24333 years
Explanationto solve this we need to use the time formula ,it says
[tex]time=\frac{distance}{speed}[/tex]Step 1
a)given
[tex]\begin{gathered} distance=4.67*10^9\text{ miles} \\ speed=1.92*10^5\text{ }\frac{miles}{year} \end{gathered}[/tex]b) now, replace in the formula and calculate
[tex]\begin{gathered} time=\frac{distance}{speed} \\ time=\frac{4.67*10^9}{1.92*10^5}=2.43*10^{9-5}=2.43*10^4 \\ time=2.43*10^4\approx24333\text{ years} \end{gathered}[/tex]therefore, the answer is
24333 years
I hope this helps you
What is the value of x in the equation7 (4x + 1) – 32 5.7 · 13?X=
Given
[tex]\begin{gathered} 7(4x+1)-3x=5x-13 \\ 28x+7-3x=5x-13 \\ 25x-5x=-13-7 \\ 20x=-20 \\ x=-1 \end{gathered}[/tex]if f(x)=3x-2/x+4 and g(x)=4x+2/3-x,prove that f and g are inverses of each other
Which of the following options correctly represents the complete factored form of the polynomial F(x)= x - x2 - 4x-6?
Notice that:
[tex]F(3)=3^3-3^2-4\cdot3-6=27-9-12-6=27-27=0.[/tex]Therefore 3 is a root of the given polynomial.
Now, we can use this root to factor the polynomial:
[tex]F(x)=(x-3)\frac{x^3-x^2-4x-6}{x-3}.[/tex]Using the synthetic division algorithm we get that:
[tex]\frac{x^3-x^2-4x-6}{x-3}=x^2+2x+2.[/tex]The roots of the above polynomial are:
[tex]\begin{gathered} x=-1+i, \\ x=-1-i\text{.} \end{gathered}[/tex]Therefore:
[tex]F(x)=\mleft(x-3\mright)(x+1+i)(x+1-i)\text{.}[/tex]Answer:
[tex]F(x)=(x-3)(x+1+i)(x+1-i)\text{.}[/tex]Find the measure of the indicated amgle to the nearest degree.
The correct option is
C. 69 degrees
Explanation:Let the indicated angle be represented by x, then
[tex]\begin{gathered} \cos x=\frac{Adjacent}{Hypotenuse}=\frac{13}{36} \\ \\ \\ x=\cos^{-1}(\frac{13}{36})\approx69^o \end{gathered}[/tex]Fill in the gaps to factorise the expression.
2x^2+7x+3
The factorised form of the expression given in the task content is; 2x² + 7x + 3 is; (2x + 1) (x + 1).
Factorisation of quadratic expressions.It follows from the task content that the factorised form of the expression is to be determined.
On this note, the factorised form of the expression is as follows;
2x² + 6x + x + 3.
By grouping terms; we have;
(2x² + 6x) + (x + 3).
Factorise two terms each at as follows;
2x(x + 1) + 1(x+3)
(2x + 1) (x + 1)
Therefore, the factorised form of the expression; 2x² + 7x + 3 is; (2x + 1) (x + 1).
Read more on factorisation;
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can you please help me. I am running out of time and I really need this grade.
A system of equations is consistent if the system has a solution and it is inconsistent if it has no solution.
Since the lines intersect at a point, the system has a solution and the solution is unique.
If a system has a unique solution, then the system is independent.
Therefore, the given system of equations is consistent and independent. It has a unique solution.
(30 points) Solve for the missing side of the triangle. Round to the hundredths place if needed.
Answer:
[tex]6 \sqrt{6} [/tex]
Step-by-step explanation:
The square value of hypotenuse is equal to the square value of sum of the two legs:
[tex] {15}^{2} + {x}^{2} = {21}^{2} [/tex]
225 + x^2 = 441 subtract 225 from both sides
x^2 = 216 find the root of both sides
x = 6√(6)
At the airport, the new runway will be parallel to a nearby highway. The equation that represents the highway is 6y = 8x - 11. Which equation could represent the new runway? A. 9y = 12x + 5B. 9x = 12y + 8C. 12y = -9x + 2 D. 12x = -9y + 4
At the airport, the new runway will be parallel to a nearby highway. The equation that represents the highway is 6y = 8x - 11. Which equation could represent the new runway?
