Answer:w = 74.66 mph
d = 19.92 degrees
Step-by-step explanation:
Let's call the speed of the wind "w" and the direction angle of the wind "d". We can use vector addition to solve for these unknowns.
First, let's find the direction of the plane. The bearing of N * 65 deg * E can be represented as a vector with an initial point at the North pole and a terminal point 65 degrees east of due north. Since the plane is flying on this bearing, its direction vector is the same as the bearing vector. We can find the components of this vector as follows:
cos(65) = x / 1
x = cos(65)
y = sin(65)
So the direction vector of the plane is <cos(65), sin(65)>.
Next, let's find the ground speed vector. We can represent this vector as the sum of the plane's airspeed vector and the wind vector:
ground speed = airspeed + wind speed
We know that the magnitude of the ground speed vector is 390 mph, and we know the direction angle of the ground speed vector is 30 degrees. We can use this information to set up two equations:
|airspeed + wind speed| = 390
tan(d) = (wind speed)_y / (wind speed)_x
Since we know the direction vector of the plane, we can express the airspeed vector in terms of this vector as follows:
airspeed = 360 <cos(65), sin(65)>
Now we can substitute the airspeed vector and the wind speed vector into the equation for the ground speed vector, and use the fact that the magnitude of the ground speed vector is 390 to solve for the components of the wind speed vector:
|360 <cos(65), sin(65)> + <(wind speed)_x, (wind speed)_y>| = 390
Squaring both sides and using the fact that cos^2(x) + sin^2(x) = 1, we get:
129600 cos^2(65) + 129600 sin^2(65) + 720(wind speed)_x cos(65) + 720(wind speed)_y sin(65) + (wind speed)_x^2 + (wind speed)_y^2 = 152100
Simplifying, we get:
51840 + 720(wind speed)_x cos(65) + 720(wind speed)_y sin(65) + (wind speed)_x^2 + (wind speed)_y^2 = 152100
Substituting the equation for the direction angle of the wind and simplifying, we get:
51840 + 720w cos(65 - d) + w^2 = 152100 tan^2(d)
We now have two equations and two unknowns: w and d. We can solve for them using algebra or a numerical solver. Using a numerical solver, we find:
w = 74.66 mph
d = 19.92 degrees
Therefore, the speed of the wind is 74.66 mph, and its direction angle is 19.92 degrees.
In the figure, TR−→− and TV−→− are secants to circle A.
mRV=99∘
mSU=45∘
What is the measure of ∠RTV?
The measure of <RTV = 1/2 * (99 - 45) = 27 degrees
What is a Secant of a Circle?Geometrically speaking, a secant is an intersecting line that marks two separate points on the circumference of a circle.
Primarily, it serves as a chord drawn across the diameter which transverses through each endpoint connecting them. The magnitude of the secant is determined by the distance between these intersectional points. This particular element of geometry has various applications in trigonometry, particularly in computing angles and lengths within circles.
According to the Exterior Angle of a Circle Theorem, the measure of an exterior angle of a circle formed by two secants is equal to half the difference of the measures of the intercepted arcs:
Using this theorem,
Thus, the measure of ∠RTV is given as 27
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please help me with this problem
what principal will earn $67.14 interest at 6.25% for 82 days?
Answer:
I'm pretty much confused abt this one bc I didn't get an exact answer. Anyway I think it's 13.1
Step-by-step explanation:
The pic
HELP FAST! EASY ALGEBRA 2!
A graph of the functions with the asymptotes is shown in the image below.
The pre-image of the function y = log₂(x + 1) was horizontally shifted to the left by 1 unit.
The pre-image of the function y = log₂(x) + 4 was vertically shifted up by 4 units.
What is a translation?In Mathematics, the translation a geometric figure or graph to the left means subtracting a numerical value to the point on the x-coordinate of the pre-image;
g(x) = f(x + N)
In Mathematics and Geometry, the translation a geometric figure upward means adding a numerical value to the point on the positive y-coordinate (y-axis) of the pre-image;
g(x) = f(x) + N
Since the parent function f(x) was horizontally translated 1 unit left, we have the following transformed function;
y = log₂(x + 1)
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someone pls help me with this question!!
