Simplify. Show your work.
5 1/3 + (-3 9/18)
Answer: Hello there!
I understand the notation 5 1/3 is equivalent to 5 + 1/3 = 5.333...
our equation is 5 +1/3 +(-3 +9/18)
first we could simplify the 9/18 as 1/2 (dividing both numerator and denominator by 9)
then the equation is:
=5+ 1/3 - (3 +1/2)
=5 + 1/3 - 3 - 1/2
=5 -3 + (1/3 - 1/2)
the common factor betwe 3 and 2 is 6, then:
=2 + (2/6 - 3/6) = 2 -1/6
this can be written as:
= 2 - 1/6 = 1 + 1 -1/6 = 1 + ( 1-1/6) = 1 + 5/6
or = 1 5/6 using the original notation.
A bag contains 10 black jellybeans, 12 green ones, 3 orange ones, and 20 blue ones. if you reach in and grab one randomly, what is the probability of picking
evaluate 3log3^21 ...?
PB is a line segment on a number line. It has endpoints at -2 and 12. What is the coordinate of its midpoint.
Answer:
pb and 5
Step-by-step explanation:
If ef = 6 and eg = 21 what is the value of fg
If EF = 6 and EG = 21 what is the value of FG?
The answer is 15.

The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function?
The domain is all real numbers. The range is {y|y < 16}.
The domain is all real numbers. The range is {y|y ≤ 16}.
The domain is {x|–5 < x < The range is {y|y < 16}.
The domain is {x|–5 ≤ x ≤ The range is {y|y ≤ 16}.
Answer with explanation:
⇒Domain:
f(x)= -x² -2 x +15
= - (x²+2 x -15)
Splitting the middle term
= - (x²+5 x - 3 x -15)
= -[ x × (x+5) -3× (x+5)]
= -(x-3)(x+5)
y=f(x)=(3 -x)(x+5)
Domain of the function is defined as set of all values of x, for which y is defined.
f(x) is defined as all real values of x.So, Domain = R.
⇒Range:
[tex]y=-x^2-2 x +15\\\\y=-(x^2+2 x-15)\\\\ y=-[(x+1)^2-1-15]\\\\y= -(x+1)^2+16\\\\ 16 -y=(x+1)^2\\\\x+1=\pm\sqrt{16-y}\\\\x=\pm\sqrt{16-y}-1[/tex]
Range of the function is defined as set of all values of y, for which x is defined.
⇒16 -y ≥ 0
⇒y ≤ 16
Option B
The domain is all real numbers. The range is {y|y ≤ 16}.
PLEASE HELPPP!!!
1. Choose the equation that could be used to solve the given number problem.
The sum of two consecutive integers is 141. Find the integers.
n + 1= 141
2n + 2 = 141
2n = 141
2n + 1 = 141
2. Choose the equation that could be used to solve the given number problem.
The sum of two consecutive odd integers is 112. Find the integers.
2n + 3 = 112
2n + 2 = 112
2n + 1 = 112
n + 2 = 112
PTG has side lengths of 12 cm, 25 cm, and 19 cm. Which type of triangle is PTG?
right
acute
obtuse
isosceles ...?
Write a polynomial function to the least degree with these roots 2 &3i ...?
Angie needs to buy 156 candles for a party instead each package has 8 candles how many packages should angie buy
2 3/4 + 12 6/8 = HOW DO I FIGURE THIS
what is the answer to 3/5 3/20
Jasmine wants to organize her books in order of most number of pages to least number of pages. Jasmine's longest book has 396 pages and her shortest book has one-fourth as many pages as the longest. If the book in the middle of her shelf has three times the number of pages of the shortest book. Then how many pages does the middle book have?
Answer:
297 pages
Step-by-step explanation:
Number of pages of longest book = 396 pages
Now we are given that her shortest book has one-fourth as many pages as the longest.
Number of pages of shortest book = [tex]\frac{\text{Number of pages in longest book}}{4}[/tex]
= [tex]\frac{396}{4}[/tex]
= [tex]99[/tex]
Now we are given that the book in the middle of her shelf has three times the number of pages of the shortest book.
So, Number of pages in middle book:
= [tex]3 \times \text{Number of pages of shortest book}[/tex]
= [tex]3 \times 99[/tex]
= [tex]297[/tex]
Hence the middle book have 297 pages.
how do you derive the lens maker's equation? ...?
Using Snell’s law ( n1 sin θi = n2 sin θr ) at point A gives
1) sin i1 = n sin r1
2) i1 = n r1
3) i1 = α1 + β1
4) r1 = β1 - γ
5) α1 + β1 = n(β1 - γ)
6) sin i2 = n sin r2
7) i2 = n r2
8) i2 = α2 + β2
9) r2 = β2 + γ
10) α2 + β2 = n(β2 + γ)
11) α1 + α2 = (n - 1)(β1 + β2)
12) 1/s + 1/s' = (n - 1)(1/R1 + 1/R2)The lens maker's equation is derived by considering the image formed by the first refracting surface (left surface) and then using this image as the object for the second refracting surface. The equation takes into account the radii of curvature and the refractive indices of the lens and the surrounding medium.
