The value of the given functions are:
(i) f + g = x² + x - 6
(ii) f - g = -x² + x - 4
(iii) f . g = x³ - 5x² - x + 5
(iv) f/g = ( x - 5)/(x +1)(x - 1)
(v) g(f(x)) = x² - 10x + 24
The two functions are given that
f(x) = x - 5
g(x) = x² - 1
We have to find
(i) f + g
f(x) + g(x) = ( x-5) + (x² - 1)
= x² + x -5 -1
= x² + x -6
(ii) f - g
f(x) - g(x) = (x-5)- (x² - 1)
= -x² + x -5 +1
= -x² + x -4
(iii) f . g
f(x) . g(x) = (x-5)(x²-1)
=x(x² - 1) -5(x² - 1)
= x³ - x - 5x² + 5
= x³ - 5x² - x + 5
(iv) f/g
f(x) / g(x) = (x-5) / ( x² - 1)
= (x - 5) / (x+1)(x-1)
(v) g(f(x)) = - 1 + ( -5 + x )²
= -1 + 25 + x² - 10x
= x² - 10x + 24
Therefore we get the value of the function, (i) f + g = x² + x - 6, (ii) f - g = -x² + x - 4,(iii) f . g = x³ - 5x² - x + 5, (iv)f/g = ( x - 5)/(x +1)(x - 1), (v) g(f(x)) = x² - 10x + 24.
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The complete question is:
F(x)=x-5 and g(x)=x2 - 1 find (i) f + g , (ii) f-g, (iii) f. g (iv) f/g (v) g(f(x)).
Which number doesn't share the same pattern as 12,24,9,3,300,39
The number doesn't share the same pattern 12,24,9,3,300,39 is 39.
A pattern is a series or sequence that generally repeats itself. Color, exertion, shape, number, and other patterns that we see in our diurnal lives are exemplifications of patterns.
They might be finite or horizonless and can be tied to any event or object. In mathematics, a pattern is a sequence of integers that are related to each other according to a specified rule. These rules specify how to cipher or break issues. In a sequence of,,, for illustration, each number increases by 3. So, following the pattern, the final number will be 12 3 = 15.
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select all numbers in which the place value of the digit 6 is equal to 1/10 of the place value of the digit 6 in the number 760.000
The place value of the digit "6" in the given number 760,000 is Ten thousand's i.e., sixty thousand.
Definition of place value
The numerical value of the digit in the given number is based on its position in the number.
The place values are:
Hundred thousands(Hth) - 100,000
Ten thousands(Tth) - 10,000
Thousands(Th) - 1,000
Hundreds(H) - 100
Tens(T) - 10
Ones(O) - 1
Given number is 760,000
The place values for the given number are:
Hth Tth Th H T O
7 6 0 0 0 0
So, the digit '6' is in the ten thousand's place. So, its place value is "ten thousand" i.e., "sixty thousand".
In math, every digit in more than a few has an area cost. place value can be described as the value represented by a digit in quite a number on the premise of its position within the number.
for instance, the region value of seven in 3,743 is 7 loads or seven-hundred. but, the place value of seven in 7,432 is 7 thousands or 7,000. here, we will see that despite the fact that the digits are identical in both the numbers, it’s region cost adjustments with the exchange in it’s position.
area value Chart is a completely beneficial table format that helps us in finding the place value of each digit primarily based on it’s function in various.
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An account into which someone deposits an equal amount of money at equal periods or equal intervals of time is an ________________.
Group of answer choices
Annual compounding
annuity
annual rate
APR(Annual Percentage Rate)
An account into which someone deposits an equal amount of money at equal periods or equal intervals of time is an annuity.
What is Annuity?A predetermined sum of money that you will receive annually for the rest of your life is called an annuity. An annuity is a contract that you have with an insurance provider that calls for regular payments to be made by the insurer to you, either now or in the future.
Certain annuities have payments that are made for a set (limited) amount of time known as the annuity's term. A 30-year mortgage payment is one illustration. With a contingent annuity, payments are made up to a specific occurrence.
As, the deposits have an equal amount with equal intervals.
Hence, An account into which someone deposits an equal amount of money at equal periods or equal intervals of time is an annuity.
