Answers
Graph A is the graph of arc sin x.
Graph D is the graph of sin x.
Graph F is the graph of tan x.
Graph C is the graph of arc tan x.
Graph B is the graph of arc cos x.
Graph E is the graph of cos x.
Related Questions
The number of members for an e-commerce company was 1,700 in the year that the company started and has increased by 10% per year since then. Theexponential function of the number of members, M(f), in terms of t, the number of years since the year the company started, can be described by M(t) =1700(1.10). What is M(5) and its interpretation in the context of the problem?OM(5)-9350; After 5 years, there are approximately 9,350 members in the company.OM(5)=2737.867; After 5 years, there are approximately 2,737 members in the company.OM(5) 1786.717; After 5 years, there are approximately 1,786 members in the company.OM(5) 1870: After 5 years, there are approximately 1,8705 members in the company.W
Answers
Solution
Step 1
Given data
Initial members p = 1700
Rate of increase = 10% = 10/100 = 0.1
time t = 5
Step 2
Using exponential increase formula
[tex]\begin{gathered} A\text{ = p\lparen1 + r\rparen}^t \\ \\ A\text{ = 1700}\times(1\text{ + 0.1\rparen}^5 \end{gathered}[/tex]Step 3
Simplify the expression for the value of A
[tex]\begin{gathered} A\text{ = 1700}\times1.1^5 \\ \\ A\text{ = 2737.867} \end{gathered}[/tex]Final answer
After 5 years, there are approximately 2,737 members in the company.
could you help with the problemfactor find the gcm greatest common monomial[tex]16x2y2 - 8xy2 - 4y2[/tex]
Answers
Factor the following;
[tex]\begin{gathered} 16x^2y^2-8xy^2-4y^2 \\ \text{The greatest common factor in all parts of the expression is } \\ 4y^2 \\ \text{Therefore, we have;} \\ 4y^2(4x^2-2x-1) \end{gathered}[/tex]describe the end behavior of each function f(x)=x^3-4x^2+5
Answers
Solution:
The determine the end behavior of the function below
[tex]f(x)=x^3-4x^2+5[/tex]We will use the image of the function below
The end behavior of a function f describes the behavior of the graph of the function at the "ends" of the x-axis. In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).
Step 1:
From looking at the graph above, we can see that
Since the leading term of the polynomial (the term in the polynomial which contains the highest power of the variable) is x3, the degree is 3, i.e. odd, and the leading coefficient is 1, i.e. positive.
The domain of the function is given below as
[tex]-\inftyTherefore,The end behavior of the function above is
[tex]\begin{gathered} x\rightarrow+\infty,f(x)\rightarrow+\infty,\text{and} \\ x\rightarrow-\infty,f(x)\rightarrow-\infty \end{gathered}[/tex]Given ABC has interior angle measures with:
Answers
For this exercise it is important to remember the de sum of the interior angles of a triangle is 180 degrees.
For this case, you have the triangle ABC, and according to the information given in the exercise:
[tex]\begin{gathered} \angle A=3x-15 \\ \angle B=x+5 \\ \angle C=x-10 \end{gathered}[/tex]Knowing the above, you can set up the following equation:
[tex](3x-15)+(x+5)+(x-10)=180[/tex]Now you must solve for "x":
[tex]\begin{gathered} 3x-15+x+5+x-10=180 \\ 5x-20=180 \\ 5x=180+20 \\ 5x=200 \\ \\ x=\frac{200}{5} \\ \\ x=40 \end{gathered}[/tex]Now, substitute the value of "x" into this equation:
[tex]\angle A=3x-15[/tex]Evaluating, you get that the measure of the angle A is:
[tex]\angle A=3(40)-15=105\degree[/tex]The answer is:
[tex]\angle A=105\degree[/tex]A company makes regular and tall boxes. The base area of each box is 5 ft. The volume of the regular box is 40 ft. The tall box is 3 ft taller. What is the volume of the tall box?
Answers
The base area of each box (regular and tall boxes) = 5 ft².
The volume of the regular box = 40 ft³.
The height of the regular box is given by:
[tex]\text{ height = }\frac{\text{ volume}}{a\text{rea}}=\frac{40}{5}=8\text{ ft.}[/tex]The tall box is 3 feet longer than the regular box.
Hence, the height of the tall box = 8 + 3 = 11 ft.
