We are given points on trig graph as
[tex](0,-4)[/tex]
[tex](\frac{\pi}{2} ,0)[/tex]
[tex](\pi ,4)[/tex]
[tex](\frac{3\pi}{2} ,0)[/tex]
[tex](2\pi ,-4)[/tex]
now, we can find rate of change from x = π to x = 2π
so, we will select two points
[tex](\pi ,4)[/tex] and [tex](2\pi ,-4)[/tex]
we can also write as
[tex]a=\pi , f(a)=4[/tex]
[tex]b=2\pi , f(b)=-4[/tex]
now, we can use average rate of change formula
[tex]A=\frac{f(b)-f(a)}{b-a}[/tex]
now, we can plug values
and we get
[tex]A=\frac{-4-4}{2\pi -\pi}[/tex]
[tex]A=\frac{-8}{\pi }[/tex]
so, option-C.............Answer
Cheryl volunteers to mow the lawn at a retirement home.She can mow 1/4 of the lawn in 3/4 of an hour .At what rate ,how many hours will it take Cheryl to mow the entire lawn
Explain what needs to happen to the inequities sign when dividing or multiplying by a negative number
What is the simplified form of (x – 2)(2x +3)? Use the Distributive Property. (1 point)
2x2 – x – 6
2x2 – 6
2x2 – 7x – 6
2x2 + x – 6
2. What is the simplified form of (3x + 2)(4x – 3)? Use a table. (1 point)
12x2 + 18x + 6
12x2 + x – 6
12x2 + 18x – 6
12x2 – x – 6
3. What is the simplified form of (4p – 2)(p – 4)? (1 point)
4p2 + 6p – 16
4p2 – 18p + 8
4p2 – 14p – 6
4p2 – 6p + 16
4. The radius of a cylinder is 3x – 2 cm. The height of the cylinder is x + 3 cm. What is the surface area of the cylinder? Use the formula A = 2r2 + 2rh.,
Find the volume for the regular pyramid.
4 cu. units
6 cu. units
12 cu. units
Answer:
[tex]4\ cu.\ units[/tex]
Step-by-step explanation:
we know that
The volume of the pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base of the pyramid
h is the height of the pyramid
Find the area of the base
[tex]B=2^{2}=4\ units^{2}[/tex]
[tex]h=3\ units[/tex]
Find the volume
[tex]V=\frac{1}{3}(4)(3)=4\ units^{3}[/tex]
Leyla drops a penny from a height of 150m. How long will it take to hit the ground? Round to the nearest tenth of a second. use the formula h(t)=-4.9t²+v₀t+h₀, where v₀ is the initial velocity and h₀ is the initial height.
It will take approximately 5.5 seconds for the penny to hit the ground.
To determine the time it takes for the penny to hit the ground, we can use the given formula for the height as a function of time:
[tex]\[ h(t) = -4.9t^2 + v_0t + h_0 \][/tex]
Given that the penny is dropped and not thrown, the initial velocity [tex]\( v_0 \)[/tex] is 0. The initial height [tex]\( h_0 \)[/tex] is 150 meters. We want to find the time [tex]\( t \)[/tex] when the height [tex]\( h(t) \)[/tex] is 0, which is when the penny hits the ground.
Plugging in the known values, we get:
[tex]\[ 0 = -4.9t^2 + 0 \cdot t + 150 \][/tex] Simplifying, we have:
[tex]\[ 4.9t^2 = 150 \][/tex]
Now, we solve for [tex]\( t \)[/tex]:
[tex]\[ t^2 = \frac{150}{4.9} \][/tex]
[tex]\[ t^2 \approx 30.612244898 \][/tex]
Taking the square root of both sides to solve for [tex]\( t \)[/tex]:
[tex]\[ t \approx \sqrt{30.612244898} \][/tex]
[tex]\[ t \approx 5.532851414 \][/tex]
Rounding to the nearest tenth of a second, we get:
[tex]\[ t \approx 5.5 \][/tex]
The original value of a car is 18000, and it depreciates (loses value) by 15% each year. What is the value of the car after three years?
find the exact value of cos285 using the fact that 285=330-45
Given that the points (-3, 8), (2, 8), (2, -2), and (-3, -2) are vertices of a rectangle, what is the ratio of the rectangle's length to its width?
