Answer:
90 degrees is the amount of degrees in a right angle
4. (02.08 MC)
Let
f(x) = 2x²5x - 7
and
g(x) = x² - 2.
Find f(g(x)). Show each step of your work. (10 points)
Answer:
Step-by-step explanation:
[tex]f(x) = 2x^{2} + 5x - 7\\\\g(x) = x^{2} -2\\ \\f(g(x)) = 2(x^{2}-2) + 5(x^{2} -2) - 7\\ \\= 2x^{2} - 4 +5x^{2} -10 - 7\\= 2x^{2} + 5x^{2} -4-10-7\\\\\\f(g(x)) = 7x^{2} -21[/tex]
Find the equation of the line that is parallel to another line whose equation is x+2y+8=0 and passes though the point(-2,-3)
There is no line parallel to the line x + 2 · y + 8 = 0, as point (x, y) = (- 2, - 3) lies on the original line.
How to determine the equation of a line parallel to another line and that passes through a given point.
In this problem we need to determine the equation of line based on its slope relationship respect to another line and a given point. Two lines are parallel if and only if they have the same slope (m) and two distinct intercepts (b). First, transform the given equation of the line into slope-intercept form:
x + 2 · y + 8 = 0
2 · y = - x - 8
y = - (1 / 2) · x - 4
Then, the resulting line has a slope of - 1 / 2.
Second, determine the intercept of the resulting line:
y = m · x + b
b = y - m · x
b = - 3 - (- 1 / 2) · (- 2)
b = - 3 - 1
b = - 4
The intercept of the resulting line is - 4.
Third, transform the equation of the resulting line into standard form:
y = - (1 / 2) · x - 4
- 2 · y = x + 8
x + 2 · y + 8 = 0
There is no parallel line for the point (x, y) = (- 2, 3).
To learn more on parallel lines: https://brainly.com/question/2456036
#SPJ1
what's the answer to this amthswatxh qu
The equation of the line is y=3x+1 when the line is on the graph of the given picture.
Given that,
In the picture we have a graph.
We have to find the equation of the line.
We know that,
From the graph we can see the points,
(1,4) and (0,1)
We know that the equation of the line is y=mx +b
The y and x value are from the points and the m is the slope that is rise by run and b is the y intercept.
m is rise/run
m= 1-4/0-1
m=-3/-1
m=3
b is 4=3(1)+b
4=3+b
b=4-3
b=1
The equation of the line is y=3x+1
Therefore, The equation of the line is y=3x+1 when the line is on the graph of the given picture.
To learn more about equation visit: https://brainly.com/question/10413253
#SPJ9
r is a relation on the set of all nonnegative integers. (a,b) is in r if a and b have the same remainder when divided by 5
The relation accepts reflexive, symmetry, and transitive.
Recall that a relation R is reflexive if the element (x, x) belongs to R for all elements X in the domain of R.
If (x, y) belongs to R, then follows that (y, x) must likewise belong to R, making the situation symmetric.
And it is transitive if (x, y) and (y, z) belongs to R necessarily implies that (x, z) belongs to R.
Given r is a relation on the set of all nonnegative integers R(a,b)
Reflexive - YES. A given number a will always have the same remainder when divided by 5.
Symmetric - YES. If a and b have the same remainder when divided by 5, then b and a are the same pair, so again they will have the same remainder.
Transitive - YES. If a and b as well as b and c have the same remainder when divided by 5, this is possible if both a and c also have the same remainder when divided by 5.
Therefore the relation accepts reflexive, symmetry, and transitive.
To learn more about reflexive & symmetry visit
https://brainly.com/question/3014815
#SPJ4
The presense of a midpoint will result in what type of segments?
The presense of a midpoint will result in congruent segments.
What are congruent segments?Congruent segments are just equal-length line segments. Congruent means similar. Congruent line segments are typically represented by drawing the same number of little tic lines perpendicular to the segments in the middle of the segments.
