It will take 6 seconds for the acorn to be 1 foot above the ground.
What is linear equation?A linear equation is an algebraic equation of the form y=mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
A typical form linear equation is, for instance, 2x+3y=5. When an equation is provided in this format, finding both intercepts is rather simple (x and y).
Given:
acorn is falling from 13 feet
Every seconds it descends = 4.8 feet
let us assume that the equation for the distance between the acorn from the ground is
x =13 - 4.8 y
where is y is time in seconds and x is the distance
if x = 1 foot
1 = 13 -4.8y
-12 = -4.8y
y = -12 / -4.8
y = 2.5 seconds
Hence, it will take 6 seconds for the acorn to be 1 foot above the ground.
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When you looked at the thermometer last night, the temperature was 5° C. By morning, the temperature had risen 13°. By afternoon, the temperature had risen another 5°. Afterwards, the temperature dropped 10°. What is the temperature now?
Answer:
Step-by-step explanation:
13
Use the give piece wide function to answer the questions below
F(-4)= f(2)= f(6)= f(0)=
The values of the following functions are:-
f(-4) = 20
f(2) = -1
f(6) = 11
f(0) = -5
Given that ,
-3x + 8, -6 ≤ x ≤ -3
f(x) = [tex]x^2-5[/tex], -2 ≤ x ≤ 3
(1/2)x + 8 , 5 ≤ x ≤10
We have to find the values of f(-4) , f(2), f(6) and, f(0).
As, -6 < 4 < -3
So, we will write,
f(-4) = -3(-4) + 8 = 12 + 8= 20
As, -2 < 2 < 3
So, we will write,
f(2) = [tex](2)^2-5[/tex] = 4 - 5 = -1
As, 5 < 6 < 10
So, we will write,
f(6) = (1/2)(6) + 8 = 3 + 8 = 11
As, -2 < 0 < 3
So, we will write,
f(0) = [tex](0)^2-5[/tex] = 0 - 5 = -5
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Four friends on a ski trip pay $210 each to share the rent of a cabin. The cost per person varies inversely
the number of persons. How many people sharing the rent would make the cost $120 per person?
Seven people sharing the rent would make the cost $120 per person.
What is Inversely Proportional?When two quantities are inversely proportional, that is, when an increase in one causes a decrease in the other and vice versa, they are said to be inversely proportional.
The general equation for inverse variation is y = k/x, where k is the proportionality constant and x and y are two variables.
Given:
The price paid by Four friends on a ski trip to share the rent of a cabin = $210
The cost per person varies inversely with the number of persons.
Let the cost be C and the number of persons be n,
C ∝ 1/n
So, the equation becomes, k = Cn.
Putting the values in the equation we obtain the value of k,
k = 210×4 = 840
We have to find the number of people sharing the rent that would make the cost $120 per person.
Using the equation,
k = Cn
840 = 120 × n
n = 840/120 = 7
Therefore, seven people sharing the rent would make the cost $120 per person.
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Which postulate could we use to prove that the angles
The Supplement postulate can be used to prove that the angles ∠CAB and ∠CAD are supplementary.
According to the Supplement Postulate, two angles are supplementary if they create a linear pair.
What are Supplementary angles?The pair of angles known as supplementary angles always add up to 180 degrees. These two perspectives are known as each other's supplements.If two angles sum up to 180 degrees, they are referred to as supplementary angles. When combined, supplementary angles make a straight angle (180 degrees). In other words, if angle 1 plus angle 2 equals 180 degrees, angle 1 and angle 2 are supplementary. In this instance, Angles 1 and 2 are referred to as "supplements" of one another.There are two types of supplementary angles: neighboring and non-adjacent.
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a spherical ball is measured to have a radius of 5 mm, with a possible measurement error of 0.1 mm. use the differential to estimate the possible change in volume (in mm3) resulting from the error in measuring the radius.
