Answer:
A. The multiplication that takes place while distributing comes before addition and subtraction in order of operations.
Step-by-step explanation:
You want to know the error that adding -4+4 on the left and 1+1 on the right represents in the solution of the equation ...
4x -2(3x -4) +4 = -x +3(x +1) +1SolutionThe correct solution procedure would be to eliminate the parentheses using the distributive property as a first step:
4x -6x +8 +4 = -x +3x +3 +1
Comparing this to Maricella's first step, we see that she ignored the step of using the distributive property to multiply the constants inside parentheses by the factor outside. The appropriate description of Maricella's mistake is ...
A. The multiplication that takes place while distributing comes before addition and subtraction in order of operations.
__
Additional comment
Adding like terms would give ...
-2x +12 = 2x +4
8 = 4x . . . . . . . . . . . add 2x-4 to both sides
2 = x . . . . . . . . . . divide by 4
<95141404393>
Find the measure of the indicated angle.
20°
161°
61°
73°
H
G
F
73 ° E
195 °
Answer:
(c) 61°
Step-by-step explanation:
You want the measure of the external angle formed by a tangent and secant that intercept arcs of 73° and 195° of a circle.
External angleThe measure of the angle at F is half the difference of intercepted arcs HE and EG.
(195° -73°)/2 = 122°/2 = 61°
The measure of angle F is 61°.
<95141404393>
9497 ÷ 16 _R_ please
what is the midpoint of 70 and 90
Answer:
80
Step-by-step explanation:
Just average the two numbers to get (70+90)/2 = 160/2 = 80
Answer:
Step-by-step explanation:
To find the midpoint between two numbers, you add them together and divide the sum by 2.
In this case, the midpoint between 70 and 90 would be:
(70 + 90) / 2 = 160 / 2 = 80.
Therefore, the midpoint between 70 and 90 is 80.
pls help !!!!!! geometry
How much fencing is required to enclose a circular garden whose radius is 21 m
Answer:182.12 meters of fencing required.
Step-by-step explanation:
Which function is graphed ?
Reynold’s company has a product with fixed costs of $334,000, a unit selling price of $22, and unit variable costs of $19. The break-even sales (units) if the variable costs are decreased by $4 is
The break-even sales (units) when the variable costs are decreased by $4 is approximately 47,714 units.
To find the break-even sales (units) when the variable costs are decreased by $4, we need to calculate the new unit variable costs and then use the break-even formula.
Fixed costs (F) = $334,000
Unit selling price (P) = $22
Unit variable costs (V) = $19
Change in unit variable costs = $4
New unit variable costs (V') = V - Change in unit variable costs
= $19 - $4
= $15
Now, let's calculate the break-even sales (units) using the formula:
Break-even sales (units) = Fixed costs / (Unit selling price - Unit variable costs)
Break-even sales (units) = $334,000 / ($22 - $15)
= $334,000 / $7
= 47,714.29
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I don’t understand can I get answers please
Answer:
c=25
Step-by-step explanation:
Since you are given [tex]x^{2}[/tex]+10x+c
We know that in an equation of [tex]ax^{2}+bx+c[/tex], when a = 1, c can be found by [tex](\frac{b}{2})^{2}[/tex]
So c = [tex](10/2)^{2}[/tex]=[tex]5^{2}[/tex]=25
Algebra
Solve for k: 10-10|-8k+4|=10
Write your answer in set notation.
The solution for k in the equation 10 - 10|-8k + 4| = 10, expressed in set notation, is {1/2}.
