Answer: Six Thousand Two Hundred
Step-by-step explanation:
Write the quotient for 5/6 ÷ 1/3 and the multiplication equation used to solve for the quotient. A) 2 1/2 5/6 × 3B) 2 1/25/6 × 1/3C) 2/31/3 × 5/6D) 2/33 × 5/6
We can write the quotient as:
[tex]\frac{\frac{5}{6}}{\frac{1}{3}}[/tex]We can use the fact that:
[tex]\frac{a}{b}=a\cdot\frac{1}{b}[/tex]to transform the quotient into a multiplication.
If b=1/3, then 1/b=3/1.
Then the expression becomes:
[tex]\frac{\frac{5}{6}}{\frac{1}{3}}=\frac{5}{6}\cdot\frac{3}{1}=\frac{15}{6}=\frac{5}{2}=2.5[/tex]The fraction 5/2 can be expressed as mixed number as:
[tex]\frac{5}{2}=\frac{2\cdot2}{2}+\frac{1}{2}=2\frac{1}{2}[/tex]Answer: the result is 2 1/2 or 2.5.
The quotient becomes the multiplication 5/6 * 3.
[Option A]
IIIDECIMALSRounding decimalsRound 0.434 to the nearest hundredth.0x
Answer
Explanation
In rounding off numbers, when the number after the required level of precision is less than 5, we round it down. But if that number is 5 or more, we round it up.
100 POINTS!! I NEED THIS KNOWW!!!!The number line shows the distance in meters of two birds, A and B, from a worm located at point X:A horizontal number line extends from negative 3 to positive 3. The point labeled as A is at negative 2.5, the point 0 is labeled as X, and the point labeled B is at 2.5.Write an expression using subtraction to find the distance between the two birds.Show your work and solve for the distance using additive inverses.
The expression used to represent the distance between the two birds on the number line is 2.5 - (-2.5) and the distance is 5 units.
Let us represent the bird A is sitting at one point on the number line.
Bird B is sitting at another point.
Both of them are at a an equal distance from a worm which is at the position O which is the origin.
Now it is given that A and B are at the positions of the number line marked 2.5 and -2.5
Now the distance between A and B can be calculated by finding the distance between A and O and adding the additive inverse to it to get the distance between O and B using subtraction.
AO = 2.5 - 0 = 2.5 units
The additive inverse of this is -2.5 units.
Therefore the distance AB :
= AO - BO
= 2.5 -(-2.5)
=2.5 +2.5
=5 units.
Hence they are at a distance of 5 units from each other.
To learn more about number line visit:
https://brainly.com/question/20887529
#SPJ9
Hi! I have a question and I don't understand it's answer. Could you help me?It's in the attachment below.
To solve this question, we just need to evaluate our set of points in the standard form equation of a Hyperbola, and find the coefficients. This will give to us the equation for our Hyperbola. The standard form is
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]Let's start with the easier points, the x-intercepts (5, 0) and (-1, 0).
Since this hyperbola has two x-intercepts, we're dealing with a horizontal hyperbola, and the center is the midpoint between the x-intercepts.
[tex]\begin{gathered} \bar{x}=\frac{x_1+x_2}{2}=\frac{-1+5}{2}=2 \\ \bar{y}=\frac{y_1+y_2}{2}=\frac{0+0}{2}=0 \end{gathered}[/tex]The center coordinates are (2, 0), then, our equation is
[tex]\frac{(x-2)^2}{a^2}-\frac{y^2}{b^2}=1[/tex]To find the missing coefficients, we can just substitute the remaining points and solve the system for a and b. Our final equation is
[tex]\frac{(x-2)^2}{9^{}}-\frac{y^2}{4}^{}=1[/tex]Find the future value$4013 invested for 9 years at 4.1% compounded quarterly.
