanation:
[tex]2*cos^2\theta-1=0\ \ \ \ (0^0\leq \theta\leq 360^0)\ \ \ \ \ \theta=?\\2*cos^2\theta-(sin^2\theta+cos^2\theta)=0\\2*cos^2\theta-sin^2\theta-cos^2\theta=0\\cos^2\theta-sin^2\theta=0\\cos2\theta=0\\0^0\leq \theta\leq 360^0\ \ \ \ \Rightarrow\\\left \{ {{2\theta=\frac{\pi }{2}\ |:2 } \atop {2\theta=\frac{3\pi }{2}\ |:2 }} \right. \ \ \ \ \left \{ {{\theta_1=\frac{\pi }{4} } \atop {\theta_2=\frac{3\pi }{4} }} \right. .[/tex]
Good luck and have a nice day!
The area of a rectangular pool is (x 2 + 17x + 72) square meters. There is a 3-meter-wide concrete
walkway around the pool. Write expressions to represent the dimensions of the outside border of the
walkway. (Lesson 8.1)
Step-by-step explanation:
the area is
(x² + 17x + 72) m²
it is the result of the usual
length × width
calculation.
length = x + g
width = x + h
length × width = x² + gx + hx + ab = x² + (g+h)x + gh =
= x² + 17x + 72
g + h = 17
gh = 72
just by looking at it that gives us 9 and 8 as g and h.
FYI - formally to calculate them we can say
g = 17 - h
(17 - h)h = 72
17h - h² = 72
h² - 17h + 72 = 0
the solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = h
a = 1
b = -17
c = 72
h = (17 ± sqrt(17² - 4×1×72))/(2×1) =
= (17 ± sqrt(289 - 288))/2 = (17 ± 1)/2
h1 = (17 + 1)/2 = 18/2 = 9
h2 = (17 - 1)/2 = 16/2 = 8
as we can see
g = 17 - h
if we say h = 9, then g = 8.
if we say h = 8, then g = 9.
so, these are our solutions.
we simply pick that length is longer than width, so, g = 9, h = 8.
the area including the walkway is then
(length + 3)(width + 3) =
= (x + 9 + 3)(x + 8 + 3) = (x + 12)(x + 11) m²
and the dimensions incl. the walkway are
length = x + 9 + 3 = x + 12
width = x + 8 + 3 = x + 11
A student submitted the following work that is not correct. Can you find the mistake?
Explain the mistake the student made.
Simplify (assuming all variables are positive): √32x³y²z7
Step 1: √8.4.x².xy².26. z
Step 2: 2xyz³ √8xz
Step-by-step explanation:
so you have the equation: [tex]\sqrt{32x^3y^2z^7}[/tex] which I'm assuming is what you meant to input. and the next step I'm assuming you wrote: [tex]\sqrt{8} * \sqrt{4} * \sqrt{x^2} * \sqrt{y^2} * \sqrt{x} * \sqrt{z^6} * \sqrt{z}[/tex], although I'm not 100% sure, I'm basing this assumption off of step 3. Anyways this will simplify to [tex]2xyz^3\sqrt{8xz}[/tex] which is correct kind of, but since they were asked to FULLY SIMPLIFY, then it's not completely done. This is because 8 has a factor of 4 which is a perfect square. This is because in step 1, the student rewrote 32 as sqrt(8) * sqrt(4) instead of writing it as sqrt(2) * sqrt(16) which is the greatest factor of 32 that is a perfect square. So they could've either done that in step 1, or they could've realized in step 2, that they can further simplify sqrt(8) and then have a step 3 showing that.
Enter the correct answer in the box.
What is the inverse of function f?
f(x)=-7x-4
Answer:
The inverse is -1/7(x+4)
Step-by-step explanation:
We have the function
y = -7x-4
To find the inverse, exchange x and y
x = -7y -4
Solve for y
Add 4 to each side
x+4 = -7y -4+4
x+4 = -7y
Divide each side by -7
-1/7(x+4) = -7y/-7
-1/7(x+4) = y
The inverse is -1/7(x+4)
Which expression is the factorization of x2 + 10x + 21?
