Answer:
The function f(x) = -8t(t - 8) represents the height of the soccer ball at any given time t, where t is the time in seconds after the ball was kicked.
To find out how long the ball spends in the air, we need to determine the time at which the ball hits the ground. The ball hits the ground when its height is zero, so we can set f(x) = 0 and solve for t:
-8t(t - 8) = 0
This equation has two solutions: t = 0 and t = 8. The first solution corresponds to the time when the ball is kicked and the second solution corresponds to the time when the ball hits the ground. Since we're interested in the time the ball spends in the air, we need to subtract the time the ball was kicked from the time the ball hits the ground:
t = 8 - 0 = 8 seconds
Therefore, the ball spends 8 seconds in the air.
Find the equation of a straight line with the following gradients and points .1. 2,(7,2) .2. -2(6,-3)
Answer:
The gradient is given as m=1, and the point (7,2) lies on the line. Thus:
y - y1 = m(x - x1)
y - 2 = 1(x - 7)
y - 2 = x - 7
y = x - 5
So the equation of the line is y = x - 5.
Again, using the point-slope form of a straight line:
The gradient is given as m=-2, and the point (6,-3) lies on the line. Thus:
y - y1 = m(x - x1)
y - (-3) = -2(x - 6)
y + 3 = -2x + 12
y = -2x + 9
So the equation of the line is y = -2x + 9.
Find the value of x. 20 degrees and 114 degrees
By answering the presented question, we may conclude that as we know the sum of all angles is a triangle is 180; x = 46
What precisely is a triangle?A polygon is a triangle with four or more parts. It has a straightforward rectangular shape. Triangle ABC denotes a rectangle with the edges A, B, and C. Euclidean geometry produces a single plane and cube when the sides are not collinear. A triangle is a polygon if it contains three components and three angles. The corners are the points where a triangle's three edges meet. The angles of a triangle sum up to 180 degrees.
as we know the sum of all angles is a triangle is 180.
so, here,
20+114+x = 180
x = 180 - 134
x = 46
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CAN SOMEONE HELP WITH THIS QUESTION?✨
By answering the presented question, we may conclude that As a result, trigonometry the abbreviated phrase is: 8 sin(c+l)
what is trigonometry?Trigonometry is the field of mathematics that explores the connection between triangle side lengths and angles. The issue first originated in the Hellenistic era, during the third century BC, as a result of the use of geometry in astronomical investigations. The subject of mathematics known as exact techniques is concerned with certain trigonometric functions and their possible applications in calculations. Trigonometry contains six commonly used trigonometric functions. Their separate names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle characteristics, particularly those of right triangles. As a result, geometry is the study of the properties of all geometric forms.
tan (7 sin(c) + 8 cos(c)) (l)
We may utilise the trigonometric identity to simplify this expression:
sin(l) / cos(l) = tan(l) (l)
When we insert this into the original phrase, we get:
sin(l) / cos(c) (7 sin(c) + 8 cos(c)) (l)
By increasing the numerator, we get:
8 cos(c) sin + 7 sin(c) sin(l) (l)
Now we can apply the trigonometric identities:
(1/2) sin(a) cos(b)
[sin(a+b) plus sin(a-b)]
(1/2) cos(a) sin(b)
[sin(a+b) minus sin(a-b)]
We can write using these identities:
7 sin(c) sin(l) + 8 cos(c) sin(l) equals 7 (1/2).
[sin(c+l) minus sin(c-l)] + 8 (1/2) [sin(c+l) plus sin(c-l)]
= (7/2)sin(c+l) + (8/2)sin(c-l) + (8/2)sin(c+l) + (7/2)sin(c-l) - (7/2)sin(c-l) = 8 sin(c+l)
As a result, the abbreviated phrase is:
8 sin(c+l)
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25. A large ship is sailing between three small islands. To do so, the ship must sail between two pairs of islands, avoiding sailing between a third pair. The safest route is to avoid the closest pair of islands. Which is the safest route for the ship?
