Final answer:
To divide 2y² + 8 by 2y + 4, use long division to find the quotient and remainder.
Explanation:
To divide 2y² + 8 by 2y + 4, we can use long division. Here are the steps:
Divide the first term of the dividend by the first term of the divisor, which gives us y.
Multiply the entire divisor by y to get 2y² + 4y.
Subtract 2y² + 4y from the dividend 2y² + 8 to get 4.
Next, divide 4 by 2y + 4, which gives us 2.
Finally, we have a remainder of 0.
Therefore, the quotient is y + 2 and the remainder is 0.
divide (x^3-20x+16)divide (x-4)
The spring has a stiffness k=200n/m and is unstretched when the 25 kg block is at
a. Determine the acceleration of the block when s=0.4m. The contact surface between the block and the plane has
This is a Physics problem involving Hooke's Law and Newton's second law of motion. The acceleration of a 25kg block when a spring it's resting on is extended by 0.4m is determined. The calculated acceleration is -3.2m/s², indicating the direction is opposite to the direction of displacement.
Explanation:The subject matter of this question is physics, specifically the area of mechanics dealing with forces, mass, and acceleration (Newton's Laws). The stiffness of a spring is given as k=200N/m and it is unstretched when the 25 kg block is resting on it. We're tasked with finding the acceleration of the block when the spring is extended by s=0.4m.
Firstly, let's find the force on the block using Hooke's Law which states that the force exerted by a spring is equal to the spring constant times the displacement (F=-kx). So, F=-200N/m*(0.4m)=-80N. The negative sign just indicates that the force is in the opposite direction of the displacement.
Secondly, we apply Newton's second law of motion (F=ma), where m is the mass and a is the acceleration. Rearranging the equation to find acceleration gives us a=F/m. Substituting our values gives a=-80N/25kg = -3.2m/s². The negative sign here indicates the direction of the acceleration, opposite to the direction of displacement. So, the acceleration of the block when the spring is extended by 0.4m is -3.2m/s².
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The graph of f(t) = 3 • 2^t shows the value of a rare coin in year t. What is the meaning of the y-intercept?
A. When it was purchased (year 0), the coin was worth $3.
B. In year 1, the coin was worth $6.
C. When it was purchased (year 0), the coin was worth $2.
D. Every year the coin is worth 3 more dollars.
Answer:
The answer is the option A
When it was purchased (year [tex]0[/tex]), the coin was worth [tex]\$3[/tex]
Step-by-step explanation:
we know that
The y-intercept of a function is the value of the function when the value of the independent variable is equal to zero
In this problem we have
[tex]f(t)=3(2^{t})[/tex]
the independent variable is the variable t
so
Find the y-intercept
For [tex]t=0[/tex] ------> year zero
Find the value of the function
[tex]f(0)=3(2^{0})=\$3[/tex]
That means ----> When it was purchased (year [tex]0[/tex]), the coin was worth [tex]\$3[/tex]
how do you evaluate 71 - b, if b is 27
Wich statement about the following equation is true ? 3x^2-8x+5=5x^2
A triangle has sides with lengths: 6, 9, and 5. How do you find the area of the triangle using Heron's formula?
Marcia has $84 less than three times as much as sue. together they have $132. how much money does marcia have?
To find out how much money Marcia has, a system of linear equations is set up and solved. Sue has $54, which means Marcia has $78 since she has $84 less than three times Sue's amount. They together have $132.
Explanation:The question involves solving a system of linear equations to determine how much money Marcia has if she has $84 less than three times as much as Sue. Together they have $132. To solve this, let's name the amount Sue has as S, and consequently, Marcia has 3S - $84. Adding both amounts, we get the equation S + (3S - 84) = $132.
Combining like terms gives us 4S - 84 = $132. We solve for S by first adding 84 to both sides, which yields 4S = $216. Dividing both sides by 4 gives us S = $54. Knowing Sue's amount, we can compute Marcia’s by multiplying Sue’s amount by three and then subtracting 84, so 3 x $54 - $84 = $162 - $84 = $78. Therefore, Marcia has $78.
Find the volume of a cube that is 7 cm on each edge.
Final answer:
The volume of a cube with each edge measuring 7 cm is calculated using the formula V = s^3, which results in a volume of 343 cubic centimeters (cm3).
