If f(x) =3x^2 and g(x) =4x^3 +1 what is the degree of fg (x)
Given △PQR≅△STU, m∠R=80°, and m∠S=70°, what is the measure of ∠Q?
Enter your answer in the box.
Congruent triangles have equal corresponding angles
The measure of <Q is 30 degrees
The given parameters are:
m∠R=80°, and m∠S=70°
△PQR≅△STU
Given that both triangles are congruent, then the measure of Q is calculated using:
Q = 180 - 80 - 70
Evaluate the difference
Q = 30
Hence, the measure of <Q is 30 degrees
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All of the items in a bicycle shop are on sale for 30% off the regular price. Rene spends $74.90 to buy a bicycle and a helmet (without taxes). If the regular price of the bicycle is $85, which equation can be used to find the regular price of the helmet, h?
Answer:
0.7 (85 + h) = 74.90
Step-by-step explanation:
A publisher claims that the average salary paid at its company is $37,500 but it could differ as much as $4,500. Write and solve an absolute value inequality to determine the range of salaries at this company.
|x − 37500| ≤ 4500; The salaries range from $33,000 to $42,000
|x − 37,500| ≤ 4500; The salaries are less than $33,000 or greater than $42,000.
|x − 37500| ≥ 4500; The salaries range from $33,000 to $42,000
|x − 37,500| ≥ 4500; The salaries are less than $33,000 or greater than $42,000.
Line GH contains points G(–2, 6) and H(5, –3). What is the slope of ?
We will use the slope formula and fill it in accordingly.
[tex] m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
Our x2 is 5 and x1 is -2; our y2 is -3 and y1 is 6
[tex] m=\frac{-3-6}{5-(-2)}=\frac{-9}{7} [/tex].
The slope of your line is -9/7
Answer
Find out the slope of the points G(–2, 6) and H(5, –3).
To prove
The equation for finding the slope of two points be
[tex]m = \frac{y_{2} -y_{1}}{x_{2} - x_{1}}[/tex]
where m represented the slope .
As given
points G(–2, 6) and H(5, –3).
[tex]m = \frac{-3-6}{5+2}[/tex]
solving the above terms
[tex]m = \frac{-9}{7}[/tex]
Therefore the slope of points G(–2, 6) and H(5, –3) is
[tex]m = \frac{-9}{7}[/tex]
Find the probability that when a couple has two children, at least one of them is a boy. (Assume that boys and girls are equally likely.)
The probability that when a couple has two children, at least one of them is a boy is 0.75.
Based on the information given, the sample space will be (BB, BG, GB, GG)
where,
B = Boy
G = Girl
Therefore, based on the sample space given, at least a boy occurs in 3 places out of 4. This will be 3/4 = 0.75.
In conclusion, the correct option is 0.75.
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The probability of a couple having at least one boy when they have two children is 75%, as three out of four possible outcomes include at least one boy. These outcomes are two boys, a boy then a girl, and a girl then a boy.
Explanation:The subject of the question is probability which is a branch of mathematics. In order to find the probability that when a couple has two children, at least one of them is a boy, we need to analyze possible outcomes. The couple could have two boys (BB), a boy and a girl (BG), a girl and a boy (GB), or two girls (GG). Hence, the total unique outcomes are 4 (BB, BG, GB, GG).
Considering at least one boy, the possible outcomes could be BB, BG, GB, which are 3 possibilities. Finally, the probability is given as the ratio of favorable outcomes to the total number of outcomes. So the probability of having at least one boy is 3/4 or 75%.
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describe the steps you would follow to write a two-step inequality you can use to solve a real-world problem.
Final answer:
To write a two-step inequality for a real-world problem, first identify the unknowns and known quantities related to the problem. Next, construct an inequality that represents the problem, and finally solve the inequality for the unknown variable. For example, budgeting for a party with a savings goal can be represented as an inequality.
Explanation:
To write a two-step inequality to solve a real-world problem, follow these steps:
Identify the unknowns: Understand what needs to be determined. This involves defining the variable(s) that will represent the unknown quantity(ies) in the problem.
Identify the known quantities: Make a list of the quantities that are given or can be inferred from the problem. These are the values you will use to construct your inequality.
Construct the inequality: Use the information from steps 1 and 2 to create an inequality that represents the problem. This often involves expressing the relationship between the known and unknown quantities using an inequality symbol (such as <, >, ≤, ≥).
Solve the inequality: Apply algebraic methods to solve for the unknown variable. This may involve isolating the variable on one side of the inequality.
