Answer:
40 days
Step-by-step explanation:
If in one day and night the worm goes 1m then it will take 40 days to go 40m
40 days will it take the worm to crawl out of the hole
Given:
A worm is at the bottom of a 40m hole. It can crawl upwards at a rate of 4m in a day, but at night, it slips back 3m.
Worm is at the bottom of a 40m wall.
Worm crawls up the distance = 4m per day
and slips down the distance = 3m per day
Everyday it crawls up by the distance = 4 - 1 = 1m
Time taken to crawl up to the height 40m = 4 days [ Since it crawls up 1 m per day
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What is the smallest positive integer n for which [tex]n^{2}[/tex] is divisible by 18 and [tex]n^{3}[/tex] is divisible by 640?
Answer:
120
Step-by-step explanation:
n^2 has a factor of 18, so factors of 3^2·2. Since n^2 is a perfect square, we know n must have a factor of 3·2 = 6.
n^3 has a factor of 640, so factors of 2^7·5. Since n^3 is a perfect cube, we know n must have a factor of 2^3·5 = 40.
The least common multiple of 6 and 40 is 120.
The smallest positive integer n is 120.
_____
Check
120^2/18 = 800
120^3/640 = 2700
If f(x) = X over 2+8, what is f(x) when X equals 10?
Answer:
[tex] \boxed{\huge{\sf f(x) = 1}} [/tex]
Given:
[tex] \sf f(x) = \frac{x}{2 + 8} [/tex]
To Find:
[tex] \sf f(x) \: when \: \bold{x} = 10[/tex]
Step-by-step explanation:
[tex] \sf Evaluate \: f(x) = \frac{x}{2 + 8} \: where \: \bold{x} = 10 : \\ \sf \implies f(x) = \frac{x}{2 + 8} = \frac{10}{2 + 8} \\ \\ \sf 2 + 8 = 10 : \\ \sf \implies f(x) = \frac{10}{ \boxed{\sf 10}} \\ \\ \sf \frac{ \cancel{\sf 10}}{ \cancel{\sf 10}} = 1 : \\ \sf \implies f(x) = 1[/tex]
The numbers -1/5 and -5 are 'negative reciprocals.' True or False?
Answer:
False
Step-by-step explanation:
The negative reciprocal of -1/5 would be 5, and the negative reciprocal of -5 is 1/5. A way to double-check is all negative reciprocals add to -1.
-1/5 + -5= -5 1/5
Hope this helps and you understand negative reciprocals more for future problems ahead.
Find the point-slope equation for the line that passes through the points (-8,-32) and (3,1). Use the first point in your equation.
Hey there! :)
Answer:
y + 32 = 3(x + 8)
Step-by-step explanation:
Begin by finding the slope of the line using the slope formula:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in the coordinates of the points into the equation:
[tex]m = \frac{1 - (-32)}{3 - (-8)}[/tex]
Simplify:
[tex]m = \frac{33}{11}[/tex]
m = 3.
Point-slope form is:
y-y₁=m(x-x₁)
Plug in the coordinates of the first point, as well as the slope:
y - (-32) = 3(x - (-8)
y + 32 = 3(x + 8)
Answer: y+32=3(x+8)
Step-by-step explanation:
First you need to find the slope.The slope is the change in y divided by the change in x values.
-32 - 1 = -33
-8 - 3 = -11
-33/-11 = 3 the slope is 3
and in point-slope form is like y-b= m(x-a) where b is a y coordinate and a is the x coordinate.
it could be like y-1=3(x-3) or y+32= 3(x+8)
Melinda sold packages of gourmet coffee, x, and pastries, y, at a school fundraiser. The packages of coffee sold for $6 each and pastries sold for $4 each. At the end of the fundraiser, she had sold 2 more packages of coffee than pastries and made $72 in total sales for the fundraiser. Create and graph system of linear equations that model this situation.
Answer:
Please find the attached graph
Melinda sold 8 packages of coffee and 6 packages of pastries
Step-by-step explanation:
The parameters given are;
Number of Packages of coffee = x
Number of Packages of pastries = y
Price of each package of coffee = $6
Price of each package of coffee = $4
Number of packages of packages of coffee sold = 2 more than packages of packages pastries sold
x = 2 + y
y = x - 2................(1)
Sum of money made in the fundraiser = $72
∴ x × $6 + y × $4 = $72
y = ($72 - x × $6)/$4 = 18 - 3/2·x
y = 18 - 3/2·x.........(2)
The solution is
x - 2 = 18 - 3/2·x
x + 3/2 = 18 + 2 = 20
5/2·x = 20
x = 2/5×20 = 8
y = x - 2 = 8 - 2 = 6
This is the answer from plato/edmentum.
