Answer:
Golf ball = 4.5, Baseball = 2.25Step-by-step explanation:
The average rate of change between two points is the slope of the line between those points.
Golf ballThe points are:
(3, 14) and (7, 32)The slope is:
m = (32 - 14)/(7 - 3) = 18/4 = 4.5BaseballThe points are:
(3, 6) and (7, 15)The slope is:
m = (15 - 6)/(7 - 3) = 9/4 = 2.25Answer:
[tex]\textsf{Average rate of change of the golf ball}=\dfrac{9}{2}\; \sf m/s[/tex]
[tex]\textsf{Average rate of change of the baseball}=\dfrac{9}{4}\; \sf m/s[/tex]
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\boxed{\dfrac{f(b)-f(a)}{b-a}}[/tex]
To find the average rate of change from 3 to 7 seconds:
a = 3b = 7Therefore, use the formula:
[tex]\implies \dfrac{f(7)-f(3)}{7-3}[/tex]
Golf Ball
[tex]\begin{array}{|c|c|}\cline{1-2} \sf Seconds & \sf Meters \\\cline{1-2} 0&0\\\cline{1-2} 3&14\\\cline{1-2} 7&32\\\cline{1-2} 9&24\\\cline{1-2} 12&2\\\cline{1-2}\end{array}[/tex]
From inspection of the table:
f(3) = 14f(7) = 32Substitute these values into the formula to find the average rate of change of the golf ball from 3 seconds to 7 seconds:
[tex]\implies \textsf{Average Rate of Change}=\dfrac{f(7)-f(3)}{7-3}=\dfrac{32-14}{7-3}=\dfrac{9}{2}\; \sf m/s[/tex]
Baseball
[tex]\begin{array}{|c|c|}\cline{1-2} \sf Seconds & \sf Meters \\\cline{1-2} 0&0\\\cline{1-2} 3&6\\\cline{1-2} 7&15\\\cline{1-2} 9&13\\\cline{1-2} 12&0\\\cline{1-2}\end{array}[/tex]
From inspection of the table:
f(3) = 6f(7) = 15Substitute these values into the formula to find the average rate of change of the baseball from 3 seconds to 7 seconds:
[tex]\implies \textsf{Average Rate of Change}=\dfrac{f(7)-f(3)}{7-3}=\dfrac{15-6}{7-3}=\dfrac{9}{4}\; \sf m/s[/tex]
Which of the following is an example of a conditional statement?
How do you find cos 60 degrees?
Answer:The value of cos 60 degrees can be calculated by constructing an angle of 60° with the x-axis.
Step-by-step explanation:
Then finding the coordinates of the corresponding point (0.5, 0.866) on the unit circle.
The value of cos 60° is equal to the x-coordinate (0.5).
∴ cos 60° = 0.5.
The value of cos 60° using trigonometric ratio is 1/2 or 0.5 .
What is trigonometric ratios?
There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their relative angles using trigonometric ratios.
Here , the given is ,
=> cos60°
Since the cosine function is a periodic function, we can represent cos 60° as, cos 60 degrees = cos(60° + n × 360°),
Then
=> Cos 60° = 1/2 = 0.5.
Hence the value of cos 60° is 1/2 or 0.5.
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I need help with the last two questions please
For the image 1, the angular values are x=9⁰ and y=23⁰
For the image 2, the angular values are x=9⁰ and y=14⁰
What is meant by an angle?An angle is a figure in Euclidean geometry made up of two rays that share an endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are located in the plane where the rays are located. The meeting of two planes can also create an angle. Dihedral angles are what they are. A measure of an angle or of a rotation is also referred to as an angle. The ratio of a circular arc's length to radius is known as this quantity. A geometric angle's arc is centered at the vertex and is bound by its sides.
For the first image x and y values are,
As from the given figure,
(4y-2)⁰=90⁰
4y=90+2
y=92/4
y=23⁰
3x-6=21⁰
3x=27
x=9⁰
Therefore, x=9⁰ and y=23⁰
For the second image x and y values are,
2x+27=90/2
2x+27=45
2x=18
x=9⁰
4y-19=y+23
3y=42
y=14⁰
Therefore, x=9⁰ and y=14⁰
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A coach has to form 4 doubles teams from 8 badminton players. In how many ways can he form the teams? (A doubles team is a pair of players, and a player cannot be a member of more than one doubles team.)
