(Precalc) NEED HELP 100PTS: (−2 ≤ x ≤ 2) f(x) = csc(x)
A. Find the intervals on which the graph of y = f(x) is increasing and the intervals on which the graph of y = f(x) is decreasing. Answer in interval notation.
Increasing: ___
Decreasing: ___
B. Find all relative extrema, if any, of the graph of y = f(x).
Relative min: ___
Relative max: ___
Thank youu!! <333
Answers
Answer:
Step-by-step explanation:
y=csc(x) x∈ [-2,2]
[tex]A.\\\displaystyle\\Increasing: \ [-2,-\frac{\pi }{2})U(\frac{\pi }{2},2]\\\\Decreasing:\ (-\frac{\pi }{2},0)U(0,\frac{\pi }{2} ) \\\\B.\\\\Relative\ min:\ 1\\\\Relative \ max:\ -1[/tex]
Watching the graph:
Answer:
[tex]\textsf{Increasing}:\left[-2,-\dfrac{\pi}{2}\right) \textsf{ and }\left(\dfrac{\pi}{2},2\right][/tex]
[tex]\textsf{Decreasing}:\left(-\dfrac{\pi}{2}, 0\right) \textsf{ and }\left(0, \dfrac{\pi}{2}\right)[/tex]
[tex]\textsf{Relative min}: \left(\dfrac{\pi}{2},1 \right)[/tex]
[tex]\textsf{Relative max}: \left(-\dfrac{\pi}{2},-1 \right)[/tex]
Step-by-step explanation:
Part A
Given function:
[tex]f(x)=\csc (x), \quad -2\leq x\leq 2[/tex]
[tex]\csc(x)=\dfrac{1}{\sin(x)}[/tex]
Therefore, the function f(x) is undefined when sin(x) = 0, leading to vertical asymptotes at the value of x where sin(x) = 0.
[tex]\sin(x) = 0 \textsf{ at }x = 0\pm 2 \pi n, \pi \pm 2 \pi n[/tex]
Therefore, f(x) has a vertical asymptotes at x = -2π, -π, 0, π, 2π etc.
Where the graph of the sine function increases, the graph of the cosecant function decreases.
Where the graph of the sine function decreases, the graph of the cosecant function increases.
The sine function increases on the intervals:
[tex]\left(-\dfrac{\pi}{2}\pm 2 \pi n, \dfrac{\pi}{2}\pm 2 \pi n\right)[/tex]
and decreases on the intervals:
[tex]\left(\dfrac{\pi}{2}\pm 2 \pi n, \dfrac{3\pi}{2}\pm 2 \pi n\right)[/tex]
Therefore, for the interval -2 ≤ x ≤ 2, the cosecant function f(x):
Increases on the intervals:
[tex]\left[-2,-\dfrac{\pi}{2}\right) \textsf{ and }\left(\dfrac{\pi}{2},2\right][/tex]
Decreases on the intervals:
[tex]\left(-\dfrac{\pi}{2}, 0\right) \textsf{ and }\left(0, \dfrac{\pi}{2}\right)[/tex]
Part B
The relative minimums of the graph of the sine function are the relative maximums of the graph of the cosecant function.
The relative maximums of the graph of the sine function are the relative minimums of the graph of the cosecant function.
The sine function has a range of -1 ≤ sin(x) ≤ 1.
Therefore, its minimum points are when sin(x) = -1 and its maximum points are when sin(x) = 1.
