Answer:
t = 0.5 seconds
Step-by-step explanation:
Given formula:
[tex]h=-16t^2+s[/tex]
where:
h = height above the ground (in feet)t = time after dropping the treat (in seconds)Dan drops the treat 5 feet above the ground.
Therefore, when t = 0, h = 5 ft.
To find the value of s, substitute these values into the given formula:
[tex]\implies -16(0)^2+s=5[/tex]
[tex]\implies s=5[/tex]
Therefore:
[tex]h=-16t^2+5[/tex]
To calculate how long the treat falls before Lola catches it, substitute h = 1.5 into the formula:
[tex]\implies -16t^2+5=1.5[/tex]
[tex]\implies -16t^2=-3.5[/tex]
[tex]\implies t^2=0.21875[/tex]
[tex]\implies t=\sqrt{0.21875}[/tex]
[tex]\implies t=\pm0.467707173...[/tex]
[tex]\implies t=\pm0.5\; \; \sf (nearest\;tenth)[/tex]
As time is positive, t = 0.5 seconds (nearest tenth) only.
Therefore, it took 0.5 seconds for Lola to catch the treat after it fell.
To prevent deer from running across highways, researchers are investigating sound-emitting devices that would frighten deer before they reach the highway. As part of the investigation, the researchers set up 20 devices along a two-mile stretch of road. When a deer approached a device, the device would activate and emit a sound. The researchers recorded whether the deer moved toward the highway (positive response), away from the highway (negative response), or did not move (neutral response).
The researchers kept the loudness of the sound constant at 60 decibels. However, they varied the pitch of the sound. There were 6 treatment levels, all measured in kilohertz (kHz): 0, 0.28, 1, 8, 15, and 28. The order of the treatments was randomly assigned.
(a) The control in the experiment was 0 kHz, or no sound. What information is gained by using the control with no sound that could not be obtained if no control were used?
(b)(i) What is one advantage to keeping the loudness at a constant 60 decibels for all treatments?
(b)(ii) What is one disadvantage to keeping the loudness at a constant 60 decibels for all treatments?
(c) The results of the experiment are shown in the following bar chart.
Based on the results, would you recommend using a sound-emitting device to keep deer from running across highways? Explain your answer.
Answer: a) The control in the experiment, 0 kHz, or no sound, serves as a baseline against which to compare the other treatments. By using the control with no sound, researchers can determine whether the deer's response to the sound-emitting devices is due to the sound itself or some other factor. Without the control, it would be unclear what caused any differences in the deer's responses to the different sound treatments.
(b)(i) One advantage to keeping the loudness at a constant 60 decibels for all treatments is that it allows researchers to directly compare the deer's responses to the different sound pitches without the added variable of loudness.
(b)(ii) One disadvantage to keeping the loudness at a constant 60 decibels for all treatments is that loudness may also play a role in deer's response. So, it would be unclear if the different in deer's responses are due to sound frequency only or also caused by sound loudness
(c) Based on the results shown in the bar chart, it can be seen that the deer's response to the sound-emitting devices varies depending on the pitch of the sound. At lower pitches, around 0.28 kHz, the deer's response is more likely to be negative or neutral, indicating that they move away from or don't move towards the highway. At higher pitches, around 15 kHz, the deer's response is more likely to be positive, indicating that they move towards the highway. It suggests that the frequency of sound has an impact on the deer's response. So, based on this data, we cannot recommend using a sound-emitting device to keep deer from running across highways without further research on the optimal frequency and loudness that should be used to make sure that it is effective and safe for the deer.
Step-by-step explanation:
The sound-emitting device may have both advantages and disadvantages depending on the pitch. More research is necessary to find the optimal frequency and volume for the device to be effective and safe.
Explanation:Based on the results of the experiment, it would not be advisable to use a sound-emitting device to prevent deer from running across highways without further research. The experiment showed that the deer's response varied depending on the pitch of the sound. Although the device showed some advantages, such as moving deer away from the highway at lower pitches, it also presented potential disadvantages. At higher pitches, the deer had a tendency to move towards the highway, which could increase the risk of accidents. More research would be needed to determine the optimal frequency and volume to use for the device to be both effective and safe for the deer.
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What are the origins of matrices?
Answer: The origins of matrices can be traced back to the 18th century, with the work of mathematicians such as Gabriel Cramer, Leonhard Euler, and Joseph-Louis Lagrange. These mathematicians developed the idea of using arrays of numbers to represent systems of linear equations, which led to the development of the concept of matrices.
The term "matrix" itself was first used by James Joseph Sylvester in 1850, although it had been in use informally for some time before then. In 1858, the English mathematician Arthur Cayley first published a systematic theory of matrices, which further developed the field.
Matrix theory was primarily used in the early days to solve systems of linear equations, but it soon found applications in areas such as linear algebra, multivariate statistics, and even quantum mechanics.
