The average speed calculated over the given time intervals is
48.42 m/s, 49.35 m/s, 50.09 m/s, 50.26 m/s, and 50.29 m/s. The estimated speed when t = 1 is 50.28 m/s.Given formula is y = 54t - 1.86t²
Speed = dy/dt = 54 - 3.72t
a) Average speed over the time intervals given below are:
In [1, 2] time interval, it is [tex]\frac{54t - 1.86t^{2} }{2-1} = \frac{54t - 1.86t^{2} }{1}[/tex] = 48.42 m/sIn [1, 1.5] time interval, it is[tex]\frac{54t - 1.86t^{2} }{1.5-1} = \frac{54t - 1.86t^{2} }{0.5}[/tex] = 49.35 m/sIn [1, 1.1] time interval, it is [tex]\frac{54t - 1.86t^{2} }{1.1-1} = \frac{54t - 1.86t^{2} }{0.1}[/tex] = 50.09 m/sIn [1, 1.01] time interval, it is [tex]\frac{54t - 1.86t^{2} }{1.01-1} = \frac{54t - 1.86t^{2} }{0.01}[/tex] = 50.26 m/sIn [1, 1.001] time interval, it is [tex]\frac{54t - 1.86t^{2} }{1.001-1} = \frac{54t - 1.86t^{2} }{0.001}[/tex]= 50.29 m/sb) When t = 1, the speed is v = 50 - (3.72*1) = 50.28 m/s
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In the linear equation y=4x +2, the value “2” represents which of the following?
Answer:
The y-intercept
Answer:
b
Step-by-step explanation:
I am thinking it would be "b" because y=mx+b so not the multiple choice but whichever one says b
Expand the following expression.
2/5(2x-7)
(just checking again)
Answer:
b
Step-by-step explanation:
2 x 2 = 4/5
2 x -7 = -14 / 5
Answer:
B) 4/5x-14/5
Step-by-step explanation:
2/5(2x-7)
2/5*2x= 4/5x
2/5*7=14/5
The age of Noelle’s dad is 6 less than 3 times Noelle’s age. The sum of their ages is 74 . Find their ages.
Answer:
The age of Noelle's dad is 54 years and that of Noelle is 20 years.
Step-by-step explanation:
Let the age of Noelle's dad is x years and that of Noelle is (74 - x) years.
{Since, the sum of their ages is 74}
Now, given that the age of Noelle's dad is 6 less than 3 times Noelle's age.
So, 3(74 - x) - 6 = x
⇒ 4x = 222 - 6 = 216
⇒ x = 54
So, the age of Noelle's dad is 54 years and that of Noelle is (74 - 54) = 20 years. (Answer)
Which choice shows the coordinates of C’ if the trapezoid is reflected across the y-axis?
On a coordinate plane, trapezoid A B C D has points (2, 1), (3, 5), (5, 3) and (3, 1).
(–5, 3)
(3, –5)
(5, –3)
(–3, 5)
The coordinates of C’ is (-5,3), the correct option is A.
How does reflection across axis work?When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if we're seeing it in a mirror.
If you study it more, you will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.
Thus, if you're reflecting a point (x,y) along x axis, then its x
abscissa will stay same but y
ordinates will negate. Thus (x,y) turns to (x, -y)
Similarly, if you're reflecting a point (x,y) along y axis, the resultant image of the point will be (-x,y)
Given;
On a coordinate plane, trapezoid A B C D has points (2, 1), (3, 5), (5, 3) and (3, 1).
Now,When a point is reflected across the y-axis, the rule is:
(x,y)→ (-x,y)
C (5.3)= C' (-5,3)
Therefore, the reflection on C will be C (5.3) C' (-5,3).
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Find the sum 5/10 + 3/100 =
Answer:
0.53
Step-by-step explanation:
5/10 + 3/100=0.53
Answer:
0.53
Step-by-step explanation:
5/10 + 3/100
by Elysium
(50 +3)/100
53/100
0.53
Write an equation that you can use to find the value of x. Perimeter of square: 30 mm An equation that you can use is =30.