For example, if you are planning a party and know you have a budget of $200 for decorations but want to save at least $50, you could set up the inequality x + 50 ≤ 200, where x represents the amount you can spend on decorations.
Which ordered pair is a solution of the inequality y>4x-5? A.(3,4) B.(2,1) C.(3,0) D.(1,1)
Mrs evans has 120 crayons and 30 pieces of paper to give to her students. what is the largest number of students she can have so that each student gets equal number of crayons and equal number of pieces of paper
The maximum number of students that will receive the paper and crayons are 30.
What is ratio?
Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
Given is Mrs. Evans who has 120 crayons and 30 pieces of paper to give to her students.
We have 120 crayons and 30 pieces of paper.
Then for 1 paper, we will have (120/30) which is equivalent to 4 crayons.
So, every student will get 1 paper and 4 crayons.
Assume that the maximum number of students that will receive the paper and crayons are [x]. Then, we can write -
x + 4x = 120 + 30
5x = 150
5x = 150
x = 30
Therefore, the maximum number of students that will receive the paper and crayons are 30.
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Which expression is equivalent to 12x^4(x-3)(x+5)/ 30x(x+3)(x+5)
The equation which is equivalent to the given expression is 4x + y = 21.
What is an expression?Expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An expression is a combination of numbers, variables, or a combination of numbers and variables, and symbols and it is connected by the sign of equal.
We have,
Expression [tex]\frac{12x^4(x-3)(x+5)}{30x(x+3)(x+5)}[/tex]
So,
Now,
To get the equivalent expression,
Cancel the common factor (x + 5) of the given expression,
On solving,
We get,
[tex]\frac{12x^4(x-3)}{30x(x+3)}[/tex],
Now,
On solving further,
We get,
[tex]=\frac{2x^3(x-3)}{5(x+3)}[/tex]
So, We can not solve it further,
So, This is the expression that is equivalent to the given expression.
Hence, we can say that the equation which is equal to the given expression is [tex]\frac{2x^3(x-3)}{5(x+3)}[/tex].
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Which expression is equivalent to the following complex fraction?
The programmer can type 55 words per minute.
At that rate, how many words can the programmer type in 11 min?
66
550
605
655
Answer:
605 words per 11 minutes!
Step-by-step explanation:
60 / 55 = 1.0909
11 x 60 = 660
660 / 1.0909 = 605 + (6x - [tex]\int\limits^a_c {b} \, dx[/tex]) / 10
605 + (6x - [tex]\int\limits^a_c {b} \, dx[/tex]) / 10 rounded = 605
What is the GCF of 15 and 27 ?
A regulation baseball field measures 90 feet between each base. What is the distance around the bases in yards?
The distance around the bases in yards is 30 yards.
In order to determine the distance between each base in yards the unit of conversion of feet to yards have to be first determined. 1 foot is equivalent to 0.333333 yards.
1 feet = 0.333333 yards
The second step is to multiply the distance between each base by the unit of conversion.
Distance between each base x unit of conversion
90 x 0.333333
= 30 yards
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What is the return value of "select".substring(4, 4)?
The expression "select".substring(4, 4) will return an empty string, as the start and end indices are the same and no characters are included in the specified range.
Explanation:The substring method in many programming languages, including Java and JavaScript, is used to extract a portion of a string between two specified indices. In the expression "select".substring(4, 4), we are asking for the part of the string starting at index 4 and up to, but not including, index 4. Since the start and end indices are the same, the method will return an empty string.
It's important to note that string indices are zero-based, meaning that the first character of the string is at index 0. The string "select" has six characters, with indices ranging from 0 to 5. Therefore, calling substring with identical start and end indices will not include any characters in the resulting string.
Example:To retrieve the first character of "select", you would use "select".substring(0, 1).To retrieve "lec" from "select", you would use "select".substring(1, 4).PLEASE HELP!!!!!!!!!!!!!!!!!!!!!
How many solutions does the equation have?
2x+3+4x x2
A)many solutions
B)no solutions
C)1 solution
Solve:C=10d + 5n for n
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Mrs. Mac puts money in her piggy bank every week. The function graphed can be used to model the total amount of money in her piggy bank x week after her birthday given Mrs. Mac’s birthday is at x = 0.
1.What is the x intercept and what does it represent?
2.What is the y-intercept and what does it represent?
3.What is the slope and what does it represent?