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Use the diagram to find the angle measures that satisfy each case. Find the measures of all 4 angles if m<2-m<1=30 degrees
m<1=__, m<2=__, m<3=__, m<4=__
The measures of the angles are <1 = 85, <2 = 105, <3 = 85 and <4 = 105
How to use the diagram to find the angle measures that satisfy each case?The diagram that completes the question is added as an attachment
From the diagram, we have
<1 + <2 = 180 degrees --- supplementary angles
Given that
<2 - <1 = 30 degrees
Add the above equations
So, we have
2<2 = 210
Divide both sides by 2
<2 = 105
Substitute <2 = 105 in <2 - <1 = 30
So, we have
105 - <1 = 30
Evaluate
<1 = 85
Also, we have
<3 = <1
<4 = <2
This means that
<3 = 85
<4 = 105
Hence, the measures of the angles are <1 = 85, <2 = 105, <3 = 85 and <4 = 105
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Ann and Ben translate documents from German into English.
A set of documents that would take Ann 10 days would take Ben 12 days
Ann starts to translate the documents.
After 2 days Ann and Ben both work on translating the documents.
How many more days will it take to complete the work?
they will approximately require 4.4 days to complete the remaining work together.
Ann alone take = 10 days to translate a document.
Work done in 1 day by Ann = 1 / 10
In 2 days = 2 / 10
Work left = 8 / 10
Now, Ben alone take = 12 days to translate a document.
Work done in 1 day by Ben = 1 / 12
We will now use addition.
Combined work of both Ann and Ben in 1 day = 1 / 10 + 1 / 12 = 11 / 60
Time taken to complete the rest of the work = 8 / 10 ÷ 11 / 60
= 48 / 11 = 4.4 days.
Therefore, they will approximately require 4.4 days to complete the remaining work together.
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*Note, my question had Ann as 8 days and Ben as 12, so adjust accordingly*
Answer:
3 3/5
Step-by-step explanation:
After 2 days, 1/4 are done so 3/4 are left
1/8 + 1/12 = 10/48
3/4 ÷ 10/48
3/4 × 48/10 = 144/40 = 3 24/40 = 3 6/10 = 3 3/5
in how many ways can 5 students line up for lunch
Answer:
There are many formations a group of 5 can make. Examples could be STS (Shoulder To Shoulder), single file, and double column with one leader. There are many more formations that could be made but these three would be the most acceptable line formations in a school environment.
17 POINTS HELP I GIVE BRAINLIEST A line is defined by the equation y = negative x + 3. Which shows the graph of this line?
On a coordinate plane, a line goes through points (0, 3) and (3, 0).
On a coordinate plane, a line goes through points (0, negative 3) and (0, 3).
On a coordinate plane, a line goes through points (0, 0) and (2, 6).
On a coordinate plane, a line goes through points (negative 2, 6) and (0, 0).
Answer:
The first answer is correct.
Step-by-step explanation:
Write the fraction below as a sum or difference.
7-9x/3
Answer:The answer is -2 over 3
Step-by-step explanation:
Please solve quick i need this done and i need both parts for the first box and the second
The equation of the linear function in slope intercept form is f(x) = -2x + 1
How to represent function in slope intercept form?The table can be used to write linear equation in slope intercept form.
Therefore, the equation of the linear function in slope intercept form is as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore,
m = 3 - 5 / -1 + 2
m = - 2 / 1
m = -2
Therefore, the y-intercept can be solved as follows;
using (0, 1)
y = -2x + b
1 = -2x + b
1 = -2(0) + b
b = 1
Hence, the the equation of the linear function in slope intercept form is f(x) = -2x + 1
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Ana has 4 pots and 7 seeds. How many fewer pots does ana have?
Ana has 3 fewer pots than she has the number of flowers.
What are some alternative names for arithmetic operations?Additions have an alternative name which is sum. Multiplication can also be called as the product, Subtraction can be called the difference and division can be called as the ratio.
To Obtain the number of fewer pots Ana has for flowers is the same as the difference between number of seeds and pots.
Number of seeds she has is 7 and the number of pots she has is 4.
∴ The number of fewer pots Ana has is ,
= (7-4) pots.
= 3 pots.
So, Ana has 3 fewer pots or Ana has 3 more seeds than the number of pots she has.
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pls help asap negative five and one third times negative four and fifteen hundredths
The product will be 332 / 15 .
Given : - 5[tex]\frac{1}{3}[/tex] , - 4[tex]\frac{15}{100}[/tex]
To find : the product of two given nos.
We are given mixed fractions .
