[tex](g\circ f)(x)=(2x-1)^2-2=4x^2-4x+1-2=4x^2-4x-1[/tex]
Answer:
[tex]4x^2 -4x -1[/tex]
Step-by-step explanation:
Given functions,
[tex]f(x) = 2x - 1-----(1)[/tex]
[tex]g(x) = x^2 -2-----(2)[/tex]
∵ (gof)(x) = g[f(x)] ( Composition of functions )
[tex]\implies (gof)(x) = g(2x-1)[/tex] ( From equation (1) )
[tex]=(2x-1)^2 - 2[/tex] ( From equation (2) )
[tex]=4x^2 + 1 - 4x - 2[/tex]
[tex]=4x^2 -4x -1[/tex]
A map has a scale of 3.5 inches = 20 kilometers. If the distance between two cities on the map is 4.9 inches, what is the actual distance between the two cities?
Answer:
28 i think.
Step-by-step explanation:
Answer:
The actual distance between the two cities is 28 kilometers
Step-by-step explanation:
A map has a scale of 3.5 inches = 20 kilometers
Distance between two cities on the map = 4.9 inches
We can use the unitary method in this question to get the actual distance between two cities
∵ 3.5 inches on the map = 20 kilometers
∴ 1 inch distance on the map = [tex]\frac{20}{3.5}[/tex] kilometers
∴ 4.9 inches on the map = [tex]\frac{20}{3.5}\times 4.9[/tex]
= 28 kilometers
Therefore, the actual distance between the two cities is 28 kilometers.
What values are excluded from the domain and range of the function f(x)= x+3/2x+5?
Answer:
B. Domain: -5/2
Range: 1/2
Step-by-step explanation:
If you plug -5/2 for x, it becomes no solution due to the zero in the denominator.
If you plug 1/2 for y and let your calculator do its thing, it becomes no solution.
Because these values cannot be solved for in the equation, they are excluded from the domain and range.
Edit: I got it correct on the Unit Review on edge.
The domain and range values that are excluded from the function given as f ( x ) = ( x + 3 ) / ( 2x + 5 ) are x = -5/2 and y = 0
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
The function f(x) = (x + 3)/(2x + 5) has certain values that are excluded from its domain and range.
The function f(x) is defined for all real numbers except for the values of x that make the denominator (2x + 5) equal to zero.
Therefore, the values of x that are excluded from the domain of f(x) are those that satisfy the equation 2x + 5 = 0.
2x + 5 = 0
2x = -5
x = -5/2
The range of f(x) is all real numbers except for zero (0), because it is never equal to zero.
Hence , the values excluded from the domain of f(x) are x = -5/2 and the values excluded from the range of f(x) are y = 0
To learn more about domain and range click :
https://brainly.com/question/28135761
#SPJ7
What is the length of AC? Round to the nearest tenth.
Answer:
AC ≈ 10.5 cm (1 dec. place )
Step-by-step explanation:
Given
tan55° = [tex]\frac{15}{b}[/tex]
Multiply both sides by b
b × tan55° = 15 ( divide both sides by tan55° )
AC = b = [tex]\frac{15}{tan55}[/tex] ≈ 10.5 cm
Which expression is equivalent to -2 1/4÷ (-2/3)
Answer:
[tex]-2\dfrac{1}{4}\div\left(-\dfrac{2}{3}\right)=\dfrac{27}{8}=3\dfrac{3}{8}}[/tex]
Step-by-step explanation:
[tex]-2\dfrac{1}{4}\div\left(-\dfrac{2}{3}\right)\qquad\text{the quotient of two negative numbers is positive}\\\\=2\dfrac{1}{4}\div\dfrac{2}{3}\qquad\text{convert the mixed number to the improper fraction}\\\\=\dfrac{2\cdot4+1}{4}\div\dfrac{2}{3}=\dfrac{9}{4}\div\dfrac{2}{3}\\\\\text{dividing by a fraction is the same as multiplying by its reciprocal.}\\\\=\dfrac{9}{4}\cdot\dfrac{3}{2}=\dfrac{9\cdot3}{4\cdot2}=\dfrac{27}{8}\qquad\text{convert to the mixed number}\\\\=3\dfrac{3}{8}[/tex]
What is the value of x?
Two intersection lines. Angle formed at the top is labeled 2 x plus 2 degrees. Angle formed at the bottom is labeled 3 x minus 52 degrees.
