Answer:
16,500 miles
Step-by-step explanation:
In 12 minutes, the satellite travels 3,300 miles around Earth. To find how far the satellite travels around Earth in 1 hour, we can use unit conversion:
1 hour = 60 minutes
So, the number of 12-minute intervals in 1 hour is:
1 hour / 12 minutes = 5 intervals
Therefore, in 1 hour, the satellite travels:
3,300 miles/interval × 5 intervals = 16,500 miles
So the satellite travels around Earth at a distance of 16,500 miles in 1 hour.
A fence 2 feet tall runs parallel to a tall building at a distance of 6 feet from the building. What is the length of the shortest ladder that will reach
from the ground over the fence to the wall of the building?
Answer:
10.81 ft
Step-by-step explanation:
You want the length of the shortest ladder that will reach over a 2 ft high fence to reach a building 6 ft from the fence.
Trig relationsRelevant trig relations are ...
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Ladder lengthIn the attached diagram, the ladder is show as line segment CD, intersecting the top of the fence at point B. The length of the ladder is the sum of segment lengths BD and CB.
Using the above trig relations, we can write expressions that let us find these lengths in terms of the angle at D:
sin(D) = AB/BD ⇒ BD = AB/sin(D)
cos(D) = BG/CB ⇒ CB = BG/cos(D)
Then the ladder length is ...
CD = BC +CB = AB/sin(D) +BG/cos(D)
CD = 2/sin(D) +6/cos(D)
MinimumThe minimum can be found by differentiating the length with respect to the angle. This lets us find the angle that gives the minimum length.
CD' = -2cos(D)/sin²(D) +6sin(D)/cos²(D)
CD' = 0 = (6sin³(D) -2cos³(D))/(sin²(D)cos²(D)) . . . common denominator
0 = 3sin³(D) -cos³(D) . . . . the numerator must be zero
Factoring the difference of cubes, we have ...
0 = (∛3·sin(D) -cos(D))·(∛9·sin²(D) +∛3·sin(D)cos(D) +cos²(D))
The second factor is always positive, so the value of D can be found from
∛3·sin(D) = cos(D)
D = arctan(1/∛3) . . . . . . . divide by ∛3·cos(D), take inverse tangent
D ≈ 37.736°
CD = 2/sin(37.736°) +6/cos(37.736°) = 3.51 +7.30 = 10.81 . . . feet
The shortest ladder that reaches over the fence to the building is 10.81 feet.
__
Additional comments
The second attachment shows a graphing calculator solution to finding the minimum of the length versus angle in degrees.
The ladder length can also be found in terms of the distance AD.
L = BD(1 +BG/AD) = (1 +6/AD)√(4+AD²)
The minimum L is found when AD=∛(BG·AD²) = ∛24 ≈ 2.884.
According to a recent survey, the salaries of entry-level positions at a large company have a mean of $40,756 and a standard deviation of $7500. Assuming that the salaries of these entry-level positions are normally distributed, find the proportion of
employees in entry-level positions at the company who earn at most $53,000. Round your answer to at least four decimal places.
Answer:
We can use the standard normal distribution to solve this problem, by standardizing the salary value of $53,000 using the given mean and standard deviation:
z = (X - μ) / σ
where X is the salary value of $53,000, μ is the mean of $40,756, and σ is the standard deviation of $7500.
z = (53,000 - 40,756) / 7500 = 1.63547
Using a standard normal distribution table or calculator, we can find the proportion of employees who earn at most $53,000 by finding the area to the left of the standardized value of 1.63547:
P(Z ≤ 1.63547) = 0.9514
Therefore, approximately 95.14% of employees in entry-level positions at the company earn at most $53,000.
PLEASE HELP AGAIN.. It takes Adrian 15 minutes to run around the track one time. He runs around the track with Mateo. It takes 30 minutes for both boys to return to the starting point at the same time. If mateo runs faster than Adrian, how long does it take Mateo to run around the track once, assuming that Adrian runs at the same speed as before?
