The intervals on which the function is increasing are: (-∞, -2) and (7, ∞), and the intervals on which the function is decreasing are: (-2, 7). In interval notation, this is written as (-∞, -2), (7, ∞) and (-2, 7).
The given function is h(x) = (x + 2)^2 x (x-7)^1/3. This is a polynomial function with two terms. The first term, (x + 2)^2, is a quadratic function, and the second term, (x-7)^1/3, is a cube root function.
We can use the derivative of the function to determine the intervals on which the function is increasing and decreasing. Taking the derivative of the function yields: h'(x) = 2(x + 2)(x - 7)^1/3 + (x + 2)^2 x (1/3)(x - 7)^-2/3. Setting the derivative equal to zero, we can solve for x and find where the function is not increasing or decreasing. Solving this equation yields x = -2 and x = 7, the points of inflection.
Therefore, the intervals on which the function is increasing are: (-∞, -2) and (7, ∞), and the intervals on which the function is decreasing are: (-2, 7). In interval notation, this is written as (-∞, -2), (7, ∞) and (-2, 7).
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A triangular prism is attached to a rectangular prism as shown below.If W= 6 1/5th inches, x= 5 inches, y= 20 inches, and z=8 3/4th inches, what is the surface area of the figure
Answer: To find the surface area of the figure, we need to add up the areas of all the individual faces. The triangular prism has three rectangular faces and three triangular faces, and the rectangular prism has six rectangular faces.
The triangular prism:
The area of one of the rectangular faces is (x * z)/2 = (5 * 8.75)/2 = 21.875 inches^2
The area of one of the triangular faces is (x * W)/2 = (5 * 6.2)/2 = 15.5 inches^2
The rectangular prism:
The area of one of the rectangular faces is x * y = 5 * 20 = 100 inches^2
So, the total surface area of the figure is
(3 * 21.875) + (3 * 15.5) + (6 * 100) = 65.625 + 46.5 + 600 = 712.125 inches^2
So the surface area of the figure is 712.125 inches^2
Step-by-step explanation:
Someone Help me Please.
Rewrite the following multiplication problem using the associative property and then show that both results will be the same.
3/7 x 5/6 x1/4
The answer is the same i. e., 4.375 in all the cases as shown
What is multiplication problem ?There are two terms which describe the three numbers in a multiplication problem. The factors are the numbers that are being multiplied together. The product is the result or answer of multiplying the multiplicand by the multiplier.
= 3/7 x 5/6 x1/4
= 38/8
= 3/7 x 1/4 x 5/6
= 5/6 x 1/4 x3/7
= 5/6 x 3/7 x 1/4
= 1/4 x 5/6 x 3/7
=1/4 x 3/7 x 56
= 4.375
The answer is the same i. e., 4.375 in all the cases as shown.
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you throw a small rock straight up with initial speed v0 from the edge of the roof of a building that is a distance h above the ground. the rock travels upward to a maximum height in time tmax, misses the edge of the roof on its way down, and reaches the ground in time ttotal after it was thrown. neglect air resistance. if the total time the rock is in the air is three times the time it takes it to reach its maximum height, so ttotal
The initial velocity is related to the maximum height by the relation [tex]v_{0}=\sqrt{\frac{2gH}{3} }[/tex]
The initial velocity (v0) is the velocity of an object at the beginning of its motion. In the scenario you described, the initial velocity of the rock is the velocity at which it is thrown upward from the edge of the roof of a building.
Without any information about the velocity at which the rock is thrown, it is not possible to determine the initial velocity.
