Answers
a) Since the relation is proportional, the graph is a line.
In order to graph a line we only need two points and connecting them we get the line.
In this case, we know that at 4h the pool has 5200 gallons. The point woud be (4, 5200)
Now we need another point. The simplest one is the origin. When the time is zero, the amount of water in the pool is also 0, then we have another point (0, 0)
Now with the points (0, 0) and (4, 5200) we can graph the relationship.
b) We need to compair the filling rates. In the graph provided we can see that in 3 hours, there is 10,800 gallons. Since the other pool had 5,200 gallons in 4 hours, is clear that the second pool fills much more quicker.
Related Questions
2) write the equation of a line that passes through the point ( 4, 5) and is perpendicular to a line that passes through the points ( 6 8) and (10 0)
Answers
We have the following:
First we calculate the slope of the line where we are given two points (6,8) and (10,0)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]repplacing:
[tex]m=\frac{0-8}{10-6}=\frac{-8}{4}=-2[/tex]now, when two lines are perpendicular:
[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ -2=-\frac{1}{m_2} \\ 2=\frac{1}{m_2} \\ m_2=\frac{1}{2} \end{gathered}[/tex]now,
[tex]y=mx+b[/tex]with the point (4,5), replacing:
[tex]\begin{gathered} 5=\frac{1}{2}\cdot4+b \\ 5=2+b \\ b=5-2 \\ b=3 \end{gathered}[/tex]Therefore, the equation is:
[tex]\begin{gathered} y=\frac{1}{2}x+3 \\ y=\frac{x}{2}+3 \end{gathered}[/tex]check:
[tex]\begin{gathered} y=\frac{4}{2}+3 \\ y=2+3 \\ y=5 \end{gathered}[/tex]Therefore, the answer is y = x/2 + 3
Hello can someone help me in this pls i need it today now PLS i will give 25 points
Answers
Answer:
Look below
Step-by-step explanation:
Convert -8/5 into a decimal
-8/5 = -1 3/5 = -1.6
6.4 times m minus 12 equals 45.6
Answers
Given
6.4 times m minus 12 equals 45.6
To find: The value of m.
Explanation:
It is given that,
6.4 times m minus 12 equals 45.6.
Then,
[tex]\begin{gathered} 6.4m-12=45.6 \\ 6.4m=45.6+12 \\ 6.4m=57.6 \\ m=\frac{57.6}{6.4} \\ m=9 \end{gathered}[/tex]Hence, the value of m is 9.
Find the slope of the secant line for the g(x) = -20 SQRT x between x = 2 and x = 3
Answers
Given:
Equation of line is,
[tex]g(x)=-20\sqrt[]{x}[/tex]The slope of the secant line between x =a and x= b is calculated as,
[tex]\begin{gathered} m=\frac{f(b)-f(a)}{b-a} \\ m=\frac{f(3)-f(2)}{3-2} \\ m=\frac{-20\sqrt[]{3}-(-20\sqrt[]{2})}{1} \\ m=-20\sqrt[]{3}+20\sqrt[]{2} \\ m=20(\sqrt[]{2}-\sqrt[]{3}) \\ m=-6.36 \end{gathered}[/tex]Answer: slope of the secant line is m = -6.36
1) Is F increasing on the interval (2.10)? 2) List the interval(s) on which F is increasing. Justify your answer. 3) List the intervalis) on which F is decreasing Justify your answer. 4)List the value(s) of x at which has a local maximum. Justify your answer.5) List the value(s) of x at which F has a local minimum. Justify your answer. 6) Find the X -intercepts 7) Find the Y-intercepts.
Answers
1)
in the interval (2,5) decreases and then increases , but We cant say that it is growing since it had a fall in the middle, so isnt increasing
2)
(-8,-2) (0,2) (5,10)
It is increasing because, from left to right, it comes from a low point to a higher point
3)
(-10,-8) (-2,0) (2,5)
It is decreasing because, from left to right, it comes from a high point to a lower point
4)
x=-2 and 2
are the highest values of the function
5)
x=-8, 0 and 5
are the lowest values of the function
6)
x=-5, 0 and 5
values where y = 0, therefore intersects the x axis
7)
y=0
values where x = 0, therefore intersects the y axis
Find the shaded area (round answer to 3 sig figs).