We are to find the future value
The future value can be calculated using
[tex]FV=PV(1+\frac{r}{100\alpha})^{n\alpha}[/tex]From the given information
PV = $4013
r = 4.1
n = 9 years
Since the investment is compounded quarterly then
α = 4
By substituting these values we get
[tex]FV=\text{ \$4013(1 }+\frac{4.1}{100(4)})^{9(4)}[/tex]Simplifying the equation we get
[tex]\begin{gathered} FV=\text{ \$}4013(1\text{ }+\frac{4.1}{400})^{36} \\ FV=\text{ \$}4013(1\text{ }+0.01025)^{36} \\ FV=\text{ \$}4013(1.01025)^{36} \\ FV=\text{ \$}4013(1.44436) \\ FV=\text{\$}5793.17 \end{gathered}[/tex]Therefore,
The Future Value is $5793.17
If f -1(x) = (6/5)x - 9, find f (x).
Solution
Step 1
Write the inverse function:
[tex]f^{-1}(x)\text{ = }\frac{6}{5}x\text{ - 9}[/tex]Step 2
[tex]\begin{gathered} Let\text{ f}^{-1}(x)\text{ = y} \\ \\ y\text{ = }\frac{6}{5}x\text{ - 9} \\ \\ Make\text{ x the subject of the formula} \\ \\ y\text{ + 9 = }\frac{6}{5}x \\ \\ Divide\text{ both sides by }\frac{6}{5} \\ \\ x\text{ = }\frac{5}{6}(y\text{ + 9\rparen} \\ \\ f(x)\text{ = }\frac{5}{6}(x\text{ + 9\rparen} \end{gathered}[/tex]Final answer
[tex]f(x)\text{ = }\frac{5}{6}(x\text{ + 9\rparen}[/tex]Find the simplified product.3-532 + 3823B-5ob+32B + 32+325 + 6
Answer:
[tex]\frac{b+3}{2}[/tex]Explanation:
Given the below expression;
[tex]\frac{b-5}{2b}\times\frac{b^2+3b}{b-5}[/tex]Let's go ahead and simplify the expression as shown below;
[tex]\frac{b-5}{2b}\times\frac{b(b+3)}{b-5}=\frac{b(b+3)}{2b}=\frac{b+3}{2}[/tex]Consider the function g. 9(-) = 6() For the x-values given in the table below, determine the corresponding values of g(x) and plot each point on the graph.. -1 0 1 2 g(x) Drawing Tools Click on a tool to begin drawing * Delete Undo Reset Select Point 14 13 12 11 10 9 00 reserved.
we have the function
[tex]g(x)=6(\frac{3}{2})^x[/tex]Find out the value of function g(x) for each value of x
so
For x=-1
substitute the value of x in the function g(x)
[tex]\begin{gathered} g(-1)=6(\frac{3}{2})^{-1} \\ g(-1)=6(\frac{2}{3}) \\ g(-1)=4 \end{gathered}[/tex]For x=0
[tex]\begin{gathered} g(0)=6(\frac{3}{2})^0 \\ g(0)=6 \end{gathered}[/tex]For x=1
[tex]\begin{gathered} g(1)=6(\frac{3}{2})^1 \\ g(1)=9 \end{gathered}[/tex]For x=2
[tex]\begin{gathered} g(2)=6(\frac{3}{2})^2 \\ g(2)=13.5 \end{gathered}[/tex]using a graphing tool
plot the different points
so
we have
(-1,4)
(0,6)
(1,9)
(2,13.5)
see the attached figure to better understand the problem
please wait a minute
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 98 m long and 70 m wide,Find the area of the training field. Use the value 3.14 for I, and do not round your answer. Be sure to include the correct unit in your answer.98 m
We are asked to determine the area of the given figure. The figure is composed of two semi-circles and a rectangle, therefore, the total area of the figure is:
[tex]A=A_s+A_r+A_s[/tex]The area of the semicircle is given by:
[tex]A_s=\frac{1}{8}\pi D^2[/tex]Where "D" is the diameter. Replacing the values we get:
[tex]A_s=\frac{1}{8}(3.14)(70m)^2[/tex]Solving the operations:
[tex]A_s=1923.25m^2[/tex]Now we determine the area of the rectangle using the following formula:
[tex]A_r=wh[/tex]Where "w" and "h" are the dimensions of the rectangle. Replacing the values we get:
[tex]\begin{gathered} A_r=(98m)(70m) \\ A_r=6860m^2 \end{gathered}[/tex]Now we replace the values in the formula for the total area:
[tex]A=1923.25m^2+6860m^2+1923.25m^2[/tex]Solving the operations:
[tex]A=10706.5m^2[/tex]What is the correct classification of the system of equations below?14x + 2y = 10y + 7x = -5A. parallelB. coincidentC. intersecting
Given:
14x + 2y = 10
y + 7x = -5
Required:
To tell which option is correct
Explanation:
14x + 2y = 10
y + 7x = -5
the given two lines intersect each other
Required answer:
Option C
What would be 2 radians converted into degrees? Need help cant include square units in my answer
REQUIRED:
We are required to convert an angle measure of 2 radians into degrees.