[tex]\sin(x)=-1 \implies x=\dfrac{3\pi}{2}\pm 2 \pi n \implies \textsf{Minimum points}: \left(\dfrac{3\pi}{2}\pm 2 \pi n ,-1 \right)[/tex]
[tex]\sin(x)=1 \implies x=\dfrac{\pi}{2}\pm 2 \pi n \implies \textsf{Maximum points}: \left(\dfrac{\pi}{2}\pm 2 \pi n,1 \right)[/tex]
Therefore, the minimum and maximum points of the cosecant function in the given interval -2 ≤ x ≤ 2 are:
[tex]\textsf{Relative min}: \left(\dfrac{\pi}{2},1 \right)[/tex]
[tex]\textsf{Relative max}: \left(-\dfrac{\pi}{2},-1 \right)[/tex]
Note in the attached graph:
The given interval -2 ≤ x ≤ 2 is shown shaded in green.Vertical asymptotes are shown as red dashed lines.Function f(x) is the black curve.The sine function is the blue dashed curve.Relative min/max shown as black points.
Related Questions
Show that the point (1,-1,2) is common to the lines which join (6,-7,0) to (16,-19,-4) and (0,3,-6) to (2,-5,10).
Answers
Answer:
The given point satisfies both equations of a line, hence is common to the two lines.
Step-by-step explanation:
Given two lines, one joining the points (6,-7,0) to (16,-19,-4), and the other joining the points (0,3,-6) to (2,-5,10), you want to show that the point (1, -1, 2) is common to those lines.
Equation of a lineThe equation of a line through points (x1, y1, z1) and (x2, y2, z2) can be written:
(x -x1)/(x2 -x1) = (y -y1)/(y2 -y1) = (z -z1)/(z2 -z1)
For the first pair of points, the equation of the line is ...
(x -6)/(16 -6) = (y +7)/(-19 +7) = (z -0)/(-4 -0)
(x -6)/10 = -(y +7)/12 = -z/4 . . . . . line 1
For the second pair of points, the equation of the line is ...
(x -0)/(2 -0) = (y -3)/(-5 -3) = (z +6)/(10 +6)
x/2 = -(y -3)/8 = (z +6)/16 . . . . . line 2
Point on the line?If the given point is on each of these lines, then it will satisfy each of the equations.
Line 1: (1 -6)/10 = -(-1 +7)/12 = -2/4 ⇒ -5/10 = -6/12 = -2/4 . . . true
The given point is on Line 1.
Line 2: (1)/2 = -(-1-3)/8 = (2+6)/16 ⇒ 1/2 = 4/8 = 8/16 . . . true
The given point is on Line 2.
The given point is common to both lines.
__
Alternate solution
For points A and B and parameter p, we can write the parameterized equation of each line as ...
(x, y, z) = A +p(B -A)
Using parameters t and s for the two lines, we get ...
Line 1: (x, y, z) = (6, -7, 0) +t(16 -6, -19 +7, -4 -0) = (6 +10t, -7 -12t, 0 -4t)
Line 2: (x, y, z) = (0, 3, -6) +s(2 -0, -5 -3, 10 +6) = (0 +2s, 3 -8s, -6 +16s)
A common point will be found where (x, y, z) for some value of t matches (x, y, z) for some value of s. We can find those values of s and t by solving simultaneous equations for any pair of the variables (x, y, z). The equations are ...
6 +10t = 2s-7 -12t = 3 -8s-4t = -6 +16sBy any of your favorite methods, these equations have the solution (t, s) = (-0.5, 0.5). The point the lines have in common is ...
(6 +10(-0.5), -7 -12(-0.5), 0 -4(-0.5)) = (6 -5, -7 +6, 2) = (1, -1, 2)
The common point to the two lines is (1, -1, 2).
The ratio of a to b is constant, and
a = 9 when b = 6. What is the value of
b when a = 2?
Answers
Answer:
Step-by-step explanation:
a : b
9 : 6
2 : x
Cross multiply
6*2 = 9x
12 = 9x
12/9 = x
4/3 = x
What is 8.7x3.9 in a step by step
Answers
X3.9
———
87 times 9 is 783 + 30 times 87 is 2610 so 3393 now since there are 2 decimal spots you put a decimal 2 over to make 33.93
Use integration and trigonometric substitution to find the area enclosed by the ellipse: x 2 4 y 2 81 = 1 .
