Given the functions:
[tex]\begin{gathered} g(x)=\frac{1}{\sqrt[]{x}} \\ m(x)=x^2-4 \end{gathered}[/tex]I would like to find their domain as well and then complete the answers:
[tex]\begin{gathered} D_g=(0,\infty) \\ D_m=(-\infty,\infty) \end{gathered}[/tex]For the first question: g(x) / m(x)
[tex]\begin{gathered} \frac{g(x)}{m(x)}=\frac{\frac{1}{\sqrt[]{x}}}{x^2-4}=\frac{1}{\sqrt[]{x}\cdot(x^2-4)}=\frac{1}{x-4\sqrt[]{x}} \\ x-4\sqrt[]{x}\ne0 \\ x\ne4\sqrt[]{x} \\ x^2\ne4x \\ x\ne4 \end{gathered}[/tex]As we can see, the domain of this function cannot take negative values nor 4, 0. So, its domain is
[tex]D_{\frac{g}{m}}=(0,4)\cup(4,\infty)[/tex]For the second domain g(m(x)), let's find out what is the function:
[tex]\begin{gathered} g(m(x))=\frac{1}{\sqrt[]{x^2-4}} \\ \sqrt[]{x^2-4}>0 \\ x^2>4 \\ x>2 \\ x<-2 \end{gathered}[/tex]This means that x cannot be among the interval -2,2:
[tex]D_{g(m)}=(-\infty,-2)\cup(2,\infty)[/tex]For the last domain m(g(x)) we perfome the same procedure:
[tex]m(g(x))=(\frac{1}{\sqrt[]{x}})^2-4=\frac{1}{x}-4[/tex]For this domain it is obvious that x cannot take the zero value but anyone else.
[tex]D_{m(g)}=(-\infty,0)\cup(0,\infty)_{}[/tex]The quadratic equation y= -16t^2 +4t+2 represents a moving objects trajectory where y is the objects height in feet above the ground after t seconds . At what time will the objects hit the ground ?
Since y is the object's height, it will be on the ground when y = 0. So let's do that:
[tex]0=-16t^2+4t+2[/tex]Here, we can use Bhaskara's Formula to find the roots of the equation:
[tex]\begin{gathered} t=\frac{-4\pm\sqrt[]{4^2-4\cdot(-16)\cdot2}}{2\cdot(-16)} \\ t=\frac{-4\pm\sqrt[]{16+128}}{-32}=\frac{-4\pm\sqrt[]{144}}{-32}=\frac{-4\pm12}{-32} \\ t_1=\frac{-4+12}{-32}=\frac{8}{-32}=-0.25 \\ t_2=\frac{-4-12}{-32}=\frac{-16}{-32}=0.5 \end{gathered}[/tex]Since the time at start is 0, we can't have a negative sign, it would be like saying what happened before the object was in the air. The it will hit the ground at t = 0.5 s.
in slope intercept form what is the line perpendicular to y=2x -5 that passes through the (2, -5) point
The most appropriate choice for equation of line in slope intercept form will be given by-
[tex]y = -\frac{1}{2}x - 4[/tex] is the required equation of line
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
The given equation of line is y = 2x-5
Slope of this line = 2
Slope of the line perpendicular to this line = [tex]-\frac{1}{2}[/tex]
The line passes through (2 , -5)
Equation of the required line = [tex]y - (-5) = \frac{1}{2}(x - 2)[/tex]
[tex]y +5=-\frac{1}{2}x+1\\y = -\frac{1}{2}x +1 -5\\y = -\frac{1}{2}x -4[/tex]
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Parallel and Perpendicular LinesDetermine whether the following lines are parallel, perpendicular, orneither. Write the corresponding letter on the line next to the question.A = parallel, B = perpendicular, or C = neither1. y = }x+6 and y =- *x + 4
One of the criteria for lines being perpendicular is the fact that the slope of the function in a perpendicular line is the inverse of the slope of the first times -1.
And as you can see m (being the slope of the first equation) is the inverse of the second equiation:
[tex]m=\frac{7}{3},m_1=-\frac{1}{m}[/tex][tex]-\frac{1}{m}=-\frac{1}{\frac{7}{3}}=-\frac{3}{7}[/tex]Therefore line 1 is perpendicular to line 2.
