The domain of the composite function is the intersection of the domain of f(x) and G(x). D f(x) intersection D g(x) The range of the function is now restricted by the domain of the composite function.
Therefore, the range is found by evaluating the function at the points in the domain of f(x).
You find the domain of the function by finding all numbers that can't go into the equation. Usually all that prevents this is whether or not it contains a fraction with x on the bottom or a x under a square root .
The range is found by finding the vertex and noting that it is the minimum or maximum (depending on direction) of the graph. You can find the vertex by using -b/2a for the x value and then plugging in to get y value.
The given function f(x) = –37 is a horizontal line which goes from negative infinity to positive infinity.
In this case, the domain can be any number since there is no limit on what the x value can be.
So, the domain of the given function f(x) = –37 will be all real numbers.
And, the range will always be y = –37 because no matter what x value will equal, y will always be equal to –37 in the function of f(x) = –37.
So, the range of the given function f(x) = –37 will be y = –37.
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Choose the equation for the graph.
A. Y=|x/2|-5
B. Y=2|x|+5
C. Y=2|x|-5
D. Y=|x/2|+5
E. Y= |x/5|-2
The correct equation of the given graph is; Option A: y = |x/2| - 5
How to find the equation of a graph?
From the given graph, we can see the following coordinates;
At x = 0, y = -5
At x = 1, y = -4.5
At x = -1, y = -4.5
At x = 2, y = -4
At x = -2, y = -4
Since the y-intercept is at y = -5, looking at the given options, the only one that is correct will be;
y = |x/2| - 5
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Solution
We can start with the pythagorean theorem:
(leg 1)2 + (leg 2)² = (hypotenuse)²
Solve for x.
Substitute the values we know.
18² + x² = 27²
x=0√O
Step-by-step explanation:
324+x²=729
x²=405===> x=√405===> 9√5
The pythagorean theorem (leg 1)2 + (leg 2)² = (hypotenuse)² the values is about 8.5, -8.5.
The Pythagorean theorem is used to find the length of the sides of a right triangle, not for solving equations like x² = 72.
To solve the equation x² = 72, to take the square root of both sides to find the value of x:
√(x²) = √(72)
Since the square root of x² is x (the absolute value of x), the equation simplifies to:
x = √(72)
Now, let's find the approximate value of √(72):
√(72) ≈ 8.49
So, the equation becomes:
x≈ 8.49
Now, remember that the absolute value of x is a positive value, so the equation gives two possible solutions for x:
x= 8.49 → x = 8.49
x = -8.49 → x = -8.49
Rounded to the nearest tenth, the solutions are:
x ≈ 8.5 and x ≈ -8.5
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Jasmine buys a turkey every year . The first time she bought a turkey, in year 0, it cost $15.50. She notices the price is getting more expensive, at a rate of 2%
The price of the turkey based on the percentage given is $15.81.
How to illustrate the information?It was stated that the cost is $15.50 but that there was a 2% increment in price.
Therefore, the new price will be:
= $15.50 + (2% × $15.50)
= $15.50 + $0.31
= $15.81
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Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted: rectangle with a length of x plus 20 and width of x plus 10 with a rectangle in the bottom right corner labeled bench that has a length of 6 and width of 2 write an equation to determine the area, a, of the patio that will be painted. a = (x 20)(x 10) 12 a = (x 20)(x 10) − 12 a = (x 26)(x 12) a = (x 14)(x 8)
The area of the rectangular patio to be painted is: B. A = (x + 20)(x + 10) - 12.
What is a Rectangle?A rectangle, by definition, is a quadrilateral with two pairs of opposite that have the equal lengths. All four angles of a rectangle are right angles (90 degrees).
What is the Area of a Rectangle?The area of a rectangle = (length of rectangle)(width of rectangle).
Given the following parameters for the patio and the bench:
Length of rectangular patio = x + 20Width of rectangular patio = x + 10Length of rectangular bench = 6Width of rectangular bench = 2Area to be painted = area of rectangular patio - area of rectangular bench
Area of rectangular patio = (x + 20)(x + 10)
Area of rectangular bench = (6)(2) = 12
Area to be painted = (x + 20)(x + 10) - 12
The answer is: B. A = (x + 20)(x + 10) - 12.
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[tex]x^{2} +x-12[/tex]
solve this polynomial by class 9 corse
The factored expression of the polynomial is (x - 3)(x + 4)
How to solve the polynomial?The polynomial expression is given as;
x^2 + x - 12
Expand the expression
x^2 + 4x - 3x - 12
Factorize the expression
x(x + 4) -3(x + 4)
Factor out x + 4
(x - 3)(x + 4)
Hence, the factored expression of the polynomial is (x - 3)(x + 4)
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y square plus 5y equals to 0
Answer:
y^2 + 5y = 0
y(y + 5) = 0
y = 0, -5
The answer is y = 0 and y = -5.