The possible change in volume (in mm3) resulting from the error in measuring the radius is 32. 06 mm³
How to determine the volumeThe formula for volume of a sphere is expressed by;
Volume = 4/3 πr³
Where;
r is the radius of the spherepi takes the value 3.14From the information given, we have that the measured radius is 5 mm, with a possible measurement error of 0.1 mm
Then, radius a = 5mm
Radius b = 5 + 0. 1 = 5. 01mm
Now, substitute the values into the formula
Volume, v = 4/ 3 (3.14)(5)³
expand the bracket
Volume, v = 4/ 3 (392.5)
Volume, v = 523. 3 mm³
For radius of 5.01mm
Volume = 4/ 3 (3.14)(5.1)³
expand the bracket
Volume = 4/3 (416.52)
Volume = 555. 4 mm³
The change in volume = 555. 4 - 523. 3 = 32. 06 mm³
Hence, the change in volume is 32. 06 mm³
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use your equation from part b to predict the highway MPG for a car that gets 68 MPG in the city.part b equation:[tex]y = \frac{7x}{9} + \frac{125}{9} [/tex]
ok
[tex]\begin{gathered} \text{ y = }\frac{7(68)}{9}\text{ + }\frac{125}{9} \\ \\ \text{ y = }\frac{476}{9}\text{ + }\frac{125}{9} \\ \\ \text{ y = }\frac{601}{9} \\ \\ \text{ y = 66.8 } \end{gathered}[/tex]MPG = 66.8
help me with this please
Answer:
-21/2
Step-by-step explanation:
-5-2= - 7
7-4=3(+, - = -)
-7×3/2= - 21/2
The figures below are congruent. Name the corresponding angles.
Answer:
A goes to K. C goes to M. B goes to L.
Step-by-step explanation:
:)
Approximate −12 + the square root of thirty-two to the nearest tenth
The approximate value of the expression given will be equal to -6.3.
An approximation may be defined bringing the value of a certain entity which is almost similar, but not exactly equal to the correct value. The expression can be written as −12 + √32. The value of √32 can be written as 5.656. Since, after decimal 6 to the right of 5 is greater than 5 so to the nearest tenth, we can write as 5.66. Therefore, √32 = 5.66
For the required value of the expression we can write,
−12 + √32
Putting the value of √32 = 5.66 in the expression we get
-12 + √32 = -12 + 5.66
After solving we get
⇒ -12 + √32 = -6.34
To the nearest tenth it will be -6.3.
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when 64 is increased in the ratio 9 : 8, it becomes?
Recall that the ratio 9:8 can be written as follows:
[tex]\frac{9}{8},[/tex]therefore, when 64 is increased in the ratio 9:8 we get:
[tex]64\times\frac{9}{8}=72.[/tex]Answer: 72.
Answer:
72
Step-by-step explanation:
Since X : 64 = 9 : 8
Then we know X/64 = 9/8
Multiplying both sides by 64 cancels on the left64 × (X/64) = (9/8) × 64
X = (9/8) × 64Then solving for X X = 64 × (9/8)X = 72
Therefore 72 : 64 = 9 : 8
1. Explain why the slope of line a is 2/6
7. Find the area of the regular polygon.
12 km
14 km
Answer:
672 sq km
Step-by-step explanation:
Area of a regular polygon
[tex]A = \dfrac{P}{2} \times a[/tex]
P = perimeter of the polygon
a = apotherm which is defined as
The distance from the center of a regular polygon to the midpoint of a side.
The given polygon has 8 sides and each side is 12 km
So the perimeter P = 12 x 8 = 96 km
The apotherm is given as 14 km
So area
[tex]A = \dfrac{96}{2} \times 14 = 672 \text { sq km}[/tex]
Please help me this is due in an hour
Answer:
Your missing number is -87.5.
Step-by-step explanation:
You want to follow reverse order of operations to isolate your variable x
First, you plug in y= 700 to get::
700 = (24x)/7 +1000
Then subtract 1000 from both sides to get:
-300 = (24x)/7
Then multiply both sides by 7 to get:
-2100 = 24x
Then, divide by 24 to get:
-87.5 = x
Thus, your answer x= -87.5
Tell which set or sets the number below belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers.
27
Select all that apply.
A. natural numbers
B. whole numbers
C. rational numbers
D. real numbers
E. integers
. F. irrational numbers
The number 27 is a natural number, whole number, rational, real and an integer .
The number 27
And this number is a natural number and thus it is a natural number and a rational number too.
This is also an integer .
Reason: Natural number : A natural number is one that naturally and frequently appears. It is a whole, non-negative number as a result. N, the collection of natural numbers, can be defined in one of two ways: N = {0, 1, 2, 3, ...}
whole number: the sum of all natural numbers plus zero. neither a decimal nor a fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. 0, the negative, or a counting number.
Rational number: A rational number is a number that is in the form of p/q, where p and q are integers, and q is not equal to 0. Some of the examples of rational numbers include 1/3, 2/4, 1/5, 9/3, and so on.
Real number: Rational, irrational, entire, and natural numbers are all examples of real numbers. Negative, positive, and zero numbers are all examples of integers.
Integer : An integer, pronounced is a whole number that can be positive, negative, or zero and is not a fraction.
