Answer:
h'(1) = 19
Step-by-step explanation:
if h(x) = f(x) + g(x), and f(x) = x³ and g(x) = 4x⁴,
then h(x) = (x³) + (4x⁴)
h(x) = x³ + 4x⁴
h'(x) is the derivative of h(x), which = 3x² + 16x³. Thus, h'(1) = 3(1)² + 16(1)³ = 19
Which form most quickly reveals the zeros (or "roots") of the function?
All forms are equal.
1.[tex]f(x) = -3x^2+12x+15[/tex]
2.[tex]-3(x+1)(x-5)[/tex]
3. [tex]-3(x-2)^2+27[/tex]
What are the zeros?
By answering the above question, we may infer that Hence, x = -1 and x = equation 5 are the zeros of the function f(x).
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
To apply this technique, the quadratic function must be rewritten in vertex form as follows: f(x) = a(x-h)2 + k, where (h,k) is the vertex of the parabola.
The coefficient -3 from the first two terms is first removed by factoring: [tex]f(x) = -3(x^2 - 4x) + 15.[/tex]
After that, we finish the square enclosed in parenthesis by calculating (4/2)2 = 4:
[tex]F(x) = -3[(x-2)2 - 4] + 15 F(x) = -3(x-2)2 + 27 F(x) = -3[(x-2)2 - 4] + 15[/tex]
The parabola is at (2, 27), and because the squared term's coefficient is negative, the parabola widens downward. Set f(x) = 0 and solve for x to discover the zeros: [tex]0 = -3(x-2)2 + 27 3(x-2)2 = 27 (x-2)2 = 9 x-2 = 9 x = 2 3[/tex]
Hence, x = -1 and x = 5 are the zeros of the function f(x).
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Find the height of the trapezoid.
Area = 600 yd²
25 yd
23 yd
Answer:
the height of the trapezoid is 25 yards.
Step-by-step explanation:
The area of a trapezoid is given by the formula:
Area = (1/2) * (b1 + b2) * h
where b1 and b2 are the lengths of the parallel bases and h is the height of the trapezoid.
In this problem, we are given the area of the trapezoid (600 yd^2), as well as the lengths of the two parallel bases (25 yd and 23 yd). Let's use this information to find the height of the trapezoid.
We can start by rearranging the formula for the area to solve for the height:
h = (2 * Area) / (b1 + b2)
Substituting the given values, we get:
h = (2 * 600 yd^2) / (25 yd + 23 yd)
Simplifying, we get:
h = 1200 yd^2 / 48 yd
h = 25 yd
Therefore, the height of the trapezoid is 25 yards.
Explain how to identify the major and minor axes of an ellipse are by looking at both the graph and the equation.
In the graph, the major axis is the horizontal axis, while the minor axis is the vertical axis.
What is ellipse?An ellipse is a geometric shape that is a type of curve. In mathematics, an ellipse is defined as a set of points in a plane, such that the sum of the distances between any point on the curve and two fixed points is a constant which is known as foci.
To identify the major and minor axes of an ellipse, you can use both the graph and the equation of the ellipse.
Identify the major and minor axes using the graph: The major axis is the longest diameter of the ellipse, which passes through the center and touches the curve at two points called the vertices. The minor axis is the shortest diameter of the ellipse, which also passes through the center and touches the curve at two points called the co-vertices. On the graph, the major axis is the horizontal axis, while the minor axis is the vertical axis.
Identify the major and minor axes using the equation: The equation of an ellipse can be written in the standard form:
[tex]\frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} = 1[/tex]
where the ellipse's center is (h, k), the semi-major axis' length is a, and the semi-minor axis' length is b. The semi-major axis is half the length of the major axis, while the semi-minor axis is half the length of the minor axis. Therefore, you can identify the major and minor axes by looking at the denominators of the terms that contain x and y in the equation. The larger denominator corresponds to the semi-major axis, while the smaller denominator corresponds to the semi-minor axis.
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Juan made 13 out of 20 free throws. If Botina shoots 25 free thows, what's the minimum number she has to make in order to have a better free-throw percentage than Juan?
Answer:
16 1/4
Step-by-step explanation
Pls help i don’t know how to do this
Answer:
Step-by-step explanation:
y = √24²+32² = √1600 = 40
find base angle Ф on the right:
Ф = sin⁻¹(32/40) = 53.13
find other base angle (sum of interior angles of a Δ is 180):
180 - 90 - 53.13 = 36.87
now you can use the Law of Sines to find z, x:
40/sin36.87 = z/sin53.13 = (x+24)/sin90
z = 40(sin53.13)/sin36.87 = 53.33
sin36.87(x+24) = 40(sin90)
x+24 = 40/sin36.87 = 66.66
x = 66.67 - 24 = 42.67
double check the answers:
y² + z² = (x+24)²
40² + 53.33² = (42.67 + 24)²
1600 + 2892 = 4444
4444 = 4444 answers are correct!