Answer:30=4x
Step-by-step explanation:
what is maximum and minimum of f(x)=7x^2
Answer:
Minimum value is 0
Maximum value is undefined.
Step-by-step explanation:
The given function is [tex]f(x)=7x^2[/tex]
This function is a parabola that has its vertex at the origin.
The coefficient of the quadratic term is 7, which is greater than zero.
This means that, the graph will open up.
The graph will therefore have a minimum value of y=0
The graph of this function does not have a maximum value.
The product of a non-zero rational number and an irrational number can always be
Answer:
The product of a non-zero rational number and an irrational number will always be an irrational number.
Step-by-step explanation:
Here's a proof by contradiction for this claim.
Consider an irrational number [tex]x[/tex]. Assume by contradiction that this claim isn't true. In other words, assume that there exist a non-zero rational number [tex]y[/tex] such that [tex]x \cdot y[/tex] is a rational number.
By the definition of rational numbers, a number is a rational number if and only if it can be written as the quotient of two integers.
[tex]y[/tex] is a rational number ⇔ there exist two integers [tex]a[/tex] and [tex]b[/tex] such that [tex]\displaystyle y = \frac{a}{b}[/tex].[tex]x \cdot y[/tex] is a rational number ⇔ there exist two (other) integers [tex]c[/tex] and [tex]d[/tex] such that [tex]\displaystyle x \cdot y = \frac{c}{d}[/tex].Divide [tex]y[/tex] from both sides of the equation:
[tex]\displaystyle \frac{x\cdot y}{y} = \left.\frac{c}{d}\right/y[/tex].
The left-hand side of this equation is now equal to [tex]x[/tex].
Since [tex]\displaystyle y = \frac{a}{b}[/tex] by assumption, the [tex]y[/tex] on the right-hand side of this equation can be replaced with [tex]\displaystyle \frac{a}{b}[/tex]. Hence, the right-hand side of this equation would become
[tex]\displaystyle \frac{x\cdot y}{y} = \left.\frac{c}{d}\right/\frac{a}{b} = \frac{c}{d}\cdot \left(\frac{b}{a}\right) = \frac{b \cdot c}{a \cdot d}[/tex].
Combine the two sides of the equation to obtain:
[tex]x = \displaystyle \frac{b \cdot c}{a \cdot d}[/tex].
Since [tex]b[/tex] and [tex]c[/tex] are both integers, their product [tex]b \cdot c[/tex] would also be an integer. Similarly, since [tex]a[/tex] and [tex]d[/tex] are both integers, their product [tex]a \cdot d[/tex] would also be an integer.
In other words, [tex]x[/tex] can now be represented as the quotient of two integers. By the definition of rational numbers,
Hence, the original assumption that this claim isn't true, is not true. That verifies the claim that the product of a non-zero rational number and an irrational number would be an irrational number.
Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use / for the fraction bar(s).
What is the mean of the given distribution, and which type of skew does it exhibit?
{4.5, 3, 1, 2, 4, 3, 6, 4.5, 4, 5, 2, 1, 3, 4, 3, 2}
The mean of the distribution is
, and it exhibits a
skew.
Mean = 3.25
Solution:
Step 1 : Given data:
4.5, 3, 1, 2, 4, 3, 6, 4.5, 4, 5, 2, 1, 3, 4, 3, 2
Step 2:
Sum of the numbers
= 4.5 + 3 + 1 + 2 + 4 + 3 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2
= 52
Sum of the numbers = 52
Number of terms = 16
Step 3:
[tex]$\text{Mean}=\frac{\text{Sum of the numbers}}{\text{Number of terms}}[/tex]
[tex]$=\frac{52}{16}[/tex]
= 3.25
Mean = 3.25
Mean of the distribution is 3.25.
Answer: Mean= 3.25 with a POSITIVE skew
Step-by-step explanation:
edmentum
URGENT! PLEASE HELP!