Answers
The area enclosed by the ellipse [tex]\frac{x^2}{4}+\frac{y^2}{81}=1[/tex] is 60 square units.
The general form of the equation of ellipse is [tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]
Given the equation of ellipse is, [tex]\frac{x^2}{4}+\frac{y^2}{81}=1[/tex]
⇒ [tex]\frac{x^2}{2^2}+\frac{y^2}{9^2}=1[/tex]
That is, a = 2 and b = 9
Now, [tex]\frac{y^2}{9^2} = 1 -\frac{x^2}{2^2}[/tex]
⇒ [tex]y=\frac{9}{2} \sqrt{4-x^2}[/tex]
Area enclosed by the ellipse = 4 x Area of ellipse in the first quadrant
Therefore, Area of ellipse in the first quadrant, A = [tex]\int\limits^a_0{\frac{9}{2} \sqrt{4-x^2}} \, dx[/tex]
Using Substitution ,x = 2cosθ, then dx = -2sinθdθ and x = 0⇒ θ = π/2 and x = 2⇒ θ = 0
A = [tex]\int\limits^a_0{\frac{9}{2} \sqrt{4-4cos^2\theta}} \, dx[/tex]
= [tex]\int\limits^2_0{\frac{9}{2}\times2 \sqrt{1-cos^2\theta}} \, dx[/tex]
= [tex]\int\limits^2_0{9 sin^2\theta} \, dx[/tex]
= [tex]\int\limits^0_\frac{\pi}{2} {9 sin^2\theta} (-2sinx)\, d\theta[/tex]
= [tex]\int\limits^\frac{\pi}{2} _0{18 sin^3\theta} \, d\theta[/tex]
= [tex]\int\limits^\frac{\pi}{2} _0{18 (\frac{3sin\theta-sin3\theta}{4} )} \, d\theta[/tex]
= [tex]\frac{9}{2} \int\limits^\frac{\pi}{2} _b {3sin\theta} \, d\theta -\frac{9}{2} \int\limits^\frac{\pi}{2} _0 {sin3\theta} \, d\theta[/tex]
= 27/2 x (-cosθ) - 9/6 x (-cos3θ) | θ = 0 to θ = π/2
= 15 square units.
Therefore, the area enclosed by ellipse [tex]\frac{x^2}{4}+\frac{y^2}{81}=1[/tex] = 4 x A = 4 x 15 = 60 square units.
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A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as
editing) and variable costs (such as printing). The one-time fixed costs will total $32,060. The variable costs will be $12.75 per
book. The publisher will sell the finished product to bookstores at a price of $21.50 per book. How many books must the
publisher produce and sell so that the production costs will equal the money from sales?
Answers
In linear equations x = 3,664 books are the production costs will equal the money from sales .
What is a formula for linear equations?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.fixed cost = $32,060
variable cost = $12.75
here cost function
c(x) = fixed cost + x( variable cost )
c(x) = $32,060 + x($12.75) ................. 1
now revenue function
R(X) = (Selling price ).x
r(x) = ( 21.50)x .............2
where production cost is wqual to selling
c (X) = r (x)
32,0 60 + x($12.75) = ( 21.50)x
32,060 = ( 21.50)x - (12.75)x
32,060 = 8.75 x
x = 3,664 books
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Are these good grades for middle school
Answers
Answer: kinda
Step-by-step explanation:
as long as you have a passing grade you will be fine, just work on the "F" :)
When the same number is added to the numerator and denominator of 5/7, the result is 17/23. what is that number?
Answers
The number added to the numerator and the denominator is 2/3.
It is given in the question that when the same number is added to the numerator and denominator of fraction 5/7, the result is 17/23.
We have to find the number added to the numerator and the denominator.
Let the number be x.