26. Three cell phone towers form APQR.
The measure of ZQ is 10° less than the measure of LP. The measure of Ris 5° greater than the measure of ZO. Which two towers are closest together?
Answer:
These distances show that AB, which is only 10 nautical miles apart, and AB are the closest pair of islands.
Step-by-step explanation:
We must first locate the three pairs of islands in order to establish which pair is nearest before determining the safest route for the ship.
Give the three islands the letters A, B, and C. The three island groups are designated as AB, AC, and BC. Finding the closest pair is necessary.
We can leverage the separation between the islands to do this. Assuming that the islands are separated by the following distances:
A and B are separated by 10 nautical miles.
A and C are separated by 15 nautical miles.
B and C are separated by 12 nautical miles.
These distances show that AB, which is only 10 nautical miles apart, and AB are the closest pair of islands.
Tara creates a budget for her weekly expenses. The graph shows how X much money is in the account at different times. Find the slope of the line. Then tell what rate the slope represents.
The slope of the line is -50 and it means that the amount of money in the account is decreasing at a rate of $50 every week.
What is meant by the slope of the line?
A line's slope is defined as the ratio of the change in the y coordinates to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
As a result, m = change in y/change in x is the formula for the change in the y-coordinate with respect to the change in the x-coordinate.
where "m" represents a line's slope.
A line's slope provides information on the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them.
The complete question is given below.
The two points on the graph are (4, 2400) and (12, 2000).
(x₁ , y₁) = (4, 2400)
(x₂ , y₂) = (12, 2000)
The slope of the graph can be found using the following formula.
Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{2000-2400}{12-4}[/tex] = [tex]\frac{-400}{8}[/tex] = -50
Therefore the slope of the line is -50 and it means that the amount of money in the account is decreasing at a rate of $50 every week.
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 Find the area of the shaded sector.
Answer In Exact Form (don't put pi in calculator, simplify your decimal answer to a fraction, and put pi symbol in answer).
The area of the shaded sector is equal to: A. 415π/2 ft².
How to calculate the area of a sector?Mathematically, the area of a sector can be calculated by using this formula:
Area of sector = θπr²/360
Where:
r represents the radius of a circle.θ represents the central angle.Substituting the given parameters into the area of a sector formula, we have the following;
Area of sector = 332(π/180) × (15)²/2
Area of sector = 74,700π/180 × 1/2
Area of sector = 415π/2 ft²
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Determine whether y varies directly with x if so, solve for the constant of variation k. 3y= -7x-18
This shows that any increase in x by a certain factor results in an increase in y by the same factor, confirming that y varies directly with x.
What is Linear equation ?
Linear equation can be defined as equation in which highest degree is one.
To determine if y varies directly with x, we need to check if there is a constant ratio between y and x. In other words, if we increase x by a certain factor, does y also increase by the same factor?
The equation 3y = -7x - 18 can be rewritten as y = (-7/3)x - 6. This is in the form of y = kx + b, where k is the constant of variation and represents the ratio between y and x.
Since the equation is in this form, we can say that y varies directly with x, and the constant of variation is k = -7/3.
To verify that y varies directly with x, we can check that any increase in x by a certain factor results in an increase in y by the same factor, as given by the constant of variation. For example, if we increase x by 3, then y will increase by (-7/3)(3) = -7. If we increase x by 6, then y will increase by (-7/3)(6) = -14.
Therefore, This shows that any increase in x by a certain factor results in an increase in y by the same factor, confirming that y varies directly with x.
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Question 10
Solve for b.
b³ = 8
Enter your answer in the box.
Answer:
[tex]{ \sf{ {b}^{3} = 8}} \: \: \\ { \sf{ {b}^{3} = {2}^{3} }} \\ { \sf{ {(b}^{3}) {}^{ \frac{1}{3} } = {( {2}^{ 3}) }^{ \frac{1}{3} } }} \\ { \sf{b ={ \boxed{ 2}}}}[/tex]
Answer:
b=2
Step-by-step explanation:
[tex]b^{3} = 8\\\\b^{3} = 2^{3} \\\\b=+2[/tex]
HELP FAST PLEASE, CONFUSED!!