Answer:
2:1
Step-by-step explanation:
Somebody help. I can’t figure this question out. thanks
A horizontal line goes through the point (–7,10). Which statements are true about this line? Check all that apply. The slope of the line is zero. Another point on the line is (3,10). The y-intercept of the line is –7. The equation of the line is y = 10.
The statement 1,2, and 4 are true and 3 is not true below given the reason behind it.
What is a graph?The link between lines and points is described by a graph, which is a diagrammatic representation of a network.
A graph is made up of some points and the distance between two It doesn't matter how much time the lines are or where the points are located. A node is a name for each constituent in a graph.
The given statement is a line passing through ( -7, 10 ) so
Option 1 ⇒ the slope of that line will be zero because it is a horizontal line so it will be true.
Option 2 ⇒another point on this line will be (3,10) since it is a horizontal line so the y coordinate is the same and the x coordinate can vary so it is also true.
Option 3 ⇒ the y-intercept of this line will be 10 which is not true and can be confirmed by options 1 and 2.
Option 4 ⇒ the equation of the line will be y =10 which is true hence it is a horizontal line.
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The triangles are congruent by SSS or HL. The diagram shows the sequence of three rigid transformations used to map ABC onto A"B"C". What is the sequence of the transformations? rotation, then reflection, then translation rotation, then translation, then reflection reflection, then translation, then rotation reflection, then rotation, then translation
Answer:- The sequence of the transformations for the given diagram must be reflection, then rotation, then translation.
Explanation:-
Given : Four triangles which are congruent by SSS postulate or HL theorem.
According to the given diagram , the rigid transformations are as follows
1. Reflection: ΔABC is flipped about BC to form ΔA'BC such that AC=A'C and its is already given that they are congruent thus the rigid transformation used here is reflection.
2. Rotation:- ΔA'BC is rotated about point A' at some angle to form ΔA'B'C' , and they are congruent (given). Thus the rigid transformation used here is rotation.
3.Translation:- ΔA'B'C' is translated exactly right by some factor to form ΔA"B"C" ∵ all the points have changed but as these triangles are congruent (given) then corresponding parts must be equal.Thus the rigid transformation used here is translation.
The sequence should be in the order for the given transformation as, reflection, then rotation, then translation. Thus the option D is the correct option.
How to rotate, reflect, and translation the figure?Rotation, reflection and translation is the way of transformation of an figure.
Rotation- Rotation of an object is rotating it about a fixed point without changing its shape and size.Reflection- Reflecting of an object is flipping it across a line without changing its shape and size.Translation- Translation of an object is the shifting of the object without changing its dimensions, without rotating it and without reflecting it.Given information-
In the given diagram the, triangle ABC is transformation into the three stages.
First the figure ABC is just flipped into the triangle A'BC by keeping the side BC fixed.Then the triangle A'BC is rotated around the point A' and to place of A'B'C'.Finally the figure is transact right from one place to another which is A"B"C".Hence the correct sequence of the transformations is reflection, then rotation, then translation. Thus the option D is the correct option.
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Laila is having shirts made with a logo printed on them to promote her band. The total cost consists of a one-time fee of $75 to have the logo designed, plus $8 per shirt to print the logo. Write an equation that Laila can use to determine the total cost c, in dollars, to make x shirts
Find the ratio of the longest side to the perimeter of the right-triangular-shaped billboard. 20 feet 21 feet 29 feet
Solution:
we have been asked to find the ratio of the longest side to the perimeter of the right-triangular-shaped billboard.
Sides of the right-triangular-shaped billboard are 20 feet 21 feet 29 feet.
As we know perimeter is just the sum of all the sides.
Perimeter[tex]=20+21+29=70\\[/tex]
And the longest side is 29 feet.
Hence the required ratio [tex]=\frac{29}{70}=29:70[/tex]
how fast is the water level rising in a rectangular fish tank whose base is 20 ft^2 if the tank is being filled at a rate of 0.5ft^3/min
The water level is rising at a rate of 0.025 ft/min.
