A ball is thrown into the air from the edge of a 48 foot cliff so that it eventually lands on the ground. The graph below shows the height, y, of the ball from the ground after x seconds.
For which interval is the ball’s height always decreasing?
A. 48
B.0
C.2.5
D.146
Answers
2.5 < x < 5.5 seconds is the time interval when ball's height always decreasing.
What is time interval?" Time interval is the division of time into small equal intervals to have a proper observation of any data."
According to the given graph,
x represents time in seconds along x-axis
y represents height in foot of the ball along y-axis
As per observation,
Height of the ball increasing from 48 to 146 in the time interval
0< x < 2.5.
Height of the ball decreasing from 146 to 0 in the time interval 2.5< x < 5.5.
Hence, we conclude that 2.5 < x < 5.5 seconds is the time interval when ball's height always decreasing.
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Related Questions
Two isosceles triangles have the same base length. the legs of one of the triangles are twice as long as the legs of the other. find the lengths of the sides of the triangles of their perimeters are 23 cm and 43 cm.
Answers
Final answer:
To find the lengths of the sides of two isosceles triangles with equal bases and perimeters of 23 cm and 43 cm, we calculate based on the known relations. The smaller triangle has sides of 10 cm and 3 cm, while the larger triangle has sides of 20 cm and 3 cm.
Explanation:
The problem involves two isosceles triangles with the same base length, but the legs of one triangle are twice as long as the other. One triangle has a perimeter of 23 cm, and the other has a perimeter of 43 cm. To solve this, let's denote the common base of both triangles as b, the legs of the smaller triangle as l, and the legs of the larger triangle as 2l.
For the smaller triangle, the perimeter P is given by P = b + l + l or P = b + 2l. For the larger triangle, the perimeter P is P = b + 2l + 2l or P = b + 4l. Since the perimeters are 23 cm and 43 cm respectively, we can set up two equations: b + 2l = 23 and b + 4l = 43.
Solving these simultaneous equations, subtract the first from the second to find 2l = 20, so l = 10. Substituting l = 10 into the first equation gives us b + 20 = 23, thus b = 3.
Therefore, the sides of the smaller triangle are 10 cm (legs) and 3 cm (base), and the sides of the larger triangle are 20 cm (legs) and 3 cm (base).
Use the Law of Sines to find the missing side of the triangle. Find b.
Answers
Answer:
43.82 units.
Step-by-step explanation:
We have been given a triangle. We are asked to find the value of b using Law of Sines.
[tex]\frac{a}{\text{sin}(A)}=\frac{b}{\text{sin}(B)}=\frac{c}{\text{sin}(C)}[/tex], where, a, b and c are opposite sides of angles A, B and C respectively.
Upon substituting our given values in above formula, we will get:
[tex]\frac{50}{\text{sin}(58^{\circ})}=\frac{b}{\text{sin}(48^{\circ})}[/tex]
Switch sides:
[tex]\frac{b}{\text{sin}(48^{\circ})}=\frac{50}{\text{sin}(58^{\circ})}[/tex]
[tex]\frac{b}{0.743144825477}=\frac{50}{0.848048096156}[/tex]
[tex]\frac{b}{0.743144825477}*0.743144825477=\frac{50}{0.848048096156}*0.743144825477[/tex]
[tex]b=43.81501643866[/tex]
[tex]b\approx 43.82[/tex]
Therefore, the value of b is approximately 43.82 units.
What is the 4th term in the sequence of
c(n)=-7+6(n-1)
....Please help ME!!!
Answers
.. c(4) = -7 +6(4 -1)
.. = -7 +18
.. = 11
The 4th term is 11.
Two angles of a triangle measure 58° and 42°. What is the measure, in degrees, of the third angle?
A.60 degrees
B. 90 degrees
C.75 degrees
D.80 degrees
The correct answer will receive full points and the brainiest
Answers
ANSWER THIS BEFORE 3 MINUTES, AND I WILL GIVE YOU BRAINIEST AND 15 POINTS!!!