Using the fact that the velocity at maximum height is zero, we can write the following:
[tex]v_{y}=v_{y_{0,t} }+ a_{y}t[/tex]
at maximum height, the equation becomes
[tex]0=v_{0}-gT_{max}[/tex]
=> [tex]T_{max}=\frac{v_{0} }{g}[/tex]
Now, the displacement is (-H)−H) when the rock hits the ground, so we can use one of the kinematic equations to write the following
[tex]y-y_{0}=v_{0}t+\frac{1}{2}a_{y}t^{2}[/tex]
where [tex]y_{0} =0 and y=-H[/tex]
On substituting the values and rearranging we get:
[tex]v_{0}=\sqrt{\frac{2gH}{3} }[/tex]
Therefore, The initial velocity is related to the maximum height by the relation [tex]v_{0}=\sqrt{\frac{2gH}{3} }[/tex].
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QUIZ:
Composite Figures
What is the best approximation for the area of this figure?
The best approximation for the area of this figure is A = 12+9.125π units²in the given figure.
What is the diameter of triangle?
In a triangle, the diameter is a line segment that passes through the midpoint of one side of the triangle and is perpendicular to that side. It is also the longest chord of the triangle. The length of the diameter is called the diameter of the triangle.
Draw the diameter from point (-1, -5) to point (2, 3).
The triangle has base 3 and height 8.
The diameter of the semicircle is the hypotenuse of the triangle.
d = root(3² + 8²)
d = 8.544
The radius is half the diameter.
r = d/2 = 8.544/2 = 4.272
The total area is the area of the triangle plus the area of the semicircle.
A = 3*8/2 + π*4.272²/2
A = 12+9.125pi units²
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can someone please answer this question
Sarah and Winston buy the same brand of T-shirts from different stores. Sarah pays $8 and Winston pays $4.The simplest way of writing this as a ratio 2:1.
What is Ratio?
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
The relationship between the amounts of two or more objects—referred to as a ratio—indicates how much of one object is contained in the other. The ratio formula can be used to represent a ratio as a fraction. The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.
Two quantities are compared to form a ratio. An equality of two ratios is a proportion. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.
We are given;
Sarah pays $8 for t shirt
Winston Pays $4 for t shirt
So, Simplest way of writing this as in ratio is ;
Sarah/Winston = 8/4=2/1
Hence , this is written in ratio as 2:1.
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please convert 1/6 to a decimal probability and round to 2 decimal places students often get exam questions wrong, since they convert to a whole number. you can only do this if you include the ____ %.
You can only convert 1/6 to a decimal probability and round to 2 decimal places if you include the percentage sign (%) at the end.
When converting fractions to decimal probabilities, it is important to include the percentage sign (%) at the end. This is because when converting a fraction to a decimal, the result is not a whole number, but a decimal probability. For example, 1/6 can be written as a decimal probability of 0.17, but it is usually written as 0.17% to indicate the probability of an event occurring. The percentage sign is essential for students to understand that the decimal is a probability, rather than an incorrect answer. Percentage sign also allows the decimal to be rounded to two decimal places, giving a more precise answer. Without the percentage sign, the decimal will appear to be a whole number, which is not the correct answer.
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saac Newton was consulted about the following problem by Samuel Pepys, who wanted the information for gambling purposes. Which of the following events has the highest probability?
A: At least one 6 appears when 6 fair dice are rolled.
B: At least two 6’s appear when 12 fair dice are rolled.
C: At least three 6’s appear when 18 fair dice are rolled
Event A has the highest probability, which is "at least one 6 appears when 6 fair dice are rolled.
Event A: At least one 6 appears when 6 fair dice are rolled has the highest probability. The probability of rolling at least one 6 with a fair die is 5/6, and the probability of rolling at least one 6 with 6 fair dice is (5/6)^6.
Event B: At least two 6's appear when 12 fair dice are rolled has a lower probability than A.
Event C: At least three 6's appear when 18 fair dice are rolled has a lower probability than B.
So among these three events, this is event A with the highest probability.
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or
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
A boutique in Belmont specializes in leather goods for men. Last month, the company sold 20 wallets and 14 belts, for a total of $2,202. This month, they sold 20 wallets and 83 belts, for a total of $5,859. How much does the boutique charge for each item?
the boutique charges $
for a wallet, and $
for a belt.
