choose yes or no to indicate which of the equations can be used to describe the pattern in the table (am i correct??????)
Answers
the only equation that seems to describe the pattern is:
[tex]\( b = a - 5 \)[/tex]. Therefore, option C is correct
To determine whether the given equations can describe the pattern in the table, we need to look at the values in the table and see if they satisfy the equations. However, the provided image is not completely clear, and it seems like part of the table or the values might be missing.
From what is visible in the image, it seems we have a table with two columns labeled 'a' and 'b', with 'a' taking on values from 5 to 9 and 'b' from 0 to 4. We need to check if the equations given describe the relationship between 'a' and 'b' according to the table.
The equations given are:
1. [tex]\( b + a = 5 \)[/tex]
2. [tex]\( b = a + 5 \)[/tex]
3. [tex]\( b = a - 5 \)[/tex]
4. [tex]\( a = b - 5 \)[/tex]
Without the complete table, we can't perform a full analysis, but we can explain how you would generally approach this:
- For equation 1 [tex](\( b + a = 5 \))[/tex], check if the sum of each pair of 'a' and 'b' equals 5.
- For equation 2 [tex](\( b = a + 5 \))[/tex], check if 'b' is always 5 more than 'a'.
- For equation 3 [tex](\( b = a - 5 \))[/tex], check if 'b' is always 'a' minus 5.
- For equation 4 [tex](\( a = b - 5 \))[/tex], check if 'a' is always 'b' minus 5.
Given the values for 'a' and 'b' in the table:
a | 5 | 6 | 7 | 8 | 9
b | 0 | 1 | 2 | 3 | 4
We can analyze each equation to see if it describes the pattern in the table.
1. [tex]\( b + a = 5 \)[/tex]
Let's check if the sum of 'a' and 'b' equals 5 for each pair:
- For [tex]\( a = 5 \), \( b = 0 \): \( 5 + 0 = 5 \)[/tex] (True)
- For [tex]\( a = 6 \), \( b = 1 \): \( 6 + 1 = 7 \)[/tex] (False)
- Since it is false for [tex]\( a = 6 \), \( b = 1 \)[/tex], we can already conclude that this equation does not describe the pattern.
2. [tex]\( b = a + 5 \)[/tex]
Let's check if 'b' equals 'a' plus 5:
- For [tex]\( a = 5 \), \( b = 0 \): \( 5 + 5 = 10 \)[/tex] (False)
- Since it is false for [tex]\( a = 5 \), \( b = 0 \)[/tex], this equation does not describe the pattern.
3. [tex]\( b = a - 5 \)[/tex]
Let's check if 'b' equals 'a' minus 5:
- For [tex]\( a = 5 \), \( b = 0 \): \( 5 - 5 = 0 \)[/tex] (True)
- For [tex]\( a = 6 \), \( b = 1 \): \( 6 - 5 = 1 \)[/tex] (True)
- Continuing this pattern, this equation seems to be true for all given pairs of 'a' and 'b'.
4. [tex]\( a = b - 5 \)[/tex]
This is not likely to be true since subtracting 5 from 'b' would result in negative numbers, which are not present in the 'a' values.
From the analysis, the only equation that seems to describe the pattern is:
[tex]\( b = a - 5 \)[/tex]
Let's confirm that this equation is true for all pairs of 'a' and 'b'.
The equation [tex]\( b = a - 5 \)[/tex] holds true for all pairs of 'a' and 'b' values in the table. Therefore, this equation correctly describes the pattern in the table.
Related Questions
40 POINTS
Simplifying exponents and rules of exponents simplify the expressions below:
2 4 3 0 4 6 4 -3 2 3 2
Answers
ANSWER
a. 16
b. 1
c. 64
d. 64
EXPLANATION
We want to simplify the following exponential expressions
a.
[tex] {2}^{4} [/tex]
This implies that
[tex] {2}^{4} = 2 \times 2 \times 2 \times 2[/tex]
[tex] {2}^{4} = 16[/tex]
b. Any non-zero number exponent zero is 1.
This implies that,
[tex] {3}^{0} = 1[/tex]
c. The given exponentiial expression is,
[tex] {4}^{6} \times {4}^{ - 3} [/tex]
The bases are the same so we add the exponents.
