The value of the sum, difference and composite function a[b(x)] are 19x - 8, -5x + 28 and 84x - 136 respectively
Sum and difference of functionsGiven the following functions a(x) = 7x + 10 and b(x) = 12x - 18
Take the sum
(a+b)(x) = a(x) + b(x)
(a+b)(x) = 7x + 10 + 12x - 18
(a+b)(x) = 19x- 8
Take the difference
(a-b)(x) = a(x) - b(x)
(a-b)(x) = 7x + 10 - 12x + 18
(a-b)(x) = -5x + 28
For the composite function a[b(x)].
a(12x- 18) = 7(12x-18) - 10
a[b(x)] = 84x - 126 - 10
a[b(x)] = 84x - 136
Hence the value of the sum, difference and composite function a[b(x)] are 19x - 8, -5x + 28 and 84x - 136 respectively
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What is the directrix of the parabola defined by `(1)/(4)(y + 3) = (x − 2)^2`?
The directrix of the parabola is [tex]y = \frac {-49}{16}[/tex]
How to determine the equation of the directrix?The parabola equation is given as:
[tex]\frac 14(y + 3) = (x -2)^2[/tex]
A parabola is represented as:
[tex]4p(y - k) =(x -h)^2[/tex]
By comparing both equations, we have:
4p = 1/4 ==> p = 1/16
-k= 3 ==> k = -3
The directrix is represented as:
y = k - p
So, we have:
[tex]y = -3 - \frac 1{16}[/tex]
Take the LCM
[tex]y = \frac {-16 * 3- 1}{16}[/tex]
Evaluate
[tex]y = \frac {-49}{16}[/tex]
Hence, the directrix of the parabola is [tex]y = \frac {-49}{16}[/tex]
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Find the value of cos (2pie/3)
Answer:
-1/2 or - 0.5
Step-by-step explanation:
[tex]cos (\frac{2\pi }{3}) = cos 120^{o} = -\frac{1}{2}[/tex]
Which graph represents f(x)= | x+3|
The graph of the function looks like V. And the vertex of the function will be at (-3, 0).
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The function is given below.
f(x) = |x + 3|
Then the graph of the function looks like V. And the vertex of the function will be at (-3, 0).
The graph of the function is given below.
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Which of the following rational functions is graphed below
Answer:
A.
Step-by-step explanation:
if x≠-4, then the correct answer is
[tex]A. \ F(x)=\frac{1}{x+4}.[/tex]
The diagram shows a circle inside a square (16cm)
work out the area of the circle
The area of the circle inside the square shape is 200.96 cm²
How to determine the area of the circle?The length of the square is given as:
L = 16 cm
This represents the diamater (d) of the circle.
The area of the circle is then calculated as:
Area = π(d/2)²
This gives
Area = 3.14 * (16/2)²
Evaluate
Area = 200.96
Hence, the area of the circle is 200.96 cm²
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Solve 10x + 16 2 6x + 20.
A. x29
B. x=9
c. x=1
D. x21
An equation is formed of two equal expressions. The value of x for which the equation has a solution is 1.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution for 10x+16=6x+20 is,
10x + 16 = 6x + 20
10x - 6x = 20 - 16
4x = 4
x = 1
Hence, the value of x for which the equation has a solution is 1.
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Factor out the GCF from the given polynomial.
14x-2
Answer:
2(7x-1)
Step-by-step explanation:
14 & 2 gcf 2 factor and wal lah!
Please solve with explanation (high points)
Answer:
see the attachment photo!
Write an equation for a line perpendicular to y = − 4 x + 5 and passing through the point (-12,-4)
Answer:
[tex]y=\frac{1}{4} x-1.[/tex]
Step-by-step explanation:
1) if the lines are perpendicular, then the second slop is 0.25;
2) the equation of the 2d line is y=0.25x+i, where i - unknown intercept;
3) it is possible to calculate the unknown intercept, if to substitute the given coordinates into the equation y=0.25x+i:
-4=-12*0.25+i; ⇔ i=-1.
4) finally, the required equation is:
[tex]y=\frac{1}{4} x-1.[/tex]
What is the volume of this rectangular
pyramid?
3 m
4 m
Submit
5 m
cubic meters
The volume of the given rectangular pyramid.
Solution:[tex]\large\boxed{Formula:V=\frac{1}{3}lbh}[/tex]
First, multiply the length (5), breadth (4) and height (3).
[tex]5×4×3[/tex]
[tex]= 60 \: cm [/tex]
Now, divide 60 by 3.
