F(x)=5/6x+3 Which of the following is true
How to write an equation of the line through the point (-2,1) that is perpendicular to the line 5x+9y=-9
Answer:
[tex]\large\boxed{y=\dfrac{5}{9}x+\dfrac{19}{9}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\\text{We have the equation i the standard form.}\\\text{ Convert it to the slope-intercept form}\ y=mx+b:\\\\5x+9y=-9\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\9y=-5x-9\qquad\text{divide both sides by 9}\\\\y=-\dfrac{5}{9}x-1\to m_1=-\dfrac{5}{9}\\\\m_2=-\dfrac{1}{m_1}\to m_2=-\dfrac{1}{-\frac{5}{9}}=\dfrac{9}{5}[/tex]
[tex]\text{We have the equation:}\\\\y=\dfrac{5}{9}x+b\\\\\text{Put the coordinates of the point (-2, 1) to the equation:}\\\\1=\dfrac{5}{9}(-2)+b\\\\1=-\dfrac{10}{9}+b\qquad\text{add}\ \dfrac{10}{5}\ \text{to both sides}\\\\\dfrac{19}{9}=b\to b=\dfrac{19}{9}[/tex]
which function is represented by the graph?
a. f(x)=|x-1|+3
b. f(x)=|x+1|-3
c. f(x)=|x-1|-3
d. f(x)=|x+1|+3
Answer with Step-by-step explanation:
As we can clearly see from the graph the value of f(x)=0 at x=2 and x= -4
a. f(x)=|x-1|+3
at x=2
f(2)=|2-1|+3
= 1+3
=4
Hence, this function is not represented by the graph
c. f(x)=|x-1|-3
at x=2
f(2)= |2-1|-3
= 1-3
= -2
Hence, this function is not represented by the graph
d. f(x)=|x+1|+3
at x=2
f(2)= |2+1|+3
= 3+3
= 6
Hence, this function is not represented by the graph
Hence, Correct option is:
b. f(x)=|x+1|-3
Answer:
The answer is B
Step-by-step explanation:
If 32x+1 - 3^x+5, what is the value of x?
Answer:
x = 4
Step-by-step explanation:
hope this helps!!!
Solve the following system of equations using any method
2x+4y+1z=−35
3x+7y+7z=−34
2x+10y+6z=−64
Answer:
values of x,y and z are x = -2, y= -9 and z=5
Step-by-step explanation:
2x+4y+1z=−35 eq(1)
3x+7y+7z=−34 eq(2)
2x+10y+6z=−64 eq(3)
We can solve using elimination method
Subtracting eq (1) from eq(3)
2x + 10y +6z = -64
2x +4y +1z = -35
______________
6y + 5z = -29 eq(3)
Multiplying eq(2) with 2 and eq(3) with 3 and subtracting
6x + 14y +14z = -68
6x + 30y +18z = -192
- - - +
_________________
-16y -4z = 124 eq(4)
Multiply eq(3) with 4 and eq(4) with 5 and add both equations
24y + 20z = -116
-80y - 20z = 620
______________
-56y = 504
y = -504/56
y= -9
Putting value of y in equation(3)
6y + 5z = -29
6(-9) + 5z = -29
-54 + 5z = -29
5z = -29+54
5z = 25
z = 25/5
z =5
Now, putting value of y and z in eq(1)
2x + 4y +1z = -35
2x + 4(-9) +1(5) = -35
2x -36+5 = -35
2x -31 = -35
2x = -35+31
2x = -4
x= -4/2
x=-2
So, values of x,y and z are x = -2, y= -9 and z=5
The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same. The volume of pyramid A is the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is the volume of pyramid A.