Mateo takes 20 minutes to run around the track once.
What is speed?The rate at which an object goes from one location to another is known as its speed. It is described as the distance that an object covers in a certain amount of time. The distance traveled in one unit of time is typically used to express speed, such as meters per second (m/s), kilometers per hour (km/h), or miles per hour (mph) (mph).
[tex]Speed = \frac{distance}{time }[/tex]
Here we assume that the distance around the track is 'd', Adrian's speed is 'a' (in distance per minute) and Mateo's speed is 'm' (also in distance per minute).
Since Adrian takes 15 minutes to run around the track once, we have:
a = d/15
Let's use the formula: time = distance/speed
to write two equations for the total distance traveled by each boy.
For Adrian: 2d = a × 30
For Mateo: 2d = m × t
where 't' is the time it takes Mateo to run around the track once.
Since we know that Mateo runs faster than Adrian, we have:
m > a
Substituting the expression we found for 'a' into the equation for Adrian, we get:
2d = (d/15) × 30
d = 225
Now, we can solve for Mateo's speed using the equation for the total distance traveled by Mateo:
2d = m × t
2(225) = m × t
m = 450/t
Substituting this expression for 'm' into the inequality m > a, we get:
450/t > d/15
15×450 > d×t
6750 > d×t
Substituting d = 225, we get:
6750 > 225t
t < 30
Since Mateo takes less than 30 minutes to run around the track once, and we know that Adrian takes 15 minutes, the possible value for t is 20 minutes: t = 20.
Therefore, Mateo takes 20 minutes to run around the track once.
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Solve. Write the solution set in interval notation.
2 − 5(x + 1) ≥ 3(x − 1) − 24
Answer:
Let's first simplify the left-hand side and right-hand side of the inequality:
2 - 5(x + 1) = 2 - 5x - 5 = -5x - 3 3(x - 1) - 24 = 3x - 27
So the inequality becomes:
-5x - 3 ≥ 3x - 27
Now we can solve for x:
-5x - 3 ≥ 3x - 27 -8x ≥ -24 x ≤ 3
The solution set is all x-values less than or equal to 3. We can express this in interval notation as:
(-∞, 3]
The solution set in interval notation is (-∞, 4].
To solve the inequality 2 − 5(x + 1) ≥ 3(x − 1) − 24 and write the solution set in interval notation, we need to follow these steps:
Distribute the -5 and 3 on the left and right sides of the inequality, respectively:
2 - 5x - 5 ≥ 3x - 3 - 24
Simplify both sides of the inequality by combining like terms:
-3x - 3 ≥ 3x - 27
Add 3x to both sides of the inequality to isolate the variable on one side:
-3 ≥ 6x - 27
Add 27 to both sides of the inequality:
24 ≥ 6x
Divide both sides of the inequality by 6 to solve for x:
4 ≥ x
Write the solution set in interval notation. Since the inequality is "greater than or equal to," we use a closed bracket for the lower bound and an open bracket for the upper bound:
(-∞, 4]
Therefore, the solution set in interval notation is (-∞, 4].
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An open-topped box is constructed from a rectangular piece of cardboard that is twice as long as it is wide by removing a square of size 3 inches from each corner and turning up the edges.
If the box is to hold 1,620 in3, how big should the originial piece of cardboard be?
The original piece of cardboard should be approximately 32.86 inches by 16.43 inches.
To find the size of the original piece of cardboard, we can use the formula for the volume of the box, which is V = l × w × h. Since the box is open-topped, the height will be the size of the square that was removed from each corner, which is 3 inches. Also, given that the length of the original piece of cardboard is twice the width, we can substitute l = 2w in the formula. Therefore, the formula becomes:
V = (2w) × w × 3
Now, we can plug in the given volume of 1,620 in3 and solve for w:
1,620 = (2w) × w × 3
540 = 2w^2
270 = w^2
w = √270
w ≈ 16.43 inches
Now, we can use the value of w to find the length of the original piece of cardboard:
l = 2w = 2(16.43) = 32.86 inches
Therefore, the original piece of cardboard should be approximately 32.86 inches by 16.43 inches.