1. Start with the equation: 10 - 10|-8k + 4| = 10.
2. Simplify the expression inside the absolute value brackets: -8k + 4.
3. Remove the absolute value brackets by considering two cases:
Case 1: -8k + 4 ≥ 0 (positive case):
-8k + 4 = -(-8k + 4) [Removing the absolute value]
-8k + 4 = 8k - 4 [Distributive property]
-8k - 8k = -4 + 4 [Group like terms]
-16k = 0 [Combine like terms]
k = 0 [Divide both sides by -16]
Case 2: -8k + 4 < 0 (negative case):
-8k + 4 = -(-8k + 4) [Removing the absolute value and changing the sign]
-8k + 4 = -8k + 4 [Simplifying the expression]
0 = 0 [True statement]
4. Combine the solutions from both cases: {0}.
5. Check if the solution satisfies the original equation:
For k = 0: 10 - 10|-8(0) + 4| = 10
10 - 10|4| = 10
10 - 10(4) = 10
10 - 40 = 10
-30 = 10 [False statement]
6. Since k = 0 does not satisfy the equation, it is not a valid solution.
7. Therefore, the final solution expressed in set notation is {1/2}.
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Please help! Will give brainliest
The z - score z = (x - μ)/σ equals z = (p' - p)/[√(pq/n)]
What is z-score?The z-score is the statical value used to determine probability in a normal distribution
Given the z-score z = (x - μ)/σ where
x = number of successes in a sample of nμ = np and σ = √npqWe need to show that
z = (p' - p)/√(pq/n)
We proceed as follows
Now, the z-score
z = (x - μ)/σ
Substituting in the values of μ and σ into the equation, we have that
μ = np and σ = √(npq)So, z = (x - μ)/σ
z = (x - np)/[√(npq)]
Now, dividing both the numerator and denominator by n, we have that
z = (x - np)/[√(npq)]
z = (x - np) ÷ n/[√(npq)] ÷ n
z = (x/n - np/n)/[√(npq)/n]
z = (x/n - p)/[√(npq/n²)]
z = (x/n - p)/[√(pq/n)]
Now p' = x/n
So, z = (x/n - p)/[√(pq/n)]
z = (p' - p)/[√(pq/n)]
So, the z - score is z = (p' - p)/[√(pq/n)]
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8. Amy has $30 to spend. She wants to buy pounds of lemons at $2 per pound, a box for $4, and 7 frozen dinners for $3 each Choose True or False for each statement. A She will not have enough money to buy everything O True O False 8 She will have $1 left over. O True O False C The total cost is $39. O True O False
Answer:she will actually need 1 dollar because all of that would be 31 dollars.
Step-by-step explanation:
3 pounds of lemons= $6
1 box of rice= $4
7 frozen diners= $21
6+4=10
10+21=31
two points A and B, due to two spheres X and Y 4.0m apart, that are carrying charges of 72mC and -72mC respectively. Assume constant of proportionality as 9×10^9Nm²/C². Find the electric field strength at points A and B due to each spheres presence
Due to the presence of spheres X and Y, the electric field strength at point B is [tex]1.01 * 10^6 N/C[/tex] and [tex]-4.05 * 10^6 N/C[/tex], respectively.
Given that two spheres X and Y are carrying charges of 72mC and -72mC respectively, and they are located 4.0 m apart from each other. The electric field strength at points A and B due to the presence of each sphere is to be determined.
Let's begin by calculating the electric field strength at point A due to sphere X. Electric field strength is given by E=kq/r², where k is Coulomb's constant, q is the charge and r is the distance between the two charges. The electric field strength at point A due to sphere X, E₁=kq₁/r₁² [tex]= (9*10^9Nm^2/C^2) * (72mC) / (4.0m)^2 = 4.05 * 10^6 N/C[/tex] (approx.)
Similarly, the electric field strength at point A due to sphere Y can be calculated as follows, E₂=kq₂/r₂² [tex]= (9*10^9Nm^2/C^2) * (72mC) / (4.0m)^2 = 4.05 * 10^6 N/C[/tex] (approx.). Here, the negative sign indicates that the electric field due to sphere Y is in the opposite direction to the electric field due to sphere X. Now, let's calculate the electric field strength at point B. The electric field strength at point B due to sphere X, E₁=kq₁/r₁² [tex]= (9*10^9Nm^2/C^2) * (72mC) / (8.0m)^2 = 1.01 * 10^6 N/C[/tex] (approx.)
