A sunflower in Julia Rosario's garden was 12 centimeters tall when it was first planted. Since then, it has grown approximately 0.6 meters per day. Write an equation in slope-intercept form that models this situation. How tall will her sunflower be after two weeks?
An equation in slope-intercept form models given situation is y=0.6x+20 and the length of the sunflower after two weeks is 21.2 meters.
Given that, a sunflower in Julia Rosario's garden was 12 centimetres tall when it was first planted. Since then, it has grown approximately 0.6 meters per day.
We need to write an equation in slope-intercept form that models this situation.
What is the slope-intercept form?The slope-intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis). The equation of the line is the equation that is satisfied by each point that lies on that line.
The slope intercept form equation for a straight line with a slope, 'm', and 'b' as the y-intercept can be given as y = mx + b.
Let y be the length of a sunflower plant and the number of days be x.
Now, y=0.6x+20
The length of the sunflower after two weeks is y=0.6×2+20
⇒y=1.2+20=21.2 meters
Therefore, an equation in slope-intercept form models given situation is y=0.6x+20 and the length of the sunflower after two weeks is 21.2 meters.
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What's 3/4 times 168
A building is 2 ft from a 12 ft fence that surrounds the property. A worker wants to wash a window in the building 17 ft from the ground. He plans to place a ladder over the fence so it rests against the building. He decides he should place the ladder 8 ft from the fence for stability. To the nearest tenth of a foot, how long of a ladder will he need?
Using Pythagoras theorem, the ladder must be 19.7ft long.
What is Pythagoras theorem?Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
Perpendicular = height of the window from the ground = 17ft
Base = distance of the foot of the ladder from the base of the building = 10ft
Hypotenuse = [tex]\sqrt{perpendicular^{2} +base^{2} }[/tex]
H = [tex]\sqrt{17^{2}+10^{2} }[/tex] = 19.4ft
Length of ladder = 19.4ft
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Which rational number equals 0.1 repeating?
Answer:
0.1111.... = [tex]\frac{1}{9}[/tex].
Step-by-step explanation:
Given : 0.1 repeating
To find : Which rational number equals 0.1111......
Solution : We have given 0. 11111.........
We can see there is only one number is repeating , we will multiply it by 10
Let x = 0.1111.......
Multiply both sides by 10
10x = 10 * 0.1111.......
10x = 1.1111.......
We can write it in terms of x
10x = 1. 000 + 0.11111....
10 x = 1 + x
On subtracting both sides by x
10 x -x = 1
9 x = 1
On dividing both sides by 9
x = [tex]\frac{1}{9}[/tex].
0.1111.... = [tex]\frac{1}{9}[/tex].
Therefore, 0.1111.... = [tex]\frac{1}{9}[/tex].
The rational number that equals 0.1 repeating is 1/9.
The rational number that equals 0.1 repeating can be represented as follows:
Let x = 0.1 repeating
To convert the repeating decimal to a fraction, we can use the following method:
Let's multiply both sides of the equation by 10 to shift the decimal point one place to the right:
10x = 1.1 repeating
Now, subtract the original equation from this new equation to eliminate the repeating part:
10x - x = 1.1 repeating - 0.1 repeating
9x = 1
Divide both sides of the equation by 9 to solve for x:
x = 1/9
Therefore, the rational number that equals 0.1 repeating is 1/9.
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Beatrice has 15 glasses and 20 mugs. She would like to set them out in identical groups, with none left over. In preparation for a dinner party. What is the greatest number of groups Beatrice can set out?
If x=√987678948729 and y=15927085, then what is (x÷9.5357)π + y/9743268?
Can you help me with theses problems plz.Also can you explain to me how to get it.Thank you
divide
7,647÷34=
a.224 r31
b.227 r29
c.251 r13
d.254 r11
What's an improper fraction is equal in mixed numbers 6 4/7
multiply the 7 (the denominator), and the 6 (the whole number). To this product, add the 4 (the numerator)
giving 46, to form the new numerator, and use the 7 as the new denominator.
So, 6 4/7 as an improper fraction is 46/7
The improper fraction equivalent to [tex]6\frac{4}{7}[/tex] is [tex]\frac{46}{7}[/tex].
An improper fraction is a fraction where the numerator is greater than the denominator.
A mixed fraction is defined as a fraction formed by combining a whole number and a fraction.