Answers
1. Let us find the area of the sector:
[tex]\begin{gathered} \frac{\theta}{360}\cdot\pi\cdot r^2\text{ (Area of a sector formula)} \\ \frac{85}{360}\cdot\pi\cdot(12\operatorname{cm})^2\text{ (Replacing)} \\ \frac{85}{360}\cdot\pi\cdot144cm^2\text{ (Raising 12 to the power of 2)} \\ 0.236\cdot\pi\cdot144cm^2\text{ (Dividing)} \\ 106.814cm^2\text{ (Multiplying)} \end{gathered}[/tex]2. The area of the triangle would be:
[tex]\begin{gathered} At=\frac{1}{2}\cdot ab\cdot\sin (\theta)\text{ (Area of a non right-angled triangle)} \\ At=\frac{1}{2}\cdot(12)\cdot(12)\cdot\sin (85)\text{ (Replacing)} \\ At=71.726cm^2 \end{gathered}[/tex]3. Subtracting the area of the triangle from the area of the sector, we have:
106.814 cm^2 - 71.726 cm^2 = 35.088 cm^2
The answer is 35.088 cm^2
Double a number and add 12 and the result will be greater than 20. The number is less than 6. What is the number?
Answers
The following expression is equivalent to "double a number and add 12":
[tex]2x+12[/tex]since the result is greater than 20, we have the following:
[tex]\begin{gathered} 2x+12>20 \\ \Rightarrow2x>20─12=8 \\ \Rightarrow x>\frac{8}{2}=4 \\ x>4 \end{gathered}[/tex]the number is also less than 6. Then we have that:
[tex]4therefore, the number is 5You recently bought a new car and arecurious how much it's value drops over timeYou do some research and find out that yourbrand of car depreciates 10% per year andyou bought it new for $12,000. Write anexponential equation to represent the valueof the car, f(x), based on the number of yearssince you bought it (x) (show work)A) how much will your car be worth after5 years?B) how much will your car be worth after12 years?
Answers
SOLUTION
The price of the car = $12,000
The depreciate by 10%
[tex]\begin{gathered} \text{ The depreciating value for the first year } \\ 12,000\times(\frac{10}{100})^1 \\ \text{Then} \\ 12,000\times0.1 \end{gathered}[/tex]Then
[tex]12,000-12,00(0.1)[/tex]Then
[tex]\begin{gathered} 12000(1-0.1) \\ 12,000(0.9) \end{gathered}[/tex]For the first year the depreciating value will be
[tex]12,000(0.9)[/tex]Base on the number of years, the exponential equation will be
[tex]\begin{gathered} f(x)=12,000(0.9)^x \\ \text{where } \\ x=\text{ number of years } \end{gathered}[/tex]Therefore
The exponential equation that represent the value of the car is
F(x)=12,000(0.9)^x
The price of the car in 5 yeras will be obtain by substituting x=5 into the equation above
[tex]\begin{gathered} f(x)=12,000(0.9)^x \\ \text{where x=5} \\ f(x)=12,000(0.9)^5=7085.88 \end{gathered}[/tex]The car will worth $7085.88 after 5 years
Similarly, The for 12 years we have x=12
[tex]f(x)=12,000(0.9)^{12}=3389.15[/tex]The car will worth $3389.15 after 12 years
24 cm 12 cm find the volume of the figure and leave pi in the answer
Answers
Explanation:
The volume of a cone is one third the area of the base times the height of the cone:
[tex]V=\frac{1}{3}\pi r^2h[/tex]r is the radius of the base and h is the height.
