Evaluate r2h for = 3.14, r = 1 and h = 2. Round your answer to the nearest whole number and type a numerical answer in the space provided.
Answer:
The answer in the procedure
Step-by-step explanation:
we have
[tex]\pi=3.14[/tex]
[tex]r=1\ units[/tex]
[tex]h=2\ units[/tex]
case a) If the expression is
[tex]\pi r^{2} h[/tex]
then
substitute
[tex](3.14)(1)^{2} (2)=6.28\ units^{3}[/tex]
Round to the nearest whole number
[tex]6.28=6\ units^{3}[/tex]
case b) If the expression is
[tex](1/3)\pi r^{2} h[/tex]
then
substitute
[tex](1/3)(3.14)(1)^{2} (2)=2.09\ units^{3}[/tex]
Round to the nearest whole number
[tex]2.09=2\ units^{3}[/tex]
3 out of every 5 picks are orange. If 12 picks are orange,how many picks are they in all
Answer: The answer to your question is 20
Step-by-step explanation: We know that 3 out of every 5 picks are oranges. And if the next 12 picks are orange, what is the total number of oranges in all?
So first, you would set up a proportion, which would look like this:
3 oranges/ 5 picks = 12 oranges/ x picks
Let the number of picks be known as x, our variable, since we don't know how many oranges are there total.
Next, when you have a proportion that you are trying to solve, the best thing to do is cross multiply, which will look this:
3x = 12(5)
3x = 60
3x/3 = 60/3
x=20 picks
Therefore, the answer is 20 picks
A 4-digit number ends in 3. If you put the number 3 in the first position, the number will decrease by 738. Find the original 4-digit number.
Answer:
4153. Read the explanation please. There is no point in just reading the answer because the same type of problem can come up in the RSM homework or in a test and you will have no idea how to solve it.
Step-by-step explanation:
Form an equation with the information you know.
1. Moving the last digit, 3, to the first position is the same as doing (x-3)/10 +3000, where x is the original 4-digit number.
Why it works: This expression works because first, you subtract 3 from the original number. This removes 3 from the last digit, but leaves a zero there. To remove the zero, you divide by 10. Finally, to put the 3 at the first position, you add 3000.
2. Since you know that the number will decrease by 738, you can do the second part of forming the equation. Make the expression equal to x - 738, like so --> (x-3)/10 + 3000 = x - 738
Solve the equation.
3. (x-3)/10 + 3000 = x-73
(x-3)/10 = x - 3738
x-3 = 10x - 37380
x = 10x - 37377
-9x = -37377
x = 4153
Well, I've got to get back to my RSM homework. I hope this helped!
P.S.- The next time you have a question, email your RSM teacher (I'm assuming you go to RSM) because he/she is much more qualified then me (I'm only 12) and you don't really know if you can trust people giving you answers on Brainly.com.
Find two additional polar representations of the point. Write each coordinate in simplest form with the angle in
Answer:
The other two other representation are (6 , -4π/3) and (-6 , -π/3)
Step-by-step explanation:
* Lets revise some important facts about the polar form of a point
- In polar coordinates there is an infinite number of coordinates for a
given point
- The point (r , θ) can be represented by any of the following coordinate
pairs (r , θ+2πn) , (-r , θ + [2n+1]π) , where n is any integer
* Now lets solve the problem
∵ A point has polar coordinates (6 , 2π/3)
- We can find many points as the same with this point
- The point (r , θ) can be represented by any of the following coordinate
pairs(r , θ + 2πn) and (-r , θ + (2n + 1)π), where n is any integer.