In summary, the origins of matrices can be traced back to the 18th century as an idea to represent systems of linear equations, which developed over time with contributions of many mathematicians over the centuries, and now it plays an important role in many field of mathematics and science.
Step-by-step explanation:
Any help please, - What is the area for this?
Answer:
109.18
Step-by-step explanation:
Subtract 13.4-7.2 then solve the triangle (base x height) getting 32.86. Next solve the rectangle getting 76.32. Then add all of it concluding in 109.18.
Name the image of p (9, 1.5) after being translated along the vector <3, -0.5>
The image for P(9, 1.5) after Translation is P'( 12, 1).
What is Translation?Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.
For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .
Given:
P(9, 1.5) with Translating Vector (3, -0.5).
So, Applying the Translation we get
P(9 + 3, 1.5 + (-0.5))
= P(12 , 1.5- 0.5)
= P(12, 1)
hence, the image is P'( 12, 1).
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A line passes through the point (-10,1) and has a slope of 3/2. Write an equation in point-slope form for this line.
The line passes through the point (-10,1) and has a slope of 3/20 has the equation as: y - 1 = 3/2 (x + 10)
How to write the equation of the lineThe general form of a linear equation is y - y₁ = m (x - x₁).
It draws attention to the line's slope and one of the line's points (that is not the y-intercept)
The point slope formula is given by y - y₁ = m (x - x₁), where:
y = output value
y₁= the given y coordinate point
m = slope
x = input value
x₁ = the given x coordinate
substituting the point (-10,1) and slope 3/2
y - y₁ = m (x - x₁)
y - 1 = 3/2 (x + 10)
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whats the answer??
its math related
Answer:
30
Step-by-step explanation:
x + 2x + 3x = 180 (the total angle of a triangle)
6x = 180
x = 180 : 6 = 30
Answer:
x = 30°
2x = 60°
3x = 90°
Step-by-step explanation:
Internal angles of a triangle sum 180°
Then:
x + 2x +3x = 180
6x = 180
x = 180/6
x = 30°
2x = 60°
3x = 90°
a) calculer: f(1,5); f(2,5); f(2)
Answer:
Step-by-step explanation:
you should give the function, if i haven't it, how can i help you.
i can give u some tips, put 1.5, 2.5, 2 in function respectively. then calculate them, u will get the answer.
PLEASE HURRY BE FAST
A fishing map is laid out on a coordinate plane with each unit equal to 1 mile. The boat is launched from the point (−3, 0) and goes to point (−3, 3) to fish. From there, the boat travels to (0, 0) to fish and then goes back to the launch point.
Determine the total number of miles traveled. Round to the nearest mile.
3 miles
6 miles
10 miles
24 miles
Answer:
24 miles
Step-by-step explanation:
each distance between points is 6.
6+6+6+6=24 miles
Rose bushes are planted in a line on both sides of a path. The distance between the
bushes is 2 meters. What is the largest number of rose bushes that can be planted if
the path is 20 meters long?
Math I need help I’m very confused and I don’t understand I’m sorry it’s hard to see the photo I need answers.
For each of the following , find
the coordinates of a or b and : the x-intercept, the coordinates of C: the y-intercept the axis of symmetry,
the coordinates of the vertex,
The maximum or minimum value,
The graph's X-intercepts are ((9+55)/2,0) and ((955)/2,0), and its Y-intercept is (0,13).
what is coordinates ?When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.
given
Axis of symmetry:
x=9 /2
Vertex (minimum point): (9/2,−55/2)
X-intercepts: ((9+√55)/2,0) and ((9−√55)/2,0)
Y-intercept: (0,13)
The graph's X-intercepts are ((9+55)/2,0) and ((955)/2,0), and its Y-intercept is (0,13).
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Which of the following statements must be true based on the diagram below?
Select all that apply. (Diagram is not to scale.)
The following statements are true based on the diagram below
I is a vertex of right angleK is a vertex of right angleWhat is vertex?When two or more curves, lines, or edges come together, it is called a vertex (plural: vertices or vertexes) in geometry. As a result of this definition, polygonal and polyhedral corners as well as the intersection of two lines to form an angle are referred to as vertices.
The vertex of an angle is the point at which two rays start or meet, where two line segments join or meet, where two lines intersect (cross), or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location.
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Find the range of values of k for which the equation 4x² + 12x + k = 0 has no real roots.
Hello there!