A congruent line segment is any line segment with equal measure. Congruent line segments, for example, are the sides of an equilateral triangle since they all have the same length.
When we insert a midpoint to a line segment, it divides the line into two equal portions. Because equal segments are congruent, we can say that congruent segments are generated.
Learn more about segment on:
https://brainly.com/question/24434623
#SPJ1
The equation P = 6.31H + 41.5 can be used to predict the points earned P, buy a student on an organic chemistry final, based on the number of hours H, that he, or she studies. To earn 95 points on the final, how many hours does the model suggest someone should study?
The number of hours it is suggested to study is 8.5 hours using the concept of the equation.
What are equations?Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. LHS = RHS (left-hand side = right-hand side) appears in all mathematical equations. The value of an unknown variable, or unknown quantity, can be determined by solving equations.
Given,
The given linear equation P = 6.31H + 41.5, is used to predict the points earned P.
Also P = 95,
Now, we will find the value of H by using LHS=RHS
95 = 6.31H+41.5
Subtract 41.5 from both sides,
53.5 = 6.31H
Now, divide both sides by 6.31,
8.5 = H
Therefore, the number of hours it is suggested to study is 8.5 hours.
To know more about linear equations, visit:
https://brainly.com/question/24267899
#SPJ1
What is -68 as a quotient of integers?
-68 as a quotient of integers is -680/10.
The given integer is -68.
What is a quotient of integers?In arithmetic, a quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.
Here, -68/1
Multiply 10 to both the numerator and denominator, we get
= -680/10
= -68
Therefore, -68 as a quotient of integers is -680/10.
Learn more about the quotient here:
https://brainly.com/question/16134410.
#SPJ1
Hannah prepares 44 pies for the thanksgiving feast at her school. each pie is cut into 8 pieces. approximately how many students can hannah feed? round to the nearest ten.
Answer:352
Step-by-step explanation:
rationalise the denominator of \frac{26}{4+\sqrt{3}}
The rationalization of the denominator of the given fraction gives 8 -2√3
Rationalizing the denominatorFrom the question, we are to rationalize the denominator of the given fraction
The given fraction is
26 / (4+√3)
To rationalize the given expression, we will multiply both the numerator and the denominator of the fraction by the conjugate of the denominator.
The denominator is 4+√3
Thus,
The conjugate of the denominator is 4-√3
Now, multiply the numerator and the denominator by the conjugate.
That is,
(26 × (4-√3)) / ((4+√3) × (4-√3))
(104 - 26√3) / (16 - 3)
(104 - 26√3) / 13
= 104/13 - (26√3)/13
= 8 - 2√3
Hence,
The result of rationalizing is 8 -2√3
Learn more on Rationalizing the denominator here: https://brainly.com/question/25222850
#SPJ1
Solve each system by substitution.
4x + y = 19
6x + 7y=1
Step-by-step explanation:
that simply means we use one equation to express one variable by the other, and then we use that identity in the second equation (substituting one variable by the expression of the other variable. and then we solve for that remaining variable.
finally we use one of the original equations to solve for the second variable.
4x + y = 19
so, that gives us
y = 19 - 4x
we use that now in the second equation :
6x + 7(19 - 4x) = 1
6x + 133 - 28x = 1
-22x + 133 = 1
-22x = -132
22x = 132
x = 6
now, let's use e.g.
4x + y = 19
4×6 + y = 19
24 + y = 19
y = -5
ABCD, BEG and CEF are straight lines. Find a and b
Answer:A=72
B=108
Step-by-step explanation:
The solution is, angle a = 72 & b = 108
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
given that,
from the given figure we get,
∠ABC = 180
∠BCD = 180
so, we have,
∠ABC + ∠BCD = 180 + 180
ABE + EBC + a + b = 360
again, we know that,
EBC + a = 180 - 38 = 142
[we know, from property of triangle's angle]
now, we get,
ABE + 142 + b = 360
or, 110 + 142 + b = 360
or, b = 108
so, we get,
a = 180 - 108 = 72
Hence, The solution is, angle a = 72 & b = 108.