The cost of one belt is $53 and the cost of one wallet is $ 73.
What is the cost of each item?The first step is to set up a system of equation using the information in the question:
20w + 14b = 2202 equation 1
20w + 83b = 5859 equation 2
Where:
b= number of belts sold
w = number of wallets sold
In order to determine the value of b, take the following steps:
Subtract equation 2 from equation 1 :
69b = 3657
Divide both sides of the equation by 69
b = 3657 / 69
b = 53
Substitute for b in equation 1:
20w + 14(53) = 2202
20w + 742 = 2202
20w = 2202 - 742
20w = 1460
w = 1460 / 20
w = 73
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an appliance store manager noted that the sales of home appliances contributed 74% of the store's profits in the year 2010 and 82% in the year 2011. of the following choices, which statement about home appliance sales is true?
- Home appliance sales increased profits by 9.75%. - Home appliance sales increased profits by 9.75 percentage points. - Home appliance sales increased profits by 8%. - Home appliance sales increased profits by 8 percentage points.
The statement is true about the home appliances sales is "Home appliances sales increased profits by 8 percentage points".
Given that ,
The right answer is that 90% of all random samples of 50 students from this high school would produce a 90% confidence interval that contains the actual mean amount of money students spend on lunch.
an appliance store manager noted that the sales of home appliances contributed
74 % of the store profits in the year 2010, and 82 % in the year 2011.
Thus, the profit in the year 2010 is 74 %.
The profit in the year 2011 is 82 %.
The increased profit from year 2010 to 2011 is ( 82-74 ) % = 8%
Hence, the statement true about the home appliances sales is "Home appliances sales increased profits by 8 percentage points".
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use the definition of the riemann integral in terms of riemann sums to prove property (3) of definite integrals. that is, if f(x) is continuous on [a, b] and k is any constant, then: Integral from b ( k f(x) dx) = k integral fromb ( f(x) dx)
The integral of k*f(x) equals the integral of f(x) multiplied by k because the total of k*f(x) equals the sum of f(x) multiplied by k.
K*F(x) Integral = K*Fintegral (x). This is inferred from the description of a definite integral as the upper limit of a term sum. The area under the curve can be divided into a number of rectangles and their areas added if we are taking the integral of a function from a to b. The integral then equals the maximum value of this total. The result is identical to the original sum increased by k if we multiply each term of the sum by a constant called k. as a result, the maximum allowed f(x) multiplied by k because the total of k*f(x) equals the sum of f(x) multiplied by k.
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let z be a b digit positive integer such as 247247 whose first three digits are the same as its last 3 digits taken in the same order. which of the following numbers must be a factor of z
The number which must be a factor of 247247 is 11.
Given integer = 247247
To find the factor, we can add and minus signs alternately in front of each digit to determine whether a number is divisible by any of the given options. and then compute the answer. For example: If the integer is divisible by 11 if this result is divisible by 11 (including 0), if not, the number is not divisible by 11.
As per the question, and given integer -
+2 - 4 + 7 -2 + 4 - 7
= 0
Since the outcome is 0, the number 247247 can be divided by 11.
Complete Question:
Let Z be a 6-digit positive integer, such as 247247, whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor of Z$
a) 11
b) 19
c) 101
d) 111
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Which of the following graphs has a slope of negative three halves and a y-intercept of 2?
graph of a line passing through the points 0 comma 2 and 3 comma 0
graph of a line passing through the points 0 comma 2 and 2 comma negative 1
graph of a line passing through the points 0 comma 3 and 2 comma 0
graph of a line passing through the points 0 comma 3 and 3 comma 1
Answer:
3 3
Step-by-step explanation:
graph of a line passing through the points 0 comma 3 and 3 comma 1
If 7i is a root of a polynomial equation, which of the following is also a root?