(x + 3)(x + 7)
(x + 4)(x + 6)
(x + 6)(x + 15)
(x + 7)(x + 14)\
Equation: x² + 10x + 21
Step 1: Find two numbers that can add up to 10 and be multiplied to 21. We have: 7 & 3, in the sense that 7+3=10, and 7×3=21. Replacing 10 with 7+3, the equation is now → x² + 7x + 3x + 21
Step 2: Get the new equation bracketed → (x² + 7x) (+3x + 21)
Step 3: Use 'x' in the equation. For the first part, we have 'x'. x² = x × x so, bring out one x out side the bracket, divide 7x by = 7 → x (x +7). Do the same for the second part by dividing 21 by 3 = 7, and then bringing out 3 from the bracket → 3 (x + 7).
Bringing everything together, we have: x(x+7) +3(x+7) → (x+3) (x+7)
Final answer:(x+3) (x+7)
Answer:
A. (x + 3)(x + 7)
Step-by-step explanation:
Got it correct… You’re welcome
3. If the perimeter of an equilateral triangle is 36 ft, what is the length of one side?
O 18 ft
O 6 ft
12 ft
9 ft
Answer:
The length of one side is 12ft
Step-by-step explanation:
The triangle is equilateral so all the sides are the same length.
So you are simply going to divide 36ft by the 3 sides.
36ft/3 = 12ft
In the given figure, ΔABC is a right triangle.
The figure shows the right-angle triangle ABC. B is the length of AC and a is the height of BC and c is the base of AB.
What is true about ΔABC?
A.
sin(A) = cos(C) and cos(A) = sin(C)
B.
sin(A) = sin(C) and cos(A) = cos(C)
C.
sin(A) = cos(A) and sin(C) = cos(C)
D.
sin(A) = cos(C) and cos(A) = cos(C)
The true statement about right-angle triangle ABC is that: A. sin(A) = cos(C) and cos(A) = sin(C).
How to apply basic trigonometry?In order to determine the angles, we would apply basic trigonometry. From the diagram of the right-angled triangle shown below, we can deduce the following parameters:
Angle (θ) = 45°.Opposite (Opp) side = a.Hypotenuse (Hyp) = c.Adjacent (Adj) side = b.By applying the basic trigonometry functions, we have:
sin(A) = Opp/Hyp = a/c.
sin(C) = Opp/Hyp = c/b.
cos(A) = Adj/Hyp = c/b.
cos(C) = Adj/Hyp = a/c.
From the above, we can logically deduce that sin(A) is equal to cos(C) and cos(A) is equal to sin(C).
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Answer:
Step-by-step explanation:
The true statement about right-angle triangle ABC is that: A. sin(A) = cos(C) and cos(A) = sin(C).
How to apply basic trigonometry?
In order to determine the angles, we would apply basic trigonometry. From the diagram of the right-angled triangle shown below, we can deduce the following parameters:
Angle (θ) = 45°.
Opposite (Opp) side = a.
Hypotenuse (Hyp) = c.
Adjacent (Adj) side = b.
By applying the basic trigonometry functions, we have:
sin(A) = Opp/Hyp = a/c.
sin(C) = Opp/Hyp = c/b.
cos(A) = Adj/Hyp = c/b.
cos(C) = Adj/Hyp = a/c.
From the above, we can logically deduce that sin(A) is equal to cos(C) and cos(A) is equal to sin(C).
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Identify all of the root(s) of g(x) = (x2 3x - 4)(x2 - 4x 29). -1 1 -4 4 2 5i 2 - 5i -2 10i -2 - 10i
The roots are (x + 1), (x - 4), (2 + 5i), and (2 - 5i).