Multiplying both the nos . we get ,
( - 5[tex]\frac{1}{3}[/tex] ) * ( - 4[tex]\frac{15}{100}[/tex] )
On converting mixed fractions we get ,
= ( - 16 / 3 ) * ( - 83 / 20 ) ( multiplication of a fraction with a fraction )
= ( 4 * 83 ) / 15
= 332 / 15
Hence , the product will be 332 / 15 .
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An engineering school reports that 55% of its students were male (M), 33% of its students were between the ages of 18 and 20 (A), and that 26% were both male and between the ages of 18 and 20.
What is the probability of a random student being male or between the ages of 18 and 20?
Your answer should be rounded to two decimal places.
The probability of a random student being male or between the ages of 18 and 20 will be 0.07.
How to calculate the probability?From the information, 55% of its students were male (M), 33% of its students were between the ages of 18 and 20 (A), and that 26% were both male and between the ages of 18 and 20.
Therefore, the probability of a random student being male or between the ages of 18 and 20 will be:
= 33% - 26%
= 7%
Therefore, the probability of a random student being male or between the ages of 18 and 20 will be 7%.
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Given the quadratic function g(x)=
ax^2 - 7x - 15, and given that one root of the quadratic is 5,
which of the following could be a factor of g (x)? More than one can apply.
a. (2x-1) b. (x+3) c. (x-3) d. (2x+3)
we get that option (d) 2 x + 3 is a factor of the quadratic function g (x)= a x² - 7 x - 15.
We are given a quadratic function:
g (x)= a x² - 7 x - 15
We also know that 5 is a root for it.
So, we get that:
a (5)² - 7 (5) - 15 = 0
25 a - 35 - 15 = 0
25 a - 50 = 0
25 a = 50
a = 50 / 25
a = 2
So, the function becomes:
g (x)= 2 x² - 7 x - 15
Now factorizing the function:
2 x² - 7 x - 15
2 x² - 10 x + 3 x - 15
2 x ( x - 5 ) + 3 ( x - 5 )
( 2 x + 3 ) ( x - 5 )
Therefore, we get that option (d) 2 x + 3 is a factor of the quadratic function g (x)= a x² - 7 x - 15.
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This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Mrs. Jameson paid $202.50 for a group of 9 students to visit an amusement park.
Write an equation relating the total cost, y, and the number of students, x, attending the park.
The equation relating to the total cost and number of students attending the park is $22.5x = y
According to the question we have been given that
Total money paid by Mrs. Jameson = $202.50
Total number of the students = 9
Let the amount of one student to visit the amusement park be X
Thus first we have to find the value of X by following equation,
9X = $202.50
Solving for X we get,
X = 202.50/9
X = $22.5
That is amount for one student is = $22.5
Now we will solve the second part
Let the total cost be represented as y
Let the number of students attending the park be represented as x
Then the equation related to total cost and number of students is given as
$22.5x = y
Hence the equation is given above
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two streets are parallel in a map, chestnut street and walnut street. the map is put on a coordinate plane and the equation for chestnut is y=2x-6. walnut street goes through the coordinates (1,3) on the map. write an equation for the line for walnut street
An equation for the line for walnut street is: y = 2x + 1.
What is defined as the slope intercept form?An intercept is a y-axis point whereby the slope of a line passes. It is the y-coordinate of a point on the y-axis where a straight line or a curve intersects.The slope intercept form for line is given by;
y = mx + c
where
m = slope
c = y-intercept
As, the two streets chestnut street and walnut street are parallel in a map, their slopes are also equal.
The equation of chestnut is y = 2x-6; comparing with general form;
m = 2.
The coordinates of walnut street is (1, 3) = (x₁, y₁)
Thus, equation is;
(y - y₁) = m(x - x₁)
Put the values.
(y - 3) = 2( x - 1)
simplify,
y - 3 = 2x - 1
y = 2x + 1
Thus, the equation for the walnut street is found as; y = 2x + 1.
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I need some help with this! Finish this correctly for Brainliest! It’s about Commutative/Associative Properties!
I think this is the last one I’ll need help on :)
Answer:
The first one and the third one. 1/9 and 3^(-6) x 3^(4)
Step-by-step explanation:
3^3 x 3^(-2) is 3^ 3-2, or 3^1. 3^1 is just 3, and so 3^-2 is the answer. The choices that are equal to 3^-2 are 1/9 and 3^-6 x 3^4
Use the slope formula to solve for the slope
Answer:
1/6 pretty sure
Step-by-step explanation:
rise - 1
run - 6
going from (-5, -4) to (1, -3)
What is the scale factor of the dilation?