Which of the following tables represents a linear relationship that is also proportional? Choose one of the tables below. Not sure if it’s the first one?
The table that represents a proportional relationship is the option (d) i.e. x: 6, 3, 0,
y: -2, -1, 0
Which one of the linear relationships is proportional?A general linear relationship is written as:
[tex]y = a*x + b[/tex]
Where a is called as the slope and b is called the y-intercept.
Proportional relationship is what we get when the y-intercept is 0, so we get an equation in the form:
[tex]y = a*x[/tex]
And in this case we can say, the slope is called the "constant of proportionality"
All proportional relationships of this property is given by , if we take x = 0 we get:
[tex]y = a*0 = 0[/tex]
So they always pass through the point (0, 0).
Now if we look at the given tables, the only option that passes through that point is the last table:
x: 6, 3, 0
y: -2, -1, 0
So that is the correct option.
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T is the reflection of t across the line x=6 if the coordinates t are(-3,7) what are the coordinates of t
Therefore , the solution of the given problem of coordinates comes out to be , T's values are (15, 7).
Describe coordinate.
A coordinate system can be used to precisely find points or additional mathematical objects on such a space, including Euclidean space, by using one or more variables or coordinates. To find a point or item on a double plane, one uses coordinates, which are pairs of numbers. Two numbers called the y and x matrices are used to describe a point's location on a two-dimensional plane. a set of numbers used to identify specific locations. The number usually consists of two digits.
Here,
In other terms, the x-coordinate of T is 6 times the difference between t and 6, or:
=> T's x-coordinate is 6 plus (6 minus (-3)) = 15
We can use the fact that the line of reflection is just the perpendicular bisector of the section joining t and to determine the y-coordinate of T. T's separation from the line
=> x=6 is 6 - (-3) = 9,
which is also T's separation from the line x=6.
The y-coordinate of T is the same as the y-coordinate of t because the line of reflection is the perpendicular bisector of the section joining t and T, which is:
=>T has a y-coordinate of 7.
Consequently, T's values are (15, 7).
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After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1980, the hay in that country was contaminated by a radioactive isotope (half-life 6 days). If it is safe to feed the hay to cows when 14% of the radioactive isotope remains, how long did the farmers need to wait to use this hay?
Answer:
22
Step-by-step explanation:
The time required for a radioactive isotope to decay to a certain percentage of its initial amount can be found using the following formula:
t = (t1/2 / ln(2)) * ln(N0/N1)
where:
t is the time elapsed since the release of the radioactive material
t1/2 is the half-life of the radioactive isotope (6 days in this case)
N0 is the initial amount of the radioactive isotope
N1 is the remaining amount of the radioactive isotope (14% of N0 in this case)
ln is the natural logarithm
We can solve for t by plugging in the given values:
t = (6 / ln(2)) * ln(1 / 0.14)
t ≈ 22.4 days
Therefore, the farmers needed to wait about 22.4 days to use the hay safely.
What are three ratios that are equivalent of the given ratio of 9/7
Answer: 18/14, 27/21, 36/28
Step-by-step explanation:
5. A rock is thrown directly upward with an initial velocity of 79 feet per second from a cliff 50 feet above a beach. The height of the rock above the beach (h) after t seconds is given by the equation h = -16t² + 79t + 50. The graph below shows the rock's height as a function of time.
The rock will be at a height of 125 feet after 0.49 and 4.76 seconds.
Finding the time:In the given problem we have a function h(t) that represents the height of the rock that is from the ground of the beach where the variable represents the time travel by the rock.
Assume t as required time equates the given function to the given height and solve for the value of 't'.
Here we have
A rock is thrown directly upward with an initial velocity of 79 feet per second from a cliff 50 feet above a beach.
The height of the rock above the beach (h) after t seconds is given by the equation h(t) = -16t² + 79t + 50.