Answer:
x < -1 or x ≥ 5
Step-by-step explanation:
You want the solution and its graph for the compound inequality ...
3x -2 < -5, or-2x ≤ -10SolutionAdding 2 to the first inequality gives ...
3x < -3
x < -1 . . . . . divide by 3
Multiplying the second inequality by -1/2 gives ...
x ≥ 5
The solution is x < -1 or x ≥ 5.
Find the equation of the quadratic function g whose graph is shown below.
The equation of the quadratic function g whose graph is shown above is g(x) = -(x + 4)² - 4
How to determine the factored form of a quadratic equation?In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:
f(x) = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about the vertex and other points, we can determine the value of a as follows:
g(x) = a(x - h)² + k
-13 = a(-7 + 4)² - 4
-13 = a(-3)² - 4
-13 + 4 = 9a
-9 = 9a
a = -1.
Therefore, the required quadratic function is given by:
g(x) = a(x - h)² + k
g(x) = y = -(x + 4)² - 4
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What is the p value of a right tailed one-mean hypothesis test with a test statistic of z0-1.74
Answer:
The p-value is the probability of observing a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true. In this case, since it is a right-tailed test, the p-value is the area to the right of the observed test statistic Z=1.74 under the standard normal distribution curve.
Watch help video Triangle QRS is formed by connecting the midpoints of the side of triangle NOP. The lengths of the sides of triangle QRS are shown. Find the perimeter of triangle NOP. Figures not necessarily drawn to scale. N S 6 5 P 7 R
Since Q is the midpoint of NP, we know that NQ = QP. Similarly, we know that RS is the midpoint of OP, so we have RS = SO.
Let's label the length of QS as x. Then, we know that QR = 2x and SR = 3x.
To find the perimeter of triangle NOP, we need to find the lengths of NO, OP, and NP.
Using the Pythagorean Theorem, we can find that:
NO^2 = NQ^2 + OQ^2
NO^2 = (QP)^2 + (SO)^2
NO^2 = (x)^2 + (2x)^2
NO^2 = 5x^2
NO = x√5
Similarly, we can find that:
OP^2 = OQ^2 + PQ^2
OP^2 = (SO)^2 + (QP)^2
OP^2 = (3x)^2 + (x)^2
OP^2 = 10x^2
OP = x√10
Finally, we know that NP = NO + OP, so:
NP = x√5 + x√10
NP = x(√5 + √10)
To find the perimeter of NOP, we add up the three sides:
Perimeter of NOP = NO + OP + NP
Perimeter of NOP = x√5 + x√10 + x(√5 + √10)
Perimeter of NOP = x(2√5 + 2√10)
Perimeter of NOP = 2x(√5 + √10)
We can substitute the value we found for QS, which is x, to get:
Perimeter of NOP = 2(5 + 2√10)
Perimeter of NOP = 10 + 4√10
Therefore, the perimeter of triangle NOP is 10 + 4√10 units.
IF THERE ARE 12 RUNNERS IN A RACE , HOW MANY DIFFERENT ORDERS COULD THE ALL RUNNERS FINISH?
Answer:
12
1,2,3,4,5,6,7,8,9,20,11,12
Which ordered pair is a solution of y = x – 4?
A. (–3, 7)
B. (3, –7)
C. (–3, –7)
D. (3, 7)
Answer:
C. (–3, –7)
Step-by-step explanation:
We can check each ordered pair by substituting the values of x and y into the equation y = x - 4 and see if the equation is true.
A. (-3, 7)
y = x - 4
7 = -3 - 4
7 = -7
This is not true, so (-3, 7) is not a solution.
B. (3, -7)
y = x - 4
-7 = 3 - 4
-7 = -1
This is not true, so (3, -7) is not a solution.
C. (-3, -7)
y = x - 4
-7 = -3 - 4
-7 = -7
This is true, so (-3, -7) is a solution.
D. (3, 7)
y = x - 4
7 = 3 - 4
7 = -1
This is not true, so (3, 7) is not a solution.
Therefore, the only ordered pair that is a solution of y = x - 4 is (–3, –7).
Let $a_1, a_2, a_3,\dots$ be an arithmetic sequence.
If $a_1 + a_3 + a_5 = -12$ and $a_1a_3a_5 = 80$, find all possible values of $a_{10}$.
(There are multiple)
The possible values of [tex]$a_{10}$[/tex] are [tex]$-\frac{263}{4}$[/tex]and [tex]$-\frac{13}{5}$[/tex].
Since [tex]$a_1, a_2, a_3,\dots$[/tex] is an arithmetic sequence, we can write[tex]$a_3 = a_1 + d$[/tex] and [tex]$a_5 = a_1 + 2d$[/tex] where [tex]$d$[/tex] is the common difference between consecutive terms. Then the given equations become[tex]$3a_1 + 4d = -12$ and $a_1(a_1 + d)(a_1 + 2d) = 80$.[/tex] Simplifying the second equation gives $a_[tex]1^3 + 3da_1^2 + 2d^2a_1 - 80 = 0$.[/tex]
We can solve for [tex]$d$[/tex] in the first equation: [tex]$d = \frac{-3a_1-12}{4} = -\frac{3}{4}a_1 - 3$[/tex]. Substituting this into the second equation yields a cubic equation in terms of[tex]$a_1$[/tex]:
[tex]a\frac{3}{1}-[/tex] [tex]\frac{9}{4} a\frac{2}{1} -[/tex] [tex]\frac{15}{4} a_{1}- 80=0[/tex]
Using synthetic division or another method, we can find that [tex]$a_1 = -5$[/tex] is a root of this equation. Dividing by [tex]$a_1 + 5$[/tex] yields the quadratic [tex]$a_1^2 - \frac{1}{4}a_1 - 16 = 0$[/tex], which has roots [tex]$a_1 = -4$[/tex] and [tex]$a_1 = 4/5$[/tex].Therefore, the possible values of the common difference [tex]$d$[/tex] are [tex]$-\frac{27}{4}$[/tex] and [tex]\frac{4}{5}$[/tex]
Using [tex]$a_1 = -5$[/tex] and [tex]$d = -\frac{27}{4}$[/tex], we find that [tex]$a_{10} = a_1 + 9d = -5 - \frac{243}{4} = -\frac{263}{4}$.[/tex]
Using [tex]$a_1 = -5$[/tex] and [tex]$d = \frac{4}{5}$[/tex], we find that [tex]$a_{10} = a_1 + 9d = -5 + \frac{36}{5} = -\frac{13}{5}$.[/tex]
Therefore, the possible values of [tex]$a_{10}$[/tex] are [tex]$-\frac{263}{4}$[/tex]and [tex]$-\frac{13}{5}$[/tex].
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How much work does an elevator motor need to do to lift a 1400kg elevator a height of 100m?
ans. 1400000
we know that
work done by gravity = mgh
just putting values we get
= 1400x 100 x 10
= 1400000
hence,work done an elevator motor need to do to lift a 1400kg elevator a height of 100m is 1400000
Can someone help me with dosage calculation problems #46 and #47.
Would greatly appreciate if you explain how it was solved. Thanks!
46. There are 9 complete doses available from the bottle. 47. There are 8 full doses available in the 120 mL bottle.
What is weight and mass?Although weight and mass are frequently used interchangeably, they have distinct meanings in the study of physics. Weight is a measurement of the force of gravity acting on an item, whereas mass is a measure of the amount of matter that makes up an object. Weight is typically expressed in newtons (N) or pounds, while mass is typically expressed in kilogrammes (kg) (lb). While an object's mass remains constant, its weight can change depending on how strongly gravity is pulling on it.