Similarly, the electric field strength at point B due to sphere Y can be calculated as follows, E₂=kq₂/r₂² [tex]= (9*10^9Nm^2/C^2) * (-72mC) / (4.0m)^2 = -4.05 * 10^6 N/C[/tex] (approx.). Therefore, the electric field strength at point A due to the presence of sphere X is [tex]4.05 * 10^6 N/C[/tex] and due to the presence of sphere Y is [tex]-4.05 * 10^6 N/C[/tex]. The electric field strength at point B due to the presence of sphere X is [tex]1.01 * 10^6 N/C[/tex] and due to the presence of sphere Y is [tex]-4.05 * 10^6 N/C[/tex].
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What is the symbol ~, if you're trying to find the probability of ~A?
the addition probability
the probability of the event not happening
the multiplication probability
None of these choices are correct.
A bacteria culture triples every 5 minutes. At 4:27 P.M. the population is . Determine what the population was 27 minutes earlier, at 4:00 P.M.
The population at 4:00 P.M., 27 minutes earlier, is[tex]3^3[/tex] times the initial population P.
To determine the population of a bacteria culture 27 minutes earlier, we need to calculate the population growth from 4:00 P.M. to 4:27 P.M. given that the bacteria culture triples every 5 minutes.
Let's break down the time period into intervals of 5 minutes:
From 4:00 P.M. to 4:05 P.M., the population triples once.
From 4:05 P.M. to 4:10 P.M., the population triples again.
From 4:10 P.M. to 4:15 P.M., the population triples for the third time.
From 4:15 P.M. to 4:20 P.M., the population triples for the fourth time.
From 4:20 P.M. to 4:25 P.M., the population triples for the fifth time.
From 4:25 P.M. to 4:27 P.M., the population undergoes partial growth.
Since the population triples every 5 minutes, we can express the population at 4:27 P.M. as 3^5 times the initial population at 4:00 P.M.
Let's denote the initial population at 4:00 P.M. as P. Then, the population at 4:27 P.M. is [tex]3^5[/tex] * P.
To find the population 27 minutes earlier, we need to reverse the growth from 4:27 P.M. to 4:00 P.M. Since the population triples every 5 minutes, we need to divide the population at 4:27 P.M. by [tex]3^{(27/5).[/tex]
Therefore, the population at 4:00 P.M., 27 minutes earlier, can be calculated as:
Population at 4:00 P.M. = (Population at 4:27 P.M.) / [tex]3^{(27/5)[/tex]
[tex]= (3^{5} * P) / 3^{(27/5)\\\\\\\\= 3^{(25/5)} * P\\= 3^5 * P / 3^2\\= 3^3 * P[/tex]
Hence, the population at 4:00 P.M., 27 minutes earlier, is 3^3 times the initial population P.
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find the value of b
A. 14
B. 15
C. 64
D. 289
[tex] \sf \hookrightarrow \: {8}^{2} + {b}^{2} = {17}^{2} [/tex]
[tex] \sf \hookrightarrow \: 8 \times 8 + {b}^{2} = 17 \times 17[/tex]
[tex] \sf \hookrightarrow \: 8 \times 8 + {b}^{2} = 289[/tex]
[tex] \sf \hookrightarrow \: 64 + {b}^{2} = 289[/tex]
[tex] \sf \hookrightarrow \: {b}^{2} = 289 - 64[/tex]
[tex] \sf \hookrightarrow \: {b}^{2} = 225[/tex]
[tex] \sf \hookrightarrow \: b = \sqrt{225} [/tex]
[tex] \sf \hookrightarrow \: b = \sqrt{15 \times 15} [/tex]
[tex] \sf \hookrightarrow \: b = 15[/tex]
B) b = 15 ✅How do you find the circumference of a circle with a diameter of 6 inches. Use 3.14 as estimate of tt that's correct to two decimal places
Answer: 18.84
Step-by-step explanation : To find the circumference you use the formula:
2πr
Since we have the diameter (6), divide by 2 to find the radius, or r.