In this problem, the radius is 12cm and the height is 24cm. The volume is:
[tex]V=\frac{1}{3}\pi\cdot12^2\cdot24=\pi\cdot\frac{144\cdot24}{3}=\pi\cdot\frac{3456}{3}=\pi\cdot1152[/tex]Answer:
The volume is V = 1152 π
Consider the following functions. Find four ordered pairs that satisfy the function
Answers
Since the function f(x) is
[tex]f(x)=\sqrt[]{x-7}[/tex]Since there is no square root for negative numbers, then
[tex]x-7\ge0[/tex]We will solve it by adding 7 to both sides
[tex]\begin{gathered} x-7+7\ge0+7 \\ x\ge7 \end{gathered}[/tex]Then we can choose values of x from 7 and greater
Let x = 7
[tex]\begin{gathered} f(7)=\sqrt[]{7-7} \\ f(7)=\sqrt[]{0} \\ f(7)=0 \end{gathered}[/tex]The 1st ordered pair is (7, 0)
Let x = 11
[tex]\begin{gathered} f(11)=\sqrt[]{11-7} \\ f(11)=\sqrt[]{4} \\ f(11)=2 \end{gathered}[/tex]The 2nd ordered pair is (11, 2)
Let x = 8
[tex]\begin{gathered} f(8)=\sqrt[]{8-7} \\ f(8)=\sqrt[]{1} \\ f(8)=1 \end{gathered}[/tex]The 3rd ordered pair is (8, 1)
Let x = 16
[tex]\begin{gathered} f(16)=\sqrt[]{16-7} \\ f(16)=\sqrt[]{9} \\ f(16)=3 \end{gathered}[/tex]The 4th ordered pair is (16, 3)
The 4 ordered pairs are (7, 0), (8, 1), (11, 2), (16, 3)
give an example of a positive tempature and a negative tempature that have a diffrence of 5 fedagree
Answers
We can think of temperatures above zero F and below zero F. For example weather conditions in cold places like Alaska.
In the morning, the temperature could be 2 degrees F (above zero)), but later towards the night, the temperature could be below zero in three units : -3 degrees F.
So the difference is the distance from zero to 2 (above) and the distance to zero from below 3 (below the zero mark. so these two differences from zero add up as 2 + 3 = 5
The way to do such in one go with math is to write the "difference" (normally associated with a SUBTRACTION, of the form: 2 - (-3), and therefore use that the negative (or opposite) of a negative number is a positive number:
- (-3) = +3
The same happens when we want to compare the difference between
9 - (-15) = 9 + 15 = 24
with the difference:
-15 - 9 = -24
The important thing is to consider the absolute value if we just want to find the number of units between the values, how many units they are separated.
And if we need to find what needs to be added or subtracted to one of them, at that point the sign of the difference is critical. This is because in one case we will need to add to get to the other number, while in the other case we need to subtract.
Write the equation of the line that is perpendicular to the line 8y−16=5x through the point (5,-5).A. y=5/8x+3B. y=−8/5x−3C. y=−8/5x+3D. y=8/5x+3
Answers
Given the equation of the line below,
[tex]8y-16=5x[/tex]If the line passes through the point,
[tex](5,-5)[/tex]Re-writing the eqaution of the line in slope intercept form,
[tex]\begin{gathered} 8y-16=5x \\ 8y=5x+16 \\ \text{Divide both sides by 8} \\ y=\frac{5x}{8}+\frac{16}{2} \\ y=\frac{5}{8}x+2 \end{gathered}[/tex]The slope of the perpendicular line is the negative reciprocal of the slope of the eqaution of the line in the slope-intercept form given above
The general form of the slope-intercept form of the equation of a straight line is,
[tex]\begin{gathered} y=mx+c \\ \text{Where m is the slope} \\ y=\frac{5}{8}x+2 \\ m=\frac{5}{8} \\ \text{Slope of the perpendicular line is} \\ m_1=-\frac{1}{m} \\ m_{1_{}}=-\frac{1}{\frac{5}{8}}=-1\times\frac{8}{5}=-\frac{8}{5} \end{gathered}[/tex]The formula to find the equation of a line with point (5, -5) below is,
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=m_1 \\ \text{Where} \\ (x_1,y_1)=(5,-5) \\ m_1=-\frac{8}{5} \end{gathered}[/tex]Substitute the values into the formula of the eqaution of a straight line,
[tex]\begin{gathered} \frac{y-(-5)}{x-5}=-\frac{8}{5} \\ \frac{y+5}{x-5}=-\frac{8}{5} \\ \text{Crossmultiply} \\ 5(y+5)=-8(x-5) \\ 5y+25=-8x+40 \\ \text{Collect like terms} \\ 5y=-8x+40-25 \\ 5y=-8x+15 \\ \text{Divide both sides by 5} \\ \frac{5y}{5}=-\frac{8}{5}x+\frac{15}{5} \\ y=-\frac{8}{5}x+3 \end{gathered}[/tex]Hence, the right option is C
What is the value of x in the triangle below?2460O 12813O 122O 12/3
Answers
The question gives us a right-angled triangle and find the value of x.