Answer:
[tex](9, +\infty)[/tex]
Step-by-step explanation:
It has no real roots only if
[tex] \sqrt{b {}^{2} - 4ac } [/tex]
has no roots. That means that b² - 4ac is smaller than 0:
[tex]b {}^{2} - 4ac < 0 \\ 12 {}^{2} - 4 \times 4 \times k < 0 \\ 144 - 16k < 0 \\ 144 - 144 - 16k < - 144 \\ - 16k < - 144 \\ k > 9 \\ k \: \: \: in \: \: \: (9, +\infty)[/tex]
we can approach this from the standpoint of the discriminant, if the discriminant is negative then we only get complex roots or namely "imaginary" solutions or values, well, let's check before that happens, when the discriminant is 0.
[tex]\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{4}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{+k} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases}[/tex]
[tex]0=(12)^2 - 4(4)(k)\implies 0=144-16k\implies 16k=144 \\\\\\ k=\cfrac{144}{16}\implies k=9\hspace{5em} \stackrel{if~k > 9\textit{, then we land on negative territory}}{{\Large \begin{array}{llll} k > 9 \end{array}}}[/tex]
can anyone help me out with this question
Answer:
[tex] \sf \: b) \: 45[/tex]
Step-by-step explanation:
The values given are,
→ u = 7
→ d = 10
→ e = 3.2
Now the expression is,
→ 15(d - u)
Evaluating the expression,
→ 15(d - u)
→ 15(10 - 7)
→ 15 × 3
→ 45
Hence, option (b) is correct.
Answer:45
Step-by-step explanation:
15(10-7)
15(3)
multiply and get 45
ABC is an equilateral triangle. A circle with radius 1 is tangent to the line
AB at the point B and to the line AC at point C. What is the side length of
ABC? Show your work?
The equilateral triangle ABC have a side length of 2 units of the radius length of the circle tangent to the line AB.
How to evaluate for the side length of the triangleAn equilateral triangle have all its side lengths equal so;
line AB = line BC = line AC
At points B and C where the lines AB and AC are tangent to the circle is the a side length BC of the equilateral triangle
Line BC form the diameter of the circle which is 2 radius of the circle so;
line BC = 2 × radius of the circle
line BC = 2 × 1
line BC = 2
Therefore, the side length of the equilateral triangle is 2 units of the radius of the circle tangent at point B and C.
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You buy 4 pounds of steak at Store A for $25.50. Your friend buys 6 pounds
of steak at Store B for $40.25. Which store is cheaper?
O No answer text provided.
O They're the same
O Store A
O Store B
Question 3
Answer: To determine which store has the cheaper steak, you need to compare the price per pound of steak at each store. To do this, divide the total price by the number of pounds of steak at each store.
At Store A, the price per pound of steak is $6.38 because 25.50 / 4 = <<25.50/4=6.375>>6.375.
At Store B, the price per pound of steak is $6.71 because 40.25 / 6 = <<40.25/6=6.708>>6.708.
Therefore, Store A is cheaper because it has a lower price per pound of steak. The correct answer is Store A.
Step-by-step explanation:
1.) The acceleration of a particle moving along the x-axis at time t is given by a(t) = 6t-2. If the position is 10 when
t= 1, then which of the following could be the function for position x(t) = ?
The function for position x(t) could be x(t) = 3t^2 - 2t + 10.
What is function?In mathematics, a function is a relation between two sets that assigns to each element of the first set exactly one element of the second set. In other words, it is a rule that describes how one set of values is related to another set of values. Functions are used to model real-world scenarios and to solve mathematical problems. Examples of functions include linear equations, polynomials, and trigonometric functions.
This is determined by using the equation x'(t) = a(t). Differentiating both sides of the equation, we get x'(t) = 6t - 2. Integrating this equation, we get x(t) = 3t^2 - 2t + C, where C is the constant of integration. Since x(1) = 10, we can substitute this value into the equation and solve for the constant of integration. Therefore, we get x(t) = 3t^2 - 2t + 10.
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Please help me please
WHAT IS THE RECIPOCAL OF 6/5
Answer: 5/6
Step-by-step explanation:
The reciprocal of a number is 1 divided by that number. The reciprocal of 6/5 is 5/6.
Answer:
5/6
Step-by-step explanation:
Well to find a fraction's reciprocal all you need is to flop it like this
6/5 => 5/6
so 5 takes the place of 6 and 6 takes the place of 5
that's how 6/5 turns into 5/6
hence, the reciprocal is 5/6 .Please help with homework
Solve
2(x+4)=3(-2+x)
Answer:
x = 14
Step-by-step explanation:
2(x + 4) = 3( -2 + x) distribute the 2 and the 3.
2(x) + 2(4) = 3(-2) + 3(x)
2x + 8 = -6 + 3x Subtract 2x from both sides
2x - 2x + 8 = -6 +3x -2x
8 = -6 +x Add 6 to both sides
8 + 6 = 6 - 6 + x
14 = x
A rope 15 inches long has been divided into the greatest possible number of pieces in such a way that each piece has a different length, and each of these lengths in inches is expressed by a whole number. How many cuts were made?