The volume of the tall box is given by:
[tex]\begin{gathered} \text{ Volume = Area x height} \\ =5ft^2\text{ x 11 ft} \\ =55ft^3 \end{gathered}[/tex]Therefore, the volume of the tall box is 55 ft³
2n ≤ 128 :this is the whole equation
Answers
The question asks to solve for n
We can get this by dividing both sides by 2
We have this as;
[tex]\begin{gathered} 2n\leq\text{ 128} \\ n\text{ }\leq\frac{128}{2} \\ \\ n\text{ }\leq\text{ 64} \end{gathered}[/tex]which of the following values are in the range of the function graphed below? check all that apply A. -1B. 1C.-2D. 2E. -6
Answers
The range of the function is the values of the y coordinates of the graph.
In the given options, the y coordinates of the graph are -1, -2 and -6.
Therefore, options A, C and E are correct.
The length of a rectangle is three times its width. If we decrease the length by two meters and increase the width by 4 meters, the surface increases by 52m².Find the dimensions of the rectangle
Answers
Let the length of rectangle is l and width of the rectangle is w.
The area of rectangle obtained is
[tex]A=l\times w[/tex]It is given that length of rectangle is three times the width.
[tex]l=3w[/tex]It is also given that the length decrease by 2 m and width increase by 4 m andsurface increases by 52 sq.m.
[tex]l\times w^{}+52=(l-2)(w+4)[/tex]Now susbtitute the length equals to 3w in the equation.
[tex]3w^2+52=lw+4l-2w-8[/tex][tex]3w^2+52=3w^2+12w-2w-8[/tex][tex]52=10w-8[/tex][tex]10w=60[/tex][tex]w=6m[/tex]Therefore , the length of the rectangle is
[tex]l=3\times6=18m[/tex]Hence the length of rectangle is 18 m and width is 6m.
an 1,020 + (n-1)(-20) find a12
Answers
we have the expression
an= 1,020 + (n-1)(-20)
find a12
For n=12
a12=1,020+(12-1)(-20)
a12=1,020+(11)(-20)
a12=1,020-220
a12=800write the slope intercept form of the equation given the point (2, 9) and a slope of 1/2
Answers
Given a point and a slope, use slope point form to find the intercept slope form.
[tex]\begin{gathered} y-9=\frac{1}{2}(x-2) \\ y-9=\frac{1}{2}x-1 \\ y=\frac{1}{2}x-1+9 \\ y=\frac{1}{2}x+8 \end{gathered}[/tex]a metal alloy weighing 6 mg and containing 32% gold is melted and mixed with 12 mg of a different alloy which contains 2% gold. what % of the resulting alloy is gold? explain all of your work.
Answers
12% of the resulting alloy is gold
Here, we want to calculate the percentage of the resulting alloy that is gold
We proceed as follows;
(32% of 6mg) + (2% of 12mg)
That would be;
1.92 + 0.24 = 2.16
What means that of the total (6mg + 12mg) , 2.16 mg is gold
Thus the gold percentage will be;
[tex]\frac{2.16}{18}\text{ }\times\text{ 100 = 12 percent}[/tex]Last question for tonight! Can anybody help me out with it? I don't need a huge explanation just the answer and a brief explanation on how you got it :)
Answers
We have a direct variation between x and y.
We can write this as:
[tex]y=k\cdot x[/tex]where k is a constant.
Knowing one point of the relation, like (-2,-8) we can calculate k as:
[tex]k=\frac{y}{x}=\frac{-8}{-2}=4[/tex]Then, if we have the point (x,36), we have to calculate the value of x.
As we know that y = 36 and k = 4, we can find x as:
[tex]\begin{gathered} y=k\cdot x \\ x=\frac{y}{k}=\frac{36}{4}=9 \end{gathered}[/tex]Answer: the missing value is x = 9
Can you help me review these questions for Algebra I? I am trying to see which of my answers are possibly incorrect.
Answers
To find:
The value of given expression at x = 1 and y = 2.
[tex](3x\times x)^2-(\frac{x}{y})^{-2}[/tex]Solution:
It is known that
[tex]a^{-b}=(\frac{1}{a})^b[/tex]Substitute x = 1 and y = 2, in the expression and simplify as follows:
[tex]\begin{gathered} (3x\times x)^2-(\frac{x}{y})^{-2}=(3(1)\times1)^2-(\frac{1}{2})^{-2} \\ =(3)^2-(2)^2 \\ =9-4 \\ =5 \end{gathered}[/tex]Thus, the answer is 5.
find the distance between (14,-6) and (12,8)
Answers
For explanation purposes I'll call Point A (14,-6) and Point B (12,8) the given points.
To calculate the distance between both points you have to calculate the distance between each coordinate over the x and y axis.
Then apply the Phytagoras theorem to calculate its length.
