Enrollment in a photography class increased from 25 to 35 students. What was the percent of increase in enrollment?
14%
29%
40%
Answer:
40%
Step-by-step explanation:
formula change/original
change: 10
original: 25
10/25 = 0.4
0.4 = 40%
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The sum of two nonnegative numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible.
To find the numbers with the largest and smallest sums of their squares, we can use the fact that the sum of two numbers is constant. By rearranging the equation and finding the maximum or minimum of a quadratic function, we can determine the numbers that yield the desired sums of squares.
Explanation:To find the numbers, let's call them x and y. We know that the sum of two nonnegative numbers is 20, so we can write the equation x + y = 20. To find the numbers that yield the largest sum of their squares, we can use the fact that the sum of two numbers is constant. Let's rearrange the equation as y = 20 - x and substitute it into the equation for the sum of squares: x^2 + (20 - x)^2.
Expanding and simplifying the equation, we get f(x) = 2x^2 - 40x + 400. Since this is a quadratic function, we can find the maximum by finding the vertex. The x-coordinate of the vertex can be found using the formula -b/2a, where a = 2 and b = -40. Plugging in the values, we get x = 10. Substituting this value back into the equation for y, we find that y = 20 - 10 = 10. Therefore, the numbers that yield the largest sum of their squares are 10 and 10.
Similarly, to find the numbers that yield the smallest sum of their squares, we can find the minimum of the quadratic function. The x-coordinate of the minimum can also be found using -b/2a. Plugging in the values, we get x = 20/2 = 10. Substituting this value back into the equation for y, we find that y = 20 - 10 = 10. Therefore, the numbers that yield the smallest sum of their squares are also 10 and 10.
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Name the set(s) of numbers to which 1.68 belongs.
none of the above
rational numbers, irrational numbers
rational numbers
natural numbers, whole numbers, integers, rational numbers
Answer:
The correct option is C) rational numbers
Step-by-step explanation:
Consider the provided number 1.68
Natural numbers: The natural numbers are 1, 2, 3, 4, 5,…
Whole number: Whole numbers are the set of natural numbers but starts with 0. i.e. 0, 1, 2, 3, 4, 5,…
Integers: Integers are the set of whole number and the negatives of the natural numbers, i.e, … ,-2, -1, 0, 1, 2, …
Rational number: A number is said to be rational, if it is in the form of p/q. Where p and q are integer and denominator is not equal to 0.
Irrational number: A number is irrational if it cannot be expressed be expressed by dividing two integers. The decimal expansion of Irrational numbers are neither terminate nor periodic.
Real numbers: All rational and Irrational numbers are called real number.
Now consider the provided number 1.68
The number has 2 digit after decimal point its means it is neither natural nor whole number, also it is not an integer.
The number 1.68 can be written in the form of p/q. Thus, it is a rational number.
As it is rational it can't be irrational. The number 1.68 is real number.
Hence, the correct option is C) rational numbers.
The graph of g(x) is f(x) translated to the left 8 units and up 2 units. What is the function rule for g(x) given f(x)=x²?
To translate the function f(x) = x² to the left 8 units and up 2 units, the function rule for g(x) is g(x) = (x - 8)² + 2.
Explanation:To translate the function f(x) = x² to the left 8 units and up 2 units, we can use the transformation rules. The leftward translation can be achieved by subtracting 8 from the variable x in the function, resulting in g(x) = (x - 8)². The upward translation can be achieved by adding 2 to the function, resulting in g(x) = (x - 8)² + 2.
Therefore, the function rule for g(x) given f(x) = x² is g(x) = (x - 8)² + 2.
Final answer:
To find the function rule for g(x) when the graph of f(x)=x² is translated left by 8 units and up by 2 units, the new function is g(x) = (x + 8)² + 2.
Explanation:
The question pertains to transforming a function graphically. Given the original function f(x) = x² (a parabola opening upwards with its vertex at the origin), we are to translate this function to the left by 8 units and up by 2 units to get the new function g(x). To translate a function to the left by a units, you replace x with x + a. Similarly, to translate a function up by b units, you add b to the function.
Therefore, to translate the original function f(x) = x² to the left by 8 units and up by 2 units, the new function g(x) would be:
g(x) = (x + 8)² + 2
Find m∠1 in each figure
To find m∠1, you typically use geometry knowledge, including understanding the properties of polygons and triangles. Without a specific diagram or context, however, it's impossible to provide explicit steps or an exact answer for m∠1.