Which of the following is the horizontal asymptote for the graph below?10A x=-7B. X=0ООC. y - 0C D. y = -7
A horizontal like y = k, where k is not part of the graph, but guides the function for x-values “far” to the right and/or “far” to the left.
The horizontal asymptote can be observed in the figure below:
Answer: y = 0.
h(x) = 3a + 410-8-h612-X10-8-668-2-2-10Select the correct answer from each drop-down menu.Function h is alwaysThe function'sis located at (0,5), and there is noThe function isfor all values of x.
We are given the following exponential function.
[tex]h(x)=3^x+4_{}[/tex]The function h(x) is always increasing as can be seen in the given graph.
The y-intercept of a graph is the point where the function intersects/crosses the y-axis.
As you can see from the graph, the graph intersects the y-axis at the point (0, 5)
Therefore, the function's y-intercept is located at (0, 5)
The x-intercept of a graph is the point where the function intersects/crosses the x-axis.
As you can see from the graph, the graph does not intersect the x-axis at any point.
Therefore, there is no x-intercept.
Notice that the graph of the function h(x) is always positive for all values of x.
Answer:
Step-by-step explanation:
IN Date OUT IN OUT Employee Time Card: 7:30 10/1 11:30 4:15 12:00 John Apple 10/2 8:15 11:00 5:15 11:45 10/3 11:15 3:55 7:00 12:10 Dept: Cust. Serv. 4:30 10:55 12:00 6:25 10/4 NOTE: NO OVERTIME 1:30 5:00 12:45 10/5 6:00 TOTAL HOURS RATE per hour: $13.75 What is John's total pay for the week? deneaker notes
I can see it now
thank you
11:30-7:30= 4h
11:00-8.15=2:45h
11:15-7:00=4:15h
10:55-6:25=4:30h
10:45-6:00=4:45h
Total = 4+2.75+4.25+4.5+4.75=20.25
4:15-12:00=4:15h
5:15-11:45=5:30h
3:55-12:10=3:45h
4:30-12:00=4:30h
5:00-1:30=3:30h
Total = 4.25+5.5+3.75+4.5+3.5=21.5
Total hours = 21.5+20.25=41.75
ok, the total pay would be:
Rate per hour * total hours:
[tex]13.75\times41.75=574.0625[/tex]Did you get the same value? hello? are you still with me? ok
do you have any question? oh, remember: After our session, the answer is saved in your profile . My pleasure
To mail the envelope first class do US post office charges $.39 for the 1st ounce and $.22 for each additional ounce . use inequality to find the maximum number of whole ounce of that can be mailed for $7.24
Let N be the total amount of whole ounces that are mailed.
Since mailing the first ounce has a cost of $0.39, then there will be N-1 ounces charged for $0.22 each.
The total cost of mailing N ounces will be:
[tex]0.39+0.22\times(N-1)[/tex]If that cost cannot exceed $7.24, then:
[tex]0.39+0.22\times(N-1)\le7.24[/tex]Solve the inequality for N:
[tex]\begin{gathered} \Rightarrow0.22\times(N-1)\le7.24-0.39 \\ \Rightarrow0.22N-0.22\le6.85 \\ \Rightarrow0.22N\le6.85+0.22 \\ \Rightarrow0.22N\le7.07 \\ \Rightarrow N\le\frac{7.07}{0.22} \\ \Rightarrow N\le32.136\ldots \end{gathered}[/tex]Since N must be a whole number, the maximum value of N that satisfies the inequality is 32.
Therefore, the maximum number of whole ounces that can be mailed for $7.24 is:
[tex]32[/tex]The area of a semicircle is 0.5652 square inches. What is the semicircle's diameter? Use 3.14 for a inches Submit can you explain
Given :
The area of semicircle is given as 0.5652 sq.inches.
To find:
The diameter of semicircle which is denoted as d.
Explanation:
The area of semicircle is given as
[tex]A=\frac{\pi r^2}{2}[/tex]The relation between radius and diameter is
[tex]d=2r[/tex]Now substitute the given area in the area of semicircle formula.