I'll sketch the points:
x-axis
[tex]base=d_{AB}=x_A-x_B=14-12=2[/tex]y-axis
[tex]heigth=d_{AB}=y_B-y_A=8-(-6)=8+6=14[/tex]Now according to the Phythagoras theorem, the sum of the squared base and the squared heigth of a triangle is equal to the squared hypotenuse:
[tex]a^2+b^2=c^2[/tex]For this triangle:
[tex]\begin{gathered} 2^2+14^2=c^2 \\ c^2=200 \\ c=\sqrt[]{200}=10\sqrt[]{2}=14.14 \end{gathered}[/tex]The distance between both points is 14.14 units.
The accurate scale diagram shows a telephone mast and a box. Find an estimate for the real height, in metres, of the telephone mast. telephone mast +2.5 m box
Answers
The estimate for the real height of the telephone mast is of 9 meters, using proportions.
What is a proportion?A proportion is a fraction of a total amount, and equations are built with these fractions and estimates to find the desired measures in the problem using basic arithmetic operations such as multiplication and division.
In this problem, the telephone box and the mast are similar figures, hence their side lengths are proportional.
The, the following proportional relationship is established:
10.8 cm / 1.8 cm = x / 1.5 cm.
The left side of the relationship can be simplified, as follows:
6 = x / 1.5 cm.
Then the estimate is found applying cross multiplication, as follows:
x = 6 x 1.5 cm = 9.5 cm².
Missing InformationThe diagram is given by the image at the end of the answer.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
I need help with this math problem because I am having a hard time understanding the problem and finding the answer. Can u help me
Answers
Answer:
[tex]h(x)=\frac{x+1}{5x+7},Domain=All\text{ }Real\text{ }numbers,\text{ }except\text{ }x=-\frac{3}{2}\text{ }and\text{ }x=-\frac{7}{5}[/tex][tex]h^{-1}(x)=\frac{1-7x}{5x-1},Domain=All\text{ }Real\text{ }numbers,\text{ }except\text{ }x=\frac{1}{5}[/tex]
Explanation:
The notation for composition of functions is:
[tex](f\circ g)(x)=f(g(x))[/tex]In this case:
[tex]\begin{cases}f(x)={\frac{x}{x+2}} \\ g(x)={\frac{x+1}{2x+3}}\end{cases}[/tex]To do the composition, we replace the x in the f(x) with the function g(x):
[tex](f\circ g)(x)=f(g(x))=\frac{g(x)}{g(x)+3}=\frac{\frac{x+1}{2x+3}}{\frac{x+1}{2x+3}+2}[/tex]And solve:
[tex]=\frac{\frac{x+1}{2x+3}}{\frac{x+1}{2x+3}+2}=\frac{\frac{x+1}{2x+3}}{\frac{x+1}{2x+3}+\frac{2(2x+3)}{2x+3}}=\frac{\frac{x+1}{2x+3}}{\frac{5x+7}{2x+3}}=\frac{(x+1)(2x+3)}{(2x+3)(5x+7)}[/tex]Here, we can calcualte the domain. The function is not defined when teh denominator is 0, thus:
[tex]2x+3=0\Rightarrow x=-\frac{3}{2}[/tex][tex]5x+7=0\Rightarrow x=-\frac{7}{5}[/tex]Since the function can't be evaluated when x = -3/2, we can cancel the terms (2x+3) in the numerator and denominator:
[tex]\frac{(x+1)(2x+3)}{(2x+3)(5x+7)}=\frac{x+1}{5x+7}[/tex]Thus:
[tex]\begin{equation*} h(x)=\frac{x+1}{5x+7},Domain=All\text{ }Real\text{ }numbers,\text{ }except\text{ }x=-\frac{3}{2}\text{ }and\text{ }x=-\frac{7}{5} \end{equation*}[/tex]Now, to find the inverse of the function, we first switch the variables:
[tex]y=\frac{x+1}{5x+7}\Rightarrow x=\frac{y+1}{5y+7}[/tex]And solve for y:
[tex]\begin{gathered} \begin{equation*} x=\frac{y+1}{5y+7} \end{equation*} \\ . \\ x(5y+7)=y+1 \\ . \\ 5xy+7x=y+1 \\ . \\ 5xy-y=1-7x \\ . \\ y(5x-1)=1-7x \\ . \\ y=\frac{1-7x}{5x-1}\Rightarrow h^{-1}(x)=\frac{1-7x}{5x-1} \end{gathered}[/tex]And since the denominator can't be 0:
[tex]5x-1=0\Rightarrow x=\frac{1}{5}[/tex]Thus:
[tex]\begin{equation*} h^{-1}(x)=\frac{1-7x}{5x-1},Domain=All\text{ }Real\text{ }numbers,\text{ }except\text{ }x=\frac{1}{5} \end{equation*}[/tex]Enter the correct answer in the box. Simplify the expression [tex]x - 4 |5.x 7 \8[/tex]
Answers
Question
[tex]x^{\frac{-4}{5}}.x^{\frac{7}{8}}[/tex]Apply multiplication law of exponent.