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Davis subtracted two polynomials as shown. Identify/explain David's error and correct it. Show work for full credit.
Answer:
Below
Step-by-step explanation:
p^2 + 7mp + 4 - (-2p^2 - mp +1) =
(p^2 + 2p^2) + ( 7mp + mp) + ( 4 - 1) <==== two errors made here
3p^2 + 8mp + 3
3randon Vasquez percent More or Less (Formula ) L^(1) reb 21, 8:52:44 PM Watch help video What is the result when the number 72 is decreased by 50% ? Answer: Submit Answer
The result when the number 72 is decreased by 50% is 36.
We can use the formula:
Result = Original Number - (Original Number x Percent Decreased)
In this case, the original number is 72 and the percent decreased is 50%.
So, we can plug in the values into the formula:
Result = 72 - (72 x 0.50)
Result = 72 - 36
Result = 36
Therefore, the result when the number 72 is decreased by 50% is 36.
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[tex]\sqrt{x} 150\\[/tex]
If √x = 150, then the value of x will be 22,500.
What is the value of x in the root function?
If √x = 150, then we can find the value of x by squaring both sides of the equation:
(√x)² = (150)²
Simplifying the left side of the equation:
x = (150)²
x = 150 x 150
x = 22,500
Therefore, the value of x for the given root function is determined as 22,500.
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The complete question is below:
If √x = 150, find the value of x
In the figure above, R is the midpoint of QS and U is the midpoint of QT. If ST = 70, what is RU?
The value of RU, considering the Triangle Midsegment Theorem, is given as follows:
RU = 35.
How to obtain the value of RU?The value of RU is obtained applying the proportions in the context of the problem.
A proportion is applied as the Triangle Midsegment Theorem states that the midsegment of a triangle is parallel to it's base, and has the length half as long.
The length of the base is of ST = 70, hence the length of the midsegement is given as follows:
RU = 0.5ST
RU = 0.5 x 70
RU = 35.
(the length of the midsegment is half the length of the base, hence we apply the proportion multiplying by 0.5).
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find the hcf of 24x (cubed) yz (power 4) ; 30x (squared) y (squared) z (cubed) and 36x (cubed) y (squared) z (cubed)
The Highest Common Factor is: [tex]{6x^2yz^3}[/tex].
What is HCF ?
HCF stands for "Highest Common Factor", which is the largest number that divides two or more integers without leaving a remainder. It is also known as GCD (Greatest Common Divisor).
The given expressions are:
[tex]$$24x^3yz^4, \quad 30x^2y^2z^3, \quad 36x^3y^2z^3$$[/tex]
To find the HCF, we need to find the common factors of the given expressions.
We can write each expression as a product of prime factors:
[tex]$$24x^3yz^4 = 2^3 \cdot 3 \cdot x^3 \cdot y \cdot z^4$$[/tex]
[tex]$$30x^2y^2z^3 = 2 \cdot 3 \cdot 5 \cdot x^2 \cdot y^2 \cdot z^3$$[/tex]
[tex]$$36x^3y^2z^3 = 2^2 \cdot 3^2 \cdot x^3 \cdot y^2 \cdot z^3$$[/tex]
The common factors among these expressions are [tex]2, 3, $x^2$, $y$, $z^3$.[/tex]
Therefore, the Highest Common Factor is:
[tex]{6x^2yz^3}[/tex].
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A supermarket has a total of 1350 packs of milk, including full cream , low fat and skimmed milk . There are 150 more packs of skimmed milk than low fat milk . How man packets are full cream , if there are 465 packs of low fat milk
Answer:
Let's call the number of packs of skimmed milk "S" and the number of packs of full cream milk "F".
