The value of the function g(f(x))=4x²+4x-15 if f(x) = x²+x-6
g(x) = 4x +9.
What is meant by a function?An exact one of each element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are denoted by the terms "domain" and "codomain," respectively.
The fundamental concept of functions was the connection between fluctuating quantities and other variables. One illustration of this is the impact of time on a planet's position. Beginning at the end of the 17th century and continuing until the 19th century, the concept was developed using the infinitesimal calculus.
Given,
f(x) = x²+x-6
g(x) = 4x +9
f(g(x))=f(4x+9)
g(f(x))=4(x²+x-6)+9
g(f(x))=4x²+4x-24+9
g(f(x))=4x²+4x-15
Therefore, the value of the function g(f(x))=4x²+4x-15 if f(x) = x²+x-6
g(x) = 4x +9.
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regression analysis invites us to think in terms of an independent variable resulting from or being caused by a dependent variable's actions. true false
The given statement , regression analysis invites us to think in terms of an independent variable resulting from or being caused by a dependent variable's actions is true.
Regression analysis is a group of statistical procedures used in statistical modelling to determine the relationships between a dependent variable (often referred to as the "outcome" or "response" variable, or a "label" in machine learning jargon), and one or more independent variables (often referred to as "predictors," "covariates," "explanatory variables," or "features").
In linear regression, the most typical type of regression analysis, the line (or a more complicated linear combination) that most closely matches the data in terms of a given mathematical criterion is found.
When using the ordinary least squares method, for instance, the specific line (or hyperplane) that minimizes the sum of squared differences between the genuine data and that line is computed (or hyperplane).
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Write the answer in the blank.
What number is 280 more than 220?
Answer: 500
Step-by-step explanation:
280 + 220 is 500
Answer:
The number is 500.
Step-by-step explanation:
Let's assume that,
→ Missing number = x
Forming the equation,
→ x = 220 + 280
Now the value of x will be,
→ x = 220 + 280
→ [ x = 500 ]
Hence, the number is 500.
if two vectors are perpendicular to each other, their cross product must be zero.
true
false
Answer: False
Step-by-step explanation: This is false because perpendicular mean that 2 lines cross to make a 90 degree angle. If a cross product is 0 the lines never touch meaning its parallel.
Is this statement true or false?
TRUE: The given condition is correct that m ≤ 10 and m > 4.
Explain the term inequality of the numbers?An inequality in mathematics depicts the relationship between these two values in an unbalanced algebraic expression. A sign of inequality can be used to show that one of the two variables is larger than, greater than or comparable to, less than, or equal to some other value.Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two parameters are not equal. But several inequalities are utilized to compare the numbers, either it is less than or higher than.For the given statement;
m ≤ 10 and m > 4, the number for the value of m be;
m = 5, 6, 7, 8, 9, 10.
Thus, the given condition is correct that m ≤ 10 and m > 4.
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If you vertically compress the absolute value parent function, F(x) = |x|, by multiplying by 3/4, what is the equation of the new function?
A. G(x) = | 3/4 x |
B. G(x) = |x| - 3/4
C. G(x) = 3/4 |x|
D. G(x) = | x + 3/4 |
Answer:G(x) = 3/4 |x|, nevertheless that is the same that G(x) = |3/4x|.
Step-by-step explanation:
Note that given that 3/4 is less than 1 the original function is compressed.
- Take care <3
PLEASE EXPLAIN AND SHOW YOUR WORK THANK YOU!!
Solve as a MIXED NUMBER:
-2.25 + 0.4x = -2.8
THANK YOU!
Answer:
-1 3/8
Step-by-step explanation:
-2.25 + 0.4x = -2.8
-2.25 + 2.25 + 0.4x = -2.8 + 2.25 ==> add 2.25 on both sides to isolate x
0.4x = -0.55
(0.4x = -0.55)*20 ==> multiply the equation by 20 to remove decimals
8x = -11
x=-11/8
x=-(3+8)/8 ==> turn x into a mixed number
x=-3/8 - 8/8
x=-3/8 - 1 ==> simplify
x=-1 - 3/8
x=-(1 + 3/8)
x=-1 3/8
Can you please give me the answer you don’t have to solve all but please!!!!!!