∵ The angle in [-2π , 2π]
∵ r = 6 and Ф = 2π/3
- Let n = -1
∴ (r , Ф + 2πn) = (6 , 2π/3 + 2π(-1)) = (6 , 2π/3 - 2π) = (6 , -4π/3)
* One point is (6 , -4π/3)
∴ (-r , θ + (2n + 1)π) = (-6 , 2π/3 + (2(-1) + 1)π) = (-6 , 2π/3 + (-2 + 1)π)
∴ (-r , θ + (2n + 1)π) = (-6 , 2π/3 + (-1)π) = (-6 , 2π/3 - π)
∴ (-r , θ + (2n + 1)π) = (-6 , -π/3)
* One point is (-6 , -π/3)
Final answer:
To find two additional polar representations of a point, you can add or subtract 2π radians (or 360° if using degrees) from the original angle, while keeping the radius the same.
Explanation:
A student has asked for two additional polar representations of a point. Polar coordinates specify the location of a point in a plane by a distance from the origin (r) and an angle (φ) with respect to the positive x-axis. To find additional representations, we can add 2π radians to the angle for each full rotation around the circle, keeping the same distance 'r'. For example, if a point has polar coordinates (r, φ), two other representations could be (r, φ + 2π) and (r, φ - 2π), or if in degrees, (r, φ + 360°) and (r, φ - 360°).
The base of an isosceles triangle is 21 cm long. The altitude to the base is 9 cm long. What is the approximate measure of a base angle of the triangle?
Answer:
Step-by-step explanation:
tan α=9÷(21/2)=18/21=6/7
α=arc tan(6/7)≈40.6°
Solve ax – 5 = b for a
ax - 5 = b
ax = b + 5
a = [tex]\frac{b+5}{x}[/tex]
Answer:
[tex]a=\frac{b+5}{x},x\ne0[/tex]
Step-by-step explanation:
The given equation is:
[tex]ax-5=b[/tex]
We want to solve this equation for a.
We add 5 to both sides of the equation to get:
[tex]ax=b+5[/tex]
We divide both sides by x to get:
[tex]a=\frac{b+5}{x},x\ne0[/tex]
We must restrict the domain because a is not defined for all values of x.
Match the polynomials with their factors. 2a2 + 5a − 3 (a + 1)(2a − 3) 2a2 − a − 3 (a − 1)(2a + 3) 2a2 − 5a − 3 (2a − 1)(a + 3) 2a2 + a − 3 (2a + 1)(a − 3)
Answer:
2a² + 5a - 3 = (2a - 1)(a + 3)
2a² - a - 3 = (2a - 3)(a + 1)
2a² - 5a - 3 = (2a + 1)(a - 3)
2a² + a - 3 = (2a + 3)(a - 1)
Step-by-step explanation:
* To factor a trinomial in the form ax² ± bx ± c:
- Look at the c term
# If the c term is positive
∵ c = r × s ⇒ r and s are the factors of c
∴ r and s will have the same sign (sign of b)
∵ a = h × k ⇒ h , k are the factors of a
∴ rk + hs = b
∴ (hx + r)(kx + s) ⇒ if b +ve OR (hx - r)(kx - s) ⇒ if b -ve
# If the c term is negative
∵ c = r × s ⇒ r and s are the factors of c
∴ r and s will not have the same sign
∵ a = h × k ⇒ h and k are the factors of a
∴ rk - hs = b OR hs - rk = b
(hx + r)(kx - s) OR (hx - r)(kx + s)
* Now lets solve the problem
∵ 2a² + 5a - 3
∴ c = -3 ⇒ -ve term
∴ r , s have different sign
∵ 3 = 1 × 3 then r = 1 , s = 3
∵ a = 2
∵ a = h × k
∵ 2 = 2 × 1 then h = 2 , k = 1
∵ rk = 1
∵ sh = 6
∴ sh - rk = 5 ⇒ same value of b
∵ (hx - r)(kx + s)
∴ 2a² + 5a - 3 = (2a - 1)(a + 3)
∵ 2a² - a - 3
∴ c = -3 ⇒ -ve term
∴ r , s have different sign
∵ 3 = 3 × 1 then r = 3 , s = 1