A) X intercept is -12, this represent the number of weeks before her birthday she started saving money
B) Y intercept = 3, this is the amount of money she has in her piggy bank before her birthday
C) slope = change in Y over the change in X = 1/4, this means she is saving 25 cents per week
What is m∠AEB?
(See attachment)
Unfortunately, without the attachment or diagram, it is not possible to determine the measure of angle AEB.
Explanation:The question asks for the measure of angle AEB. In order to find this angle, we need to refer to the given diagram or attachment. Unfortunately, there is no attachment provided with the question, so it is not possible to provide a specific answer to the question. Please provide the diagram or attachment so that I can accurately determine the measure of angle AEB.
Find the exact coordinates of the centroid for the region bounded by the curves y=x, y=1/x, y=0, and x=2
The centroid of the region bounded by [tex]\(y=x\), \(y=\frac{1}{x}\), \(y=0\),[/tex] and [tex]\(x=2\)[/tex] is at [tex]\((\frac{2}{3}, 0)\).[/tex]
To find the centroid of the region bounded by the curves[tex]\(y=x\), \(y=\frac{1}{x}\), \(y=0\), and \(x=2\),[/tex]we need to first find the area of the region and then compute the coordinates of the centroid using the following formulas:
The centroid of a region with area[tex]\(A\)[/tex] is given by [tex]\((\bar{x}, \bar{y})\)[/tex]where
[tex]\[\bar{x} = \frac{1}{A} \int\int_R x \, dA\][/tex]
[tex]\[\bar{y} = \frac{1}{A} \int\int_R y \, dA\][/tex]
First, let's find the points of intersection for the curves:
1. [tex]\(y=x\) and \(y=1/x\):[/tex]
[tex]\[ x = \frac{1}{x} \implies x^2 = 1 \implies x = 1 \][/tex]
So, the intersection point is [tex]\((1,1)\).[/tex]
2. [tex]\(y=0\) and \(x=2\):[/tex]
This intersection occurs at [tex]\((2,0)\).[/tex]
Now, we'll integrate to find the area and then the centroid:
1. Area:
[tex]\[ A = \int_{0}^{1} (x - \frac{1}{x}) \, dx + \int_{1}^{2} (\frac{1}{x}) \, dx \][/tex]
[tex]\[ A = \left[\frac{x^2}{2} - \ln|x|\right]_{0}^{1} + \left[\ln|x|\right]_{1}^{2} \][/tex]
[tex]\[ A = \left(\frac{1}{2} - 0 - (0 - \infty)\right) + (\ln(2) - \ln(1)) \][/tex]
[tex]\[ A = \frac{1}{2} + \ln(2) \][/tex]
2. Centroid[tex](\(\bar{x}\)):[/tex]
[tex]\[ \bar{x} = \frac{1}{A} \left[\int_{0}^{1} x(x - \frac{1}{x}) \, dx + \int_{1}^{2} x(\frac{1}{x}) \, dx\right] \][/tex]
[tex]\[ \bar{x} = \frac{1}{A} \left[\left[\frac{x^3}{3} - \frac{1}{2}\ln|x|\right]_{0}^{1} + \left[\ln|x|\right]_{1}^{2}\right] \][/tex]
[tex]\[ \bar{x} = \frac{1}{A} \left(\frac{1}{3} - 0 - (0 - \infty) + (\ln(2) - \ln(1))\right) \][/tex]
[tex]\[ \bar{x} = \frac{\frac{1}{3} + \ln(2)}{\frac{1}{2} + \ln(2)} \][/tex]
[tex]\[ \bar{x} = \frac{2}{3} \][/tex]
3. Centroid [tex](\(\bar{y}\)):[/tex]
[tex]\[ \bar{y} = \frac{1}{A} \left[\int_{0}^{1} (x - \frac{1}{x}) \cdot 0 \, dx + \int_{1}^{2} (\frac{1}{x}) \cdot 0 \, dx\right] \][/tex]
[tex]\[ \bar{y} = 0 \][/tex]
Therefore, the centroid of the region is at the point [tex]\(\left(\frac{2}{3}, 0\right)\).[/tex]
which of the following answer choices describes all the transformation found in the cubic function f(x)=-(x+2)3-5
Foster is centering a photo that is 1/1 2 inches wide on a scrapbook page that is 10 inches wide. How far from each side of the page should he put the picture? Please enter it as a mixed number
I will give 39 points if you answer this question
Answer: 4.25
Step-by-step explanation:
If a line has a positive slope what is its general direction
A line with a positive slope generally moves upward from left to right, representing an increase in y-values as x-values rise.