Hence, according to the data given in the question, we get,
(5 + x)/(7 + x) = 17/23
By cross - multiplication, we get
23(5 + x) = 17 (7 + x)
Opening the bracket according to the distributive property of addition and multiplication, we get,
115 + 23x = 119 + 17x
23x - 17x = 119 - 115
6x = 4
x = 4/6
x = 2/3
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Which numbers in Set A = {5, 9, 12, 14, 18} are elements of both Set B and Set C, shown below? Set B = {even numbers} Set C = {multiples of 3}
Answers
The numbers in Set A = {5, 9, 12, 14, 18} that are elements of both Set B and Set C, shown below Set B = {even numbers} Set C = {multiples of 3} will be 12 and 18.
How to illustrate the information?It should be noted that even numbers can be divided by 2.
The multiple of 3 in the numbers are 12 and 18 that can be divided by 2 as well.
Therefore, the numbers in Set A = {5, 9, 12, 14, 18} that are elements of both Set B and Set C, shown below Set B = {even numbers} Set C = {multiples of 3} will be 12 and 18.
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Pia poured 1/4 pint of milk into an empty mug. The milk filled 2/3 of the mug.
How many pints of milk will fill an empty mug of the same size?
Answers
3/8 pints of milk will fill an empty mug of the same size.
In this question, we have been given Pia poured 1/4 pint of milk into an empty mug.
The milk filled 2/3 of the mug.
We need to find the pints of milk that will fill an empty mug of the same size.
Let 'm' pints of milk will fill an empty mug of the same size.
From given data, we get proportion.
⇒ (1/4) / (2/3) = m / 1
We simplify above equation to find the value of m.
⇒ (2/3) m = 1/4
⇒ m = (1/4) × (3/2)
⇒ m = 3/8
Therefore, 3/8 pints of milk will fill an empty mug of the same size.
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in the sketch below abc is not drawn to scale constuct abc next to its sketch below
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The letter A is not drawn to scale in the sketch below. construct ABC next to its below-listed sketch The amount of force applied over a specific distance is referred to as work. Since the problem already specifies the force's value and the length of the distance it is exerted across, the quantity of labor completed requires multiplying these two numbers. As demonstrated below:
work, in physics, measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement.
Work: Force times Distance
Work = 250 J x 50 N * 5 m
Work = 250 J
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Solve the conjunction and graph it’s solution set
y = -1 and y≥ 3
Answers
Maybe this will help
please help me as soon as possible with this
Answers
Part A: The student was supposed to divide before subtracting
Part B: The student was supposed to simplify the parentheses before finding the exponents
Part C: The simplification of the expression gives -16.
From the question, we are to simplify the given expression
The given expression is
(∛64 - 16 ÷ 2)(2 - 4)²
Part A:
The mistake the student made was not applying the PEMDAS rule
P - Parentheses
E - Exponent
M - Multiplication
D - Division
A - Addition
S - Subtraction
Since division comes before subtraction, the student was supposed to divide before subtracting
Part B:
The student mistake was trying to simplify the exponent before simplifying the parentheses. The student was supposed to simplify the parentheses before finding the exponents.
Part C:
Simplifying the expression
(∛64 - 16 ÷ 2)(2 - 4)²
Simplify the cube root
(4 - 16 ÷ 2)(2 - 4)²
Divide
(4 - 8)(2 - 4)²
Simplify the parenthesis
(-4)(-2)²
Simplify the exponent
(-4)(4)
Evaluating
-16
Hence, the simplification of the expression gives -16.
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Solve the system:
c+12d=-66
-4c+3d=-42
Answers
Answer: c=6, d=-6
Step-by-step explanation:
c+12d=-66
-4c+3d=-42
(-4c+3d=-42)*4
-16c+12d=-168 ==> subtract this
c+12d=-66 ==> by this
-17c=-168-(-66) ==> subtract the top two equations
-17c=-168+66
-17c=-102
c=6
c+12d=-66
6+12d=-66
12d=-72
d=-6
y(a-b)=c(y+a) what's the answer
Answers
Linear equation: a, b, c, and r are real numbers (and if a, b, and c are not all equal to 0)
then ax + by + cz = r is called a linear equation in three variables. (The
“three variables” are the x, the y, and the z.)
