Consider that we need to find [tex](a+b)(x), (a-b)(x), (ab)(x),\left(\dfrac{a}{b}\right)(x)[/tex].
Given:
The functions are:
[tex]a(x)=4x+9[/tex]
[tex]b(x)=3x-5[/tex]
To find:
The function operations [tex](a+b)(x), (a-b)(x), (ab)(x),\left(\dfrac{a}{b}\right)(x)[/tex].
Solution:
We have,
[tex]a(x)=4x+9[/tex]
[tex]b(x)=3x-5[/tex]
Now,
[tex](a+b)(x)=a(x)+b(x)[/tex]
[tex](a+b)(x)=4x+9+3x-5[/tex]
[tex](a+b)(x)=7x+4[/tex]
Similarly,
[tex](a-b)(x)=a(x)-b(x)[/tex]
[tex](a-b)(x)=4x+9-(3x-5)[/tex]
[tex](a-b)(x)=4x+9-3x+5[/tex]
[tex](a-b)(x)=x+14[/tex]
And,
[tex](ab)(x)=a(x)b(x)[/tex]
[tex](ab)(x)=(4x+9)(3x-5)[/tex]
[tex](ab)(x)=12x^2-20x+27x-45[/tex]
[tex](ab)(x)=12x^2+7x-45[/tex]
And,
[tex]\left(\dfrac{a}{b}\right)(x)=\dfrac{a(x)}{b(x)}[/tex]
[tex]\left(\dfrac{a}{b}\right)(x)=\dfrac{4x+9}{3x-5}[/tex]
Therefore, the required functions are [tex](a+b)(x)=7x+4[/tex], [tex](a-b)(x)=x+14[/tex], [tex](ab)(x)=12x^2+7x-45[/tex] and [tex]\left(\dfrac{a}{b}\right)(x)=\dfrac{4x+9}{3x-5}[/tex].
Plot the points (-6,8) and (-6,-3) on the coordinate plane below.
What is the distance between these two points?
units
Step-by-step explanation:
the distance between these two points is 11 units
PLEASE HELP, I AM MARKING BRAINLEST, dont forget to show work please :)
Value of g(-2) = -8
hope it helps you.....
Answer:
-12
Step-by-step explanation:
-4(-2)^2 -3(-2) -2
-4(4) +6 -2
-16 +6 -2
-12
A function is shown in the table at the right. Find the rate of change over the interval 1≤ x≤ 3 .
Given:
The table of values of a function.
To find:
The rate of change of the function over the interval [tex]1\leq x\leq 3[/tex].
Solution:
The rate of change of a function over the interval [a,b] is:
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
The rate of change of the given function over the interval [tex]1\leq x\leq 3[/tex] is:
[tex]m=\dfrac{f(3)-f(1)}{3-1}[/tex]
From the given table, it is clear that the value of the function is 4 at [tex]x=1[/tex] and 16 at [tex]x=3[/tex].
[tex]m=\dfrac{16-4}{2}[/tex]
[tex]m=\dfrac{12}{2}[/tex]
[tex]m=6[/tex]
Therefore, the rate of change of the given function over the interval [tex]1\leq x\leq 3[/tex] is 6.
Please help ASAP
Will give Brainliest
Want explanation
Answer:
1.73 or 3+√6/√3+√2
Step-by-step explanation:
1. Simplify the Numerator...3+ the square root of 6 cannot be simplified, so the answer is 5.45
2. Simplify the Denominator.
[tex]17 \sqrt{3} - 2 \sqrt{4} \sqrt{4} \sqrt{2} + 3 \sqrt{9} \sqrt{2} - 4 \sqrt{4} \sqrt{4} \sqrt{3} = 17 \sqrt{3} - 8 \sqrt{2} + 9 \sqrt{2} - 16 \sqrt{3} = \sqrt{3} + \sqrt{2} = 3.15[/tex]
3. Divide. 5.45/3.15= 1.73
Choose an equation of a line through the point (-4, 1) perpendicular to y=−12x+3.
Answer:
[tex]y = \frac{1}{12}x + \frac{4}{3}[/tex]
Step-by-step explanation:
slope of perpendicular line: m = [tex]\frac{1}{12}[/tex]
solve for b:
[tex]1 = \frac{1}{12}(-4) + b[/tex]
solve parenthesis:
[tex]1 = -\frac{1}{3}+b[/tex]
add [tex]\frac{1}{3}[/tex] to both sides:
[tex]b = \frac{4}{3}[/tex]
final equation: [tex]y = \frac{1}{12}x + \frac{4}{3}[/tex]
Anita can exercise for 20 minutes on her lunch break and 30 minutes after work on her 5 work days. She exercises 35 minutes on the weekend. How many hours per week does Anita exercise? 4 hours per week 4 hours per week 4 hours per week 5 hours per week
Answer:
4 3/4 hours per week
Step-by-step explanation:
Solve for x
11^x = 11^4* 11^5
Answer:
x = 9 hope i helped and sorry if I'm wrong :)
The value of the square root of 42
[tex]\sqrt{42} =6.480740698/\sqrt{42}[/tex]
Answer:
6.4807 Step-by-step explanation:
The square root of 42 is 6.4807.
is this linear, exponential, or quadratic?