Answer:
Part 1) The volume of pyramid A is two times the volume of pyramid B
Part 2) The new volume of pyramid B is equal to the volume of pyramid A
Step-by-step explanation:
we know that
The volume of a pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base of pyramid
h is the height of the pyramid
Part 1
The heights of the pyramids are the same
Find the volume of pyramid A
Find the area of the base B
[tex]B=10*20=200\ m^{2}[/tex]
substitute
[tex]VA=\frac{1}{3}(200)h[/tex]
[tex]VA=\frac{200}{3}h\ m^{3}[/tex]
Find the volume of pyramid B
Find the area of the base B
[tex]B=10^{2}=100\ m^{2}[/tex]
substitute
[tex]VB=\frac{1}{3}(100)h[/tex]
[tex]VB=\frac{100}{3}h\ m^{3}[/tex]
Compare the volumes
[tex]VA=2VB[/tex]
The volume of pyramid A is two times the volume of pyramid B
Part 2)
If the height of pyramid B increases to twice that of pyramid A
we have that
[tex]VA=\frac{200}{3}h\ m^{3}[/tex]
Find the new volume of pyramid B
we have
[tex]B=100\ m^{2}[/tex]
[tex]h=2h\ m[/tex]
substitute
[tex]VB=\frac{1}{3}(100)(2h)[/tex]
[tex]VB=\frac{200}{3}h\ m^{3}[/tex]
Compare the volumes
[tex]VA=VB[/tex]
The new volume of pyramid B is equal to the volume of pyramid A
Answer:
The volume of pyramid A is twice the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is equal to the volume of pyramid A.
Step-by-step explanation:
Correct for plato :)
d/dx(1+x^4+x^6/x^2+x+1)
A)2x+1
B)2x-1
C)2
D)0
\frac{d}{dx}\left(\frac{1+x^4+x^6}{x^2+x+1}\right)=\frac{4x^7+5x^6+8x^5+3x^4+4x^3-2x-1}{\left(x^2+x+1\right)^2}
copy and paste that into a URL
Which is an equivalent form of the compound inequality −44 > −2x − 8 ≥ −8?
Answer:
22 and 0
Step-by-step explanation:
−44 > −2x − 8 ≥ −8?
/-2 - 44 > -2x / . -2 -8 ≥ -8
= 22 +8 =0
Answer:
An equivalent form of the compound inequality is the pair of single inequalities:
-2x - 8 < - 44, and −2x − 8 ≥ −8Explanation:
You can split the compound inequality into two equivalent inequalities by taking each side from the variable.
The compound inequality −44 > −2x − 8 ≥ −8 means that two conditions must be satisfied:
1. From the left side: - 44 > - 2x - 8
2. From the right side: −2x − 8 ≥ −8
Then, as a first approach you can tell that an equivalent form of the compound inequality is the pair of single inequalities:
-44 > -2x - 8, and −2x − 8 ≥ −8You should put the variable on the left sides, which will yield the best form of an equivalent pair of inequalitis.
- 2x - 8 < -44, and- 2x - 8 ≥ - 8That is the best choice of an equivalent form, and from there you can solve the inequalities which will permit to obtain the solution. Of course, you can manipulate the variable and find many other equivalent forms.
Notice, that both inequalities must be satisfied simultaneously.
This is how you solve that system
- 2x - 8 < -44nAdd 8 to both sides: - 2x < -36
Divide both sides by - 2 (you have to change the sign): x > 18
- 2x - 8 ≥ - 8-
Add 8 to both sides: - 2x ≥ 0
Divide by - 2 (again, you must change the sign): x ≤ 0
Then, the solution set is:
x > 18 and x ≤ 0 and that is an empty set, since x cannot be at the same time greater than 18 and less or equal to 0.This is, you conclude that the compound inequality is false, because there is not a value of x which is a solution.
The figure shown is a composite figure. What is its volume?
2,622
2,109
3,648
1,387
Answer:
2622
Step-by-step explanation:
The answer can be found by adding up the volume of the two parts of the composite figure, which consists of a triangular prism and a rectangular prism
Volume of the rectangular prism=(Width)(Height)(Length)
=12*7*19
=1596
Volume of the triangular prism=(Base area)(Height)
If the triangle consisting of the sides 9, 12, 15 is a right angled triangle, 9²+12²=15²
The statement above is true
The triangle above is a right angled triangle, where 9 is the height and 12 is the base
Triangle area=(height)(base)(0.5)
=9*12*0.5
=54
Volume of triangular prism=54*19
=1026
Adding up both=1596+1026=2622
V = V1 + V2
V1 = 0.5 x 9 x 12 x 19
V1 = 1,026
V2 = 12 x 19 x 7
V2 = 1,596
V = V1 + V2
V = 1,026 + 1,596
V = 2,622
The answer is 2,622.