Answer:
54 is x
Step-by-step explanation:
Sounds like you describing vertical angles. Vertical angles are congruent so that means 2x+2=3x-52
2=1x-52. Subtracted 2x on both sides
54=1x. Added 52 on both sides
54=x. Since 1 times x is x
Which of the following shows a number in a fraction form? A. 3/7 B.3 C.1/2 D.3.7
A. and C. are fractions. this is because they are only proportions of a whole unless they are a mixed number. but in this case, these numbers do not go over 1 (a whole).
Answer: Option A and Option C
[tex]\frac{3}{7}[/tex] and [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The numbers in the form of fraction have the following form:
[tex]\frac{b}{c}[/tex]
Where b is known as numerator and c is known as denominator.
To know which of the numbers shown has a fraction form, identify all those with the form [tex]\frac{b}{c}[/tex]
Then you can see that the answer is option A and option C
[tex]\frac{3}{7}[/tex] and [tex]\frac{1}{2}[/tex]
jillian calculates that see will take 95 minutes to run 7 miles. she runs the distance in 80 minutes. what is jillians percent error.
Answer:
15.79%
Step-by-step explanation:
do 95-80 which is 15
then do 15/95 as a fraction then multiply that number by 100 to get 15 15/19 then turn that into a decimal and you get 15.79%
Jillian's percent error in estimating the time it would take her to run 7 miles is 15.79%.
Jillian's percent error in her run can be calculated by taking the absolute value of the difference between her estimated time and actual time, divided by the estimated time, and then multiplied by 100 to get the percentage. Here is the calculation step-by-step:
Calculate the absolute difference between estimated time and actual time: |95 minutes - 80 minutes| = 15 minutes.Divide the difference by the estimated time: 15 minutes / 95 minutes = 0.1579.Multiply by 100 to convert to a percentage: 0.1579 times 100 = 15.79%.Therefore, Jillian's percent error in her estimation is 15.79%.
Given the coordinates of the vertices of a pre-image figure, describe how to find the coordinates of the image vertices if the figure is translated vertically.
Step-by-step answer:
Step 1:
find out the amount and direction of the vertical translation.
+3 means translating 3 units up, and -6 means translating 6 units down.
Step 2:
to each of the coordinate pairs, add the value of the translation to the y-coordinate (i.e. the second number of the pair).
For example, if the translation is +3, and if one of the vertices is (4,1), then the image of the vertex is (4,1+3) = (4,4).
Repeat for the rest of the vertices.
Step 3:
Check by graphing both image and preimage to see if the shapes are identical. If not, look for a mistake in the translation process.
To translate a figure vertically, add the translation value to the y-coordinates of each vertex. For a translation of 'k' units, the new vertices will be (x, y + k). This keeps the shape the same and only changes its position vertically.
To find the coordinates of the image vertices when a figure is translated vertically,
you need to follow these simple steps:
Identify the translation value: Determine the distance by which the figure is to be translated vertically. Let's say the translation value is 'k' units.Add the translation value to the y-coordinates: For each vertex of the pre-image figure, a translation involves modifying only the y-coordinate.If the original vertices of the pre-image are (x, y), then the new vertices (image) will be (x, y + k).Suppose you have a triangle with vertices A(2,3), B(5,4), and C(1,7). If the figure is translated vertically by 3 units up, the coordinates of the image vertices will be:This method ensures that the shape of the figure remains unchanged and it is only shifted up or down vertically.
Solve for x: y = x + 4
That's too easy...
[tex]y=x+4\\x=y-4[/tex]
A family membership at a tennis club cost a flat fee of $150, plus $25 per person. If n stands for the number of people, then the membership cost is modeled by ?
Answer:
total cost = 150 + 25n
Step-by-step explanation:
total cost = flat fee + cost per person* number of people
total cost = 150 + 25n
one hundred fifty-six thousandths in decimals Can u please answer this ASAP I will give you 20 points
Here it is: 0.156
That is the decimal representation of 156/1000
.156.
If they are “thousandths” then you know there is 3 decimal places.
Hope this helps!
what is 6 times the quantity x plus 4?
Answer: 6x + 4
6x represents 6 times the quantity x.
+ 4 represents plus 4.
Put 6x and + 4 together to get 6x + 4.
An angle measuring pi/8 radians is equal to which of the angle measures given
below? Round your answer to 2 decimal places after each conversion step.
Check all that apply.
A. 22.50
B. 39.25
c. 22°5
D. 22°30
Answer:
A. 22.5° AND D. 22°30’
Step-by-step explanation:
First of all, it's the correct answer on ap*x
To convert π/8 to degrees, replace π with 180°.