In order to solve the problem, we use SOHCAHTOA. In this case, we will use "SOH" from SOHCAHTOA because we have the Opposite as x and Hypotenuse as 24, while the relevant angle is 60 degrees.
Let us apply this formula:
[tex]\begin{gathered} \text{ SOH implies:} \\ \sin \theta=\frac{\text{Opposite}}{\text{Hypotenuse}} \\ \\ \theta=60^0,\text{Opposite}=x,\text{Hypotenuse}=24 \\ \\ \therefore\sin 60^0=\frac{x}{24} \end{gathered}[/tex]We simply need to make x the subject of the formula and we shall also represent sin 60 with its surd form.
This is done below:
[tex]\begin{gathered} \sin 60^0=\frac{x}{24} \\ \text{ Multiply both sides by 24} \\ 24\times\sin 60^0=\frac{x}{24}\times24 \\ \therefore x=24\times\sin 60^0 \\ \\ \sin 60^0=\frac{\sqrt[]{3}}{2} \\ \\ x=24\times\frac{\sqrt[]{3}}{2}=12\times2\times\frac{\sqrt[]{3}}{2}\text{ (2 crosses out)} \\ \\ x=12\sqrt[]{3} \end{gathered}[/tex]Therefore, the final answer is Option 4
limit using L'Hopital's rule . I just want to make sure if my answer is correct or not?
Answers
In order to use L'Hopital's rule, it is necessary to rewrite the limit as the quotient of two functions. Notice that:
[tex]\begin{gathered} 6x^{\sin (4x)}=e^{\ln (6x^{\sin (ex)})^{}} \\ =e^{\sin (4x)\cdot\ln (6x)} \end{gathered}[/tex]Since the exponential function is a continuous function, then:
[tex]\lim _{\text{x}\rightarrow0}e^{\sin (4x)\cdot\ln (6x)}=e^{\lim _{x\rightarrow0}\sin (4x)\cdot\ln (6x)}[/tex]Find the following limit using L'Hopital's rule:
[tex]\lim _{x\rightarrow0}\sin (4x)\cdot\ln (6x)[/tex]Write the function as a fraction:
[tex]\lim _{x\rightarrow0}\frac{\ln (6x)}{(\frac{1}{\sin (4x)})}[/tex]Use L'Hopital's rule to rewrite the limit as the limit of the quotient of the derivatives:
[tex]\begin{gathered} \lim _{x\rightarrow0}\frac{(\frac{1}{x})}{(-\frac{4\cos(4x)}{\sin^2(4x)})}=\lim _{x\rightarrow0}-\frac{\sin ^2(4x)}{4x\cdot\cos (4x)} \\ =\lim _{x\rightarrow0}\sin (4x)\cdot\frac{\sin(4x)}{4x}\cdot\frac{-1}{\cos (4x)} \\ =\lim _{x\rightarrow0}\sin (4x)\cdot\lim _{x\rightarrow0}\frac{\sin(4x)}{4x}\cdot\lim _{x\rightarrow0}\frac{-1}{\cos (4x)} \\ =0\cdot1\cdot-1 \\ =0 \end{gathered}[/tex]Therefore:
[tex]\lim _{x\rightarrow0}6x^{\sin (4x)}=e^0=1[/tex]solve the system by subsitution method
Answers
Substitute Y = 3X - 6
in second equation
-15X + 5•(3X - 6) = -30
Now solve for X, cancel parenthesis
use a(b+c) = ab + ac
-15X + 15 X - 30 = -30
. -30 = -30
Then we see that, have infinite solutions
In consecuence, ANSWER IS
OPTION D) (x , 3x - 6 )
936.1 ÷ 2.3how do i calculate this without a calculator
Answers
Using long division:
Move the decimal point in the divisor and the dividend 1 unit
Estimate 20 x 37 x 21/5 ÷ 98. Is it an overestimate or underestimate? Explain.