[tex] {4}^{6} \times {4}^{ - 3} = {4}^{6 + - 3} [/tex]
This simplifies to,
[tex]{4}^{6} \times {4}^{ - 3} = {4}^{3} [/tex]
[tex]{4}^{6} \times {4}^{ - 3} = 4 \times 4 \times 4 = 64[/tex]
d. We want to simplify:
[tex] { ({2}^{3}) }^{2} [/tex]
This is the same as
[tex]{ ({2}^{3}) }{ ({2}^{3}) }[/tex]
We add the exponents now to get:
[tex]{2}^{3 + 3} = {2}^{6} = 64[/tex]
Find the height of a rectangular prism if the surface area is 868, the width is 7 and the length is 31.
A.) 434
B.) 2.85
C.) 76
D.) 5.7
Answers
Answer:
D
Step-by-step explanation:
[tex]\rm\red{\overbrace{\underbrace{\tt\color{orange}{\:\:\:\:\:\:\:\:Question \: and \: Choices:\:\:\:\:\:\:\:\:\:}}}}[/tex]
Find the height of a rectangular prism if the surface area is 868, the width is 7 and the length is 31.
A.) 434
B.) 2.85
C.) 76
D.) 5.7
[tex]\rm\red{\overbrace{\underbrace{\tt\color{orange}{\:\:\:\:\:\:\:\:Answer:\:\:\:\:\:\:\:\:\:}}}}[/tex]
[tex]\huge\colorbox{pink}{\color{black}{\boxed{D.) 5.7}}}[/tex]
[tex]\large\purple{ChaEunWoo2009}[/tex]
#CarryOnLearning
Shravan is ten years older than Gaurav’s age. Five years ago, one –seventh of shravan’s age was equal to one- fifth of Gaurav’s age. Find their present ages.
Answers
Answer:
Shravan's age is 40 years old
Gaurav’s age is 30 years old
Step-by-step explanation:
Let
x-----> Shravan's age
y-----> Gaurav’s age
we know that
x=y+10 -----> equation A
(1/7)(x-5)=(1/5)(y-5) ----> equation B
substitute equation A in equation B and solve for y
(1/7)(y+10-5)=(1/5)(y-5)
(1/7)(y+5)=(1/5)(y-5)
5(y+5)=7(y-5)
5y+25=7y-35
7y-5y=25+35
2y=60
y=30 years
Find the value of x
x=y+10 ----> x=30+10=40 years
therefore
Shravan's age is 40 years old
Gaurav’s age is 30 years old
Identify each expression and value that represents the area under the curve y=x^2+4 on the interval [-3,2]
Answers
This result represents the total area under the curve y = x^2 + 4 between x = -3 and x = 2.
The area under the curve y = x^2 + 4 on the interval [-3,2] can be found using definite integration. The definite integral of a function gives us the net area between the function and the x-axis across the specified interval. To compute the area, we set up the integral from -3 to 2 of the function x^2 + 4.
To solve this, we integrate the function with respect to x:
Integrate the function x^2 to get (1/3)x^3.Integrate the constant 4 to get 4x.Combine the results to form the antiderivative, which is (1/3)x^3 + 4x.Evaluate the antiderivative from -3 to 2. This gives us:[(1/3)(2)^3 + 4(2)] - [(1/3)(-3)^3 + 4(-3)]Calculate each part to obtain:[(1/3)(8) + 8] - [-(1/3)(27) - 12]Simplify to find: (8/3 + 8) - (-9 - 12)Add up to get the total area: (8/3 + 8 + 9 + 12)Which simplifies to: (8/3 + 29)Final result: 35/3 or 11.67 square unitsThis result represents the total area under the curve y = x^2 + 4 between x = -3 and x = 2.
the sum of the ages of Nicole and Kristen and 32 in two years Nicole would be three times as old as Kristen how old are they now
Answers
Answer:
Kristen would be 7.5 yo and Nicole would be 24.5 years old
Step-by-step explanation:
let x= kristen's age
3x+2= nicole's age
(3x+2)+x=32
4x+2=32
4x=30
x=7.5
3(7.5)+2= 24.5
At the start of 2014 Lucy's house was worth £200,000.
The value of the house increased by 5% every year.
Work out the value of her house at the start of 2017.
Answers
To find the value of Lucy's house at the start of 2017, calculate a 5% increase each year from the initial £200,000 value in 2014. The compound value over the three years results in a house value of £231,525 at the start of 2017.
To calculate the value of Lucy's house at the start of 2017, we need to apply a 5% annual increase to the initial value of the house for three consecutive years (2014 to 2017).