Hello, someone knows the answer, could you help me thank you please ;(
Answer:
22/33and 14/21
1/3
mark as brainiest please
What is wrong with these statements? Correct each one.
2to the power of 3 x 2 to the power of 5 = 215
2^3 x 2^5
8 x 32
256
2^3 x 2^5 = 256
Can someone help i'm struggling!
Answer:$499.20
Step-by-step explanation:
12% of 960 = 115.20
115.20 x 4
= 460.80
960 - 460.80
= $499.20
Answer:
Step-by-step explanation:
960(.88)^4 = $575.71
answer is A
Help me please the numbers I am using is 1,2,2,3,4,5,6,7,8,9
Answer:
2, 4.5 and 8
Step-by-step explanation:
(1)
The mode is the number which occurs most often , then
mode = 2
(2)
The median is the middle value of the numbers arranged in ascending order. If there is no exact middle value then it is the average of the numbers either side of the middle.
1, 2, 2, 3, 4, 5, 6, 7, 8, 9
↑ middle
median = [tex]\frac{4+5}{2}[/tex] = [tex]\frac{9}{2}[/tex] = 4.5
(3)
The range is the difference between the largest and smallest values
range = 9 - 1 = 8
Answer:
If your numbers are 1,2,2,3,4,5,6,7,8,9
Step-by-step explanation:
1.Mode is the data in the value which occurs most frequently.
The mode of your number is 2 cause its frequency is 2 times and its known as bimodal.
2.Median is the middle value when the data is arranged in order of size.
The median of your number is
1,2,2,3,4,5,6,7,8,9
4+5=9
2
=4.5 So,the median is 4.5
3.Range is the difference between the highest value and the smallest value of a given data.
Your range is
Range=9-1=8
I THINK IT MIGHT HELP YOU!!!
Y = -8
Y = -2x - 12
Solve this equation by substitution
Answer:
x = - 2
Step-by-step explanation:
- 8 = - 2x - 12
- 8 + 12 = - 2x - 12 + 12
- 2x = 4
- 2x ÷ - 2 = 4 ÷ - 2
x = - 2
Quick please someone help!!! This is my last day to turn in work and if I don’t I’m getting my phone, tv and privileges to go hang out with friends taken away. I would really like to keep my friends so please help me!!! :,(
Answer:
angle MPN = 79°
angle MPQ = 101°
Given f(x) = x − 7 and g(x) = x2 . What does f(g(4)) =
Answer:
9
Step-by-step explanation:
f(x) = x − 7
g(x) = x^2
Find g(4) = 4^2 = 16
Then find f(g(4)) = f(16) = 16 -7 = 9
Answer:
f(g(4)) = 9
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationComposite FunctionsStep-by-step explanation:
Step 1: Define
Identify
f(x) = x - 7
g(x) = x²
Step 2: Find f(g(4))
Substitute in x [Function g(x)]: g(4) = 4²Evaluate exponents: g(4) = 16Substitute in x [Function f(x)]: f(g(4)) = 16 - 7Subtract: f(g(4)) = 9Which best describes the relationship between the line that passes through the points (-9, -7) and (-12, -2) and the line
that passes through the points (1,9) and (6, 6)?
A. same line
B. perpendicular
C. parallel
D. neither perpendicular nor parallel
Answer:
D
Step-by-step explanation:
y2 - y1 / x2 - x1
-2 - (-7) / -12 - (-9)
5/-3
= -5/3
y2 - y1 / x2 - x1
6 - 9 / 6 - 1
= -3/5
Find mZHFG if mZEFG = 2x + 52, mZEFH = 21°, and mZHFG = 1 + 31
Answer:
m<HFG = 31
Step-by-step explanation:
We can say that m<EFH + m<HFG = m<EFG because of angle addition postulate. Now, we can substitute the values of the angles in.
21 + x + 31 = 2x + 52
x + 52 = 2x + 52
x = 0
Now, we substitute x into the expression of m<HFG:
m<HFG = x + 31
m<HFG = 0 + 31
m<HFG = 31
Can someone help me with this now !
Answer:
its either B or D.
Step-by-step explanation:
could you mark me brainliest pls or even hit the thanks button
What is the complement that is given from the angle?
Answer:
59 is the complement of the angle ABC.