Explanation:Without specific figures, it's impossible to determine exact angle measures. However, in general to find m∠1, you will need to draw upon your knowledge of geometry, particularly angle properties. If the angle is part of a polygon, its measure can often be determined by the other angle measures in the shape. Similarly, if the angle is part of a triangle, you could use the fact that the sum of all angles in a triangle is 180°. If angle properties like supplementary or complementary are mentioned, it means two angles add up to 180° or 90° respectively. Without a diagram or further context, I cannot provide particular steps to find m∠1.
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write the standerd form for thirty thousand,four hundred five and three thousandths.
If the measure of angle 1 the measure of angle 2 = 180 and the measure of angle 3 the measure of angle 2 = 180 then the measure of angle 1 is congruent to angle 3 explain why its true
Can someone give me the answer to this question??? And please explain :/
Jenna and her friend, Khalil, are having a contest to see who can save the most money. Jenna
has already saved $110 and every week she saves an additional $20. Khalil has already saved $80
and every week he saves an additional $25. Let x represent the number of weeks and y represent
the total amount of money saved.
So far I've got 110+20x= ??? for jenna because I don't know what goes after the equal sign and 80+25x=???
How many subsets of at least four elements does a set of seven elements have?
Find the value of x. Round the answer to the nearest tenth, if needed.
A.
9
B.
18.9
C.
22
D.
32.1
Emily has a coupon for 20% off her purchase. She finds a backpack on the discount rack. It's original price is $60 but is 30% off.
Emily thinks 30% & 20 % make 50% so the backpack will be $30.
Is Emily correct? Explain your answer.
Use the graph shown to find one of the solutions to the quadratic equation
x^2-7x 10 = 0.
A)-7
B)-6
C)-3
D)2
How to use the distributive property to express 24 36?
The slope of a line is -1/5, and the y-intercept is 5. What is the equation of the line written in general form? x - 5y - 25 = 0 x - 5y - 5 = 0 x + 5y - 25 = 0
Step-by-step explanation:
Equation of straight line is given by y = mx + c
Slope of line , m = -1/5
y- intercept, c = 5
Substituting
[tex]y=mx+c\\\\y=\frac{-1}{5}x+5\\\\y=\frac{-x+25}{5}\\\\5y=-x+25\\\\x+5y-25=0[/tex]
x + 5 y - 25 = 0
Option C is the correct answer.
i have alg 2 midterms tomorrow, does anyone know a good site to study?
3/5 is 30% of what number
Jackson bought a commercial vehicle for his business, Cleaners Inc., and paid by check. How will he journal this financial transaction?
A 7-foot ladder is leaned against a building in such a way that the bottom of the ladder is 4 feet from the base of the wall. Find the angle formed between the ladder and the ground.
A.30
B.35
C.55
D.60
Carroll bikes 1 kilometer east, 4 kilometers north, and then 5 kilometers east again. How far is Carroll from her starting position, to the nearest tenth of a kilometer?
Answer:
Distance of Carroll from the starting point is 7.2 km.
Step-by-step explanation:
Carroll bikes 1 km east, then 4 kilometers North, and 5 kilometers east again.
We have to calculate the distance from the starting point of Carroll.
Here we can find the distance finally from the starting point with the help of Pythagoras theorem.
Diagonal² = (Side 1 of the rectangle)² + (Side 2 of the rectangle)²
Diagonal² = 4² + 6²
= 16 + 36
= 52
Diagonal = √52
= 7.21
≈ 7.2 kilometers
Therefore, distance of Carroll form her starting point is 7.2 kilometers.
14 karat gold is a mixture of pure gold and other metals. One ounce of 14 karat gold weighs 0.58 ounce of pure gold. If a 14 karat gold necklace weighs 1.8 ounces, how many ounces of pure gold does it contain?
Answer: 1.044 ounces
Step-by-step explanation:
Given : One ounce of 14 karat gold = 0.58 ounce of pure gold.
i.e. Weight of pure gold in 1 ounce of 14 karat gold = 0.58 ounce of pure gold.
Then, Weight of pure gold in 1.8 ounces of 14 karat gold = 1.8 x (Weight of pure gold in 1 ounce of 14 karat gold)
Weight of pure gold in 1.8 ounces of 14 karat gold = 1.8 x ( 0.58) ounces of pure gold.
It implies 1.8 ounces of 14 karat gold = 1.8 x ( 0.58) ounces of pure gold.
= 1.044 ounces of pure gold.
Therefore, If a 14 karat gold necklace weighs 1.8 ounces that means it contains 1.044 ounces of pure gold.
an arrow is fired directly horizontal off a cliff that is 10 meters tall with a velocity of 65.5m/s.
A. How long is the arrow in the air?
B. What is the range of the arrow?
A circle is centered at the point (-7, -1) and passes through the point (8, 7).
The radius of the circle is ___ units. The point (-15, ___) lies on this circle.