PROBLEM:
In a heptagon, the degree measures of the interior angles are
x, x, x-2, x-2, x + 2, x + 2 and x + 4 degrees. What is the degree measure of the largest interior angle?
Answers
The largest interior angle of the heptagon, given the angle measures as x, x, x-2, x-2, x+2, x+2, x+4, is 132 degrees after solving for x.
The problem is to determine the degree measure of the largest interior angle in a heptagon. The degree measures of the interior angles are given as x, x, x-2, x-2, x+2, x+2, and x+4 degrees. To solve this, we first use the fact that the sum of the interior angles of a heptagon (7-sided polygon) is given by the formula (n-2) 180 degrees, where n is the number of sides. So, for a heptagon, the sum is
(7-2) 180 = 900 degrees.We then set up the equation based on the given interior angles: 3x + (2x - 4) + (2x + 4) + (x + 4) = 900. Simplifying, we get 7x + 4 = 900. Solving for x, we find x = 896/7 = 128 degrees. The largest interior angle is x + 4, which equals
128 + 4 = 132 degrees.Find the value of a and b
Answers
Answer:
The value of a is 14 unit and the value of b is [tex]6\sqrt{2}[/tex] unit
EXPLANATION:
Draw a perpendicular line from vertex B to DC at E.
Labeling the diagram as shown in the attachment:
Now, as you can see from the Figure as shown in the attachment that [tex]ABDE[/tex] represents the rectangle because a rectangle is a quadrilateral with four right angles and their opposite sides would be parallel.
Therefore, we have the sides [tex]AB=DE=8[/tex] unit , and [tex]AD=BE=6[/tex] unit.
Consider the right triangle BEC
BY 45 45 90 triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.
therefore, the length of side, [tex]BE=EC=6[/tex] unit
Using trigonometric ratio; to find the value of b:
[tex]\sin \theta =\frac{perpendicular}{Hypotenuse}[/tex]
∴ using trigonometric sine ratio in triangle BEC, we have
[tex]\sin 45^{\circ} =\frac{6}{b}[/tex] or
[tex]\frac{1}{\sqrt{2} }= \frac{6}{b}[/tex]
On Simplify:
[tex]b=6\sqrt{2}[/tex] unit
and the value of a = DC = DE+EC=8+6=14 unit
Therefore, the value of a is 14 unit and b is [tex]6\sqrt{2}[/tex] unit
3 is less than or equal to x, and x is less than or equal to 9
Answers
Hope this helped!
What is 1,400,000 multiplied by 3.5x10^5 expressed in scientific notation?
Answers
One can solve this question by converting 1,400,000 into scientific notation. The equation then becomes --> (1.4x10^6)(3.5x10^5). Then, one can multiply 1.4 by 3.5 and use exponent laws to get x10^11.
1.4x3.5 = 4.9
(10^6)(10^5)=10^11
Therefore, the answer will be 4.9x10^11.
The answer is [tex]\( 4.9 \times 10^{11} \)[/tex].
To solve the given mathematical problem, we will multiply the two numbers and then express the result in scientific notation.
First, let's multiply 1,400,000 by 3.5x10^5 without converting them to scientific notation:
[tex]\[ 1,400,000 \times 3.5 \times 10^5 \][/tex]
[tex]\[ = 1400000 \times 3.5 \times 10^5 \][/tex]
[tex]\[ = 4900000 \times 10^5 \][/tex]
Now, we have the product 4900000. To express this in scientific notation, we must write it as a number between 1 and 10 multiplied by a power of 10. The number 4900000 can be written as 4.9 followed by 11 zeros, which in scientific notation is [tex]\( 4.9 \times 10^{11} \)[/tex].
Therefore, the final answer, expressed in scientific notation, is:
[tex]\[ \boxed{4.9 \times 10^{11}} \][/tex]
Which statement is true about the product of a non-zero rational number and an irrational number?
A) The product of a non-zero rational number and an irrational number is always a rational number.
B) The product of a non-zero rational number and an irrational number is never an irrational number.
C) The product of a non-zero rational number and an irrational number is sometimes a rational number.
D) The product of a non-zero rational number and an irrational number is always an irrational number.