∵ a = 2
∵ a = h × k
∵ 2 = 2 × 1 then h = 2 , k = 1
∵ rk = 3
∵ sh = 2
∴ sh - rk = -1 ⇒ same value of b
∵ (hx - r)(kx + s)
∴ 2a² - a - 3 = (2a - 3)(a + 1)
∵ 2a² - 5a - 3
∴ c = -3 ⇒ -ve term
∴ r , s have different sign
∵ 3 = 1 × 3 then r = 1 , s = 3
∵ a = 2
∵ a = h × k
∵ 2 = 2 × 1 then h = 2 , k = 1
∵ rk = 1
∵ sh = 6
∴ rk - hs = -5 ⇒ same value of b
∵ (hx + r)(kx - s)
∴ 2a² - 5a - 3 = (2a + 1)(a - 3)
∵ 2a² + a - 3
∴ c = -3 ⇒ -ve term
∴ r , s have different sign
∵ 3 = 3 × 1 then r = 3 , s = 1
∵ a = 2
∵ a = h × k
∵ 2 = 2 × 1 then h = 2 , k = 1
∵ rk = 3
∵ sh = 2
∴ rk - sh = 1 ⇒ same value of b
∵ (hx + r)(kx - s)
∴ 2a² + a - 3 = (2a + 3)(a - 1)
Which polynomial represents the difference below (8x2+9) - (6x2+2x+2)
Answer:
2x² - 2x + 7
Step-by-step explanation:
Given
(8x² + 9) - (6x² + 2x + 2) ← distribute by - 1
= 8x² + 9 - 6x² - 2x - 2 ← collect like terms
= (8x² - 6x²) - 2x + (9 - 2)
= 2x² - 2x + 7
Answer:
2x² - 2x + 7
Step-by-step explanation:
Ape-x
The population of a town went from 18,000 to 17,460
Which would mean that 540 people died or left the town.
I hope that this helps! :D
Zachary purchased a new car for $27,995. The value of the car linearly depreciated to 9,300 over 10 years. Write a liner equation to represent the value y of Zachary’s car(in dollars) after x years since it’s purchase
Answer:
[tex]y=-1,869.5x+27,995[/tex]
Step-by-step explanation:
Let
x-----> the time in years
y----> value of Zachary’s car in dollars
[tex]A(0,27,995), B(10,9,300)[/tex]
step 1
Calculate the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{9,300-27,995}{10-0}=-1,869.50[/tex]
step 2
Find the equation of the line
The equation of the line into slope intercept form is equal to
[tex]y=mx+b[/tex]
we have
[tex]m=-1,869.50[/tex]
[tex]b=27,995[/tex] -----> the y-intercept is the point A
substitute
[tex]y=-1,869.5x+27,995[/tex]
The linear equation to represent the value of Zachary's car after x years since its purchase is y = -1869.5x + 27995.
Explanation:To write a linear equation to represent the value of Zachary's car after x years since its purchase, we need to determine the slope and y-intercept. The initial value of the car is $27,995, and after 10 years it depreciates to $9,300. The slope (m) can be calculated as (9300 - 27995) / (10 - 0) = -1869.5. The y-intercept (b) is the initial value, which is $27,995. Therefore, the linear equation that represents the value of Zachary's car is y = -1869.5x + 27995.
Learn more about Linear equations here:https://brainly.com/question/32634451
#SPJ3
An angle measures 41 degrees. What is its supplement?
An angle measures 31 degrees. What is its compliment?
Answer:
139 and 59, respectively
Step-by-step explanation:
By definition, supplementary means that the angles all add up to equal 180 degrees. Therefore, 180 - 41 = 139.
By definition, complementary means that the angles all add up to equal 90 degrees. Therefore, 90 - 31 = 59.
i dont know whats the answer can someone help me ?
