Step-by-step explanation:
false.
3a²b≠3ab².
If a is 3 and b is3 it is not equal
The length x of a rectangle is decreasing at the rate of 5 cm/min and the width y is increasing at the rate of 4 cm/min. When x = 8 cm and y = 6 cm, find the rate of change of
(i) the perimeter.
(ii) area of rectangle.
How can you divide polynomials? What are the different methods you can use?Which method do you prefer and why?
I just need help appreciate it and have a great day
On solving the provided question, we can say that - by doing the fraction we have 3/12 = 1/4
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
balloons is 12
blew up is 1/3
friend blew up is 5
1/3*12 = 4
4+5 = 9
3/12 = 1/4
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Roller coaster A can reach a top speed of 110 ft./s roller coaster B can reach the top speed of 85 mph which roller coaster has a greater top speed
Roller coaster B has greater top speed than roller coaster A.
What is unit conversion?Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters.
Given,
speed of roller coaster A = 110ft./s
speed of roller coaster B = 85mph
1 mile = 5280 feet
⇒ 85 mile = 5280 × 85 = 448800 feet
1 hour = 3600 seconds
speed of roller coaster B = 448800/3600 ft/s = 124.67 ft/s
comparing speed of both
Speed of roller coaster B > speed of roller coaster A
Hence, Top speed of roller coaster B is greater than roller coaster A.
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Help please! How do I write an equation in standard form using the information on the graph?
Answer:
3x -y = 2
Step-by-step explanation:
You want a standard form equation for the line through the points (0, -2) and (2, 4).
SlopeThe slope of the line is the "rise" divided by the "run". The given point on the right is 3 grid squares above the one on the left. It is one grid square to the right. So, the slope is ...
m = (squares above)/(squares to the right) = 3/1 = 3
If we consider the actual x- and y-values represented by these grid squares, then the slope is ...
m = (4 -(-2))/(2 -0) = 6/2 = 3
InterceptThe point (0, -2) tells you the y-intercept is -2. That is where the line crosses the y-axis.
Slope-intercept equationWith this information, we can write the slope-intercept form equation for the line:
y = mx +b . . . . . . . line with slope m and y-intercept b
y = 3x -2 . . . . . . . . line with slope 3 and y-intercept -2
Standard formThe standard form of an equation for a line is ...
ax +by = c
where a, b, c are generally mutually-prime integers with a ≥ 0. If a=0, then b > 0.
We can rearrange the slope-intercept equation to put it into this form.
y = 3x -2
3x -y -2 = 0 . . . . . subtract y
3x -y = 2 . . . . . . . add 2. This is the standard-form equation of the line.
1000(9x-10)=50(976+100x)
Katrina buys a 76-ft roll of fencing to make a rectangular play area for her dogs. Use
2({+w) = 76 to write a function for the length, given the width. Graph the function.
What is a reasonable domain for the situation? Explain.
Therefore , As a result 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64..
The definition of functionA connection between a group of sources and one output for each input is referred to as a function. A function is, to put it simply, a collection of equation connected to a single, unique output. In mathematics, a function is a statement, rule, or law that describes the connection between two variables (the dependent variable). One input leads to one output when a rule of this type is used. by Alex Federspiel, the photographer. This statement gives an example of y=x2. There is just one output for y from any input for x. According to our definition, y is a function of x since x is the input value.
Here,
We have the following for the rectangle's perimeter:
2 ( l + w ) = 64
Here,
W = width, and L = length.
We must determine the length and breadth values necessary to make the rectangle's perimeter 64.
Now,
2 ( l + w ) = 64
l + w = 32
Thus, the sum of the length and breadth measurements must equal 32.
The possible widths are 5, 10, 15, 20, and 25.
Now,
l + 5 = 32
l = 27
l + 10 = 32
l = 22
l + 15 = 32
l = 17
l + 20 = 32
l = 12
l + 25 = 32
l = 7
We think about
The domain has widths of 5, 10, 15, 20, and 25.
The range for length is: 27, 22, 17, 12, and 7.
Values for width and length are used as the x- and y-axes, respectively.
Below is a graph of the data.
The following is the reasonable domain for the aforementioned situation:
5, 10, 15, 20, and 25
Below is a graph of the function 2 (l + w) = 64.
Therefore , As a result, 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64.
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A rectangular tennis court has a length of 24 m and a width of 11m what is the length of the diagonal court explain how you worked out your answer
The length of the diagonal of the rectangular tennis court is given as follows:
26.4 meters.
How to obtain the length of the diagonal?The tennis court is rectangular, meaning that the diagonal is the hypotenuse of a right triangle, in which the sides are the length and the width.