[tex]\frac{60}{3}[/tex]
[tex]\large\boxed{V= 20 \: {m}^{3}}[/tex]
Therefore, the volume of the given rectangular pyramid is 20 cubic meters.
Thandi has decided to make grocery combo’s for her shop. The wholesaler where she buys from, sells sugar in packets of 20 in a carton, flour in packets of 12 a carton, and there are 15 bags of rice in a carton. How many of each item should she buy so there are an equal number of packets of sugar, packets of flour and bags of rice in each combo?
Answer:
3 cartons of sugar 5 cartons of flour and 4 cartons of rice
Step-by-step explanation:
First find the least common factor being 60 then divide by the number of packets each carton comes with to find how many cartons you need of each
A) 16/12
B) 12/20
C) 12/16
D) 16/20
Answer:
COA opposite/ adjacent
16/12
A
Silas is researching the cost of a specific souvenir he wants to buy on his international trip. Use the table to answer the question.
Answer:
Egypt.
Step-by-step explanation:
We need to set up our conversion factors for each currency.
British Pounds and Egyptian Pounds:
0.83 £ (Europe) = 1 U.S. Dollar
18 E£ (Egypt) = 1 U.S. Dollar
Cost of a Souvenir in Europe:
The cost of souvenir in Europe is 13£. Using our conversion rate, we get
[tex]13\pounds \cdot \frac{\$1}{0.83 \pounds}=\$15.66[/tex]
Cost of a Souvenir in Egypt:
The cost of a souvenir in Egypt is 342 E£. So we have
[tex]342 \text{ E}\pounds\cdot \frac{\$1}{18 \text{ E}\pounds}=\$19[/tex]
Based on our calculations, it is cheaper to buy a souvenir in Europe than in Egypt.
Is this sequence arithmetic? Why or why not?
11, 11, 11, 11, 11
The height in feet of 25 trees is shown below (lowest to highest). 25, 27, 33, 34, 34, 34, 35, 37, 37, 38, 39, 39, 39, 40, 41, 45, 46, 47, 49, 50, 50, 53, 53, 54, 54
outlier if any
There are no outliers in the dataset of the heights in feet of 25 trees
How to determine the presence of outliers?The sorted dataset is given as:
25, 27, 33, 34, 34, 34, 35, 37, 37, 38, 39, 39, 39, 40, 41, 45, 46, 47, 49, 50, 50, 53, 53, 54, 54
Outliers are relatively far from other elements of the dataset.
The highest and the least elements are 54 and 25, respectively.
Other elements of the dataset are relatively close to these two elements
Hence, there are no outliers in the dataset of the heights in feet of 25 trees
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Give the standard form 80,000+200+2
Answer:
80,202 = 8.0202 × 10⁴
two dozen of pen cost rupee 60.find the cost of 25 such pens.
Answer:
it costs rupee 3000 of 50 such pens
Explanation:
first, you have to multiply 50 x 60 which is 3000
second, two dozens of pens, right? so i add double 25 up which is 50 pens.
hope it helps and stay safe! (brainliest me pls)
Find the number of students that play
A basketball and football but not volleyball
B basketball only
C none
#15 play
basketball and volleybal
Answer:
#16 play basketball and football
Y
5
What is the equation of the graphed line written in
standard form?
4
3
2
1
O 2x + 3y = -6
O 2x + 3y = 6
O y=-{x-2
O y=x-2
5-4-3-2 12
1 2 3 4 5
x
2
-3
The equation of the graphed line 2x + 3y = -6 written in standard form is,[tex]\rm y= -\frac{2}{3}x -2[/tex] and for line 2x + 3y = 6 will be,[tex]\rm y = \frac{-2}{3}x+2[/tex]
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
a) 2x + 3y = -6
The line in which the standard form is found as;
Ax + By + C = 0
The typical form of a slope intercept is
y = mx+c
where m denotes the slope and b the line's y-intercept.
[tex]3y= -6-2x\\\\ y=\frac{-6-2x}{3}\\\\ y= -\frac{2}{3}x -2[/tex]
To obtain the slope standard form, we rewrite. The obtained equation is in the form of the slope-intercept.
b) 2x + 3y = 6
The line in which the standard form is found as;
Ax + By + C = 0
The typical form of a slope intercept is
y = mx+c
where m denotes the slope and b the line's y-intercept.
[tex]\rm 3y= 6-2x \\\\ y= \frac{6-2x}{3} \\\\ y = \frac{-2}{3}x+2[/tex]
Hence, The equation of the graphed line 2x + 3y = -6 written in standard form is,[tex]\rm y= -\frac{2}{3}x -2[/tex]
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What is the equation of the graphed line written in standard form?