Terri rode her bike very slowly to the top of a big hill. Then she coasted back down the hill at a much faster speed. The distance from the bottom to the top of the hill is 3 kilometers. It took Terri ¼ hour to make the round trip. What was her average speed for the entire trip?
Answer:
Terri’s speed can be calculated like this:
her speed- [tex]\frac{6km}{0.25h}[/tex]=24km/h
Step-by-step explanation:
Write the equation of the line that passes through (1,5) and (-2, 14) in slope-intercept form
Answer:
y = -3x + 8
Step-by-step explanation:
(1, 5) ; (-2, 14)
[tex]Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{14-5}{-2-1}\\\\=\frac{9}{-3}\\\\=-3[/tex]
m = -3 ; (1 , 5)
Equation: [tex]y-y_{1}=m(x-x_{1})[/tex]
y - 5 = (-3)(x - 1)
y - 5 = -3x + 3
y = -3x + 3 + 5
y = -3x + 8
what is the method and answer for brainliest
Equal steps mean each number is the same distance from the previous one
From -2 to 28 is 28 units
There are 4 spaces between the numbers
28/4 = 7
Each number is in increase of 7
-2 + 7 = 5
5+7 = 12
12+7 = 19
19+7 = 26
The third number would be 12
What is true about the domain and range of the function?
The graph of the function f(x) = (x +2)(x + 6) is shown
below.
у
6
The domain is all real numbers, and the range is all
real numbers greater than or equal to 4.
O The domain is all real numbers greater than or equal to
4, and the range is all real numbers.
O The domain is all real numbers such that -65x3-2,
and the range is all real numbers greater than or equal
to-4.
The domain is all real numbers greater than or equal to
4, and the range is all real numbers such that -63x3
-2.
4
N
-6 -4 +2
4
6
х
N
-2-
-4
6t
Answer:
The correct option is;
The domain is all real numbers and the range is all real numbers greater than or equal to -4
Step-by-step explanation:
A function defines an output given an input and the set of all the possible inputs to a function is the domain of a function such that there is an output, such that the domain is the set of x values which are points on the curve of the function
The set of outputs that are produced from a given input is the range of a function
The given function is f(x) = (x + 2)(x + 6)
From the curve we see that the minimum y-coordinate, f(x), value is at -4, which is the lower bound of the range, while the x-coordinate values, the domain can be seen extending past the graph sheet which from the expression for the function also (f(x) = (x + 2)(x + 6)) indicates that the x values is the set of all real numbers (on the number line)
Therefore, the correct option is;
The domain is all real numbers and the range is all real numbers greater than or equal to -4.
Answer:
The domain is all real numbers and the range is all real numbers greater than or equal to -4
Step-by-step explanation:
Divide a24 − a18 + a12 by a6. What is the quotient? A. a4 − a3 + a2 B. a18 − a12 + a6 C. a18 + a12 − a6 D. a30 − a24 + a18
Answer:
A
Step-by-step explanation:
Choose the graph represents the function y-3=3/2(x-4)?
Hope this helps have a nice day! :)
What is the approximate distance between points A and B? A coordinate grid is shown from negative 5 to 0 to 5 on both axes at increments of 1. The ordered pair 4, 3 is labeled as A, and the ordered pair negative 2, negative 4 is labeled as B 3.61 9.22 10.35 12.62
Answer:
[tex]\large \boxed{9.22}[/tex]
Step-by-step explanation:
The formula for the distance between two points is
[tex]d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}[/tex]
x₂ - x₁ = 4 - (-2) = 9
y₂ - y₁ = 3 - (-4) = 7
The formula, in effect, creates a right triangle, so we can use the Pythagorean theorem to calculate the distance.
[tex]\begin{array}{rcl}AB & = & \sqrt{6^{2} + 7^{2}}\\& = & \sqrt{36 + 49}\\& = & \sqrt{85}\\& \approx & \mathbf{9.220} \end{array}\\\text{The approximate distance between the points is $\large \boxed{\mathbf{9.220}}$}[/tex]
The approximate distance between points A and B will be equal to 9.220.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. The length of the line segment between two places represents their distance.
