Consider functions f and g. f ( x ) = 1 − x 2 g ( x ) = 11 − 4 x Evaluate each combined function, and match it to the corresponding value.
The value of the combined function f(g(x)) will be -16x^2+88x-120.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
There are several types of functions in math. Some important types are:
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
Now,
Given functions are f(x)=1-x^2 and
g(x)=11-4x
Therefore,
the combined function will be f(g(x))=1-(11-4x)^2
=1-121-16x^2+88x
Hence,
The value of the combined function f(g(x)) will be -16x^2+88x-120.
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Right question would be :-
Consider functions f and g. f ( x ) = 1 − x 2 g ( x ) = 11 − 4 x Evaluate f(g(x))?
If a number has a factor, then both 2 and 4 are factors?
Answer:
Step-by-step explanation:
when 2 and 4 are factors of a number then 8 will also be factor of that number. Example: let's take the number 8 here 2,4 and 8 are factors of the number.
Please help me someone
Answer:
6/8
Step-by-step explanation:
1/8+1/4+3/8
1/8+2/8+3/8
What is the equation of the slant asymptote of the function?
f(x)=2x^3 + 5x^2 + x-5/x^2 +1
The equation of the slant asymptote of the function is y=2x³+5x²+1.
What is the slant asymptote?A slant asymptote, also known as an oblique asymptote, occurs when the degree of the numerator polynomial is greater than the degree of the denominator polynomial. The slant asymptote gives the linear function which is neither parallel to x-axis nor parallel to the y-axis.
The given function is f(x)=2x³+5x²+(x-5)/x² +1
Find the oblique asymptote using long polynomial division.
Vertical Asymptotes: x=0
No Horizontal Asymptotes
Oblique Asymptotes: y=2x³+5x²+1
Therefore, the equation of the slant asymptote of the function is y=2x³+5x²+1.
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Find the value of g(3) for the function below g(x)=39•(1/3)
A. 13/9
B.1/27
C.1,053
D.2,197
Answer: A
Step-by-step explanation: To solve any problem where we are given a function f(x) and asked to find f(n), we replace the number n will all Xs in the function.
For this problem g(x) = 39 * (1/3)^x and we are asked to find g(3). We plug in 3 for x in g(x) and get 39*(1/3)^3. Now we just simplify.
39*1/27, 39/27, 13/9
The value of g(3) for the function below g(x)=39•(1/3) is A. 13/9.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
We are given a function f(x) and asked to find f(n), we replace the number n will all Xs in the function.
For this problem [tex]g(x) = 39 (1/3)^x[/tex]
We need to find g(3).
We plug in 3 for x in g(x) and get [tex]39(1/3)^3[/tex].
Now we just simplify;
39 1/27, 39/27, 13/9
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How many groups of 1 2/3 are in 5/6?
In fraction 5 / 6 the number of the groups of 1²/₃ is only 1.
What is a fraction?The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.
A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given that there are two fractions 5/6 and 1²/₃. The group will be calculated as,
Fraction = 1²/₃ = 5 / 3
Fraction = 5 / 6 = ( 5 / 3 ) x ( 1 /2 )
Here in the above fraction of 5 / 6 there is only one 5 / 3 or 1²/₃.
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the scatter plot shows the number of hours Nisha works an d the numbers of pairs of ghungaroos she makes the equation y= 4.75x - 2.5 is a good line fit for the data. using the equation of the line how many hours will it take Nisha to make 64 pairs of ghungaroos
The hours that it would take Nisha to make the gungharoos is 301.5 hours
How to solve for the hoursThe equation of the line in the scatter plot is given as
y= 4.75x - 2.5
Where x is the number of ghungaroos that Nisha would make
We have to put in the value of x as 64 because the question tells us that She made a total of 64 gungharoos
Hence we would have:
y = 4.75 * 64 - 2.5
y = 304 - 2.5
y =301.5
The hours that it would take Nisha to make the gungharoos is 301.5 hours
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Divisibility rules for 2, 5, and 10
Answer: not sure if this is what you want but a number is divisible by 2 if it ends in 2, 4, 6, 8 or 0 a number is divisible by 5 if it ends in 5 or 0 a number is divisible by 10 if it ends in a 0
Step-by-step explanation:
.