A. 4
B. 6
C. 12
D. 16
Scale Factor is defined as the ratio of the size of the new image to the size of the old image. The center of dilation is a fixed point in the plane. Based on the scale factor and the center of dilation, the dilation transformation is defined. If the scale factor is more than 1, then the image stretches.
For example, if a square is dilated and the side of the smaller (original) square is 4 units and the side of the dilated square (enlarged) is 12 units, then, in this case, the scale factor will be: 12 ÷ 4 = 3.
Perform a Dilation of 4 on point A (2, 3) which you can see in the picture below. Multiply the coordinates of the original point (2, 3), called the image, by 4. Image's coordinates = (2 * 4, 3 * 4) to get the coordinates of the image (8, 12).
And so if you dilate it with a factor of three, then you're going to want to go three times as far down. So minus three, and three times as far to the left, so you'll go minus six.
The basic formula to find the scale factor of a dilated figure is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
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4. What value is needed to complete the square? Show all steps.
x²-2x+_
The value of the square in the mathematical identity is 1.
According to the statement, We have to find that the value of the square.
So, For this purpose, we know that the
An Mathematical identity is an equality relating one mathematical expression A to a different mathematical expression B, such A and B produce the identical value for all values of the variables within a specific range of validity.
From the given information:
The statement is the [tex]x^{2} -2x+.....[/tex]
Then
According to the squaring identity,
[tex](A-B)^2 = A^2 + B^2 -2AB[/tex]
compare it with the statement
[tex](x-1)^{2} = x^{2} -2x+1[/tex]
The value of the square is a 1.
So, The value of the square in the mathematical identity is 1.
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Find the equation of a line perpendicular to y=−10+3x that passes through the point (9,-2).
The equation of a line perpendicular to y = -10 + 3x that passes through the point (9,2) is y = -1/3x + 1
How to find the equation of a line perpendicular to y = -10 + 3x that passes through the point (9,2)?The equation of the line is given as
y = -10 + 3x
Rewrite the equation as
y = 3x - 10
A linear equation is represented as
y = mx + c
Where
Slope = m
So, we have
m = 3
The slopes of perpendicular lines are opposite reciprocals
This means that
m2 = -1/m1
So, we have
m = -1/3
Evaluate
m = -1/3
The equation of the perpendicular line is then calculated as
y = m(x - x1) + y1
Where
(x1, y1) = (9, -2)
This gives
y = -1/3(x - 9) - 2
Evaluate
y = -1/3x + 3 - 2
Evaluate the sum and the difference
y = -1/3x + 1
So, the equation of a line perpendicular to y = -10 + 3x that passes through the point (9,2) is y = -1/3x + 1
Hence, the required equation of a line perpendicular to y = -10 + 3x that passes through the point (9,2) is y = -1/3x + 1
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one number is 4 times a first number. a third number is 100 more thann the first number. if the sum of the three numbers is 562, find the numbers
The numbers are 77 , 177 and 308 .
Numbers are the building blocks in mathematics. It is an arithmetic value that is used to represent a quantity. Real numbers , integers , natural numbers, whole numbers , irrational numbers are are various types of numbers.
Let us consider the first number to be x . Then the second number is 4x+100 , and the third number is 100 more than the first number. Therefore the the sum of the three numbers will be:
x+4x+(x+100)=6x+100
Now the sum of all the numbers is 562.
Therefore we can write a linear equation in x to find the values of x.
∴ 6x+100=562
or, 6x = 562 - 100
or, 6x = 462
or, x = 462 ÷ 6
or, x = 77
Therefore the second number is 4x = 4 × 77 = 308 and the third number is x + 100 = 77 + 100 = 177 .
So the numbers are 77 , 177 and 308 .
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Using the Pythagorean Theorem, find the side lengths of the triangle above. Choose all that apply.
Answer:
4 units
5 units
6.4 units
Step-by-step explanation:
we have two catheti, one measures 4 units and one measures 5 units, with Pythagoras we find the hypotenuse
hypotenuse = √(4²+5²)
hypotenuse = √(16 + 25)
hypotenuse = √41
hypotenuse = 6.4 units
(WILL GIVE BRAINLIEST)
Answer: 1) slope of 2/3.
2) slope of -1/2
3) slope of 3
4) slope of -2/3
5) slope of undefined
6) slope of -1 1/2
7) slope of 1
8) slope of 0
Step-by-step explanation:
R 2x+21 Q 12 x + 24 P
The value of function R+Q is 14x+45.