Explanation:The lens maker's equation is derived by considering the image formed by the first refracting surface (left surface) and then using this image as the object for the second refracting surface.
The equation takes into account the radii of curvature and the refractive indices of the lens and the surrounding medium.
The lens maker's equation can be stated as: 1/f = (n₂ - n₁)((1/R₁) - (1/R₂)), where f is the focal length, n₂ is the refractive index of the lens, n₁ is the refractive index of the surrounding medium (usually air), R₁ is the radius of curvature of the first surface of the lens, and R₂ is the radius of curvature of the second surface of the lens.
What are the abbreviations in the dictionary for?
Write an equation of the line that passes through (−5, −2)(−5, −2) and is parallel to y=23x+1y=23x+1.
The equation of a line parallel to y=23x+1 that passes through the point (-5, -2) is y = 23x + 113.
Explanation:The subject of this question is geometry, specifically, the formulation of a linear equation. You're asked to write an equation of a line that passes through point (-5,-2) and is parallel to the line defined by the equation y=23x+1.
Parallel lines have the same slope, so since the given line has a slope of 23, our line will also have a slope of 23. The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. Here, 'm' is already known as 23. So, our equation currently is y = 23x + b.
We can determine 'b' using the given point (-5,-2). Substituting these coordinates into our equation gives -2 = 23*(-5) + b. Solving for 'b' renders b = -2 - (23*-5) = 113.
Therefore, the equation of the line that passes through (-5, -2) and is parallel to y=23x+1 is y = 23x + 113.
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The period of y = cos x occurs every 2pi units.
T/F?
True, the period of y = cos x occurs every 2pi units.
What are the trigonometric identities?Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.
Given:
Trigonometric function,
y = cosx.
To find the period:
Use formula,
period = 2π/the coefficient of cosx.
Period = 2π
Therefore, the period of y = cosx is 2π.
To learn more about the trigonometric identities;
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24 is 30% of what number
24 is 30% of 80
Image provided.
Jim earns $1,600 per month after taxes. He is working on his budget and has the first three categories finished.
Housing $576
Food $272
Transportation $320
Why will he have a problem with the rest of his budget?
Find dy/dx by implicit differentiation and evaluate the derivative at the given point.
xy = 35 ...?
Final answer:
To find dy/dx by implicit differentiation of the equation xy=35, differentiate both sides with respect to x. Use the product rule to obtain x * (dy/dx) + y = 0 and solve for dy/dx, giving dy/dx = -y / x. Evaluate this at a specific point by substituting the x and y values from that point into the derived formula.
Explanation:
To find dy/dx by implicit differentiation of the equation xy = 35, we differentiate both sides of the equation with respect to x. Since y is a function of x, when we differentiate y we must apply the chain rule, resulting in the derivative y with respect to x, or dy/dx.
Starting with the original equation:
xy = 35
We apply differentiation to both sides with respect to x:
Using the product rule for the left side: d/dx (xy) = d/dx (35)
This gives us x * (dy/dx) + y * (1) = 0 because the derivative of a constant, like 35, is 0.
We then solve for dy/dx: dy/dx = -y / x.
To evaluate the derivative at a given point, you substitute the x and y coordinates of that point into the derivative equation. For example, if we are given a point (5,7), we substitute into the dy/dx equation to find the derivative at that point:
dy/dx = -y / x = -(7) / (5)
Therefore, dy/dx at the point (5,7) is -7/5 or -1.4.
*PLEASE HELP ME!!!!!**
!!!STUCK ON 2 QUESTIONS!!!!
The time is takes to mow the lawn at a large park m(x) varies inversely with the numbers of workers assigned to the job x. It takes 90 minutes to complete the job when 3 workers are assigned to it.
which equation can be used to find the time to complete the job when x workers are assigned to it?
A.) m(x)= 270/x
B.) m(x) = 270x
C.) m(x) = 30/x
D.) m(x) = 30x
2. Suppose that H(x) varies inversely with x and H(x)=50 when x =0.25
What is H(x) when x =2?
A.) 0.5
B.) 6.25
C.) 12.5
D.) 24
Can you also provide how you got the answer as well :)
3. You are buying potato chips at the grocery store. You have a manufacturer’s coupon for $0.50 off and the store is offering 50% off if you buy 2 bags. How do you compute your final cost?
Subtract $0.50 off of each bag and then divide by 2.
Divide each bag by 2, subtract $0.50 off of each bag, and then add them together.
Add the two bags together, divide by 2, and then subtract $0.50.
Subtract $0.50 from the first bag, add them together, and then divide by 2.