Answers
The answer is defiantly D
If t(n) 2n+3 what is the 3rd term
Answers
t(3)=2(3)+3
6+3 = 9
In triangle QRS, QR is congruent to SR and RT bisects QS. What justification can you give for QRT congruent to SRT and give the Triangle Congruence Postulate that supports your reason.
Answers:
Midpoint Theorem, SSS
Given, SSS
Definition of a segment bisector; SSS
Definition of an isosceles triangle, SAS,
Answers
Explanation:
Since RT bisects QS, we have QT congruent to ST.
By SSS, we have triangle QRT congruent to triangle SRT
so, since QT is congruent to ST, RT is congruent to RT, and QR is congruent to SR.
All these sides are congruent to each other that gives the proof of "SSS(SIDE, SIDE, SIDE)"
Part A: Explain why we do not measure the rate at which water flows out through a shower head in cubic meters per second? In your explanation, use reasoning based on appropriate units to model this situation. (5 points) Part B: What are the two quantities that should be measured to find the rate at which water flows out of a shower head? Explain how the rate can be determined. (5 points)
Answers
We have that we can calculate the rate if we know the surface area of the flow and the speed of the water. If one multiplies those 2 together, one gets the rate because the speed of water is pretty much how much a front of water is moving per second; if you multiply it by its surface area, you get how much a volume of water is moving.
The units to measure the rate of water flow from a shower are smaller than cubic meters per second due to the typical small value of this rate. To determine the rate, you need to know the cross-sectional area of the outlet and the water speed, multiplying the area by the speed.
Explanation:Part A: We do not measure the rate at which water flows out through a shower head in cubic meters per second because the typical rate of water flow from a shower is much smaller compared to one cubic meter per second. Using such a large unit for a typically small value would result in decimal figures that are often difficult to comprehend. For instance, a regular shower might output 0.01 cubic meters per minute, which convert to a very small number in cubic meters per second; hence cubic centimeters per second or liters per minute are more practical units.
Part B: To calculate the rate of flow from a showerhead, you need to know two quantities: the cross-sectional area of the outlet (which can be calculated if you know the diameter), and the speed at which the water is moving. The rate of flow (volume per unit time) can then be determined by multiplying the area by the speed of the water. Based on the given data from your textbook - a faucet with a 1.80-cm diameter and a speed of 0.500 m/s - the flow rate can be determined using the formula for the volume of a cylinder (Area of the base x Height), where in this case the 'height' would be the speed.
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in the formula for a sphere what is decimal that represents the fraction 4.3
Answers
the volume of a sphere is V = 4/3 πr³
the fraction (4/3) is equal to 1.33
the answer is 1.33
will give medal to best answer!
The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used.
C = 38°, a = 19, c = 10,
Answers
Begin with applying the Law of Sines to find angle A:
[tex] \frac{sin A }{a} [/tex] = [tex] \frac{sin C }{c} [/tex]
Then, solve for sin A:
sin A = [tex] \frac{a sinC}{c} [/tex]
Now, plug in numbers:
sin A = 19 × sin(38) / 10 = 1.17
We know that it does not exist an angle whose sin is bigger than 1, therefore
no triangle is formed.
Answer:
No triangle is formed
Step-by-step explanation:
took test
Ppose you have two coins, one biased, one fair, but you don't know which coin is which. coin 1 is biased. it comes up heads with probability 2/3, while coin 2 comes up heads with probability 1/2. suppose you pick a coin at random and flip it. let ci denote the event that coin i is picked. let h and t denote the possible outcomes of the flip. given that the outcome of the flip is a head, what is p[c1|h], the probability that the biased coin is picked?
Answers
Which of the following is not an identity?
A. cos^2 x csc x - csc x = -sin x
B. sin x(cot x + tan x) = sec x
C. cos^2 x - sin^2 x = 1- 2sin^2 x
D. csc^2 x + sec^2 x = 1
***i don't really get this one :( @terenzreignz? what do u think?,
Answers
The process for each option is to rewrite the equation, attempting to obtain the identity sin^2 x + cos^2 x = 1. In general convert each function to its equivalent using just sin and cos.