Let after t seconds the height will be 125 feet
=> h(t) = 125
=> -16t² + 79t + 50 = 125
=> -16t² + 79t - 75 = 0
To solve this quadratic equation, we can use the quadratic formula:
=> x = [-b ± √(b² - 4ac)]/ 2a
Here a = -16, b = 79, and c = -75.
t = [-79 ± √(79² - 4(-16)(-75))] / 2(-16)
t = (-79 ± √(6241 - 4800)) / -32
t = (-79 ± √1441) / -32
So, the two solutions are:
t = (-79 + √1441) / -32 and t = (-79 - √1441) / -32
t ≈ 0.497 or t ≈ 4.763
Therefore,
The rock will be at a height of 125 feet after 0.49 and 4.76 seconds
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which one of the following greater
a, 20% of 45
b, 25% of 60
c, 2%of 800
d, 74% of 20
Answer:
2% of 800, which is 16
Solve this proof. (Flow chart proof)
Given: HF || GK, angle F and angle K are right angles.
Prove: FG congruent to KH
FG and KH are congruent using the AAS theorem. ∠F = ∠K and ∠G = ∠H
What is the AAS congruence theoremThe AAS (Angle-Angle-Side) Congruence Theorem is a geometric theorem that states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.
In other words, if two triangles have two corresponding angles that are congruent, and the included side between these angles is also congruent in both triangles, then the two triangles are congruent.
The diagram shows that we have two triangles here. The first triangle is equal to the second triangle.
This is shown by the fact that the angle at F = angle at K
the angle at H = angle at G
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Answer:
use AAS for this
Step-by-step explanation:
Find the volume of the composite figure.
Figure not drawn to scale
The volume of the two cuboid added together will be 192 cm³.
what exactly is a cuboid?
A cuboid, also known as a rectangular prism, is a three-dimensional solid shape that has six rectangular faces. It is a type of polyhedron, a geometric figure with flat faces and straight edges.
A cuboid has three pairs of congruent and parallel faces, with each pair being congruent to the other. These pairs of opposite faces are known as bases, and the other four faces are called lateral faces. The lateral faces are also rectangles and are perpendicular to the bases.
Now,
As Volume of the cuboid= L*B*H
where l=length, B=Breadth and H=Height
and volume of the figure =volume of 2 cuboids
=8*4*3+10*3*4
=72+120
=192 cm³
Hence,
The volume of the two cuboid added together will be 192 cm³.
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In a school survey, Randy found that 5/12 of the students normally wear sneakers, and that
8/25 OF those who wear sneakers normally wear white sneakers. What fraction of the student body normally wears white sneakers?
Answer: 2/15
Step-by-step explanation:
S: student wearing an sneakers
W: student wearing a white sneakers
Data given:
P(S) = 5/12
P(S∩W) = 8/25
so to find
P(W) = P(S)*P(S∩W) = 8/25* 5/12 = 2/15
This is 2/15 of the total students wears white sneakers
Answer:
2/15 of the student body normally wears white sneakers
Step-by-step explanation:
5/12
multiplied by
8/25
equals
40/300 = 4/30 =
after simplification
2/15
Four yards of fabric will be cut into pieces so that each piece is thirteen inches long. How many pieces can be cut?
11 pieces can be cut frοm the 4 yards οf fabric.
In math, what is a fractiοn?An element οf a whοle is a fractiοn. The quantity is mathematically represented as a quοtient, where the numeratοr and denοminatοr are split in half. Bοth are integers in a simple fractiοn. A fractiοn can be fοund in either the numeratοr οr the denοminatοr οf a cοmplex fractiοn. The numeratοr οf an apprοpriate fractiοn is less than the denοminatοr.
1 yard = 36 inches (since 1 yard is equal tο 3 feet and 1 fοοt is equal tο 12 inches)
Sο, 4 yards οf fabric = 4 x 36 = 144 inches οf fabric.