If f(x) = 4x + 3 and g(x) = 3x, evaluate for X = -1/2
Answer:
[tex]f(-\frac{1}{2}) = 1[/tex]
[tex]g(-\frac{1}{2} ) = -\frac{3}{2}[/tex]
Step-by-step explanation:
Given the function [tex]f(x) = 4x + 3[/tex] and the function [tex]g(x) = 3x[/tex], to evaluate for [tex]x=-\frac{1}{2}[/tex], you need to substitute it into each function.
Then, for the function f(x), when [tex]x=-\frac{1}{2}[/tex], you get:
[tex]f(-\frac{1}{2}) = 4(-\frac{1}{2}) + 3[/tex]
[tex]f(-\frac{1}{2}) = 4(-\frac{1}{2}) + 3[/tex]
[tex]f(-\frac{1}{2}) = -\frac{4}{2}+ 3[/tex]
[tex]f(-\frac{1}{2}) = -2 + 3[/tex]
[tex]f(-\frac{1}{2}) = 1[/tex]
For the function g(x), when [tex]x=-\frac{1}{2}[/tex], you get:
[tex]g(-\frac{1}{2} ) = 3(-\frac{1}{2})[/tex]
[tex]g(-\frac{1}{2} ) = -\frac{3}{2}[/tex]
Answer:
f(-1/2) = 1
g(-1/2) =-3/2
Step-by-step explanation:
f(x) = 4x+3
Let x = -1/2
f(-1/2) = 4(-1/2) +3
f(-1/2) = -2 +3
f(-1/2) =1
g(-1/2) = 3(-1/2)
= -3/2
help pleeesea!!!!!!!!!!!.Trina downloaded 3 music albums and 5 audio books one week at a cost of $49.60. The next week she downloaded 1 music album and 2 audio books at a cost of $20.50. Her mother wants to write a system of equations to determine the price of one music album and one audio book. She uses the variables x and y. She lets x represent the cost of one music album. What will y represent?
Y is the Audio Book.
"determine the price of one music album and one audio book"
"She lets x represent the cost of one music album."
According to this information "One Audio Book" should be the correct answer. Have a great day!
Answer:
y will represent the cost of one audio book.
Step-by-step explanation:
Here, the cost of 3 music albums and 5 audio books is $49.60 and 1 music album and 2 audio books is $20.50,
Since, there are two unknown values,
First one is the cost of one music album,
Second one is the cost of one audio book,
We know that, for finding an unknown value we take a variable,
If we have variables x and y in which x represent the cost of one music album, then y must represent the cost of one audio album.
find the interior angle of a regular polygon which has 6 sides
Answer:
120°.
Step-by-step explanation:
The sum of all interior angles in a polygon with [tex]n[/tex] sides ([tex]n\in \mathbb{Z}[/tex], [tex]n \ge 3[/tex]) is equal to [tex](n - 2) \cdot 180^{\circ}[/tex]. (Credit: Mathsisfun.)
The polygon here has 6 sides. [tex]n = 6[/tex]. Its interior angles shall add up to [tex](6 - 2) \times 180^{\circ} = 720^{\circ}[/tex].
Consider the properties of a regular polygon. (Credit: Mathsisfun.)
All sides in a regular polygon are equal in length. All angles in a regular polygon are also equal.There are six interior angles in a polygon with 6 sides. All six of them are equal. Thus, each of the six interior angle will be
[tex]\displaystyle \frac{1}{6}\times 720^{\circ} = 120^{\circ}[/tex].
help answer question 2
A spinner is divided into 8 equal sections, and each section contains a number from 1 to 8. What is the probability of the spinner landing on 5?
A. 1/13
B.1/8
C. 5/13
D. 5/8
A line passes through the point (8.-8) and has a slope of -5/4.
Write an equation in point-slope form for this line.
plz
[tex]\bf (\stackrel{x_1}{8}~,~\stackrel{y_1}{-8})~\hspace{10em} slope = m\implies -\cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-8)=-\cfrac{5}{4}(x-8)\implies y+8=-\cfrac{5}{4}(x-8)[/tex]
The equation in point-slope form for this line is 4y = -5x + 8.