Find the roots of f(x)=x^2+10x−96
Question 6 options:
x=8 or x=−12
x=6 or x=−16
x=−6 or x = 16
x =8 or x =12
Answer:
the answer is x=6 or x=-16
The correct answer is x = 6 or x = -16.
To find the roots of the quadratic function f(x) = x2 + 10x - 96, we need to solve the equation x2 + 10x - 96 = 0 using the quadratic formula.
Using the quadratic formula, x = (-b ± √(b2 - 4ac)) / 2a, where a = 1, b = 10, and c = -96, we get x = 6 or x = -16 as the roots of the function f(x).
Therefore, the correct answer is x = 6 or x = -16.
x = 5
y = -3 What is the solution to the system of equations?
Answer:
y=5m-3
Step-by-step explanation:
Which equation represents the line shown in the graph below ? *20 points* I NEED IT ASAP !!!
Answer:
B
Step-by-step explanation:
Write a number of your choice, using the following clues:
a two digit number
greater than 40
divisible by both 2 and 3
Answer:
42 and 72
Step-by-step explanation:
Which describes how to graph h (x) = negative RootIndex StartRoot x + 8 EndRoot by transforming the parent function?
Reflect the parent function over the y-axis, and translate it 3 units to the right.
Reflect the parent function over the y-axis, and translate it 3 units to the left.
Reflect the parent function over the x-axis, and translate it 8 units to the right.
Reflect the parent function over the x-axis, and translate it 8 units to the left.
Answer:
Reflect the parent function over the x-axis, and translate it 8 units to the left.
Step-by-step explanation:
The given function is
[tex]y = - \sqrt{x + 8} [/tex]
The parent function is
[tex]y = \sqrt{x} [/tex]
Since there is a negative multiply the transformed function, there is a reflection in the x-axis.
Since 8 is adding, within the square root, there is a horizontal translation of 8 units to the left.
Therefore to graph the given function, reflect the parent function over the x-axis, and translate it 8 units to the left.
Take the reflection of the graph about the x-axis and then translate the graph of the function by 8 units in the left direction and this can be determined by using the rules of transformation.
Given :
Function -- [tex]\rm y = - \sqrt{x+8}[/tex]
The following steps can be used in order to determine the correct statement:
Step 1 - The parent function is given below:
[tex]\rm y = \sqrt{x}[/tex]
Step 2 - Now, draw the graph of the parent function.
Step 3 - Take the reflection of the graph about the x-axis. So, the function becomes:
[tex]y =- \sqrt{x}[/tex]
Step 4 - Now, translate the graph of the function obtained in the above step by 8 units in the left direction. So, the function becomes:
[tex]y = -\sqrt{x+8}[/tex]
Therefore, the correct option is D).
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Mutliply x - 3 and x + 3
Answer:
Step-by-step explanation:
(x-3)*(x+3)
we begin by expanding and then simplifying
= (x²+3x-3x-9)
= x² - 9
Answer:
x² - 9
Step-by-step explanation:
hello :
(x - 3 ) (x + 3) = x²+3x-3x-9
(x - 3 ) (x + 3) = x² - 9
HELP NOW PLS what is (x+6)
x+6 is x+6. It's an expression. Not sure what you need help with.
Answer:
You set the problem =0, so (x+6)=0.
Then, you do the inverse to get x alone. 6-6(cancels out) and 0-6 is -6.Now your equation should look like x=-6 and you’re done.
Step-by-step explanation:
Farmer Jones raises ducks and cows. He looks out his window and sees 54 animals with a total of 122 feet. If each animal is “normal”, have many of each type of animal does he have
Answer:
He have 47 ducks and 7 cows.
Step-by-step explanation:
Given:
Farmer Jones raises ducks and cows.
He looks out his window and sees 54 animals with a total of 122 feet.
Now, to find the each type of animal he have.
Let the number of ducks be [tex]x.[/tex]
And the number of cows be [tex]y.[/tex]
So, total number of animals are:
[tex]x+y=54[/tex]
[tex]x=54-y[/tex] ....( 1 )
As, the feet of cows are 4 and ducks are 2.
