The height of the plant after it grows 1 7/8 inches is 81/8 inches.
Explanation:To find the height of the plant after it grows 1 7/8 inches, we need to add 1 7/8 to the current height of 8 1/4. First, we can convert 8 1/4 to an improper fraction by multiplying the whole number (8) by the denominator (4) and then adding the numerator (1). This gives us 33/4 inches. Next, we can add 1 7/8 by finding a common denominator (8) and adding the numerators (1+7=8). So, 1 7/8 is equivalent to 15/8. Adding 33/4 and 15/8, we first need to find a common denominator which is 8. Multiplying the numerator and denominator of 33/4 by 2 gives us 66/8. Now, we can add 66/8 and 15/8 to get a total of 81/8 inches. Therefore, the height of the plant after it grows 1 7/8 inches is 81/8 inches.
Final answer:
After adding the growth of 1 7/8 inches to the original plant height of 8 1/4 inches, the new height of the plant is calculated to be 10 1/8 inches.
Explanation:
To calculate the new height of the plant after it grows an additional 1 7/8 inches, we simply need to add this growth to the plant's original height of 8 1/4 inches. The sum of these two measurements will give us the plant's total height.
Begin by converting the mixed numbers to improper fractions to make addition easier: 8 1/4 inches becomes 33/4 inches and 1 7/8 inches becomes 15/8 inches. Next, find a common denominator and add the two fractions.
Common denominator for 4 and 8 is 8.Convert 33/4 to an equivalent fraction with a denominator of 8, which is 66/8.Add 66/8 inches and 15/8 inches.(66/8) + (15/8) = 81/8 inches.Now, convert the improper fraction back to a mixed number to determine the plant's new height:
81 divided by 8 is 10 with a remainder of 1.So, 81/8 inches is equal to 10 1/8 inches.Therefore, after growing an additional 1 7/8 inches, the plant's new height is 10 1/8 inches.
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Candice paid $2,000 for her whole life insurance policy this year. A term insurance policy with the same coverage would cost her about $700 a year. Assuming she decides to buy the term policy and invest the difference, earning a rate of 6 percent, how much money could she "make" in a year?
The sum of three consecutive even integers is 174 what are the integers?
The required three consecutive even integers are 56, 58, and 60.
Given that,
The sum of three consecutive even integers is 174 what are integers is to be determined?
Arithmetic progression is the series of numbers that have common differences between adjacent values
Here,
Let the three even integers be 2x, 2x+ 2 and 2x + 4
Now, accoding to the question,
2x + 2x + 2 + 2x + 4 = 174
6x + 6 = 174
x = 28
Now,
2x =28 * 2 = 56
2x + 2 = 56 + 2 = 58
2x + 4 = 56 + 4 = 60
Thus, the required three consecutive even integers are 56, 58, and 60.
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Four less than half a number is 17 .How would I solve this?
First, let's define the number we are looking for as n.
So "half a number" is (1/2)×n
Therefore, "four less than" this would be: ((12)×n)−4
And if this is or, in other words, = to #17 we can write the equation:
((12)×n)−4=17
Solving for n while keeping the equation balanced gives:
((12)×n)−4+4=17+4
(12)×n=21
(21)×(12)×n=21×(21)
((21)×(12))×n=421
1×n=42
n=42
What is the slope of line represented by 1/8x + 3y =3
Find a general form of an equation of the line through the point a that satisfies the given condition. a(6, −5); parallel to the line 9x − 2y = 7
To find the parallel line's equation through the point (6, -5), we identify the slope of 9x - 2y = 7 as (9/2), and then use the point-slope form with the given point to derive the new line's equation. The final general form of this equation is 9x - 2y - 64 = 0.
Explanation:To find the general form of an equation of the line that is parallel to the line 9x - 2y = 7 and passes through point a(6, -5), we first need to identify the slope of the given line. The slope-intercept form of the line can be found by rearranging the equation into y = mx + b, where m is the slope. For the given equation 9x - 2y = 7, we solve for y to get the slope:
2y = 9x - 7
y = (9/2)x - 7/2
The slope of the given line is (9/2). Since parallel lines have the same slope, our new line will also have a slope of (9/2). Using the point-slope form of a line's equation, we can insert the slope and the coordinates of point a to determine the equation of our new line:
y - y₁ = m(x - x₁)
y - (-5) = (9/2)(x - 6)
y + 5 = (9/2)x - 27
Finally, we rearrange this equation to its general form, Ax + By + C = 0:
(9/2)x - y - 32 = 0
or
9x - 2y - 64 = 0
This is the general form of the equation of the line that is parallel to 9x - 2y = 7 and passes through point (6, -5).