Applying the Pythagorean Theorem, the diagonal length can be obtained as follows:
d² = 24² + 11²
d² = 697
[tex]d = \sqrt{697}[/tex]
d = 26.4 m.
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WILL GIVE POINTS
Three Algebra 1 students are comparing how fast their social media posts have spread. Their results are shown in the following table:
Student Amber Ben Carter
Description Amber shared her photo with 3 people. They continued to share it, so the number of shares increases every day, as shown by the function. Ben shared his post with 2 friends. Each of those friends shares with 3 more every day, so the number of shares triples every day. Carter shared his post with 10 friends, who each share with only 2 people each day.
Social Media Post Shares f(x) = 3(4)x
Day Number of Shares
0 2
1 6
2 18 Carter shared his post with 10 friends, who each share with only 2 people each day.
Write an exponential function to represent the spread of Ben's social media post.
Write an exponential function to represent the spread of Carter's social media post.
Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology.
Using the functions for each student, predict how many shares each student's post will be received on Day 3 and then on Day 10. Justify your answers.
If Amber decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, the new function representing her photo shares is f(x) = 3(4)x + 45. How does this graph compare with the original graph of Amber's photo share?
Based on your results, which student's post travels the fastest? How is this shown in the equation form of the functions?
If you had to choose, would you prefer a post with fewer friends initially but more shares, like Amber, or more friends initially but fewer shares? Justify your answer with your calculations from previous questions.
a. The exponential function to represent the spread of Ben's social media post is f(x) = 2(3)^x
b. The exponential function to represent the spread of Carter's social media post is f(x) = 10(2)^x
c. On Day 3, Ben's post will have 2(3)^3 = 227 = 54 shares, Carter's post will have 10(2)^3 = 108 = 80 shares. On Day 10, Ben's post will have 2(3)^10 = 259049 = 118098 shares, Carter's post will have 10(2)^10 = 101024 = 10240 shares.
d. Adding 45 to the function representing Amber's photo shares changes the function to f(x) = 3(4)x + 45. The new function will shift the graph upward by 45 units.
e. Based on the functions, Ben's post travels the fastest because the base of the exponent, 3, is greater than the base of the exponent, 2, for Carter's post.
f. It depends on the goal of the post. If the goal is to reach a larger audience quickly, then having more friends initially but fewer shares like Carter is preferable. But if the goal is to reach a smaller audience but with a more engaged audience, then having fewer friends initially but more shares like Amber is preferable.
What is exponential function examples?An exponential function is one in which the variable is an exponent. Mathematically, it is defined as f of R in R, such that f(x) = ax, where a ϵ R, a > 0 and a ≠ 1. The graph of this function is a curve obtained by finding some ordered pairs that belong to the function and drawing this curve that passes through them.
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How much did the population change between 1970 and 1980? population change between 1990 and 1995? What was the average annual change for that period?
Hint: Calculate the changes, then calculate the mean, or average, by dividing by the number of years. State the units clearly. The units are listed on the chart.
The population change for each period is given as follows:
1970 to 1980: 0.748 billion.1990 to 1995: 0.407 billion.Hence the average annual change for the period between 1970 and 1995 is given as follows:
7,932,000 people a year.
How to obtain the population change?The population change over a period is given by the subtraction of the population at the end of the period by the population at the beginning of the period.
The population data for each year is given by the table on the image presented at the end of the answer.
Hence the changes are obtained as follows:
1970 to 1980: 4.456 - 3.708 = 0.748 billion.1990 to 1995: 5.691 - 5.284 = 0.407 billion.The change between 1970 and 1995 is of:
5.691 - 3.708 = 1.983 billion.
This period is composed by 25 years, hence the average annual change is of:
1.983/25 = 0.07932 billion people a year = 7,932,000 people a year.
Missing InformationThe chart is given by the image presented at the end of the answer.
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What is the value of X in the triangle below?
Answer:
x=29
Step-by-step explanation:
(2x-2)+(x+5)+90= 180 (sum of angles in a triangle)
2x-2+x+5=90
3x+3=90
3x=87
x=29
What is the circumference of this circle? Use π = 3.14
The circumference of this circle is equal to 50.24 centimeters.
What is a circle?In Mathematics, a circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Additionally, a circle simply refers to the set of all data points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
How to calculate the circumference of a circle?Mathematically, the circumference of a circle can be calculated by using this mathematical expression:
C = 2πr or C = πD
Where:
C represents the circumference of a circle.D represents the diameter of a circle.r represents the radius of a circle.Based on the image of this circle (See attachment), we can logically deduce that its radius is equal to 8 centimeters.
Substituting the given parameters into the circumference of a circle formula, we have;
Circumference of circle, C = 2 × 3.14 × 8
Circumference of circle, C = 50.24 centimeters.