Find the increase for the first year:
Initial value for 2014: £200,000
5% increase: £200,000 * 0.05 = £10,000
Value at the start of 2015: £200,000 + £10,000 = £210,000
Calculate the increase for the second year:
Value at the start of 2015: £210,000
5% increase: £210,000 * 0.05 = £10,500
Value at the start of 2016: £210,000 + £10,500 = £220,500
Calculate the increase for the third year:
Value at the start of 2016: £220,500
5% increase: £220,500 * 0.05 = £11,025
Value at the start of 2017: £220,500 + £11,025 = £231,525
Therefore, the value of Lucy's house at the start of 2017 would be £231,525.
A study estimates that the cost of tuition at a university will increase by 2.8% each year. The cost of tuition at the University in 2015 was $33,741 the function b(x) , models the estimated tuition cost , where x is the number of years since 2015.
finds the expression that completes the function b(x)
Answers
so, the cost will increase 2.8% per annum... so that simply means is a compound interest rate, so let's use the compound interest formula for this one.
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$33741\\ r=rate\to 2.8\%\to \frac{2.8}{100}\dotfill &0.028\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=\textit{years after 2015}\dotfill &t \end{cases} \\\\\\ A=33741\left(1+\frac{0.028}{1}\right)^{1\cdot t}\implies b(x)=33741(1.028)^x[/tex]
The complete expression for the compounding tuition fee function is [tex]b(x) = 33741(1.028) {}^{x} [/tex]
Using the compound interest relation :
[tex] b = P(1 + \frac{r}{n} ) {}^{nx} [/tex]
Where ;
b = final amount after x years P = Initial amount = 33741 r = rate = 2.8% = 0.028x = number of years since 2015 n = number of compounding times per period = 1 (yearly)The function b(x) can be written as :
[tex]b(x) = 33741(1 + \frac{0.028}{1} ) {}^{x} [/tex]
Therefore, the expression for the function b(x) is :
[tex]b(x) = 33741(1.028) {}^{x} [/tex]
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Match each pair of polynomials to their sums.
Answers
Answer:
12x^2+3x+6 and -7x^2-4x-2 -> 5x^2-x+4
2x^2-x and -x-2x^2-2 -> -2x-2
x^3+x^2+2 and x^2-2-x^3 -> 2x^2
x^2+x and x^2+8x-2 -> 2x^2+9x-2
hope this helps :)
Find the average rate of change for the given function x=-1 to x=2
A. 4/3
B. -4/3
C. -3/4
D. 3/4
Answers
Answer:
The Average rate of change (the slope) is -4/3
Step-by-step explanation:
Find two Exact point like point A (-1,4) and point B (2,0)
Then count how many spaces does point A have to move left to right and down to get to point B.
since it moves down the number will be negative.
You will have to go 3 spaces to the right and 4 spaces down.
therefore giving you a slope of -4/3
To find the average rate of change for a given function, evaluate the function at the two given points and use the formula (f(2) - f(-1)) / (2 - (-1)).
Explanation:To find the average rate of change for a given function, we need to calculate the difference in the values of the function between the two given points, and then divide that difference by the difference in the x-coordinates of the points. In this case, we are given x=-1 and x=2.
Let's evaluate the function at these two points:
f(-1) = ?, f(2) = ?
Once we have the values, we can calculate the average rate of change using the formula:
Average Rate of Change = (f(2) - f(-1)) / (2 - (-1))
Substitute the values and calculate to find the answer.
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Find the equation of the circle with center at (3, -2) and radius of 3.
Answers
Answer:
[tex](x-3)^{2} +(y+2)^{2}=9[/tex]
Step-by-step explanation:
we know that
the equation of a circle into center radius form is equal to
[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]
In this problem we have
center ( 3,-2)
radius r=3 units
substitute
[tex](x-3)^{2} +(y+2)^{2}=3^{2}[/tex]
[tex](x-3)^{2} +(y+2)^{2}=9[/tex]
Answer: A on edg
Step-by-step explanation:
91) (5, 4) is a solution to which of the following
systems of linear equations?
A) x + 6y = 18 B) 4x + 2y = 12
3x-27=-6
3x - y = -15
C) 2x - 3y = -2 D) 8x + 5y = 40
4x + y = 24
x-7y=-14
Answers
Answer:
2x - 3y = -2 AND 4x + y = 24
Step-by-step explanation:
Simply plug in the coordinates into each answer choice, evaluate them, and you will have your answer.
I hope this helps you out, and as always, I am joyous to assist anyone at any time.