What is point-slope form of equation of straight line ?The equation of a straight line in the form y = mx + c where m is the slope of the line and c is its y-intercept is known as the point-slope form. Here both the slope (m) and y-intercept (c) have real values. It is known as point-slope form as it gives the definition of both the slope, y-intercept and the points mentioned in the line.
How to form the given equation of straight line ?It is given that the line passes through the point (8.-8) and has a slope of -5/4.
The general representation for straight line is y = mx + c .
Here, m = -5/4 , x = 8 and y = -8 .
Thus we have ,
⇒ -8 = -5/4 * 8 + c
⇒ c = 10 - 8
∴ c = 2
The y-intercept is 2.
The equation of straight line becomes,
⇒ y = -(5/4)x + 2
∴ 4y = -5x + 8
Therefore, the equation in point-slope form for this line is 4y = -5x + 8.
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How is a system of equations created when each linear function is given as a set of two ordered pairs? Explain
Answer:
If each linear function is given as a set of two ordered pairs, you need to use those points to find the equation of each line, and then solve the system of equations.
For example:
Let's say that f(x) has the following ordered pais: (a, b) and (c, d) and g(x) has the following ordered pais: (e, f) and (g, h). We know that the general equation of a line is the following:
(y - yo) = m(x-xo), where 'm' represents the slope and (xo, yo) any point from the line.
The slope will be given by: (y1 - yo)/(x1 - x0).
For example, the equation of the line of f(x) is:
f(x) = (y - b) = [(d - b)/(c - a)](x-a)
You do the same for the function g(x), and then you are all set to solve the system of equations!
Answer:
Sample response: Use the two points of a linear function to write an equation in slope-intercept form by first finding the slope of the function, and then using a point and the slope to determine the y-intercept. Write the equations in slope-intercept form.
Which is a reasonable first step that can be used to solve the equation
Answer:
Use distributive property:
2x + 12 = 3x - 12 + 5
Step-by-step explanation:
This can allow for combining like terms later on, and eventually isolating x as a variable.
For this case we have the following equation:
[tex]2 (x + 6) = 3 (x-4) +5[/tex]
The first step we must follow to solve the equation is to apply distributive property to the terms within the parenthesis:
[tex]a (b + c) = ab + ac[/tex]
Then, the equation is:
[tex]2x + 12 = 3x-12 + 5[/tex]
Answer:
The first step is to apply distributive property to the terms within parentheses.
geometry archive find x simplify completely triangle with 16,25, and x
Answer:
x = 20
Step-by-step explanation:
see attached
From Pythagoras, [tex]\(z^2 - y^2 = 369\)[/tex]. Solving, z - y = 19, z + y = 19, yielding z = 19. Substituting, x = 17.
Given that Triangle A and Triangle B are right angle triangles with similar heights 'x' and different perpendicular (say 'y' and 'z' respectively).
From the Pythagoras theorem, we know that:
[tex](Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2[/tex]
Substituting the given values, we get:
[tex]y^2 = 16^2 + x^2[/tex]
[tex]z^2 = 25^2 + x^2[/tex]
Subtracting the two equations, we get:
[tex]z^2 - y^2 = 25^2 - 16^2[/tex]
(z - y)(z + y) = 625 - 256 = 369
z - y = 19
z + y = 369 / 19 = 19
Adding the two equations, we get:
2z = 38
z = 19
Substituting the value of 'z' in the equation:
[tex]z^2 = 25^2 + x^2[/tex]
[tex]19^2 = 25^2 + x^2[/tex]
[tex]x^2 = 19^2 - 25^2 = 289[/tex]
[tex]x = sqrt(289)[/tex] = 17
Therefore, the value of 'x' is 17.
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What is the value of m in the figure below? If necessary,round your answer to the nearest tenth of a unit
Answer:
D
Step-by-step explanation:
It turns out from similar triangles, that 7/BD = BD / 18. Use triangles ABD and BDC to show this relationship. Solving this equation will give you BD
BD^2 = 7*18
BD^2 = 126 Just leave it in this form. Do your rounding at the end.
Because triangle BDC is a right angle triangle, use the Pythagorean Theorem to solve for m
m^2 = BD^2 + 7^2
m^2 = 126 + 49
m^2 = 175 Take the square root of both sides.
sqrt(m^2) = sqrt(175)
m = 13.22
so the answer is D
Solve the formula Ax+ By = C for x.