Answer: Reduction: 1/3
Step-by-step explanation:
Remember that if you are dilating it to be larger, it will be a whole number. If it is less than one, then it is dilating to be smaller.
Answer: Reduction 1/3.
Step-by-step explanation: When a shape is transformed into a smaller version of the original, it's a reduction. Reductions are less than 1 so the answer I provided above is what you're looking for.
Have a great day! :)
This graph shows all the key characteristics of a particular polynomial function. Drag tiles to complete the function rule that could be represented by the graph
The function that can be represented by this graph is defined as follows:
f(x) = 2x³ + x - 3.
How to define the function?
The function is defined looking at the features of the graph.
The first feature which we look at is the y-intercept, as the graph of the function crosses the y-axis at y = -3, hence the function can be defined as follows:
f(x) = ax^n + x - 3.
The function has an inflection point, as it has a change in it's concavity, thus the function has a second derivative of the first degree, meaning that the function is of the third degree, that is:
n = 3.
The x-intercept is when the function crosses the x-axis, meaning that when x = 1, y = 0, then the leading coefficient a is obtained as follows:
0 = a + 1 - 3
a = 2.
Which means that the function rule can be given by:
f(x) = 2x³ + x - 3.
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in 12 years a man will be twice as old as he was 12 years ago . find his present age
His present age is 36 years.
Let his present age = x
Given,
2(x − 12) = x +12
2x - 24 = x + 12
2x - x = 12 + 24
x = 36
Therefore, his present age is 36 years.
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Eva bought seven and one-half pounds of chocolate chips. She used three and three-fourths pounds in some cookies and two and five-sixths pounds in some muffins. How many pounds of chocolate chips were left?
A three-twelfths pounds
B eleven-twelfths pounds
C one and two-twelfths pounds
D one and seven-twelfths pounds
Answer:
B
Step-by-step explanation:
[tex]7\frac{1}{2} - 3\frac{3}{4} - 2\frac{5}{6} \\= \frac{15}{2} - \frac{15}{4} - \frac{17}{6} \\(common denominate is 12)\\=\frac{90}{12} -\frac{45}{12} -\frac{34}{12} \\\\=\frac{11}{12}[/tex]
a friend of yours who works in the it department of a bank tells you that tellers are allowed to log in to their terminals only from 9 a.m. to 5 p.m., monday through saturday. what is this restriction an example of?
Given restriction is an example of Time-of-day restrictions
The correct answer is an option (C)
In this question we have been given a friend tells you that tellers
are allowed to log in to their terminals only from 9 a.m. to 5 p.m., Monday through Saturday.
We need to identify the type of restriction in this example.
We know that time-of-day restrictions are the restrictions that often used to limit the hours during which a user is allowed to log into or access a system.
This type of restrictions helps prevent unauthorized access outside that user's normal working hours .
Therefore, given restriction present in this example: Time-of-day restrictions
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The complete question is:
A friend of yours who works in the IT department of a bank tells you that tellers are allowed to log in to their terminals only from 9 a.m. to 5 p.m., Monday
through Saturday. What is this restriction an example of?
A. User auditing
B. Least privilege
C. Time-of-day restrictions
D. Account verification
PLEASE HELLPPPP
The White Chuck Glacier is in the Cascade Range of western North America. In 1958 it covered 3.1 km?.
By 2002 it had lost about 70% of its area. What was the area of the glacier in 2002? Show your thinking.
Answer:
0.93 km
Step-by-step explanation:
The White Chuck Glacier lost 70% of its area between 1958 and 2002, which means that its area was reduced by 70/100 = <<70/100=0.7>>0.7.