So (2)(3.14)(3)
What is the distance between points R (5, 7) and S(-2,3)?
Answer:
d ≈ 8.1
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = R (5, 7 ) and (x₂, y₂ ) = S (- 2, 3 )
d = [tex]\sqrt{(-2-5)^2+(3-7)^2}[/tex]
= [tex]\sqrt{(-7)^2+(-4)^2}[/tex]
= [tex]\sqrt{49+16}[/tex]
= [tex]\sqrt{65}[/tex]
≈ 8.1 ( to 1 decimal place )
(08.01 MC)
The function h(x) is a continuous quadratic function with a domain of all real numbers. The table
x h(x)
-6 12
-57
-4 4
-3 3
-24
-1 7
What are the vertex and range of h(x)?
The vertex of h(x) is (-3, 3), and the range is y ≥ 3.
To find the vertex of the quadratic function h(x), we can use the formula x = -b/2a, where the quadratic function is in the form [tex]ax^2 + bx + c[/tex].
From the given table, we can observe that the x-values of the vertex correspond to the minimum points of the function.
The minimum point occurs between -4 and -3, which suggests that the x-coordinate of the vertex is -3. Therefore, x = -3.
To find the corresponding y-coordinate of the vertex, we look at the corresponding h(x) value in the table, which is 3. Hence, the vertex of the function h(x) is (-3, 3).
To determine the range of h(x), we need to consider the y-values attained by the function.
From the table, we see that the lowest y-value is 3 (the y-coordinate of the vertex), and there are no other y-values lower than 3. Therefore, the range of h(x) is all real numbers greater than or equal to 3.
The vertex of h(x) is (-3, 3), and the range is y ≥ 3.
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The vertex of the quadratic function is (-4, 12).
The range of h(x) is [3, ∞).
To find the vertex and range of the quadratic function h(x) based on the given table, we can use the properties of quadratic functions.
The vertex of a quadratic function in the form of f(x) = ax² + bx + c can be determined using the formula:
x = -b / (2a)
The domain of h(x) is all real numbers, we can assume that the quadratic function is of the form h(x) = ax² + bx + c.
Looking at the table, we can see that the x-values are increasing from left to right.
Additionally, the y-values (h(x)) are increasing from -6 to -4, then decreasing from -4 to -1.
This indicates that the vertex of the quadratic function lies between x = -4 and x = -3.
To find the exact x-coordinate of the vertex, we can use the formula mentioned earlier:
x = -b / (2a)
Based on the table, we can choose two points (-4, 4) and (-3, 3).
The difference in x-coordinates is 1, so we can assume that a = 1.
Plugging in the values of (-4, 4) and a = 1 into the formula, we can solve for b:
-4 = -b / (2 × 1)
-4 = -b / 2
-8 = -b
b = 8
The equation of the quadratic function h(x) can be written as h(x) = x² + 8x + c.
Now, let's find the y-coordinate of the vertex.
We can substitute the x-coordinate of the vertex, which we found as -4, into the equation:
h(-4) = (-4)² + 8(-4) + c
12 = 16 - 32 + c
12 = -16 + c
c = 28
The equation of the quadratic function h(x) is h(x) = x² + 8x + 28.
The range of the quadratic function can be determined by observing the y-values in the table.
From the table, we can see that the minimum y-value is 3.
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determine the surface area and volume
The surface area and the volume of the rectangular prism are 280 and 300
How to determine the surface area and volumeFrom the question, we have the following parameters that can be used in our computation:
The rectangular prism
The surface area is caculated as
Surface area = 2 * (10 * 5 + 10 * 6 + 5 * 6)
Evaluate
Surface area = 280
For the volume, we have
Volume = 10 * 5 * 6
Evaluate
Volume = 300
Hence, the surface area and the volume are 280 and 300
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In ΔBCD,
B
D
‾
BD
is extended through point D to point E,
m
∠
C
D
E
=
(
9
x
−
12
)
∘
m∠CDE=(9x−12)
∘
,
m
∠
B
C
D
=
(
2
x
+
3
)
∘
m∠BCD=(2x+3)
∘
, and
m
∠
D
B
C
=
(
3
x
+
5
)
∘
m∠DBC=(3x+5)
∘
. Find
m
∠
B
C
D
.
m∠BCD.
m∠BCD = 31.57° (approx). Hence, the answer of the angle is 31.57 degrees.