We know that the total number of packs of milk is 1350:
F + L + S = 1350
We also know that there are 150 more packs of skimmed milk than low fat milk:
S = L + 150
And we know that there are 465 packs of low fat milk:
L = 465
We can substitute L=465 into the equation S=L+150 to get:
S = 465 + 150 = 615
Now we can use the first equation to solve for F:
F + L + S = 1350
F + 465 + 615 = 1350
F = 270
Therefore, there are 270 packs of full cream milk.
what is the nearest 5 of 562817
The nearest 5 integers of 562817 are:
562815, 562816, 562817, 562818, 5628179
Explain about the integers?An integer comprises a whole number which can be positive, negative, and zero and is not a fraction. Integer examples include: -5, 1, 25, 18, 97, as well as 3,043. 1.43, 21 3/4, 3.84, and other numbers that don't constitute integers are some examples.
Positive, negative, and zero are all examples of integers. As a result, integers include numbers like 0, 1, 2, 3, in addition to -1, -2, and 3. There are no additional parts, such as fractions or decimals, in integers. As a result, fractional values like 3 1/2 and decimal numbers like -7.5 are Really not integers.Thus,
The nearest 5 integers of 562817 are obtained by subtracting and adding the smallest integer that is 1 from the given number.
562815, 562816, 562817, 562818, 5628179
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Of the following parent functions, which one has an infinite number of zeroes? (Select all that apply) linear o quadratic exponential o reciprocal absolute value 0 square root sine cosine This is a re
The parent functions that have an infinite number of zeroes are sine and cosine. A zero of a function is a value of x for which the function equals zero. For example, the function f(x) = x has a zero at x = 0, because f(0) = 0.
The parent functions sine and cosine have an infinite number of zeroes because they are periodic functions, meaning they repeat their values at regular intervals.
The sine function has zeroes at every multiple of π, or 0, π, 2π, 3π, etc. The cosine function has zeroes at every odd multiple of π/2, or π/2, 3π/2, 5π/2, etc.
In contrast, the other parent functions listed have a finite number of zeroes. The linear function has one zero, the quadratic function has at most two zeroes, the exponential function has at most one zero, the reciprocal function has no zeroes, the absolute value function has at most one zero, and the square root function has at most one zero.
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See the image below.
Answer and Explanation:
The expression [tex](3y + 5) + \frac{1}{2}(3y + 5)[/tex] is equivalent to the expression [tex]1.5(3y + 5)[/tex] because of the distributive property and the equivalence of [tex]1 \frac{1}{2}[/tex] and [tex]1.5[/tex].
In other words:
We know that
[tex]1 + \frac{1}{2} = 1 \frac{1}{2} = 1.5[/tex],
and that
[tex](B + C)(A) = BA + CA[/tex].
Therefore,
[tex]1A + \frac{1}{2}A = 1 \frac{1}{2}A = 1.5A[/tex]
and
[tex](3y + 5) + \frac{1}{2}(3y + 5) = 1.5(3y + 5)[/tex].
To simplify [tex]1.5(3y + 5)[/tex], we can distribute the 1.5.
[tex]1.5(3y + 5) = (1.5) (3y) + (1.5)(5)[/tex]
[tex]= \boxed{4.5y + 7.5}[/tex]
Long division what is the quotient
(2x^3+ 6x²- 6x + 2)divided by (2x-3)
The quotient (2x^3+ 6x²- 6x + 2)divided by (2x-3) is: [tex]x^2 + 4x + 3[/tex].
How to find the quotient?Quotients are often used in algebra to solve equations and expressions involving division. They are used in everyday life such as when calculating the average speed of a journey.