If each piece is 13 inches lοng, we can find the number οf pieces by dividing the tοtal length οf fabric by the length οf each piece:
Number οf pieces = Tοtal length οf fabric / Length οf each piece
Number οf pieces = 144 / 13
Number οf pieces ≈ 11.08
Since we cannοt have a fractiοn οf a piece, we must rοund dοwn tο the nearest whοle number. Therefοre, 11 pieces can be cut frοm the 4 yards οf fabric.
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Imagine that you’re studying the relationship between newborns’ weight and length.
You have the weights and lengths of the 10 babies born last month at your local hospital.
Calculate the r for this sample.
Therefore , the solution of the given problem of expression comes out to be the correlation coefficient for this group is r = 0.9446.
What does an expression precisely mean?Calculations like multiplication, variable splitting, joining, and presently removing are required. Combining them would result in the following: An equation, some statistics, and a mathematical formula. A declaration of truth is composed of values, components, mathematical processes like additions, subtractions, errors, and subdivisions as well as arithmetic formulas. Words and phrases can be evaluated and analysed.
Here,
You must use the following method to determine the r (Pearson correlation coefficient) for this sample:
=> r = (NΣXY - ΣXΣY) / √((NΣX² - (ΣX)²) (NΣY² - (ΣY)²))
where:
N stands for notes (in this case, 10)
Sum of each newborn's weight is equal to X.
Y = the measure of each infant
We can compute the following using the formula:
=> ΣX = 29.5
=> ΣY = 509
=> ΣXY = 1576.7
=> ΣX² = 97.95
=> ΣY² = 26757
When these numbers are added to the formula, we obtain:
=> r = (10 * 1576.7 - 29.5 * 509) / √((10 * 97.95 - (29.5)^2) * (10 * 26757 - (509)^2))
=> r = 0.9446
Since length and weight of newborns are strongly positively correlated, the correlation coefficient for this group is r = 0.9446.
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4. In a batch of 100 CDs, 6 are defective. A sample of three CDs is to be selected at random. What is the probability that two of the three CDs will be defective?
Answer: The probability that two of the three CDs will be defective is approximately 0.01044 or 1.044%.
Step-by-step explanation: We can use the binomial distribution to solve this problem. Let X be the number of defective CDs in a sample of three. Then X follows a binomial distribution with parameters n = 3 and p = 6/100, where n is the sample size and p is the probability of a CD being defective.
The probability of getting exactly two defective CDs in a sample of three can be calculated using the binomial probability formula:
P(X = 2) = (3 choose 2) * (6/100)^2 * (94/100)^1
where (3 choose 2) = 3 is the number of ways to choose 2 defective CDs out of 3.
Simplifying this expression, we get:
P(X = 2) = 3 * (6/100)^2 * (94/100)
P(X = 2) = 0.01044
Therefore, the probability that two of the three CDs will be defective is approximately 0.01044 or 1.044%.
Answer: working on it
Step-by-step explanation:
Solve for s. 0.5s + 1=7+4.5s=
Answer:
s = -1.5
Step-by-step explanation:
0.5s + 1 = 7 + 4.5s
So we can combine like terms
Put 0.5s to other side
Put 7 to other side
Then you get the equation:
1 - 7 = 4.5s - 0.5s
So we simplify:
-6 = 4s
That means
s = -6/4
s = -1.5
Hope this helps!
What is the equation of the line in slope-intercept form that goes thru the point (8, -2) and has a slope of 1/4?
The equation of the line in slope-intercept form that goes through the point (8, -2) and has a slope of 1/4 is y = 1/4x - 4.
What is slope-intercept form?In slope-intercept form, the equation of a line is expressed as y = mx + b, where m denotes the slope of the line and b the y-intercept, or the location at where the line intersects the y-axis. In this form, the slope m denotes the line's steepness or the rate at which y changes in relation to x. A positive slope causes the line to go upward from left to right, whereas a negative slope causes the line to move downward from left to right. The value of y when x is 0, or the line's origin, is represented by the y-intercept, or b.
Given that, point (8, -2) and a slope of 1/4.