To learn more on angle click:
brainly.com/question/28451077
#SPJ2
Two integers, a and b, have different signs. They absolute value of integer a is divisible by the absolute value of integer b. Find two integers that fit this description. Then decide if she product of the integers is greater than or less than the quotient of the integers. Show your work.
Answer:
Step-by-step explanation:
One example is a=-6 and b=3
-6/3=-2
-6*3=-18
-2 is greater than -18; the quotient is greater than the product in this case.
Another example is a=6 and b=3
6/3=2
6*3=18
2 is smaller than 18; the quotient is smaller than the product in this case.
Someone has the answer?
Find the value of x so that the function has the given value. j(x) = 3-x;j(x) = -5
The input value x in the function j(x) = 3-x as j(x) equals -5 is 8.
What is the value of x in the given function?A function is simply a relationship that maps one input to one output.
Given the function in the question;
j( x ) = 3 - xj( x ) = -5x = ?To determine the value x or input value, equate the function to -5 and solve for x.
j( x ) = 3 - x
j( x ) = -5
-5 = 3 - x
Add 5 to both sides
-5 + 5 = 3 + 5 - x
0 = 8 - x
Add x to both sides
0 + x = 8 - x + x
x = 8 - x + x
x = 8
Therefore, the value of x is 8.
Learn more about functions here: brainly.com/question/2541698
#SPJ1
You multiply two integers and the product is -18. List 4 possible pairs of integers
The possible pairs of integers that has product -18 is: (9, -2), (18, -1), (6, -3), (3, -6), (2, -9)
We need to find the four possible pairs of integers that has product -18
Let x and y be two required integers.
Since the product is negative, one of the integer must be negative integer.
x y x*y
9 -2 -18
2 -9 -18
18 -1 -18
-1 18 -18
6 -3 -18
3 -6 -18
Therefore, the possible pairs of integers that has product -18 is: (9, -2), (18, -1), (6, -3), (3, -6), (2, -9)
Learn more about product here:
https://brainly.com/question/16941498
#SPJ9
WORTH 100 POINTS
Write [tex]\frac{3}{2}[/tex] As a Tape Diagram
Answer:
Step-by-step explanation:
Dibuja una diagrama de cinta dividido en 3 y pinta 2 de los espacios
De nada :>
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The Maximum and Minimum values of x is = (3,30)
The maximum of a quadratic function occurs at
x = − b/2a
If a is negative, the maximum value of the function is
f ( − b/2a).
f max x =ax^2+bx+c occurs at
x = −b/2a
Finding the value of
x = −b/2a
Substitute in the values of a and b.
x = − 18/2(3)
Simplify
x = -3
Replace the variable x with -3 in the expression
f (-3) = -3(-3)^2+18(-3)+3
f(-3) = - 27 +54 +3
f(-3) = -30
f(3) = 30
The maximum of -3x^2+18x+3 = (3,30)
Learn more about the maximum value here :
https://brainly.com/question/14316282
#SPJ1
Rotate the yellow dot to a location of two pi radians. After you rotate the angle, determine the value of cos 2pi, to the nearest hundredth.
Answer:
Step-by-step explanation:
the student council at a local college has 8 seniors, 7 juniors, 5 sophomores and 3 freshmen. if 3 of them are randomly chosen to be on a committee, what is the probability that none of them are seniors?
The probability is 0.6 that if randomly choosen none of them are senior.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin. The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half .acc to our question-
total people in council= 23The number of committees that have no seniors: In this case, we have to select 5 people from a group of 1+3+4=8 people. This can be done in 8C5 ways.The number of committees that have no seniors: In this case, we have to select 5 people from a group of 1+3+4=8 people. This can be done in 8C5 ways.Hence,the probability is 0.6 that if randomly choosen none of them are senior.
learn more about probability click here:
https://brainly.com/question/13604758
#SPJ4
Eric's city took a telephone poll about a plan to build a new hotel downtown. 200 people took
the poll. 25% of them were in favor of the new hotel. How many people were in favor of the
new hotel?