π/8 = 180°/8 = 22.5° (A)
Convert 22.5° to degrees minutes seconds
22.5° = 22°30’ (D)
To convert an angle from radians to degrees, multiply by 180/π. The angle measuring π/8 radians is equal to 22.5°.
Explanation:To convert an angle from radians to degrees, we use the conversion factor 180/π. So, an angle of π/8 radians is equal to:
π/8 * 180/π = 22.5°π/8 * 180/π = 22.5°π/8 * 180/π = 22.5°π/8 * 180/π = 22.5°π/8 * 180/π = 22.5°π/8 * 180/π = 22.5°Therefore, the angle measuring π/8 radians is equal to 22.5°.
Learn more about Angle Conversion here:https://brainly.com/question/29689160
#SPJ2
The mass of a marine organism, in pounds, p years after it is born is given by the polynomial function R(p)=−4p2+300p. Find the mass when p=20 years .
Answer:
R(p) = -4p^2 + 300p when p=20.
R(p) = -4(20)^2 + 300(20)
R(p) = -1600 + 6000
R(p) = 4400
The mass when p=20 years is 4400.
A scientist cools some water at a constant rate. the graph and table show how the temperature of the water changes with time.
CAN SOMEONE ANSWER THIS. ?
Answer:
C
Step-by-step explanation:
The easiest way to determine this is to realize that time is the independent variable (n) and temperature is the dependent variable (a).
From the table, we can plug in the two points (n) into n of each equation and see if that equals the temperature values (a).
A little thinking would get us to plug the numbers in C first.
[tex]a(n)=46-(n-1)*4\\46-(5-1)*4=30[/tex]
Works!!
Now, second number:
[tex]a(n)=46-(n-1)*4\\46-(6-1)*4=26[/tex]
Works!!
Hence, C is the correct answer.
Answer:
[tex]a(n)=46-(n-1) \times 4[/tex]
Step-by-step explanation:
It's important to know that the graph is showing a linear function, which means its equation cannot be exponential. So, choices A and B are not correct here.
To find the correct equation, we could find the slope first with the following formula and the two given points
[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\ m=\frac{26-30}{6-5}=4[/tex]
Now, we use the point-slope formula to find the equation
[tex]y-y_{1} =m(x-x_{1} )\\y-30=4(x-5)\\y=4x-20+30\\y=4x+10[/tex]
Notice that choice C has the same coefficient of 4, which is the slope of the line. Therefore, that's the right answer.
Let's prove it for [tex]n=6[/tex]
[tex]a(n)=46-(n-1) \times 4\\a(6)=46-(6-1) \times 4=46-20=26[/tex]
As the table shows.
Therefore, choice C is correct.
NEED URGENT HELP!!!!!!!!)
A bag has 7 blue marbles, 3 red, 2 green, and 8 white. You pick a marble, record its color, and return it. If you repeat this process 150 times, how many times can you expect to pick a blue or red marble? Write your answer as a percent!
Answer:
50%
Step-by-step explanation:
The total number of marbles is 7 + 3 + 2 + 8 = 20
Blue or red means that the total on any one draw is 7 + 3 = 10
You would expect to draw blue or red 1/2 the time.
Out of 150 throws, you would get 1/2 * 150 which is 75 but that is not what you are asked.
% = (1/2 ) * 100 = 50% of the time
multiply the polynomial (2x^2+5x+5)(4x-3)
So I simplify the expression and it is..
8x^3 + 14x^2 + 5x − 15
____
I hope this helps, as always. I wish you the best of luck and have a nice day, friend..
Find the equation of the line that passes through the pair of points.
(1,5), (1, - 3)
Answer:
x = 1Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (1, 5) and (1, -3).
Substitute:
[tex]m=\dfrav{-3-5}{1-1}=\dfrac{-8}{0}\ \bold{!}[/tex]
Dividing by zero is not possible.
The slope does not exist.
Conclusion: this is a vertical line with the equation x = a
From the points
(1, 5) → x = 1, y = 5
(1, -3) → x = 1, y = -3
we have the equation x = 1.
Sam and Erica are playing a board game. They spin a pointer to determine whether to move forward or back. They call a number cube to determine how many spaces to play. What is the probability of moving forward an even number of spaces?
Answer:
Answer is 1/4.
Step-by-step explanation:
The sample space of an event is the list of all possible outcomes.
Let F represent moving forward and B represent moving backward.