Since the given fraction is in mixed fraction so on solving it we get,
[tex]\dfrac{46}{7}[/tex].
Hence the required improper fraction will be [tex]\dfrac{46}{7}[/tex].
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you have 2 quaters and 5 dimes in your pocket write the ratio of quaters to the total number of coins
the angle of elevation from a ship to the top of a 35 m lighthouse on the shore measure 28 degrees. How far is the ship from shore
what is 3.45 repeating as a mixed number
Answer:
3 9/20
Step-by-step explanation:
3.45 is 69/20
60 goes into 20 3 times
which leaves you with 3 9/20
Solve for c.
a(c−b)=d
A)c=d − ab/a
B)c=d − ab/b
C)c=ab − d/a
D)c=d + ab/a
Answer: the correct option is
(D) [tex]c=\dfrac{d+ab}{a}.[/tex]
Step-by-step explanation: We are given to solve the following equation for the value of c :
[tex]a(c-b)=d~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To solve the given equation for c, we need to take c on one side and all other values on the other side of the equation.
The solution for c of equation (i) is as follows :
[tex]a(c-b)=d\\\\\Rightarrow ac-ab=d\\\\\Rightarrow ac=d+ab\\\\\Rightarrow c=\dfrac{d+ab}{a}.[/tex]
Thus, the required value of c is [tex]c=\dfrac{d+ab}{a}.[/tex]
Option (D) is CORRECT.
what is 89972 rounded to 3 significant figures
The approximation of 89972 to three significant digits is 900
How to round the number?The number is given as:
89972
To round to three signficant digits, we simply count three digits from the left.
i.e. 899
Next, we start the approximation from the next digit
i.e. 7
Hence, the approximation of 89972 to three significant digits is 900
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Mia needs to bring ar least 25 pieces of fruit to the school picnic. She suggested both apples and oranges and was told to be sure to bring more that 10 apples
the temperature is -4f a high pressure front increases the temperature to 8f by how many degrees did the temperature increase
What does volume measure?
Volume is a measurement that quantifies the amount of three-dimensional space occupied by an object, substance, or region.
What is a volume?Volume is a fundamental physical quantity that describes the extent or size of an object in the context of its three dimensions: length, width, and height.
Volume is commonly expressed in cubic units, such as cubic meters (m³), cubic centimeters (cm³), cubic inches (in³), or cubic feet (ft³), depending on the system of measurement used. It can apply to various entities, including solid objects, liquids, gases, or even abstract concepts like the volume of data.
For solid objects, the volume represents the total amount of space enclosed within its boundaries. It is typically determined by measuring or calculating the product of the object's length, width, and height or through more complex mathematical formulas for irregular shapes.
In the case of liquids or gases, the volume refers to the amount of space occupied by the substance within a container. It can be measured directly using tools such as graduated cylinders or indirectly through displacement methods.
Understanding volume is essential in fields like physics, engineering, architecture, chemistry, and many others where knowledge of spatial quantities is required for designing, analyzing, or describing various objects or systems.
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x+6 /3 = 2+x-2/5
x+6 is a fraction so it's the numerator and the 3 is underneath
same with the right side, x-2 is the numerator and 5 is denominator. help please, i know the answer but I don't know how to get it
How many quarts of water must be added to 4 quarts of an 80% mixture to obtain a 50% mixture?
To obtain a 50% mixture, 2.4 quarts of water must be added to 4 quarts of an 80% mixture.
To solve this problem, we'll use the concept of mixtures.
Let's denote:
x = the number of quarts of water to be added.
We have 4 quarts of an 80% mixture. This means that in these 4 quarts, 80% is the actual substance (let's call it A) and 20% is water.
So, the amount of substance A in the 4 quarts is [tex]\(0.80 \times 4 = 3.2\)[/tex]quarts, and the amount of water is [tex]\(0.20 \times 4 = 0.8\)[/tex] quarts.
When we add \(x\) quarts of water, the total amount of water becomes 0.8 + x, and the total volume of the mixture becomes 4 + x quarts.