In the given diagram, BD is extended through point D to point E, m∠CDE = (9x - 12)°, m∠BCD = (2x + 3)°, and m∠DBC = (3x + 5)°. We need to find m∠BCD.
Use the Angle Sum Property of a Triangle.The Angle Sum Property of a Triangle states that the sum of all the angles in a triangle is equal to 180°.The angle sum of ΔBCD is:m∠BCD + m∠DBC + m∠CDE = 180°Substituting the given angles, we get:(2x + 3)° + (3x + 5)° + (9x - 12)° = 180°Simplifying the above expression, we get:14x - 4 = 180°14x = 180° + 4x = 184/14x = 92/7Find m∠BCDWe know that m∠BCD = (2x + 3)°
Substituting x = 92/7, we get:
m∠BCD = (2 × 92/7 + 3)° = (184/7 + 3)° = 221/7°
Therefore, m∠BCD = 31.57° (approx). Hence, the answer is 31.57.
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What is the radius of a circle that has a circumference of 68 cm
Step-by-step explanation:
The formula to calculate the circumference (C) of a circle is C = 2πr, where r represents the radius of the circle.
In this case, the given circumference is 68 cm. Plugging this value into the formula, we can solve for the radius (r):
68 = 2πr
To find the radius, we can divide both sides of the equation by 2π:
r = 68 / (2π)
Using an approximate value of π ≈ 3.14159, we can calculate the radius:
r ≈ 68 / (2 × 3.14159) ≈ 10.8419 cm
Therefore, the radius of the circle, which has a circumference of 68 cm, is approximately 10.8419 cm.
Therefore, The Radius of the Circle is 10.8 cm.
(-14)+x=14[/tex] what is the answer
The equation (-14) + x = 14 is solved by adding 14 to both sides of the equation, resulting in x = 28. This means that 28 is the value of x that satisfies the equation and makes it true.
To solve the equation (-14) + x = 14, we need to isolate the variable x on one side of the equation. Let's go through the steps:
Step 1: Add 14 to both sides of the equation to eliminate the -14 on the left side.
(-14) + x + 14 = 14 + 14
x = 28
The solution to the equation (-14) + x = 14 is x = 28.
In this equation, we start with (-14) on the left side, and we want to determine the value of x that makes the equation true. To do that, we need to isolate x. By adding 14 to both sides of the equation, we cancel out the -14 on the left side, leaving us with just x. On the right side, 14 + 14 simplifies to 28.
Therefore, the solution to the equation is x = 28. This means that if we substitute 28 for x in the original equation, (-14) + 28 will indeed equal 14. Let's verify this:
(-14) + 28 = 14
14 = 14
The left side of the equation simplifies to 14, and the right side is also 14. Since both sides are equal, it confirms that x = 28 is the correct solution to the equation.
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CAPM Elements
Value
Risk-free rate (rRF
)
Market risk premium (RPM
)
Happy Corp. stock’s beta
Required rate of return on Happy Corp. stock
An analyst believes that inflation is going to increase by 2.0% over the next year, while the market risk premium will be unchanged. The analyst uses the Capital Asset Pricing Model (CAPM). The following graph plots the current SML.
Calculate Happy Corp.’s new required return. Then, on the graph, use the green points (rectangle symbols) to plot the new SML suggested by this analyst’s prediction.
Happy Corp.’s new required rate of return is .
The new required rate of return for Happy Corp. can be calculated using the Capital Asset Pricing Model (CAPM). The formula for CAPM is:
Required rate of return = Risk-free rate + Beta * Market risk premium
Since the analyst believes that the market risk premium will be unchanged, the only factor that will affect the new required return is the risk-free rate.