A. 9y = 12x + 5
B. 9x = 12y + 8
C. 12y = -9x + 2
D. 12x = -9y + 4
______________________________________________________
Parallel equations have the same slope
6y = 8x - 11
y= 8/6 x - 11/6
y= 4/3 x-11/6
y = m x +b (m is the slope )
_____________________________________________
You need to find the other equation with the same slope
____________________________
A. 9y = 12x + 5
y = 12/ 9 x + 5/9
y = 4/3 x + 5/9
_________________________
B. 9x = 12y + 8
12 y= 9x-8
y= 9/ 12 x- 8/12
y= 3/4 x - 4/6
discarded
________________________
C. 12y = -9x + 2
y = -9/12 x + 2/12
y = -3/4 x + 1/6
discarded
_________________________
D. 12x = -9y + 4
12x -4 = -9y
y = -12/9 x +4/9
y = -4/3 x+4/9
discarded
_______________
So then, A 9y = 12x + 5 is the equation that could represent the new runway because is parallel to the highway 6y = 8x - 11.
Which of the following is equivalent to the expression below? (2+31) + (8-21) O A. 6+1 O B. 6+5; O C. 10+57 O D. 10 + 1
Given the expression:
[tex](2+3i)+(8-2i)[/tex]Let's find the equivalent expression from the choices given.
To find the equivalent expression, let simplify.
To simplify the expression, take the following steps:
• Remove the parentheses:
[tex]2+3i+8-2i[/tex]• Combine like terms:
[tex]\begin{gathered} 2+8+3i-2i \\ \\ 10+i \end{gathered}[/tex]Therefore, the equivalent expression is:
[tex]10+i[/tex]ANSWER: D
D. 10 + i
f (x) = 4x^2+2x+6find the value of the discriminate of f and how many distinct real number zeros f has.
The Solution:
Given:
Required:
To find the discriminant of f.
By formula, the discriminant (D) is:
[tex]D=b^2-4ac[/tex]Where:
[tex]\begin{gathered} a=4 \\ b=2 \\ c=6 \end{gathered}[/tex]Substitute:
[tex]\begin{gathered} D=2^2-4(4)(6)=4-96=-92 \\ No\text{ real root since D}<0 \end{gathered}[/tex]Therefore, the correct answers are:
Discriminant = -92
No distinct real root.
x^2 = 16, therefore x = 4.
Is this a valid conclusion? If not, give a counterexample.
Yea I think and her dad is doing great so
Given the following function:
[tex]tan\text{ }\theta=\frac{10}{y}[/tex]Both θ and y are functions of the time (t)
We will find the derivatives of θ and y with respect of the time (t) as follows:
[tex]sec^2θ*\frac{dθ}{dt}=-\frac{10}{y^2}*\frac{dy}{dt}[/tex]Now, we will find dy/dt when θ = π/6 and dθ/dt = π/12
First, we need to find the value of y when θ = π/6
[tex]\begin{gathered} tan(\frac{\pi}{6})=\frac{10}{y} \\ \frac{1}{\sqrt{3}}=\frac{10}{y} \\ \\ y=10\sqrt{3} \end{gathered}[/tex]so, we will substitute the values to find dy/dt as follows:
[tex]\begin{gathered} sec^2(\frac{\pi}{6})*\frac{\pi}{12}=-\frac{10}{(10\sqrt{3})^2}*\frac{dy}{dt} \\ \\ so,\frac{dy}{dt}=-\frac{(10\sqrt{3})^2}{10}*sec^2(\frac{\pi}{6})*\frac{\pi}{12}=-10.4719755 \end{gathered}[/tex]Rounding to 2 decimal places
So, the answer will be:
[tex]\frac{dy}{dt}=-10.47\text{ feet/hour}[/tex]help meeeee pleaseeeee!!!
thank you
The values of the given polynomial are:-
f(0) = 12
f(2) = 28
f(-2) = 52
Given polynomial:-
[tex]f(x)=-x^3+7x^2-2x+12[/tex]
We have to find the values of f(0), f(2) and f(-2).
Putting x = 0 in f(x), we get,
[tex]f(0)=-(0)^3+7(0)^2-2(0)+12[/tex]
f(0) = 0 +0 - 0 + 12 = 12
Hence, the value of f(0) is 12.
Putting x = 2 in f(x), we get,
[tex]f(2)=-(2)^3+7(2)^2-2(2)+12[/tex]
f(2) = -8 + 28 - 4 + 12 = 28
Hence, the value of f(2) is 28.
Putting x = -2 in f(x), we get,
[tex]f(-2)=-(-2)^3+7(-2)^2-2(-2)+12[/tex]
f(-2) = 8 +28 + 4 +12 = 52
Hence, the value of f(-2) is 52.