Answers
20 x 37 x 21/5 ÷98
Find if 20 x 37 x 21/5 is bigger or lower than 98
20x37x21/5= 15540/5= 3108
Then 3108/98 is an overestimate
= 3108/98=31. 71
Answer is 31.71
in the equation 4x^3=56, what is the value of x
Answers
The given equation is
[tex]4x^3=56_{}[/tex]First, we divide the equation by 4.
[tex]\begin{gathered} \frac{4x^3}{4}=\frac{56}{4} \\ x^3=14 \end{gathered}[/tex]At last, we take the cubic root on each side.
[tex]\begin{gathered} \sqrt[3]{x^3}=\sqrt[3]{14} \\ x\approx2.41 \end{gathered}[/tex]Therefore, the value of x is 2.41, approximately.Graph the line with slope -3/4 passing through the point (4,3)
Answers
The graph is displayed after the explanation
Explanation:The slope is rise/run = -3/4
The line passes through (4, 3)
The run is 4, we add 4 to the x-coordinate
The rise is -3, we add -3 to the y-coordinate
We have:
(4 + 4, 3 - 3) = (8, 0)
We use (4, 3) and (8, 0) to graph the line
The graph is shown below:
PLS HELP 99 POINTS! GEOMETRY & ALGEBRA QUESTION
find m
a-52
b-142
c-24
d-50
e-64
Answers
Since we know that a right angle (Q) is 90 degrees we can use it to add to (x+2) to get the exterior angles measure.
So our equation would be X+2+90= 3x-8
Then : X+92=3x-8
X+100 =3x
100= 2x
50 = x
BUT THATS NOT OUR ANSWER!
Now we must substitute X into the exterior angles equation!
So: 3(50) -8
150-8
142
So your exterior angle (PRS) would be B.) 142 degrees
Answer:
b
Step-by-step explanation:
∠ QRP and ∠ PRS are a linear pair and sum to 180° , that is
∠ QRP + 3x - 8 = 180 ( subtract 3x - 8 from both sides )
∠ QRP = 180 - (3x - 8) = 180 - 3x + 8 = 188 - 3x
the sum of the 3 angles in Δ PQR = 180° , that is
188 - 3x + x + 2 + 90 = 180
- 2x + 280 = 180 ( subtract 280 from both sides )
- 2x = - 100 ( divide both sides by - 2 )
x = 50
Then
∠ PRS = 3x - 8 = 3(50) - 8 = 150 - 8 = 142°
Practice Skills_Simplifying Equations1. 3( 1/2 - y) = 3/5 + 15y. What isthe solution to the given equation?
Answers
You have the following equation:
3(1/2 - y) = 3/5 + 15y
In order to solve the previous equation you proceed as follow:
3(1/2 - y) = 3/5 + 15y eliminate parenthesis
3/2 - 3y = 3/5 + 15y multiply by 5 both sides
15/2 - 15y = 3 + 75y multiply by 2 both sides
15 - 30y = 6 + 150y sum 30y both sides and subtract 6 both sides
15 - 30y + 30y - 6 = 6 + 150y + 30y - 6 simplify
9 = 180y divide by 180 both sides
9/180 = 180y/180 simplify
1/20 = y
(the multiplication by 5 and 2 is for eliminating denominator with the same number)
Hence, the solution to the given equation is y = 1/20
An office uses paper drinking cups in the shape of a cone, with dimensions as shown.-23 in.4 in.To the nearest tenth of a cubic inch, what is the volume of each drinking cup?A. 2.5B. 7.9C. 23.7D. 31.7
Answers
According to the formula for volume of a cone and rounding to the nearest tenth of cubic inch, we find out that the volume of each drinking cup is 7.9 cubic inch. Thus, option B is correct.
From the given figure, we have
Diameter of the cone-shaped cups, d = [tex]2\frac{3}{4}[/tex] in = 2.75 in
Height of the cone-shaped cups, h = 4 in
We have to find out the volume of each drinking cup.
