The equation that describes the relationship between n, the step number, and h, the height from the base is [tex]\mathbf{h = 0.2n}[/tex]
The sets of step are given as:
Step number (n) Height from the base (h)
50 10
90 18
110 22
The above table represents a linear relationship.
So, we start by calculating the slope (m)
[tex]\mathbf{m = \frac{h_2 -h_1}{n_2 -n_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{18 - 10}{90 - 50}}[/tex]
[tex]\mathbf{m = \frac{8}{40}}[/tex]
Simplify
[tex]\mathbf{m = 0.2}[/tex]
The equation is then calculated as:
[tex]\mathbf{h = m(n -n_1) + h_1}[/tex]
So, we have:
[tex]\mathbf{h = 0.2(n -50) + 10}[/tex]
Expand
[tex]\mathbf{h = 0.2n -10 + 10}[/tex]
Evaluate like terms
[tex]\mathbf{h = 0.2n}[/tex]
Hence, the equation that describes the steps is [tex]\mathbf{h = 0.2n}[/tex]
Read more about linear equations at:
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Answer:
h=0.2n
Step-by-step explanation:
I'm too lazy to do a step-by-step but this is correct on khan academy.
Use the function below to find f(-2)
F(x)=3x
Answer:
B
Step-by-step explanation:
Using the rule of exponents
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
Then
f(- 2) = [tex]3^{-2}[/tex] = [tex]\frac{1}{3^2}[/tex] = [tex]\frac{1}{9}[/tex] → B
3. Solve the equation shown below for x.
6(x - 1) = 42
Answer:
Answer:
x=8
Step-by-step explanation:
open the brackets to be
6x-6=42
then collect like tems
6x=48
x=8
Convert the binary number 10101 to its base 10 equivalent.
12
21
22
31
10101₂ = 1×2⁴ + 0×2³ + 1×2² + 0×2¹ + 1×2⁰
10101₂ = 16 + 0 + 4 + 0 + 1
10101₂ = 21
Here see below
[tex]\\ \sf\Rrightarrow (10101)_2[/tex]
[tex]\\ \sf\Rrightarrow 1\times 2^0+0\times 2^1+1\times 2^2+0\times 2^3+1\times 2^4[/tex]
[tex]\\ \sf\Rrightarrow 1+4+16[/tex]
[tex]\\ \sf\Rrightarrow (21)_{10}[/tex]
Match each operation to its opposite
Which linear inequality is represented by the graph?
6-
-5
y s 2x + 4
oys 2x + 3
O y2+x+3
-3
O yz 2x + 3
Please help!!
Answer: y ≤ (1/2)x + 3
Step-by-step explanation:
The slope is 1/2 and the y-intercept is 3.
The linear inequality represented by the graph is [tex]y \le \frac 12x + 3[/tex]
From the graph, we have the following highlights:
The inequality has a closed line, and the bottom part is shadedThe slope of the line is 1/2The y-intercept is 3The first highlight implies that the inequality sign to use is ≤
The slope (m) is calculated as:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{3 -4}{0-2}[/tex]
[tex]m = \frac{-1}{-2}[/tex]
[tex]m = \frac{1}{2}[/tex]
The y-intercept (b) is where the line crosses the y-axis:
b = 3
The linear inequality is represented as:
[tex]y \le mx + b[/tex]
So, we have:
[tex]y \le \frac 12x + 3[/tex]
Hence, the linear inequality is [tex]y \le \frac 12x + 3[/tex]
Read more about linear inequality at:
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A store manager is marking down microscopes from $1,000 to $620. What is the discount, as
a percentage?
if it's 11:24 what time will it be in 49 minutes
Hi,
if it's 11:24, it wil be 12:13
✅(◠‿◕)
What is the range of the relation?
Question 9 options:
{–4, –2,–1, 2}
{–4, 4}
{–3, –2, 0, 2}
{–4, –2, –1, 0, –2}
Answer:
{- 3, - 2, 0, 2 }
Step-by-step explanation:
The range is the y- coordinates of the points
(- 4, - 3 ) , (- 1, - 2 ) , (- 2, 0 ) , (0, 2 )
The y- coordinates are - 3, - 2, 0, 2
Then the range is { - 3, - 2, 0, 2 }
1. A vendor at the farmer's market was selling a bag of 8 potatoes for $2.56. Another
vendor was selling a bag of 10 potatoes for $4.32. Which bag is the better deal?