The number of ways he can form the teams would be = 336 ways.
What is badminton?Badminton is a type of racket game that makes use of single or double players where by they make use of a racket to hit a shuttlecock over the net to their opponents side.
The number of players available for the badminton game = 8
The number of teams to the formed = 4
To find the number of ways to form 4 double teams from these 8 players would be to find the factorials of 8 divided by factorial 4.
That is ;
8!/4! = 8×7×6×4×3×2×1/4×3×2×1
= 8064/ 24
= 336 ways.
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V(d)V, left parenthesis, d, right parenthesis models Aria's vertical distance from the top of the valley (in kilometers) after walking ddd kilometers along the trail.
What does the statement V(3)<3V(3)<3V, left parenthesis, 3, right parenthesis, is less than, 3 mean?
Aria's vertical distance from the top of the valley after walking 3 km along the trail is less than 3 km.
Since Here d represents distance along the trail.
And, V(d) represents the vertical distance from the top of the valley (in kilometers) after walking d kilometers along the trail.
If the distance along the trial is 3 km.
That is, d = 3
Then the vertical distance she walked from the top of the valley = V(3)
But According to the question,
V(3) < 3
Her vertical distance from the top of the valley after walking 3 km along the trail is less than 3 km.
Hence, For going 3 km along the trail her vertical distance from the top of the valley is less than 3.
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which expressions describe the end behaviors of the function, f(x)=(3.25)^x+6, modeled by the graph.
Select each answer,
As x decreases without bound, f(x) increases without bound
As x increases wthout bound f(x) increases without bound
As x decreases without bound, f(x) approaches the line y=6
As x increases without bound, f(x) approaches the line y=6
For the given function, f(x)=(3.25)^x+6 As x decreases without bound, f(x) increases without bound
To describe the end behaviors of the function modeled by the graph,
f(x)=(3.25)^x+6
What are functions?
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.
Here,
The function given is,
f(x)=(3.25)^x+6
Given function contains equality so the function has no boundaries and the function is described from negative infinity to positive infinity, But the function has inverse behavior as when x is negative the function is positive.
Thus, for the given function, f(x)=(3.25)^x+6 asAs x decreases without bound, f(x) increases without bound
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617/50 into simplest form
Since fractions are the same as division, divide 617 by 50. The remainder will remain in fraction form.
617/50
600/50 = 12
617/50 = 12 17/50
Bro... Please.. Help im desperate. I swear I will give brainliest.
Answer:
A: Ira begins walking
B: Ira stops at a diner
C: Ira leaves the diner
D: Ira visits his grandmother
E: Ira walks from grandma’s house to home
Step-by-step explanation:
Hopes this helps please mark brainliest
Solve the system of equations by graphing
u=v
4u=2v-12
The solution to the system of linear equations u = v and 4u = 2v - 12 is (-6, -6)
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
u = v and 4u = 2v - 12
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (-6, -6)
Hence, the solution is (-6, -6)
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-6.4 = x + 4.3 how do I figure this question out (I’m trying to figure out what number x is)
Answer: x = -10.7
Step-by-step explanation:
-10.7 + 4.3 = -6.4
6. Given AACP ALNX, find each missing measure. N 29° 13 cm P CX V L 21 cm a) XL = b) AC= c) PC = d) m/L= e) m/C= f) m/X=
The missing measure is ∠P =∠X = 122°
Given △ACP ≅ △LNX
XL = 13 cm, m∠L = 29°
AC = 21 cm, m∠C = 29°
PC = 13 cm, m∠Y = ?? (there is no angle Y)
On the right shows the triangles are isosceles, with XL = XN. That means also PA = PC. Those side lengths are all the same: 13 cm.
PA = PC = XL = XN = 13 cm
In the same way, ...
LN = AC = 21 cm
Of course, the angles have a similar relationship:
∠A = ∠C = ∠L = ∠N = 29°
The two base angles in the triangle add to 58°, so the third angle is ...
180° -58° = 122°
∠P =∠X = 122°
As is often the case in over-specified problems, the numbers shown are not consistent. The length LN is actually incorrect for the angle and side specified for triangle ACP, or the angles are incorrect for the side lengths specified. What this means is that the answers you get will depend on how you work the problem. Above, we have taken the given numbers and relationships at face value, even though we know they are incorrect.