Since, d = 2.75 in (Given), we can say that
The radius of the cone-shaped cups, r = [tex]\frac{1}{2}*2.75[/tex]
=> r = 1.375 in
We know that the volume of a cone can be represented as -
[tex]V = \frac{1}{3} \pi r^{2}h[/tex]
Putting the value of radius, r and height, h in the above equation of volume of the cone, we get
Volume, [tex]V = \frac{1}{3} \pi r^{2}h[/tex]
=> [tex]V = \frac{1}{3}\pi (1.375)^{2}*4\\= > V = 7.919 in^{3}[/tex]
Thus, using the formula for volume of a cone and rounding to the nearest tenth of cubic inch, we find out that the volume of each drinking cup is 7.9 cubic inch. Thus, option B is correct.
To learn more about volume of a cone visit https://brainly.com/question/1984638
#SPJ9
Answer:According to the formula for volume of a cone and rounding to the nearest tenth of cubic inch, we find out that the volume of each drinking cup is 7.9 cubic inch. Thus, option B is correct.
Step-by-step explanation:
how would I figure this out (this assignment is just a practice but I dont have any notes to look off of and I'm confused)
Answers
We have the following:
We have the following points that are on the graph:
(-2, 1); (0, -1); (2, 1); (4, 3)
We must evaluate each point in the functions to know which is correct
F
y = x - 1
[tex]y=-2-1=-3[/tex]the first point does not match, therefore this function is not correct
H
y = x^2 - 1
[tex]y=(-2)^2-1=4-1=3[/tex]the first point does not match, therefore this function is not correct
G
y = |x| - 1
[tex]\begin{gathered} y=|-2|-1=2-1=1 \\ y=|0|-1=0-1=-1 \\ y=|2|-1=2-1=1 \\ y=|4|-1=4-1=3 \end{gathered}[/tex]In this function, all the points coincide, therefore the answer to the question is the function G
How do you subtract 5/6 - 5/9 then write it as a fraction in simplest form?
Answers
To subtract two fractions we can use the following:
[tex]\frac{a}{b}-\frac{c}{d}=\frac{(a\cdot d)-(b\cdot c)}{b\cdot d}[/tex]So 5/6 - 5/9 is equal to:
[tex]\frac{5}{6}-\frac{5}{9}=\frac{(5\cdot9)-(6\cdot5)}{6\cdot9}=\frac{45-30}{54}=\frac{15}{54}[/tex]Finally, we can simplify the fraction dividing the numerator and denominator by 3, as:
[tex]\frac{15}{54}=\frac{15/3}{54/3}=\frac{5}{18}[/tex]So, the answer is 5/18
Answer: 5/18
1/2 n + 3 < 5 how would it be shown on a graph
Answers
To solve this inequality we need to isolate the variable "n" on the left side.
[tex]\frac{1}{2}n<5-3[/tex]Since there was a "+3" on the left side we needed to change its side, by inverting the number's signal.
[tex]\begin{gathered} \frac{1}{2}n<2 \\ n<2\cdot2 \\ n<4 \end{gathered}[/tex]Since the variable we need to calculate was multiplying "1/2" we needed to multiply both sides by 2 in order to find its value. The solution is n < 4.
Identify the following series as geometric or arithmetic. Also identify the series as infinite or finite.5, 10, 20, 40, 80, 160, 320geometricarithmeticinfinitefinite
Answers
the series is geometric and finite
Explanation:Given:
5, 10, 20, 40, 80, 160, 320
To find:
if the series is arithmetic or geometric; infinite or finite
a) For a series to be arithmetic, it must have a common difference
common difference = next term - previous term
For the series to be geometric, it must have a common ratio
common ratio = next term/previous term
We need to check if it has a common difference or common ratio
let next term = 10, previous term = 5
common difference = 10 - 5 = 5
let next term = 20, previous term = 10
common difference = 20 - 10 = 10
The difference is not common, it is different
common ratio = next term/previous term
let next term = 10, previous term = 5
common ratio = 10/5 = 2
let next term = 20, previous term = 10
common ratio = 20/10 = 2
The ratio is common
As a result, the series is geometric
b) Infinite series cannot be counted and totaled. This is because they do not end
Finite series can be counted and summed up. This is because the series has an end.
The series is finite
Answer:
geometric
finite
Step-by-step explanation:
Correct on Odyssey.