The yearly growth of a new population of gnats can be modeled by the equation G(t) = 500(1.182)t, where G(t) is the number of gnats, t is the time in years, and 500 is the starting population. Write an equivalent equation using the weekly growth factor. What is the weekly growth rate of these gnats?
The weekly growth rate of these gnats is approximately 1.38%.
What is continuous growth rate?With discrete growth, we may observe change taking place following a particular event. We receive fresh options when we flip a coin. We pay interest once a year. After a successful mating season, young are produced. Change occurs continuously in an economy that is growing. We are unable to remark, "It changed here," in reference to an occurrence. The pattern is always changing (radioactive decay, a bacteria colony, or perfectly compounded interest).
Given that,
G(t) = 500(1.182)t
Using the growth function for 52 weeks = 1 year we have:
= 500(1 + r)⁵²ˣ
where r is the weekly growth rate.
To find the weekly growth rate, we can first rewrite the equation as:
1 + r = (1.182)⁽¹⁾⁵²
1 + r = 1.0138
r = 0.0138
The equivalent equation using the weekly growth factor is:
G(t) = 500(1.0138)⁵²ˣ
The weekly growth rate of these gnats is approximately 1.38%
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PLEASE HELP The toll to cross a bridge is $1.25. If $72.50
was collected at a toll booth in one hour,
how many cars went through the booth? How would you put that in an equation with the letter C?
The answer to this question is as follows The formula for the letter C is: equation $1.25C = $72.50
What is equation?A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.
Let C represent the volume of vehicles that passed through the booth.
As $1.25 is the amount collected per vehicle, the following equation represents the total amount collected:
Total = $1.25 plus C
Also, we are aware that $72.50 was collected in one hour, allowing us to create another equation:
$72.50 = $1.25 × C
We may divide both sides by $1.25 to find C:
C = $72.50 ÷ $1.25
C = 58
58 vehicles passed through the booth as a result.
The formula for the letter C is:
$1.25C = $72.50
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10. An elevator at the 25th floor went down 16 floors and then up 11 floors. How far from the 25th floor was it?
Answer:
5 floors
Step-by-step explanation:
25 - 16 +11 = 20
The elevator is now on the 20th floor. That is 5 floors away from the 25th floor.
Helping in the name of Jesus.
You want to learn Latin salsa dancing at a fitness center. You have two options, option A is to pay a $260 registration fee plus $10 per lesson. Option B is to pay $30 for each lesson you attend. After how many lessons will the total costs of the two options be the same?
Answer:
Step-by-step explanation:
Let's call the number of lessons attended "x".
Option A: Total cost = $260 + $10x
Option B: Total cost = $30x
We want to find when the two options have the same cost:
$260 + $10x = $30x
Subtracting $10x from both sides:
$260 = $20x
Dividing both sides by $20:
x = 13
Therefore, after attending 13 lessons, the total cost for both options will be the same.
You work for a pet-grooming service. You record the number of animals you groomed each day over a 10-day period: 7, 10, 8, 9, 7, 11, 8, 6, 7, and 9. You state that the typical number of animals that you can groom is the mean of 8.2 animals per day.
Does this measure of central tendency describe the data well?
Yes, because the mean always describes data well.
Yes, because there are no outliers to skew the data.
No, because it is not possible to groom 0.2 of an animal.
No, because the most common number of dogs groomed is 7.
Yes, because half of the time, it is possible to groom more than 8.2 and half the time less than 8.2.
No because it is not possible to groom 0.2 of an animal.
What is median ?
The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, the median is helpful. The median is one of the simple to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the center of a sequence to determine its value.
To support this, we can also calculate the median and mode of the data set to see if they are close to the mean. The median is the middle value of the sorted data set, which is 8 in this case, and the mode is the most common value, which is also 7 and 8 in this data set. So, the mean, median, and mode are all relatively close to each other, indicating that the data is roughly symmetric around the center.
Based on the given data, the mean of 8.2 animals per day can be considered as a reasonable measure of central tendency.
Hence the answer is No because it is not possible to groom 0.2 of an animal.
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Answer:
Yes, because there is no outliers to skew the data.