Since the glacier-covered 3.1 km. in 1958, its area was reduced by 0.7 * 3.1 km? = <<0.7*3.1=2.17>>2.17 km.
Therefore, the area of the White Chuck Glacier in 2002 was 3.1 km. - 2.17 km? = <<3.1-2.17=0.93>>0.93 km.
Find an equation that fits this question please
y = [tex]\frac{3}{4} x[/tex] is the relationship between two variables x and y.
What is a direct variation relationship?The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation. For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation if b is directly proportional to a. (where k is a constant).When one variable changes and the second variable varies proportionally while the ratio of the second variable to the first variable stays constant, the relationship is said to have direct variation. For instance, there is a constant, k, which is the ratio of y:x when y varies directly as x.from the Table x and y in the ratio 4 : 3
i. e
The equation related to x and y is :
y = [tex]\frac{3}{4} x[/tex].
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What is the interest earned in a savings
account after 12 months on a balance of
$3500 if the interest rate is 1.5% APY
compounded yearly?
Answer:
The interest earned on a savings account with a balance of $3500 and an interest rate of 1.5% per year compounded yearly would be $52.50 after 12 months.
Step-by-step explanation:
To calculate the interest earned on a savings account, you need to know the interest rate, the length of time the money is deposited, and the starting balance. Based on the information provided, it appears that the interest rate is 1.5% per year, the money is deposited for 12 months, and the starting balance is $3500.
To calculate the interest earned, you would first need to convert the interest rate to a decimal by dividing it by 100. In this case, the interest rate would be 0.015. You would then multiply the interest rate by the starting balance to get the amount of interest earned in a year. In this case, the interest earned would be $3500 * 0.015 = $52.50.
Since the interest is compounded yearly, the total balance after one year would be the starting balance plus the interest earned. In this case, the total balance would be $3500 + $52.50 = $3552.50. Therefore, the interest earned on a savings account with a balance of $3500 and an interest rate of 1.5% per year compounded yearly would be $52.50 after 12 months.
The answers are
A. Statement: FDC≈FAB Reason: SAS
B. Statement FDC~FBA Reason: AA
C. Statement FDC≈FBA Reason: SAS
D. Statement FDC~FAB Reason: AA
Can I get an answer as well as how it makes sense?
Answer:
Step-by-step explanatihelpson:
is c hope it
Find the slope and the y-intercept.
Then use them to graph the line. -2x + 5y = -15
Answer:
Step-by-step explanation:
this is easy
Find the inverse of the following function. f(x) 8√ x for x > 0
Inverse function of f(x) 8√ x for x > 0 is f^-1(y)is 8√y for y > 0. The inverse of a function is a function that "undoes" the original function.
What is inverse of a function?In order for a function to have an inverse, it must be one-to-one, meaning that each input value must correspond to a.
if the original function maps input values to output values, the inverse function maps the output values back to the input values.
To find the inverse of the function f(x) = 8√x for x > 0, we can use the following steps:
Replace f(x) with y. This gives us y = 8√x for x > 0.
Replace x with f^-1(y). This gives us f^-1(y) = 8√y.
Solve for y. To solve for y, we can square both sides of the equation:
y^2 = (8√y)^2
y^2 = 64y
y^2 - 64y = 0
y(y - 64) = 0
This equation has two solutions: y = 0 or y = 64. However, the original function is only defined for x > 0, so the inverse function is only defined for y > 0. This means that the inverse function is f^-1(y) = 8√y for y > 0.
Therefore, the inverse of the function f(x) = 8√x for x > 0 is f^-1(y) = 8√y for y > 0.
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Select the correct answer from each drop-down menu. circle a has diameters ef and ih intersecting approximately at 90 degrees, radius ad with point d lies on minor arc hf, and chord bc intersecting diameter ef near point e at a right angle. point a is the center of this circle. the ratio of the lengths of and is 2 : 1.
Answer:EF to AD
Step-by-step explanation:
A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.
Determine the distance between the Trolley Train and the Silly Slide.