The slope-intercept form is given as:
y - y1 = m(x - x1)
Substituting the values:
y - (-2) = 1/4(x - 8)
y + 2 = 1/4x - 2
y = 1/4x - 4
Hence, the equation of the line in slope-intercept form that goes through the point (8, -2) and has a slope of 1/4 is y = 1/4x - 4.
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85 cm with area base of 245cm
The Volume of rectangular prism (V) = 20,825 [tex]cm^{3}[/tex]
What is rectangular prism?A rectangular prism is a three-dimensional geometric shape that is formed by six rectangular faces joined together at right angles.
I think the question is, find out the volume of the rectangular prism in cubic centimeters? Given that the height is 85cm and area of base is 245cm².
We know that the formula for calculating the volume of a rectangular prism is as follows,
Volume of rectangular prism (V) = Area of base × height of the prism
Volume of rectangular prism (V) = 245cm² × 85cm
Volume of rectangular prism (V) = 20,825 [tex]cm^{3}[/tex]
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Multiply 2 1. Simplify the answer and write as a mixed number.
O 4/
O
88
18
18
0416
25/
229
4
After simplifying a mixed number is 5 1/16
A mixed number is a combination of a whole number and a fraction.
It is typically written in the form "a b/c", where "a" is the whole number, "b" is the numerator of the fraction, and "c" is the denominator of the fraction.
For example, 3 1/2 is a mixed number, where 3 is the whole number, 1 is the numerator of the fraction, and 2 is the denominator of the fraction. This mixed number can also be expressed as an improper fraction as follows:
3 1/2 = (3 × 2 + 1) / 2 = 7/2.
Conversely, an improper fraction can be converted to a mixed number by dividing the numerator by the denominator to obtain the whole number and expressing the remainder as a fraction.
To multiply 2 1/4, follow these steps:
1. Convert the mixed number to an improper fraction: 2 1/4 = (2 × 4 + 1) / 4 = 9/4
2. Multiply the improper fraction by itself: (9/4) × (9/4)
3. Multiply the numerators: 9 × 9 = 81
4. Multiply the denominators: 4 × 4 = 16
5. Write the result as a fraction: 81/16
6. Simplify the fraction by converting it to a mixed number:
81 ÷ 16 = 5, with a remainder of 1.
So, 81/16 = 5 1/16.
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What does f(x)=12^x and g(x)=square root x-12 have in common?
Both f(x) and g(x) include domain values of [12,), and both functions increase over the interval (12, ∞).
What is the Function?A relationship between a set of inputs (the domain) and a set of potential outputs (the range) is known as a function. This relationship has the feature that each input is associated to exactly one output.
The notation f(x) is often used to express a function in mathematics, where f is the name of the function and x is the input value, also known as the argument of the function. When f(x) is calculated, it indicates the function's output value for the given input value x.
First, both functions have a domain that includes all values of x greater than or equal to 12, which is expressed as [12,) in interval notation.
Second, both functions increase over the interval (12, ∞), meaning that as x increases beyond 12, the values of the functions also increase without bound. This is because the exponential function 12^x and the square root function √(x - 12) both become increasingly steep as x increases, leading to a sharp increase in their values.
Therefore, Both f(x) and g(x) include domain values of [12,), and both functions increase over the interval (12, ∞).
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7(y-5)=21 Help Please!!
Answer:
Y=8
Step-by-step explanation:
7(y-5)=21
distribute the 7
7y-35=21
get y by itself
7y=56
divide by 7
y=8
HOPE THIS HELPS YOU UNDERSTAND!
Example 3: Solve the word problems involving angles of elevation and depression.
You are flying a kite overhead. The angle of elevation is 65°. The length of string used is 75 ft. How high is the
kite?
a.
b. Joe is standing in a bell tower 210 feet tall. He looks down at an angle of depression towards Jill who is standing
on the ground. How far is Jill from the bell tower?
Example 4: Additional Word Problems
2.