Answer:
17, 14
Step-by-step explanation:
In math class, a student has an average grade of 85% for five tests so far. What grade must that student earn on the next test to reach an average grade of 90% for all six tests?
Factor completely 3x3 – 21x2 – 27x
...?
Answer:
Given an equation: [tex]3x^3-21x^2-27x[/tex]
A given equation is trinomials have three terms( i.e, [tex]3x^3[/tex] , [tex]21x^2[/tex] and [tex]27x[/tex] )
Factoring is the division of the polynomial terms to the simplest forms.
A greatest common factor (GCF) identifies a factor that all terms within the polynomial have in common.
[tex](3x)(x^2) - (3x)(7x) - (3x)(9)[/tex]
now, 3x can be removed from the polynomial to simplify the factoring process.
i.e,
[tex]3x(x^2-7x-9)[/tex]
Therefore, the factor completely of [tex]3x^3-21x^2-27x[/tex] is,[tex]3x(x^2-7x-9)[/tex]
To factor the expression 3x³ - 21x² - 27x, we first factor out the common term 3x, which leaves us with 3x(x² - 7x - 9). The quadratic expression does not factor any further.
The expression 3x³ - 21x²- 27x can be factored by looking for common factors in each term. First, we can see that each term has a factor of 3x. We can factor out this common term which gives us:3x(x² - 7x - 9)
Next, we can factor the quadratic expression within the parentheses. However, this quadratic expression does not factor neatly, and it seems we've reached the simplest form by just factoring out 3x. Therefore, the completely factored form of the expression is:3x(x² - 7x - 9)
Based on the graph, what is the initial value of the linear relationship?
A coordinate plane is shown. A line passes through the x-axis at negative 3 and the y-axis at 5.
–4
–3
five over three
5
Answer-
The initial value of the linear relationship is 5.
Solution-
The initial value, also know as y-intercept, is the output value when the input of a linear function is zero. It is the y-value of the point where the line crosses the y-axis or x=0 line.
As the line passes through the y-axis at 5, i.e 5 is the y intercept of the line.
Therefore, the initial value of the linear relationship is 5.
70,231 to the nearest ten thousand.
Based on the data provided, which type of transaction is likely to bring in the most income during a month?
The transaction most likely to bring in the most income is from individuals who use credit cards offering air miles and charge over $2,000 per month.
Explanation:Based on the data provided, the type of transaction likely to bring in the most income during a month involves credit cards that offer a mile of air travel for every dollar charged, particularly among users who spend over $2,000 monthly. To assess this, we can perform a simple calculation. With 30% of respondents charging more than $2,000, and 80% of those using the air miles card, we can infer that 0.30 × 0.80 = 0.24 or 24% of all respondents represent this high-earning transaction category.
Gathering data at the local supermarket on the total amounts of grocery receipts or from cashiers could provide additional insights into shopping trends and payment methods. The student can collect the data, analyze spending habits, and cross-reference those with preferred payment methods to identify the most profitable transaction. However, the information about the income related to U.S. international financial flows, like exports in goods and services or income received by U.S. investors, while related to economic transactions, does not directly answer the question about the most income-producing type of credit card usage during a month.
The most income-generating transaction per month is likely to be credit card transactions offering air miles for users who charge more than $2,000.
Explanation:Analysis of the Most Income-Generating Transaction
According to the provided data, the transaction likely to bring in the most income during a month would be transactions made with a credit card that provides a mile of air travel for every dollar charged, especially for users who charge more than $2,000 per month. The data indicates that 30% of respondents charge more than $2,000 monthly, and of those, a significant 80% use a credit card offering air miles. Given this high rate, it is reasonable to infer that a credit card transaction yielding air miles for users spending over $2,000 a month would generate the most income.
To illustrate the calculation: If we consider 100 respondents, 30 of them would charge over $2,000, and 80% of these 30 people use the air miles card, resulting in 24 people. If each of these 24 people spends exactly $2,000, this equates to $48,000 possibly earned.
Prime factor 4x^2-81=0
Answer:
[tex]4 {x}^{2} - 81 = 0 \\ 4 {x}^{2} = 81 \\ {x}^{2} = \frac{81}{4} \\ x = \sqrt{ \frac{81}{4} } \\ x = \frac{9}{2} \\ {x = 4.5}[/tex]
help..?
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Determine the contrapositive of the conditional statement: If my mom has to work, then I babysit my little sister.
Answer: If my mom does not have to work, then I do not babysit my little sister.
Step-by-step explanation:
The contrapositive of a statement of the form " If a then b" is given by :-
"If not a then not b."
The given conditional statement :" If my mom has to work, then I babysit my little sister.”
Then the contrapositive statement of the conditional statement will be
"If my mom does not have to work, then I do not babysit my little sister.”