Step-by-step explanation:
complement is what adds to that angle to make it 90 degrees. 31+59=90
Answer:
59 is the complement of the angle ABC.
Step-by-step explanation:
Please help fast it’s subtraction
Answer:
17
220
Result in decimals: 0.077272727272727
Step-by-step explanation:
Answer:
[tex]7\frac{17}{220}[/tex]
Step-by-step explanation:
[tex]9\frac{8}{11} -2\frac{13}{20}=\\[/tex]
[tex]9\frac{160}{220} -2\frac{143}{220}=[/tex]
[tex]=7\frac{17}{220}[/tex]
Hope this helps
What trig ratio would you use to solve for x?
O Cosine
O Tangent
O Sine
Answer: Cosine
This is because cosine involves the adjacent over hypotenuse
cos(angle) = adjacent/hypotenuse
Which answer choice shows a solution set in which all values, when input for x, will be true?
12−(x+2)>2
Answer:
It would be x < 8
Step-by-step explanation:
The interval notation is (-∞, 8)
Hope this helps:)
Consider a single spin on the spinner shown below. A circle is split into sections 1, 2, 4, and 3. A spinner is pointing at number 2. Sections 1 and 2 are shaded. Which events are mutually exclusive? Check all that apply. landing on an unshaded portion and landing on 2 landing on a shaded portion and landing on 3 landing on a shaded portion and landing on an even number landing on an unshaded portion and landing on a number greater than 3 landing on a shaded portion and landing on an unshaded portion
Answer:
The answer is "Options A, B, and E represent mutually exclusive events".
Step-by-step explanation:
Two occurrences that can happen immediately called mutually incompatible. Let's now glance at our options and figure out where the statements are mutually incompatible events.
In Option A: You could see that landing on an unwanted portion and arriving on 2 are events that are locally incompatible, even as undesirable portion contains 3 and 4, and 2 were shaded.
In Option B: Arriving on a shaded part and falling on 3 are also mutually incompatible because there are 3 on a windows azure.
In Option C: A darkened portion and an increasing amount can land while 2 would be an even number as well as on the shaded portion. That number is very much the same.
In Option D: At the same time as 4 is greater than 3 and it is situated upon an undistressed section, landing and attracting a number larger than 3 can happen.
In Option E: Landing on a shaded part and landing on even a shaded part is an excluding event, since shaders may either be shaded or unlit.
Answer:
first, second and fifth
Step-by-step explanation:
edge 2021
Find the value of x. Express your answer in simplest radical form.
Answer:
D
x=5*sqrt(2)/2
Step-by-step explanation:
since it is a right triangle, and one of the other angles is 45, we know that the last angle must also be 45 since the 3 interior angles must be 180
then using pythagroem theorem
sqrt(a^2+b^2)=c
sqrt(x^2+x^2) = 5
square both sides
x^2+x^2=25
2x^2=25
x^2=25/2
square root both sides
x= sqrt(25/2)=5/sqrt(2)
rationalize the demonominator by multiplying by sqrt(2)/sqrt(2)
x=5*sqrt(2)/2
Algebra 2 Problem! Rational Roots
Answer:
este no hablo inglés
In the following function defined by an equation in the form y = ax + bx+c, identify the values of a, b, and c.
y = 5x2 + 2x-1
a. d=-1, b = 2,0 = 5
b. a = -2, b = 5,0 = 1
C. a = 1, b = 5,0 = 2
d. a = 5,6 = 2,0 = -1
Answer:
d
Step-by-step explanation:
just compare,
y = aX^2+bX+C and
y = 5X^2 + 2X - 1
i need help asap …………..
Step-by-step explanation:
since the radii are all congruent, you can just draw a new one and call it KP. KP = 5 because all radii are congruent. By doing this, point P is now a tangent.
the measures of the angles of a triangle are shown in the figure. solve for x
Answer:
10
Step-by-step explanation:
First, we know that the angles of a triangle add up to 180 degrees. We can then sum up our angles as 90 (since it's a right triangle, represented by the square in the bottom left angle) +27+6x+3=180
90+27+6x+3=180
Add up left side
120+6x=180
Subtract 120 from both sides
6x=60
Divide both sides by 6
x=10
Area of circle =
A) 36 pie square units
B) 6 pie square units
C) 12 pie square units
Answer:
36 pi
Step-by-step explanation:
The radius is 6
A = pi r^2
A = pi 36
Answer:
Area of circle = 36 π square unit
Step-by-step explanation:
To calculate area of circle simplify formula area of circle . we have given radius of circle which is 6.
Area of circle = π × r²
where,
r is the radius of circlesubstitute the value
Area of circle = π × ( 6 ) ²
expand the exponent
Area of circle = π × 36
multiply
Area of circle = 36 π square unit