Answer:
x = (C-By)/A
Step-by-step explanation:
Ax+ By = C
We want to isolate x
Subtract By from both sides
Ax+ By-By = C-By
Ax = C - By
Now divide both sides by A
Ax/A = (C-By)/A
x = (C-By)/A
[tex]Ax+ By = C\\Ax=C-By\\x=\dfrac{C-By}{A}[/tex]
Find y. Round to the nearest tenth.
Please help me!!!
Answer:
y ≈ 358.3 ft
Step-by-step explanation:
The angle in the right side of the triangle = 28° ( alternate angle )
Using the tangent ratio in the right triangle to solve for y
tan28° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{350}{y}[/tex]
Multiply both sides by y
y × tan28° = 350 ( divide both sides by tan28° )
y = [tex]\frac{350}{tan28}[/tex] ≈ 658.3 ft
y = 658.3ft. The value of the side y of the right triangle shown in the image is 658.3ft.
The key to solve this problem we have to use the trigonometric functions tan θ = opposite leg/adjacent leg
To find side y, where opposite leg = 350ft, adjacent leg = y, and θ = 28° by symmetry:
tan θ = opposite leg/adjacent leg
tan 28° = 350ft/y
Clear y:
y = 350ft/tan 28°
y = 658.254ft
Round to the nearest tenths y = 658.3ft
Which best describes the transformation that occurs from
the graph of f(x) = x² to g(x) = (x - 2)2 + 3?
right 2, up 3
left 2 down 3
right 2, down 3
left 2, up 3
Answer:
right 2, up 3
Step-by-step explanation:
The original function is:
[tex]f(x) = x^2[/tex]
Translated to:
[tex]g(x)=(x-2)^2+3[/tex]
Lets look at the constants that are added or subtracted to determine the transformation.
As -2 is is added to x (grouped with x), the transformation is a horizontal transformation. The shift is of two to the right.
As +3 is not grouped with x, the transformation is vertical. The shift is vertical shift of 3 to upward direction.
So the correct answer is:
right 2, up 3 ..
what is the equation of the linear function represented by the table?
Answer:
y = -3x+17
Step-by-step explanation:
1. Find the change in y corresponding to the change in x. In this case x is changing by +3 and y is changing by -3. That is your m in y=mx=b.
2. y= -3x + b
To find b substitute a set into the equation. I used 4 and 5.
5= -3(4) +b
3. 5= -12 +b ,add 12 to both sides.
17= b
4. y = -3x+17
Answer:
a y= -x+9
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar. Consider the given table. x -2 2 5 9 f(x) 5 17 26 ?
The "?" in the table represents the number because the average rate of change on every interval of the function is .
The missing value in the table is 38, obtained by using the concept of average rate of change which is consistent across the given values, suggesting that the function is linear.
Explanation:In this question, the student needs to find the unknown value denoted by the "?" in the table of a function f(x), whose x-values are -2, 2, 5, 9, and the corresponding f(x)-values are 5, 17, 26, and unknown (?) respectively.
To predict the next value, we can use the concept of the average rate of change which is defined as the difference in the y-values divided by the difference in the x-values over the interval. This rate of change is the same between every pair of successive x-values in this table which suggests that the function might be linear.
We can calculate this using the formula, Average Rate of Change = Δf(x) / Δx. To illustrate, the average rate of change from x = -2 to x = 2 is (17-5) / (2 - (-2)) = 12 / 4 = 3. Similarly, the change from x = 2 to x = 5 is (26 - 17) / (5 - 2) = 9 / 3 = 3. Thus, the average rate of change is constant and equals 3.
If we follow the same pattern, then the missing f(x) value when x = 9 should be 26 (the last provided y-value) plus 4 (which is the next x interval) times 3 (the average rate of change) = 26 + 4*3 = 38. Hence, the missing value denoted by "?" is 38.
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Quotient of 32 and -8
Answer:
-4
Step-by-step explanation:
mark branliest :))
Hello There!
The quotient of 32 and -8 is -8.
When dividing a positive number by a negative number, your final result will always end up with a negative number so 32 divided by 8 is 4 but it will be -4 instead of 4
a negative slope means that the line moves up from left to right
No the negative slope means the line moves down from left to right.