To determine how fast the water level is rising in the rectangular fish tank, you can use the formula for the volume of a rectangular prism:
V = base area × height
Given that the base area is 20 [tex]ft^2[/tex] and the tank is being filled at a rate of
0.5 cube ft/min, you want to find the rate at which the height (h) is changing [tex](\frac{dh}{dt} )[/tex].
V = base area × height
[tex]\frac{d V}{d t}=\text { base area } \times \frac{d h}{d t}[/tex]
Substitute the known values:
0.5 = 20 x [tex](\frac{dh}{dt} )[/tex]
Now, solve for [tex](\frac{dh}{dt} )[/tex]
[tex]\frac{d h}{d t}=\frac{0.5}{20}[/tex] = 0.025 ft/min
Thus, the required answer is 0.025 ft/min.
Factor completely: 9ab + 12ax - 6b - 8x (1 point)
1. Prime
2. (3b - 4x)(3a - 2)
3. (3b + 4x)(3a - 2)
4. (3b + 4x)(3a + 2)
If arc XV = 68° and ∠YUV = 36°, what is the measure of arc VY?
Regard triangleTRI and the following facts:
Segment IR || Segment NA
TA= 12 cm, RA= 3 cm, NT= 18 cm, AN= 22
(a)What theorem or postulate proves Triangle ANT similar to RIT?(b)Solve for NI by using the Side-Splitting Theorem.Show all work.(c)What is the scale factor for similar triangles ANT and RIT?
(d)Calculate RI. Show your work.
(e)What is the ratio of the areas of the two triangles? Show your work.
A circular piece of glass has a radius of 2.1 meters. The glass sells for $1.70 per square meter. What is the total cost of the circular piece of glass?
$23.54
$94.16
$3.57
$11.21
Where is the centroid of any given triangle?
A. the point of concurrency of the altitudes of the triangle.
B. the point of concurrency of the medians of the triangle.
C. the point of concurrency of the perpendicular bisectors of the triangle.
D. the point of concurrency of the angle bisectors of the triangle.
Which of the following best describes the altitude of a triangle?
A. a segment perpendicular to a side of the triangle.
B. a segment that passes through the midpoint and is perpendicular to a side of a triangle.
C. a segment drawn from the ve
trevor needs to let his puppy outside every quarter (1 fourth) hour to potty train him. draw and label a number line from 0 hours to 1 hour to show every 1 fourth hour.
A rectangular prism has a length of 2 1/2 centimeters, a width of 2 1/2 centimeters, and a height of 5 centimeters. Justin has a storage container for the prism that has a volume of 35 cubic centimeters. What is the difference between the volume of the prism and the volume of the storage container?
Answer:
3.75
Step-by-step explanation:
please help me thank you.
can someone help me with this?
If one angle of a triangle measures 32 degrees and another angle measures 71 degree, what is the measure of the third angle?
Which ordered pair is a solution for this system of inequalities?
2x + 3y > 1 and y < 5/4 x - 1
A.(3, 9)
B.(-4, 2)
C.(8, -1)
D.(-2, -5),
A cell phone weighs about 2.8X10^n pounds. Which value of n is most reasonable? A)-3 b)-1 c)0 d)1
please help im stuckk
Jose owns 40 shares of stock A whose price increased by $0.75 per share. He also owns 100 shares of stock B whose price decreased by $0.20 per share. What is the total change in the value of Paul’s stock (A and B together)?
PLEASE HELP!
Is the mean always a more accurate measure of center than the median
A rectangle is 7 feet long by 2 feet wide. If 2 feet are added to the length of the rectangle, what would be the area, in square feet, of the new rectangle?
If a rectangle is 7 feet long by 2 feet wide and 2 feet are added to the length of the rectangle then the area of rectangle is 18 square feet.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that a rectangle has a length of 7 feet.
The width of rectangle is 2 feet.
We have to find the area of rectangle when 2 feet is added to the length of rectangle
Initial length is 7 feet
When 2 feet is added the length will be 7+2, 9 feet.
Area of rectangle = Length × width
=9×2
Nine times two is eighteen.
=18 square feet.
Hence, if a rectangle is 7 feet long by 2 feet wide and 2 feet are added to the length of the rectangle then the area of rectangle is 18 square feet.
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