Most notably, segments that have the same length are referred to as congruent segments and the distance between two places is always positive.
The formula for the distance between two points is,
[tex]D =\sqrt{(x_2-x_1)+y_2-y_1)^2[/tex]
x₂ - x₁ = 4 - (-2) = 9
y₂ - y₁ = 3 - (-4) = 7
The formula, in effect, creates a right triangle, so we can use the Pythagorean theorem to calculate the distance.
AB = √( 6² + 7² )
= √ ( 36 + 49 )
= √85
= 9.22
Therefore, the approximate distance between points A and B will be equal to 9.220.
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Solve each system by the addition method.
x + 2y = -1
5x - 4y = 16
Put your answer in ordered pair (x, y) DECIMAL form.
Answer:
(x, y) = (2, -1.5)
Step-by-step explanation:
x + 2y = -1
5x - 4y = 16
<=>
(2)x + (2)2y = (2)(-1)
5x - 4y = 16
<=>
2x + 4y = -2
5x - 4y = 16
<=>
7x = 14
<=>
x = 2
(*)x + 2y = -1
=> 2 + 2y = -1
=> 2y = -3
=> y = -1.5
=> (x, y) = (2, -1.5)
You own a comic book store. When you order comic books for your store to sell, you get 18 comic books per bundle. How many comic books would you have to sell if you ordered 7 bundles?
Answer:
the answer is 126
Step-by-step explanation:
beacuse if you sell 7 bundles for every one you get 18 so 18+18+18+18+18+18+18=126
Answer:
126 books
Step-by-step explanation:
There are 18 books per bundle and 7 bundles
So you would multiply 7 with 18 and get your answer of 126 books to sell
simplify radical sign 16a^8b^-2
Answer:
[tex] \frac{ {4a}^{4} }{b} [/tex]solution,
[tex] \sqrt{16 {a}^{8} {b}^{ - 2} } \\ [/tex]
Use negative power rule:
[tex] {x}^{ - a} = \frac{1}{ {x}^{a} } [/tex]
[tex] \sqrt{ {16}^{8} \times \frac{1}{ {b}^{2} } } \\ [/tex]
Simplify:
[tex] \sqrt{ \frac{ {16a}^{8} }{ {b}^{2} } } \\ = \frac{ \sqrt{ {16a}^{8} } }{ \sqrt{ {b}^{2} } } \\ [/tex]
Use this rule:
[tex] \sqrt{ab} = \sqrt{a} . \sqrt{b} [/tex]
[tex] \frac{ \sqrt{16. \sqrt{ {a}^{8} } } }{ \sqrt{ {b}^{2} } } [/tex]
Since, 4*4=16 ,the square root of 16 is 4
[tex] \frac{ \sqrt{ {4}^{2} } \sqrt{ {a}^{8} } }{ \sqrt{ {b}^{2} } } \\ = \frac{4 \sqrt{ {a}^{8} } }{ \sqrt{ {b}^{2} } } [/tex]
Simplify:
[tex] \frac{4 \: \sqrt{ {(a}^{4) ^{2} } } }{ \sqrt{ {b}^{2} } } \\ = \frac{4 {a}^{4} }{b} [/tex]
Hope this helps...
Good luck on your assignment...
What is the result of substituting for y in the bottom equation?
y = x + 3
y= x2 + 2x-4
A. x+ 3 = x2 + 2x - 4
B. X+ 3 = x2
C. y= (x+3)2 + 2(x + 3) - 4
D. y= x2 + 2x - 4 - (x+3)
Answer:
(A)[tex]x + 3= x^2 + 2x-4[/tex]
Step-by-step explanation:
Given the equations:
[tex]y = x + 3\\y= x^2 + 2x-4[/tex]
Substitution simply means replacing the variable y in the second equation with its equivalent x+3 from the first equation.
Substitution of y into [tex]y=x^2 + 2x-4[/tex] gives us:
[tex]x + 3= x^2 + 2x-4[/tex]
The correct option is A.
John is filling a bathtub that is 12 inches deep. He notices that it takes two minutes to fill the tub with three inches of water. He estimates it will take 10 more minutes for the water to reach the top of the tub if it continues at the same rate. Is he correct?