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Johnny bought a candy bar for $0.89 and a soda for $1.50. How much did Johnny spend in all?
Answer:
$2.39, hope this helps,
Step-by-step explanation:
1.50+0.89=2.39
Answer: $2.39
Step-by-step explanation: 0.89 + 1.50
0.8 + 1.5 = 2.3
89 + 50 = 139
2.39
time remaining 47:17 felipe used a 40 percent off coupon on a single item at the craft store which saved him $16.42. what would the item have cost if he had not used the coupon? $22.99 $32.84 $41.05 $56.42
The Item would cost if he had not used the coupon 41.05, this is the amount where he is not availing the offer percent.
Felipe has a limited time period to use the 40 percent off coupon on a single item. First, we suppose he avail the 40 percent coupon in the given mean time which is 47:17 then that single item would have cost the Felipe
According to the question, the item have cost if he had not used the coupon, so let the value of the single item is x
x × 40 % = $ 16.42
x × [tex]\frac{40}{100}[/tex] = $ 16.42
40 × x = 16.42 × 100
x = [tex]\frac{16.42 * 100}{40}[/tex]
x = $ 41.05
The Item would cost if he had not used the coupon 41.05, this is the amount where he is not availing the offer percent.
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1 2/3 divided by 4/5
1 2/3 divided by 4/5
= 5/3 ÷ 4/5
make common denominators:
[tex]\frac{25}{15} /\frac{12}{15}[/tex]
invert one and multiply across:
[tex]\frac{25}{15} * \frac{15}{12}[/tex]
= 375/180
reduce:
25/12 or 2 1/12
10b4 +3b²-11 can you help
Answer: your answer in in the screenshot
Step-by-step explanation:
Simplify (574)-3. Assume n # 0.
1
57 ¹2
1
1257¹2
n'
125
125
DONE ✔
Simplified expression for [tex] \frac{1}{( {5n⁴})^{- 3} } [/tex] is 1/125n¹².
As per the rule of exponents, the powers will be multiplied. Representing the mentioned rule in the form of example -
[tex]( {{a}^{m} })^{n} = {{a}^{m} }^{ \times n} [/tex]
Another rule of exponent to be used in the question is : [tex] {a}^{ - x} = \frac{1}{ {a}^{x} } [/tex]
Now, simplifying the expression mentioned in question as per the above written rule.
Rewriting the equation according to second rule.
Value = [tex] \frac{1}{( {5n⁴})^{ 3} } [/tex]
Now, solving the equation by taking cube according to first rule
Value = 1/125n¹²
Thus, the simplified expression is 1/125n¹².
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Use the following function rule to find f(38). f(x) = x/2
The output value of f( 38 ) in the function f( x ) = x/2 is 19.
What is the output value of f( 38 ) in the given function?A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.
Given the data in the question;
f( x ) = x/2f( 38 ) = ?To determine the output value of f( 38 ), replace all the occurrence of x with 38 in the function and simplify.
f( x ) = x/2
f( 38 ) = 38/2
Divide 38 by 2
f( 38 ) = 38/2
f( 38 ) = 19
Therefore, the output value is 19, this forms an ordered pair of ( 38,19 ).
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Question 19
There are 118 different elements in the periodic table. While giving a presentation, Clark says that there are 128 different
elements. Select each true statement.
A) There are actually 118 elements
B) The amount of error in Clark's estimate is 10.
C) The amount of error in Clark's estimate is 118.
D) To the nearest tenth percent, the percent error in Clark's estimate is 8.5%.
E) To the nearest tenth percent, the percent error in Clark's estimate is 10%.
Next Question Check Answer
Rotate ∆ABC by 90° clockwise, about the origin, and then reflect in the x-axis.
What are the coordinates of the new triangle?
Answer:
A = (1, 1)
B = (3, 2)
C = (2, 4)
Step-by-step explanation:
Vertices of the triangle:
A = (1, 1)B = (2, 3)C = (4, 2)Mapping rule for a 90° clockwise rotation about the origin:
(x, y) → (y, -x)
Therefore:
A' = (1, -1)B' = (3, -2)C' = (2, -4)Mapping rule for a reflection in the x-axis:
(x, y) → (x, -y)
Therefore:
A'' = (1, 1)B'' = (3, 2)C'' = (2, 4)Therefore, the coordinates of the new triangle are:
A = (1, 1)B = (3, 2)C = (2, 4)The associative property works with expressions that use
Question 7 options:
division and subtraction
multiplication and addition
The associative property can be applied to addition and multiplication.
When more than two numbers are added together or multiplied, the outcome is always the same, regardless of how the numbers are arranged. This is known as the associative property.