Explanation:
To find the volume of a cube that is 7 cm on each edge, we use the formula for the volume of a cube, which is V = s3, where s is the length of one side of the cube. In this case, s is 7 cm. Therefore, the volume can be calculated as follows:
V = 7 cm imes 7 cm imes 7 cm = 343 cm3
So the volume of the cube is 343 cubic centimeters (cm3).
A graph of a linear function intersects the coordinate axes in points (1, 0) and (0, 2). What is the equation of this function?
Please answer! Thank you!!!
Assume we have two lines which are perpendicular. If one line has a slope of 3, what is the slope of the other line? Enter your answer as an integer or fraction in lowest terms.
The slope of a line perpendicular to a line with a slope of 3 is -1/3. This is because perpendicular lines have negative reciprocal slopes.
Explanation:In mathematics, when two lines are perpendicular, their slopes are negative reciprocals of each other because the product of their slopes equals to -1. This means that if one line has a slope of 3, the slope of the other line would be the negative reciprocal of 3, which is -1/3. So, the slope of the other line is -1/3.
To understand this further, let's delve into the figure of Slope and the Algebra of Straight Lines. Here, 'm' represents the slope which is the rise over the run and 'b' is the y-intercept, which is the point at which the line crosses the y-axis. Considering the fact that the slope of the line is 3, there is an increase of 3 in the y-coordinate (or vertical axis) for every increase of 1 in the x-coordinate (or horizontal axis).
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What’s the answer for No.29 & 30 please hurry
Eliminate the parameter to find a cartesian equation of the curve. x = 3sin(t), y = 4cos(t)
To eliminate the parameter and find the cartesian equation of the curve x=3sin(t), y=4cos(t), we can use trigonometric identities. The cartesian equation of the curve is (x/3)^2 + (y/4)^2 = 1.
Explanation:To eliminate the parameter and find the cartesian equation of the curve x=3sin(t), y=4cos(t), we can use trigonometric identities. Starting with the given equations:
x = 3sin(t)
y = 4cos(t)
We can rewrite the equation for x as:
x/3 = sin(t)
And the equation for y as:
y/4 = cos(t)
Using the identities sin2(t) + cos2(t) = 1, we can square both equations and add them together:
(x/3)2 + (y/4)2 = (sin2(t) + cos2(t)) = 1
This is the cartesian equation of the curve.
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36 ants including the queen created a new colony. after 9 monthe there are now 766 ants. at 17 months how many ants will live in the conoly
Use the graph below to answer the question that follows:
What are the amplitude, period, and midline of the function?
Amplitude: 4; period: 2π; midline: y = −1
Amplitude: 8; period: 2π; midline: y = 1
Amplitude: 8; period: π; midline: y = −1
Amplitude: 4; period: π; midline: y = 1
Answer:
Amplitude : 4
Period: 2π
Mid-line: y=-1
A is correct
Step-by-step explanation:
We are given graph of periodic function.
We need to find amplitude, period and midline of the function.
From graph:
Maximum value = 3
Minimum value = -5
[tex]\text{Mid-Line }=\dfrac{Max+Min}{2}[/tex]
[tex]\text{Mid-Line }=\dfrac{3-5}{2}=-1[/tex]
The mid-line equation, y=-1
Amplitude: Distance between mid-line and maximum value
Amplitude = 3-(-1) = 4
The amplitude of given graph is 4
Period: It is time when graph repeat their path.
In the given graph repeat their in 2π of interval.
The period of graph is 2π
In 2010, a city's population was 1,405,233 and it was decreasing at a rate of 1.1%. At this rate when will the city's population fall below 1,200,000?
a. 2024
b. 2027
c. 2036
d. 2049
A log function is a way to find how much a number must be raised in order to get the desired number. The population of the city will be 1,200,000 in the year 2024.
What is Logarithm?A log function is a way to find how much a number must be raised in order to get the desired number.
[tex]a^c =b[/tex]
can be written as
[tex]\rm{log_ab=c[/tex]
where a is the base to which the power is to be raised,
b is the desired number that we want when power is to be raised,
c is the power that must be raised to a to get b.
For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.
