Answer:
Slope of the line 12=4x−6y is [tex]\frac{2}{3}[/tex] .
Step-by-step explanation:
The slope line form is denoted by
y = mx + c
Where m is the slope and c is the y- intercept .
As given
The equation of the line is given by .
12=4x−6y
It is also written as
6y = 4x - 12
[tex]y = \frac{4x}{6} -\frac{12}{6}[/tex]
Simplify the above
[tex]y = \frac{2x}{3} -2[/tex]
(Compare with y = mx + c )
Thus
[tex]m = \frac{2}{3}[/tex]
Therefore the slope of the line 12=4x−6y is [tex]\frac{2}{3}[/tex] .
With a tail wind, a plane traveled 840 miles in 3hrs. With the same wind as a head wind, the return trip took 30 minutes longer. Find the plane's airspeed(in still air) and the wind speed....
So lost smh
To find the plane's airspeed (in still air) and wind speed, we can use the concept of relative velocity. By setting up a system of equations using the distances and times for the outbound and return trips, we can solve for the values of the airspeed and wind speed. Solving these equations, we find that the plane's airspeed is 230 mph and the wind speed is 70 mph.
Explanation:To find the plane's airspeed and wind speed, we can use the concept of relative velocity. Let's assume the plane's airspeed (in still air) is P mph and the wind speed is W mph.
On the outbound trip, with a tailwind, the plane's groundspeed (the speed relative to the ground) will be the sum of its airspeed and the wind speed: P + W mph. Since the distance traveled is 840 miles and the time taken is 3 hours, we have the equation: Distance = Speed * Time, where Speed is the groundspeed. Therefore, we can write the equation as: 840 = (P + W) * 3.
On the return trip, with the same wind as a headwind, the plane's groundspeed will be the difference between its airspeed and the wind speed: P - W mph. As it took 30 minutes longer, the time taken will be 3 hours + 0.5 hours = 3.5 hours. Using the same equation, we have: 840 = (P - W) * 3.5.
Now we have a system of equations, which we can solve to find the values of P and W. Solving these equations, we get:
Airspeed (in still air) = 230 mph
Wind speed = 70 mph
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Jake is comparing the prices of two laundry service companies . company a charges $20 per load and an additional $8 as service charges . company B charges $24 per load and an additional $4 as service charges .
part A: write equations to represent company a's and company b's total laundry charges for a certain number of loads. define the variable used in the equations
part B: which company would charge less for 5 seconds of laundry ?
part C: how much money is saved by using the services of company A instead of company B to clean 9 loads of laundry
What is the slope?
What is the y intercept?
What is the x intercept?
What is the equation of the line in slope intercept form?
What is the equation of the line in standard form?
Answer: Slope- (-1/2)
Y intercept- (-4)
the x intercept is -8
the equation of the line in slope intercept form is y= -1/2x-4
the equation of the line in standard form is -1/2x-4y=0
What is the exterior angle of triangle ABC
These are the points:
A=3, B=10, C=6
You are designing a rectangular sign for your school’s football team. The sign will be 6 yd wide and 9 ft high. How many square yards of material do you need?
Which equation can be used to find the value of b if side a measures 8.7 cm? 8.7 + b = 54.6 17.4 + b = 54.6 26.1 + b = 54.6 34.8 + b = 5
What is the product written in scientific notation? (5.91×10−3)⋅(8.7×1010)
Answer:
Product [tex]5.1417 *10^{8})[/tex].
Step-by-step explanation:
Given : [tex](5.91* 10^{-3} )(8.7*10^{10})[/tex].
To find : What is the product written in scientific notation.
Solution : We have given
[tex](5.91* 10^{-3} )(8.7*10^{10})[/tex].
Combine like terms
[tex]5.91 * 8.7 * 10^{-3}*10^{10})[/tex].
[tex]51.417 * 10^{-3}*10^{10})[/tex].
[tex]51.417 *10^{7})[/tex].
In scientific notation
[tex]5.1417 *10^{8})[/tex].
Therefore, Product [tex]5.1417 *10^{8})[/tex].