Step-by-step explanation:
I did the quiz
The question is present in the image
It is the last one ...................
Explain why the following function F : [tex]R^{2}[/tex]⇒[tex]R^{2}[/tex] is not a linear transformation:
F([tex]\left[\begin{array}{ccc}x\\y\end{array}\right][/tex]) = x[tex]\left[\begin{array}{ccc}1\\3\end{array}\right][/tex] + 8[tex]\left[\begin{array}{ccc}1\\x+y\end{array}\right][/tex]
The function F: R²⇒R²
where, [tex]F([/tex] [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex][tex])[/tex] [tex]= x[/tex][tex]\left[\begin{array}{ccc}1\\3\\\end{array}\right][/tex] [tex]+ 8[/tex] [tex]\left[\begin{array}{ccc}1\\x+y\\\end{array}\right][/tex], is not a linear transformation, as the y-intercept of the given function is not zero, so, we can say that, given function is not a linear transformation.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
given that,
the function is defined as, F: R²⇒R²
where,[tex]F([/tex] [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex][tex])[/tex] [tex]= x[/tex][tex]\left[\begin{array}{ccc}1\\3\\\end{array}\right][/tex] [tex]+ 8[/tex] [tex]\left[\begin{array}{ccc}1\\x+y\\\end{array}\right][/tex]
so, here, the y-intercept of the function is, [tex]8[/tex][tex]\left[\begin{array}{ccc}1\\x+y\\\end{array}\right][/tex]
now, we know that, [tex]8[/tex][tex]\left[\begin{array}{ccc}1\\x+y\\\end{array}\right][/tex] ≠ 0
so, the y-intercept is not zero.
again, we have,
now, we know that,
A single variable function f(x)=ax+b is not a linear transformation unless its y-intercept b is zero.
we have that,
the given function doesn't have y-intercept = 0.
so, we get, given function is not a linear transformation.
Hence, The solution is, as the y-intercept of the given function is not zero, so, we can say that, given function is not a linear transformation.
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Qashley has 85 cents.
Noah has 50 cents, and his mother gives him 3
quarters. How much money does Noah have?
Answer: $1.25
Step-by-step explanation: Noah has $1.25 because since Noah has 50 cents, and you add on another 75, you get $1.50
Answer:
Noah has 50 cents initially and his mother gives him 3 quarters, which is 75 cents (3 quarters x 25 cents/quarter).
Therefore, in total, Noah has 50 cents + 75 cents = 125 cents.
In dollars, that is $1.25.
You are really excited to have found a Puch Maxi Moped from the mid Eighties, and the spring weather is making you want to get out and ride it around. It doesn't run on straight gasoline, you have to mix the oil and gas together in a specific ratio of 2.4 fl. oz. of oil for every gallon of gasoline. You have 1.5 quarts of gas. How much oil should you add?
You should add 115.2 fluid ounces of oil to your 1.5 quarts of gasoline.
What is an expression?An expression is a group of symbols and/or numbers used to represent a quantity or a mathematical relationship between two quantities in mathematics. Variables, constants, as well as operators like addition, subtraction, multiplication, and division, can all be found in an expression.
Since there are 4 quarts in a gallon, 1.5 quarts is equal to 1.5/4 = 0.375 gallons of gasoline.
To determine how much oil to add, we need to use the ratio of 2.4 fl. oz. of oil for every gallon of gasoline.
First, we need to convert the amount of gasoline we have from gallons to fluid ounces:
0.375 gallons x 128 fluid ounces per gallon = 48 fluid ounces of gasoline.
Next, we can use the ratio to find how much oil to add:
2.4 fl. oz. oil: 1 gallon gasoline
x fl. oz. oil: 48 fl. oz. gasoline
Cross-multiplying, we get:
2.4 x 48 = 1 x (x)
115.2 = x
So you should add 115.2 fluid ounces of oil to your 1.5 quarts of gasoline.
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Answer the following questions on the basis of the following three sets of data for the country of North Vaudeville:
(A)
Price Level
110
100
95
90
Real GDP
(A)
275
250
225
200
The data in
Price
Level
(B)
100
100
100
100
Real GDP
(B)
200
225
250
275
Price
Level
(C)
110
100
95
90
Real GDP
(C)
225
225
225
225
a. Which set of data illustrates aggregate supply in the immediate short run in North Vaudeville?
The data in B
The short run?
The long run?
The data in C
b. Assuming no change in hours of work, if real output per hour of work increases by 10 percent, what will be the new levels of real
GDP in the right column of A?
Instructions: Enter your answers rounded to the nearest whole number.