Now, the total number of feet are:
[tex]2(x)+4(y)=122[/tex]
[tex]2x+4y=122[/tex]
Substituting the value of [tex]x[/tex] from equation (1) we get:
[tex]2(54-y)+4y=122[/tex]
[tex]108-2y+4y=122[/tex]
[tex]108+2y=122[/tex]
Subtracting both sides by 108 we get:
[tex]2y=14[/tex]
Dividing both sides by 2 we get:
[tex]y=7.[/tex]
The number of cows = 7.
Now, to get the number of ducks we substitute the value of [tex]y[/tex] in equation (1):
[tex]x=54-y\\x=54-7\\x=47.[/tex]
The number of ducks = 47.
Therefore, he have 47 ducks and 7 cows.
2 is underlined 12.917 what is the place value for 2
Answer: 2 is the nearest whole number.
Step-by-step explanation:
An airplane flying at a velocity of 610 m/s lands and comes to a complete stop
over a 53 second period.
a) Did this airplane speed up or slow down? Explain your reasoning.
b) Did this airplane accelerate or decelerate? Explain your reasoning.
c) Should your answer be positive or negative? Explain your reasoning.
d) Calculate the acceleration.
A) The airplane slowed down. It states that the plane lands and come to a complete stop over a 53 second period.
B) It decelerates. The speed doesn't increase. It slows down.
C) The answer should be positive. Although the deceleration is slowing down the plane, it's not going at a negative speed.
D) The answer is 11.5m/s. I divided the velocity by the amount of seconds it takes to make a complete stop.
The following information should be considered;
A) The airplane falled down. It states that the plane lands and come to a complete stop over a 53 second period.
B) It decelerates. The speed doesn't increase. It slows down.
C) The answer should be positive. The deceleration is slowing down the plane, it's not going at a negative speed.
D) The answer is 11.5m/s. I divided the velocity by the amount of seconds it takes to make a complete stop.
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What is the measure of angle x
Enter your answer in the box
x = 83°
Solution:
The reference image to the answer is given below.
Sum of the adjacent angles in a straight line = 180°
⇒ ∠1 + ∠2 + ∠3 = 180° (Refer image)
⇒ 56° + ∠2 + 41° = 180°
⇒ 56° + 41° + ∠2 = 180°
⇒ 97° + ∠2 = 180°
⇒ ∠2 = 180° – 97°
⇒ ∠2 = 83°
In the given image ∠5 and ∠2 are vertically opposite angles.
Vertical angle theorem:
Vertically opposite angles are equal.
⇒ ∠5 = ∠2
⇒ x = ∠2
⇒ x = 83°
Hence the measure of angle x is 83°.
In a short story, a character decides to distance himself
from his family by moving away. When he does, life
becomes difficult. He realizes how often he had relied on
his family for support and encouragement. In order to
respect his plea for independence, his family had refrained from contacting him. In the end, the character moves back to his hometown and is happier because of it.
Which common literary theme is best illustrated by the passage?
Answer:
A)
Step-by-step explanation:
The theme is a message that the story was trying to portray. In the story, it seems that the character realizes that his home life and family matter more to him than he thought which is why he moved back to his hometown and became happy from that. He moved away thinking that life would be better without his family and soon regrets it.
Supria and Elle live 21 miles apart. They leave their respective homes at the same time to go for
a jog. They begin running toward each other with the intent of meeting. Supria runs at a
constant rate of 8 miles per hour and Elle runs at a constant rate of 8 miles per hour. A third
friend starts at Supria's house and rides her bike toward Elle's house and rides her bike toward
Elle's house at a constant rate of 10 miles per hour. How far will the bicyclist have ridden when
Supria and Elle finally meet?
Answer:
[tex]d3=13.125[/tex] [tex]miles[/tex]
Step-by-step explanation:
Given data:
[tex]total[/tex] [tex]distance = 21[/tex] [tex]miles[/tex]
[tex]s1=8[/tex] [tex]miles/hr[/tex]
[tex]s2=8[/tex] [tex]miles/hr[/tex]
[tex]s3=10[/tex] [tex]miles/hr[/tex]
First we have to find out the how much time it takes when Supria and Elle meet.