Customers have two options when renting video games from a rental store. Plan A requires a $5 monthly fee and $1 per video rental. Plan B requires an $8 monthly fee and $0.75 per video rental. How many video rentals would be required each month for the plans to cost the same amount?
Find measure of angle d A. 122 degrees B. 61 degrees C. 238 degrees D. Not enough information
To find the measure of angle d, you can use the dot product formula and inverse cosine function.
Explanation:To find the measure of angle d, we need to consider the given information about vectors A and B. The vector A is represented as (122 cm, <145°) and the vector B is represented as (110 cm, <270°). The angle between two vectors can be found using the dot product formula: cos(theta) = A · B / (|A| * |B|). So, we can calculate the dot product and magnitude of vectors A and B, and then use the inverse cosine function to find the angle between them. The measure of angle d is __ degrees.
arlene grossman earns $235 per week her federal income tax is $36.00 her FICA tax is 6.2% arlene is also subject to a 3% state income tax and a 1% city tax whats her net pay
what did the candle say to the match
Can someone explain 15-20? I really need help and it's due tomorrow. Thank you in advance!
What was the approximate number of mobile cellular subscriptions per 100 people in Zimbabwe in 2003?
The display gives the result of performing an exponential regression on a data set where the inputs are years since 2000 and the outputs are the corresponding mobile cellular subscriptions per 100 on Zimbabwe.
ExpReg
y=a*b^x
a=1.067905095
b=1.501755837
r^2=.9525580427
r= .9759908005
A. 2
B. 4
C. 6
D. 8
Answer:
B. 4
Step-by-step explanation:
Given exponential model that shows the number of mobile cellular subscriptions per 100 people in Zimbabwe since 2000,
[tex]y=a b^x[/tex]
Where,
a=1.067905095
b=1.501755837,
[tex]\implies y=1.067905095(1.501755837)^x[/tex]
Since, the number of years from 2000 to 2003 = 3,
Thus, for finding the number of subscriptions in 2003,
x = 3,
Hence, the number of mobile cellular subscriptions per 100 people in Zimbabwe in 2003 is
[tex]y=1.067905095(1.501755837)^3=3.61685122094\approx 4[/tex]
Option 'B' is correct.
If x is an even number, the function f(x) = 2x − 1 gives an odd number. Identify the set of odd numbers corresponding to this set of even numbers: {0, 2, 4, 6, 8}.
Find the perimeter of the figure. 2 1/4 in, 4 1/12in, 3 2/3in
If f(x) = 5x, what is f–1(x)?
A. f–1(x) = –5x
B. f-1(x)=-1/5x
C. f-1(x)=1/5x
D. f–1(x) = 5x
Interchange to get:
x=5y-7
Solve for y to get:
y=(1/5)x+(7/5)
so I think it might be c
Answer:
The answer is C.
Step-by-step explanation:
Step 1: Replace f(x) with y.
f(x)=5x >>>>> y=5x
Step 2: Switch x and y.
y=5x >>>>> x=5y
Step 3: Solve for y
x=5y >>>> y= x/5
Then you have to do the inverse of dividing by 5. Which is multipilying by 1/5. This leaves you with,
y= 1/5x
Step 4: Write in standard inverse notation (Replace y with f^-1(x))
f^-1(x)=1/5x
Note: These steps work with ANY problem where you have to find the inverse function. I hope this helps :)
What is the point slope form of the line with slope −1/4 that passes through the point (−2, 9) ?
y+9=−14(x−2)
y−2=−14(x+9)
y+2=−14(x−9)
y−9=−14(x+2)
Answer:
Step-by-step explanation:
Point slope form of the equation with point (a,b) and slope m is given by this equation
y-b=m(x-a)
Here we are given that the slope is -1/4 so m= -1/4
and the point is (-2,9) so a =-2 and b =9
Hence plugging the values in the equation we get
y-9 = -1/4 (x-(-2))
y -9 =-1/4 (x+2)
What is the area of a rectangle with vertices at (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1) ? Enter your answer in the box. Do not round any side lengths.
The area of the rectangle is 18 square units if the vertices at (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1).
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is defined as the two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.