Answer:
50 people
Step-by-step explanation:
Solution
25% as a fraction is 25/100 which reduces down to 1/4. What this tells you is that 1/4 of the people asked want the hotel
1/4 * 200 = 50
50 people want the hotel.
What is the image of (1, 0) after a counterclockwise rotation of 60°?
Answer: I'm pretty sure this is the same question. https://brainly.com/question/16428516
A real estate company balances the books for its business on the first day of each month. It hopes to sell houses
every other day of the month. The average number of houses, S, the company sells each day, t, is represented by the inverse of the function S^-1 = t^2+4t-12/t^2-9t+14
-
Which equation represents the average sales each day for the real estate company?
The inverse function is given as s⁻¹ = [tex]\frac{t^2+4t-12}{t^2-9t+14}[/tex] and the equation represents the average sales each day for the real estate company would be [tex]s^{-1}=\frac{t+6}{t-7}[/tex].
What is an equivalent expression?
The equivalent is the expression that is in different forms but is equal to the same value.
A real estate company balances the books for its business on the first day of each month.
It hopes to sell houses every other day of the month.
The average number of houses, S, the company sells each day, t is represented by the inverse of the function given below.
[tex]s^{-1}=\frac{t^2+4t-12}{t^2-9t+14}[/tex]
Then the inverse function can be written as
[tex]s^{-1}=\frac{t^2+4t-12}{t^2-9t+14}\\\\s^{-1}=\frac{t^2+6t-2t-12}{t^2-7t-2t+14}\\\\s^{-1}=\frac{(t+6)(t-2)}{(t-7)(t-2)}\\\\s^{-1}=\frac{t+6}{t-7}[/tex]
To learn more about the equivalent equations, visit:
brainly.com/question/889935
#SPJ1
Answer:
C. [tex]S=\frac{7t+6}{t-1}[/tex]
Step-by-step explanation:
I got it right on the exam.
First, take the equation and inverse it, replace and t with y and the y with t
[tex]y=\frac{t^{2}+4t-12}{t^{2}-9t+14} \\\\t=\frac{y^{2} +4y-12}{y^{2}-9y+14}[/tex]
Then, factor both the top and bottom
[tex]t=\frac{(y+6)(y-2)}{(y-7)(y-2)}[/tex]
You see that there is a duplicate of the (y-2) in the numerator and denominator, so they cancel out,
[tex]t=\frac{(y+6)}{(y-7)}[/tex]
Now you can start getting the y alone to make an equation,
[tex]t(y-7)=\frac{(y+6)}{(y-7)} (y-7)\\t(y-7)=(y+6)[/tex]
[tex]ty-7t=y+6\\ty-7t-y+7t=y+6-y+7t\\ty-y=7t-6\\y(t-1)=7t-6\\\frac{y(t-1)}{(t-1)} =\frac{7t-6}{t-1} \\y=\frac{7t-6}{t-1}[/tex]
PLEASE HELP
In November's Math Meet, the Little Monsters of Beast Academy solved $\frac{1}{5}$ of the problems. In March's Math Meet, they solved $\frac23$ of the problems. (There might be different numbers of problems asked in November and March.)
In total, the Little Monsters solved $13$ of $30$ problems over both Math Meets. How many problems were asked at March's Math Meet?
The number problems solved by the little Monsters of Beast Academy in March's meet is 15.
How to determine the number of problems solved in March meetThe problem is a simultaneous equation of two unknowns with two equations.