At a price level of 110:
At a price level of 100:
At a price level of 95: [
At a price level of 90:
The solutions are given below.
What is GDP?Gross domestic product is a monetary measure of the market value or the market value of all the final goods and services produced and sold in a specific time period by a country or countries, generally "without double counting the intermediate goods and services used up to produce them".
here, we have,
1a. We can see immediate short run aggregate supply in North vaudeville in column A. This is because the price is fixed while output increases
1b. We can see short run aggregate supply in North vaudeville in column c. This is because output increases with price increase.
1c we can see long run aggregate supply in North vaudeville in column B. This is because output is constant with price increase.
Assuming output per hour of work decreases by 25% for column C then for each price, output is:
2A. Given price P= 110, output is 285(1-0.25) = 213.75
2B. Given price P = 100, output is 260(1-0.25) = 195
2C. Given price P = 95, output is 235(1-0.25) = 176.25
2D. Given price P = 90, output is 210(1-0.25) = 157.50
3. The new data from question 2 reflects a decrease in aggregate supply.
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Find the quotient.
9.9) 80.19
Answer:
8.10
Step-by-step explanation:
Solve this please. 3(-2)(5)(-1)(0)
Answer:
0.
Step-by-step explanation:
Multiplying 3, -2, 5, -1, and 0, we get:
3 x -2 x 5 x -1 x 0 = 0
So, 3(-2)(5)(-1)(0) = 0.
Answer:
Step-by-step explanation:
5x-2=-10x-1=10x3=30x0=0
0 is the very last answer
Let h = height. Write an
inequality to show that a child must be at least 48 inches tall to ride the rollercoaster.
Answer:
h [tex]\ge[/tex] 48
Step-by-step explanation:
This inequality states that the height h, must be either equal to 48 to greater than 48.
This scale drawing shows a enlargement in a figure.
What is the value of the missing side, x?
x= 10
x=18
x = 24
x=30
Answer:x=18
Step-by-step explanation:
12/x=16/24
12/x=2/3
x=12*2/3
x=18
If f(x) = Sin3x+x , verify that f(-x)=-f(x).
Answer:
True
Step-by-step explanation:
Given a function:
[tex]\displaystyle{f(x)=\sin 3x + x}[/tex]
Verify that f(-x) = -f(x) by substitution -- therefore:
[tex]\displaystyle{f(-x) = -f(x)}\\\\\displaystyle{\sin 3\left(-x\right)+\left(-x\right) = -\left(\sin 3x + x\right)}\\\\\displaystyle{\sin \left(-3x\right) - x = -\sin 3x - x}\\\\\displaystyle{-\sin 3x - x = -\sin 3x - x}[/tex]
Both sides are equal, hence f(-x) = -f(x).
Salma and her children went into a bakery and will buy cupcakes and brownies. She must buy no less than 15 cupcakes and brownies altogether.
Write an inequality that would represent the possible values for the number of cupcakes purchased, c, and the number of brownies purchased, b.
The inequality that represents possible values for the number of cupcakes purchased, c, and the number of brownies purchased, b is:
(c+b) ≥ 15
What is meant by inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. However several inequalities are utilised to compare the numbers, whether it is less than or higher than. An inequality symbol has non-equal expressions on both sides. It indicates that the expression on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using inequality symbols.
It is given that the least number of cupcakes and brownies that Salma should buy is 15.
Let the number of cupcakes purchased be c and the number of brownies purchased, b.
Then the total number of cupcakes and brownies is c + b
This sum should be greater than or equal to 15.
Then the inequality is (c+b) ≥ 15
Therefore the inequality that represents possible values for the number of cupcakes purchased, c, and the number of brownies purchased, b is:
(c+b) ≥ 15
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The pH of a solution ranges from 0 to 14. An acid has a pH less than 7. Pure water is neutral and has a pH of 7. The pH of a solution is given by pH = -logx where x represents the concentration of the hydrogen ions in the solution in moles per liter. Find the hydrogen ion concentration of the pH=5.4
Answer:The easiest way to do this is to just raise 10 to the negative value of the pH. Thus, in this case hydrogen ion concentration would be 1x10-2.4. However, one doesn't usually leave it that way, so you put it in to the more conventional form as
3.98x10-3 and this would be the hydrogen ion concentration. If you take the negative log of this number (pH) you will get 2.4
Identify the inequality graphed on the number line.