To learn more about polynomial, here:-
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9. A researcher gathered data on hours of video games played by school-aged children and young adults. She collected the following data:601241215171711409914110131015163915121698131016651717129(a) Complete the frequency distribution for the data.HoursFrequencyRelative Frequency0-23-56-89-1112-1415-17(b) Which of the following is the correct histogram for this data?246810Hours0369121518Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(0,18,0,10);axes(34,2,1,null,2); fill="blue"; textabs([165,0],"Hours","above");line([0,-0.2],[0,0.2]); text([0,0],"0","below");line([3,-0.2],[3,0.2]); text([3,0],"3","below");line([6,-0.2],[6,0.2]); text([6,0],"6","below");line([9,-0.2],[9,0.2]); text([9,0],"9","below");line([12,-0.2],[12,0.2]); text([12,0],"12","below");line([15,-0.2],[15,0.2]); text([15,0],"15","below");line([18,-0.2],[18,0.2]); text([18,0],"18","below");textabs([0,115],"Frequency","right",90);rect([0,0],[3,6]);rect([3,0],[6,4]);rect([6,0],[9,5]);rect([9,0],[12,7]);rect([12,0],[15,6]);rect([15,0],[18,10]);]246810121416Hours061218Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(0,18,0,16);axes(34,2,1,null,2); fill="blue"; textabs([165,0],"Hours","above");line([0,-0.32],[0,0.32]); text([0,0],"0","below");line([6,-0.32],[6,0.32]); text([6,0],"6","below");line([12,-0.32],[12,0.32]); text([12,0],"12","below");line([18,-0.32],[18,0.32]); text([18,0],"18","below");textabs([0,115],"Frequency","right",90);rect([0,0],[6,10]);rect([6,0],[12,12]);rect([12,0],[18,16]);]2468101214Hours061218Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(0,18,0,14);axes(34,2,1,null,2); fill="blue"; textabs([165,0],"Hours","above");line([0,-0.28],[0,0.28]); text([0,0],"0","below");line([6,-0.28],[6,0.28]); text([6,0],"6","below");line([12,-0.28],[12,0.28]); text([12,0],"12","below");line([18,-0.28],[18,0.28]); text([18,0],"18","below");textabs([0,115],"Frequency","right",90);rect([0,0],[6,12]);rect([6,0],[12,14]);rect([12,0],[18,12]);]2468Hours0369121518
Remember that the frequency refers to the number of times a data shows up. In this case, the frequency is the number of data that falls into each interval.la
To find the relative frequency is calculated by dividing each frequency by 38 (the total number of data).
[tex]\begin{gathered} \frac{6}{38}=0.1579 \\ \frac{4}{38}=0.1053 \\ \frac{4}{38}=0.1053 \\ \frac{8}{38}=0.2105 \\ \frac{7}{38}=0.1842 \\ \frac{9}{38}=0.2368 \end{gathered}[/tex]Let's include the relative frequencies in the table.
On the other hand, the correct histogram has to show the frequencies in the same order. The following histogram shows the correct frequency distribution.
Referring to the figure, find the unknown measure of ABC.
According to the Inscribed Angle Theorem, the measure of an angle inscribed in a circle equals half the arc that it intercepts.
Then:
[tex]m\angle ABC=\frac{1}{2}m\overset{\frown}{AC}[/tex]Since the measure of the arc AC is equal to 84º, then:
[tex]m\angle ABC=\frac{1}{2}(84º)=42º[/tex]Therefore, the answer is:
The measure of ABC is 42º.
A bank offers a CD that pays a simple interest rate of 8.0%. How much must you put in this CD now in order to have $2500 for a home-entertainment center in 3 years.
Okay, here we have this:
Considering that the formula for the simple interest rate is:
A = P (1 + rt)
In this case A is equal to $2500, P is the value we need to find, r is the interest rate (in decimal) 0.08, and t is the time, so it's 3 years, replacing we obtain:
2500=P(1+0.08*3)
Now, let's clear P:
2500=P(1+0.24)
2500=P(1.24)
2500/1.24=P
P=2016.13
Finally we obtain that the bank must put $ 2016.13 on a CD to get $ 2,500 in three years.
There's a roughly linear relationship between the number of times a species of cricketwill chirp in one minute and the temperature outside. For a certain type of cricket,this relationship can be expressed using the formula I = 0.3lc + 36, where Trepresents the temperature in degrees Fahrenheit and c represents the number oftimes the cricket chirps in one minute. What is the meaning of the I'-value whenc= 148?