The given question :
y² + 5y = 0y (y + 5) = 0y = 0, y = -5if three pies require 2 dozen apples, then four bird require ? dozen apples?
What are the solutions of the equation6x^2-x-1=0
Answer:
1/2
1/3
Step-by-step explanation:
x=1/2
x=-1/3
Answer:
[tex]x_{1} =-\frac{1}{3} \\x_{2} =\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]6x^{2} -x-1=0[/tex]
Factoring the equation:
[tex](3x+1)(2x-1)=0[/tex]
Extract the roots:
First factor
[tex]3x+1=0\\3x=-1\\x_{1} =-\frac{1}{3}[/tex]
Second factor
[tex]2x-1=0\\2x=1\\x_{2} =\frac{1}{2}[/tex]
Hope this helps
Katie has 100 apples, and she plans on eating 2 of them every day.
True or false...the number of apples Katie has left is proportional to the number of days that pass.
use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos^4
The expression cos⁴ θ in terms of the first power of cosine is [ 3 + 2cos 2θ + cos 4θ]/8.
The power-reducing formula, for cosine, is,
cos² θ = (1/2)[1 + cos 2θ].
In the question, we are asked to use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos⁴ θ.
We can do it as follows:
cos⁴ θ
= (cos² θ)²
= {(1/2)[1 + cos 2θ]}²
= (1/4)[1 + cos 2θ]²
= (1/4)(1 + 2cos 2θ + cos² 2θ] {Using (a + b)² = a² + 2ab + b²}
= 1/4 + (1/2)cos 2θ + (1/4)(cos ² 2θ)
= 1/4 + (1/2)cos 2θ + (1/4)(1/2)[1 + cos 4θ]
= 1/4 + cos 2θ/4 + 1/8 + cos 4θ/8
= 3/8 + cos 2θ/4 + cos 4θ/8
= [ 3 + 2cos 2θ + cos 4θ]/8.
Thus, the expression cos⁴ θ in terms of the first power of cosine is [ 3 + 2cos 2θ + cos 4θ]/8.
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Help me:-
Distribute to create an equivalent expression with the fewest symbols possible.
4(5+y) =
Answer:
20 + 4y
Step-by-step explanation:
The 4 multiplies the 5 and the y, i.e., it distributes over the terms of the expression in ( ).
help please a.-5 b.-1/5 c1/5 d.5
Answer:
-5
Step-by-step explanation:
Slope is rise over run. The graph decreases by 5 units every 1 unit to the right, so the slope is -5.
Lola has collected 935 buttons. what is the number of buttons rounded to the nearest ten?
Answer:
940
Step-by-step explanation:
Since there is a 5 in the ones spot we round the number is the tens spot up by 1: 935 --> 940
________ 11B. If m∠ABC = 74, then what is the measure of AB ?
what is the domain of f(x)=√11-x?
The domain of the function f(x) is:
11 ≥ x
What is the domain of the function f(x)?
Here we have the function:
[tex]f(x) = \sqrt{11 - x}[/tex]
Now, remember that the argument of a square root can only be a number equal to or larger than zero, so the domain of our function is defined by:
11 - x ≥ 0
Then, solving this for x, we get:
11 ≥ x
Concluding, the domain of the function f(x) is:
11 ≥ x
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Consider the polynomial function of g(x)= -2x^8 +5x^6 -3x^5+50
Answer:
C) as x –> ∞, q(x) –> –∞, and as x –> -∞, q(x) –> –∞
Step-by-step explanation:
use the end behavior chart to figure out the end directions of the graph. remember these
E O
+|↑↑|↓↑
–|↓↓|↑↓
all you need to do is look at the first number of the equation and ask yourself:
1. Is the first number even or odd?
2. is the first number positive or negative?
find where the answers to both meet on the chart.
so, in this question, the first number is even and negative. when using the chart we see that they meet at the ↓↓ which means that the end behavior on both sides is going towards negative infinity.
Two ways to measure the relationship between the returns of two securities are ______ and blank______.
a. standard deviation
b. variance
c. covariance
d. correlation
Two ways to measure the relationship between the returns of two securities are correlation and covariance. That is options C and D.
What is Correlation?Correlation can be defined as the measure of the difference between two variables in a statistical analysis.
Covariance can be defined as the measure of the relationship between two variables in statistical analysis.
Therefore, Two ways to measure the relationship between the returns of two securities are correlation and covariance.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each scenario with its effect on the PPC.
These are the effect on the PPC
1st pairs with a point original to PPC. and 2nd pairs with PPC shifts to the left. and 3rd pair with PPC shifts to the right.