Explanation:If a line has a positive slope, its general direction is upward from left to right. This means that as the x-values increase, the y-values also increase. The slope of a line in mathematics represents the rate at which y changes with respect to x. A positive slope indicates a direct relationship between the two variables involved; as one increases, so does the other. In the context of a graph, this manifests as a line that rises as it moves along the x-axis.
The nature of the slope determines the line's direction. A higher positive slope indicates a steeper ascent, while a smaller positive slope results in a less steep, flatter incline. The concept of slope is crucial in economics as well, as it measures the relationship between two variables, such as price and quantity supplied, where a positive slope illustrates that firms supply more as the price goes higher.
Can Anyone Help Me
The number of e-mails sent each day in the United States is measured in the thousands.
A. True
B. False
c = 0.20m + 2.00 what is the charge for 1mile ride?
Part of a tiling design is shown. The center is a regular hexagon. A square is on each side of the hexagon, and an equilateral triangle joins the squares. Complete the pattern around the hexagon and calculate the total area of the pattern.
A.
403.1 in.^2
B.
503.1 in.^2
C.
1,119.6 in.^2
D.
1,379.4 in.^2
Elliot has a collection of 20 toy cars. Will he be able to put an equal number of toy cars on 3 shelves
He will not be able to put an equal number of toy cars on 3 shelves.
He can put only 18 toy cars in equal number of toy cars of 6 on 3 shelves.
What is division?Division is a simple operation in which a number is divided. It's easiest to think of it as a number of objects being divided among a certain number of people.
According to the question
Elliot has a collection of 20 toy cars.
Put an equal number of toy cars on 3 shelves.
= [tex]\frac{20}{3}[/tex]
= 6.6
Thus, He can put only 18 toy cars in equal number of toy cars of 6 on 3 shelves.
He will not be able to put an equal number of toy cars on 3 shelves.
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Which expression will produce a positive product:
(-12)(12)(-6.3)(-0.2)(-15.9)
(12)(-6.3)(-0.2)(-15.9
(-12)(12)(-6.3)(-0.2)(-15.9)(0)
(12)(12)(6.3)(0.2)(-15.9)
Final answer:
To produce a positive product, the expression (12)(-6.3)(-0.2)(-15.9) should be used.
Explanation:
To determine which expression will produce a positive product, we need to consider the sign rules for multiplication.
If we have an even number of negative signs within a set of parentheses, the product will be positive. If we have an odd number of negative signs, the product will be negative.
Let's analyze the given expressions:
(-12)(12)(-6.3)(-0.2)(-15.9): This expression has five negative signs, which means it will produce a negative product.(12)(-6.3)(-0.2)(-15.9): This expression has four negative signs, which means it will produce a positive product.(-12)(12)(-6.3)(-0.2)(-15.9)(0): This expression includes a 0, and any product multiplied by 0 will be 0, which is neither positive nor negative.(12)(12)(6.3)(0.2)(-15.9): This expression has one negative sign, which means it will produce a negative product.Therefore, the expression (12)(-6.3)(-0.2)(-15.9) will produce a positive product.
The expression that will produce a positive product is (12)(-6.3)(-0.2)(-15.9) because it contains an even number of negative signs, which results in a positive product according to the rules of multiplication regarding signs.
Explanation:To find which expression will produce a positive product, we must recall the rules of multiplication regarding signs:
When two positive numbers multiply, the result is positive (e.g., 2x3 = 6).When two negative numbers multiply, the result is also positive (e.g., (-4) x (-3) = 12).When multiply numbers with opposite signs, the result is negative (e.g., (-3) x 2 = -6 and 4 x (-4) = -16).When any number is multiplied by zero, the result is always zero.We can now evaluate the expressions given:
(-12)(12)(-6.3)(-0.2)(-15.9): This expression has an odd number of negative signs, so the product is negative.(12)(-6.3)(-0.2)(-15.9): This has an even number of negative signs, making the product positive.(-12)(12)(-6.3)(-0.2)(-15.9)(0): The presence of a zero means the product is zero.(12)(12)(6.3)(0.2)(-15.9): This has one negative sign, so the product is negative.The correct expression that will produce a positive product is (12)(-6.3)(-0.2)(-15.9).
What is 4x+5(7x-3)=9(x-5)
Write the equation you would use to solve each problem; then solve.
The quotient of a number and 15 is 120. Find the number