In the accompanying diagram, isosceles trapezoid has bases DC and AB with measures of 6 meters
and 18 meters respectively. If altitude CE is drawn and AC has a measure of 14 meters, find the length
of altitude CE to the nearest meter.
The length of the isosceles trapezoid height CE is 14 meters.
How do you calculate the length?To find the length of the height CE of the isosceles trapezoid, we can use the Pythagorean theorem.
The isosceles trapezoid CE is the hypotenuse of the right triangle formed by height CE and distance AC. CE is also the height of the trapezoid. Let the length of CE be 'x'
The Pythagorean theorem states that the square of the length of the hypotenuse of a right triangle (CE) is equal to the sum of the squares of the lengths of the other two sides (AC and CE).
x² = AC² + CE²
We know that AC = 14 meters and CE = x.
So x² = 14² + x²
x² = 196 + x²
x² = x² + 196
0 = 196
x = √196 = 14
Therefore, the length of height CE is 14 meters.
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22. Represent Real-World Problems The railroad
tracks meet the road as shown. The town will
allow a parking lot at angle Jif the measure of
angle Jis greater than 38° Can a parking lot be
built at angle J? Why or why not?
If the town will permit a parking lot at angle J if the measure of angle Ji is greater than 38°, then yes, a parking lot can be erected at angle K.
what is angle ?In Euclidean geometry, an angle is a shape that is made up of two rays, known as the hood's sides, that meeting at a middle point known as the wall's apex. Two rays may combine to form an angle in the planes where they are positioned. When two planes collide, an angle is also created. They are referred to as dihedral angles. An angle in plane geometry is the possible configuration of two photons or lines that share a termination. The origin of the English term "angle" is the Latin word "angulus," which meaning "horn." The vertex is the point where the two rays, sometimes known as two sides of the angle, converge.
given
Find the measure of angle K
we know that
m <K = m < green ------> by vertical angles
so
-----> by complementary angles
solve for m<K
m<K > 38
therefore
If the town will permit a parking lot at angle J if the measure of angle Ji is greater than 38°, then yes, a parking lot can be erected at angle K.
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Is side lengths 4 8 9 obtuse right or acute
The side lengths given as 4 8 9 shows that it is an obtuse Triangle.
How to illustrate the triangle?It should be noted that to determine whether the triangle is acute, right, or obtuse, add the squares of the two smaller sides, and compare the sum to the square of the largest side. Since this sum is greater, the triangle is acute
In a situation if the sum of the squares of the two shorter sides of a triangle is smaller than the square of the longest side, the triangle is obtuse
This will be:
4² + 8² < 9²
16 + 64 < 81
80 < 81
It is obtuse.
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Meg's mom makes homemade salad dressing by mixing oil and vinegar in
a measuring cup. When the mixture settles, Meg can see how much
every ingredient was used. Look at the measuring cup and
determine how much oil and vinegar was used to
prepare the dressing.
vinegar
oil
NO LINKS!!
Finish the table below:
n t(n)
4 33
5 43
6 53
7
8
b. Name the type of sequence
c. Find an equation for the sequence
Answer:
a) See below.
b) Arithmetic sequence
[tex]\textsf{c)} \quad a_n=10n-7[/tex]
Step-by-step explanation:
Part (a)From inspection of the given table, t(n) increases by 10 each time n increases by 1.
Therefore:
[tex]\implies a_7=53+10=63[/tex]
[tex]\implies a_8=63+10=73[/tex]
Completed table:
[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&t(n) \\\cline{1-2} \vphantom{\dfrac12} 4& 33\\\cline{1-2} \vphantom{\dfrac12} 5& 43\\\cline{1-2} \vphantom{\dfrac12} 6&53 \\\cline{1-2} \vphantom{\dfrac12} 7&63\\\cline{1-2} \vphantom{\dfrac12} 8& 73\\\cline{1-2} \end{array}[/tex]
Part (b)As the given sequence has a constant difference of 10, it is an arithmetic sequence.