Hope this helps.
r3t40
Answer:
It slopes upwards from right to left.
Step-by-step explanation:
A negative slope means that a line rises from right to left. Like a back slash \.
Please help me! I don’t need a long explanation
Answer:
- [tex]\frac{\sqrt{2-\sqrt{2} } }{2}[/tex]
Step-by-step explanation:
Note that [tex]\frac{5\pi }{8}[/tex] is in the second quadrant
where cos < 0 , hence overall sign will be negative
Using the half- angle formula
cos [tex]\frac{5\pi }{8}[/tex]
= - [tex]\sqrt{\frac{1+cos\frac{5\pi }{4} }{2} }[/tex]
= - [tex]\sqrt{\frac{1-\frac{\sqrt{2} }{2} }{2} }[/tex]
= - [tex]\sqrt{\frac{2-\sqrt{2} }{4} }[/tex]
= - [tex]\frac{\sqrt{2-\sqrt{2} } }{2}[/tex]
edgar divided a five digit number by a two digit number.there was no remainder. what is the least possible quotient of the two numbers? A.100 B.102 C.111 D.1000
the least possible quotient of the two numbers would be C.) 111
What is the distance between (-5,8) and (4,6)
Answer:
[tex]\sqrt{85}[/tex] (about 9.2195) units
Step-by-step explanation:
The formula for the distance between two points is: [tex]\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Substitute the values. [tex]\sqrt{(-5 - 4)^2 + (8 - 6)^2}[/tex]
Subtract. [tex]\sqrt{(-9)^2 + 2^2}[/tex]
Solve the exponents. [tex]\sqrt{81 + 4}[/tex]
Add. [tex]\sqrt{85}[/tex]
This is as simple as the solution can get without estimating, but we can use a calculator to estimate that the distance is about 9.2195 units.
Hey there! :)
Find the distance between (-5, 8) (4, 6)
The formula to find the distance is : d = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2[/tex]
Where : -5 = x1 , 4 = x2 , 8 = y1 , 6 = y2
Now, simply plug everything into our equation.
[tex]d = \sqrt{(4 + 5)^2 + (6 - 8)^2}[/tex]
Let's simplify this now.
[tex]d = \sqrt{9^2 - 2^2}[/tex]
Simplify again.
[tex]d = \sqrt{81 + 4} = \sqrt{85}[/tex]
Therefore, our distance is [tex]\sqrt{85}[/tex] OR 9.22
Hope this helped! :)
Select all the correct statements.
The amount in dollars an electrician charges in terms of the number of hours worked is represented by the function y = 22x + 42.
From the function, identify all the phrases that hold true for the situation.
The electrician charges an initial fee of $22
The y-variable represents the number of hours
The electrician charges an initial fee of $42
The electrician charges $22 for every hour worked
The X-variable represents the electricians charges in dollars
The electrician charges $42 for every hour worked
Answer:
"The electrician charges an initial fee of $42", AND "The electrician charges $22 for every hour worked" is true.
Step-by-step explanation:
The equation is y=22x+42.
The formula is y=mx+b.
m is the slope, or is this case, the number of dollars for every "x", which is the number of hours worked. So you have to pay $22 for every hour the electrician works.
b is the y-intercept, or the amount it starts with, in this case, you have to pay a fee of $42 even when the electrician worked 0 hours. This is because $42 is the amount it starts with.
On a graph, the line will start at (0,42) because that is when you start paying. And then it will increase by 22 for each hour, so the next coordinate would be (1,64).
The equation y = 22x + 42 indicates that an electrician charges a base fee of $42, plus an additional $22 for every hour worked. Thus, the correct statements are 'The electrician charges an initial fee of $42' and 'The electrician charges $22 for every hour worked.'
Explanation:The equation y = 22x + 42 is a linear function where the y-variable represents the total dollars the electrician charges and the x-variable represents the number of hours worked. From this equation, we can immediately discern two truths:
The electrician charges an initial fee of $42. This is the y-intercept of the function, indicating the base charge before any work has been done.The electrician charges $22 for every hour worked. This is the slope, or 'm', of the function and indicates the rate at which the total cost changes per hour of work.Learn more about Linear Function Interpretation here:https://brainly.com/question/32914656
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