:)
(6.4x10^5)-(5.4x10^4)
Answers
Solution:
Given:
[tex](6.4\times10^5)-(5.4\times10^4)[/tex][tex]\begin{gathered} (6.4\times10^5)-(0.54\times10^5)=(6.4-0.54)\times10^5 \\ =5.86\times10^5 \end{gathered}[/tex]Also, we can rewrite the numbers as ordinary number and get the difference;
[tex]\begin{gathered} 640000-54000=586,000 \\ \\ As\text{ scientific notation;} \\ 586,000=5.86\times10^5 \end{gathered}[/tex]Therefore;
[tex](6.4\times10^5)-(5.4\times10^4)=5.86\times10^5[/tex]
Answer:
586000
Step-by-step explanation:
(6.4×10^5)-(5.4×10^4)
=640000-54000
=586000
Crystal earns $4.75 per hour mowing lawns. A. write a rule to describe how the amount of money M earned is a function of the number of hours H that mowing lawns. B. l how much does crystal earn if she works 1 hour and 15 minutes?
Answers
Given:
Crystal earns $4.75 per hour mowing lawns.
Let the money earned = M
And the number of hours = H
So, the relation between M and H will be :
[tex]M=4.75\cdot H[/tex]B. how much does crystal earn if she works 1 hour and 15 minutes?
Time = 1 hours and 15 minutes
AS 1 hour = 60 minutes
So,
[tex]H=1+\frac{15}{60}=1+\frac{1}{4}=1+0.25=1.25[/tex]Substitute with H to find M
So,
[tex]M=4.75\cdot1.25=5.9375[/tex]So, she will earn $5.9375
A group of friends will buy at most 8 snacks at a movie theater and spend no more than $42. They will pay $4.00 for each box of candy and $7.00 for each bag of popcorn. The system of inequalities graphed below represents this information.
Answers
Let x = candy , y = popcorn
so,
the cost of one box of candy = $4
The cost of one bag of popcorn = $7
so, the solution of part A
The system of inequalities represents the situation is as following:
[tex]\begin{gathered} x+y\leq8 \\ 4x+7y\leq42 \end{gathered}[/tex]========================================================================
Part B:
We need to find which combination of candy and popcorn could the group buy:
a. 2 candy and 6 popcorn
check for the first inequality : 2 + 6 = 8
check for the second inequality : 2 * 4 + 7 * 6 = 8 + 42 = 50 > 42
So, this option is wrong
b. 3 candy and 4 popcorn
check for the first inequality : 3 + 4 = 7 < 8
check for the second inequality : 4 * 3 + 7 * 4 = 12 + 28 = 40 < 42
So, this option is true
c. 5 candy and 4 popcorn
check for the first inequality : 5 + 4 = 9 > 8
So, this option is wrong
d. 8 candy and 1 popcorn
check for the first inequality : 8 + 1 = 9 > 8
So, this option is wrong
so, the answer of part B is:
option b
the group could by 3 boxes of candy and 4 bags of popcorn
If segments WY and XZ are diameters of circle T, and WY=XZ=6. If minor arc XY= 140 degrees, what is the length of arc YZ?
Answers
hello
to solve this question, we need to draw an illustration
since we are looking for the major arc, we would subtract the minor arc from 360 degrees
major arc YZ =
[tex]\begin{gathered} yz=360-xy \\ yz=360-140=220 \end{gathered}[/tex]now, we know the angke on the major arc is equal to 220 degrees, we can use this information to solve for the length of the arc.
length of an arc
[tex]\begin{gathered} L_{\text{arc}}=\frac{\theta}{360}\times2\pi r \\ \theta=angle \\ r=\text{radius} \\ \pi=3.14 \end{gathered}[/tex]but in this question, we were given the diameter of two segements. we can use that information to solve for the radius
[tex]\begin{gathered} radius=\frac{diameter}{2} \\ \text{diameter}=wx=xz=6 \\ \text{radius(r)}=\frac{6}{2}=3 \end{gathered}[/tex]let's insert this and other variables into our equation
[tex]\begin{gathered} L_{\text{arc}}=\frac{\theta}{360}\times2\pi r \\ \text{L}_{\text{arc}}=\frac{220}{360}\times2\times3.14\times3 \\ L_{\text{arc}}=11.513 \end{gathered}[/tex]from the calculations above, the length of the arc YZ is equal to 11.513