It is given that:
A rectangle with vertices at a (−6, 3) , b (−3, 6) , c(1, 2) , and d(−2, −1)"
As we know,
The distance formula can be given as:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
ab = √(x₁-x₂)²+(y₁-y₂)²
=√(-6+3)²+(3-6)²
= √18
cd =√(1+2)²+(2+1)²
= √18
Area= lxw
A=√18x√18
a=18
Thus, the area of the rectangle is 18 square units if the vertices at (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1).
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What is the equation of a line with a slope of 2 that goes through the point (4,12)?
A new car has an msrp of $20,150, and it comes with a sport package priced at $1500, a stereo package priced at $500, and a destination charge of $700. what is the sticker price of this car?
Jacks wild souvenirs shop is selling all shirts for $10 each and all flip flops for $5 per pair. At the end of one day jacks shirts and flip flops sales totaled $325 for $41 items. How many shirts and flip flops did jack sell?
A local charity sponsors a 5K race to raise money. It receives $25 per race entry and $5,000 in donations, but it must spend $5 per race entry to cover the cost of the race. Write and solve an inequality to determine the number of race entries the charity needs to raise more than $25,000. Show your work!
What is the square root of 99 simplified?
Step-by-step explanation: To simplify the square root of 99, first create a factor tree that has 2 branches.
99 factors as 11 × 9 and 9 factors as 3 × 3.
Since we have a pair of 3's in our factor tree, a 3 can come out of the radical. Since we have a 11 that doesn't match up, it stays inside the radical and this gives us the answer of [tex]\sqrt[3]{11}[/tex].
I have also attached my work in the image provided.
The square root of 99, when simplified as much as possible, is approximately 9.94987437.
We have,
The square root of a number is a value that, when multiplied by itself, gives the original number.
In the case of the square root of 99, there is no whole number that can be multiplied by itself to result in 99.
Therefore, the square root of 99 is an irrational number.
To find an approximate value for the square root of 99, we can use a calculator or mathematical methods.
The square root of 99 is approximately 9.94987437.
This means that when we multiply 9.94987437 by itself, we get a value close to 99.
Since 9.94987437 cannot be simplified further as a whole number or a simplified radical, it is the most accurate representation of the square root of 99.
Thus,
The square root of 99, when simplified as much as possible, is approximately 9.94987437.
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If 5 is transformed into 11 and 12 is transformed into 25, then what does 15 become
what is the estimate of 39% of 120
A diver descends to a location of −5014 meters relative to the surface of the water. He then descends another 1012 meters.
What is the diver’s final location relative to the surface of the water?
Enter your answer as a simplified mixed number in the box.
Answer: Using operations with fractions, the diver's final location is:
- 60 3/4 meters relative to the surface of the water (60 3/4 meters below the surface of the water).
Solution:
Initial location: -50 1/4 meters
He descends another 10 1/2 meters: -10 1/2 meters
Final location = Initial location - 10 1/2 meters
Final location = - 50 1/4 meters - 10 1/2 meters
Final location = - (50+10) (1/4+1/2) meters
Final location = - 60 [(1)(1)+2(1)]/4 meters
Final location = - 60 (1+2)/4 meters
Final location = - 60 3/4 meters
Which graph represents the solution set of the system of inequalities?
{3y≥x−9
3x+y>−3
WHICH ONE ?
the first graph
the solid line passes through (0,-3) and (0,9)
dotted line passes through (0,-3) and (0,-1)
see attached sketch
A 120 lb person would weight about 20 lb on the earth's moon .A 150 lb. person would weight 28lb. on lo, a moon of jupiter.
Write a compound inequality that represents the situation.
all real numbers at least –6 and at most 3
Answer:
[tex]\[-6 \leqslant x \leqslant 3\][/tex]
Step-by-step explanation:
The requirement is to represent a compound inequality with all real numbers at least –6 and at most 3.
This can be broken into two parts:
a) All real numbers at least -6
[tex]\[x\geqslant -6\][/tex]
b) All real numbers at most 3
[tex]\[x \leqslant 3\][/tex]
Combining the two inequalities to generate the compound inequality:
[tex]\[-6 \leqslant x \leqslant 3\][/tex]
What is the answer to p/3 -2=1