Hence the answer is The missing measure is ∠P =∠X = 122°
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12. Brandi solves the problem
could she check her answer?
1,621 /4 = 404 R1
Using simple mathematical operations, we know that Brandi's answer which is 404 is incorrect.
What are mathematical operations?A mathematical function known as an "operation" in mathematics is one that converts zero or more input values into a precisely specified output value.
The quantity of operands has an impact on the operation's complexity.
Exponents, PEMDAS, parenthesis, multiplication, and division.
So, to check whether Brandi's answer is correct:
1621/4 = 404
So, to check it is ts correct, multiply 404 by 4.
If the answer is correct, then the product will be 1621.
If the answer is wrong, the product will not be 1621.
Calculate as follows:
404 × 4 = 1,616
Therefore, using simple mathematical operations, we know that Brandi's answer which is 404 is incorrect.
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There are 4 times as many alligators as crocodiles. If the total number of alligators and crocodiles is 35 , how many alligators are there
Answer:
140
Step-by-step explanation:
It's 140 because 35 x 4 (4 TIMES) meaning you multiply. 35 x 4 is 140, meaning there are 140 alligators.
Four children (Sam, Inez, Mahmoud and
Katrina) are running a race. They are each
wearing a distinctive article of clothing (a
red shirt, a hat, sunglasses and a scarf).
Consider the following statements:
The child wearing a red shirt finished
before Sam but after the child wearing a
hat.
Katrina is wearing sunglasses.
The child wearing a scarf finished the race
last.
Inez finished the race before the person
wearing sunglasses.
Mahmoud is not wearing a hat.
Who won the race?
Inez had won the race.
What is sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has members (also called elements, or terms). The length of the series is the number of elements (potentially infinite).
Sam finished the race after the youngster wearing the shirt, who finished after the child wearing the hat, according to the information provided.Sam, red shirt, hat is the order from last to first.Inez also finished before to Katrina. Sam must be the last person to put on a scarf because Mahmoud doesn't wear a cap.Sam, Mahmoud, Katrina, and Inez are listed in order from last to first.Thus, Inez had won the race.
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A square banquet hall has an area of 3600m², what is the length of the room?
If the square banquet has area = 3600m² then length of the room is 60 m .
The Area of the Square with side "s" can be calculated using the formula
Area = s × s
In the question ,
it is given that ,
the area of the Square banquet is = 3600m² ,
let the length of the side of the room be "s" .
So , By the Area of the Square formula ,
we get ,
s × s = 3600
s² = 3600
taking quare root both the sides ,
we get
√s² = √3600
s = 60
the side = 60m
Therefore , If the square banquet has area = 3600m² then length of the room is 60 m .
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Use the discriminant to describe the roots of each equation. Then select the best description. 6x2 + 13x + 6 = 0
The quadratic equation 6 · x² + 13 · x + 6 = 0 has a positive discriminant and its roots are two distinct real numbers.
What is the nature of the roots of a quadratic equation?
In this problem we must infer the features of the two roots of a quadratic equation of the form a · x² + b · x + c = 0, this can be done by means of the discriminant from the quadratic formula:
D = b² - 4 · a · c
Where a, b, c are real coefficients of the quadratic equation.
There are three possibilities for the results of the discriminant:
D < 0, conjugated complex numbers.D = 0, equal real numbers.D > 0, different real numbers.First, write the quadratic equation:
6 · x² + 13 · x + 6 = 0
Second, collect the real coefficients of the polynomial:
(a, b, c) = (6, 13, 6)
Third, calculate the discriminant:
D = 13² - 4 · 6²
D = 169 - 144
D = 25
The quadratic equation has two roots that are real and different.
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Simplify the power (-3x^2y)^4
⇒In this case I will use the law of exponents that states:
[tex](x^{m} )^{n} \\=x^{m*n}[/tex]
⇒[tex]=(-3x)^{2y*4} \\=(-3x)^{8y}[/tex]
Answer: 81x^8y^4
Step-by-step explanation:
1. DISTRIBUTE EXPONENT by using the power rule: (ab)^n = (a^n)(b^n)
> Apply PRODUCT RULE: -3x^2y = (-3x^2)^4y^4
>Apply PRODUCT RULE: -3x^2 = (-3)^4 (x^2)^4y^4
2. RAISE -3 to the power of 4 = 81(x^2)^4y^4
3. MULTIPLY THE EXPONENTS in (x^2)^4
> Apply POWER RULE and MULTIPLY EXPONENTS, (a^m)^n = a^mn
(81x^2*4)(y^4)
> MULTIPLY 2 by 4 = 81x^8y^4
And that is your answer, 81x^8y^4
At the end of year 5, the account was valued at $3203.19. At the end of year 6, the account was valued at $3315.30. What was the interest rate, as a percent?