A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions are everywhere, and they are crucial for constructing physical relationships in the sciences.
Four broad categories can be used to classify different types of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.
An output variable and one or more input variables are the minimum number of variables in a function. An equation can have any number of variables and declares that two expressions are equal (none, one, or more).
Disclaimer:
If the value of R = 2x+21, Q= 12 x + 24, P =2x-9, then find the value of R+Q ,where R and Q are functions.
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Mai says x is a number that makes Equation A true and also a number that makes Equation B true. Equation A: − 3 ( x + 7 ) = 24 Equation B: x + 7 = − 8 Which statement explains why this is true? Multiple choice question. A) Adding 3 to both sides of Equation A gives x + 7 = − 8 . B) Applying the distributive property to Equation A gives x + 7 = − 8 . C) Subtracting 3 from both sides of Equation A gives x + 7 = − 8 . D) Dividing both sides of Equation A by -3 gives x + 7 = − 8 .
The statement that explains why this is true is (d) dividing both sides of Equation A by -3 gives x + 7 = − 8 .
How to determine which statement explains why this is true?The equations are given as
Equation A: −3(x + 7) = 24 Equation B: x + 7 = −8In equation A, we have
-3(x + 7) = 24
Divide both sides of this equation by -3
So, we have
-3(x + 7)/-3 = 24/-3
Evaluate the quotient
So, we have
x + 7 = -8
The above equation is the same as equation B
Hence, the statement that explains why this is true is (d) dividing both sides of Equation A by -3 gives x + 7 = − 8 .
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5. A rugby team scores the following number of points in 12 matches: 21, 18, 3, 12, 15, 21, 42, 24, 31, 3, 12, 21 a) The mean score: b) The mode: c) The range:
PLEASEE HELPP ME
The mean score is 18.5833 , Mode is 21 and Range is 39 of the given scores.
Mean is the average value of all the given numbers
To calculate the mean we have to add all the values and divide the sum by the numbers of values.
Total of all value = 21+18+3+12+15+21+42+24+31+3+12+21 = 223
No of values = 12
Mean = [tex]\frac{223}{12} =18.58333[/tex]
Mode is the value which comes frequently in data set
In the given data 21 is come three times which is most frequently so Mode is 21.
Range is the difference between the largest number and the smallest number of the given data set.
Largest number of the data set is 42 and smallest number is 3 so the range is 42-3 = 39.
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In how many ways can the digits in the number 7,444,000 be arranged?
The digits of 7,444,000 can be only be arranged in 140 ways
What are combinations?Combinations are used to determine the number of selections of an item within another
How to determine the number of arrangement?The arrangements of the digits is an illustration of factorials
The number is given as: 7,444,000
From the given number, we have the following parameters:
Total (n) = 7 i.e. number of digits
n(4) = 3 i.e. number of digit-4
n(0) = 3 i.e. number of digit-0
So, the number (N) of arrangements is:
N = n!/(n(4)! * n(0)!)
Substitute known values in the above equation
So, we have
N = 7!/(3! * 3!)
Evaluate the factorials in the above equation
So, we have
N = 5040/(6 * 6)
Evaluate the quotients in the above equation
N = 140
Hence, the digits of 7,444,000 can be arranged in 140 ways
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If cos(t)=17cos(t)=17 and tt is in the fourth quadrant, find sin(t).
The value of sin(t) in fourth quadrant is -120/169.
What is a quadrant ?Given that cos(t)= 17
t is in fourth quadrant, so sint<0 and cost>0
So sint = -sqrt(1-cos^2(t))= -sqrt(1-25/169)= - sqrt((169-25)/169)= -12/13
Sin(2t) = 2sin(t)cos(t)= 2*-12/13* 5/13 = -120/169
The region enclosed by such an arc and two sketched radii, one at each extremity. a component of a machine that has a quarter-circle form.
Each of the four divisions of the coordinate plane is referred to as a quadrant. Additionally, when we refer to the sections, we mean the sections as they are divided by the coordinate axes. The x-axis is located here, and the y-axis is located on this up-down axis. As you can see, it creates four portions on a coordinate plane.
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The Miller family is taking a road trip. They will drive a total of 1,372 miles. So far they have driven 648 miles. How many miles do they have left to drive?
Answer:
724 miles
Step-by-step explanation:
subtract the values(1372-648)