According to the statement
we have given the some conditions and we have to match the each scenario with the effect of the PPC.
So, The given effect on the tiles are Tiles
- the PPC shifts to the right
- the PPC shifts to the left
- a point on the original PPC
- a point inside the PPC
- a point outside the PPC
And we have to join it with its pairs.
So,
First :
A manufacturing unit uses all its resources efficiently = A point on the original PPC
Second :
Andrew has 5 hours to complete his homework but uses only 3 hours, so he doesn’t complete it. = The PPC shifts to the left
Third :
A country acquires part of its neighboring country = The PPC shifts to the right
These are the conditions that satisfy the effect of PPC.
So, These are the effect on the PPC
1st pairs with a point original to PPC. and 2nd pairs with PPC shifts to the left. and 3rd pair with PPC shifts to the right.
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Disclaimer: This question was incomplete. Please find the full content below.
Question:
Match each scenario with its effect on the PPC.
Tiles
- the PPC shifts to the right
- the PPC shifts to the left
- a point on the original PPC
- a point inside the PPC
- a point outside the PPC
Pairs
- A manufacturing unit uses all its
resources efficiently.
- Andrew has 5 hours to complete his
homework but uses only 3 hours, so
he doesn’t complete it.
- A country acquires part of its neighboring
country.
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^it doesn't need to be this complicated
Find the smallest number by which 1008 must be multiplied to get a perfect square. also, find the square root of the perfect square so obtained
Answer:
7
Step-by-step explanation:
we have 1008=2×2××2×3×3×3
The smallest whole number is 7, by which 1008 should be multiplied so as to get a perfect square.
Now 1008×7=2×2×2×2×3×3×7×7
7056=2×2×3×7
=84
Answer : 7
Answer:
1. 7
2. square root is 84.
Step-by-step explanation:
First find the prime factors:
1008 =2*2*2*2*3*3*7
There's an even number of 2's and 3's but only one 7, so we multiply by 7
Smallest number = 7.
The square number is 1008 * 7
= 7056.
Its square root is 2*2*3*7 = 84.
If the value of the sample standard deviation increases, what happens to the confidence interval?
If the value of the sample standard deviation increases, the confidence interval becomes wider and is denoted as option A.
What is Confidence interval?This term is used in statistics and refers to the probability that a population parameter will fall between two set values.
it has a direct relationship with standard deviation in which its increase will also lead to the set of values being wider thereby making it the most appropriate choice.
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The options are :
a. It becomes wider
b. It becomes more precise
c. It does not change
d. It narrows
Alejandro wants to determine the average shoe size of all of the male students in his school. Which sample is likely to yield the most biased results?.
The sample that is likely to yield the most biased results is; B) every member of the boys’ basketball team
How to identify a bias in sampling?The sample that is likely to yield the most biased results is; B) every member of the boys’ basketball team.
The reason option B is the most biased is because members of a basketball team are typically taller than other people. We know that taller people generally have larger feet, and larger shoe sizes, than shorter people. Thus, choosing only people from this area would lead to a biased sample.
The missing options are;
A) every tenth boy on the school’s phone list
B) every member of the boys’ basketball team
C) every boy in a randomly selected ninth-, tenth-, eleventh-, and twelfth-grade gym class
D) every fifth boy who walks through the front doors of the school in the morning
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Answer:
B)
Step-by-step explanation:
HELP!!!!!!!!!!!!!!!!!!!! I WELL GIVE BRAINLIST AND 100 point if answered in less the 20 mins
If I have 419 assignments to do and i have pleated completed 79 how much work will I need to do every day to finish in one week
Answer:
10
Step-by-step explanation:
Answer:
You have to complete around 49 assignments everyday to finish in one week.
Step-by-step explanation:
• First, we have to calculate the number of assignments left to do:
Assignments remaining = 419 - 79
= 340
• There are 7 days in a week, which means 340 assignments need to be completed in 7 days.
7 days ⇒ 340 assignments
1 day ⇒ 340 ÷ 7
= 48.6
≅ 49 assignments
∴ You have to complete around 49 assignments everyday to finish in one week.
Bob grows tomatoes in his garden. He picked four tomatoes, and weighed every possible grouping of three tomatoes. The results are 900 grams, 1400 grams, 1600 grams, and 1800 grams. What is the weight of the biggest tomato?
Answers could be 600, 800, 900, 1000, 1200
Answer:
1000.
Step-by-step explanation:
We need 4 weights where 3 of them add up to
900, 1400, 1600 or 1800g.
Not sure of the method for doing this!
Lets assume that the answer is 1000 g.