The decrease in the population of the city can be written as,
[tex]\rm Final\ population=(Initial\ population)\times (1-r)^n[/tex]
[tex]1,200,000=1,405,233(1-0.011)^n\\\\0.8539=(0.989)^n\\\\\rm log(0.8539)=n\ log(0.989)\\\\n= \dfrac{log(0.8539)}{log(0.989)}\\\\n=14.279 \approx 14.3[/tex]
Since the initial population was 1,405,000 in the year 2010, then the population of the 1,200,000 will be 14 years later.
Thus, the population of the city will be 1,200,000 in the year 2024.
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if a recipe calls for 0.800 kg of flour , about how many ounces of flour does it need? (1lb=16 oz, 1 lb = 0.454 kg )
5.8 oz
11.0oz
28.2oz
227oz
Answer: The correct option is (C) 28.2 oz.
Step-by-step explanation: Given that a recipe calls for 0.800 kg of flour.
We are to find the number of ounces of flour that the recipe needs.
Given that
1 lb=16 oz and 1 lb = 0.454 kg
We will be using the UNITARY method for solving the given problem.
We have
0.454 kg = 1 lb
So, 1 kg will be equal to [tex]\dfrac{1}{0.454}~\textup{lb}.[/tex]
Therefore, 0.8000 kg is equal to
[tex]\dfrac{1}{0.454}\times 0.800=1.762~\textup{lb}.[/tex]
Now, 1 lb = 16 oz.
So, 1.762 lb = 16 × 1.762 = 28.19 = 28.2 oz.
Thus, the recipe needs 28.2 oz of flour.
Option (C) is CORRECT.
A gas station sells regular gas for $2.20 per gallon and premium gas for $3.00 a gallon. at the end of a business day 300 gallons of gas has been sold, and receipts totaled $700. how many gallons of each type of gas had been sold
Find the ranges of the function ƒ(x) = |x + 4| + 1 and the range of the exponential function g(x) represented by the graph below.
Are they the same? Explain.
Jayden wants to find the dimensions of this parallelogram. He knows that the first step is to find the value of x. Which of these equations will result in the correct value of x?
A. 2x – 1 = x + 8
B. 2x – 1 = x + 1
C. x + 1 + 2x – 1 = 180
D. x + 1 = x + 1
Answer:
2x – 1 = x + 8
Step-by-step explanation:
Make b the subject of the formula p=2a+b
What is the vertex of the absolute value function defined by f (x) = |x - 7| + 1?
A. (7,1)
B. (-7, -1)
C. (-7, 1)
D. (7, -1)
In the figure above, Angle FEB is a central angle. True or False?
A. True
B. False
We know that the central angle is an angle subtended at the center of the circle by any two points on the circle.
In the given figure of the circle, the center of the circle is C. Hence, the central angle must be subtended at the center C.
Since, angle FEB is not subtended at the center of the circle.
Hence, angle FEB is not a central angle.
Therefore, the given statement is FALSE.
Joe will go to the swimming pool on 20 different days this month. • a one-day pass to the pool is $2.25. • a monthly pass to the pool is $30.00. how much money will joe save by buying a monthly pass
What is the sum of the arithmetic sequence 153, 139, 125, ..., if there are 22 terms?
Answer:
Sum of the sequence = 132.
Step-by-step explanation:
The given sequence is 153, 139, 125,.......n terms.
Sum of the arithmetic sequence will be
S = n/2[2a + (n -1)d]
where n = number of terms
a = first term of the sequence
d = common difference
for the given sequence
a = 153
n = 22
d = 139 - 153 = -14
Therefore sum of 22 terms of the sequence will be
S = (22/2)[2×153 - (22-1)14]
= 11×[306 - 21×14]
= 11×[306 - 294] = 11×12 = 132
Sum of 22 terms of this sequence is 132.
I am really bad at math can someone please help and explain ?
When it comes to reimbursement packages, company a offers $175 plus $0.55 per mile. company b offers $200 plus $0.45 per mile. what number of miles driven would make the two reimbursement packages equal?
Answer:250
Step-by-step explanation:
!!!!!!!!!!!!!which answe
Answer:
I think it's D
Step-by-step explanation:
Anyone know this geometry question?
Which one is it? Will give brainiest
Aaron took three times as many pictures as jennifer.jennifer has 16 fewer pictures than aaron.which system of equations can be used to find the number of oictures each person took?