[tex]0.5652=\frac{3.14\times r^2}{2}[/tex][tex]r=\sqrt[]{\frac{2\times0.5652}{3.14}}=\sqrt[]{0.36}[/tex][tex]r=0.6in[/tex]The semicircle diameter is determined as
[tex]d=2r\Rightarrow2\times0.6=1.2in[/tex]Answer:
Hence the diameter of semicircle is determined as 1.2 in.
Four times a number decreased by three is between -15 and 41?
Answer:
The number will lie between -3 and 11
Step-by-step explanation:
Let the number be 'x'
According to the question,
-15 < 4x - 3 < 41
-12 < 4x < 44 (Adding 3)
-3 < x < 11 (Dividing by 4)
Solve the following compound inequality:0< x+7< 9
you need to subtract 7 in each section of the inequality is
-7< x<2
-7< x and x<2
What is an equation of the line that passes through the points (-3,-5) and (-5, -3)? Put your answer in fully reduced form.
Express the general equation of a line passing through two points (x1,y1) and (x2,y2).
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Put (-3,-5) for (x1,y1) and (-5,-3) for (x2,y2) implies,
[tex]\begin{gathered} y+5=\frac{-3+5}{-5+3}(x+3) \\ y+5=\frac{2}{-2}(x+3) \\ y+5=-x-3 \end{gathered}[/tex]Further simplifying gives,
[tex]y=-x-8[/tex]Therefore, the equation of the line is y=-x-8.
a point is chosen at random in the large square. find the probability that the point is in the smaller shaded square. each side of the large square: 16 cmeach side of the shaded square: 6 cm*round to the nearest hundredth
The Probability of the point being in the smaller shaded square is 0.79.
What is meant by probability?Probability equals possibility. It is a branch of mathematics concerned with the occurrence of a random event. The value ranges from 0 to 1. Probability has been introduced in mathematics to predict how likely events are to occur.Probability = the number of possible outcomes. the total number of possible outcomes For example, the probability of flipping a coin and getting heads is 12, because there is only one way to get a head and the total number of possible outcomes is two (a head or tail).The probability is a measure of the likelihood of an event occurring. It assesses the event's likelihood. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the probability formula.Therefore,
|Ω| = 6² = 36
< br / > |A| = 3.14.3² = 278.26
Then we get,
< br / > P |A| = 28.26/36 ≈ 0.79
∴ the probability that the point is in the smaller shaded square is 0.79
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Let v be the vector from initial point P1=(−4,−9) to terminal point P2=(6,2). Write v in terms of i and j.
Step 1;
P1 = ( - 4 , -9 )
P2 = ( 6 , 2 )
Step 2:
[tex]\begin{gathered} \text{Let P}_1=(x_1,y_1)_{} \\ P_2=(x_2,y_2\text{ ) } \end{gathered}[/tex]Step 3:
[tex]\text{v = (x}_2-x_1)i+_{}(y_2-y_1\text{ ) j}[/tex]Step 4:
[tex]\begin{gathered} \text{v = (x}_2-x_1)i+_{}(y_2-y_1\text{ ) j} \\ \text{v = (6}-(-4))i+_{}(2-(-9)\text{) j} \\ v\text{ = (6+4)i + (2 + 9)j} \\ v\text{ = 10i + 11 j} \end{gathered}[/tex]what is the answer to a negative 4 divided by a positive 6?
The expression given as negative 4 divided by a positive 6 has a value of -2/3
How to evaluate the expression?From the question, the expression is given as
negative 4 divided by a positive 6
Rewrite the expression properly
This is rewritten as follows
-4 divided by +6
This can be represented as
-4/6
There are no like terms in the above expression
So, we have the following equation
-4/6 = -4/6
Divide 4 and 6 by a common factor
The common factor is 2
So, we have
-4/6 = -2/3
The expression cannot be further simplified
So, we have the following equation
-4/6 = -2/3
Hence, the value of the expression is -2/3
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The expression given as "negative 4 divided by a positive 6" has a value of that is -2/3
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
From the problem, the expression is given as;
"negative 4 divided by a positive 6"
Rewrite the expression properly then;
-4 divided by +6
This can be express as;
-4/6
There are no like terms in the expression
So, we have the equation;
-4/6 = -4/6
Divide 4 and 6 by a common factor;
The common factor is 2
-4/6 = -2/3
So, we have the equation;
-4/6 = -2/3
Hence, the value of the expression will be; -2/3
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The volume of the rectangular prism is 105 cubic yards. What is the surface area of the prism in square feet?