Pls hurry
Answer:
8 potatoes for $2.56 is the better deal.
Step-by-step explanation:
unit price formula; cost ÷ quantity
2.56 ÷ 8 = $0.32
4.32 ÷ 10 = 0.432
round to the nearest hundredth
= $0.43
compare the answers
Answe 42.2
Step-by-step explanation:
The other vender because he got 42.2 dollar other got 20.48
The bottom of a rectangular swimming pool has a perimeter of 62 meters. Its area is 220 square meters. What are the dimensions of the pool?
_____meters by ____ meters
PLEASEE HELPP MEE PLEASEEEE!
Half the perimeter is the length + the width
62/2 = 31
Area = length x width
16 + 15 = 31, 15 x 16 = 240
17 + 14 = 31, 17 x 14 = 238
20 + 11 = 31, 20 x 11 = 220
Answer: 20 meters x 11 meters
Solve w + 1∕4 < 7∕8.
Question 10 options:
A)
w < 5∕8
B)
w = 5∕8
C)
w > 5∕8
D)
w ≤ 5∕8
Answer:
w < 5/8
Step-by-step explanation:
Check
Match the solution set given in inequality notation with the solution set given in interval notation.
17,88
(-0, 7.8)
7.8
(7.8,00)
> 7.8
[7.8,00)
V
7.8
(-0, 7.8)
The Matching of the inequality is
x ≤ 7.8 -> (-∞,7.8]
x < 7.8 -> (-∞,7.8).
x > 7.8 -> (7.8,∞)
x ≥ 7.8 -> [7.8,∞).
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
1. x ≤ 7.8
Here the value of is less than equal to 7.8 which means starting from -∞ to 7.8
Thus, the interval is (-∞,7.8]
2. x < 7.8
Here the value of is less than 7.8 which means starting from -∞ to less than 7.8.
Thus, the interval is (-∞,7.8).
3. x > 7.8
Here the value of is greater than 7.8 which means starting from 7.9 to ∞.
Thus, the interval is (7.8,∞)
4. x ≥ 7.8
Here the value of is greater than equal to 7.8 which means starting from 7.8 to ∞.
Thus, the interval is [7.8,∞).
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Under his cell phone plan, Nathaniel pays a flat cost of $41 per month and $4 per gigabyte. He wants to keep his bill at $45.80 per month. Write and solve an equation which can be used to determine 2, the number of gigabytes of data Nathaniel can use while staying within his budget.
Answer:
equation: 41+4x=45.80
answer: x=1.20
Step-by-step explanation:
The equation is $45.80 = $41 + ($4 × x) which can be used to determine the number of gigabytes of data Nathaniel can use while staying within his budget. And Nathaniel can use up to 1.2 gigabytes of data while staying within his budget of $45.80 per month.
Let's denote the number of gigabytes of data Nathaniel can use as x.
Then the equation representing his cell phone bill can be set up as:
Total cost = Flat cost + (Cost per gigabyte × Number of gigabytes)
$45.80 = $41 + ($4 × x)
Now, we can solve for x:
$4 × x = $45.80 - $41
$4 × x = $4.80
x = $4.80 / $4
x = 1.2
So, Nathaniel can use up to 1.2 gigabytes of data while staying within his budget of $45.80 per month.
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Evaluate -(2-6)(23).
O A. -8
B.
1/8
C. 8
O D.
- 1 / 8
Answer:
92
Step-by-step explanation:
- ( 2 - 6 )
= - ( - 4 )
= 4
- ( 2 - 6 ) ( 23 )
= 4 x 23
= 92
The evaluation of - (2- 6) ( 23) is 92
In mathematics, evaluation is a systematic method used in solving expressions. From the given information, we need to first solve the expressions in the brackets before multiplying them together.
From the given information:
= - ( 2 - 6) (23)
= - ( -4) (23)
= 4 × 23
= 92
Learn more about how to evaluate in mathematics here:
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What number is halfway between 6.7 and 11.9
Answer:
2.05
Step-by-step explanation:
To find the Median value, we begin by sorting Or arranging our numbers In ascending Or descending order.
-8.8,-5.7,-2.6,0.5,3.6,6.7,9.8,11.9
Having an even (8) number of values, the median is the midway point between the two middle numbers.