g(x) = (x2 - 3x - 4)(x2 - 4x + 29)
Let us first consider x^2 - 3x - 4
By splitting the middle term
= x^2 + 1x - 4x - 4
= x(x + 1) - 4(x + 1)
= (x + 1)(x - 4)
Now let us consider x^2 - 4x + 29
First group the terms with variable on LHS and move the constant on the other side
x^2 - 4x = -29
Add 4 on both sides
x^2 - 4x + 4 = -29 + 4
x^2 - 4x + 4 = -25
It can be written as perfect squares
(x - 2)^2 = -25
We know that
i =√1
Take square root on both sides
x - 2 = ± 5i
x = 2 ± 5i
So we get,
x = 2 + 5i and x = 2 - 5i
g(x) = (x + 1)(x - 4)(2 + 5i)(2 - 5i)
A square root of a number is a price that, whilst extended by means of itself, offers variety. instance: four × four = 16, so a square root of 16 is four. The word that (−four) × (−four) = 16 too, so −four is likewise a square root of sixteen. The symbol is √ usually way the wonderful rectangular root. example: √36 = 6 (because 6 x 6 = 36).
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please help me find the solution
Answer:
22
Step-by-step explanation:
BD bisects <ABC, this means the half-line divided the angle into two equal parts.
If m<ABC is equal to 44 then m<ABD is
44/2 = 22
E represents a number. For example, if E is 5, EE equals 55 and 4E equals 45. If 1E x E = 9E, what number should be in the place of E?
Answer:
E represents a number, for this question we need to keep in mind that the product of 1E and E must end in E.
E must be 6.
E = 6
Step-by-step explanation:
16 * 6 = 96
Which linear function represents the line given by the point-slope equation y 1 = –3(x – 5)? f(x) = –3x – 6 f(x) = –3x – 4 f(x) = –3x 16 f(x) = –3x 14
The linear function which represents the line given by the point slope equation y+1=-3(x-5) is f(x) =-3x+14 which is option D.
Given the equation y+1=-3(x-5) and we have to find the equation of line that represents this equation.
An equation is a relationship between two or more variables which are expressed in equal to form. Equation of two variables looks like ax+ by=c. It is solved in order to get the values of variables. Linear function is like equation whose graph shows a straight line.
We have to just find out the value of y in terms of x to find the linear function which can be done as under:
y+1=-3x(x-5)
y+1=-3x+15
y=-3x-1+15
y=-3x+14
Hence y=-3x+14 is the linear equation which represents the point slope equation y+1=-3(x-5).
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Answer:
So the shorter version of what the guy above me is saying is that it is:
[tex]f(x) = -3x + 14[/tex] or
D
Step-by-step explanation:
I got it right on the test.
Determine whether you would use the Law of Sines or the Law of Cosines to solve each triangle. Do not solve the triangle.
A triangle is a three-edged polygon with three vertices. Only the law of Sine can be applied to solve the triangle.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The sum of all three angles can be written as,
118° + 22° + x = 180°
x = 40°
For the sine rule to be applicable, two angles and a side or an angle and two sides are needed. Therefore, the law of Sine can be applied to solve the triangle.
For the cosine rule to be applicable, two sides and an angle between them is needed to be known, hence, the law of cosine can not be applied.
Hence, Only the law of Sine can be applied to solve the triangle.
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Please help ASAP
Please help ASAP
Please help ASAP
Please help ASAP
Answer:
y-intercept: (0,2)
x-intercepts: (-4,0), (2,0)
Step-by-step explanation:
y-intercepts are found where the graph intersects the y-axis
same with x-intercepts, are found where the graph intersects the x-axis
The y-intercept is 2, and the x-intercept is -4 and 2 where the line segment crosses the y-axis and x-axis.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Where the line segment crosses the y-axis is the y-intercept,
And where the line segment crosses the x-axis is the x-intercept,
From the graph,
y-intercept is at (0,2)
x-intercepts is at (-4,0), (2,0)
Thus, the y-intercept is 2, and the x-intercept is -4 and 2 where the line segment crosses the y-axis and x-axis.
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The sum of three numbers is 131. the second of three numbers is seven more than twice the first. the third number is 12 less than the first. what equation can be used to solve the problem? x x x = 131 x (x 7) (x – 12) = 131 x (2x 7) (x – 12) = 131 x (2x 7) – 12 = 131
Answer:
C. x + (2x + 7) + (x - 12) = 131
Step-by-step explanation:
Let the first number be x.
Then, given:
The second number is 2x + 7The third number is x - 12Since their sum is 131, we get the following equation:
Sum of x, (2x + 7) and (x - 12) is 131,or
x + (2x + 7) + (x - 12) = 131This is matching the answer choice C.