Answer:
No
Step-by-step explanation:
2 = 3 inches
2x5=10
10 = 3x5 of 15 inches
so no and it would take 8 minutes to fill up the tub
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. (2 points)
Answer:
4 (20) + 6(6) = 120
4(20) + 4 (6) = 100
Step-by-step explanation:
Hi, to answer this question we have to write a system of equations with the information given:
Build time (hours) = 4c + 6a = 120
Test time (hours) = 4c + 4 a = 100
Where c represents the number of child bikes and a represents adult bikes.
So, for 20 child bikes and 6 adult bikes:
4 (20) + 6(6) = 120
4(20) + 4 (6) = 100
Feel free to ask for more if needed or if you did not understand something.
Which are steps in the process of completing the square used to solve the equation 3 – 4x = 5x2 – 14x? Check all that apply 3 = 5(x2 + 2x) 3 = 5x2 – 10x 4 = 5(x2 – 2x + 1) 8 = 5(x2 – 2x + 1) 3 = 5(x – 1)2 4 = 5(x – 1)2 StartFraction 8 Over 5 EndFraction = (x – 1)2
Answer:
1. 3 = 5x2 – 10x
2. 8 = 5(x2 – 2x + 1)
3. StartFraction 8 Over 5 EndFraction = (x – 1)2
Step-by-step explanation:
3-4x=5x^2-14x
3=5x^2-14x+4x
3=5x^2-10x
5x^2-10x-3=0
1. 3 = 5x2 – 10x
2. 8 = 5(x2 – 2x + 1)
8=5x^2-10x+5
8-5=5x^2-10x
3=5x^2-10x
3. StartFraction 8 Over 5 EndFraction = (x – 1)2
8/5=x^2-2x+1
Cross product
8=5(x^2-2x+1)
8=5x^2-10x+5
8-5=5x^2-10x
3=5x^2-10x
Answer:
2,4,7
Step-by-step explanation:
Trey is running for president of the chess club, and he received 8 votes. There are 80 members in the club. What percentage of the club members voted for Trey?
Answer:10
Step-by-step explanation:
8/80=1/10*100=10
the illumination due to a source of light varies directly as the strength of the source and inversely as the square of the distance from the source. two sources are 6 meters apart and one of them is 8 times stronger than the other. at what distance from the weaker source on the line segment joining them is the illumination the least
Answer:
Point is at x = 4 m
Step-by-step explanation:
From the question, we can write the formula for intensity as;
I = strength/distance²
Now,
- Let x be the position from the stronger source
- Let k be the strength of the weaker light source
- 8k will be the strength of the stronger light source.
We are told that the two sources are 6 meters apart and one of them is 8 times stronger than the other.
Thus, the total illumination is;
I(x) = (8k/x²) + k/(6 - x)²
Using chain rule to get the critical points, let's find the first derivative and equate to zero;
I'(x) = -16k/x³ + 2k/(6 - x)³ = 0
Adding -16k/x³ to both sides, we have;
2k/(6 - x)³ = 16k/x³
Cross multiply to get;
2kx³ = 16k(6 - x)³
Dividing both sides by 16k to give;
x³/8 = (6 - x)³
Taking cube root of both sides to give;
x/2 = 6 - x
Multiply both sides by 2 to give;
x = 12 - 2x
x + 2x = 12
3x = 12
x = 12/3
x = 4 m
The expression (1/23) ^1000 is closest to what integer?
HELP QUICK PLS
Answer:
The expression is close to 0Step-by-step explanation:
Given the expression [tex](\frac{1}{23} )^{1000} \\[/tex], for us to know the closest integer, the following step must be carried out;
[tex](\frac{1}{23} )^{1000} \\=\frac{1^{1000} }{23^{1000} } \\= \frac{1}{23^{1000}} \\= \frac{1}{5.34 * 10^{1361} }} \\= 1.87*10^{-1362}[/tex]
The value gotten is a very small value which is close to 0
dalanay enlarges a photograph tahst is 3 inches long and 2 inches wide. the length of the enlarged photograph is 15 inches. what is the width of the enlarged photograph, in inches?