Box of 12 golf balls costs $45. what is the unit rate
The table shows ordered pairs of the function y = 16 + 0.5x
Which ordered pair could be the missing values represented by (x, y)?
a) (0, 18)
b) (5, 19.5)
c) (8, 20)
d) (10, 21.5)
the answer is C (8,20)
Answer:
c) (8, 20)
Step-by-step explanation:
We must plug in the given value of x in the function and confirm that the value of y that is returned to us is the correct one.
a) (0, 18)
[tex]x=0,y=18[/tex]
[tex]y = 16 + 0.5(0)=16+0=16[/tex]
the values for y do not match, so it is not a solution.
b) (5, 19.5)
[tex]x=5,y=19.5[/tex]
[tex]y = 16 + 0.5(5)=16+2.5=18.5[/tex]
again, the values for y do not match so it is not a solution.
c) (8, 20)
[tex]x=8,y=20[/tex]
[tex]y = 16 + 0.5(8)=16+4=20[/tex]
For this option, the values of y do match, so (8, 20) are the missing values.
A farmer's land is separated into sections of size
2 1/5
acres. Suppose there are
4 4/9
such sections. How many acres of land does the farmer own?
The farmer owns 8 10/45 acres of land.
Explanation:To find out how many acres of land the farmer owns, we need to multiply the number of sections by the size of each section. The size of each section is 2 1/5 acres.
The number of sections is 4 4/9. Using multiplication, we can calculate the total number of acres:
(2 1/5) x (4 4/9) = 10/5 x 40/9 = 400/45 = 8 10/45
Therefore, the farmer owns 8 10/45 acres of land.
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You are on a 650-mile trip. your car used eight gallons of gas to travel the first 210 miles of the trip. how much more gas will you need to make it the rest of the way at the same rate?
The car will need approximately 8.76 more gallons of gas to complete the remaining 440 miles of the 650-mile trip, assuming it continues to get the same mileage rate of 26.25 miles per gallon.
Explanation:To calculate the additional amount of gas needed to complete the 650-mile trip, given that the car used eight gallons to travel the first 210 miles, we need to find the car's mileage rate and then determine how much more gas is required for the remaining distance.
Step-by-Step Explanation
Therefore, the car will need approximately 8.76 more gallons of gas to complete the rest of the trip at the same rate.
To calculate the additional gas needed for the remainder of a 650-mile trip after using 8 gallons for the first 210 miles, first determine the gas mileage and then calculate the gas required for the remaining 440 miles. The car will need approximately 16.76 more gallons of gas to complete the trip.
Explanation:To determine how much more gas you will need to complete your 650-mile trip, after having used 8 gallons for the first 210 miles, you need to calculate your car's gas mileage and then use that information to find the amount of gas needed for the remaining distance.
First, let's compute your car's mileage:
Gas mileage = Distance driven / Gallons of gas usedGas mileage = 210 miles / 8 gallonsGas mileage = 26.25 miles per gallon (mpg)Now, let's subtract the miles you have already traveled from the total trip length to find the remaining miles:
Remaining distance = Total distance - Distance already traveledRemaining distance = 650 miles - 210 milesRemaining distance = 440 milesFinally, we calculate the amount of gas needed for the remaining distance:
Gallons needed = Remaining distance / Gas mileageGallons needed = 440 miles / 26.25 mpgGallons needed = approximately 16.76 gallonsTherefore, you will need approximately 16.76 more gallons of gas to complete your trip, assuming the gas mileage remains consistent.
HELPPP! true or false and explain pls!!
22. All kites are quadrilaterals.
24.A kite can have congruent diagonals.
Rewrite the function in intercept form y=x^2+8x+15
How to solve the formula for Vf in the formula of acceleration?
Final answer:
To solve for final velocity (Vf) in acceleration calculations, identify the initial velocity (Vo), acceleration (a), and time (t), then use the formula Vf = Vo + at to find Vf. Substitute the known values into the formula to calculate the final velocity.
Explanation:
To solve for final velocity (Vf) in the formula for acceleration, follow these steps:
Identify the initial velocity, Vo, and any other known variables such as acceleration (a) and time (t).
Determine which equation to use, using the relationship that acceleration is the change in velocity over time (Δv/Δt). The formula to calculate final velocity is v = Vo + at.
Substitute the known values into the equation to solve for Vf. For example, with an initial velocity (Vo) of 30.0 km/h (which converts to 8.333 m/s), an unknown final velocity (Vf), and a time (Δt) of 8.00 seconds, the change in velocity (Δv) would be Vf - Vo.
To find Vf, rearrange the equation: Vf = Vo + (a Δt). Insert the known values into the equation and calculate the result.
As an example, if the initial velocity Vo is 0 and the acceleration is 0.40 m/s² over a time of 100 seconds, then the final velocity Vf is calculated as:
Vf = Vo + at = 0 + (0.40 m/s²) (100 s) = 40 m/s.
This procedure will yield the final velocity of an object assuming constant acceleration over the given time period.
Explain the difference between f and f(x).