This makes the sample space for the game
F1, F2, F3, F4, F5, F6
B1, B2, B3, B4, B5, B6
There are 6 ways to move forward; only 3 of these are even numbers.
This is 3 ways out of 12 possible moves.This makes the probability
3/12.
3/12=1/4
Thus the probability of moving forward an even number of spaces
is 1/4....
Answer:the answer is 1/4
Step-by-step explanation:
Desmond wants to sell his car that he paid $8,000 for 2 years ago. The car depreciated, or decreased in value, at a constant rate each month over a 2-year period. If x represents the monthly depreciation amount, which expression shows how much Desmond can sell his car for today?
8,000 + 24x
8,000 − 24x
8,000 + 2x
8,000 − 2x
Answer:
8,000-24x
Step-by-step explanation:
there's 24 months in 2 years. If it's value decreased from 8,000 at a constant rate over a 2 year period, the equation would be 8,000-24x
Answer:
B. [tex]8,000-24x[/tex].
Step-by-step explanation:
We have been given that Desmond wants to sell his car that he paid $8,000 for 2 years ago. The car depreciated, or decreased in value, at a constant rate each month over a 2-year period.
Since the value of car depreciates at a constant rate each month, so the value of car depreciated in 2 years would be [tex]2\times 12=24[/tex].
There are 24 months in two years, so value of car depreciated in 2 years would be 24x.
The initial value of car is $8,000, so value of car after 2 years would be [tex]8,000-24x[/tex].
Therefore, option B is the correct choice.
Simplify the expression.
(a^3/2)^3
The simplified expression is [tex]\(\frac{a^9}{8}\)[/tex].
To simplify the expression [tex]\((a^3/2)^3\)[/tex], follow these steps:
1. Apply the power of a power rule, which states that [tex]\((x^m)^n = x^{m \times n}\)[/tex]. In this case, [tex]\(x = a^3/2\)[/tex], [tex]\(m = 1\)[/tex], and [tex]\(n = 3\)[/tex].
2. Distribute the exponent over the numerator and the denominator:
[tex]\((a^3/2)^3 = (a^3)^3 / (2)^3\)[/tex].
3. Apply the power of a power rule to [tex]\((a^3)^3\)[/tex]:
[tex]\((a^3)^3 = a^{3 \times 3} = a^9\)[/tex].
4. Apply the power of a power rule to [tex]\(2^3\)[/tex]:
[tex]\(2^3 = 8\)[/tex].
5. Combine the results to get the simplified expression:
[tex]\(\frac{a^9}{8}\)[/tex].
Therefore, the expression [tex]\((a^3/2)^3\)[/tex] simplifies to [tex]\(\frac{a^9}{8}\)[/tex].
Which is the graph of y – 3 =-2/3 (x + 6)?
Answer:
First graphStep-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point on a line
We have the equation:
[tex]y-3=-\dfrac{2}{3}(x+6)\\\\y-3=-\dfrac{2}{3}(x-(-6))[/tex]
the coordinates of the point is (-6, 3).
Only on the first graph the line passes through the point (-6, 3).
Answer:
A
Step-by-step explanation:
I WILL GIVE BRAINLIEST What is the value of x?
Answer:
A 30
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
100 = 70+x
Subtract 70 from each side
100-70 = 70-70 +x
30 =x
y ≥-1/3 x + 2
y < 2x + 3
(2, 2), (3, 1), (4, 2)
(2, 2), (3, –1), (4, 1)
(2, 2), (1, –2), (0, 2)
(2, 2), (1, 2), (2, 0)
Answer:
(2, 2), (3, 1), (4, 2)
Step-by-step explanation:
y ≥-1/3 x + 2
y < 2x + 3
(2, 2), (3, 1), (4, 2)
(2, 2), (3, –1), (4, 1)
(2, 2), (1, –2), (0, 2)
(2, 2), (1, 2), (2, 0)
I will assume which we determining which set of points is a solution
(2,2) is in all the sets, so we ignore it
Looking at the graph, we do not have negative solutions for y when x >0 so (3,-1) cannot be a solution and (1,-2) cannot be a solution
(2, 2), (3, 1), (4, 2)
(2, 2), (3, –1), (4, 1) x
(2, 2), (1, –2), (0, 2) x
(2, 2), (1, 2), (2, 0)
Again looking at the graph (2,0) is not a solution
(2, 2), (3, 1), (4, 2)
(2, 2), (3, –1), (4, 1) x
(2, 2), (1, –2), (0, 2) x
(2, 2), (1, 2), (2, 0) x
Answer:
(2, 2), (3, 1), (4, 2)
Step-by-step explanation:
What is the solution to this equation?