well, from the end of year 5 to the end of year 6 is only 1 year later, so
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$3315.30\\ P=\textit{original amount deposited}\dotfill & \$3203.19\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 3315.30=3203.19[1+(\frac{r}{100})(1)] \implies \cfrac{3315.30}{3203.19}=1+\cfrac{r}{100} \\\\\\ \cfrac{3315.30}{3203.19}-1=\cfrac{r}{100}\implies 100\left( \cfrac{3315.30}{3203.19}-1 \right)=r\implies \stackrel{\%}{3.5}\approx r[/tex]
Solve for x: 6 over x equals 4 over 8 a 10 b 12 c 24 d 48
Answer:
B. 12
Step-by-step explanation:
Question 8 of 25
f(x) = 2x³ + 6x² - 5x - 3
g(x) = 3x - 4
Find (f - g)(x).
A. (f- g)(x) = 2x³ + 6x²
OB. (f-g)(x) = 2x³ + 6x²
Oc. (f- g)(x) = 2x³ + 6x²
D. (fg)(x) = 2x³ + 6x²
www
*****
www
2x+1
8x7
2x - 7
8x +1
For the given function f(x) = 2x³ + 6x² - 5x - 3 , g(x) = 3x - 4 , the value of
(f -g)(x) = 2x³ + 6x² -8x + 1 .
As given in the question,
Function is given by :
f(x) = 2x³ + 6x² - 5x - 3 , g(x) = 3x - 4
Substitute the value in the given function and simplified it ,
( f - g )(x)
= { 2x³ + 6x² - 5x - 3 } - { 3x - 4 }
= 2x³ + 6x² - 5x - 3 -3x + 4
= 2x³ + 6x² -5x -3x -3 + 4
= 2x³ + 6x² - 8x + 1
Therefore, for the given function f(x) = 2x³ + 6x² - 5x - 3 , g(x) = 3x - 4 , the value of (f -g)(x) = 2x³ + 6x² -8x + 1 .
The complete question is:
If for the given function ,
f(x) = 2x³ + 6x² - 5x - 3 , g(x) = 3x - 4
Find the value of (f - g)(x).
a. 2x³ + 6x² -8x + 1
b. 2x³ + 6x² + 2x+1
c. 2x³ + 6x² + 2x -7
d. 2x³ + 6x² + 8x⁷
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MP Use Tools A bobsled team is practicing runs on
a track. Their first run takes 4.85 minutes. On each
of the next two runs, the team's time changes by
-0.27 minute compared to the previous time.
A. What was the team's time on their final run?
The team's time on their final run is 4.31 minutes.
According to the question,
We have the following information:
Their first run takes 4.85 minutes. On each of the next two runs, the team's time changes by -0.27 minute compared to the previous time.
Now, the second run will be 0.27 minutes less than 4.85 minutes.
Time for the second run = 4.58 minutes
Now, the third run will be the final run and 0.27 minutes less than the previous run.
Now, the time for the final run will be as given below:
4.58-0.27
4.31 minutes
Hence, the team's time on their final run is 4.31 minutes.
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Purchase price $ 70,000
Delivery cost $ 3,000
Installation charge $ 1,000
Estimated life 5 years
Estimated units 140,000
Salvage estimate $ 4,000
Purchase price $ 70,000
Delivery cost $ 3,000
Installation charge $ 1,000
Estimated life 5 years
Estimated units 140,000
Salvage estimate $ 4,000
Straight-line YR1 and YR2
Double-declining YR1 and YR2
Unit-of-production YR1 and YR2
($$ amounts)
Using the straight line method, the depreciation expense in year 1 and 2 is $14,000.
Using the double declining method, the depreciation expense in year 1 is $29,600 and $17,760 in year 2.
Using the unit of production method, the depreciation expense in year 1 is $18,000 and $19,000 in year 2.
What are the depreciation expenses?The straight line depreciation method is a depreciation method in which the the depreciation amount each year of the asset's useful life is the same.