25 units
7 units
5 units
3 units
The distance between the Trolley Train and the Silly Slide is 5 units. The 3rd option is the answer
How to determine the distance between the Trolley Train and the Silly Slide?From the map, the coordinate of the Trolley Train is (-2, -6) and the coordinate of the Silly Slide is (2, -3)
The formula for finding the distance between the two points is given as:
d=√(x₂ – x₁)² + (y₂ – y₁))²).
where
x₁ = -2,
y₁ = -6 (Trolley Train)
x₂ = 2
y₂ = -3 (Silly Slide)
d = √((2 – (-2))² + (-3 – (-6))²)
d = √((4)² + (3)²)
d = √25
d = 5 units
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Chang and Carlotta solve this problem in two different ways.
You have $50 in your bank account.
You make $8 per hour mowing lawns.
How many hours must you mow lawns to have a total of $130 in your account?
Use the drop-down menus to complete the sentences below.
What are variables ?
There are certain things in real life that never change, like your birthday. However, other factors, such as temperature, age, height, etc., change with place and time. These amounts might be referred to as variables because they are changeable.
A symbol (often a letter) used in mathematics to represent an unknowable numerical value in an equation or algebraic statement. A variable can be defined as a quantity that is changeable and not fixed. Variables are crucial since they make up a significant portion of algebra.
Typically, "x" and "y" are used to denote unknowable integers. However, it is not required; any letter will do.
If I have $50 in my bank account and i have to make it $130 by mowing a lawn that means i need to earn on $80 by mowing the lawn
($130 - $50 =$80)
I can earn $8 per hour by mowing the lawn which means in only need to work for 10 hours to earn $80 ($8 per hour x 10 hours= $80 )
Chang and Carlotta method use different operations to simplify the expression in same order
Chang's method uses variable but Carlotta doesn't
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A window company makes two square windowpanes. Windowpane A
has an area of 176 square inches. Windowpane B has an area of 275
square inches. How much longer is a side of Windowpane B than a
side of Windowpane A? Study the pictures.
Answer: 99.
If you take 275 and subtract it by 176, it should be 99, if I’m correct.
Jacob is practicing the 100 meter dash. the data shows his time in seconds. 14, 13, 13.5, 16, 14 15.5, 14.5 Which box plot shows the data?
The box plot for given minimum, maximum, median, Q1 and Q3 is plotted below.
What is a box and whisker plot?A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median.
The given data set is 14, 13, 13.5, 16, 14, 15.5, 14.5.
Order of data is 13, 13.5, 14, 14, 14.5, 15.5, 16.
Here, minimum is 13
Maximum is 16
Median is 14
Lower quartile range(Q1) is 13.5
Upper quartile range(Q3) is 15.5
Therefore, the box plot for given minimum, maximum, median, Q1 and Q3 is plotted below.
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If three hens can lay 3 eggs in 3 days how many days can 7 hens lay 7 eggs? Pls help!!
Answer:
3 days
Step-by-step explanation:
Please help me with my geometry work
In geometry, the ray, line, or segment that splits a given angle into two equal pieces is known as the angle bisector. ,m∠2 = 40°.
What is a straight line?An unending, one-dimensional figure with no breadth is a straight line. It consists of an infinite number of points connected on either side of a point. A straight line has a 180° measurement.
Definition of angle bisector.In geometry, the ray, line, or segment that splits a given angle into two equal pieces is known as the angle bisector. For instance, a 60-degree angle will be split into two angles of 30 degrees each by an angle bisector. Alternatively said, it divides two smaller congruent angles. Given below is an image of an angle bisector of ∠AOB.