Part (c)[tex]\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a_n$ is the nth term. \\ \phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
The common difference is 10. Therefore:
d = 10To find the first term, a, substitute the value of d and one of the terms into the formula:
[tex]\begin{aligned}\implies a_4=a+(4-1)(10)&=33\\a+3(10)&=33\\a+30&=33\\&a=3\end{aligned}[/tex]
Therefore, to write an equation for the given arithmetic sequence, substitute the found values of a and d into the formula:
[tex]\implies a_n=3+(n-1)(10)[/tex]
[tex]\implies a_n=3+10n-10[/tex]
[tex]\implies a_n=10n-7[/tex]
120 + 18 1/4x = 180 –134x
The solution to the equation 120 + 18 1/4x = 180 –13/4x is x = 120/43
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
120 + 18 1/4x = 180 –134x
Express the equation properly
This gives
120 + 18 1/4x = 180 –13/4x
Collect the like terms in the above equation
So, we have the following representation
18 1/4x + 13/4x = 180 - 120
Evaluate the like terms in the above equation
So, we have the following representation
21 1/2 x = 60
Express as decimal
21.5x = 60
Divide both sides by 21.5
x = 60/21.5
Simplify the fraction
x = 120/43
Hence. the solution is x = 120/43
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Find the slope of the line that passes through (3, 14) and (7, 7).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
The slope of the given line that passes through (3, 14) and (7, 7) is m = - 7/4.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is a straight line that passes through points (3, 14) and (7, 7).
It is given that the line passes through (3, 14) and (7, 7). We can write the slope as -
m = (7 - 14)(7 - 3)
m = - 7/4
Therefore, the slope of the given line that passes through (3, 14) and (7, 7) is m = - 7/4.
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If ab = 3600 and b/a= 4/9, then determine the value of a
Answer:
90
Step-by-step explanation:
a times by b is equal to 3600 and b divided by a is equal to 4/9 which means that a must be a mulitiple of 4 and b must be a multiple of 9. An easy multiple of 4 and a easy mulitple of 9 that times together eqaul 3600 is 90 and 40. So therefore a= 90
When numbers are very small or very large, it is convenient to either express the value in scientific notation and/or by using a prefix with the unit.
A pain-relieving pill has a mass of 0.005 g
g
. Express the pill’s mass in grams using scientific notation or in milligrams.
The scientific notation of Pill's mass 5 × 10⁻³ g.
And, In milligrams, The pill's mass is 5.0 milligram.
What is Scientific notation?Scientific notation is a way of writing a very large or very small numbers. For example; 230,000,000 can be written in scientific notation as 2.3 x 10⁸.
Given that;
A pain-relieving pill has a mass of 0.005 g.
Now, We can write the mass in scientific notation as;
⇒ 0.005 g
⇒ 5 × 10⁻³ grams
And, We can write the pill's mass in milligram as;
Since, 1 g = 1000 milligram
Hence, We get;
⇒ 0.005 g = 0.005 × 1,000 milligrams
= 5.0 milligrams.
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80 points!!
Graph
y+4=25(x−3)
Answer: Attached
Step-by-step explanation:
Use the marginal tax rate chart to answer the question.
Tax Bracket Marginal Tax Rate
$0–$10,275 10%
$10,276–$41,175 12%
$41,176–$89,075 22%
$89,076–$170,050 24%
$170,051–$215,950 32%
$215,951–$539,900 35%
> $539,901 37%
Determine the effective tax rate for a taxable income of $175,000. Round the final answer to the nearest hundredth.
20.00%
20.74%
24.95%
32.00%
Answer:
To calculate the marginal tax rate on the investment, you'll need to figure out the additional tax on the new income. In this example, $500 will be taxed at 15% and $500 at 25%. This produces tax of $200, which on income of $1,000 makes the marginal tax from making that investment equal to $200 / $1,000 or 20%.
According to a recent survey of 37 million citizens in the United States, 5 million were planning to start a new degree program or continue their education in the next year.
According to this data, what is the probability that a random U.S. citizen you meet is not planning to start a new degree program or continue their education in the next year? (Round to four decimal places.)
The probability that a random U.S. citizen you meet is not planning to start a new degree program or continue their education in the next year is; 0.8649
How to solve probability of selection?Probability of selection defines the probability that a population unit is included in a sample generated by probability sampling.
It simply means that the probability of selection.
For example, at a school board meeting there are 9 parents and 5 teachers. Two teachers and 5 parents are female. If a person at the school board meeting is selected at random, we can use the concept of probability selection to find the probability that the person is a parent or a female.