I need help please??!!!):
Answers
Answer:
-13 < 16
Step-by-step explanation:
(4 is x, -5 is y)
-5 - 8 < 4(4)
-13 < 16
It is true and is a solution
Answer:
The ordered pair is not a solution to the inequality because -13 < -16 is false.
Step-by-step explanation:
Step 1: Plug x and y into the inequality
-5 - 8 < -4(4)
Step 2: Simplify the inequality
-13 < -16
Step 3: Interpret and conclude
The ordered pair is not a solution to the inequality because -13 < -16 is false.
Let
x^2−12x=61
.
What values make an equivalent number sentence after completing the square?
Enter your answers in the boxes.
x2−12x+_____=______
Answers
Answer:
Step-by-step explanation:
Add the square of half the x-coefficient to both sides.
x² -12x +(-6)² = 61 +(-6)²
x² -12x +36 = 97Answer:
x² - 12x + 36 = 97
Step-by-step explanation:
Given
x² - 12x = 61
To complete the square
add (half the coefficient of the x- term)² to both sides
x² + 2(- 6)x + (- 6)² = 61 + (- 6)², so
x² - 12x + 36 = 61 + 36
x² - 12x + 36 = 97
Solve for the equation for x; ax-y=bx
X=a+b/y
X= a-b/y
X= y/ a+b
X= y/ a-b
Help!
Answers
Final answer:
To solve the equation ax - y = bx for x, add y to both sides, combine x terms, factor x out, and divide by (a - b) resulting in the solution x = y / (a - b).
Explanation:
To solve the given equation ax - y = bx for x, we aim to isolate x on one side of the equation:
First, we add y to both sides of the equation: ax = bx + y.
Next, we group the x terms together: ax - bx = y.
Then, we factor out x: x(a - b) = y.
Finally, we divide both sides by (a - b) to solve for x: x = y / (a - b).
So, the solution is x = y / (a - b).
if one bucket + 5 jars equal one tub and three buckets plus two jars equal to tubs how many jars are there equal to one tub
Answers
Answer:
Simplify 4y + 7x = 2t and there you go that's your answer☺
Step-by-step explanation:
Bucket = y
Jars = x
Tubs = t
y + 5x = t
3y + 2x = t
Answer:
Number of jars in one tub is:
13
Step-by-step explanation:
Let b denote the buckets, j denotes the jars and t denotes the tubs
One bucket + 5 jars equal one tub
b+5j=t ----------------(1)
Three buckets plus two jars equal two tubs
3b+2j=2t ------------------(2)
equation (1)×3- equation (2)
3(b+5j)-(3b+2j)= 3t-2t
3b+15j-3b-2j= t
13j= t
Hence, Number of jars in one tub is:
13
2. Solve the equation p2 + 6p = 1 by completing the square method. Show your work.
Answers
Answer:
p=0.125
Step-by-step explanation:
2p+6p=1
Add like terms
8p=1
Divide both sides by 8 to get p by itself
8p/8=1/8
p=0.125
what's -1 and 3/5 divided by -2/3
Answers
Answer:
2 2/5
Step-by-step explanation:
-1 3/5 ÷ -2/3
Change the mixed number to an improper fraction
-1 3/5 = - (5*1 +3)/5 = -8/5
-8/5÷-2/3
Copy dot flip
-8/5 * -3/2
24/10
Divide top and bottom by 2
12/5
Change to a mixed number
12/5 = 2 2/5
What are the zeros of this function?
Answers
Answer:
Step-by-step explanation:
the zeroes of a function basically mean when y = 0, so basically the x-intercept(s)
in this case, the zeroes are 3 and 6
Answer:
A. x = 3 and x = 6
Step-by-step explanation:
Zeros occur when the function crosses the x - axis. In this case, the quadratic function crosses the function when x = 3 and x = 6.
find the sum of the angle measures in the figure below
Answers
Answer:
540°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 5, hence
sum = 180° × 3 = 540°
Which characteristic is correct for the function?
A. Both even and odd
B. Neither even or odd
C. Odd
D. Even
Answers
Answer:
D. Even
Step-by-step explanation:
Given function is [tex]f\left(x\right)=-2x^4+3x^2[/tex].
Now we need to check if the given function is Even/Odd.
we know that if f(-x)=f(x) then function is called Even.
we know that if f(-x)=-f(x) then function is called Odd.