Answer: 1206.37
Step-by-step explanation:
Multiply the pie times the radius and height
3.14 * 8^2 * 6
Answer:
V =384 pi units ^3
or
V =1205.76 units ^3
Step-by-step explanation:
Volume of a cylinder is given by
V = pi r^2 h
where r is the radius and h is the height
V = pi (8)^2 *6
V = pi (64)*6
V =384 pi units ^3 (exact answer)
or is we used 3.14 for pi
V = (3.14) * 384
V =1205.76 units ^3
what is the range of the data set?
61
40
41
55
Answer:
40
Step-by-step explanation:
The range is the difference between the largest value and the smallest value in the data set.
minimum value = 21 and maximum value = 61
range = 61 - 21 = 40
Answer: Range of the data set would be 40.
Step-by-step explanation:
Since we have given the data set as follows:
21,23,28,28,52,54,56,56,57,60,61,61.
We need to find the range of the data set.
As we know the formula for "Range":
Range = Highest number - Lowest number
Range = 61-21
Range = 40
Hence, range of the data set would be 40.
which of the following is the inverse of the function given below
[tex]f(x) = \frac{x + 2}{7} [/tex]
ANSWER
[tex]{f}^{ - 1} (x) = 7x - 2[/tex]
EXPLANATION
The given function is:
[tex]f(x) = \frac{x + 2}{7} [/tex]
Let
[tex]y = \frac{x + 2}{7} [/tex]
Interchange x and y.
[tex]x= \frac{y + 2}{7} [/tex]
Solve for y by first multiplying through by 7.
[tex]7x = y + 2[/tex]
Add -2 to both sides of the equation.
[tex]7x - 2 = y[/tex]
Or
[tex]y = 7x - 2[/tex]
Hence the inverse function is:
[tex]{f}^{ - 1} (x) = 7x - 2[/tex]
Answer:
p(x) = 7x - 2
The general form of the equation of a circle is x2+y2−4x−8y−5=0.
What are the coordinates of the center of the circle?
Enter your answer in the boxes.
Answer:
centre = (2, 4)
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + y² - 4x - 8y - 5 = 0
Rearrange the x/y terms together and add 5 to both sides
x² - 4x + y² - 8y = 5
Use the method of completing the square on both the x/y terms
add ( half the coefficient of the x/y terms )² to both sides
x² + 2(- 2)x + 4 + y² + 2(- 4)y + 16 = 5 + 4 + 16
(x - 2)² + (y - 4)² = 25 ← in standard form
with centre (2, 4) and r = [tex]\sqrt{25}[/tex] = 5
during the baseball season, the white sox won 15 games out of 20. what percentage of the game did they win?
Answer:
75%
Step-by-step explanation:
15 divided by 20 = .75 then convert to a percentage is 75%
If the equation below is solved by graphing, which statement is true?
log(6x+10) = log 1/2 x
a. the curves intersect at approx. x=0.46
b. the curves intersect at approx. x=0.75
c. the curves intersect at approx. x=1.11
d. the curves intersect at approx. x=3.07
Step-by-step explanation:
the curves intersect at approcx=0.46
Answer:
a. the curves intersect at approx. x=0.46Step-by-step explanation:
The given function is
[tex]log(6x+10)=log_{\frac{1}{2} }x[/tex]
If we graph this function, the result is like the image attached. There you can observe that the intersection point is at (0.464, 1.107).
If we round this points to the nearest hundred, they would be
x = 0.46 and y = 1.11.
Therefore, the right answer is
a. the curves intersect at approx. x=0.46
The diagram represents three statements: p, q, and r. For what value is both p ∧ r true and q false? 2 4 5 9
Answer:
the answer is C.5
Step-by-step explanation:
In the given right triangle, find the missing length to the nearest tenth.