2x + 3y = -6, 2x + 3y = 6
Summary:
a. The equation of the graphed line 2x + 3y = -6 written in standard form is y= -2/3 x -2.
b. The equation of the graphed line 2x + 3y = 6 written in standard form is y= -2/3 x +2.
translate the question into an equation. Do not solve. Let n be the unknown number. what is 1% of 77?
Answer:
1% × 77 = n
I used multiplication since "of" counts as multiplication.
which graph represents the linear function y=-5x+2
In the number 9,206.457138, what is the value of 1?
Answer:
0.0001 or 1/10000 or 1 ten thousandths
Step-by-step explanation:
The 1 is 4 places after the decimal point so has a value of :
0.0001 or 1/10000 or 1 ten thousandths
Hope this helped and have a good day
Given a polynomial function f(x) = –x2 + 2x + 1 and an exponential function g(x) = 2x, what key features do f(x) and g(x) have in common?
A.)Both f(x) and g(x) decrease over the interval of [1 , ∞).
B.) Both f(x) and g(x) have the same range of (–∞, 2).
C.) Both f(x) and g(x) have the same x-intercept of (–1, 0).
D.)Both f(x) and g(x) have the same y-intercept of (0, 1).
The only key feature that these functions have in common is that they have the same y-intercept. So the correct option is D.
What do these functions have in common?
Here we have the functions:
[tex]f(x) = -x^2 + 2x + 1\\\\g(x) = 2^x[/tex]
f(x) is quadratic, and g(x) is exponential.
Notice that the exponential function has a positive base, so it is increasing. For the quadratic equation we can see a negative leading coefficient, so it opens downwards. So first and second options are false.
Also, g(x) never intersects the x-axis, so third option is false.
Finally, the y-intercepts of the given functions are:
[tex]f(0) = -0^2 + 2*0 + 1 = 1\\\\g(0) = 2^0 = 1[/tex]
So the y-intercepts are equal, meaning that the correct option is D.
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Answer:
Both f(x) and g(x) have the same y-intercept of (0, 1).
Step-by-step explanation:
I got it right on the test.
I need to find values of product and quotient functions
The answers are 8 and 2
What is a function?A function is an equation that establishes a relationship between two or more variables.
Analysis:
r(x) x s(x) = 2[tex]\sqrt{x}[/tex] x [tex]\sqrt{x}[/tex] = 2x
r2(4) = 2 x 4 = 8
r(x)/s(x) = 2[tex]\sqrt{x}[/tex]/ [tex]\sqrt{x}[/tex] = 2
In conclusion, the values of the product and quotient of the functions are 8 and 2 respectively.
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f(x)=x^5+(x+3)^2 which value completed the table
Answer:
three boys shared D 10,500.00 in the ratio 6:7:8.find the largest share.
Twenty-five bakery customers were surveyed to determine if they like cake or pie. The results are shown in the Venn diagram.
Circle C and P overlap. Circle C contains 10, circle P contains 8, and the intersection contains 4. Number 3 is outside of the circles.
Given that a randomly chosen customer likes cake, what is the probability that the customer also likes pie?
The probability that a customer likes cake and pie is 0.16.
What is the probability?Probability is used to determine the odd that a random event would happen. The odds that the event happens usually lie between 0 and 1.
The probability that a customer likes cake and pie = total number of customers who like cake and pie / total number of customers
4/25 = 0.16
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three students measured the width of the whiteboard. Reggie got 2, Jackson got 72, and Pete got 6. The teacher said they were all correct. Draw lines to match each student with the unit he was using.
Answer:
2 yards ; 6 feet ; 72 inches ;
Step-by-step explanation:
2:6:72
1:3:12
1:3 is the ratio of Yards -> Feet
3:12 is the ratio of Feet -> Inch.
6ft = Pete
2 yards = Reggie
72 inches = Jackson
-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)
The ratio of black bags to blue bags is 5to 3 if there are a total of 10 black bags ,then how many blue bags are there
Answer:
6
Step-by-step explanation:
We can think of the 10 black bags as 2 sets of 5-black bags (10 divided into groups of 5; 10 / 5 ; is 2 groups/sets). So, we would also have two sets of 3 (3 x 2 = 6), or 6 bags.
5 : 3 = 10 : 6
(multiply both numbers by 2)
Which equation can be used to solve for x in the following diagram.
Answer:
C. (3x+12) + x = 180
Step-by-step explanation:
the 2 angles create a straight line which is 180 degrees, so (3x+12) + x = 180
I need help to find the coordinates