The two equal angles of an isosceles triangle are each 70°. Determine the measures of the rest of the triangle if it
has a height of 16cm.
b. A ramp leading into the public library is 25 feet long. The ramp rises a total of 2 feet. Is the ramp to code
according to ADA standards? (The angle of incline must be less than 4.76 degrees.)
Step-by-step explanation:
3)
a. To find the height of the kite, we can use trigonometry. The sine function relates the opposite side (the height of the kite) to the hypotenuse (the length of string used) and the angle of elevation. Therefore, we can write:
sin(65°) = height/75
Solving for the height, we get:
height = 75 sin(65°) = 67.8 ft
Therefore, the kite is 67.8 feet high.
b. To find the distance between Joe and Jill, we can use trigonometry again. The tangent function relates the opposite side (the distance between Joe and Jill) to the adjacent side (the height of the bell tower) and the angle of depression. Therefore, we can write:
tan(angle of depression) = opposite/adjacent
tan(angle of depression) = Jill's height/210
Solving for the distance between Joe and Jill, we get:
distance = adjacent * tan(angle of depression)
distance = 210 * tan(angle of depression)
We need to know the angle of depression to solve for the distance, which is not given in the problem.
4)
a. In an isosceles triangle with two equal angles of 70°, the third angle must be:
180° - 70° - 70° = 40°
Since the triangle is isosceles, the height must be the perpendicular bisector of the base. Therefore, we can draw an altitude from the top vertex to the base, splitting the base into two equal segments. Let x be the length of each base segment. Then we can use trigonometry to find the height:
tan(70°) = height/x
height = x * tan(70°)
Since the height is given as 16 cm, we can solve for x:
16 = x * tan(70°)
x = 16/tan(70°)
Therefore, the length of each base segment is:
x = 16/tan(70°) = 6.12 cm
And the length of the base is twice the length of each segment:
base = 2x = 2(16/tan(70°)) = 12.25 cm
Therefore, the measures of the rest of the triangle are:
base = 12.25 cm
each equal angle = 70°
height = 16 cm
b. To determine if the ramp meets ADA standards, we need to find the angle of incline. The angle of incline is the angle between the ramp and the horizontal. We can use trigonometry to find this angle:
sin(angle of incline) = rise/run
sin(angle of incline) = 2/25
angle of incline = sin^(-1)(2/25)
Using a calculator, we get:
angle of incline ≈ 4.79°
Since the angle of incline is greater than the maximum allowable angle of 4.76°, the ramp does not meet ADA standards.
9. A stainless-steel patio heater is shaped like a square pyramid. The length of one side of the base is 2 feet. The slant height is 9 feet. What is the height of the heater? Round to the nearest tenth of a foot
Answer:
The height of the patio heater is approximately 8.9 feet.
The table compares the average daily temperature and ice cream sales each day.
Temperature (°F) Ice Cream Sales
58.2 $112
64.2 $135
64.3 $138
66.8 $146
68.4 $166
71.6 $180
72.7 $188
76.2 $199
77.8 $220
82.8 $280
Using technology, determine the line of fit, where x represents the average daily temperature and y represents the total ice cream sales. Round values to the nearest tenth.
A) ŷ = 3.8x − 109.2
B) ŷ = −3.8xx − 109.2
C) ŷ = 6.5x − 279.1
D) ŷ = −6.5x − 279.1
By using technology, the line of best fit include the following: C. y = 6.5x - 279.1.
How to find an equation of the line of best fit for the data?In this scenario, the average daily temperature would be plotted on the x-axis of the scatter plot while the total ice cream sales would be plotted on the y-axis of the scatter plot.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the average daily temperature and total ice cream sales, a linear equation for the line of best fit is given by:
y = 6.5x - 279.1
In conclusion, the type of correlation between the variables is a strong positive correlation.
Read more on scatter plot here: brainly.com/question/28605735
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Answer:
ŷ = 6.5x − 279.1
Step-by-step explanation:
I will mark you brainiest!
Which of the following methods is not used to prove triangles are congruent?
A) AAA
B) SAS
C) SSS
D) ASA
Answer:
A) AAA yessss