7+i
-7i
7-i
none
By polynomial equation, 7i , −7i this we get 1, y = x² + 49 .
What is polynomial equation?The x-axis and the graph's intersection points, or the places where y = 0, are known as the roots.
The roots of y equal 0
By figuring out what x is when x ( 7 I ) = y and y = 0 we can find the root at x = 7 i.
x 7 I is the factor.
By determining the value of x at the point where x ( 7 I ) = y and y = 0, the root at x = 7 I was discovered.
x + 7 I is the factor.
One equation can be created by combining all the variables.
y = ( x − 7 i ) ( x + 7 i)
To make the equation y = (x 7 I (x + 7 I easier to understand, multiply all the elements.
Use the FOIL Method to extend (x 7 I ) (x + 7 I
Put the distributive property to use.
y = x ( x + 7 i ) − 7 i ( x + 7 i )
Put the distributive property to use.
y = x ⋅ x + x ( 7 i ) − 7 i ( x + 7 i )
Put the distributive property to use.
y = x ⋅ x + x ( 7 i ) − 7 i x − 7 i ( 7 i )
Clarify terminology.
x x + x ( 7 I ) x 7 I x ( 7 I ) is the result of combining the opposing terms.
y = x x + 7 I x + 7 I x 7 I ( 7 I ) Rearrange the elements in the terms x ( 7 I ) and 7 I x.
To get y = x x + 0 7 I ( 7 I ), subtract 7 I x from 7 I x.
y = x x 7 I ( 7 I ) is the result of adding x x and 0.
Condense each phrase.
Divide x by x to get y: x 2 7 I (7 I
7 I ( 7 I times itself..
Calculate y = x 2 49 I I by multiplying 7 by 7.
Raising I to the power of 1, y = x²- 49 ( I I
I must be raised to the strength of
1 . y = x 2 − 49 ( i i )
Raise I to the power of 1 and then find y as y = x 2 49 ( I I )
When combining exponents, use the power rule a m a n = a m + n.
y = x ² − 49 i1 + 1
To get y = x ²- 49 I ² ,add 1 and 1.
I ² should be rewritten as 1; y = x ² - 49. - 1
y = x ² + 49 multiplied by 49 by 1.
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please help!! I need this done really quick!!
Answer:
6 divided by 2/3 = 9
Step-by-step explanation:
because it is mathematically correct (can check via calculator)
and the question includes the fact that S cut the rope into 9 sections from 6.
Could someone please tell me what 18x+1 equals.
Whatever 18x+1 equals is what it equals
If the water irrigation tank holds 275 gallons, how many minutes before Angel can turn off the tap?
The answer to this question is determined on the volume of water coming from the faucet. When the tap is switched on but no water flows out, the tank can retain 275 gallons eternally. Yet, if water flows out of the tap at a constant pace, the tank will take a given period of time to empty.
What is a gallon?A gallon is a volume unit used mostly in the United States, equivalent to 128 US fluid ounces or 3.785 liters.
To establish how long it will take to empty the tank, we must first know the flow rate of the tap, which is normally measured in gallons per minute (GPM). We may use the following calculation to calculate the time it will take to empty the tank once we have known the GPM:
Time (minutes) = 275 gallons per minute / GPM
For example, if the tap is running at a rate of 10 GPM, the time required to empty the tank is:
Time (minutes) = 275 gallons /10 GPM = 27.5 minutes
As a result, if the tap is set at 10 GPM, it will take 27.5 minutes for the tank to empty before Angel can turn off the water.
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which of the following represents z = -6\sqrt(3) + 6i in trigonometric form? a. z = 12(cos 150 + i sin 150) b. z = 12(cos 210 + i sin 210) c. z = 6(cos 150 + i sin 150) d. z = 6(cos 210 + i sin 210)
The trigonometric form of complex number -6√3 + 6i will be option a. 12(cos150 + isin150)
We are given z = -6√3 + 6i
Now the polar form of a complex number is given by r(cosx + isiny)
We first need the modulus which for a complex number a + bi
r = √(a² + b²)
Hence r = √(108+36)
= √(144)
= 12
Now we need to find the angle x such that
tan x' = |b/a|
or, tan x' = |-1/√3|
or, tan x' = 1/√3
or, tan x' = tan(π/6)
or, x' = π/6
Now since a < 0 and b > 0 x will lie in Quadrant 2
Hence x = π - π/6
= 5π/6 =
Hence we get the trigonometric form to be
12(cos5π/6 + isin5π/6)
= 12(cos150 + isin150)
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In the expression n +23, 23 is a
Hey there!
Answer:
In the expression, 23 is the constant.
Hope this helps!
Find the value of x.then  round to the nearest 10th
The value of x is 10.79
What is trigonometry ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
sin (tetha) = opp/ hyp
cos ( tetha) = adj/ hyp
tan ( tetha) = opp/ adj
tetha = 26
hyp = 12
adj = x
cos 26 = x/12
cos 26 × 12 = x
x = 0.899 × 12
x= 10.79
Therefore the value if x is 10.79
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Need help with this
Answer:
f(6) = -22
g(-2) = -10
Step-by-step explanation:
Plug in 6 into f(x) = -4x + 2
f(6) = -4(6) + 2
f(6) = -24 + 2
f(6) = -22
Plug in -2 into g(x) = 2x^3 + 6
g(-2) = 2(-2)^3 + 6
g(-2) = 2(-8) + 6
g(-2) = -16 + 6
g(-2) = -10
I hope this was able to help you :D
in which row of pascal's triangle do three consecutive entries occur that are in the ratio 3 : 4 : 5
The row in Pascal's triangle where three consecutive entries are in the ratio 3:4:5 is the 62nd row.
To find the row in Pascal's triangle where three consecutive entries are in the ratio 3:4:5, we will use the concept of binomial coefficients.
The binomial coefficient C(n, k) represents the number of ways to choose k items from a set of n items, and is given by the formula -
C(n, k) = n! / (k! (n-k)!).
In Pascal's triangle, the entries are arranged such that the nth row contains n+1 entries, and the kth entry in that row is given by C(n, k).
We can determine the ratio of three consecutive entries in Pascal's triangle by looking at the binomial coefficients C(n, k), C(n, k+1), and C(n, k+2) in a particular row.
In order to find the row where the ratio of these three consecutive entries is 3:4:5, we will set up the following equation:
C(n, k) / C(n, k+1) = 3/4 and C(n, k+1) / C(n, k+2) = 4/5
We will now use the formula for binomial coefficients to simplify these equations as follows -
(n! / (k! (n-k)!) ) / (n! / ((k+1)! (n-(k+1))!)) = 3/4
Similarly,
(n! / ((k+1)! (n-(k+1))!)) / (n! / ((k+2)! (n-(k+2))!)) = 4/5
Solving for n, we can get n = 62
Therefore, the row in Pascal's triangle where three consecutive entries are in the ratio 3:4:5 is the 62nd row.
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two socks are drawn from a drawer which contains one red sock, three blue socks, two black socks, and two green socks. once a sock it is not replaced. determine the probability.
1. p(a black sock and then a green sock)
2. p(two blue socks)
3. p(a green sock and then a red sock)
4.p(two green socks)
Answer:
p(a black sock and then a green sock)
The probability of drawing a black sock first is 2/8=1/4, and then the probability of drawing a green sock next is 2/7=2/14 since we have one less sock left. So the overall probability is (1/4) * (2/14) = 1/7
p(two blue socks)
The probability of drawing a blue sock first is 3/8, and then the probability of drawing another blue sock next is 2/7 since we have one less sock left. So the overall probability is (3/8) * (2/7) = 6/56 = 3/28
p(a green sock and then a red sock)
The probability of drawing a green sock first is 2/8, and then the probability of drawing a red sock next is 1/7 since we have one less sock left. So the overall probability is (2/8) * (1/7) = 2/56 = 1/28
4.p(two green socks)
The probability of drawing a green sock first is 2/8, and then the probability of drawing another green sock next is 1/7 since we have one less sock left. So the overall probability is (2/8) * (1/7) = 2/56 = 1/28
Note that these are the theoretical probabilities, and in reality, drawing a sock and not replacing it will change the number of socks left, so the probability of the next draw will change accordingly.
Step-by-step explanation:
HELPPPpppppppppppppppppppppppppppppp
Answer:
9 cm
Step-by-step explanation:
cos B = adj/hyp
cos B = BC/AB
cos 25° = 8 m / AB
AB = 8 m / cos 25°
AB = 9 cm
find the exact length (in inches) of the arc of a circle formed by an angle that measures radians if the circle has radius 2 inches. (round you answer to two decimal places.)
The exact length (in inches) of the arc of a circle formed by given angle (in radians) and radius is 5.233 inches.
The radius of a circle and the central angle determine the length of an arc. We are aware that given an angle of 360 degrees, the arc length corresponds to the circumference. Thus, the arc length is determined by multiplying the radius by the Centre angle (in radians).
Arc length = radius x angle(in radians)
Radius = 2 inches
Angle = 5pi/6 radians
Arc length = 2 x (5pi/6)
= 5.233
Hence, the arc length is 5.233 inches.
Correct question :
find the exact length (in inches) of the arc of a circle formed by an angle that measures 5pi/6 radians if the circle has radius 2 inches. (round you answer to two decimal places.)
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14.5x35 (if you do answer can you show work because it tells me to show work and if i don't ill get it wrong.)
The value of the expression 14.5 * 35 is 507.5
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
14.5 * 35
The given expression is a simple expression that can be solved using a calculator
Using a calculator, we have the following solution
14.5 * 35 = 507.5
Hence, the solution is 507.5
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Stuart Wilkinson, the engineer of "Chew-Chew" said, "we stole the idea of eating food
from the biological world, but we are marrying that idea to useful robotic capabilities."
Which of the following would not be an application of Stuart Wilkinson's theory?
A. a trash compactor that feeds on garbage
B. a garden cultivator that feeds on soil
C. a lawn mower that feeds on grass clippings
D. a leaf mulcher that feeds on foliage
E. a recycling truck that feeds on petroleum
A recycling truck that feeds on petroleum is would not be an application of Stuart Wilkinson's theory.
What is about Stuart Wilkinson's theory?A recycling truck that runs on petroleum is designated as option E and would not be a practical application of Stuart Wilkinson's thesis in terms of merging the concept of beneficial robotic capabilities in terms of consuming food.This is referred to as a machine that can automatically mimic some human movements and functions with the help of an external control system.A recycling truck that feeds on petroleum is inaccurate since petroleum isn't a form of food because Stuart Wilkinson's thesis aims to combine the concept of beneficial robotic capabilities in terms of consuming food.To learn more about Stuart Wilkinson's theory refer to:
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Are the ratios 1:5 and 18:20 equivalent?
Answer:
No, these ratios are not equivalent.
Step-by-step explanation:
1) M.H Find the perimeter of 4.1am
Answer:
Step-by-step explanation:
helpp pls! find the value of each variable in the parallelogram.
The value of each variable in the parallelogram is h = 9 and g = 59.
What is a parallelogram?A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has neighboring angles that add up to 180 degrees. Angles on either side are equal.
We know that the opposite sides of a parallelogram and the opposite angles of a parallelogram are equal.
Using the above statement, we can write:
16 - h = 7
16 - 7 = h
h = 9
g + 4 = 63
g = 63 - 4
g = 59
Hence, the value of each variable in the parallelogram is h = 9 and g = 59.
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