Study the Proof Given.
List the reasons for Items 2,3, & 4.
Right the number and then the answer.
The selling price s, of an item is s=c+me, where c is the cost of the item and m is the percent markup based on the cost. What is the formula solved for m?
Write an equation of a vertical line passing through the point (5,-4). Show all work.
what is the result of converting 8 gallons to quarts ? remember , there are 4 quarts in a gallon
Answer: 32 quarts
Step-by-step explanation:
We know that there area 4 quarts in one gallon.
i.e.[tex]1\text{ gallon}=4\text{ quarts}[/tex]
Now, to convert 8 gallons into quart we need to apply unitary method.
Using unitary method , to convert 8 gallons into quart , multiply 8 to 4 , we get
[tex]8\text{ gallon}=8\times4\text{ quarts}\\\\\Rightarrow\ 8\text{ gallon}=32\text{ quarts}[/tex]
Hence there are 32 quarts in 8 gallons.
There are 32 quarts in 8 gallons of quantity.
The given quantity is 8 gallons.
We know that, 1 gallon = 4 quarts
Here, 8 gallons = 8×4
= 32 quarts
Therefore, there are 32 quarts in 8 gallons of quantity.
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The inner dimensions of an in-ground swimming pool are: width = 13.0ft, length = 18.0 ft, and depth = 9.0ft. the pool walls and the bottom are uniformly 1.0 ft thick and made of concrete. what is the total concrete surface area of the pool in units of ft2?
solve
5x+3y=-27
-9x+2y=19
The sum of a number and its square is 210. find the number(s).
The required number, whose sum with its square is 210, is -15 and 14.
Given that,
The sum of a number and its square is 210. To determine the number(s).
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Let the number be x,
according to the question,
x + x² = 210
x² + x -210 = 0
x² + 15x - 14x - 210 = 0
x(x + 15) -14 (x + 15) = 0
(x + 15)(x - 14) = 0
x = -15 and 14
Thus, the required number, whose sum with its square is 210, is -15 and 14.
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Suppose you write a sum of numbers as a product of their GCF and another sum. What is the GCF of the number in the other sum? Explain
What is the length of line segment KJ?
A. 2√3 units
B. 3√2 units
C. 3√5 units
D. 3√3 units
Answer:
the answer is the option C
[tex]KJ=3\sqrt{5}\ units[/tex]
Step-by-step explanation:
we know that
The triangle KMJ is a righ triangle
so
Applying the Pythagoras Theorem
[tex]KJ^{2}=KM^{2}+MJ^{2}[/tex]
in this problem we have
[tex]KM=6\ units[/tex]
[tex]MJ=3\ units[/tex]
substitute
[tex]KJ^{2}=6^{2}+3^{2}[/tex]
[tex]KJ^{2}=45[/tex]
[tex]KJ=\sqrt{45}=3\sqrt{5}\ units[/tex]
What is the solution to the equation using the replacement set {2, 3, 4} 6+x/2=8
How do I construct angle XYZ with a measure of 2 times the measure of angle ABC
Which is a way to check the answer 120 divided by 4 = 30
Andrea is selling candles as a fundraiser. she spent $50 on supplies for making the candles. she plans to sell the candles for $10 each. her profit can be modeled by c(x)=10x-50. what is the domain and range of the function
The domain will consist of all non-negative real numbers (x ≥ 0).
And, the range will consist of all real numbers (-∞, +∞).
Given that;
The function is,
c (x) = 10x - 50
Now for the domain and range of the function c(x) = 10x - 50,
Since the domain refers to all the possible input values (x) for the function.
In this case, since c(x) represents the profit from selling candles, x would represent the number of candles sold.
The number of candles sold cannot be negative, as it wouldn't make sense to sell a negative number of candles.
So, the domain will consist of all non-negative real numbers (x ≥ 0).
And, The range refers to all the possible output values (c(x)) of the function.
In this case, c(x) represents the profit. The profit can be any real number because it can be positive, negative, or zero.