8.5 ft
7.9 ft
24.1 ft
25 ft
Answer:
25 ft
Step-by-step explanation:
a² + b² = c²
7² + 24² = c²
49 + 576 = c²
c² = 625
c = √625
c= 25
Answer:
D. 25 ft.
Step-by-step explanation:
To find the missing length of any right triangle, you can use the Pythagorean Theorem (A^2+B^2=C^2) to solve. A and B represent the legs (which we do have) and C represents the hypotenuse (which we are trying to find). Insert our known values into the theorem, and we will get 24^2+7^2=C^2. Now we just do the basic math for the numbers that we have (24^2 is 576; 7^2 is 49), and that added up would equal to 625. Now, since C is being squared on the other side, we now have to root both sides. On the side where C is, the radical and the square will cancel out each other, leaving us with just C. But, on the side where 625 is, it should root to 25. Since C is by itself now, the number on the other side (25) will be our answer. Therefore, the missing side is 25 feet long.
Answer soon please. I will mark brainiest!
Answer:
Exponential function.
[tex]y = - 6( {3}^{x - 1} ) = - 2( {3}^{x} )[/tex]
As the x-values are increased by a constant amount, the y-values are multiplied by a constant amount.
Find the value of a and b
Answer:
[tex]\large\boxed{a=\dfrac{58}{25},\ b=0}[/tex]
Step-by-step explanation:
[tex]\dfrac{3\sqrt3+\sqrt2}{3\sqrt3-\sqrt2}+\dfrac{3\sqrt3-\sqrt2}{3\sqrt3+\sqrt2}\qquad\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\dfrac{(3\sqrt3+\sqrt2)(3\sqrt3+\sqrt2)}{(3\sqrt3-\sqrt2)(3\sqrt3+\sqrt2)}+\dfrac{(3\sqrt3-\sqrt2)(3\sqrt3-\sqrt2)}{(3\sqrt3+\sqrt2)(3\sqrt3-\sqrt2)}\\\\=\dfrac{(3\sqrt3+\sqrt2)^2}{(3\sqrt3)^2-(\sqrt2)^2}+\dfrac{(3\sqrt3-\sqrt2)^2}{(3\sqrt3)^2-(\sqrt2)^2}\qquad\text{use}\ (a\pm b)^2=a^2\pm2ab+b^2[/tex]
[tex]=\dfrac{(3\sqrt3)^2+2(3\sqrt3)(\sqrt2)+(\sqrt2)^2}{3^2(\sqrt3)^2-2}+\dfrac{(3\sqrt3)^2-2(3\sqrt3)(\sqrt2)+(\sqrt2)^2}{3^2(\sqrt3)^2-2}\\\\=\dfrac{3^2(\sqrt3)^2+6\sqrt6+2}{9\cdot3-2}+\dfrac{3^2(\sqrt3)^2-6\sqrt6+2}{9\cdot3-2}\\\\=\dfrac{9\cdot3+6\sqrt6+2}{27-2}+\dfrac{9\cdot3-6\sqrt6+2}{27-2}\\\\=\dfrac{27+6\sqrt6+2}{25}+\dfrac{27-6\sqrt6+2}{25}\\\\=\dfrac{29+6\sqrt6}{25}+\dfrac{29-6\sqrt6}{25}\\\\=\dfrac{29+6\sqrt6+29-6\sqrt6}{25}\\\\=\dfrac{58}{25}[/tex]
25 points Please explain your answer, thank you!
Which expression is not a polynomial?
( ACCIDENTALLY PUT ONLY 10 POINTS ON THE LAST ONE SORRY)
A. -5x+6y
B. -3/x
C. 2p^3q^2-pq^3
D. 7-z
The answer is B.
For an expression to be a polynomial term, any variables in the expression must have whole number powers.
-3/x isn’t a polynomial term because the variable is in the denominator.
Answer:
D
Step-by-step explanation:
it only consists of one term.
finding x :8x + 10 - 5x = 15.
Answer:
Here you go! 8x+10-5x!