A. cos^2 x csc x - csc x = -sin x
cos^2 x * 1/sin x - 1/sin x = -sin x
(cos^2 x * 1/sin x - 1/sin x) * sin x = -sin x * sin x
cos^2 x * 1 - 1 = -sin^2 x
cos^2 x = -sin^2 x + 1
cos^2 x + sin^2 x = 1
Option A is an identity.
B. sin x(cot x + tan x) = sec x
sin x(cos x/sin x + sin x/cos x) = 1/cos x
cos x + sin^2 x/cos x = 1/cos x
cos^2 x + sin^2 x = 1
Option B is an identity.
C. cos^2 x - sin^2 x = 1- 2sin^2 x
cos^2 x - sin^2 x + 2sin^2 x = 1- 2sin^2 x + 2sin^2 x
cos^2 x + sin^2 x = 1
Option C is an identity.
D. csc^2 x + sec^2 x = 1
1/sin^2 x + 1/cos^2 x = 1
cos^2 x/(cos ^2 x sin^2 x) + sin^2 x/(cos^2 x sin^2 x) = 1
(cos^2 x + sin^2 x)/(cos ^2 x sin^2 x) = 1
1/(cos ^2 x sin^2 x) = 1
1 = cos ^2 x sin^2 x
Option D is NOT an identity.
Solve the triangle.
A = 48, a = 32, b = 27
I am completely blanking on how to do this, so if you could please do a step by step process, that would be greatly appreciated :)
Answers
sin B = (27/32)*sin 48 = 0.6270 or
B = 39°; C=180-48-39 = 93°
c^2 = a^2 +b^2 -2abcos C = 32^2 +27^2 -{2*32*27*cos 93}=1843 or
c =43
Answer:
The triangle is A = 48°, a = 32, B = 38.83°, b = 27, C = 93.17° and c = 42.99
Step-by-step explanation:
We have sine rule,
[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]
Here given A = 48°, a = 32, b = 27
Substituting
[tex]\frac{32}{sin48}=\frac{27}{sinB}=\frac{c}{sinC}\\\\sinB=0.627\\\\B=38.83^0[/tex]
We have
A + B + C = 180°
48 + 38.83 + C = 180
C = 93.17°
Using sine rule again
[tex]\frac{32}{sin48}=\frac{c}{sin93.17}\\\\c=42.99[/tex]
So the triangle is A = 48°, a = 32, B = 38.83°, b = 27, C = 93.17° and c = 42.99
(Please Help~! 20 Points~!)
Which of the following is the solution to the equation 3/4y = 24?
y = 18
y = 32
y = 64
y = 72
Answers
Brainliest please?
I am trying to move up my rank to Ace!
[tex] \dfrac{3}{4}y = 24[/tex]
Rewrite into single fractions
[tex] \dfrac{3y}{4} = \dfrac{24}{1} [/tex]
Cross multiply
[tex]3y = 24 \times 4[/tex]
Evaluate the right side
[tex]3y = 96[/tex]
Divide by 3 on both sides
[tex]y = 32[/tex]
-------------------------------
Answer: y = 32
-------------------------------
A 32 ft ladder liens against a building so that the top of the ladder touches the building at a point 23 ft above the ground. To the nearest 10th of a foot how far from the bottom of the building is the bottom of the ladder
A. 27.5 ft
B. 39.4 ft
C. 22.2 ft
D. 30.1 ft
Okay so I’m thinking between C and B. I’m more so C because I did 32 as c and 23 as be so... or it could be the other way around
I just know it’s Pythagorean theorem help. Sending stars
Answers
529 + b^2 = 1024
b^2 = 1024 -529 = 495
b = sqrt(495) = 22.24
Answer = C. 22.2 ft
Ellen has a $19,750 balance on a credit card with an APR of 18%. If she makes minimum monthly payments of $300, how much will it cost Ellen to repay the total amount on the credit card? $
Answers
Does this set of ordered pairs represent a function? Why or why not?