Straight line depreciation = (cost of the asset - salvage value) / useful life
Cost of the asset = $70,000 + $3000 + $1000 = $74,000
Straight line depreciation = ($74,000 - $4,000) / 5 = $14,000
The double declining method entails depreciating an asset at twice the rate of the straight line method.
Depreciation expense = cost of the asset x depreciation factor
Depreciation factor = 2 x (1/useful life)
Depreciation expense in year 1 = (2 /5) x $74,000 = $29,600
Book value in year 2 = $74,000 = $29,600 = $44,400
Depreciation expense in year 2 = (2 /5) x $44,400 = $17,760
The depreciation in the unit of production method depends on the output of the machine each year.
Depreciation = (output in a year / total output) x (cost of the asset - salvage value)
Depreciation in year 1 = ($74,000 - $4,000) x (36,000 / 140,000) = $18,000
Depreciation in year 2 = ($74,000 - $4,000) x (38,000 / 140,000) = $19,000
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Here is the rest of the question:
Units produced in Year 1 = 36,000 units
Units produced in Year 2 = 38,000 units.
What is 3.072 times 8 simplfyed
Please help with this quick!
rename each of the following using the distributive property of multiplication so there are no parentheses in the final answer
(a+b)(c+d)
Answer:
ac + ad + bc + ad
Step-by-step explanation:
We are going to be using the FOIL (First, Outer, Inner, Last) method.
If we use this, we end up with:
ac + ad + bc + ad
1) Graph the function by plotting the ordered pairs (0, 0) (10, 125) (20, 250) (30, 375) (40, 500) and
drawing a straight line through the points. Label the axes with appropriate
variable
quantities
and units. Label the points with the correct ordered pairs. Include a title for the graph.
The graph of the given function is attached below.
We are given a function. A function connects an input and an output. It is analogous to a machine with an input and an output. And the output is somehow related to the input.
The coordinates of several points are given. We need to graph the function by plotting the ordered pairs (0, 0), (10, 125), (20, 250), (30, 375), and (40, 500).
The function is a straight line. A straight line is a one-dimensional figure with an infinite length. It is made up of an infinite number of points connected on both sides of a point. We also need to draw the line through the points. The graph is attached below.
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Find the inverse of f(x) = 4x-1/-2x +2
The inverse of the function f(x) = (4x - 1)/(-2x +2) is equal to f⁻¹(x) = (2x + 1)/(4 + 2x).
What is an inverse function?In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of this function f(x) = (4x - 1)/(-2x +2), we would interchange both the input value (x) and output value (y) as follows:
y = (4x - 1)/(-2x +2)
x = (4y - 1)/(-2y +2)
Cross-multiplying, we have:
x(-2y +2) = 4y - 1
2x - 2xy = 4y - 1
Next, we would rearrange the function by collecting like terms as follows:
4y + 2xy = 2x + 1
y(4 + 2x) = 2x + 1
Dividing both sides of the function by (4 + 2x), we have:
y = (2x + 1)/(4 + 2x)
y = f⁻¹(x) = (2x + 1)/(4 + 2x)
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Assume that x=2 and y =9 find values of the 2 Expressions 7x +4y and 4y + 7y
Answer: 50, 99
Step-by-step explanation:
we just have to substitute the values of x and y in the given expressions.
7(2)+4(9)=50
4(9)+7(9)=99
Answer:
Step-by-step explanation:
7x + 4y= 50 and 4y + 7y= 99
Since, x=2 and y=9
7x + 4y= 7*2 + 7*9= 14 + 36= 50
and similarly
4y + 7y= 4*9 + 7*9= 36 + 63= 99
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Identify each number between 2.6×10^-1 and 29.5%. Select all that apply. Responses 2.7×10^1
0.2875
2/7
2.8%
Numbers between 2.6×10^-1 and 29.5% are
0.28752/7How to write the numbers to decimal2.6 × 10^-1 in exponential form written in decimal as 0.26
29.5% in percentage written in decimal as 0.295
2/7 in fraction written in decimal as 0.2857
2.8% in percentage written in decimal as 0.028
0.2875 already in decimal form
the problem asks of numbers from 0.26 to 0.295
comparing the numbers shows that the numbers in this range are
0.2875 and 2/7
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Jacob and his buddies paid $35.01 at a football game to buy 9 cheeseburger meals. How much did each cheeseburger meal cost?