Answer:
198.18 is the answer
Step-by-step explanation:
the answer is 198.18
hope it helps
Find the missing number so that the equation has infinitely many solutions.
we have the equation
-2x-9=-2x-?
Remember that
If in a system of two linear equations, we have two identical lines
then
The system has infinite solutions
therefore
the missing number is 9
-2x-9=-2x-954 is 120 percent of what number ?
Answer:
120% of 54 =
120% × 54 =
120/100 × 54 =
(120 ÷ 100) × 54 =
120 × 54 ÷ 100 =
6,480 ÷ 100 =
64.8
Percentage of 120% of 54
120% of 54 = 64.8
and to prove that we got the right answer do what we did above in reverse below
64.8 ÷ 54 =
1.2 =
1.2 × 100/100 =
(1.2 × 100)/100 =
120/100 =
120%
Step-by-step explanation:
Position Value of Term 1 1 2 3 -18 1-24 5 -30 What expression shows the relationship between the value of any term and n, its position in the sequence?
basically they are the negative multiples of 6, so:
[tex]a_n=-6n[/tex]graph the function y=sqrt(x+6)+2. which point lies on the graph
Explanation
We are given the following function:
[tex]y=\sqrt{x+6}+2[/tex]We are required to graph the function.
Using a graphing calculator, we have:
Hence, the answer is (-2, 4).
The last option is correct.
Solve for x in the parallelogram below.
Answer:
3
Step-by-step explanation:
In parallelogram, opposite sides are equal.
Here,
5x + 2 and 17 are opposite sides.
5x + 2 = 17
5x = 17 - 2
5x = 15
x = 15 / 5
x = 3
a triangular pyramid has four faces h = b = 1. What is the pryimands surface area?(There's no image)(
Let's find the area of one face
[tex]A=\frac{bh}{2}[/tex]Where h = b = 1.
[tex]A=\frac{1\cdot1}{2}=\frac{1}{2}[/tex]Given that there are four faces, we have to multiply the area above by 4
[tex]S=4\cdot\frac{1}{2}=2[/tex]Hence, the answer is 2 square units.If a,b ,and c represent the set of all values of x that satisly the equation below, what is the value(A+ b+ c) + (abc)?X^3-20x = x^2(A) -1(B) 0(C) 1(D) 9
First, we need to find the solutions a, b, and c of the equation:
[tex]x^3-20x=x^2[/tex]We can rewrite it as:
[tex]\begin{gathered} x^3-x^{2}-20x=0 \\ \\ x(x^{2}-x-20)=0 \\ \\ x=0\text{ or }x^{2}-x-20=0 \end{gathered}[/tex]Thus, one of the solutions is a = 0.
To find the other solutions, we can use the quadratic formula. We obtain:
[tex]\begin{gathered} x=\frac{-(-1)\pm\sqrt[]{(-1)^{2}-4(1)(-20)}}{2(1)} \\ \\ x=\frac{1\pm\sqrt[]{1+80}}{2} \\ \\ x=\frac{1\pm\sqrt[]{81}}{2} \\ \\ x=\frac{1\pm9}{2} \\ \\ b=\frac{1-9}{2}=-4 \\ \\ c=\frac{1+9}{2}=5 \end{gathered}[/tex]Now, we need to find the value of the expression:
[tex]\mleft(a+b+c\mright)+abc[/tex]Using the previous solutions, we obtain:
[tex]\mleft(0-4+5\mright)+0(-4)(5)=1+0=1[/tex]Therefore, the answer is 1.
A triangle has squares on its three sides as shown below. What is the value of x? 4 centimeters 7 centimeters 5 centimeters 3 centimeters
Simplify 2(2x-7) show work
Given:
[tex]2(2x-7)[/tex]Aim:
We need to simplify the given expression.
Explanation:
Use the distributive property.