For the mixture to be 50%, the amount of substance A in the mixture should be equal to the amount of water. So, we set up the equation:
[tex]\[3.2 = 0.5 \times (4 + x)\][/tex]
Solving for x:
[tex]\[3.2 = 2 + 0.5x\]\[0.5x = 3.2 - 2\]\[0.5x = 1.2\]\[x = \frac{1.2}{0.5}\]\[x = 2.4\][/tex]
So, 2.4 quarts of water must be added to 4 quarts of an 80% mixture to obtain a 50% mixture.
Destiny read 1/4 of a book on the day she received it. The next day, she read 5/8 of the book. On the third day, she finished reading the book. What decimal represents the fraction of the book destiny read on the third day?
After 6 months the simple interest earned annually on an investment of $3000 was $811. Find the interest rate to the nearest tenth of a percent.
the area of a four square court is 66 square feet. Estimate the side length,s, to the nearest tenth of a foot
The side of the four-square court is 8.1 ft.
Area of SquareThe area of a square is given as the square of its side. the are of a square whose side is a is given as,
Area of Square = a²
Given to usthe area of a four-square court = 66 ft²
AssumptionLet's assume that the side of the four-square court is x.
Calculationthe area of a four-square court = area of square
[tex]66 = x^2\\x^2 = 66\\x = \sqrt{66}\\x=8.124[/tex]
Thus, the side of the four-square court is 8.124 ft. but we want the value to be the nearest tenth of a foot,
[tex]\rm{8.124\ ft \approx 8.1\ ft[/tex]
Hence, the side of the four-square court is 8.1 ft.
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How to solve-3r+9=-4r+5
One of the events at the circus starred Gabriella the Human Cannonball. On Saturday she performed in four shows. Shot from a cannon, her distances measured 8.05 meters, 17.71 meters, 14.38 meters, and 19.35 meters. What was the total distance Gabriella flew that day?
Final answer:
To calculate the total distance Gabriella flew in four shows at the circus, add up the distances she covered in each performance.
Explanation:
The total distance Gabriella flew on Saturday can be calculated by adding up the distances she covered in each show:
Distance 1: 8.05 meters
Distance 2: 17.71 meters
Distance 3: 14.38 meters
Distance 4: 19.35 meters
By adding these distances together, you can find the total distance Gabriella flew that day i.e. 8.05+17.71+14.38+19.35 = 59.49 m
How can you find the sum [8 +(−4)] + (−8 + 4) using mental math?
Two Questions please help and explain
You spend $154 to make wooden bookends and plan to sell them online for $8.50 each. You will charge an additional $3.25 per bookend to wrap and ship them. How many bookends must you sell in order for your profit to be at least $600?
A) 40
B) 64
C) 65
D) 89
Erica has found a pair of running sneakers that she likes, costing $150. She has saved $31 already, and she has a job where she earns $8.50 per hour. How many hours will she have to work in order to afford the sneakers?
A) 17
B) 18
C) 22
D) 14
write write a subtraction sentence where the difference is positive. Use a positive and negative integer?
Compare 5.7145 and √29 Show work
The number 5.38516 is greater than the square root of 29 or the square root of the number 29 is less than the number 5.7145.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
It is given that:
The two numbers are:
5.7145 and √29
It is required to compare the numbers
The square root of the number 29 can be found using the division method.
The square root of the number 29 is 5.38516
As we know, the number line can be defined as the representation of the numbers on a straight line that goes infinitely on both sides.
Plotting the numbers 5.7145 and 5.38516 on a number line.
We will see the:
5.38516 < 5.7145 OR
5.7145 > 5.38516
Thus, the number 5.38516 is greater than the square root of 29 or the square root of the number 29 is less than the number 5.7145.
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Identify an ordered pair of the equation 2x = 6y – 24.
what is 320 million in scientific notation?
The scientific notation of 320 million is 3.2 x [tex]10^8[/tex].
What is scientific notation?It is the way of writing a large number between 1 to 10 with a power of 10.
Example:
2.9 x 10² is in scientific notation
3.4 x 10³ is in scientific notation
4.4 x 10³ is in scientific notation
We have,
320 million
This can be written as,
1 million = 1000000
So,
= 320 x [tex]10^6[/tex]
= 32 x [tex]10^7[/tex]
Multiply 10/10 to make a number between 1 and 10.
= 32/10 x 10 x [tex]10^7[/tex]
Make an exponent of base 10.
= 3.2 x [tex]10^8[/tex]
Thus,
The scientific notation of 320 million is 3.2 x [tex]10^8[/tex].
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