The function T = T(c) tells us the temperature based on the number of times c the cricket has chirped in one minute. In other words, if we plug c = 148 in the formula we get:
[tex]\begin{gathered} T(c)=0.31c+36 \\ T(148)=0.31\times(148)+36 \\ T(148)=81.88^oF \end{gathered}[/tex]That means if the cricket chirps 148 times per minute, the temperature must be 81.88 ºF.
Answer: The expected temperature in degrees Farenheit if the cricket has chirped 148 times perminute.
The height of a triangle is 4x more than the base, and the area of the triangle is 6 square units. Find the length of the base. Let x =the length of the base.
Write a quadratic equation in factored form. Write entire equation
Answer:
The length of the base is:
3 unitsThe resulting quadratic is
x² - 3= 0Step-by-step explanation:
Base = x
Height = 4x
Area, A = 1/2* base * Height
A = (1/2) * (x) * (4x)
A = 2x² (1)
But, A = 6 (2)
Since (1) = (2);
2x²= 6
x²= 3
Resulting quadratic:
x² - 3= 0
For the difference between 2 squares:
a² - b² = (a-b)(a+b)
Using that identity, we can factorize our quadratic:
(x-3)(x+3) = 0
So, we have 2 roots:
x = 3 and x = -3
Now, noting that length must take a positive value, we go for the first:
x = 3
CONCLUSION:The length of the base is:
3 unitsThe resulting quadratic is
x² - 3= 0How do I solve and what would the answer be?
To find the inverse of a function:
[tex]f(x)=\frac{2}{x-5}[/tex]We will follow the steps below
Step 1: Replace f(x) witth y
[tex]y=\frac{2}{x-5}[/tex]Step 2: interchange x with y
[tex]x=\frac{2}{y-5}[/tex]Step 3: Make y the subject of the formula
[tex]\begin{gathered} y-5=\frac{2}{x} \\ \\ y=\frac{2}{x}+5 \end{gathered}[/tex]Thus, the inverse of the function is:
[tex]y=\frac{2}{x}+5[/tex]Point A is shown on the complex plane.What is the standard form of the complex number that point A represents?
Hello there. To solve this question, we have to remember some properties about the representation of a complex number in the complex or Argand-Gauss plane.
Given the complex plane with the point A representing a complex number:
We have to remember that in the complex plane, a complex number z:
[tex]z=a+ib[/tex]has coordinates
[tex](a,\,b)[/tex]And it is more commonly represented by a vector starting at the origin and with the tip on this point.
In this case, we find that the coordinates of the point A are:
[tex]A=(-5,\,3)[/tex]Which means that the complex number is
[tex]-5+3i[/tex]And this is the answer contained in the last option.
AB has endpoint A(-3,-5) and midpoint M(2,-1).Find the coordinate (x,y) of B.
By definition, the formula to find a Midpoint is:
[tex]M=(\frac{x_1+x_2}{2}+\frac{y_2-y_1}{2})[/tex]Where the coordinates of the first point are:
[tex](x_1,y_1)[/tex]And the coordinates of the second point is:
[tex](x_2,y_2)[/tex]Let be the coordinates of the Midpoint:
[tex](x_M,y_M)[/tex]In this case, knowing coordinates of the point A and the Midpoint, you can set up the following equations:
- Equation 1:
[tex]x_M=\frac{x_A+x_B}{2}[/tex]- Equation 2:
[tex]y_M=\frac{y_A+y_B}{2}[/tex]Choose the Equation 1, substiutute values and solve for x-coordinate of the endpoint B:
[tex]\begin{gathered} x_M=\frac{x_A+x_B}{2} \\ \\ 2=\frac{-3+x_B}{2} \\ \\ (2)(2)=-3+x_B \\ 4+3=x_B \\ x_B=7 \end{gathered}[/tex]Now choose the Equation 2 and solve for the y-coordinate of the point B:
[tex]\begin{gathered} y_M=\frac{y_A+y_B}{2} \\ \\ -1=\frac{-5+y_B}{2} \\ \\ (-1)(2)=-5+y_B \\ -2+5=y_B \\ y_B=3 \end{gathered}[/tex]Therefore, the coordinates of P are:
[tex]B(7,3)[/tex]Answer A= f(x)>0 on the interval x <0 Answer B=f(x)>0 on the interval x<0 Answer C=is f(x)<0 on the interval 00 on the interval 00 on the interval 1
EXPLANATION
Given the function f(x)= -x ²+4x - 3, the statements that apply are:
A) TRUE
B) FALSE
C) TRUE
D) FALSE
E) FALSE
F) TRUE
G) TRUE
H) FALSE
Allison earns $6,500 per month at her job as a principal the chart below shows the percentages of her budget. how much does Allison pay for her mortgage
Total earning for Allison is $6,500 per year
mortage = 24.6%
he spent 24.6% of his salary on mortgage
24.6 / 100 x 6500
0.246 x 6500
= $ 1599
He spent $1,599 on mortgage
A blueprint shows an apartment withan area of 15 square inches. Ifthe blueprint's scale is1 inch : 8 feet, what will the actualsquare footage of the apartment be?The actual area of the apartment willbe -square feet.