Step-by-step solution;
First thing to note is that the formula for conversion from radians to degrees is an inverse of degrees to radians. The formula for conversion is;
[tex]\begin{gathered} Radians\Rightarrow Degrees: \\ r\times\frac{180}{\pi} \\ \\ Degrees\Rightarrow Radians: \\ d\times\frac{\pi}{180} \end{gathered}[/tex]For the angle given as 2 radians, we now have;
[tex]\begin{gathered} r\times\frac{180}{\pi} \\ \\ =2\times\frac{180}{\pi} \\ \\ =114.591559026 \end{gathered}[/tex]ANSWER:
[tex]2radians=114.59\degree[/tex]1. Write a function V(x) that models the volume of the box where the length of the sides of the squares is x cm. (The formula for the volume of a box is: V = l ⋅ w ⋅ ℎ).2. Graph V(x). (You may use Desmos or draw in the provided grid.)
From the problem, the length and the width will be reduced by twice the side of the square.
The length of the box will be :
[tex]26-2x[/tex]The width of the box will be :
[tex]20-2x[/tex]and the height will be the measurement of the square side :
[tex]x[/tex]Note that the volume of a box is length x width x height.
1. The volume will be :
[tex]V(x)=x(26-2x)(20-2x)[/tex]Expand and simplify the function :
[tex]\begin{gathered} V(x)=x(26-2x)(20-2x) \\ V(x)=x(520-40x-52x+4x^2) \\ V(x)=x(4x^2-92x+520) \\ V(x)=4x^3-92x^2+520x \end{gathered}[/tex]2. Graph the function using desmos.
3andLet's compare38ロ<ロ>=First, write the fractions with the same denominator.х?138-138Then, use <, = , or > to compare the fractions.m 100
To rewrite the fractions as fractions with the same denominator we have to determine the minimum number greater than 8 and 3 that can be exactly divided by 8 and 3 (LCM). Notice that the LCM of 8 and 3 is
[tex]24=8\cdot3.[/tex]Because:
[tex]\begin{gathered} 8=2\cdot2\cdot2, \\ 3=3. \end{gathered}[/tex]Therefore, we rewrite the given fractions as:
[tex]\begin{gathered} \frac{1}{3}=\frac{8}{24}, \\ \frac{3}{8}=\frac{9}{24}\text{.} \end{gathered}[/tex]From the above fractions, we get that:
[tex]\frac{3}{8}>\frac{1}{3}\text{.}[/tex]Answer:
a)
[tex]\begin{gathered} \frac{1}{3}=\frac{8}{24}, \\ \frac{3}{8}=\frac{9}{24}\text{.} \end{gathered}[/tex]b)
[tex]\frac{1}{3}<\frac{3}{8}\text{.}[/tex]is y=2x+4 a linear equation
Answer:
A linear equation is always of the form:
y = mx + c
Where m = the slope
and c = the intercept
The equation given is y = 2x + 4
and it takes the form y = mx + c
where m = 2 and
c = 4
Therefore, the equation y = 2x + 4 is a linear equation
what's the solution to this system
Remember that
when solving a system by graphing, the solution is the intersection point both graphs
so
In this problem
the intersection point is (-2,2)
therefore
the solution is (-2,2)Find an equation for the line that’s passes through the following points shown in the picture. ( Please fins answer in timely answer very brief explaination :) )
The general equation of line passing through the points (x_1,y_1) and (x_2,y_2) is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Determine the equation of line passing thgrough the point (-6,-1) and (2,5).