On a coordinate plane, quadrilateral J K L M with diagonals is shown. Point J is at (4, 5), point K is at (5, 1), point L is at (1, 2), and point M is at (1, 5).
Which statement proves that quadrilateral JKLM is a kite?
∠M is a right angle and MK bisects ∠LMJ.
LM = JM = 3 and JK = LK = StartRoot 17 EndRoot.
MK intersects LJ at its midpoint.
The slope of MK is –1 and the slope of LJ is 1.
The statement that proves that that quadrilateral JKLM is a kite is: (Option B) which indicates that:
LM = MJ = 3; a
JK = KL = √17
What is the explanation for the above?We know the following:
J = (4,5)
K = (5,1)
L = (1,2)
M = (1, 5)
What is the proof?We must commence by computing the length of the sides of the quadrilateral using:
D = [tex]\sqrt{((x1-x2)^{2} + (y1 -y2)^{2} }[/tex]
JK = [tex]\sqrt{(4-5)^{2} + (5-1)^{2} }[/tex]
= [tex]\sqrt{17}[/tex]
KL = [tex]\sqrt{(5-1)^{2} + (1-2)^{2} }[/tex]
= [tex]\sqrt{17}[/tex]
LM = [tex]\sqrt{(1-1)^{2} + (5-5)^{2} }[/tex]
= [tex]\sqrt{9}[/tex]
= 3
MJ = [tex]\sqrt{(1-4)^{2} + (5-5)^{2} }[/tex]
= [tex]\sqrt{9}[/tex]
= 3
From the above, it is clear that
LM = MJ = 3; and
JK = KL = [tex]\sqrt{17}[/tex]
QED
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Answer: B
Step-by-step explanation:
The time that passes between the time you see lightning and you hear the thunder depends on your distance from the lightning. With each km from the lightning 3 seconds pass.
a) Make a table of values for distances from 0 to 5 km.
b) Graph this relation. State whether it is a linear or non-linear relation.
c) Using your graphed relation, how much time passes before you hear lightning that occurs 4.5 km away?
d) Using your graphed relation, how far away are you if you hear the thunder in 1.5 seconds?
When the lightning occurs 4.5 km away then we will hear after 13.5 seconds and if we hear after 1.5 seconds then we are 0.5 km away from lightning.
Given With each km from the lightning 3 seconds passes.
a) The table of values for distances from 0 to 5 km.
Distances Time
0 0
1 3
2 6
3 9
4 12
5 15
b) The graph of lightning is a linear relation because it is increasing constantly by 3 seconds. f(x)=3x
c) When distance =1 , the time be 3 seconds
when distance =4.5 , the time=3*4.5
=13.5 seconds.
d) When time is 3 seconds = 1km
when time =1.5 seconds , the distance be 1/2=0.5 km.
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Mercedes receives a $25 gift card for downloading music and wants to determine how many songs she can purchase. each downloaded song costs $1.29. write and solve an inequality to determine m, the number of songs mercedes can purchase. what is the approximate solution to the inequality? round to the nearest whole number.
The solution to the inequality: [tex]1.29m\leq 25[/tex] is m=19.
What is inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Value of gift card=$25
Cost of each song=$1.29
Let m be the number of songs purchased.
Then, the required inequality is as follows:
[tex]1.29m\leq 25\\m\leq \frac{25}{1.29}\\ m\leq 19.38[/tex]
The value of m rounded to the nearest whole number is 19.
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What are the domain and range of the exponential function below?
F(x) = 4x + 3
A. Domain: All real numbers Range: All real numbers greater than 0
B. Domain: All real numbers greater than 0 Range: All real numbers greater than 3
C. Domain: All real numbers greater than 0 Range: All real numbers greater than 0
D. Domain: All real numbers Range: All real numbers greater than 3
The domain and the range of the function are all set of real numbers
How to determine the domain and the range?The function is given as:
f(x) = 4x + 3
The above function is a linear function
Linear functions have a domain and a range of all set of real numbers
Hence, the domain and the range of the function are all set of real numbers
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