Given that;
The blueprint shows an apartment with an area of 15 square inches.
With scale
1 inch : 8 feet
Recall that;
Area of a square is;
[tex]\text{A}=l^2[/tex]Let l represent the length of the side on the blueprint;
The actual length will be;
[tex]\begin{gathered} 8\times l\text{ fe}et \\ 8l\text{ f}eet \end{gathered}[/tex]So, the actual Area will be;
[tex]\begin{gathered} A_f=(8l)^2 \\ A_f=64l^2 \\ A_f=64A\text{ square f}eet \end{gathered}[/tex]substituting the valuye of the blueprint Area;
Consider these functions:/(=) =-{=2 + 51g(I) = =2 + 2What is the value of fg(-2))?
Answer: Provided the two functions, f(x) and g(x), we have to find the composite of these two functions at x = - 2:
[tex]\begin{gathered} f(x)=-\frac{1}{2}x^2+5x \\ \\ g(x)=x^2+2 \end{gathered}[/tex]
The composite function is as follows:
[tex]\begin{gathered} f(g(x))=-\frac{1}{2}(x^2+2)^2+5(x^2+2) \\ \\ \\ f(g(x))=-\frac{1}{2}[x^4+4x^2+4]+5x^2+10 \\ \\ \\ f(g(x))=-\frac{x^4}{2}-2x^2-2+5x^2+10 \\ \\ f(g(x))=-\frac{x^4}{2}-2x^2-2+5x^2+10 \\ \\ \\ f(g(x))=-\frac{x^4}{2}+3x^2+8 \\ \\ \\ f(g(-2))=-\frac{(-2)^4}{2}+3(-2)^2+8 \\ \\ \\ f(g(-2))=-\frac{(-2)^4}{2}+3(-2)^2+8=-8+12+8=12 \\ \\ \\ f(g(-2))=12 \end{gathered}[/tex]The answer is 12.
Simplify the following sum of polynomials completely ( - 12s raise to power 2 + 10s - 3) + ( 2s raise to power 2 - 12s - 2)
ANSWER
[tex]-10s^2-2s-5[/tex]EXPLANATION
Given
[tex]\mleft(-12s^2+10s-3\mright)+\mleft(2s^2-12s-2\mright)[/tex]removing the brackets, we have;
[tex]-12s^2+10s-3+2s^2-12s-2[/tex]collecting like terms, we have
[tex]\begin{gathered} -12s^2+2s^2+10s-12s-3-2 \\ \end{gathered}[/tex]adding similar terms, we have;
[tex]-10s^2-2s-5[/tex]The solution is
[tex]-10s^2-2s-5[/tex]Evaluate 7a - 5b when a = 3 and b = 4 .
I need help with my question
The opposite of a number is the same as multiplying it by -1. any negative number, it's opposite is that same number positive. And any positive number is that same number negative.
Our number W is 5. Then, the opposite number is - 5.
To draw a point at - 5 from 5, we just need to move the difference between them to the left. The difference between 5 and -5 is given by
[tex]|5-(-5)|=|5+5|=|10|=10[/tex]Then, to draw point V we need to move 10 units to the left of Point W.
need help with image
Step by step explanation:
sum of co-exterior angle is 180°
(10x-48)+(6x)=180°
4x-48=180°
4x=180-48
4x=132
x=132/4
x=33
A car drove 300 miles in four hours. How fast was the car traveling in miles per hour?
Given that,
A car drove 300 miles in four hours.
We can simply put it in this way.
In 4 hours, a total distance covered by the car = 300 miles
In 1 hour, a total distance covered by the car = 300/4 miles = 75 miles.
Hence, the car was traveling at a speed of 75 miles per hour.