[tex]\begin{gathered} y-(-1)=\frac{5-(-1)}{2-(-6)}(x-(-6)) \\ y+1=\frac{6}{8}(x+6) \\ y+1=\frac{3}{4}x+\frac{9}{2} \\ y=\frac{3}{4}x+\frac{9}{2}-1 \\ =\frac{3}{4}x+\frac{7}{2} \end{gathered}[/tex]So equation of line is y = 3/4x + 7/2.
You are given two overlaying squares with side length a. One of the squares is fixed at the
bottom right corner and rotated by an angle of α (see drawing). Find an expression for the
enclosed area A(α) between the two squares with respect to the rotation angle α.
The expression for the area enclosed between the two squares with respect to the rotation angle α is
(α/90)a².
What is a square?A Square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is given as side²
We have,
Side of the square = a
Area of the square = a²
The full angle that can be rotated is 90°.
Now,
The area enclosed if the angle is 90°.
= a²
We can write as,
The area enclosed in terms of the angle.
= (angle rotated / 90) x side²
= (angle rotated / 90) x a²
Now,
The angle rotated is α.
The area enclosed is (α/90)a².
Thus,
The expression for the area enclosed between the two squares with respect to the rotation angle α is
(α/90)a².
Learn more about squares here:
https://brainly.com/question/22964077
#SPJ1
I need to find the coordinates for this graph and place two points but every time I find the answer it’s not one they want
The equation is given as
[tex]r(x)=-\frac{7}{8}x^5[/tex]ExplanationTo find the coordinates of the function.
Draw the table for x and y coordinates.
The graph of the function is as drawn
AnswerThe other two coordinates of the equation in the grid [-10,10] by [-10,10] is
[tex](-1.18,2.002),(1.08,-1.286)[/tex]A helicopter hovers 550 feet above a small island. The figure shows that the angle of depression from the helicopter to point p is 43°. How far off the coast, to the nearest foot, is the island? (Round the answer to the nearest whole number.)
The angle of depression and angle P are alternate interior angles, then:
∠P = 43°
By definition:
tan(angle) = opposite/adjacent
In this case,
tan(43°) = 550/d
d = 550/tan(43°)
d = 590 ft
In quadrilateral ABCD, MZA = 72, mZB = 94, and m2C = 113. What is m2D?
First, let's picture the problem
Let's label the angle D as x
Remember that the sum of angles in a quadrilateral is 360
[tex]\begin{gathered} 72^0+94^0+113^0+x=360^{\square} \\ x=81^0 \\ m\angle D=81^0 \end{gathered}[/tex]1. Solve: 12 + 24 = 6 x 3 = ?
Answer:
9
Step-by-step explanation:
12 + 24 = 36
6 * 3 = 18
36 = 18 = ?
Well, 18 is 1/2 of 36, so the next sequence would be 1/2 of 18, which is 9.
I'm not quite sure that this would be correct, just because I have no more context.
need help asappppppp
Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)
For the ordered pairs given, we have inputs and outputs as shown below
The values of the input should be unique
Checking all the options given,
The pair (4,2) when added to the pairs will not make the relation a function because
4 will have two
For this problem identify P, FV, I, r, n, and t.
a) P = 180,000cents
b) FV = 298,418cents
c) I = 118,418cents
d) r = 0.003375
e) n = 12
f) t = 15 years
Explanations:a) P is the principal in the given question. The principal can be the amount invested or borrowed.