The graphic XYQ is the straight line, m∠3 = 40°, and m∠4 = 25°. YZ is the angle bisector of ∠s.
m∠2 = 40° the reason is YZ is the angle bisector of ∠s
∠s = m∠2 + m∠3
m∠2 = m∠3
therefore m∠2 = 40°
m∠1 + m∠2 + m∠3 + m∠4 = 180° the reason is XYQ is the straight line.
substitution of all values
m∠1 + 40° + 25° + 40° = 180°
m∠1 + 105° = 180°
m∠1 = 75° (straight line, substitution of all values )
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Write a recursive formula for an, the nth term of the sequence 2,-6,18,-54
Answer: The recursive formula for the sequence 2, -6, 18, -54 is given by the following:
a(n) = (-3) * a(n-1)
where a(n) is the nth term of the sequence and a(n-1) is the previous term in the sequence.
This means that each term in the sequence is equal to -3 times the previous term, with the first term being 2. For example, the third term of the sequence (a(3)) would be equal to (-3) * a(2), which is (-3) * (-6) = 18. The fourth term of the sequence (a(4)) would be equal to (-3) * a(3), which is (-3) * 18 = -54. And so on.
This recursive formula can be used to calculate the nth term of the sequence for any value of n.
how many 10-digit integers are there which are palindromes? be sure to describe the process you are using.
There are 90000 palindromes 10-digit numbers.
In this question we need to find the number of 10-digit integers are there which are palindromes.
We know that a palindrome is a number that reads the same forward and backward.
The numbers that remain same even if they are reversed.
For exa., 131, 5225
We can observe that for even digit palindromes first half should be equal second half in reversed order.
we can generalize it as variables:
abcdeedcba, for a not equal to 0
So if we know how many 5-digit numbers are there, all we have to do is reverse it and we will have our 10-digit palindrome number.
There are 10 digits in total (0 - 9)
Since the first digit cannot be zero we excluded it from our choice hence we have 1–9 i.e 9 choices for first place(hundred's place)
The second, third, fourth and fifth digit has all 10 choices.
So, in total there are 9 x 10 x 10 x 10 x 10= 90000 five digit numbers.
Therefore, the total 10-digit numbers which are palindromes = 90000
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Solve the inequality.
$-12
4
Lee has 6 pygmy goats. Their weights, in kg, are listed below.
32 23 31 28 36
26
Two of the goats wander off and don't return. The remaining 4 goats have a mean
weight of 27.25 kg. Find the weights of the two goats who wandered off.
4
GR
Answer:
The weight of the two goats is 2.08 kg
Step-by-step explanation:
Total avg
32+23+31+28+36+26 = 176176/6 = 29. 33Avg of the two goats
29.33 - 27.25 = 2.08 kgAvg of one goat
2.08 /2 = 1.04 The avg of one goat 1.04kg11-14) if b to the power x, = 7 and b > 0, then 7 / b must equal which of the following:
a) b to power (x-1)
b) b to power (x+1)
c) 7 to power x
Answer:
Here is the answer
Step-by-step explanation:
If b to the power x is equal to 7 and b is a positive number, then 7 / b must equal b to the power (x-1).
We can see this by applying the definition of an exponent: b to the power x is equal to b multiplied by itself x times. For example, if b is 2 and x is 3, then 2 to the power 3 is equal to 2 * 2 * 2 = 8.
If we divide both sides of this equation by b, we get:
7 / b = (b * b * ... * b) / b = b * b * ... * b = b to the power (x-1)
Therefore, if b to the power x is equal to 7 and b is a positive number, then 7 / b must equal b to the power (x-1). The answer is therefore a) b to the power (x-1).
the correlation between cost and distance is 0.791. describe the relationship between cost of damage and distance from the nearest fire station.
According to the question,
Given data,
The correlation between cost and distance is 0.791.
The farther the house is from a first station, the higher cost of damage tends to be.
the correlation between cost and distance
The largest single cost of liver transplantation is the cost of organ acquisition, with the variable portion of that amount being associated travel costs. We assessed the proportion of donors using ground, air, and jet transport and compared the transport costs of these three types of transport and their impact on organ procurement costs for transplant centers.
How is correlation measured?
The sample correlation coefficient r quantifies the strength of the relationship. Correlations are also tested for statistical significance.
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