[tex]\begin{gathered} \text{Multiplication law of exponent } \\ X^m.^{}X^{n\text{ }}=X^{m+n} \end{gathered}[/tex][tex]\begin{gathered} X^{\frac{-4}{5}\text{ }}.X^{\frac{7}{8}} \\ =X^{\frac{-4}{5}\text{ + }\frac{7}{8}} \\ =X^{\frac{-4\text{ x 8 + 5 x 7}}{40}} \\ =X^{\frac{-32\text{ + 35}}{40}} \\ =X^{\frac{3}{40}} \end{gathered}[/tex]you would probably use calculus to determine the area for which of the following shapes, I think it’s A
Answers
To determine the area of shape A we need to use calculus.
This comes from the fact that this is a curved figure. The other options don't need calculus since we can divide them in polygons from which we know how to determine the area.
I need help with math
Answers
We are told that in the past month, ms Jeffers flew ( 1716 +984+2058) miles for work,
This month she flew 4 x ( 1716 +984+2058)miles.
If we were to compare the distance flown this month with last month, we see that
"Ms. Jeffers flew four times more distance this month than she flew last month".
I need help solving the volume of the triangular prism
Answers
In general, the volume of a triangular prism is given by the formula below
[tex]\begin{gathered} V=\frac{\text{bhl}}{2} \\ b\to\text{ basis of the triangular base} \\ h\to\text{ height of the triangular base} \\ l\to\text{ height of the prism} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} b=9,h=5.2,l=6 \\ \Rightarrow V=\frac{9\cdot5.2\cdot6}{2}=140.4 \end{gathered}[/tex]The volume of the prism is 140.4cm^3
writw the equation of the root 8, 1/-2
Answers
Concept
To write an equation for given roots, let x variable represent the solutions
Therefore,
x = 8 and x = -1/2
x - 8 = 0 and x + 1/2 = 0
x - 8 and x + 1/2 are factors.
[tex]\text{Next, multiply the two factors, then equate it to zero.}[/tex]Next, multiply the two roots to find the equation.
[tex]\begin{gathered} (x\text{ - 8) x (x + }\frac{1}{2}\text{ ) = 0} \\ x^2\text{ + }\frac{1}{2}x\text{ }-\text{ 8x - 8 }\times\text{ }\frac{1}{2}\text{ = 0} \\ x^2\text{ + }\frac{1}{2}x\text{ - 8x - }\frac{8}{2}\text{ = 0} \\ x^2\text{ - }\frac{7}{2}x\text{ - 4 = 0} \end{gathered}[/tex]Final answer
[tex]x^2\text{ - }\frac{7}{2}x\text{ - 4 = 0}[/tex]A survey went out asking consumersabout their shopping habits. Theresults showed that 165 people weremore likely to go to a store if they hada coupon. This represents 66% of thetotal number of people who took thesurvey.How many people took the survey?25
Answers
We know that 165 people represent a proportion of 0.66 of the people surveyed (66%).
Then, if N is the number of people surveyed, we can write:
[tex]\begin{gathered} 0.66\cdot N=165 \\ N=\frac{165}{0.66}=250 \end{gathered}[/tex]Answer: 250 persons took the survey.
Tonia Sells Cars. Her yearly salary is $35,000 plus 8% of her sales. type and solve an equality to determine her necessary cells to earn over $50,000 step-by-step.
Answers
Step-By-Step Explanation:
Let x be the amount of sales of Tonia in a year.
8% of her sales is:
[tex]x\cdot\frac{8}{100}=0.08x[/tex]Her salary is this plus $35,000. If 'y' is the total yearly salary of Tonia, the equaltion is:
[tex]y=0.08x+35,000[/tex]We want y > 50,000. Replacing this value and solving for x:
[tex]\begin{gathered} 50,000<0.08x+35,000 \\ 50,000-35,000<0.08x \\ 15,000<0.08x \\ x>\frac{15,000}{0.08} \\ x>187,500 \end{gathered}[/tex]Answer:
The equality is 50,000 < 0.08x + 35,000
Tonia needs to sell over 187,500 sales to earn $50,000
The point A(8,-6) is reflected over the point (1, 1) and its image is point B. Whatare the coordinates of point B?