As we know,
[tex]Displacement=rate*time[/tex]
[tex]d1=s1*t[/tex]
[tex]d2=s2*t[/tex]
[tex]d1+d2=21[/tex]
[tex]8t+8t=21[/tex]
[tex]16t=21[/tex]
[tex]t=21/16[/tex]
Now we can find that how much the third friend had traveled during this time period
[tex]d3=s3*t[/tex]
[tex]d3=10*21/16[/tex]
[tex]d3=13.125[/tex] [tex]miles[/tex]
What is the value of F(x) = 4x+9
When x= 5
Answer:
f(5) = 29
Step-by-step explanation:
Step 1: Identify the function
f(x) = 4x + 9
Step 2: Let x equal 5 in the function
f(5) = 4(5) + 9
Step 3: Multiply
f(5) = 20 + 9
Step 4: Add
f(5) = 29
Answer: 29
Answer:
[tex]F(x)=29[/tex]
Step-by-step explanation:
Given function:
[tex]F(x) = 4x+9[/tex]
Find F(x) at , [tex]x= 5[/tex]
The value of 'x' is given for which we have to find the value of F(x)
Putting the given 'x' in the function equation
[tex]F(x) = 4x+9\\\\ F(x) = 4(5)+9\\\\ F(x) = 20+9\\\\ F(x) = 29[/tex]
So , [tex]F(x)=29[/tex] at [tex]x=5[/tex]
Write the expression in standard form.
(4f-3+2g)-(-4g+2)
To write the given expression (4f-3+2g)-(-4g+2) in standard form, change the signs of the terms subtracted and combine like terms to simplify to 4f + 6g - 5.
Explanation:To write the expression in standard form, you need to simplify the expression by combining like terms and handling the subtraction of negative numbers properly. Given the expression (4f-3+2g)-(-4g+2), you first remove the parenthesis while changing the signs of the terms inside the parenthesis being subtracted.
The expression -(-4g+2) will become +4g-2 once we apply the rule that subtracting a negative is the same as adding a positive, similarly to the example 2-(-6)=2+6=8.
Now the expression is simplified to 4f - 3 + 2g + 4g - 2. We combine like terms to get 4f + 6g - 5.
The standard form of the given expression is 4f + 6g - 5.
The expression (4f-3+2g)-(-4g+2) can be simplified using the distributive property and combining like terms.
First, distribute the negative sign to the terms inside the parentheses: (-1) * (-4g) = 4g and (-1) * 2 = -2.
The expression becomes (4f-3+2g) + (4g-2).
Next, combine like terms: 4g + 2g = 6g, and -3 - 2 = -5.
The final expression in standard form is 4f + 6g - 5.
8 cm
5 cm
10 cm
12 cm
Find the area of the figure.
41 cm
90 cm2
95 cm
100 cm?
Answer:
its 90cm^2
Step-by-step explanation:
hope d answer will help u
How fast can a car going that traveled 330 and 1/3miles in 5 and 1/4 hour
Answer:
62.9mi/hr
Step-by-step explanation:
How far the car is moving is the speed.
We need to calculate the speed given that, the distance traveled is [tex]330\frac{1}{3} \:miles[/tex]
The time given is [tex]5\frac{1}{4}[/tex] hours.
Recall that: [tex]Speed=\frac{Distance}{Time}[/tex]
We plug in the values to get:
[tex]Speed =\frac{330\frac{1}{3} }{5\frac{1}{4} }[/tex]
We simplify to get:
[tex]Speed=\frac{3964}{63} =62.\overline{920634}[/tex]
20. Math and Science There are 6 pure
spectral colors: red, orange, yellow, green,
blue, and violet. Some animals cannot
see all of these colors. Bees cannot see
orange or red. What fraction of the pure
spectral colors can bees see?
2/1 frptrhgqhgr4tjtfix jxcfh8u5t8ofszYI7wyt439tfy7efgy5g
Final answer:
Bees can see 4 out of the 6 pure spectral colors, which simplifies to the fraction 2/3 after removing the 2 colors they cannot see, orange and red.