A.3
B.4
C.5
D.6
E.7
Answer:
Below
Step-by-step explanation:
1+2+3+4+5 =15 5 lengths will require 4 cuts
find the order pairs for y=-5x-4
Answer:
(0,-4),(1,1)(2,6)
Step-by-step explanation:
type an (x,y) ordered pair to put a point on this line.
The ordered pair (x, y) for the given line can be obtained from the graph as (-4, 1).
What is the equation for a straight line?A straight line can be written in the form of an equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
The graph of the line is given.
In order to find the coordinate of a point do as follows,
Draw a perpendicular line from any point on the line to the x-axis.
The intersection of this line with the x-axis will give the x-coordinate.
Similarly, find the y-coordinate by drawing a perpendicular line to the y-axis.
Applying the above procedure, a point is obtained as (-4, 1).
Hence, the ordered pair for the line shown in the graph is (-4, 1).
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Factor the expression y^2+8x+12
Answer: y^2+8x+12
Step-by-step explanation:
a letter is chosen at random from the word FOOTBALL, the probability that the letter chosen is not an L is:
Answer:
7/8
Step-by-step explanation:
Step 1: Count the total number of letters in the word FOOTBALL
There are 8 letters in the word FOOTBALL.
Step 2: Count the number of letters that are not L
There are 7 letters that are not L.
Step 3: Calculate the probability
The probability that the letter chosen is not an L is 7/8.
what is the evaluation for 4-4y+y-3
Answer:
1-3 y
Step-by-step explanation:
Subtract the numbers 4 AND 3 WHICH WOULD EQUAL REWRITING THE ADDITON SO IT CHANGES THE MINUS SIGN TO A PLUS.
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer: option b), option c), and option e) are correct options.
Step-by-step explanation:
Given:
The area of a rectangular room= 750 square feet
The width of the room = 5 feet less than the length of the room
The length of the room = Y
To find:
Equations that can be used to solve the value of Y i.e. the length of the rectangular room.
Solution:
The equation can be derived from using the following formula:
Area of rectangle = length * width
According to the question,
Length of the rectangular room = Y
Width of the rectangular room = 5 feet less than the length of the room
= (Y-5)
Since, Area of rectangle = length * width
Area of the rectangular field = length of the room* width of the room
750 = Y (Y – 5) ………..eqn. (1)
Or, the above equation can be solved a step further and written as
750 = Y2 – 5Y ………..eqn. (2)
750- Y2 + 5Y= 0 ………..eqn. (3)
750-Y (Y- 5) =0 ………..eqn. (4)
Apart from the above equations, if we solve eqn. (2) we get the following equation:
750 = Y2 – 5Y
Y2 – 5Y- 750= 0
Y2 – 30Y + 25Y- 750 = 0
Y (Y- 30) + 25 (Y- 30) = 0
take Y- 30 common from L.H.S.
(Y -30) (Y+ 25) = 0 …………….eqn. (5)
Hence, the correct options are option b), option c), and option e).
Identify the sequence that lists sides of STU in order from shortest to longest
ST, UT, SU
UT, SU, ST
SU, ST, UT
SU, UT, ST
On soloing the provided question we can say that - Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area. A = 210-123 = 87 sq unit
what is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
the sum of the areas of the circle, the triangle, and the square.
Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area.
A = 210-123 = 87 sq unit
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Determine if each of the following statements are true or false (HELP!!! ARE MY ANSWERS CORRECT?)
Answer:
yes
Step-by-step explanation:
A recreational area is formed by a rectangular shaped pool and a cement patio surrounding the pool. the pool has a length of 3x-3 meters and a width of 2x+7 meters. The patio extends x meters around to pool, on all sides of the pool. Write a polynomial expression that gives the total area of the recreational area.
The total area of the recreational area can be represented by the polynomial expression 26x² + 57x + 35.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
The area of the rectangular pool is given by its length times its width, so the area of the pool is (3x - 3) meters × (2x + 7) meters = (6x² + x - 21) square meters.
The area of the patio is given by the length of the pool plus twice the extension (x) on each side, times the width of the pool plus twice the extension on each side, so the area of the patio is (3x - 3 + 2x) meters × (2x + 7 + 2x) meters = (5x + 4) × (4x + 14) = 20x² + 56x + 56 square meters.
The total area of the recreational area is the sum of the areas of the pool and the patio, so it can be represented by the polynomial expression:
20x² + 56x + 56 + 6x² + x - 21 = 26x² + 57x + 35
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(36)^-2 x (9)^-2 i need help
Answer: 1/104976
Step-by-step explanation:
You can get rid of negative exponents by flipping the number. So in this case, the expression would change to: 1/(36)^2 x (9)^2.
From there, simplify the expression. 36 squared is 1296. 9 squared is 81. Multiply those together to get 104,976.
1/104976 is your answer!