Julie read 79 pages after 26 minutes and Cassie read 79 pages after 26 minutes.
What are linear equations?
A linear equation is a mathematical equation that can be written in the form of Ax + By = C, where A, B and C are constants and x and y are variables.
Let's call the number of pages that both friends read x. We know that Julie's reading speed is 3 pages per minute and Cassie's reading speed is 2 pages per minute.
We can set up the equation:
x = 3t + 9 (where t is the time in minutes that Julie takes to read x pages)
x = 2t + 35 (where t is the time in minutes that Cassie takes to read x pages)
We know that they read the same number of pages, so we can set the two equations equal to each other:
3t + 9 = 2t + 35
We can then solve for t:
t = 26 minutes
So it took them 26 minutes to read the same number of pages. We can use that value to find the number of pages that they read:
x = 3t + 9 = 3(26) + 9 = 79 pages
Hence, Julie read 79 pages after 26 minutes and Cassie read 79 pages after 26 minutes.
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Julie read 79 pages after 26 minutes and Cassie read 79 pages after 26 minutes.
What are linear equations?
A linear equation is a mathematical equation that can be written in the form of Ax + By = C, where A, B and C are constants and x and y are variables.
Let's call the number of pages that both friends read x. We know that Julie's reading speed is 3 pages per minute and Cassie's reading speed is 2 pages per minute.
We can set up the equation:
x = 3t + 9 (where t is the time in minutes that Julie takes to read x pages)
x = 2t + 35 (where t is the time in minutes that Cassie takes to read x pages)
We know that they read the same number of pages, so we can set the two equations equal to each other:
3t + 9 = 2t + 35
We can then solve for t:
t = 26 minutes
So it took them 26 minutes to read the same number of pages. We can use that value to find the number of pages that they read:
x = 3t + 9 = 3(26) + 9 = 79 pages
Hence, Julie read 79 pages after 26 minutes and Cassie read 79 pages after 26 minutes.
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A helicopter pad which is in the shape of a circle has a circumference of 62. 48 feet and a diameter of 24 feet. Which expression best represents the value of ?
The expression which represents the value of the area could be the six times the circumference of the circle.
What is area of circle ?
area of circle can be defined as the product of pi(3.14) and square of radius of the circle.
Given,
helicopter pad which is in the shape of a circle has a circumference 72.48
and the diameter of 24 feet.
radius = diameter/2
radius = 24/2
radius = 12
circumference of circle = 72.48
area of circle = π*r*r
area of circle = 22/7 * 12 * 12
area of circle = 452.5
area of circle is approximately 6 times the circumference of circle.
Hence , The expression which represents the value of the area could be the six times the circumference of the circle.
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For which values of k the pair of equations KX 3y K − 3 and 12x Ky K have no solution?
K must be equal to 0, for the pair of equations to have no solution.
For the pair of equations KX + 3y - K = 0 and 12x + Ky - K = 0 to have no solution, the value of K must be such that the two equations have no common solution.
This can be done by equating the two equations and solving for K.
KX + 3y - K = 0
12x + Ky - K = 0
Subtracting equation (1) from equation (2)
11x + 3y = 0
Divide both sides by 3
x + y = 0
Therefore, K must be equal to 0, for the pair of equations to have no solution.
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Find the general solution of the given system. dx/dt = 4x+ 5y dy/dt = 10x + 9y
(x(t), y(t)) =
x(t) = [tex]c_1e^1^4^t+c_2e^-^t[/tex] , y(t) = [tex]2c_1e^1^4^t-c_2e^-^t[/tex] is the general solution of the sytem of differention eqution dx/dt = 4x+ 5y , dy/dt = 10x + 9y .
given dx/dt = 4x+ 5y and dy/dt = 10x + 9y
X'(t) = [tex]\left[\begin{array}{ccc}4&5\\10&9\end{array}\right][/tex] X
where X = [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]
so A = [tex]\left[\begin{array}{ccc}4&5\\10&9\end{array}\right][/tex]
now we need to find eigen value of the matrix and the corresponding eigen vector.
| A- λI | = 0
so after equation the value to zero
λ = 14 and λ = -1
now for the λ = 14 corresponding eigen vector = [tex]\left[\begin{array}{ccc}1\\2\\\end{array}\right][/tex]
for λ = -1 corresponding eigen vector = [tex]\left[\begin{array}{ccc}1\\-1\\\end{array}\right][/tex]
So general equation is given by:
X(t) = [tex]c_1e^1^4^t[/tex] [tex]\left[\begin{array}{ccc}1\\2\\\end{array}\right][/tex] + [tex]c_2e^-^t[/tex] [tex]\left[\begin{array}{ccc}1\\-1\\\end{array}\right][/tex]
after solving this
x(t) = [tex]c_1e^1^4^t+c_2e^-^t[/tex]
y(t) = [tex]2c_1e^1^4^t-c_2e^-^t[/tex]
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What are the 3 types of trigonometry?
the main three types of trigonometry are ,
1- sine angle (sin Q)
2- cosine angle (cos Q)
3- tangent angle (tan Q)
all the other types of trigonometry are related to these three types only.
sine angle
we can find out the sine angle by taking perpendicular of the triangle divided by hypotenuse of the triangle. sine angle is a acute angle.
cosine angle
we can find out the cosine angle by taking base of the triangle divided by hypotenuse of the triangle. cosine angle is a acute angle.
tangent angle
we can find out the sine angle by taking perpendicular of the triangle divided by base of the triangle.
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x^2+6x+8=0 complete the square method
Answer:
x = - 2 or x = - 4
Step-by-step explanation:
Via completing the square:
x^2 + 6x + 8 = x^2 + 6x + (6/2)^2 - (6/2)^2 + 8
= (x + 3)^2 - 3^2 + 8
= (x + 3)^2 - 9 + 8
= (x + 3)^2 - 1
Since x^2+6x+8=0,
(x + 3)^2 - 1 = 0
(x + 3)^2 = 1
x + 3 = +- sqrt(1)
x + 3 = +- 1
x + 3 = 1 or x + 3 = -1
x = -2 or x = -4
May someone help?...
The value of x and y in triangles AEB and BCD is 40° and 50°.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the sum of all the interior angles in a triangle is 180°.
Therefore, In ΔAEB,
(2x + 5)° + 50° + 45° = 180°.
2x + 100° = 180°.
2x = 180° - 100°.
2x = 80°.
x = 40°.
Now, ΔBCD,
x + y + 90° = 180°.
40° + y + 90° = 180°.
y = 180° - 130°.
y = 50°.
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How do you know if a triangle is a 45 45 90 triangle?
The two side lengths are congruent, and their opposite angles are congruent, and the hypotenuse is the length of either leg times the square root of two, √2.
A 45° 45° 90° triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.
A 45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2.
properties of 45°-45°-90°:
It's the only possible right triangle that is also an isosceles triangle, and it has the smallest ratio of the hypotenuse to the sum of the legs.It has the greatest ratio of the altitude from the hypotenuse to the sum of the legs.To know more about 45° 45° 90° triangle:
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A survey found the following number of pets in different households.
What is the mean absolute deviation for the number of pets?
Answer:
absolute deviation means distance between each data value and the mean of the data set.
Step-by-step explanation:
(MAD)
or
(Average)
The sales tax in one town is 8%.So, the total cost of an item can be written as c=0.08cents .what is the total cost of an that sells for $12 ?its due tmrr asap
The total cost of an item that sells for $12 is $12.96
How to determine the total cost of an item that sells for $12?From the question, we have the following parameters that can be used in our computation:
Selling price = $12
Sales tax = 8%
The total cost of an item that sells for $12 is then calculated as
Total cost = Selling price * (1 + Sales tax)
Substitute the known values in the above equation, so, we have the following representation
Total cost = 12 * (1 + 8%)
Evaluate
Total cost = 12.96
Hence, the total cost is $12.96
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PLEASE I NEED THIS NOW
Rewrite this polynomial in terms of its simplest factors using the appropriate method: x2 − 3x − 18.
Use your keyboard and the keypad to enter your answer. Then click Done.
The polynomial in terms of its simplest factors is (x + 3)(x − 6)
How to rewrite the polynomial in terms of its simplest factorsFrom the question, we have the following parameters that can be used in our computation:
x2 − 3x − 18.
Rewrite as
x² − 3x − 18
Expand
x² − 3x − 18 = x² − 6x + 3x − 18
Factorize the expression
This gives
x² − 3x − 18 = x(x − 6) + 3(x − 6)
Factor out x - 6
x² − 3x − 18 = (x + 3)(x − 6)
Hence, the expression is (x + 3)(x − 6)
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A straw is placed inside a rectangular box that is 2 inches by 1 inches by 3 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in the simplest radical form.
The length of the straw is 3.74 inches.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
In rectangular box,
Length (l) = 2 inches
Width (w) = 1 inches
Height (h) = 3 inches
Here, The straw is said to fit into the box diagonally from the bottom.
So, the length (s) of the straw is calculated as:
⇒ s = √ l² + w² + h²
⇒ s = √ 2² + 1² + 3²
⇒ s = √ 4 + 1 + 9
⇒ s = √ 14
⇒ s = 3.74 inches
Thus, The length of straw = 3.74 inches
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The length of the straw will be 3.7416 inches long in radical form.
What is Length of diagonal in cuboid?If a cuboid has length = l units, breadth = b units, and height = h units, then we can evaluate the length of the diagonal of a cuboid using the formula : X²=l²+b²+h²
Here,
As per the question the length of the straw is equal to length of the diagonal of Rectangular box.
l= 3 inch , b= 2 inch , h= 1 inch
Let us consider the length of the straw be 'x'.
As, Diagonal of Cuboid is,
X²=14
X=√14
i.e. X=3.7416
We get, X= 3.7416 (in radical form)
Hence, the length of the straw will be 5.91607 inches.
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If f(x) = x5 - 1, g(x) = 5x², and h(x) = 2x, which expression is equivalent to [go fo h](9)?
O2(5(95-1)²)
O2((5-92)5-1)
O5((2-9)5-1)²
O(5(2-9)2)5-1
The response to the given domain range questions is [go f oh]. (9) = 5(18^2 - 1 )
What are the domain and range?Domain and range. A function's authorised range of values is known as its domain. The x values in a function like f make up this set (x). A function's range is the collection of values that it can take as input. When we enter an x value, the function outputs this set of values.
According to the given information:f(x) = x^5 – 1, g(x) = 5x^2, and h(x) = 2x
[g o f o h](9)=g(f(h(9))
Let's find h(9) first
h(x)= 2x
h(9)= 2(9) =18
Now plug in 18 for h(9)
[g o f o h](9)=g(f(h(9)) = g(f(18))
now we find f(18)
f(x) = x^5 – 1, f(18)= 18^5 -1
Now we plug in 18^5 -1 for f(18)
[g o f o h](9)=g(f(h(9)) = g(18^5 -1)
Plug it in g(x)
g(x)= 5x^2
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Identify the term(s), coefficient(s), and
constant(s) in the expression
52 + 6 + ya.
Term(s) Coefficient(s) Constant(s)
In the expression 52 + 6 + ya,
"ya" is a term,The coefficient of "ya" is 1,"52" and "6" are constants.Describe Term(s), Coefficient(s), Constant(s).The terms are the individual parts of the expression that are being added together. The coefficient is the numerical factor that is multiplied by a variable in a term, and the constant is a term that has no variable.
Any expression with variables will either add or delete one or more variables. Any one of a variety of numbers to represent a generic idea. An absolute number is a constant. A constant is a number, whereas a coefficient is a number that is "in front of" a variable.
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which answer is this
A.43
B.38
C.61
D.81
An ice cream factory makes 310 quarts of ice cream in 10 hours how many quarts could be made in 48 hours what was the ate per day
The factory can make 744 quarts of ice cream per day.
To find out how many quarts of ice cream could be made in 48 hours, we can use the principle of proportionality. Since the factory makes 310 quarts of ice cream in 10 hours, we can set up a proportion:
310 quarts / 10 hours = x quarts / 48 hours
To solve for x, we can cross multiply:
310 quarts * 48 hours = 10 hours * x quarts
x = (310 quarts * 48 hours) / 10 hours = 1480 quarts
So the factory could make 1480 quarts of ice cream in 48 hours.
To find the rate per day, we need to divide the number of quarts made per hour by the number of hours in a day. Since there are 24 hours in a day, we can calculate the rate per day as:
rate per day = (310 quarts / 10 hours) * 24 hours = (31 quarts/hour) * 24 hours = 744 quarts/day
So the factory can make 744 quarts of ice cream per day.
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Add: (g2 – 4g4 + 5g + 9) + (–3g3 + 3g2 – 6)
Rewrite terms that are subtracted as addition of the opposite.
g2 + (–4g4) + 5g + 9 + (–3g3) + 3g2 + (–6)
Group like terms.
Combine like terms.
Write the resulting polynomial in standard form.
The resulting polynomial in standard form (b) –4g^4 –3g³ +4g² +5g +3
What is standard form of a polynomial?Suppose the considered polynomial is of only one variable.
Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.
The simplification process is described and partially carried out. We are to finish by combining like terms and writing the result in standard form.
Given
Add: (g² – 4g^4 + 5g + 9) + (–3g³ + 3g² – 6)
Combine Like Terms
g² + (–4g^4) + 5g + 9 + (–3g³) + 3g² + (–6)
The like terms are the g² terms and the constants;
= (1 +3)g² + (–4g^4) +5g +(9 +(–6)) +(–3g³)
= 4g² +(–4g^4) +5g +3 +(–3g³)
Write in Standard Form
In this form, the terms are written in order of decreasing degree.
= –4g^4 –3g³ +4g² +5g +3
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Using a number line, find both the intersection and the union of the following
intervals:
(-∞,2) and [0,∞)
The union of the intervals is (-∞,∞)
The intersection of the intervals is [0,2)
Hope this helped!
7. What is the most precise name for the quadrilateral?
(Show all work and explanation clearly for full credit)
P(-1,3), Q(3,0), R(0,-4), S(-4,-1)
Area of quadrilateral is 24 units and it is known as parallelogram.
A plot point in a graph is what?A point in the plane is one-to-one connected to an ordered pair of real numbers (x, y) using point plotting. The 2-dimensional Cartesian coordinate system is as a result obtained.
A parallelogram results from plotting the four points.
the lower side is between (-6,-3) and (-2,-3)
0 to 3 is at the top (4,3)
As a result, the base length is 4 because the distance
between (-6,-3) and (-2,-3) = 4
the separation between (0,3) and (4,3)
The sides are the lines that connect (0,3) to (-6,-3)
along with (4,3) to (-2,-3).
Vertical height ranges from -3 to 3 or 6.
The parallelogram's area is given by base*height = 4(6) = 24.
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Use the figure to answer the following.
The solution of given triangle is 32°.
An isosceles triangle is what?Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, and a scalene triangle is one in which none of its sides are equal.
Given,
∠BAC=52°
since, ΔBAC is isosceles triangle hence opposite angle will be equal.
∠BAC+∠ABC+∠ACB=180°
2∠BCA=180°-52°
∠BCA=128/2
∠BCA=64°
also,
∠BCA+∠DCA=180°
∠ACD=180°-64°
∠ACD=116°
since,
ΔACD is isosceles triangle, hence opposite angle is equal
∠ACD+∠CAD∠ADC=180°
2∠CAD=180°-116°
∠CAD=64/2
∠CAD=32°
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A conical paper cup is 10 cm tall with a radius of 7 cm. The cup is being filled with water so that the water level rises at a rate of 3 cm/sec. At what rate is water being poured into the cup when the water level is 9 cm
The rate exists water being poured into the cup when the water level is 9 cm exists [tex]$$1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].
What is meant by chain rule?To determine the derivative of a composite function in differential calculus, apply the chain rule formula. If y = f(g(x)), then according to the chain rule, the instantaneous rates of change of the functions f and g with respect to x produce the instantaneous rate of change of f with respect to x.
A composition of functions, such as the composition of the functions f and g, f(g(x)), can be used to determine the derivative using the chain rule.
Let us set up the following variables:
R, Radius of conical cup (cm) = 30 cm
H, Height of the conical cup (cm) = 10 cm
Our aim is to find dV/dt when h = 9 and we are given dh/dt = 2
By similar triangles we have
r : h = R : H
r/h = 30/10
⇒ r = 3h
The volume of a cone is 1/3π r²h, So:
V = 1/3π r²h
simplifying the equation, we get
= 1/3π (3h²)h
= 1/3π 9h²h
= 3π h³
Differentiating wrt h we get:
dV/dh = 9π h²
Applying the chain rule we have:
dV/dt = (dV/dh)(dh/dt)
= 9π h² × 2
= 18π h²
If h = 9 then
[tex]$\left[\frac{d V}{d t}\right]_{h=9}=18 \pi\left(9^2\right)=1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].
Therefore, the rate exists water being poured into the cup when the water level 9 cm exists [tex]$$1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].
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What is the degree of the polynomial 7x³ 5x 4x³ 2x²?
The degree of the polynomial 7x³ 5x 4x³ 2x² is 3.
The degree of a polynomial is the highest power of x in the polynomial.
In this case, the polynomial is 7x³ 5x 4x³ 2x², and the highest power of x is x³. This means that the degree of this polynomial is 3.
It's important to note that when working with polynomials it's important to pay attention to the signs of the coefficients. In this case, we have 7x³, 5x, 4x³, 2x². The x³ term has the highest degree and it's coefficient is 7, the x term has the second highest degree and it's coefficient is 5, the x³ term has the same degree as the first x³ term, but the coefficient is different, and the x² term has the fourth highest degree and it's coefficient is 2.
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Solve the system by graphing
2x-3y=-6
7x-3y=9
Following is the graph of two given equations.
The mapping of functions of two variables onto a Cartesian coordinate system, which is made up of a horizontal x-axis, or abscissa, and a vertical y-axis, or ordinate, is done analytically through the use of graphs. The intersection of each axis, which is a real number line, at its zero point is known as the origin.
On solving the two equations,
2x-3y=-6 ....(1)
7x-3y=9 .....(2)
Firstly we will find common points by elimination -
The common points are - (3,4)
Then We can find all the values of equation (1)
2x-3y=-6
x 0 3 -3
y 2 4 0
7x-3y=9
x 0 3 10
y -3 4 20.33
The respective graph is attached below
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What is the horizontal asymptote * 1 point?
The surveyor walked 120 ft away from one of the sensors so that her walking path made a 90 degree angle with the width of the lake when she stop she measured the lake when she stopped she measured the angle between her lines of sight to both sensors and it was 70 degrees
Therefore ,the answer to the above trigonometry issue is therefore that the river is 70 feet wide.
What is trigonometry?The study of the connections between the angles and sides of triangles is known as trigonometry. Due to the fact that each straight-sided figure may be reduced to a collection of triangles, trigonometry is commonly utilized in geometry. There are a mind-boggling number of connections between trigonometry and other branches of mathematics, especially algebra, real or complex, integrals, logarithms, and infinite series.
Here,
Figure depicts a right triangle which, in relation to angle, its next side has length d or its wrong side is equal to the river's width, y. As a result,
tanθ= d/ y
=> y=dtanθ
=> y = (100m)tan(35.00)=70ft
The river measures 70 feet in width.
As a result, the trigonometry problem's answer indicates that the river's width is 70 feet.
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f(x)=3^√x-1
Find f(27) and f(-343)
need to find cube root
On solving the provided question, we can say that - the value of the cube root is 19683 = 27
what is cube root?In mathematics, y3 = x since the cube root of a number x equals a number y. Each non-zero real integer has precisely one real cube root, one set of complex conjugate cube roots, and three different complex cube roots. When a number is multiplied three times, the result is the cube root of that number. Three cube roots, the final cube root, is the symbol for the cube root. The opposite of cubing an integer is finding the cube root of that number. Prime factorization is a fairly straightforward technique that may be used to get a number's cube root. The sign stands for a cube root.
here,
we have f(27)
cube will be [tex]( 27 )^3[/tex] = 19683
and f(-343) = -7
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The statements that are always true regarding the diagram are:
i. m∠5 + m∠6 =180°
ii. m∠2 + m∠3 = m∠6
iii. m∠2 + m∠3 + m∠5 = 180°
Exterior and interior angles of a triangle.A triangle is a 2 dimensional plane figure which is formed by three straight lines and has three interior angles. It has both interior and exterior angles. Some examples of a triangle are; isosceles, equilateral, scalene, right angled etc.
The interior angles of a triangle are the measure of the three internal angles of the triangle, while exterior angles are external to the interior angles of the triangle.
Note that; the exterior angle of a triangle is equal to the sum of the two adjacent interior angles.
Therefore considering the given diagram, the required statements that are always true regarding the diagram are:
i. m∠5 + m∠6 =180°
ii. m∠2 + m∠3 = m∠6
iii. m∠2 + m∠3 + m∠5 = 180°
A sketch of the diagram is herewith attached to this answer for clarity.
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3 chairs and 4 tables cost rs 7540. if the price of a chair is 220 find the price of table?
ans - 7120
Answer:
The price of a table is rs1720
Step-by-step explanation:
Let C and T be the individual prices of the tables and chairs.
We know that 3C + 4T = rs7540
We are then told that C = rs220, so we can enter that into the equation to find T:
3C + 4T = rs7540
3(220) + 4T = rs7540 [for C = rs220]
660 + 4T = 7540
4T = rs6880
T = rs1720
Check:
Do 3 chairs at 220 each and 4 tables at 1720 each add to a total of 7540?
Chairs: rs660
Tables: rs6880
Total = rs7540 YES
Kaj and her children went into a grocery store and she bought $8 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. She bought 2 more apples than bananas. By following the steps below, determine the number of apples, x,x, and the number of bananas, y,y, that Kaj bought.
Kaj bought 3 bananas and 5 apples.
Finding the numbers of apples and bananas using substitution method.To determine the number of apples and bananas that Kaj bought, we can set up a system of equations.We know that the total amount spent on apples and bananas is $8.We know that each apple costs $1 and each banana costs $0.50.We know that Kaj bought 2 more apples than bananas.From these three pieces of information, we can set up the following two equations:
x + y = 8 (The total number of apples and bananas is 8)x + 0.5y = 8 (The total amount spent is $8)x = y + 2 (Kaj bought 2 more apples than bananas)We can substitute the third equation into the first equation and get:
y+2 + y = 8
So we know that y = 3
Now we can substitute this value into the second equation and get:
x + 0.5(3) = 8
So we know that x = 5
So Kaj bought 3 bananas and 5 apples.
And also we can substitute y = 3 into the third equation and get:
x = y + 2
So we know that x = 5
So Kaj bought 3 bananas and 5 apples.
Learn more about finding number of commodities using substitution method here:https://brainly.com/question/14349317
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The points (p, -2) and (6, 8) fall on a line with a slope of -10. What is the value of p?
Thank you!
Step-by-step explanation:
(8 + 2)/(6 - p)= -10
10/6 - p = -10
-60 + 10p = 10
10p= 70
p= 7
Pam said the equations x/16=4 and x/4=16 have the same solution. Is she correct? Explain
well, maybe Pam has been eating the wrong chips or something, but if she's correct, that can only happen if both equations are exactly equal, are they?
[tex]\boxed{\cfrac{x}{16}=4}\implies x=(16)(4)\implies \cfrac{x}{4}=16 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x}{4}=16\implies x=(4)(16)\implies \boxed{\cfrac{x}{16}=4}\qquad \begin{array}{llll} \textit{yeap, Pam is correct}\\ \textit{she's Da Bomb} \end{array}[/tex]