[tex]x^2 + 4x + 3[/tex]
[tex]---------[/tex]
[tex]2x - 3 | 2x^3 + 6x^2 - 6x + 2 \\ - (2x^3 - 3x^2)[/tex]
[tex]----------[/tex]
[tex]9x^2 - 6x \\- (9x^2 - 13x)[/tex]
[tex]-----------[/tex]
[tex]7x + 2[/tex]
The quotient is:
[tex]x^2 + 4x + 3[/tex]
Therefore, (2x^3 + 6x² - 6x + 2) divided by (2x-3) is equal to (x^2 + 4x + 3) with a remainder of (7x + 2).
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What is the area of this complex figure?
A) 179 m^2
B) 128 m^2
C) 30 m^2
D) 20 m^2
The area of the complex figure is 178 m². Option A
How to determine the area of the complex figureThe formula for calculating the area of a rectangle is expressed as;
Area = lw
Given that;
l is the length of the rectanglew is the width of the rectangleFor the bigger rectangle
Area = 16(8)
Multiply
Area = 128m²
For the smaller rectangle
Area = 6(5)
Area = 30m²
For the triangle
Area = 1/ 2× base × height
Area = 1/2 × 8 × 5
Area = 20m²
Add the areas of the three figures
Total area = 128 + 20 + 30
Total area = 178 m²
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Within the case study data set what is the pearson correlation
(aka, r value) between traitanx and comanx2 (e.g., .xxx)?
The r value is close to 0, it indicates that there is no correlation between the two variables.
The Pearson correlation coefficient (r value) is a measure of the strength of the linear relationship between two variables. It is calculated using the formula:
r = (sum of the products of the paired scores) / (square root of the sum of the squares of the first scores) * (square root of the sum of the squares of the second scores)
In this case, the two variables are traitanx and comanx2. To find the Pearson correlation between these two variables, we would need to calculate the sum of the products of the paired scores, the sum of the squares of the first scores, and the sum of the squares of the second scores. Then, we would plug these values into the formula and calculate the r value.
Without the actual data set, it is not possible to calculate the Pearson correlation between traitanx and comanx2. However, if the r value is close to 1, it indicates a strong positive correlation between the two variables. If the r value is close to -1, it indicates a strong negative correlation between the two variables. If the r value is close to 0, it indicates that there is no correlation between the two variables.
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a closet in the shape of a rectangular prism measures x+3 ft. wide, x-5.5 ft. depth and x ft height. the volume is 220 ft^3. what is the height of the closet?
The height οf the clοset is x ft = 8 ft.
What is the vοlume οf a rectangular prism?The vοlume οf a rectangular prism is the amοunt οf space οccupied by the three-dimensiοnal οbject. It is calculated by multiplying the length, width, and height οf the prism.
In this prοblem, we are given that the clοset has a vοlume οf 220 ft^3 and its dimensiοns are x+3 ft. wide, x-5.5 ft. deep, and x ft. high. Sο, we can write the equatiοn:
V = (x+3)(x-5.5)(x)
where V is the vοlume οf the clοset.
Tο sοlve fοr x, we can simplify the equatiοn by multiplying the factοrs:
[tex]V = (x^2 - 2.5x - 16.5)(x) = x^3 - 2.5x^2 - 16.5x[/tex]
Nοw, we can substitute the given value οf V and sοlve fοr x:
[tex]220 = x^3 - 2.5x^2 - 16.5x[/tex]
We can rearrange this equatiοn tο get:
[tex]x^3 - 2.5x^2 - 16.5x - 220 = 0[/tex]
This is a cubic equatiοn that can be sοlved by factοring οr using numerical methοds. By using numerical methοds, we can find that οne sοlutiοn οf this equatiοn is x = 8.
Therefore, the height of the closet is x ft = 8 ft.
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Find the missing side of the triangle (h).
A central angle of a circle measures 37°. the arc intercepted by this central angle measures 16 inches. which value best approximates the radius of the circle? responses 24.78 in. 24.78 in. 25.38 in. 25.38 in. 46.44 in. 46.44 in. 50.76 in.
The value that best approximates the radius of the circle is 25.38 inches.