Answers
In point reflection, the distance from the preimage to the point of reflection is the same as the distance from the point of reflection to the image.
Hence, this means that if the preimage coordinates are
[tex](x,y)[/tex]and the image coordinates are
[tex](x\text{',y')}[/tex]and are reflected over a point
[tex](a,b)[/tex]It thus follows that
[tex]\begin{gathered} a=\frac{x+x^{\prime}}{2} \\ \text{and} \\ b=\frac{y+y^{\prime}}{2} \end{gathered}[/tex]From the question, the preimage is given as
[tex]A=(x,y)=(8,-6)[/tex]and it is reflected over the point
[tex](a,b)=(1,1)[/tex]Applying the formula above, we can calculate the coordinates of the image B
Brandon says 4 x 800 is greater than 8 x 4,000. Renee says 4 x 800 is less than 8 X 4,000.A. Without calculating the answer, explain how to use place-value strategies or the Associative Property to find which is greater
Answers
We have two multiplications:
4*800
And
8*4000
We have that 8 is higher than 4, and 4000 is higher than 800. This means that the second one is greather, which means that Renee is correct
QuestionDetermine the value(s) for which the rational expressionlist them separated by a comma, e.g. n = 2,3.-3n + 12is undefined. If there's more than one value,84n2 + 76n +16
Answers
A rational expression is defined for all real numbers except the zeros of the denominator.
Then, find the zeros of the denominator to find the values for which the given rational expression is undefined:
[tex]84n^2+76n+16=0[/tex]Use quadratic formula:
[tex]\begin{gathered} ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex][tex]\begin{gathered} n=\frac{-76\pm\sqrt[]{76^2-4(84)(16)}}{2(84)} \\ \\ n=\frac{-76\pm\sqrt[]{5776-5376}}{168} \\ \\ n=\frac{-76\pm\sqrt[]{400}}{168} \\ \\ n=\frac{-76\pm20}{168} \\ \\ n_1=\frac{-76+20}{168}=\frac{-56}{168}=-\frac{1}{3} \\ \\ n_2=\frac{-76-20}{168}=\frac{-96}{168}=-\frac{4}{7} \end{gathered}[/tex]Then, the given rational expression is undefined for:n= -1/3 , -4/71.4.8Danielle tests the following conjecture.If two angles share a common vertex, then they are adjacent.Her work is shown to the right. What error does Danielle make?Choose the correct answer below.
Answers
Explanation:
The diagram drawn shows two angles that share a common side and a common vertex.
Danielle only mentioned two angles share a common vertex in her conjecture.
Hence, the statement is false as there are angles which share a common vertex and they are not adjacent angles. These angles are called vertical angles.
Adjacent angles have both a common vertex and side.
Hence, Danielle ony gave an example of angles that share a vertex
Write all classifications that apply to the real number 4.O rational, integer, whole numberOnatural number, terminating decimalrational, integer, whole number, natural number, terminating decimalO terminating decimal, integer, rational
Answers
EXPLANATION
The classificationts that apply to the real number 4 are the following:
Rational, integer, whole number
f(x) = V2 - 1 and h(x) = x² + 5Answer three questions about these functions.What is the value of f(h(2))?f(h(2)) =What is the value of h(f (16))?h(f(16)) =Based only on the previous compositions, is it possible that f and h are inverses?Choose 1 answer:YesBNo
Answers
Given:
[tex]\begin{gathered} f(x)=\sqrt[]{x}-1 \\ h(x)=x^2+5 \end{gathered}[/tex]To find: f(h(2))
So, we get,
[tex]\begin{gathered} f(h(2))=f(2^2+5) \\ =f(9) \\ =\sqrt[]{9}-1 \\ =3-1 \\ =2 \end{gathered}[/tex]Hence, the answer is, f(h(2))=2.
To find: h(f(16))
So, we get
[tex]\begin{gathered} h(f(16))=h(\sqrt[]{16}-1) \\ =h(3) \\ =3^2+5 \\ =14 \end{gathered}[/tex]Hence, the answer is, h(f(16))=14.
Since, h(f(16))=14
And, f and h are not inverses.
A rectangular room is four times as long as it is wide, and its perimeter is 70 meters.
Find the width of the room.
Answers
Step-by-step explanation:
length = 4×width
2×length + 2×width = 70
so, we use the first equation in the second :
2×(4×width) + 2× width = 70
8×width + 2×width = 70
10×width = 70
width = 7 meters
length = 4×width = 4×7 = 28 meters