The numbers a, b, and c are called the coefficient of the equation. The
number r is called the constant of the equation
y(a-b)=c(y+a)
ya-yb=cy+ca
ya-yb-cy=ca
y(a-b-c)=ca
[tex]y=\frac{ca}{a-b-c}[/tex]
case 1:
if either C and a are zero the y is zero,
case 2:
if
[tex]c\neq 0 \\a\neq 0\\y\neq 0[/tex]
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Learning Task 2. Factor the following completely.
1. x²+3x-18
2. 3x²-9x-12
3. 18x²+3x-15
4. 5x²+32x+12
5. 3x³+24
Answers
Step-by-step explanation:
13 is the answer that is need
Rewrite 8x8x8 using exponents.
Answers
Answer:
8^3
Step-by-step explanation:
there are three 8s soo all u do is count the number and then how many of that same number you can put into an exponent
12. Jeremy has 3 pounds of ground beef to make hamburgers. How many 1/3-pound hamburgers can he make?
Answers
Answer: He can make 9 hamburgers.
Step-by-step explanation:
one hamburger can be made by 1/3 of beef,
so according to ratio and proportions ,
1 beef can make 3 hamburgers,
hence 3 pound of beef can be used to make
=3*3
=9 hamburgers
hence,
He can make 9 hamburgers.
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Answer:1
Step-by-step explanation: firstly , divide 3 by 1\3 then 3÷1\3=1
Find a₁for each arithmetic series. Sa₃₀=240 and d=-2
Answers
As a reminder, an arithmetic sequence or arithmetic progression (AP) is a progression in which the difference (called the tolerance) between two consecutive terms in the progression is constant.
Therefore, the expression for the nth term is
an = a₁ + (n − 1) d
and in general
an = am + (n - m) d.
where d is the difference.
For an arithmetic series with initial term a₁ and difference between terms of d
an = a₁ + (n − 1) d
We are told
d = -2 and
S8 = 240
So,
a1 = 240 = a1 + ( 30 - 1) * ( -2 ) = a1 - 58
a1 = 240+58 =298
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2x+9>17 or 5x+10<10 compound inequalities
Answers
Answer: 2x+9>17 or 5x+10<10 compound inequalities is x<0
Step-by-step explanation:
What is Meant by Compound Inequality?
In Mathematics, a compound inequality is a sentence which has two statements connected using the word “and” or by the word “or”. If the statements are connected using the word “and”, then both the statements of the compound sentence are true at the same time. If the statements are connected using “or”, then the compound sentence is true if at least one statement is true.
2x+9>17 or 5x+10<10
Let take 2x+9>17
Subtract -9 on both sides
2x+9-9>17-9
2x+0>8
2x>8
Now we need to divide by 2 both sides
2x÷2>8÷2
x>4
Now we solve 5x+10<10
we need to subtract -10 on both side
5x+10-10<10-10
5x+0<0
5x<0
Now we need to divide 5 on both sides
5x÷5<0÷5
x<0
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0<x>4
the value of x lies between 0 and 4.
A compound inequality is an inequality that combines two simple inequalities. A compound inequality is made up of two inequalities connected by the word “and” or the word “or.” To solve a compound inequality means to find all values of the variable that make the compound inequality a true statement.
lets take 2x+9>17
now lets subtract 9 from both sides.
2x + 9 > 17
- 9 > -9
2x > 8
now divide both sides by 2
2x ÷ 2 > 8 ÷ 2
x > 4
lets take the second part i.e 5x +10 <10
substract 10 from both sides
5x + 10 < 10
- 10 < -10
5x < 0
now divide both sides by 5
5x ÷ 5< 0 ÷ 5
x < 0
0<x>4
the value of x lies between 0 and 4.