x² + 101 = 1
A. 10i, -10i
B. 10,-10
c. -10
D. 10i
Answer:
A. 10i and -10i
Step-by-step explanation:
We are given our equation as
[tex]x^2+101=1\\[/tex]
Let us subtract 101 from both hand sides
[tex]x^2+101-101=1-101\\[/tex]
[tex]x^2=-100[/tex]
Now taking square roots on both hand sides
[tex]\sqrt{x^{2}}} = \sqrt{-100}[/tex]
[tex]x=\sqrt{100} * \sqrt{-1}[/tex]
[tex]x=10 * (+i) \\x=10*(-i)\\[/tex]
[tex]x=+10i \\x=-10i\\[/tex]
Which number can each term of the equation be multiplied by to eliminate the fractions before solving? 6 – x + = x + 5 2 3 6 12
Answer:its 12
Step-by-step explanation:
The number can each term of the equation be multiplied by to eliminate the fractions before solving is 12, the correct option is D.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that;
Equation 6 – x + = x + 5
Now,
the least common multiple of 2 and 3, which are the denominators of the fractions in the equation. Multiplying each term by 12 will clear the fractions and result in an equivalent equation without fractions. For example: 12(6 - x + ) = 12(x + 5) 2 3 Simplifying, we get: 72 - 12x + 4 = 12x + 60. This is an equation without fractions that can be solved for x.
Therefore, by the given equation the answer will be 12.
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ7
a number multiplied by 1/3 is 1/18
Answer:
1/6
Step-by-step explanation:
[tex]\frac{1}{3}x=\frac{1}{18}\\3(\frac{1}{3}x=\frac{1}{18} )\\[/tex]
[tex]x=3/18\\x=1/6[/tex]
In the problem to the left, if Tim mows 9 lawns this week, by how much will he have exceeded his goal?
Answer:
Step-by-step explanation:
a - number of lawn that Tim needs to mow
310 < 120 + 30a
190 < 30a
6.333 < a
a > 6.333
Tim needs to mow at least 7 lawns to earn more than $310
Cot^2 x-csc^2 x=-1 for all values of x. True or false
Answer:
TRUE
Step-by-step explanation:
The well known trigonometry identity states that cot^2(x) + 1 = csc^2(x), rearrangin the equation we have that cot^2(x) - csc^2(x) = -1, which is exactly the expression in the statement. Therefore, the expression is TRUE.
Choose the quadratic equation that has a leading coefficient of 1 and solutions 3 and -2.
Options:
A.) x^2+x+6=0
B.) x^2-x-5=0
C.) x^2+x+5=0
D.) x^2-x-6=0
Answer:
Option D [tex]x^{2} -x-6=0[/tex]
Step-by-step explanation:
Verify each quadratic equation
case A) we have
[tex]x^{2} +x+6=0[/tex]
This quadratic equation has a leading coefficient of 1
Substitute the value of x=3 and x=-2 in the equation
For x=3
[tex](3)^{2} +(3)+6=0[/tex]
[tex]18=0[/tex] ----> is not true
therefore
x=3 is not a solution of the quadratic equation
case B) we have
[tex]x^{2} -x-5=0[/tex]
This quadratic equation has a leading coefficient of 1
Substitute the value of x=3 and x=-2 in the equation
For x=3
[tex](3)^{2} -(3)-5=0[/tex]
[tex]1=0[/tex] ----> is not true
therefore
x=3 is not a solution of the quadratic equation
case C) we have
[tex]x^{2} +x+5=0[/tex]
This quadratic equation has a leading coefficient of 1
Substitute the value of x=3 and x=-2 in the equation
For x=3
[tex](3)^{2} +(3)+5=0[/tex]
[tex]17=0[/tex] ----> is not true
therefore
x=3 is not a solution of the quadratic equation
case D) we have
[tex]x^{2} -x-6=0[/tex]
This quadratic equation has a leading coefficient of 1
Substitute the value of x=3 and x=-2 in the equation
For x=3
[tex](3)^{2} -(3)-6=0[/tex]
[tex]0=0[/tex] ----> is true
therefore
x=3 is a solution of the quadratic equation
For x=-2
[tex](-2)^{2} -(-2)-6=0[/tex]
[tex]4+2-6=0[/tex]
[tex]0=0[/tex] ----> is true
therefore
x=-2 is a solution of the quadratic equation