According to the question, the amount invested is $1,800.00, hence the principal P is $1,800 which is equivalent to 180,000cents to the nearest cents
b) The future value is the amount after 15 years of investing the money. According to the question, Sandra earned a total interest of $1,184.18 after 15 years.
Future value = Principal + Interest
Future value = $1,800.00 + $1,184.18
Future value = $2,984.18
Hence FV to the nearest cent is 298,418cents
c) Given the total interest of $1,184.18
Convert to nearest cents
I = 1,184.18 * 100
I = 118,418cents
d) r is the rate in percentage. From the question the rate in percent is
3 3/8 %
Convert to decimal
[tex]\begin{gathered} r=3\frac{3}{8}\% \\ r=\frac{27}{8}\% \\ r=\frac{27}{800} \\ r=0.03375 \end{gathered}[/tex]e) n is the time of compounding. From the question, we are told that amount invested was compounded monthly. Since there are 12 months in a year, hence the value of n is 12.
f) "t" is the time taken by Sandra to invest $1,800 to earn the given interest. From the question, the time it takes is 15 years. Hence;
t = 15 years
According to the graph of H(w) below, what happens when w gets very large?H)5.6.20.00)A. H(w) gets very large.B. H(w) approaches a vertical asymptote.C. H(w) equals zero.D. H(w) gets very smallSUBMIT
Considering the graph H(w),
As w gets larger, H(w) continues to approach a horizontal asymptote.
Hence, H(w) gets very small.
Therefore, the correct option is option D
the points (v,-3) and (8,5) fall on a line with a slope of -8. what is the value of v?
The slope m is given by:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \text{Where:} \\ (x1,y1)=(v,-3) \\ (x2,y2)=(8,5) \\ m=-8 \\ so\colon \\ -8=\frac{5-(-3)}{8-v} \\ \text{solve for v:} \\ -8(8-v)=5+3 \\ -64+8v=8 \\ 8v=72 \\ v=\frac{72}{8} \\ v=9 \end{gathered}[/tex]Divide using synthetic division (m^4 + 7m^3 + m +13) = (m + 7)
Quotient:
[tex]m^3+1[/tex]Remainder:
[tex]6[/tex]Result:
[tex](m^3+1)\times(m+7)+6[/tex]
Find the value of r so that the line through (-4, r) and (-8, 3) has a slope of -5.
The value of r is -17.
Given,
Points (-4,r) and (-8,3)
slope=-5
Let
A(x1,y1)=(-4,r)
B(x2,y2)=(-8,3)
To find 'r' use formula,
[tex]slope=\frac{y2-y1}{x2-x1}\\ \\-5=\frac{3-r}{-8-(-4)}\\\\-5=\frac{3-r}{-8+4}\\\\-5=\frac{3-r}{-4}\\\\20=3-r\\\\20-3=-r\\\\17=-r\\\\-17=r[/tex]
Thus, the value of r is -17.
To learn more about slope of line refer here
brainly.com/question/18298097
#SPJ9
Which fraction and decimal forms match the long division problem? 15) 4.000 301 1 00 90 100 90 A. and 0.26 15 В. 15 and 0.26 C. and 0.26 15 15 and 0.266
Which fraction and decimal forms match the long division problem? 15) 4.000 301 1 00 90 100 90 A. and 0.26 15 В. 15 and 0.26 C. and 0.26 15 15 and 0.266
we have
4/15=0.26666
so
the answer is
4/15 and 0.26option Aif you shift the function F(x) = log10 x up four units, what is the new function, G(x)?*PHOTO*
Given:
The function
[tex]F(x)=log_{10}x[/tex]Required:
If you shift the function up for four units. What is the new function G(x)?
Explanation:
We have that function is shifting up for four units that is on y axis.
So, the new function will look like
[tex]G(x)=log_{10}x+4[/tex]Answer:
option A is correct.
-2(y+5)+21<2(6-y) Solving for y