The measure of the central angle in degrees is related to the length of the arc intercepted by the central angle and the radius of the circle by the formula:
Arc length = (Central angle measure / 360°) x (2πr)
where r denotes the circle's radius.
Substituting the given values, we have:
16 inches = (37° / 360°) x (2πr)
Simplifying and solving for r, we get:
r = 16 inches / [(37/360) x (2π)]
r ≈ 25.38 inches (rounded to two decimal places)
Therefore, the value that best approximates the radius of the circle is 25.38 inches.
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The matrix \[ A=\left[\begin{array}{cccc} -3 & 0 & -4 & 0 \\ 7.5 & 0 & 10 & 0 \\ 3 & 0 & 4 & 0 \end{array}\right] \] is a matrix of a linear transformation \( T: \mathbb{R}^{k} \rightarrow \mathbb{R}^
The matrix A represents the linear transformation T that maps vectors from a k-dimensional vector space to a 3-dimensional vector space and can be used to find the image of a vector under the linear transformation is:
[tex]T=\left[\begin{array}{c} -15 \\ 37.5 \\ 15 \end{array}\right][/tex]
What is linear transformation?A linear transformation is a function that maps vectors from one vector space to another and preserves the operations of vector addition and scalar multiplication. In this case, the matrix A represents the linear transformation T that maps vectors from a k-dimensional vector space to a 3-dimensional vector space.
The matrix [tex]\[ A=\left[\begin{array}{cccc} -3 & 0 & -4 & 0 \\ 7.5 & 0 & 10 & 0 \\ 3 & 0 & 4 & 0 \end{array}\right] \][/tex]
is a matrix of a linear transformation [tex]\( T: \mathbb{R}^{k} \rightarrow \mathbb{R}^{3} \).[/tex]
The matrix A can be used to find the image of a vector under the linear transformation T. For a vector [tex]\( \mathbf{x} \in \mathbb{R}^{k} \)[/tex], the image of the vector under the linear transformation T is given by the matrix-vector product [tex]\( A\mathbf{x} \).[/tex]
For example, if [tex]\( \mathbf{x} = \left[\begin{array}{c} 1 \\ 2 \\ 3 \\ 4 \end{array}\right] \)[/tex]
Then the image of the vector under the linear transformation T is given by
[tex]\[ A\mathbf{x} = \left[\begin{array}{cccc} -3 & 0 & -4 & 0 \\ 7.5 & 0 & 10 & 0 \\ 3 & 0 & 4 & 0 \end{array}\right] \left[\begin{array}{c} 1 \\ 2 \\ 3 \\ 4 \end{array}\right] = \left[\begin{array}{c} -15 \\ 37.5 \\ 15 \end{array}\right] \][/tex]
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What are the original equations to these 2 transformed
equations?
Equation 1: y= 3sin 2x-2
Equation 2: y=4sin(x-1)+3
The original equations for these two transformed equations can be found by reversing the transformations that have been applied to the standard sine function y = sin(x).
For Equation 1: [tex]y = 3sin(2x-2)[/tex], the original equation is y = sin(x). The transformations that have been applied are a vertical stretch by a factor of 3, a horizontal compression by a factor of 2, and a horizontal shift to the right by 2 units. To reverse these transformations, we would divide the y-values by 3, divide the x-values by 2, and shift the graph to the left by 2 units.
For Equation 2: [tex]y = 4sin(x-1)+3[/tex], the original equation is also y = sin(x). The transformations that have been applied are a vertical stretch by a factor of 4, a horizontal shift to the right by 1 unit, and a vertical shift up by 3 units. To reverse these transformations, we would divide the y-values by 4, shift the graph to the left by 1 unit, and shift the graph down by 3 units.
Therefore, the original equations for these two transformed equations are both y = sin(x).
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Jacques needs 5/8 kg of flour to make a loaf of bread
he tips 2/5 Kg of white flour onto a weighing scale
how much more flour does he need to add?
9/40 more flour does he need to add.