Therefore, the range will consist of all real numbers (-∞, +∞).
Thus, Domain: All non-negative real numbers (x ≥ 0).
Range: All real numbers (-∞, +∞).
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How long will it take to have R30 000 for a trip to Europe if I invest R20 000 now at 15% per year,
compounded quarterly?
Alvin is 6 years older than Elga. The sum of their ages is 106 . What is Elga's age?
Please help don’t know how to do it iv tried and can’t figure it out. Please help thank you!
how do you subract polynominals plz explain
What is 60% off of 33.00
To find 60% off of $33.00, you multiply 33 by 60, then divide the product by 100. The result is $19.80, which is the discount amount. So after the discount, the cost is $13.20.
Explanation:To find out what 60% off of $33.00 is, you need to multiply 33.00 by 60 and then divide that product by 100, as percentages are always out of 100. Here's the process:
Multiply 33.00 by 60 to get 1980.00. Then divide 1980.00 by 100 to convert the result into a dollar amount. You get 19.80.
So, 60% off of $33.00 equals $19.80. Hence, after a 60% discount, you would pay $13.20 (33 - 19.80), as this is the remaining cost after the discount has been applied.
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Match the following:
Question 1 options:
√−1
-1
-i
1
Answer options
i2
i
i3
i4
Ron is five years older than twice his cousin Pats age. The sum of their ages is less than 35.
What is the greatest age that Pat can be.
A) 7
B)8
C)9
D)10
Answer:
C. 9
Step-by-step explanation:
Ron is five years older than twice his cousin's age. Lets assume that Pat's age is 'x' years.
So Ron's age is [tex]2\times x+5=2x+5[/tex]
The question says:
[tex]x+2x+5<35[/tex]
[tex]3x+5<35[/tex]
[tex]3x<35-5[/tex]
[tex]3x<30[/tex]
[tex]x<10[/tex]
Pat's age [tex](x)[/tex] should be less than 10. Therefore, the greatest age (in integer) that Pat can be is 9 years.
The amounts of industrial waste generated in a region during two years were 31,900,000 tons and 53,400,000 tons. What was the total industrial waste generated over these two years in the region, expressed in scientific notation?
Suppose g is an odd function and let h = f ∘ g. is h always an odd function?
Final answer:
The composition h = f о g is only guaranteed to be an odd function if both g and f are odd functions. If f is an even function or neither odd nor even, h will not necessarily be an odd function. The property of the composition depends on the nature of both functions involved.
Explanation:
Whether the composition of functions h = f о g is always an odd function when g is an odd function depends on the nature of f. If g(x) is an odd function, it follows that g(-x) = -g(x). However, for h to also be odd, f must satisfy the condition h(-x) = -h(x). This can only be the case if f is also an odd function.
If f were an even function, then f(g(-x)) = f(-g(x)) would equal f(g(x)) due to the even property of f. In this scenario, h would not be an odd function since h(-x) = f(g(-x)) = f(g(x)) = h(x), which violates the definition of an odd function.
When an odd function and an even function are multiplied, the result is an odd function, as exemplified by g(x) = x³ - 3x and h(x) = x². But when composing functions, the outer function's properties dominate the result. Therefore, the composition h = f о g can only be assured to be odd if f itself is odd.
A truck travels on the highway at a speed of 72 miles per hour. What is the speed of the truck in feet per second
1 mile = 5280 feet
1 hour = 3600 seconds
72 * 5280 = 380160 feet per hour
380160/ 3600 = 105.6 feet per second ( round answer if needed)
If one foot equals 12 inches and one mile is 5280 feet, how many miles are in 50000 inches
To calculate the total miles, first convert 50000 inches to feet, then convert the result to miles. Approximately 0.790 miles are in 50000 inches.
Explanation:To answer your question, "How many miles are in 50000 inches?" We need to convert inches to miles. We have to use the given conversion rates: 1 foot = 12 inches and 1 mile = 5280 feet.
First, let's convert inches into feet by dividing the total inches by the conversion factor of inches to feet. So, 50,000 inches divided by 12 equals approximately 4166.67 feet. Then, to find the total miles, we must convert feet to miles using the conversion factor of feet to miles. So, 4166.67 feet divided by 5280 (the number of feet in a mile) equals approximately 0.790 miles. Learn more about Unit Conversion here:
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-3(-7p-6) -7< p -29 how to do