Given that the analyst predicts a 2.0% increase in inflation, the risk-free rate will also increase by that amount. Therefore, the new required rate of return for Happy Corp. will be the current risk-free rate plus the product of Happy Corp.'s beta and the market risk premium.
To plot the new Security Market Line (SML) on the graph, we would use the new required return calculated above and plot it against the corresponding beta values. The SML represents the relationship between risk (beta) and return (required rate of return).
By incorporating the new required return, we can determine the new expected returns for various levels of beta and create the updated SML.
It is important to note that without specific values provided for the risk-free rate, market risk premium, and Happy Corp.'s beta, it is not possible to calculate the exact new required return or plot the new SML accurately.
These values are crucial in determining the precise position of the SML on the graph.
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a) Write a linear system to model the situation:
For the school play, the cost of one adult ticket is $6 and the cost of one student ticket is $4. Twice as many student tickets as adult tickets were sold. The total receipts were $2016.
b) Use substitution to solve the related problem:
How many of each type of ticket were sold?
Answer:
There were 126 student tickets sold and 252 adult ticket sold.
Step-by-step explanation:
Let x be the number of adult tickets sold
y be the number of students tickets sold
Twice as many student tickets as adult tickets were sold
a.
x = 2y ---equation 1
6x + 4y = 2016 ---equation 2
b.
Substitute equation 1 to equation 2
6(2y) + 4y = 2016
12y + 4y = 2016
16y = 2016
Divide both sides of the equation by 16
16y/16 = 2016/16
y = 126
Substitute y = 126 to equation 1
x = 2y
x = 2(126)
x = 252
Select the correct answer. Which fraction converts to a terminating decimal number? A. 1\6 B. 2\9 C. 3\8 D. 4\7
The fraction that converts to a terminating decimal number is C. 3/8.
To determine which fraction converts to a terminating decimal number, we need to analyze the denominator of each fraction. A fraction will result in a terminating decimal if its denominator has only prime factors of 2 and/or 5.
Let's examine each option:
A. 1/6: The denominator is 6, which can be factored into 2 * 3. Since 3 is not a factor of 2 or 5, this fraction does not convert to a terminating decimal.
B. 2/9: The denominator is 9, which can be factored into 3 * 3. Since 3 is not a factor of 2 or 5, this fraction does not convert to a terminating decimal.
C. 3/8: The denominator is 8, which can be factored into 2 * 2 * 2. Since all the factors are 2, this fraction does convert to a terminating decimal.
D. 4/7: The denominator is 7, which cannot be factored into 2 or 5. Therefore, this fraction does not convert to a terminating decimal.
Based on our analysis, the fraction that converts to a terminating decimal number is C. 3/8.
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Find the local and absolute maximum and minimum points in (x, y) format for the
function f(x) = 3/5x^5 - 9x^3 + 2 on the closed interval [-4,5]. Answer the following
questions.
a) Find all critical numbers (x- coordinates only)
b) Find the intervals on which the graph is increasing Mark critical numbers
Please answer ASAP I will brainlist
Answer:
x = - 2 , x = 4
Step-by-step explanation:
the x- intercepts are the points on the x- axis where the graph crosses
the graph crosses the x - axis at - 2 and 4 , then
x- intercepts are x = - 2 , x = 4
A metalworker cuts out a large semicircle with a diameter of 28 centimeters.Then the metalworker is a smaller sine ait of the larger one and rives it. The der of the ticular pince that is removed a 14 centimeters. Find the distance wound the shape after the smaller circle is removed. Use 22/7
The distance around the shape after the smaller semicircle is removed is 29 cm.The correct answer is option D.
To find the distance around the shape after the smaller semicircle is removed, we need to calculate the circumference of the larger semicircle and subtract the circumference of the smaller semicircle.