What is Fraction?A fraction represents a part of a whole.
Given that Jacques needs 5/8 kg of flour to make a loaf of bread, he tips 2/5 Kg of white flour onto a weighing scale.
We need to find amount of flour he still need to make a loaf of bread.
2/5 + x =5/8
Subtract 2/5 from both sides
x = 5/8 -2/5
LCM of 8 and 5 is 40.
=25-16/40
=9/40
Hence, 9/40 more flour does he need to add.
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solve for x: 1/2x+4=9
Answer:
x=10
Step-by-step explanation:
solve for x: 1/2x+4=9
First, you need to get the variable x to be on a side of the equation, by itself. That is your goal throughout the problem. The easiest way to start this is by removing 4 from the left side of the equation. We know that before the number 4 is a plus sign. In order to remove 4 from the left side of the equation, we must do the opposite of the plus sign. The plus sign represents addition, and the opposite of addition is subtraction. This means we need to subtract 4 from the left side. Remember, that whatever we do to one side, we must do to the other side! This means we must subtract 4 on BOTH sides of the equation.
On the left side of the equation, we have 4 and we subtract it by 4.
4-4=0
Since the answer is 0 we can forget about the number, because it does not hold any value.
Next, on the right side of the equation we have 9, and we subtract it by 4, as well because whatever we do to one side, we must do to the other side.
9-4=5
Our new equation should be: 1/2x=5
Our last step is to continue our goal from the beginning of the problem; to get x alone on one side of the equation. In order to complete that goal, we must remove 1/2 from the left side of the equation. Remember when we subtracted 4 one each side, we took the opposite of the sign. In this equation, we don't necessarily see a sign like before. However, whenever x is directly beside another number, that means that it is being multiplied by that number. Just like how the opposite of addition is subtraction, the opposite of multiplication is division. We need to divide 1/2 on both sides.
On the left side, we divide 1/2x by 1/2.
1/2 divided by 1/2 is 10
One isn't necessary to keep in the equation ONLY if it is next to x, like in this case.
Lastly, whatever we do to one side, we must do to the other. We finish the problem by dividing 5 by 1/2.
5 divided by .5 is 10
We are left with x=10.
The answer is 10.
Find the volume of a cone with a diameter of 12m and height of 9m ? A.108 m3 B.1296 m3 C. 324 m4 D.108 m3
The closest choice is A. 108 which is the right response if the cone's real height is 4.5m rather than 9m.
what is volume ?The amount of space a three-dimensional object takes up is measured by its volume. It is a numerical assessment of an object's three-dimensional physical dimensions—length, breadth, and height. Cubic units, such as cubic meters, cubic feet, cubic centimeters, or cubic inches, are used to indicate volume. Mathematical equations can be used to determine the formula for calculating the volume of many geometric shapes, including a cube, rectangular prism, sphere, or cylinder.
given
Finding the cone's radius, which is equal to half of its diameter, is the first stage.
radius: (12 m / 2) = 6 m
The capacity of a cone is calculated as follows:
V = (1/3)π[tex]r^2[/tex]h
In place of the ideals we hold:
V = (1/3)π([tex]6m^2[/tex])(9m) (9m)
V = (1/3)π([tex]36^2[/tex])(9m) (9m)
V = (1/3)π(324[tex]m^3[/tex])
V = 108π [tex]m^3[/tex]
With the aid of a computer, we can roughly convert to 3.14:
V ≈ 108 x 3.14 [tex]m^3[/tex]
V ≈ 339.12 [tex]m^3[/tex]
As a consequence, the cone, which has a 12 m diameter and a 9 m height, has a capacity of about 339.12 m3.
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assume that y=C(a)^x is an exponential function. Why can a not equal zero?
The function eˣ is considered as a function of real numbers has domain (−∞,∞) and have value between 0 to ∞ . That is the reason why "a" cannot be zero.