For example,
2 × (7 × 6) = (2 × 7) × 6
2 + (7 + 6) = (2 + 7) + 6
Associative Addition Property
The associative feature of addition states that the total sum of the numbers will not change no matter how they are arranged. This may be stated as follows:
(x + y) + (z + y) = x
Associative Multiplication Property
The idea behind the associative property for multiplication is that no matter how the numbers are arranged, the result will always be the same. This may be stated as follows:
P = (q)/(r) = (q)/(r)
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the question is in the picture
Answer: y = 4x-1
Step-by-step explanation:
1) Choose two points for the later equation.
For this example, I will use (-1,-5) and (2,7)
2) Place it in a rise/run equation. (y/x)
[tex]\frac{y2-y1}{x2-x1} \\\\\frac{7-(-5)}{2-(-1)} \\\\\frac{12}{3} \\\\4[/tex]
The Slope is 4.
3) Find the y-intercept
So, we can place a given point and slope into a y=mx+b function.
[tex]y=4x+b[/tex]
Next, we can substitute the point and slope.
[tex]7 = 4(2)+b\\7=8+b\\-1=b[/tex]
4) Finally, place it all in slope intercept form
y = 4x-1
In November, the price of a cell phone was double the price in March. In December, the price was $53, which was $25 less than the price in November.
What was the price of the cell phone in March?
The price of the cell phone in March was
Based on the price of the cell phone in November and December, the price of the cell phone in March was $39
How to find the price of the cell phone?To find the price of the cell phone in March, you need to first find the price of the cell phone in November.
The price of the cell phone in November was $25 more than the price in December:
= 25 + 53
= $78
The price in November was double the price in March so the price in March was:
= 78 / 2
= $39
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Megan is in charge of housekeeping at the Seaside Hotel. She makes sure there are enough clean towels for each room that has been booked for the night.
There is a proportional relationship between the number of rooms booked, x, and the number of towels Megan needs to supply, y.
By the analysis of the graph, the constant of proportionality is 2.
By analyzing the graph given we can infer that If five rooms are reserved, he must provide ten towels.
So x is the number booked and y is the number of towels, Then
x is directly proportional to y,
The given graph is linear in nature, as we increase x, there will be a significant increase increase in y, The constant of proportionality(k) tells us how much y will change when x changes.
The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
Now, 10= k *5
[tex]k =\frac{10}{5} \\k =2[/tex]
Hence, the constant of proportionality k is 2.
and the equation of the given graph is y = 2x
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Write the coordinates of the vertices after a rotation 90° counterclockwise around the origin.
When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative
What is the explanation?
U(2, 7) → U'(-7, 2)
V(10, 7) → V'(-7, 10)
W(2, 3) → W'(-3, 2)
Step-by-step explanation:
From the picture attached,
Coordinates of the vertices of the given triangle,
U → (2, 7)
V → (10. 7)
W → (2, 3)
Since rule for the coordinates of a point P(x, y) after a rotation of 90° counterclockwise about the origin is,
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-4.2 + 3.3 in simplest form
Grayson has $1.20 worth of nickels and dimes. He has twice as many nickels as dimes. Determine the number of nickels and the number of dimes that Grayson has.
The determined value of the number of nickels and the number of dimes that Grayson has is
x=6y=2This is further explained below.
What is the determined value of the number of nickels and the number of dimes that Grayson?Generally, The following phrase represents Jayden's complete financial worth:
Nickels are worth $0.05 each.
The dime value is equal to $0.10
The total value is equal to the sum of the values of the nickels and dimes.
where;
[tex]1.20= (0.05*2 x) +(0.1*x)[/tex]
0.1 x+0.1 x=1.2
0.2 x=1.2
[tex]x=\frac{1.2}{0.2}[/tex]
x=6
y=2
In conclusion, the Total number of dimes=6
Total number of nickels=12
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What is the value of this expression
Given expression:
[tex]7p+\frac{q}{3}[/tex] , given that p = 6 and q = 12.
Here, we need to substitute the values of p and q in the given expression to obtain the value of the expression.
On substitution, the expression becomes,
[tex]7X6+\frac{12}{3}[/tex] ,
Here we use BODMAS rule ( Brackets, Orders, Division, Multiplication, Addition, Subtraction) , hence initially we do the division operation, then the multiplication operation and at last the addition operation,
= 7x6 + 4 = 42 + 4 = 46.
Hence, option D) 46 is the correct option.
These type of expressions can be solved by simply substituting the given values of the variables such as p, q and so on.
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