{(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)}
A. Yes, because there are two x-values that are the same.
B. No, because two of the y-values are the same.
C. Yes, because every x-value corresponds to exactly one y-value.
D. No, because one x-value corresponds to two different y-values.
Answers
C. Yes, because every x-value corresponds to exactly one y-value.
Final answer:
The set of ordered pairs represents a function Yes, because every x-value corresponds to exactly one y-value(C).
Explanation:
The set of ordered pairs {(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)} represents a function because every x-value corresponds to exactly one y-value. In a function, each input (x-value) has only one output (y-value). The set does not have two different y-values for the same x-value, so option D is incorrect. Therefore, option C is the correct answer.
(C). Yes, because every x-value corresponds to exactly one y-value.
You can see that each unique x-value corresponds to exactly one y-value, and there are no repeated x-values. Therefore, this set of ordered pairs represents a function.
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The musical frequency of notes is decreasing between beat numbers ___ and ___
Answers
we have that
between beats 2 and 3----------> (392-261.6)=130.4-------> increases
between beats 3 and 4----------> (392-392)=0-----> it stays with the same value
between beats 4 and 5----------> (444-392)=52--------> increases
between beats 5 and 6----------> (444-444)=0-----> it stays with the same value
between beats 6 and 7----------> (392-444)=-52-------> decreases
the answer is
between beats 6 and 7----------> (392-444)=-52-------> decreases
On Chris' birthday in 1992, he was half the age of his brother Joseph. On Chris' birthday in 1998, he was two-thirds the age of Joseph. How old will Chris be on his birthday in 2018?
Answers
Step 1: Form an equation.
We know that in 1992, Chris was HALF the age of Joseph. So Chris was x years old, while his brother was twice his age, or 2x. 6 years later, he was two-thirds the age of his brother. So, he was (x+6) while his brother was (2x+6).
So, we can form this:
(X+6)=(2/3)(2x+6)
Step 2: Simplify the equation. Distribute, Subtract, multiply
(X+6)=(2/3)(2x+6)
Distribute: X+6=(2/3)(2x)+(2/3)(6)
X+6=4/3x+4
Subtract:
X+6-4/3x=4/3x+4-4/3x
-1/3x+6=4
Subtract:
-1/3x+6-6=4-6
1/3x=-2
Multiply:
(3/-1) * (-1/3x)=(3/-1)*(-2)
X=6
This means in 1992, Chris was indeed 6 years old, while his brother was 12. 6 years later, Chris was 12 years old, while his brother was 18. (6/12=1/2; 12/18=2/3)
So, from 1992-2018=26 years.
In 1992 Chris was already 6.
26+6=32
In 2018, Chris is 32 years old, his brother is 6 years older, 38.
Chris is 32 years old.
~Hope this helps!
Let f(x)=x^2−3x−4 .
What is the average rate of change from x = 7 to x = 10?
Enter your answer in the box.
Answers
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An acidophilus culture containing 150 bacteria doubles in population every hour. (a) Write a function representing the bacteria population for every hour that passes. (b) Graph the function. (c) Use the graph to predict the number of bacteria after 12 hours.,
Answers
We have then:
y = A * (b) ^ t
Where,
A: Initial population
b: Population growth as time passes
t: time
y: population after t hours.
Part A:
The equation for this case is:
y = 150 * (2) ^ t
Part B
See attached image.
Part C:
For this case we should evaluate the function for t = 12
We have then:
y = 150 * (2) ^ (12)
y = 614400
y = 150 * (2) ^ t
t= 12
y = 150 * (2) ^ (12)
y = 614400
The answer to your questions is y is equals to 614400.
Natalie opened a bank account that earns 2.5% simple interest. If her account earned $180 over the next ten years, how much was Natalie’s initial deposit when she opened the account?
Answers
Answer: $720.
Step-by-step explanation:
The formula to find the simple interest is given by :-
[tex]I=Prt[/tex], where P is the principal amount , r is the rate of interest in decimal and t is the time in years.