Answer:
10 inches
Step-by-step explanation:
Length of photograph, L1 = 3 inches; Length of enlarged photograph, L2 = 15 inches; Width of photograph, W1 = 2 inches; Width of photograph, W2 = ?
Hence, L1/L2 = W1/W2
∴ W2 = (L2*W1)/L1 = (15 X 2)/3 = 10 inches
A basketball player's total points scored for the season went from 158 to 231 over a period of 5 games. What was his scoring rate per game over those 5 games?
Answer:
14.6
Step-by-step explanation:
(231 - 158) / 5 = 14.6
what is the solution to this equation x/5=30
Answer:
x= 150
Step-by-step explanation:
X/5 = 30
x = 5×30
x= 150
Answer:
150
Step-by-step explanation:
[tex]\frac{x}{5}[/tex] = 30
→ Multiply both sides by 5 to isolate x
x = 150
The temperatures of Charleston, South Carolina on May 3rd are recorded in the table below. Determine the equation that models this data.
Answer:
Ok, the first step to see the behavior of this data is doing a graph of it,
So we can see that it looks like an reversed V. (at the bottom of the answer you can see the graph)
Then, we can model this with a piecewise function like:
For the first part we can take the two pairs:
if 11 am is our t = 0h
(0, 85) and (6, 93)
then the linear equation
y = a*t + b
a = (93 - 85)/(6 -0) = 8/6.
and b = 85.
then the linear equation is:
y = (8/6)*t + 85. for 0h ≤ t ≤ 6h
The second part of this equation can be modeled with the points
(6, 93) and (11, 84)
then we have:
y = s*t + c
s = (84 - 93)/(11 - 6) = -7/5
and we can find the value of c as:
93 = (-7/5)*6 + c
93 + (7/5)*6 = 101.4
then this second part is:
y = (-7/5)*t + 101.4 for 6 ≤ t ≤ 11h
then, in conclusion we have:
y = (8/6)*t + 85. for 0h ≤ t ≤ 6h
f(x) =
y = (-7/5)*t + 101.4 for 6 ≤ t ≤ 11h
Answer:
y=7.496sin(0.3243x+0.315)+73.489
Step-by-step explanation:
simply put the data into a graph and graph each equation to see if its matched
NEED HELP ASAP!! RESPOND AS QUICK AS POSSIBLE!!!
Answer:
d
Step-by-step explanation:
Given: In ΔBLU, LE ⟂ BU , and BL ≅ UL Prove: ΔBEL ≅ ΔUEL STATEMENT REASON 1. LE⟂ BU and BL ≅ UL 1. Given 2. LE ≅ LE 2. Reflexive Property 3. ΔBEL ≅ ΔUEL 3. _______________ Which of the following choices will complete the reasoning for statement #3? A SSA B AAA C HL D None of these choices are correct.
Answer:
I think it is C
Step-by-step explanation:
The equation of a circle is given below. ( x + 8 3 ) 2 + y 2 = 1 (x+ 3 8 ) 2 +y 2 =1left parenthesis, x, plus, start fraction, 8, divided by, 3, end fraction, right parenthesis, squared, plus, y, squared, equals, 1 What is its center? ( (left parenthesis , ,comma ) )right parenthesis What is its radius? If necessary, round your answer to two decimal places. units
Answer:
The center is (-8/3,0) and the radius is 1
Step-by-step explanation:
(x+8/3)^2 + y^2 = 1
We know the equation of a circle is given by
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
Rewriting
(x- -8/3)^2 + (y-0)^2 = 1^2
The center is (-8/3,0) and the radius is 1
Select the correct answer from each drop-down menu. Polygon ABCDE rotates 45° clockwise about point F to form polygon FGHIJ, shown in the figure. Find the measure of each angle of polygon ABCDE. m∠ABC = ° m∠BCD = ° m∠DEA = ° m∠CDE = °
Answer and Step-by-step explanation:
As it is mentoned in the question
Polygon ABCDE rotates around point F in clockwise direction to create polygon FGHIJ
And as we can see in the figure that
So we conclude that
A = F ⇒ 117°
B = G ⇒ 90°
C = H ⇒ 127°
D = I ⇒ 90°
E = J ⇒ 117°
Therefore this is the answer and the same is to be considered
Answer:
m∠ABC = 90117127°m∠BCD = 90117127°m∠DEA = 90117127°m∠CDE = 90117127°
Step-by-step explanation: