The statement is proved: PX = 12√6/5 and PY = 12√6/7.
To prove that PX = 12√6/5 and PY = 12√6/7, we will use the properties of similar triangles and the Pythagorean theorem.
First, let's denote the intersection point of the diagonals as O.
We know that triangle ABP is similar to triangle CDP, as they share the same angles due to being vertical angles.
Therefore, we can write the following proportion:
AB/CD = BP/PD
Substituting the given values, we have:
6/12 = BP/PD
Simplifying, we find:
BP = PD/2
Since CP/PD = 1, we can conclude that CP = PD.
Now, let's consider triangle ABP and triangle CBO.
These triangles are similar because they share the same angles (due to being vertical angles) and have proportional sides.
We can write the following proportion:
AB/BC = BP/CO
Substituting the given values, we have:
6/7 = BP/CO
Rearranging the equation, we find:
CO = (7/6)BP
Now, let's focus on triangle ODP.
Using the Pythagorean theorem, we can write the following equation:
[tex]OD^2 = OP^2 + PD^2[/tex]
Since we want to find PX and PY, which are the altitudes from P to AD and BC respectively, we need to express OP in terms of PX and PD, and OD in terms of PY and PD.
Looking at triangle ODP, we can see that OP = PX + OX and OD = PY + OY.
Substituting these expressions into the Pythagorean theorem equation, we have:
[tex](PX + OX)^2 = OP^2 = (PY + OY)^2 + PD^2[/tex]
Expanding and simplifying the equation, we get:
[tex]PX^2 + 2PXOX + OX^2 = PY^2 + 2PYOY + OY^2 + PD^2[/tex]
Since OX = OY = 0 (the altitudes are perpendicular to the bases), the equation simplifies to:
[tex]PX^2 = PY^2 + PD^2[/tex]
Now, let's substitute the given values into this equation:
[tex](PX)^2 = (12\sqrt{6/7} )^2 + (PD)^2[/tex]
Simplifying further, we get:
[tex](PX)^2 = 72/7 + (PD)^2[/tex]
We know that PD = CP = CD - CP = 12 - PD, so we substitute this expression into the equation:
[tex](PX)^2 = 72/7 + (12 - PD)^2[/tex]
Now, we can solve for [tex](PX)^2:[/tex]
[tex](PX)^2 = 72/7 + 144 - 24PD + (PD)^2[/tex]
Simplifying, we find:
[tex](PX)^2 = 216/7 - 24PD + (PD)^2[/tex]
Since CP/PD = 1, we can write PD = 12 - PD, which gives us PD = 6.
Substituting this value into the equation, we have:
[tex](PX)^2 = 216/7 - 24(6) + (6)^2[/tex]
Simplifying further, we get:
[tex](PX)^2 = 72/7[/tex]
Taking the square root of both sides, we find:
PX = √(72/7) = 12√6/5
Similarly, we can prove that PY = 12√6/7.
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Help what is the answer
Answer:
175 cm²
Step-by-step explanation:
Calculate each shape separately, then add them together.
Parallelogram: A = bh = (14)(5) = 70
Trapezium: A = ((a + b)/2)(h) = ((21 + 14)/2)(11-5) = 105
Total area = 70 + 105 = 175 cm²
The equation to the graph shown is y = ax + p, where a and p are real numbers. What
is true about a and p?
The true statement about a and p is a is positive and p is positive.
We have the equation
y= ax+ p
where a and p are real numbers.
In general, "a" represents the slope of the line (the rate of change of y with respect to x).
and, "p" represents the y-intercept (the value of y when x = 0).
The specific values of a and p can be determined by examining the graph or given data points.
By looking the graph, the slope is positive
b is the y intercept, where x = 0 and that is positive.
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How do I do the problem correctly? please explain i will mark you brainliest !!
Answer:
Explanation: Since these two powers have the same base of 5, you can multiply them together by simply adding their exponents to get
5^11
A common mistake in this problem would be to multiply
the bases together and give an answer of
25^11
.
The 5's in this problem can not be multiplied together because they are not coefficients. They are bases.
When applying your exponent rules, your base will never change.
Please help with these math find the volume questions
Answer:
length A is 5 ft while width of B is 4
Spiderman ascends a building to its peak The peak is 812ft above sea level. Spiderman then descends 30ft to face the Chameleon. Find the Spiderman's evevation above the sea level after meeting the Chameleon.
A. 812 ft above sea level
B. 30 ft below sea level
C. 782 ft above sea level
Spiderman's elevation above sea level after meeting the Chameleon is 782ft.
An elevation is the view of a 3D shape when it is looked at from the side or from the front.
Angle of elevation: Angle of elevation is the angle between the horizontal line and the line of sight. It is formed at the vertex of intersection of the horizontal line and line of sight. It is the same angle as used in trigonometry.
To calculate Spiderman's elevation above sea level after descending 30ft to meet the Chameleon, we need to subtract 30ft from the initial elevation of 812ft.
812ft - 30ft = 782ft
Therefore, Spiderman's elevation above sea level after meeting the Chameleon is 782ft.
So, the correct answer is C. 782ft above sea level.
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Simone has 16 square inch tiles she glues all of them on cardboard to make two different rectangles each with the same area what are the side lengths of the two rectangles she can make
Simone can make two different rectangles with the following side lengths:
Rectangle 1: Length = 16 inches, Width = 1 inch
Rectangle 2: Length = 8 inches, Width = 2 inches
To find the side lengths of the two rectangles that Simone can make using 16 square inch tiles, we need to consider the factors of 16 and check which pairs of factors can form rectangles with the same area.
The factors of 16 are 1, 2, 4, 8, and 16. We can pair these factors to form different rectangles and calculate their areas:
Pairing: 1 and 16
Length: 16
Width: 1
Area: 16 square inches
Pairing: 2 and 8
Length: 8
Width: 2
Area: 16 square inches
Pairing: 4 and 4
Length: 4
Width: 4
Area: 16 square inches
Therefore, Simone can make two different rectangles with the following side lengths:
Rectangle 1: Length = 16 inches, Width = 1 inch
Rectangle 2: Length = 8 inches, Width = 2 inches
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A card is drawn at random from a standard deck of playing cards (no jokers). If it is red, the player wins 1 dollar; if it is black, the player loses 2 dollars. Find the expected value of the game. Express your answer in fraction form.
The expected value of the game is -1/2.
This means that, on average, the player can expect to lose 1/2 dollar per game in the long run.
To find the expected value of the game, we need to calculate the probability of each outcome and multiply it by its associated value, then sum up the results.
In a standard deck of playing cards, there are 26 red cards (13 hearts and 13 diamonds) and 26 black cards (13 clubs and 13 spades).
Since drawing a card is a random event, the probability of drawing a red card is the number of favorable outcomes (red cards) divided by the total number of possible outcomes (52 cards).
Probability of drawing a red card:
P(Red) = Number of red cards / Total number of cards = 26/52 = 1/2
Now, let's calculate the expected value:
Expected Value = (Probability of winning) × (Value of winning) + (Probability of losing) × (Value of losing)
In this game, if the player wins, they gain 1 dollar, and if they lose, they lose 2 dollars.
Expected Value = (1/2) × (+1) + (1/2) × (-2) = 1/2 - 2/2 = -1/2
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Which is more, the average of the 4 even whole numbers from 8 to
15 or the average of the 4 odd whole numbers from 8 to 15?
The average of the four odd whole numbers (12) is greater than the average of the four even whole numbers (11).
To determine which average is greater, let's calculate the average of the four even whole numbers from 8 to 15 and the average of the four odd whole numbers from 8 to 15.
The even numbers from 8 to 15 are 8, 10, 12, and 14.
To find their average, we sum them and divide by 4:
Average of even numbers = (8 + 10 + 12 + 14) / 4 = 44 / 4 = 11.
The odd numbers from 8 to 15 are 9, 11, 13, and 15.
Similarly, we find their average:
Average of odd numbers = (9 + 11 + 13 + 15) / 4 = 48 / 4 = 12.
Comparing the two averages, we find that the average of the four odd whole numbers from 8 to 15 is greater than the average of the four even whole numbers from 8 to 15.
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estion 5 (SO 3, AC 1, AC 2, AC 3) Define the following terms; Marginal cost?
Answer:
no se justamente yo tambien busco respuestas lo siento
Show that the path of a moving point parallel to the axes of x and y with velocitiesu +
ey andv + ex is a conic section
We have shown that the path of a moving point with velocities u + ey and v + ex, parallel to the axes of x and y, is either a line (when v - [tex]e^2[/tex] ≠ 0) or a horizontal line (when v - [tex]e^2[/tex] = 0), both of which are conic sections.
To show that the path of a moving point parallel to the axes of x and y with velocities u + ey and v + ex is a conic section, we can analyze the motion of the point using the principles of calculus and conic sections.
Let's denote the position of the point at any given time t as (x, y). We are given that the velocities along the x and y axes are u + ey and v + ex, respectively. This means that the derivatives of x and y with respect to time, dx/dt and dy/dt, can be expressed as:
dx/dt = u + ey
dy/dt = v + ex
Now, let's integrate these expressions to obtain x and y as functions of t. Integrating dx/dt with respect to t gives:
x = ut + eyt + C1
Similarly, integrating dy/dt with respect to t gives:
y = vt + ext + C2
Where C1 and C2 are constants of integration.
Now, we can eliminate the parameter t by expressing t in terms of x and y. From the equation y = vt + ext + C2, we can solve for t:
t = (y - ext - C2) / v
Substituting this value of t into the equation for x, we get:
x = u[(y - ext - C2) / v] + ey[(y - ext - C2) / v] + C1
Simplifying this equation, we obtain:
vx - u - evx + ue + vy - [tex]e^2[/tex]x - eyC2 = C1v
Rearranging the terms, we get:
vx - vy + ue + evx - [tex]e^2[/tex]x = C1v + eyC2 - u
Let's define new constants A = ue + ev and B = C1v + eyC2 - u. The equation then becomes:
(v - [tex]e^2[/tex])x + (u + ev)y = A + B
This equation is in the standard form of a conic section, specifically a line. However, we can manipulate this equation further to reveal other possible conic sections.
Let's consider the case when v - [tex]e^2[/tex] ≠ 0. In this case, we can divide both sides of the equation by v - [tex]e^2[/tex], yielding:
x + [(u + ev)/(v - [tex]e^2[/tex])]y = (A + B)/(v - [tex]e^2[/tex])
Now, let's define another constant C = (u + ev)/(v -[tex]e^2[/tex]) and rewrite the equation as:
x + Cy = D
Where D = (A + B)/(v - [tex]e^2[/tex]).
This equation represents a line in the x-y plane.
On the other hand, if v - [tex]e^2[/tex] = 0, the equation becomes:
0x + (u + ev)y = A + B
This simplifies to:
(u + ev)y = A + B
Which is a horizontal line parallel to the x-axis.
Therefore, we have shown that the path of a moving point with velocities u + ey and v + ex, parallel to the axes of x and y, is either a line (when v - [tex]e^2[/tex] ≠ 0) or a horizontal line (when v - [tex]e^2[/tex] = 0), both of which are conic sections.
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To estimate the height of a building, two students find the angle of elevation from a point (at ground level) down the street from the building to the top of the building is 35∘. From a point that is 150 feet closer to the building, the angle of elevation (at ground level) to the top of the building is 51∘. Assume that the street is level. What is the height of the building?
Round your answer to the nearest hundredth. Don't include the "h=" or any units - your answer should just be a number
The height of the building is 242.59 feet.
Let's denote the height of the building as h.
angle of elevation is 35 degrees.
Using the tangent function,
tan(35°) = h / x
h = x tan(35°)
From the second observation point, which is 150 feet closer to the building,
The adjacent side is now (x - 150) since we moved closer to the building.
So, tan(51°) = h / (x - 150)
Now, tan(51°) = (x tan(35°)) / (x - 150)
1.2348 = x (0.7002)/ x-150
1.2348x - 185.22 = 0.7002x
x= 346.4646 feet
and, h = 364.4646 x 0.7002 = 242.59 feet
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Suppose $6000 is invested at 3% interest compounded continuously. How long will it take for the investment to grow to $12000?
The time it takes for the investment to grow to $12,000 if the interest is compounded continuously is 23.1 years.
Given that,
Principal amount invested, P = $6000
Rate of interest, r = 3% = 3/100 = 0.03
If the interest compounded continuously,
Final amount, A = P e^(rt)
12000 = 6000 e ^(0.03t)
2 = e ^(0.03t)
Taking logarithms on both sides,
ln (2) = 0.03t
t = 23.1 year.
Hence the time is 23.1 years.
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What is the area of a triangle
Answer:A=BxH divided by 2
_
Step-by-step explanation:
On a standardized exam, the scores are normally distributed with a mean of
195 and a standard deviation of 50. Find the z-score of a person who scored
330 on the exam.
The z-score of a person who scored 330 on the exam is approximately 2.7.
To find the z-score of a person who scored 330 on the exam, we can use the formula for calculating the z-score:
z = (x - μ) / σ
where:
z is the z-score
x is the raw score (330 in this case)
μ is the mean (195 in this case)
σ is the standard deviation (50 in this case)
Substituting the values into the formula, we get:
z = (330 - 195) / 50
z = 135 / 50
z = 2.7
The z-score of a person who scored 330 on the exam is 2.7.
The z-score measures the number of standard deviations a particular data point is away from the mean.
In this case, a z-score of 2.7 indicates that the person's score of 330 is 2.7 standard deviations above the mean score of 195.
The z-score is useful for comparing data points across different normal distributions or for determining the relative position of a data point within a distribution.
A positive z-score indicates a value above the mean, while a negative z-score indicates a value below the mean.
In this context, a z-score of 2.7 suggests that the person's score is relatively high compared to the average performance on the exam.
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Find the missing parts that would make this equation true.
3, 2x(x-2y) + y(x-2y)-(x-2y) = (2x +_-_(-2y)
The missing parts that would make the equation 2x(x-2y) + y(x-2y)-(x-2y) = (2x +_ - _ -2y) true are ² - x - 3xy - 2y²
How to determine the missing parts that would make the equation true.From the question, we have the following parameters that can be used in our computation:
2x(x-2y) + y(x-2y)-(x-2y) = (2x +_ - _ -2y)
When expanded, we have
2x² - 4xy + xy - 2y² - (x - 2y) = (2x +_ - _ -2y)
Open the brackets
So, we have
2x² - 4xy + xy - 2y² - x - 2y = (2x +_ - _ -2y)
Evaluate the like terms
2x² - 3xy - 2y² - x - 2y = (2x +_ - _ -2y)
Rewrite as
2x² - x - 3xy - 2y² - 2y = (2x +_ - _ -2y)
This means that the missing parts are ² - x - 3xy - 2y²
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I have the bottom one right but I need help with the first question please.
Answer:
1 = (x/11)² +24y²/605
Step-by-step explanation:
You want the the equation of an ellipse through the point (1, 5) with ends of its major axis at (±11, 0).
Ellipse equationThe ellipse equation will have the form ...
(x/11)² + (y/b)² = 1
for some value 'b' that causes (x, y) = (1, 5) to be a solution to this equation.
Value of bUsing the given point and solving for b (or b²), we have ...
(1/11)² +(5/b)² = 1
25/b² = 1 -1/121 = 120/121
Inverting this equation and multiplying by 25, we have ...
b² = 605/24
Equation of interestUsing this value for b², we can write the equation of the ellipse as ...
[tex]\boxed{1=\dfrac{x^2}{121}+\dfrac{24y^2}{605}}[/tex]
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Use the drawing tools to form the correct answer on the provided grid.
Triangle ABC undergoes a sequence of transformations.
1. Reflection across the line x = 1.
2. Dilation by a factor of 2 centered at the origin.
What is the resulting image?
Note that the resulting image where the above transformation takes place is attached accordingly.
How did we arrive at this?Current coordinates given from the image
A( 2, 7)
B (3, 2)
C (0, 2)
1) To reflect a point across the line x = 1, we need to find the distance between the point and the line and then move it to the same distance on the other side of the line.
In this case, all points will have their x-coordinate mirrored with respect to the line x = 1.
New coordinates after reflection is
A'(0, 7)
B'(−1, 2)
C'(2, 2)
2 - Dilation by a factor of 2 centered at the origin:
To dilate a point by a factor of 2 centered at the origin, we need to multiply both the x and y coordinates of the point by 2.
New coordinates after dilation is
A''(0, 14)
B''(−2, 4)
C''(4, 4)
Plotting the above will given the resultant image int he attached.
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The formula for the volume of a cylinder with a height of 5 units is v(r)-5x2 where r is the radius of the cylinder.
What is the domain and range of this function?
Domain: r ≥ 0 (all non-negative real numbers)
Range: V ≥ 0 (all non-negative real numbers)
The formula for the volume of a cylinder with a height of 5 units, given as V(r) = 5πr², is a function that relates the radius (r) to the volume (V) of the cylinder.
Domain:
In this case, the radius (r) cannot be negative since it represents a physical measurement. Additionally, there are no other restrictions mentioned in the problem.
Therefore, the domain for this function is all non-negative real numbers: r ≥ 0.
Range:
In this case, the volume (V) of the cylinder can only be positive or zero since it represents a physical quantity. The range is determined by the values that the function can take. As the radius (r) increases, the volume (V) also increases.
Since the function is V(r) = 5πr², the range of this function includes all non-negative real numbers: V ≥ 0.
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Complete question:
The formula for the volume of a cylinder with a height of 5 units is V(r)=5πr² where r is the radius o the cylinder. What is the domain and range for this function?
in the coordinate plane, the vertices of triangle PAT are P(-1,-6), A(-4,5), and T(5,-2). Prove that PAT is an isosceles triangle.
In the coordinate plane, the vertices of triangle PAT are P(-1,-6), A(-4,5), and T(5,-2) forms an isosceles triangle.
To prove that triangle PAT is an isosceles triangle, we need to show that at least two sides of the triangle are congruent.
Let's calculate the distances between the vertices:
Distance between P and A:
PA = √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(-4 - (-1))² + (5 - (-6))²]
= √[9 + 121]
= √130
Distance between P and T:
PT = √[(5 - (-1))² + (-2 - (-6))²]
= √[(5 + 1)² + (-2 + 6)²]
= √[36 + 16]
= √52
= 2√13
Distance between A and T:
AT = √[(5 - (-4))² + (-2 - 5)²]
= √[(5 + 4)² + (-2 - 5)²]
= √130
We can see that PA = AT = √130, and PT = 2√13.
Since PA = AT, we have shown that two sides of the triangle are congruent.
Therefore, triangle PAT is an isosceles triangle.
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rewrite each of the following expressions without using absolute value:
∣4r-12∣if r<3
Answer:
12-4r
Step-by-step explanation:
4r<12 because r<3 so you flip it.
find the exact value of Sin A
Step-by-step explanation:
sin A = opposite/ Hypotenuse
Sin A = 5/7
Hello !
sin(A) = opposite/hypotenuse = 5/7
arcsin(5/7) ≈ 45,58°
sin(A) = 5/7
the angle A ≈ 45,58°
He buys atoy car for 150 the sells it for $120find his percentage loss
Answer: 80%
Step-by-step explanation:
divide 120 by 150 and you get .8 then you move the decimal over 2
Help pls What is the general solution to the trigonometric equation
The general solution to the differential equation -√3 cscθ = 2 is θ = 2π/3 + nπ.
To find the general solution to the trigonometric equation -√3 cscθ = 2, where n is an integer, we need to solve for θ.
Let's start by rewriting the equation:
-√3 cscθ = 2
Since cscθ is the reciprocal of sinθ, we can rewrite the equation as:
-√3 / sinθ = 2
To solve for θ, we can take the reciprocal of both sides:
sinθ / -√3 = 1/2
Next, we can take the reciprocal of both sides again:
-√3 / sinθ = 2
Now, we can find the values of θ that satisfy this equation. The general solution is given by:
θ = arcsin(-√3/2) + nπ
θ = 2π/3 + nπ
where n is an integer.
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1. in a deck of cards, what is the probability of
randomly selecting a Spade or a face card
given it's black?
(Please explain answer step by step)
To find the probability of randomly selecting a Spade or a face card given it's black, we need to determine the number of favorable outcomes and the total number of possible outcomes. Let's break it down step by step:
Step 1: Determine the number of favorable outcomes:
First, let's determine the number of black cards in a deck of 52 cards. In a standard deck, there are 26 black cards, which include 13 Spades (black suits) and 13 Clubs (black suits). Therefore, we have 26 favorable outcomes.
Next, we need to determine the number of face cards that are black. In each suit, there are three face cards: Jack, Queen, and King. So, there are a total of 12 face cards in the deck, out of which 6 are black (2 black face cards in each black suit). Therefore, we have 6 additional favorable outcomes.
Step 2: Determine the total number of possible outcomes:
In a standard deck of 52 cards, there are 52 possible outcomes.
Step 3: Calculate the probability:
The probability is the ratio of favorable outcomes to the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = (26 + 6) / 52
Probability = 32 / 52
Probability = 8 / 13
So, the probability of randomly selecting a Spade or a face card given it's black is 8/13.
Please note that this calculation assumes that the selection is random and the deck of cards is well-shuffled.
Explain how you know that (3, 5) is not a solution to the given inequality by looking at the graph.
The reason that the point (3, 5) is not a solution to the given inequality is given below.
We are given that;
y > 2x + 1
Now,
The inequality y > 2x + 1 can be graphed by first graphing the boundary line y = 2x + 1. Since the inequality is strict (y >), we draw a dashed line to indicate that points on the line are not solutions to the inequality. Then, we shade the region above the line to indicate all points that satisfy the inequality.
If we have (3,5) as a point, we can see that it lies on the boundary line
y = 2x + 1.
Since the inequality is strict (y >), points on this line are not solutions to the inequality
Therefore, by the inequality the answer will be given above.
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Which subset of real numbers does NOT contain the set of numbers (1, 2, 3...)?
O A Integers
OB Irrational
OC Natural
OD Whole
How d you solve this? 91+3x=25+7x
Answer:
x=16.5
Step-by-step explanation:
91+3x=25+7x
-3x -3x
91=25+4x
-25 -25
66=4x
÷4 ÷4
x=16.5
5. (a) There are 160 apples and 224 mangoes in a bag. i. ii. What is the greatest number of children to distribute these apples and mangoes equally? How many fruits of each kind will each child get?
Hello !
You find the GCD of 160 : 224
160
= 2 x 80
= 2 x 2 x 40
= 2 x 2 x 2 x 20
= 2 x 2 x 2 x 2 x 10
= 2 x 2 x 2 x 2 x 2 x 5
224
= 2 x 112
= 2 x 2 x 56
= 2 x 2 x 2 x 28
= 2 x 2 x 2 x 2 x 14
= 2 x 2 x 2 x 2 x 2 x 7
GDC = 2 x 2 x 2 x 2 x 2 = 32
=> 32 childrens
160/32 = 5
224/32 = 7
=> 5 apples and 7 mangoes per child
at least has a box of pencil each pencil weighs 3/10 Oz the empty box weighs 0.4 Oz the total weight of the box of pencils is 4 oz how many pencils are in the Box
Answer: The box of pencils has a total of 12 pencils inside the box.
Step-by-step explanation:
Each pencil weighs 3/10 or 0.3 oz.
Since the total weight of the box is 0.4 ounces, subtract that with 4 oz- the total weight of the box. You then get 3.6 ounces worth of pencils.
To find how many pencils that are in the box, you will need to divide 3.6 with the amount 0.3.
3.6/0.3 = 12
Therefore, the box of pencils has a total of 12 pencils inside the box.
I want to solve for x
Answer:
x = [tex]\frac{A*t^2}{800}[/tex]
Step-by-step explanation:
First move t² to the left side by multiplying it.
A×t² = 800x - to get rid of 800, we divide both sides by 800. This isolates x.
x = [tex]\frac{A*t^2}{800}[/tex]