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Identify two segments that are marked congruent to each other on the
diagram below. (Diagram is not to scale.)
The two congruent segments in the figure are LJ and LI.
What is congruency?
The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.
An included angle is found between two sides that are under consideration.
Thus, two triangles having two pairs of corresponding sides and one pair of corresponding angles that are congruent to each other is not enough justification for proving that the two triangles are congruent based on the SAS Congruence Theorem.
In the figure, the two segments marked are LI and LJ these two segments are congruent to each other.
Congruency means the shape and the size of the segments will be equal to each other.
Hence, the two congruent segments in the figure are LJ and LI.
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8x +1 =7x +5
Please help me
Answer:
x = 4
Step-by-step explanation:
i. 8x + 1 = 7x + 5
ii. 8x - 7x = 5 - 1
iii. x = 4
Which expression is equivalent to log 12 x^ 4 sqrt x^ 3 -2 (x+1)^ 5 ?
The equivalent expression of log₁₂(x⁴√x³) - 2(x+1)⁵ is 11/2log₁₂(x) - 2(x+1)⁵
How to determine the equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
log 12 x^ 4 sqrt x^ 3 -2 (x+1)^ 5 ?
Express properly
So, we have the following representation
log₁₂(x⁴√x³) - 2(x+1)⁵
Evaluate the exponent
log₁₂(√x¹¹) - 2(x+1)⁵
Apply the power rule of logarithm
This gives
11/2log₁₂(x) - 2(x+1)⁵
Hence, the equivalent expression is 11/2log₁₂(x) - 2(x+1)⁵
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Given the example below, determine the property displayed.
7+3=3+7
Answer:
commutative property of addition
Step-by-step explanation:
commutative property of addition
The commutative property of addition allows you to change the order of the numbers in an addition.
For example, 1 + 2 = 2 + 1
Find the measure of angle A,
helo i need help with my math please thanky uo i need help with question 3
On one tank of gas Charlie will drive 612 km
At a cost of 149.9, Charlie will fill the tank with the sum of 8994
Annual cost of filling the tank 467688
How to find how far Charlie can drive on one tank of gasInformation from the problem have it that the efficiency if the Volkswagen golf is 10.2 km/L
Hence, on one liter rides 10.2 km and on a tank which is 60 L Charlie will ride
= 60 * 10.2
= 612 km
Cost of filling the tank
The cost per liter is 149.9 for 60 L we have
= 149.9 * 60
= 8994
Filling the tank once week, the cost for filling in one year is
1 year is 52 weeks
= 8994 * 52
= 467688
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X
Let f(x) = 3x2 - 6x + 2. Find f(2)
A
B
10
16
C 12
E
D 2
8
On solving the provided question, we can say that - f(x) = 3x2 - 6x + 2, and the value of the equation f(x) = +2
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
f(x) = 3x2 - 6x + 2
x = 1
f(x) = +2
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For problems 1-3, use the information in the diagram to find the angle measure of in radians. Round your answer to the nearest ten-thousandth, if necessary.
Answer:
4.25 radians2.4 radians0.625 radiansStep-by-step explanation:
You want the angles associated with different arc lengths and radii.
AngleThe length of an arc is given by the formula ...
s = rθ . . . . . θ is the angle in radians, r is the radius
Solving for θ gives ...
θ = s/r
1.For s=17 in, r=4 in, ...
θ = (17 in)/(4 in) = 4.25 . . . . radians
2.For s=12 ft, r=5 ft, ...
θ = (12 ft)/(5 ft) = 2.4 . . . . radians
3.
For s=8.5 mm, r = 13.6 mm, ...
θ = (8.5 mm)/(13.6 mm) = 0.625 . . . . radians
Suppose a researcher compiled a data set of the following variables fora sample of 100 retired men
Answer:
The researcher compiled a data set consisting of variables such as age, income, and marital status for a sample of 100 retired men
Step-by-step explanation:
A discrete variable is a type of variable that can only take on specific, distinct values that can be counted. Examples of discrete variables include the number of countries visited, shoe size, and number of pets living in a household.
On the other hand, a continuous variable is a type of variable that can take on any value within a certain range through measurement. Examples of continuous variables include pounds of chocolate consumed in the past and height in inches.
find a number such that 30% of it is 1260
well, that number is "x", which oddly enough is the 100%, now, we also know that 30% of that is 1260, so hmmmm
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 1260& 30 \end{array} \implies \cfrac{x}{1260}~~=~~\cfrac{100}{30} \\\\\\ \cfrac{ x }{ 1260 } ~~=~~ \cfrac{ 10 }{ 3 }\implies 3x=12600\implies x=\cfrac{12600}{3}\implies x=4200[/tex]
A movie studio keeps 240 dresses in its wardrobe for historical films. Three-fifths of them can be used for movies that take place in the 1700s and 15% of them can be used for movies in the civil war era. A. What percent of the dresses are for films set in the 1700s? B. What percent of the dresses are for films not set in the 1700s? Explain how you found your answer. C. What percent of the dresses are for films set in the 1700s or during the civil war era? Explain how you found your answer. D. What percent of the dresses are not for films set during the civil war era? Explain how you found your answer.