[tex]f\left(x\right)=-2x^4+3x^2[/tex]
[tex]f\left(-x\right)=-2(-x)^4+3(-x)^2[/tex]
[tex]f\left(-x\right)=-2x^4+3x^2[/tex]
[tex]f\left(-x\right)=f\left(x\right)[/tex]
Hence given function is an Even function.
So the correct choice is D. Even.
Darren filled boxes with tins of orange juice and numbered the boxes in the order in which they were filled. He packed the 496th tin box 21 and then stopped for lunch. Box 21 was never completely filled. How many tins were in box 21?
Answers
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RectangleABCD has vertices at A(– 3, 1),B(– 2, – 1),C(2, 1), andD(1, 3). What is the area, in square units, of this rectangle? A.10 B.5 C.25 D.100
Answers
Answer:
Option A. [tex]10\ units^{2}[/tex]
Step-by-step explanation:
we know that
The area of the rectangle is equal to
A=LW
where
L is the length of rectangle
W is the width of rectangle
we have
[tex]A(-3,1),B(-2,-1),C(2,1),D(1,3)[/tex]
Plot the vertices
see the attached figure
L=AD=BC
W=AB=DC
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the distance AD
[tex]A(-3,1),D(1,3)[/tex]
substitute in the formula
[tex]AD=\sqrt{(3-1)^{2}+(1+3)^{2}}[/tex]
[tex]AD=\sqrt{(2)^{2}+(4)^{2}}[/tex]
[tex]AD=\sqrt{20}[/tex]
[tex]AD=2\sqrt{5}\ units[/tex]
Find the distance AB
[tex]A(-3,1),B(-2,-1)[/tex]
substitute in the formula
[tex]AB=\sqrt{(-1-1)^{2}+(-2+3)^{2}}[/tex]
[tex]AB=\sqrt{(-2)^{2}+(1)^{2}}[/tex]
[tex]AB=\sqrt{5}[/tex]
[tex]AB=\sqrt{5}\ units[/tex]
Find the area
[tex]A=(2\sqrt{5})*(\sqrt{5})=10\ units^{2}[/tex]
The system of linear equations -2x+y=8 and -3x-y=7 is graphed below. What is the solution to the system of equations? (–3, 2) (–2, 3) (2, –3) (3, 2)
answer is
-3,2
Answers
Answer:
x = -3 , y = 2
Step-by-step explanation:
Solve the following system:
{y - 2 x = 8 | (equation 1)
{-3 x - y = 7 | (equation 2)
Swap equation 1 with equation 2:
{-(3 x) - y = 7 | (equation 1)
{-(2 x) + y = 8 | (equation 2)
Subtract 2/3 × (equation 1) from equation 2:
{-(3 x) - y = 7 | (equation 1)
{0 x+(5 y)/3 = 10/3 | (equation 2)
Multiply equation 2 by 3/5:
{-(3 x) - y = 7 | (equation 1)
{0 x+y = 2 | (equation 2)
Add equation 2 to equation 1:
{-(3 x)+0 y = 9 | (equation 1)
{0 x+y = 2 | (equation 2)
Divide equation 1 by -3:
{x+0 y = -3 | (equation 1)
{0 x+y = 2 | (equation 2)
Collect results:
Answer: {x = -3 , y = 2
The solution to the system of equations -2x + y = 8 and -3x - y = 7 is (x, y) = (-3, 2). The correct answer is option A.
Let's use the elimination method:
-2x + y = 8
-3x - y = 7
By adding the two equations together, we can eliminate the y variable:
(-2x + y) + (-3x - y) = 8 + 7
-2x - 3x + y - y = 15
-5x = 15
Dividing both sides by -5, we get:
x = -3
Now, substitute this value of x back into one of the original equations. Let's use -2x + y = 8:
-2(-3) + y = 8
6 + y = 8
y = 8 - 6
y = 2
Therefore, the solution to the system of equations -2x + y = 8 and -3x - y = 7 is (x, y) = (-3, 2).
Therefore, the correct answer is option A.
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The complete question is as follows:
The system of linear equations -2x+y=8 and -3x-y=7 is graphed below. What is the solution to the system of equations?
A. (–3, 2)
B. (–2, 3)
C. (2, –3)
D. (3, 2)
Identify the domain for the function!!! 10 points. Help needed
Answers
Answer:
You had it correctly chosen, (9, infinity)
Step-by-step explanation:
Good job =)
ANSWER
[9,∞)
EXPLANATION
The given radical function is ;
[tex]f(x) = \sqrt{x - 9} [/tex]
This function is defined if and only if the expression under the radical sign is greater than or equal to zero.