Given : Rate of interest : r= 0.025
Simple interest : I= $180
Time : t=10
Let P be the Natalie’s initial deposit when she opened the account, then we have:-
[tex]180=P(0.025)(10)\\\\\Rightarrow\ P(0.25)=180\\\\\Rightarrow\ P=\dfrac{180}{0.25}=\dfrac{18000}{25}=720[/tex]
Hence, the Natalie’s initial deposit when she opened the account was $720.
how do i solve problem a. and problem b? (using the pythagorean theorem). a. the median to the hypotenuse. b. the altitude to the hypotenuse.
Answers
from mathopenref: median: "A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side."
if we draw a median to the hypotenuse, then we have to draw from the right angle to the hypotenuse.
we use a theorem: "In a right triangle, the median drawn to the hypotenuse has the measure half the hypotenuse. "
the length of the median to the hypotenuse is half the hypotenuse: 5
for altitude:
we draw line on hypotenuse that is perpendicular to hypotenuse to a vertex of the angle opposite to it.
look at my diagram: h is the altitude length
x and y are segments of the original hypotenuse
we have ΔABD with legs of x and h and hypotenuse of 6
ΔABD: x² + h² = 6²
we have ΔBCD with legs of 10-x and h and hypotenuse of 8
ΔBCD: (10-x)² + h² = 8²
this is a system of equations
x² + h² = 6²
(10-x)² + h² = 8²
isolate h² in x² + h² = 6² so that we can substitute:
h² = 6² - x²
h² = 36 - x²
substituting into (10-x)² + h² = 8² we have
(10-x)² + h² = 8²
(10-x)² + (36 - x²) = 8² ...............substitution done
(10-x)² expands to 100 - 20x + x²
100 - 20x + x² + (36 - x²) = 64
+x² and -x² cancel
100 - 20x + 36 = 64
136 - 20x = 64
-20x = -72
x = 3.6
Since h² = 36 - x², then h = √(36 - x²) and
h = √(36 - 3.6²) =4.8
the altitude is 4.8
The width of Zorn's patio is labeled in the diagram below. If the perimeter of the patio is (30x + 26) feet, what is the length of the patio?
2x^2=450
Determine which statement is true about the solutions to the equation.
The solutions are -15 and 15 and both are reasonable side lengths.
The solutions are -30 and 30 and both are reasonable side lengths.
The solutions are -30 and 30 but only 30 is a reasonable side length.
The solutions are -15 and 15, but only 15 is a reasonable side length.
Answers
2x²=450 ----------> x²=450/2----------> x=√225
x1=+15
x2=-15
a reasonable length measurement should be positive
therefore
the answer is
The solutions are -15 and 15, but only 15 is a reasonable side length.
Answer:
the answer is (8x+9)
Step-by-step explanation:
A cafe offers senior citizens a 15% discount off its regular price of $8.95 for the dinner buffet. How much of a discount does a senior citizen receive off of the $8.95 price?
Answers
:)
Hope this helps
Answer:
$1.3425
Step-by-step explanation:
The regular price of the dinner buffet is 8.95. If this has a discount of 15%, we would have to multiply the total price by 0.15 and this would give us how much of the total amount is 15% and therefore it would give us how much of a discount the senior receives off of the 8.95 price
8.95 x 0.15 = 1.3425
Therefore, a senior citizen gets $1.3425 discount.
HELP PLS
Let f(x)=2/5 x^2−2 .
The function g(x) is a vertical stretch of f(x) by a factor of 2.
What is the equation of g(x)?
Enter your answer in the box.
Answers
To graph y = a*f (x)
if a> 1, the graph of y = f (x) is expanded vertically by a factor a.
We have then:
f (x) = 2/5 x ^ 2-2
The function g (x) is a vertical stretch of f (x) by a factor of 2:
g (x) = 2f (x)
g (x) = 2 (2/5 x ^ 2-2)
g (x) = 4/5 x ^ 2-4
Answer:
The equation of g (x) is:
g (x) = 4/5 x ^ 2-4
Answer:
We have then:
f(x) = 2/5x^2-2 The function g (x) is a vertical stretch of f(x) by a factor of 2:
g(x) = 2f (x)
g(x) = 2 (2/5x^2-2)
g(x) = 4/5 x^2-4 is a required equation.