Now, we are told that a recent survey of 37 million citizens in the United States, 5 million were planning to start a new degree program or continue their education in the next year. Thus, we can say that;
Total number of people in survey = 37 million
Number of people planning to start a new degree program or continue their education in the next year = 5 million
Thus;
P(People starting new program) = 5 million/37 million
= 5/37
Thus;
P(People NOT starting new program) = 37/37 - 5/37
= 32/37 = 0.8649
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Combine as indicated by the signs.
4/y^2-9 + 5/y+3
The combined expression for the given expression will be ( 5y -11 ) / ( y² - 9 ).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is ( 4 / y² - 9 ) + ( 5 / y + 3 ).
The expression will be solved as below,
E = ( 4 / y² - 9 ) + ( 5 / y + 3 ).
E = 4 / ( y +3 ) ( y - 3 ) + 5 / ( y + 3 )
E = 1 / ( y + 3 ) [ ( 4 / ( y- 3 ) + 5 ]
E = 1 / ( y +3 ) [ ( 4 + 5y - 15 ) / ( y - 3 ) ]
E = ( 5y - 11 ) / ( y² - 9 )
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What do you add to 5 5/8 to make 7 as an improper fraction?
Answer: We need to add 1 7/8 to 5 5/8 to make 7 as an improper fraction. ✅
PLEASEEEE GIVE BRANLIEST
Step-by-step explanation: To add 5 5/8 to a number to make 7 as an improper fraction, we need to convert 5 5/8 to an improper fraction.
To convert a mixed number to an improper fraction, we take the whole number, multiply it by the denominator of the fraction, and add the numerator. So, 5 5/8 becomes (5 x 8) + 5 / 8 = 40 + 5 / 8 = 45/8.
Now, we can add 45/8 and the number that we need to add to make 7 as an improper fraction.
45/8 + x = 7
To find x, we can subtract 45/8 from both sides of the equation:
x = 7 - 45/8
x = 1 7/8
So, we need to add 1 7/8 to 5 5/8 to make 7 as an improper fraction. ✅
A pair of fair dice is tossed. Find the probability ofgetting;
a.) a total of 8.
b.) at most a total of 5.
Please solve and show layout and explain work..thx
The probability of total of 8 is 0.1389, the probability of at most a total of 5 is 0.2778.
A pair of fair dice is tossed.
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.
Probability of event to happen
P(E) = Number of favourable outcomes [tex]/[/tex] Total Number of outcomes(a)) A total of 8 can be obtained with the following outcomes,
The sample space S contains n(S) = 36 elements when a pair of dice is tossed.
⇒{(2,6),(3,5),(4,4),(5,3),(6,2)} i.e. 5 outcomes.
⇒Required probability = [tex]\frac{5}{36}[/tex] = 0.1389
The probability of a total of 8 is 0.1389.
(b).
At most a total of 5 can be obtained with the following outcomes:
⇒{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(4,1)} i.e. 10 outcomes.
⇒Required probability =[tex]\frac{10}{36}[/tex] =0.2778
The probability of at most a total of 5 is 0.2778.
Therefore, the probability of total of 8 is 0.1389, the probability of at most a total of 5 is 0.2778.
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HELP PLS IMMEDIATELY
The correct option is A X[tex]\neq[/tex]-2,1,5
What is quadratic equation? A quadratic equation is a second-order polynomial equation in a single variable x ax2+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex Quadratic equations are intimately connected with problems about squares and quadrangles (another name for rectangles). In fact, the word quadratic is derived from the Latin word quadratus for square.A quadratic equation is the equation of the 2nd degree. This means that it comprises at least one (1) term that is squared. One of the standard formulas for solving quadratic equations is 'ax² + bx + c = 0' here a, b, and c are constants or numerical coefficients.In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0.To learn more about quadratic equation refers to:
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Ages
15-18
19-22
23-26
27-30
31-34
35-38
Number of students
9
8
4
8
6
8
Find the relative frequency for the class with lower class limit 27
Relative Frequency =
Give your au
%
Therefore , the solution of the given problem of relative frequency comes out to be 20% of student population is between the ages of 35 and 38.
Where can I find the relative frequency?To find it, multiply the ratio of the total number of pupils (2 + 2 + 8 + 2 + 10 + (6 = 30) by 100%, which equals the number of individuals with a lower limit of 35 (of whom there are 6).
Here,
Simply put, the relative frequency in this case is
20%: RF = (6/30)*100%
Consequently, 20% of student population is between the ages of 35 and 38.