[tex]x - 9 \geqslant 0[/tex]
[tex]x \geqslant 9[/tex]
Or
In interval notation, we have
[9,∞)
Select all that apply.
A point located at (3, -2) undergoes a transformation. Its image is at (-3, -2). What was the transformation?
The point was reflected over the y-axis.
The point was translated left 6 units.
The point was reflected over the x-axis.
The point was translated right 6 units.
Answers
Answer:
The point was reflected over the y-axis.
The point was translated left 6 units
Step-by-step explanation:
step 1
we know that
When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite
In this problem
If you apply a reflection across the y-axis
(x.y)------> (-x,y)
(3,-2) ------> (-3,-2)
step 2
If you apply a translation to the left 6 units
The rule of the translation is equal to
(x,y)------> (x-6,y)
(3,-2) ------> (3-6,-2) ----> (-3,-2)
Solve the equation for x.
the square root of the quantity x minus 8 end quantity plus 2 equals 7
A. x=1
B. x=13
C. x=17
D. 33
Answers
Answer:
D. 33
Step-by-step explanation:
√(x-8) + 2 = 7
subtract 2 from both sides
√(x-8) = 5
square both sides
(√(x-8))² = 5²
x-8 = 25
add 8 to both sides
x = 33
ANSWER
D. 33
EXPLANATION
The given radical equation is
[tex] \sqrt{x - 8} + 2 = 7[/tex]
Group similar terms,
[tex]\sqrt{x - 8} = 7 - 2[/tex]
[tex]\sqrt{x - 8} = 5[/tex]
Square both sides:
[tex] {(\sqrt{x - 8})}^{2} = {5}^{2} [/tex]
Simplify
[tex]x - 8 = 25[/tex]
Solve for x
[tex]x = 25 + 8 = 3[/tex]
Three joggers are running around a circular track. One of them completes one lap in 6 minutes, the second one in 9 minutes, and the third one in 15 minutes. What time will they arrive at their starting point together if they start at the same time from the same point at 10:00 am and maintain their jogging pace
Answers
Answer:
At 11:30 am they will arrive at their starting point together
Step-by-step explanation:
we know that
One of them completes one lap in 6 minutes
The second one in 9 minutes
The third one in 15 minutes
step 1
Find the least common multiple (LCM)
6=2*3
9=3²
15=3*5
so
LCM=(3²)*(2)*(5)=90 minutes
step 2
Find the number of laps of each jogger for the LCM
jogger 1
90/6=15 laps
jogger 2
90/9=10 laps
jogger 3
90/15=6 laps
If they start at 10:00 am
then
10:00 am + 90 minutes=11:30 am
A farmer wants to build a new grain silo. The shape of the silo is to be a cylinder with a hemisphere on the top, where the radius of the hemisphere is to be the same length as the radius of the base of the cylinder. The farmer would like the height of the silo’s cylinder portion to be 4 times the diameter of the base of the cylinder. What should the radius of the silo be if the silo is to hold 35,500pie cubic feet of grain?
Answers
Answer:
[tex]r=16\ ft[/tex]
Step-by-step explanation:
we know that
The volume of the silo is equal to the volume of a cylinder plus the volume of a hemisphere
so
[tex]V=\pi r^{2}h+\frac{4}{6}\pi r^{3}[/tex]
In this problem we have
[tex]V=35,500\pi\ ft^{3}[/tex]
[tex]h=4D=8r[/tex] ----> 4 times the diameter is equal to 8 times the radius
substitute in the formula and solve for r
[tex]35,500\pi=\pi r^{2}(8r)+\frac{4}{6}\pi r^{3}[/tex]
Simplify pi
[tex]35,500=8r^{3}+\frac{4}{6}r^{3}[/tex]
[tex]35,500=r^{3}[8+\frac{4}{6}][/tex]
[tex]35,500=r^{3}[\frac{52}{6}][/tex]
[tex]r^{3}=35,500/[\frac{52}{6}][/tex]
[tex]r=16\ ft[/tex]
Why is Li incorrect in saying that the graph shows a direct variation
Answers
Answer:
The answer B
Step-by-step explanation:
11 to the power of 3 evaluate
Answers
11 is the base, meaning that it is the number being multiplied
3 is the exponent, meaning it tells you how many times you must multiply the base together
For this question we must multiply 11 together 3 times:
11*11*11 = 1331
Hope this helped!