In our case the two middle numbers are 0.5 and 3.6
(0.5+3.6)/2
Median=2.05 (In words: two && 5/100)
Sarah is 2 inches taller than the quotient of billy’s height and 5. Let b represent Billy’s height. write an expression that represents Sarah’s height
Answer:
1
Step-by-step explanation:
5(x+1) = 12
5(x+1) = 5x + 12
5(x+1) = 5x + 5
5(x=1) = 0
what one is an infinite solution
Answer:
[tex]2 + \frac{b}{5} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
A wedding venue holds no more than 185 guests. If 319 people have said they are attending, how many more people does the venue have room for?
Answer:185 guests
Step-by-step explanation: it can only hold 185 guests no more.
Ms. Vescelius wants to divide her class into cooperative learn-
ing groups. If there are 28 students in the class and she wants
all the groups to have the same number of students, how
many students should she put in each group?
Here's the Question ~
[tex] {2 - 1}^{2} [/tex]
Answer:
The answer is 1
Step-by-step explanation:
1² = 1×1
= 1
2 - 1² = 2 - 1
= 1
Two consecutive whole numbers is 57. What are the two numbers?(hint: Let n represent the first number. Then n + 1 is the next consecutive whole number.
28+29 = 57
=======================================================
Explanation:
n = first number
n+1 = second number
Add up those two items and set the result equal to 57. Solve for n.
first+second = 57
(n) + (n+1) = 57
2n+1 = 57
2n = 57-1
2n = 56
n = 56/2
n = 28
n+1 = 28+1 = 29
The two consecutive whole numbers are 28 and 29
28+29 = 57
Answer:
28 and 29
Step-by-step explanation:
Given values:
1st number = n
2nd number = n+1
n + n + 1 = 57
2n + 1 = 57
2n = 56
n = 28
n+1 = 29
Answer: 28 and 29
What is the range of the function y = x^2?
Ox>0
O all real numbers
Oy>0
Answer:
The range is y≥0
Step-by-step explanation:
The shape of this graph is a parabola
You may see this by using the Desmos calculator and typing y=x^2 if you would like to visualize.
(a) The function y = x^2 simply takes whatever number you feed it (x) and outputs x squared.
For example
y = (2)^2=4
y = (3)^2 = 9
(b) To graph x^2 simply make a table of values and plug in 0 -> however high you would like to go ( usually to 5 or so is fine but you could go to infinity).
Example
y = x^2
Y | X
________
2 | 4
3 | 9
4 | 16
In this case the function's range is y≥0 because all y values will be greater than or equal to 0.
If you are wanting to learn how to specifically graph this you can look up (Graphing y = x²) if my quick graphing explanation back at mark (b) does not help.
What is this in terms of joules?
What is 10/11x11/12 in the fraction form
Answer:
83/100
Step-by-step explanation:
10/11x11/12 is 0.8333333....
HELP ASAPPP!
Ava has $30 for a cab ride. It costs $3.50 for the cab to pick her up then $1.50 per mile after the initial pick-up fee. Which inequality best represents the real-world situation?
Answer: [tex]1.50x+3.50\leq 30[/tex]
Step-by-step explanation:
x represents how many miles after the pick-up. we add on 3.50 because that is the intial pick-up price. then the cost has to be under 30 because she only has 30 dollars
⦁ Determine the zeros of f(x) = (x + 1)^2(x – 3)(x – 4). Indicate the multiplicity of any factors that occur more than once.
Answer:
see explanation
Step-by-step explanation:
To find the zeros equate f(x) to zero , that is
(x + 1)²(x - 3)(x - 4) = 0
Equate each factor to zero and solve for x
x- 4 = 0 ⇒ x = 4
x - 3 = 0 ⇒ x = 3
(x + 1)² = 0 ⇒ (x + 1) = 0 , x + 1 = 0 ( 2 factors ) , then
x = - 1 with multiplicity 2
hi i need help with this
Answer:
15 in
Step-by-step explanation:
d^2 = w^2 + l^2
25^2 = 20^2 + l^2
l^2 = 225
l = 15
Martin drank 2/3 liter of water Monday before going jogging.He drank 3/7 liter of water after his jog.How much water did Martin drank altogether?Write your answer as a mixed number.
Why will nobody answer my questions..
Which graph represents the solution to this inequality?
-1/4(12x+8)<-2x+11
Answer: I would need a picture of the possible graphs.
(Uhm....This is a question out of maths) How many floors are 78 steps
find the value of 777^2 - 223^2
Answer:
549440
Step-by-step explanation:
777^2 = 603729
223^2 = 54289
603729 - 54289 = 549440