Therefore , the solution of the given problem of relative frequency comes out to be 20% of student population is between the ages of 35 and 38.
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Someone please help me I need to pass this before 5 o clock
By the property of parallelograms that diagonals are equal in length and they bisect each other we have determined the values of x and y.
What is a parallelogram?A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
The area of a parallelogram is base multiples by height as two triangles form a parallelogram.
We know the diagonals of a parallelogram are equal and they bisect each other, From this property, we can write,
OA = OC.
x + 23 = 31.
x = 31 - 23.
x = 8 units.
XZ = 2(OX).
26 = 2(- 44 + x).
26 = - 88 + 2x.
2x = 114.
x = 57 units.
OL = OJ
8x - 56 = 24.
8x = 80.
x = 10.
OM = OK.
36 = 4y + 20.
4y = 16.
y = 4.
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Write an equation of the line that passes through (1,2) and is perpendicular to the line y=1/3x+4
The line that cuts through (1, 2) and is perpendicular to (y = 1/3x + 4) has the equation (y = -3x + 5).
What is the equation of the line?A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.
On the y-axis, this value c is referred to as the intercept.
Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.
y = 1/3x + 4 is the line that crosses (1,2) and is perpendicular to it.
To ascertain the equation of the line, utilize the procedures below:
Step 1: Two lines that are perpendicular to one another have the following slopes:
mm' = 1
Where the slopes of the lines are m and m'.
Step 2 - The line that is perpendicular to the line (y = 1/3x + 4) has the following slope:
1/3 * m' = -1
m' = -3
Step 3: The equation for a line passing through the points (1, 2) and having a slope of -3 is as follows:
(y - 2) = -(x - 1)
Implicate the equation above:
y = -3x + 5
Therefore, the line that cuts through (1, 2) and is perpendicular to (y = 1/3x + 4) has the equation (y = -3x + 5).
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In 2020 summer camp registration was $15 more than it was in 2021 in 2020 registration was $285 by what percentage did the summer camp registration decrease in 2021
Answer:
The 2021 summer camp registration was $285, so the percent decrease would be $15/$285, or 5.26%.
Pls mark me as brainliest ty :)
Drag figures and equations to the table to show the net and surface area.
The surface area of the figure is found by multiplying the area of each face together.
Drag figures and equationsThe table below shows the net and surface area of a three-dimensional figure:Net Area Surface Area
24 cm² 22 cm³
The net area of the figure is found by adding together the areas of each of the faces. In this case, there are two squares (2 cm x 3 cm) and one rectangle (3 cm x 1 cm).This gives us the equation 2(2 cm) (3 cm) +2(3 cm) (1 cm) + 2(2 cm) (1 cm), which works out to 24 cm².The surface area of the figure is found by multiplying the area of each face together. In this case, there are two squares (2 cm x 3 cm), one rectangle (3 cm x 1 cm), and one cube (3 cm x 1 cm).This gives us the equation 11 cm (2 cm) (3 cm) (3 cm) (1 cm) + (2 cm) (1 cm), which works out to 22 cm³.Net Area: 24 cm²
Surface Area: 22 cm³ + 11 cm = 33 cm³.
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Elena wants to make. scole drawing of her bedroom. Her
bedroom is a rectangle with length
decides on a scale of 1 to 50.
m and width 3 m. She
3.
Draw and label the dimensions of a scale drawing of Elena's
bedroom, using a scale of 1 to 50,
b. Elena's bedroom m door is 0.8 m wide. How wide should the
door be on the scale drawing? Explain how you know.
Elena's bed measures 4 cm by 3 cm on the scale drawing.
What are the actual measurements of her bed?
The scale drawing is thus 10 cm long and 6 cm wide, which corresponds to the actual dimensions of her bed.
what is rectangle ?A rectangle is a type of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral.4 sides, 4 corners, and 4 right angles make up the 2D shape of a rectangle. A rectangle's diagonal sides are equal in length, with one pair being longer than the other. A rectangle would be referred to as a square if all of its sides were the same size.
given
1 m equals 100 cm, to start.
Then
3 meters are equal to 300 centimeters, while 5 meters are equal to 500 centimeters.
If Elena wishes to sketch out her bedroom in scale (1 to 50), then
The scale drawing is thus 10 cm long and 6 cm wide.
The actual measurements of her bed are the scale drawing is thus 10 cm long and 6 cm wide.
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