Explanation:
The question involves calculating a fraction, which is a basic mathematical concept. We are told there are 6 pure spectral colors: red, orange, yellow, green, blue, and violet. Bees cannot see orange or red, so we must find out what fraction of the 6 pure spectral colors bees can see. We subtract the 2 colors bees can't see (orange and red) from the total of 6, leaving us with 4 colors they can see which are yellow, green, blue, and violet.
To express this as a fraction, we take the number of colors bees can see (4) and place it over the total number of pure spectral colors (6). Therefore, the fraction of pure spectral colors that bees can see is 4/6. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. Thus, the simplified fraction is 2/3.
A tank has 15 gallons of water in it when water begins draining from the tank. (Recall that water weighs 8.345 pounds per gallon.)
Define a function f that determines the number of gallons of water in the tank, f ( w ) , in terms of the number of pounds of water that have drained from the tank since the tank started draining, w .
Answer:
[tex]f(w) = 15 - \frac{w}{8345}[/tex]
Step-by-step explanation:
Water begins draining from a tank when the tank has 15 gallons of water in it.
Now, if we define f(w) as a function that represents the number of gallons of water remains in the tank after w pounds of water that have drained from the tank since the tank started draining, then the function can be represented as
[tex]f(w) = 15 - \frac{w}{8345}[/tex]
Since, w pounds of water is equivalent to [tex]\frac{w}{8345}[/tex] gallons of water. (Answer)
(Recall that water weighs 8.345 pounds per gallon.)
The function f should be defined is [tex]f(w) = 15 - \frac{w}{8345}[/tex]
Important information:A tank has 15 gallons of water in it when water begins draining from the tank. (Recall that water weighs 8.345 pounds per gallon.)
Function:Since we have to defined the function so it is f(w) that shows the number of gallons of water remains in the tank after w pounds of water.
So, the function should be [tex]f(w) = 15 - \frac{w}{8345}[/tex]
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Another submarine descent can be represented as y= -240 x where y is the elevation and x is time in hours. How long will it take this submarine to make the descent
Answer:
8.75h
Step-by-step explanation:
8.75 hours will be taken by the submarine to make the descent.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that a submarine’s descent can be represented as y = -240x, where y is the elevation and x is time in hours.
We need to find the the time it will take this submarine to make the descent to the seafloor 2,100 feet below the surface
Since the submarine to make the descent to the seafloor 2,100 feet below the surface
So y = - 2100
So y = - 240x gives
- 2100 = - 240x
Divide both sides by -240
x=8.75
Hence, 8.75 hours will be taken by the submarine to make the descent
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Write an equation in point-slope form for the line that has a slope of 56 and contains the point (−8,−4).
Step-by-step explanation:
Given: slope of line m = 56 & line contain point is (−8,−4).
[tex] \therefore (x_1, \:\: y_1) = (-8, \:\: - 4)[/tex]
Equation of line in slope point form is given as:
[tex]y - y_1 =m(x - x_1) \\ \\ \therefore \: y - ( - 4) = 56 \{x - ( - 8) \} \\ \\ \blue{ \boxed{\therefore \: y + 4= 56 (x + 8) }}\\ ..(this \: is \: the \: equation \: of \: line \: in \: \\ slope \: point \: form)\\ \\ \therefore \: y + 4= 56x + 56 \times 8 \\ \\ \therefore \: y + 4= 56x + 448 \\ \\ \therefore \: y = 56x + 448 - 4 \\ \\ \huge \red{ \boxed{\therefore \: y = 56x + 444 }}\\ ..(this \: is \: the \: equation \: of \: line \: in \: \\ slope \: intercept \: form)[/tex]
Answer:
y+4 = 56(x+8)
Step-by-step explanation:
y-y1 = m(x-x1)
y-(-4) = 56(x-(-8))
y+4 = 56(x+8)
If needed, simply it further
y+4 = 56x+448
y = 56x+444