Then the 3 that make 1800 could be
1000 500 and 300
- then to make 900 we need a 100g tomato giving:
1000 500 300 and 100 grams
So the 1400 will be the 1000, 300 and 100 tomato
and the 1600 will be 1000, 500 and 100.
That seems to fit !!
Find the unknown angle
60°
Xº
30°
Answer:
x = 90°
Step-by-step explanation:
Hello!
The sum of angles on a straight line is 180°.
To find the value of angle x°, we can subtract all the given angles form 180°.
Find x180° - 60° - 30° = x°180° - 90° = x°90° = x°The value of x is 90°.
explanation?
please help asap
Answer:
70 degrees = a
Step-by-step explanation:
Triangle= 180 degrees.
Therefore, since a and the unmarked angle are congruent since it is an isosceles triangle, we subtract 40 from 180, with a result of 140. With 140, we divide by 2 to find the degrees for both the unmarked angle and angle a, since they are congruent. 140/2 = 70, Angle A will equal to 70 degrees
Write the standard equation of a circle that passes through(-4,0) with center (-1,-4)
The standard equation of the circle is x² + y² + 8x - 9 = 0 if the circle with center at (-1,-4) that passes through the point (-4,0).
According to the question,
The circle with center at (-1,-4) that passes through the point (-4,0).
To find the radius of the circle:
Radius r = √[(-4 - (-1))² + (0- (-4))²]
=√(-4+1)² + (4)²
=√9+16
=√25
=5.
In order to find the standard equation of the circle is
(x - (-4))² + (y - (0))² = (5)²
(x + 4)² + (y )² = 25
x² + 8x + 16 + y² = 25
x² + y² + 8x + 16 = 25
x² + y² + 8x = 25 - 16
x² + y² + 8x = 9
x² + y² + 8x - 9 = 0
Hence, the standard equation of the circle is x² + y² + 8x - 9 = 0.
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HELP PLEASE!!!!!!
Parallel lines r and s are cut by two transversals, parallel lines t and u.
How many angles are alternate exterior angles with angle 5?
Picture below:
The number of angles that are alternate exterior with angle 5 is one, which is angle 11.
What are Alternate Exterior Angles?Alternate exterior angles are formed on the outside of the two parallel lines that are intersected by a transversal, each being located on the opposite side of the transversal.
The alternate exterior angle pairs are two angles that are supplementary. This means they add up to give a sum of 180 degrees.
Considering transversal s and parallel lines t and u, the angle that is an alternate angle to angle 5 is angle 11.
Angle 11 is the only angle that is alternate exterior angles with angle 5. therefore, we can conclude that, the number of angles that are alternate exterior with angle 5 is just 1, which is angle 11.
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Can someone please help???
Answer:
A 0.08
Step-by-step explanation:
Consider dealing a hand of 8 cards from a well shuffled standard deck of playing cards. The expected value of the number of face cards in the hand is (Q
Answer:
2 face cards
Step-by-step explanation:
By definition, there are 12 face cards (Kings, queens, and jacks) and 36 numbered cards (2's through 10's) in a standard deck of 52 cards. Aces are not considered face cards (no face on the card).
The ratio of face cards in a full deck is (12/52) or slightly over 23%.
The likelihood of a face card in a hand of 8 cards is:
(8 cards)*(12 face cards/52 cards) = 1.85 cards. We need to round to the nearest whole card, so the expected number of face cards in a hand of 8 is 2 cards.
Please someone help me with question a) and b). I’ve been having so much trouble with these types of questions. The booklet says that the answers are a) 134degrees and b) 14.3km. I just don’t get how to get there. Thank you!
The bearing to take is 134 degrees and the shortest distance is 14.3 km
The bearing it would takeThe attached diagram represents a labelled version of the ship movement
The angle at Q is
Q = 180 - 155 + 90 + 120 - 90
This gives
Q = 145
The distance PR is calculated as:
PR^2 =PQ^2 + QR^2 - 2 * PQ * QR * cos(Q)
This gives
PR^2 = 9^2 + 6^2 - 2 * 9 * 6 * cos(145)
Evaluate
PR^2 = 205.46
Take the square root
PR = 14.3 km
The angle at P is then calculated as:
QR/sin(P) = PR/sin(Q)
This gives
6/sin(P) = 14.3/sin(145)
Evaluate the quotient
6/sin(P) = 24.93
Make sin(P) the subject
sin(P) = 6/24.93
Divide
sin(P) = 0.2407
Take the arc sin of both sides
P = 14
The bearing is then calculated as:
Bearing = P + 120
This gives
Bearing = 14 + 120
Evaluate
Bearing = 134
Hence, the bearing to take is 134 degrees
The shortest distanceIn (a), we have
PR = 14.3 km
This represents the shortest distance
Hence, the shortest distance is 14.3 km
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