The equations are formed as follows
let the number of questions solved by little Monsters of Beast Academy in
March's meet be xNovember's meet be yIn November's Math Meet, the Little Monsters of Beast Academy solved $\frac{1}{5}$ of the problems = y/5
In March's Math Meet, they solved $\frac23$ of the problems = 2x/3
Hence:
y/5 + 2x/3 = 12
x + y = 30
solving the equation gives
x = y = 15
Learn more on simultaneous equation here:
https://brainly.com/question/15165519
#SPJ1
How do you find the x for both of these problems?
Considering the figure the required angle is solved using the vertical angle theorem. The values are
14. 42 degrees and 16. 20 degreesHow to determine the required angleThe problem is solved considering this theorems
vertical angle theorem
According to this theorem, when two straight lines cross, they create two sets of linear pairs and the vertical opposite angles are equal.
solution for the missing angle
x + 70 + 60 = 180 sum of angles of a triangle
x = 50
Using vertical angle theorem
? + 88 + 50 = 180 sum of angles of a triangle
? = 180 - 88 - 50
? = 42
solution for the missing angle
x + 75 + 30 = 180 sum of angles of a triangle
x = 75
Using vertical angle theorem
? + 88 + 75 = 180 sum of angles of a triangle
? = 180 - 85 - 75
? = 20
Learn more on angles here:
https://brainly.com/question/29322749
#SPJ1
Rewrite in simplest terms: -5(-6k-6)-(-9k-10)−5(−6k−6)−(−9k−10)
help please n ty
The value of the expression -5(-6k-6)-(-9k-10) in simplest terms is 39k + 40
What is an algebraic expression?An algebraic expression can be described as an expression that is made up of terms, variables, coefficients, factors and constants.
These expressions are also known to be composed of certain mathematical operations, such as;
SubtractionDivisionMultiplicationBracketAdditionParenthesesWe have the expression;
-5(-6k-6)-(-9k-10)
expand the bracket
-5(-6k - 6) + 9k + 10
collect like terms
30k + 30 + 9k + 10
Add the like terms
39k + 40
Hence, the value is 39k + 40
Learn more about algebraic expressions here:
https://brainly.com/question/4344214
#SPJ1
on average dog bite victims arrive at carver memorial hospital at a rate of 2 victims per day. which probability distribution is most nearly appropriate to describe the number of dog bite victims who arrive at this hospital on a given day?
The "Poisson distribution" is the probability distribution that comes the closest to accurately describing that many dog bite patients visit this hospital across any given day.
Describe the term Poisson distribution?A discontinuous probability distribution is a Poisson distribution. It provides the likelihood that a response will occur a specific number of times (k) over a specific duration or area. The mean number of occurrences, designated by the letter "lambda," is the single parameter of the Poisson distribution.The chance of a discrete (i.e., countable) result is provided by a Poisson distribution, that is an discrete probability distribution.The discrete result for Poisson distributions is k, that also stands for the frequency of an event.For the given data of,
An average of two dog bite victims show up at Carver Memorial Hospital each day.
A probability distribution that most accurately predicts the number of dog bite victims who visit this hospital on any given day is characterized as the "Poisson distribution."