Just kidding. here you go. x=1.66
Step-by-step explanation:
you can simplifiy the x´s by making it 3x by subtracting. You can also subract 10 from both sides. That leaves you with 3x=5.
x=1.66
Answer:
[tex]\large\boxed{x=\dfrac{5}{3}=1\dfrac{2}{3}}[/tex]
Step-by-step explanation:
[tex]8x+10-5x=15\qquad\text{subtract 10 from both sides}\\\\8x+10-10-5x=15-10\qquad\text{combine like terms}\\\\3x=5\qquad\text{divide both sides by 3}\\\\x=\dfrac{5}{3}[/tex]
What’s the slope of the line?
Slope equation: y2-y1/x2-x1
7-9/-12-(-10)
-2/-2 = 1
Answer:
Slope = 1
Step-by-step explanation:
(y2 - y1) ÷ (x2 - x1) = (7 - 9) ÷ (-12 - [-10]) = -2 ÷ (-2) = 1
How to write 24.58 expanded form?
20.00 + 4.00 + 00.50 + 00.08
To write expanded from take each number from left to right and turn all the numbers that are after it into zeros (if there is a decimal then turn the numbers before it into zeros as well)
2 has 4 numbers after it so it gets 4 zeros: 20.00
4 has 2 numbers after it so it gets 2 zeros: 4.00
5 is a decimal that has two numbers before it and one after, so before the decimal there are two zeros, then after the decimal comes the five, then there is one number after the 5 so one zero after the five.
8 is a decimal that has three numbers before it , so before the decimal there are two zeros, then after the decimal is a number that becomes zero then the 8
Hopefully that made sense to you and was helpful! Let me know!
Change each mixed number into an equal improper fraction 1 7/16 11 5/9 30 5/9 10 10/ 13 24 3/5 129 1/2
Answer: Hope this helps, and hopefully this is what you needed!
1 7/16 = 23/16
11 5/9 = 104/9
30 5/9 = 275/9
10 10/13 = 140/13
24 3/5 = 123/5
129 1/2 = 259/2
Step-by-step explanation:
help me with this question
It's the second one because each means one or single and a singular subject has a singular verb...
Which number is rational?
O A. 0.7
O B. 0.31243576...
Ос. л
O D. Jo
Answer:
A. 0.7
Explanation:
B is irrational
I have no idea was c and d so that leads to A because it’s terminated
Answer:0.7
Step-by-step explanation:
A pex quiz
Andre has enough to fill 3500 in.3.. he decides to change the length of the step so that he will use all of the cement. What will be the new length of the step?
Answer:
43.75 inches or 43 and 3/4 inches.
Step-by-step explanation:
Ok, thanks for the complement of information.
So, to find the volume of that step, which is a rectangular prism, we would use the simple formula:
V = length * width * height
In this case, we have the total volume (3,500 cu in), we have the width (10 inches) and we have the height (8 inches). But we need to find out the new length in order for him to use all 3,500 cu in of cement.
So, we transform the formula above into:
length = V / (width * height)
then we plug-in the numbers:
length = 3,500 / (8 x 10) = 3,500 / 80 = 43.75
So, the new length of the step would be 43.75 inches or 43 and 3/4 inches.
Find the mean, median, and mode of the date.
4, 8, 11, 6, 4, 5, 9, 10, 10,4
Answer:
Mean: 7.1, median: 7, mode: 4
Step-by-step explanation:
The mean, also known as the average, is equal to the sum of all the numbers divided by how many numbers there are.
4 + 8 + 11 + 6 + 4 + 5 + 9 + 10 + 10 + 4 = 71
10 numbers
71/10 = 7.1
The median is the number in the middle of the set.
4, 4, 4, 5, 6, 8, 9, 10 ,10 ,11
6 and 8 are in the middle, and the number between 6 and 8 is 7.
The mode of a set of numbers is the most common number. In this case, the number is 4 as it appears 3 times.