A) The dresses for films set in the 1700s would be 60%.
B) The percentage of dresses that are not for films set in the 1700s is 40%.
C) The percentage of dresses that can be used for films set in the 1700s or during the civil war era is 75%.
D) The percentage of dresses that are not for films set during the civil war era is 85%.
What is a percentage?
The percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%". It is used to express a proportion of a number out of 100. It is useful in many applications such as finance, statistics, and other fields.
A. Three-fifths of the dresses can be used for movies that take place in the 1700s, which is 3/5 * 100 = 60%.
B. The percent of the dresses that are not for films set in the 1700s is 100% - 60% = 40%. This is found by subtracting the percentage of dresses that are used for 1700s movies from 100%.
C. The percent of the dresses that can be used for films set in the 1700s or during the civil war era is 60% + 15% = 75%. This is found by adding the percentage of dresses that can be used for 1700s movies and the percentage of dresses that can be used for civil war era movies.
D. The percent of the dresses that are not for films set during the civil war era is 100% - 15% = 85%. This is found by subtracting the percentage of dresses that are used for civil war era movies from 100%.
Hence,
A) The dresses for films set in the 1700s would be 60%.
B) The percentage of dresses that are not for films set in the 1700s is 40%.
C) The percentage of dresses that can be used for films set in the 1700s or during the civil war era is 75%.
D) The percentage of dresses that are not for films set during the civil war era is 85%.
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i need help right freaking now
Answer:
a. x^4 - 12x^3 + 2x^2 - 2x + 4
Degree: 4
b. x^4 - 2x^2 - 2x - 4
Degree: 4
Step-by-step explanation:
For part a, all you are doing is adding the polynomials together. They already set up the boxes in standard form, so all you need to do is add each like term as I wrote out in the answer. The degree is then going to be the first exponent that you see once the polynomial is in standard form, which is 4.
For part b, you are now subtracting the polynomials. Again, it is set up for you in standard form. There is no x^3 terms because they cancel out, but you basically subtract each like term from another, and remember to distribute the subtraction sign (it acts as a -1) across the parenthesis. The degree is the first exponent you see, and that is 4.
Find the value of g(f(-1))
Answer: I say 13
Step-by-step explanation:
Calculate the volume of this cylinder, giving your answer to 1 decimal place.
14 cm ( diameter )
12 cm ( height )
22/7×14×14×12
the answer is 7392
What are the features of the quadratic function ƒ(x) = (x – 3)(x + 7)?
Answer:
See below
Step-by-step explanation:
I guess if you look at the zeroes/x-intercepts, we got (3,0) and (-7,0) as zeroes.
Additionally, we can calculate the minimum by expanding the function:
[tex](x-3)(x+7)=x^2+4x-21[/tex]
[tex]\displaystyle x=-\frac{b}{2a}=-\frac{4}{2(1)}=-2\\\\f(-2)=(-2)^2+4(2)-21=4+8-21=12-21=-9[/tex]
So the minimum of the function is (-2,-9)
Also, our y-intercept is (0,-21)
There are 8 boxes of erasers in the supply closet. Each box contains 9 erasers. How many erasers are there in all?
Answer:
each box contain 8 x 9 = 72
PLEASE HELP
y = 2x + 1/3
Answer:
incorrect
Step-by-step explanation:
y= 1/3x+2 because the slope(m) going up by 1 takes up 3 spaces going out and u it in rise/run form rise being up and run being out and the y intercept(b) is where the y axis and the slope meet (basically it starts at the 2)
The altitude of the hypotenuse of a right triangle divides the hypotenuse into two segments. If the ratio of lengths of the segments is 1:9 and the length of the altitude is 6 meters, find the lengths of the two segments?
Answer:
2 m18 mStep-by-step explanation:
You want the lengths of the segments of the hypotenuse of a right triangle when an altitude of 6 m divides the hypotenuse into parts with the ratio 1:9.
Geometric meanThe altitude to the hypotenuse of a right triangle is the geometric mean of the parts it divides the hypotenuse into. If the shorter part is x, then the longer part is 9x, and their geometric mean is ...
6 = √(x(9x)) = 3√x² = 3x
x = 2 . . . . . . . divide by 3
The length of the shorter segment is 2 m; the longer one, 18 m.