The answer should be: x [tex]\geq[/tex] -10
honestly just need some help
Answer:
B
Step-by-step explanation:
The dashed lines are problem asymptotes, where the denominator is 0. It's showing those at x = 0 and x = 4. Plug in 0 to answer B and you get
(0)(0-4) and that equals 0
Plugging in 4, you get
(4)(4-4) = 4(0) and that also equals 0
0 is what creates that space in the function and disconnects it
Each day Chef Mischa wants
to plans to make at least 325 meals. Some are vegetarian and some will have meat. Preparing a vegetarian meal calls costs
with meat costs $2 to make. Chef Mischa's budget is $600.
es to represent these constraints
vegetarian meals. Let y represent the number of meat meals
The constraints of the Chef's objective function are x + y ≥ 325 and
2x + 5y ≤ 600
How to make the constraints of the Chef's objective functionTo represent Chef Mischa's constraints, we can use the following variables
x = Number of vegetarian meals
y = Number of meat meals
Using the above variable definitions and the problem statement, we have the following constraints of linear inequalities:
x + y ≥ 325 (Chef Mischa wants to make at least 325 meals)
2x + 5y ≤ 600 (Chef Mischa's budget is $600)
The above are the constraints
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1. A cone has surface area 360*pi in² and volume 800*pi in³. The cone is dilated, and the surface area of the dilated cone is 2,250*pi in². What
is the dilated cone's volume? Round your answer to the nearest hundredth
The dilated cone's with surface area of 2,250π in^2 has a volume of about 12500π in³
What is dilation?Dilation is the increase or decrease in the size of a figure.
The cone has surface area 360π in² and volume 800π in^3. the cone is dilated, and the surface area of the dilated cone is 2,250π in^2.
Hence:
Scale factor² = dilated cone area / cone surface area
scale factor² = 2250π / 360π
Scale factor = 2.5
Volume of dilated cone = 2.5³ × 800π = 12500π in³
The dilated cone's with surface area of 2,250π in^2 has a volume of about 12500π in³
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Ninety percent of juniors in high school have their driver’s license. If Eagle Mountain High has 576 juniors with a driver’s license, then
how many juniors are enrolled?
There are 640 juniors enrolled in Eagle Mountain High school.
Define the term Percentage?Percentage can be define as the way of shown a number as a fraction of 100. The word "percent" comes from the Latin per centum, which means "by the hundred." Percentages are commonly used to represent proportions or rates, and they are denoted using the symbol "%".
Let's denote the total number of juniors in the high school as "x".
From the problem, we know that 90% of the juniors have a driver's license. We can express this as:
0.9x = 576
To solve for x, we can divide both sides by 0.9:
x = 576 / 0.9
x = 640
Therefore, there are 640 juniors enrolled in Eagle Mountain High school.
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the sides of a rectangle are -x + 18 and x + 4.what is the area?
Answer:
The area of a rectangle is given by the product of its length and width. In this case, the length of the rectangle is -x + 18, and the width is x + 4. So, the area is:
Area = (length) x (width)
= (-x + 18) x (x + 4)
= -x^2 + 14x + 72
Therefore, the area of the rectangle is -x^2 + 14x + 72.
Can someone please tell me what 5.232 divided by 8 is
Answer: .654 not rounded
Step-by-step explanation:
5.232 divided by 8 is 0.654
The mean score of the students in Dr. Battle’s math class on the most recent quiz was 78 points with a standard deviation of 6 points. If these scores can be modeled using a normal distribution, which percentage best represents the number of students with quiz scores between 72 and 90 points?
Approximate Percentages of Data in a Normal Distribution:
• 68% of the data lie within 1 standard deviation of the mean.
• 95% of the data lie within 2 standard deviations of the mean.
• 99.7% of the data lie within 3 standard deviations of the mean.
Responses
A.68.0%
B.81.5%
C.95.0%
D.97.5%
The percentage of students with quiz scores between 72 and 90 points would be 81.5%.
What is standard deviations?Standard deviations is a statistical measure of the spread of data points around the mean in a set of data. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. Standard deviations are used to measure the uncertainty of a statistic or the variability of a population or sample of observations.
This answer is correct because the data is being modeled using a normal distribution. This means that the quiz scores can be described as a bell-shaped curve, with the mean score of 78 points being the highest peak. The 68% of the data that lies within 1 standard deviation of the mean would be between 72 and 90 points, which is the range specified in the question, so the answer is 81.5%. This is because 68% of the data lies within 1 standard deviation of the mean and 13.5% of the data lies within the second standard deviation of the mean. The sum of these two figures (68% + 13.5%) is 81.5%. Therefore, the percentage of students with quiz scores between 72 and 90 points would be 81.5%.
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