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help meeeeeeeeeeeeee
Answers
======================================================
Explanation:
To find the inverse, we swap x and y, then solve for y.
y = 2x-3
x = 2y-3
x+3 = 2y
2y = x+3
y = (x+3)/2
y = x/2 + 3/2
y = (1/2)x + 3/2
This shows the original function y = 2x-3 leads to the inverse y = (1/2)x+3/2, and vice versa.
--------------
Another approach:
Since we're given a list of multiple choice answers, we can rule out the non-answers.
Plug x = 0 into the first equation of choice A. It leads to y = 2
That output 2 is then plugged into the second equation for choice A. It leads to y = 13/2. We do not get the original input 0, which shows that the equations in choice A do not undo one another. They aren't inverses of each other.
This allows us to rule out choice A. Choices B and C are similar stories.
Notice that plugging x = 0 into the first equation of choice D leads to the output y = -3. Then plug this as the input into y = (1/2)x+3/2 and you should get y = 0 to get us back where we started. This partially helps confirm we have a pair of functions that are inverses of each other. I'll let you try other values.
Answer:
Step-by-step explanation:
Algorithm for deriving the formula of the inverse function
Step 1. In the formula for the original function, replace the notation of the argument and the value:
Step 2. From the resulting formula, express y(x).
Step 3. Take into account the constraints on the area of definition and the area of values of the original and/or inverse functions.
[tex]\displaystyle\\ y=\frac{1}{2}x+2\\\\ 1.\ x=\frac{1}{2}y+2\\ \Rightarrow\ x-2=\frac{1}{2}y \\2.\ Multiply\ both\ parts\ of\ the\ equation\ by\ 2:\\\\2(x-2)=y\\\\2x-4=y\\Thus,\\y=2x-4\neq 3x+\frac{1}{2} \\Answer:\ no\\\\2.\ y=5(x-2)\\\\1.\ x=5(y-2)\\\\2.\ Divide\ both\ parts\ of\ the\ equation \ by\ 5:\\\\\frac{x}{5} =y-2\\\\\Rightarrow\ \frac{x}{5}+2=y \\Thus,\\\\y=\frac{x}{5}+2 \neq \frac{1}{5}(x+2)\\ Answer:\ no[/tex]
[tex]y=2x-3\\1.\ x=2y-3\\\\2,\ x+3=2x\\\\Divide\ both\ parts\ of\ the \ equation\ by \ 2:\\\\\frac{1}{2}(x+3)=y\\\\ Thus,\\\\y=\frac{1}{2}x+\frac{3}{2} \equiv\frac{1}{2}x+\frac{3}{2} \\\\Answer:\ yes[/tex]
The number of students in the four sixth-grade classes at Northside School are 36,19,34, and 21. Use properties to find the total number of students in the four classes. PLEASE HELP I DONT UNDERSTAND!
Answers
please help! will give brainliest
Answers
1. A. 2/3 of the volume of the rectangular prism crate = 5.7 ft³
B. Amount of space the dog will occupy is: 2.55 ft³. Josiah should buy the medium crate.
2. 21.05 ft²
What is the Volume of a Rectangular Prism?The volume of a rectangular prism = (length)(width)(height).
1. Part A:
Length of the rectangular prism crate = 2.5 ft
Width = 1.7 ft
Height = 2 ft
Volume of the rectangular prism crate = (2.5)(1.7)(2)
Volume of the rectangular prism crate = 8.5 ft³
2/3 of the volume of the rectangular prism crate = 2/3(8.5) = 5.7 ft³
Part B:
Amount of space the dog will occupy = volume = (length)(width)(height).
Length = 2 ft
Height = 1 2/3 = 1.7 ft
Width = 3/4 = 0.75 ft
Amount of space the dog will occupy = volume = (2)(0.75)(1.7)
Amount of space the dog will occupy = volume = 2.55 ft³
The space the dog will occupy is less than 2/3 of the space of the crate, therefore, Josiah should buy the medium crate.