To know more about the Poisson distribution, here
https://brainly.com/question/9123296
#SPJ4
3X + 4X - 2 = 12
Please help again I’m not very smart lol
[tex]{ \pink{ \boxed{ \blue{ \sf{x = 2}}}}}[/tex]
Step-by-step explanation:
[tex]{ \red{ \sf{3x + 4x - 2 = 12}}}[/tex]
[tex]{ \red{ \sf{7x = 12 + 2}}}[/tex]
[tex]{ \red{ \sf{7x = 14}}}[/tex]
[tex]{ \red{ \sf{x = \frac{14}{7}}}} [/tex]
[tex]{ \blue{ \boxed{ \green{ \sf{x = 2}}}}}[/tex]
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
The equation of the parabola
f(x) = [tex]7x^2[/tex]
The standard vertex form of a parabola is
y = [tex]a(x-h)^2[/tex] + k
The coordinates of the vertex of a parabola = (3, 5)
Where (h, k) is the coordinates
From the given function of the parabola f(x) = [tex]7x^2[/tex]
The value of a = 7
Substitute the values in the vertex form of a parabola
y = [tex]7(x-3)^2[/tex] + 5
Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
Learn more about vertex here
brainly.com/question/29354520
#SPJ1
The tables represent two linear functions in a system. A 2 column table with 5 rows. The first column, x, has the entries, negative 4, negative 2, 0, 2. The second column, y, has the entries, 26, 18, 10, 2. A 2 column table with 5 rows. The first column, x, has the entries, negative 4, negative 2, 0, 2. The second column, y, has the entries, 14, 8, 2, negative 4. What is the solution to this system? (1, 0) (1, 6) (8, 26) (8, –22) Mark this and return
From the given table which represents the two system of linear function is given by y = -4x +10 and y = -3x +2 , the solution of the system of linear function is (x, y) = (8 , -22).
As given in the question,
Table which represents the system of linear function are as follow:
table 1:
x: -4 -2 0 2
y: 26 18 10 2
table 2:
x: -4 -2 0 2
y: 14 8 2 -4
For table1 :
System of linear function:
(x₁ , y₁) = (0,10)
(x₂ , y₂) = (2, 2)
Equation of linear function:
(y -y₁)/ (x-x₁) =(y₂ -y₁)/(x₂ -x₁)
⇒(y -10)/ (x-0) =(2-10)/(2-0)
⇒y-10 =-4(x)
⇒ y = -4x +10 __(1)
For table2 :
System of linear function:
(x₁ , y₁) = (0,2)
(x₂ , y₂) = (2, -4)
Equation of linear function:
(y -y₁)/ (x-x₁) =(y₂ -y₁)/(x₂ -x₁)
⇒(y -2)/ (x-0) =(-4-2)/(2-0)
⇒y-2 =-3(x)
⇒ y = -3x +2 __(2)
Solve system of linear function (1) and (2) we get,
-4x +10 = -3x +2
⇒4x -3x =10 -2
⇒x =8
⇒y = -4(8) +10
= -22
(x, y) = (8 ,-22)
Therefore, from the given table which represents the two system of linear function is given by y = -4x +10 and y = -3x +2 , the solution of the system of linear function is (x, y) = (8 , -22).
Learn more about linear function here
brainly.com/question/21107621
#SPJ1
Answer:
D
Step-by-step explanation:
trust
Which answer is correct?
(A) y = 3x − 2
y = 2x + 5
(B) y = −3x + 2
y = 2x − 5
(C) y = −3x − 2
y = −2x − 5
(D)y = 3x + 2
y = −2x + 5
Step-by-step explanation:
the slow of a line is the factor of x in a "y = ..." firm of equation.
the line going through (1, 5) has a slope of 3 (when x increases by +1, then y increases by +3, so the slope y/x = 3).
(B) and (C) are out, because there is no line with slope 3 (only -3).
the line going through (-2, 9) has a slope of -2 (when x increases by 1, y decreases by 2, so the slope y/x = -2/1 = -2).
(A) is out, as there is no line with the slope -2 (only +2).
so, (D) is the correct answer.
from a group of 12 students, we want to select a random sample of 5 students to serve on a university committee. how many combinations of random samples of 5 students can be selected?
The number of combinations of random samples of 5 students can be 792.
Given, 12 groups of students
We have to select random samples of 5 students,
Here we will use the combination formula,
Cₙ,ₓ = n! / x! (n - x)!
Here n=12 and x=5
Cₙ,ₓ = 12! / 5! (7!)
Cₙ,ₓ = 479,001,600 / (120) × (5040)
Cₙ,ₓ = 792
Therefore the possible ways of selecting the random samples of 5 students are 792.
To learn more about permutations and combinations
https://brainly.com/question/13387529
#SPJ4