[tex]a(b+c)=ab+ac.\text{ Here a =2, b=2x and c=-7.}[/tex][tex]2(2x-7)=(2\times2x)+(2\times(-7))[/tex]Multiply 2 and 2x, we get 4x and multiply 2 and (-7), we get (-15).
[tex]=4x+(-14)[/tex][tex]Use\text{ \lparen +\rparen\lparen-\rparen=\lparen-\rparen.}[/tex][tex]=4x-14[/tex]Final answer:
[tex]2(2x-7)=4x-14[/tex]what is 9.77 with 8% tax
it will be 9.77+0.08(9.77)=10.5516
A tank in the shape of a hemisphere has a diameter of 10 feet. If the liquid that fills the tank has a density of 74.4 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Step 1
State the volume of a hemisphere.
[tex]v=\frac{2}{3}\pi r^3[/tex]Where;
[tex]\begin{gathered} r=\frac{diameter}{2}=\frac{10}{2}=5ft \\ \end{gathered}[/tex]Step 2
Find the volume of the hemisphere
[tex]v=\frac{2}{3}\times\pi\times5^3=\frac{250\pi}{3}ft^3[/tex]Step 3
Find the total weight of the liquid in the tank
[tex]\begin{gathered} \text{Density}=\frac{mass}{\text{volume}} \\ 74.4=\frac{mass}{\frac{250\pi}{3}} \\ \text{mass}=19477.87445lb \\ \text{mass}\approx19478lb \end{gathered}[/tex]Hence the total weight of the liquid in the tank to the nearest full pound = 19478lb
The function table below is intended to represent the relationship y=-5x+1. However, one of the entries for y does not correctly fit the relationship with x.
Answer:
Step-by-step explanation:
none of the answers are correct
Find the area of a circle with a Diameter = 12 ft. Use 3.14 for π and round to 2 decimal places.
Given:
Diameter of circle = 12ft
pi = 3.14
Solution
The area (A) of a circle can be calculated using the formula:
[tex]\begin{gathered} A\text{ = }\pi r^2 \\ \text{where r is the radius of the circle} \end{gathered}[/tex]Recall that the diamter (d) and radius (r) are related by the formula:
[tex]\begin{gathered} \text{radius = }\frac{diameter}{2} \\ r\text{ = }\frac{d}{2} \end{gathered}[/tex]We can now find the radius (r) of the circle to be:
[tex]\begin{gathered} r\text{ = }\frac{12}{2} \\ r\text{ = 6 ft} \end{gathered}[/tex]We can now find the area by the applying the formula given above:
[tex]\begin{gathered} A\text{ = }\pi\times r^2 \\ A\text{ = 3.14 }\times6^2 \\ =113.04ft^2\text{ (2.dp)} \end{gathered}[/tex]Answer: 113.04 square feet
A homeowner estimates that it will take 9 days to roof his house. A professional roofer estimates that he could roof the house in 5 days. How long ( in days ) will it take if the homeowner helps the roofer?
Solution:
If x denote the days, the rate unit being Jobs per day is:
[tex]\frac{1}{x}=\frac{1}{9}+\frac{1}{5}[/tex]this is equivalent to
[tex]\frac{1}{x}=\frac{5+9}{45}=\frac{14}{45}[/tex]solving for x, we get:
[tex]x\text{ = }\frac{45}{14}=3.2\text{ days}[/tex]that is just a little more than 3 days.
Which parabola corresponds to the quadratic function y = 2x2 + 4x - 16? D. A. B. C. 10:13 1618 10- 12 =10 10 28 -20
We can see that the y-intercept would be (0,-16) since this is the result of replacing x=0 in the function.
We can also find the x-intercepts solving the equation 0=2x^2+4x-16. Doing so, we have:
[tex]\begin{gathered} 0=2x^2+4x-16 \\ 0=x^2+2x-8\text{ (Dividing by 2 on both sides of the equation)} \\ 0=(x+4)(x-2)\text{ (Factoring)} \\ \text{ We can see that the solutions of the equation are x=-4 and x=2} \\ \text{Therefore the x-intercepts are (-4,0) and (2,0)} \end{gathered}[/tex]The graph that satisfies the conditions we have found previously is the option A.