2. Amount of fabric needed to cover the crate = surface area of rectangular prism - (lw) = 2·(1.7·2.5+2·2.5+2·1.7) - (2.5)(1.7)
= 25.3 - 4.25
= 21.05 ft²
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Your car's gas tank holds 13 gallons, and you expect to get about 25 miles per gallon on this winding road. to be sure you don't run out of gas, you never want to have less than 1 gallon in the tank. you start with a full tank of gas. will you need to stop for gas during the first day's drive? explain how you know, and show your work.
Answers
If you had to drive for more than 300 miles for the first day you need to stop for gas fill up.
What is unitary method ?Unitary method is a mathematical tool for finding the value of single unit then deriving the given units according to the question.
According to the given question your car's gas tank holds 13 gallons, and you expect to get about 25 miles per gallon.
Given that you never want to run out of gas to not face this issue you always keep 1 gallon of gas in the tank.
So when you fill your tank completely you fill for 12 gallons of gas because 1 gallon is already there.
Also given that the car can go 25 miles per gallon.
So, for 12 gallons of gas you can go (25 × 12 ) miles which is
= 300 miles.
If you had to drive for more than 300 miles then you need to stop for gas in first day's drive.
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A long year-end status report for work is 163 pages long. You need to print 16 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.75 each.
Answers
Answer:
19.56
Step-by-step explanation:
Number of pages x copies
164 x 16 = 2608
Divided by number of pages per ream
2608 ÷ 50 = 5.216
Total Reams by cost
5.216 x 3.75 = 19.56
When drawing a line, use
_____ to show that the line continues endlessly in both directions. (Fill in the blank)
Answers
when drawing a line use arrows to show that the line continues endlessly in both directions.
Givien g(x) = -3x-5 , find g(4)
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Answer: g(4)=-17
Step-by-step explanation:
You just plug in 4 into x.
-3(4)-5
-12-5
=17
Answer:
g(4) = -17
Step-by-step explanation:
Hello!
Substitute 4 for x in the equation.
Evaluateg(x) = -3x - 5g(4) = -3(4) - 5g(4) = -12 - 5g(4) = -17g(4) is -17.
Please help, picture attached below
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You need to buy a 20-foot length of 15-wide carpet that costs $29.50 per square yard. How much will this cost?
Please include steps!!
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The cost of the carpet will be $983.33
Calculating costFrom the question, we are to calculate how much the carpet will cost
From the given information,
The carpet has a length of 20 feet
and a width of 15 feet
First, we will covert the dimension to yard
NOTE: 1 foot = 1/3 yards
Thus,
20 feet = 20/3 yards
and
15 feet = 15/5 yards = 5 yards
Now, we will calculate the area of the carpet
Using the formula,
Area = Length × Width
Area of the carpet = 20/3 × 5 square yard
Area of the carpet = 33.33 square yard
Now, we have that
The carpet costs $29.50 per square yard
∴ The cost of the carpet = 20/3 × 5 × $29.50
The cost of the carpet = $ 983.33
Hence, the cost of the carpet will be $983.33
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What is 90.5-7.83? Please show your work too! Thanks.
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Have a good day!!
So, the area is square units.
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The area of a triangle is 4 square units.
Given that, the coordinates of the triangle ABC are A(4, 3), B(5, 1) and C(1, 1).
We need to find the area of a triangle ABC.
What is the area of a triangle?The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.
The base of the triangle = |5-1|=4
From vertices, A(4, 3) to the base the distance is 2 units at the vertice (4, 1)
So, the height of the triangle = 2 units
Now, the area of a triangle ABC = 1/2 × 4 × 2 = 4 square units.
In the given solution the height of a triangle is wrongly calculated.
Therefore, the area of a triangle is 4 square units.
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