The circumference of a semicircle is given by the formula:
Circumference = π * radius + diameter/2
For the larger semicircle:
Radius = diameter/2 = 28/2 = 14 cm
Circumference of the larger semicircle = π * 14 + 28/2 = 22/7 * 14 + 14 = 44 + 14 = 58 cm
For the smaller semicircle:
Radius = diameter/2 = 14/2 = 7 cm
Circumference of the smaller semicircle = π * 7 + 14/2 = 22/7 * 7 + 7 = 22 + 7 = 29 cm
Therefore, the distance around the shape after the smaller semicircle is removed is:
58 cm - 29 cm = 29 cm
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The Probable question may be:
A metalworker cuts out a large semicircle with a diameter of 28 centimeters. Then the metalworker cuts a smaller semicircle out of the larger one and removes it. The diameter of the semicircular piece that is removed is 14 centimeters. What will be the distance around the shape after the smaller semicircle is removed? Use 22/7 as an approximation for π.
A. 80cm
B. 82cm
C. 85cm
D. 86cm
Find the area of quadrilateral QUAD, whose vertices are:
Q (-4, 3), U (3, 6), 1 (6, 3), and D (1, -4).
The area of quadrilateral QUAD is 2.5 square units.
To find the area of quadrilateral QUAD with vertices Q (-4, 3), U (3, 6), 1 (6, 3), and D (1, -4), we can use the Shoelace formula (also known as Gauss's area formula or the surveyor's formula).
The Shoelace formula states that the area of a polygon with vertices (x1, y1), (x2, y2), ..., (xn, yn) can be calculated as:
[tex]Area = 1/2 * |(x1y2 + x2y3 + ... + xny1) - (x2y1 + x3y2 + ... + x1yn)|[/tex]
Using this formula, we can calculate the area of quadrilateral QUAD as follows:
Area = [tex]1/2 * |(-46 + 33 + 6*(-4) + 13) - (33 + 6*(-4) + 1*(-4) + (-4)*3)|[/tex]
Simplifying the expression, we get:
[tex]Area = 1/2 * |(-24 + 9 - 24 + 3) - (9 - 24 - 4 - 12)|Area = 1/2 * |(-36) - (-31)|Area = 1/2 * |-36 + 31|Area = 1/2 * |-5|Area = 1/2 * 5Area = 5/2[/tex]
The area of quadrilateral QUAD is 2.5 square units.
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The area of quadrilateral QUAD is 17.5 square units.
The area of quadrilateral QUAD, we can use the Shoelace Formula, also known as the Gauss's Area Formula.
The formula states that if the coordinates of the vertices of a polygon are given in order, then the area of the polygon can be calculated using the following formula:
Area = 1/2 × |(x1y2 + x2y3 + ... + xn-1yn + xny1) - (y1x2 + y2x3 + ... + yn-1xn + ynx1)|
Let's apply this formula to find the area of quadrilateral QUAD:
Q (-4, 3)
U (3, 6)
A (6, 3)
D (1, -4)
Area = 1/2 × |(-4 × 6 + 3 × 3 + 6 × (-4) + 3 × (-1)) - (3 × 3 + 6 × (-4) + (-4) × (-1) + (-1) × (-4))|
Area = 1/2 × |(-24 + 9 - 24 - 3) - (9 - 24 + 4 + 4)|
Area = 1/2 × |(-42) - (-7)|
Area = 1/2 × |-42 + 7|
Area = 1/2 × |-35|
Area = 1/2 × 35
Area = 17.5
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Pls help I am stuck Tysm
The perimeter of the figure is 30 cm.
How to find the perimeter of a figure?The perimeter of the figure is the sum of the whole sides of the figure. Therefore, the perimeter of the figure can be found as follows:
perimeter of the figure = sum of the whole sides
Therefore,
perimeter of the figure = 6 cm + 9 cm + 2 cm + 3cm + 2cm + 3cm + 2cm + 3cm
Hence,
perimeter of the figure = 15 cm + 5 cm + 5cm + 5 cm
perimeter of the figure = 30 cm
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