Reason why any function of form eˣ cannot be zero:Considered as a function of real numbers, the function ex has domain (−∞,∞) and range (0,∞). Therefore, only strictly positive values can be assumed. Considering ex as a function of complex numbers, we know that there is a domain C and a range C\{0}. In other words, the only value eˣ cannot have is 0.
Thus, the base cannot be equal to 0.
What are functions in mathematics?A formula, rule, or law that defines the relationship between one variable (the independent variable) and another (the dependent variable). Functions are ubiquitous in mathematics and essential in the natural sciences for formulating physical relationships.
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a cannot be equal to zero in an exponential function because a must be greater than 0 in order for the equation to work, and because the base of an exponential function must be a positive number for it to be an exponential function.
What is an exponential function?An exponential function is a type of mathematical function that increases or decreases by a consistent rate over time. It is usually expressed in the form of y = abx, where a and b are constants and x is the independent variable. The graph of an exponential function is a curved line that starts off flat and then increases or decreases in a curved manner. The rate of change of the function is determined by the value of b, with higher values of b resulting in a steeper curve.
In this situation, a must be greater than 0 because an exponential function cannot have a base of 0. This is because any number raised to the power of 0 is equal to 1, so if the base of the exponential function is 0, then the entire equation would be equal to C1, which is simply C. Therefore, the only way to make the equation work is to make sure that a is greater than 0.
Therefore, a cannot be equal to zero in an exponential function. This is because a must be greater than 0 in order for the equation to work, and because the base of an exponential function must be a positive number in order for it to be an exponential function.
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LINEAR EQUATIONS Multiplicative property of Solve for x 24=(3)/(4)x Simplify your answer as much as x
Using multiplicative property of equations, the solution to the equation is x = 32.
The multiplicative property of equations states that if you multiply both sides of an equation by the same number, the equation will still be true.
In this case, we can use the multiplicative property to solve for x by multiplying both sides of the equation by (4/3) to cancel out the fraction on the right side of the equation.
24 = (3/4)x
(4/3)(24) = (4/3)(3/4)x
32 = x
So the solution to this equation is x = 32.
No need to further simplify your answer since the solution is already in its simplest form.
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The area of a square living room is 256 ft2
. Which is the length of the room?
The living room approximately 16 feet long based on the information provided.
What do math squares mean?A closed, such a double object known as a square has four sides that are equal and four vertices. On either side, it has parallel sides. A rectangle with equal width and length is also comparable to a square.
You may determine a square's area by multiplying one side by the square itself. As a result, we can use the scale factor of the living room's size to determine its length:
√256 ft² = 16 ft
The living room becomes 16 feet long as a result.
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I recently took a review test and it talked about amount of error (percent error) . The question said that , “the estimate number of balls in each bag was 86. It turned out to be 104. What is the percent of error? Round to the nearest tenth.” I wrote 17.3%. The teacher said it was wrong and claimed that you had to divide it by expected, not real. (Formula is (expected-real)/real.)) Can someone help me out, am I wrong or the teacher?
Percentage error is 17.30%, it can be said that the answer given by student is correct.
What is Percentage error?The percent error is the distinction between the estimated value and the actual value in relation to the actual value.
Estimated number of balls in each bag = 86
Real number of balls in the bag = 104
Percentage error = | ( estimated value - real value / real value ) | * 100
Percentage error = | ( 86 - 104 / 104 ) | * 100
Percentage error = | ( -18 / 104 ) | * 100
Percentage error = | - 17.30 | * 100
Percentage error = 17.30%
Thus, it can be said that the answer given by student is correct.
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Determine the value of x in the diagram
Answer:
x = 60
Step-by-step explanation: The sum of the exterior angles of any polygon is always equal to 360 degrees, including for a parallelogram. This means that if you add up all the exterior angles of a parallelogram, the total will always be 360 degrees.
hence :
2x + 2x + x + x = 360, for the given figure
=> 6x = 360
dividing by 6 both sides
x = 60