46. We know that,
1 fluid ounce = 29.5735 mL
4 fluid ounces = 4 x 29.5735 = 118.294 mL
Each dose is 12.5 mL:
118.294 / 12.5 = 9.46
So there are 9 complete doses available from the bottle.
47. Given, 1 tablespoon is equal to 15 mL.
Thus, doses of 15 mL are in a 120 mL bottle:
120 / 15 = 8
So there are 8 full doses available in the 120 mL bottle.
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What is it?????????!!!!!!!!!
From the attached graph the solution set is (3, 3) for the inequalities
The first inequality is y < -(2/3)x + 5.
We can graph this by plotting the y-intercept of 5 and then using the slope of -2/3 to find additional points.
We then draw a dashed line through these points to indicate that the points on the line are not included in the solution set.
Since the inequality is y <, we shade the region below the line.
The second inequality is y ≥ (4/3)x - 1.
We can graph this by plotting the y-intercept of -1 and then using the slope of 4/3 to find additional points.
We then draw a solid line through these points to indicate that the points on the line are included in the solution set.
Since the inequality is y ≥, we shade the region above the line.
Hence, from the attached graph the solution set is (3, 3) for the inequalities
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SA=3x+19 and SD=5x-11,find for x
The value of the variable x is -4
How to determine the valueFirst, we need to know that line segments are described as a section of a line that is bounded by two points or connecting two points.
From the information given, we have that;
Line SA and SD are equal segments
But SA =3x+19 and SD=5x-11
Now, equate the expressions since they are of equal lengths, we have;
3x + 19 = 5x - 11
collect the like terms
3x - 5x = -11 + 19
Add or subtract the like terms, we have;
-2x = 8
Divide both sides by the coefficient, we have;
x = -4
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how to do 0.002 / 2000
Answer:
Step-by-step explanation:
The weights of edges in a graph are shown in the table above. Find the minimum cost spanning tree on the graph above using Kruskal's algorithm. What is the total cost of the tree?
The answer is 11 or at least i think it is
Need an answer step by step for this ASAP
Answer:
Step-by-step explanation:
There are 2 parts for your function. (see image)
y=4x, which is a line with a slope of 4 but x≠0, so there is a hole there
y=1 only at x=0 so the point is above the line
(a) Domain: All real numbers. There is a value for all x's
(b) There is no x-intercept because the graph never touches x
y-intercept (1,0) That's where the graph touch y
(c) see image
(d) range: (-∞, 0) U (0, +∞) there is a stop at 0 for y values
can also be written -∞<x<1 and 1<x<+∞
(e) yes it's continuous for domain but not range. because even though there is a jump at that point, i still have an x value. The jump causes me to not have a y value at y=0, that's why range is discontinuous
Harry's older brother practiced soccer for 6.5 hours last weekend. Harry is competitive, so this weekend he plans to practice even longer than his brother.
Let p represent the time, in hours, that Harry plans to practice soccer. Which inequality models the story?
Answer: p > 6.5
Step-by-step explanation:
Let p = the time, in hours, that Harry plans to practice soccer.
Since we don't know the hours Harry will plan to practice soccer, we will replace it with p, and Harry wants to practice more than his older brother, so we put the greater than symbol.
Hope this helped!
Use the test for polar symmetry to determine which of the following types of symmetry is displayed in the equation r=4cos^2 θ−3sinθ+5θ.
Select the correct answer below:
θ=π/2
polar axis
pole
none
Answer: The Answer is NONE
Step-by-step explanation:
The test for polar symmetry is to replace θ with −θ and check if the equation remains the same. If it does, then the polar equation is symmetric about the polar axis. If replacing θ with −θ gives the same equation but with opposite signs, then the polar equation is symmetric about the pole.
Let's apply this test to the given equation:
r = 4cos^2 θ − 3sinθ + 5θ
Replacing θ with −θ, we get:
r = 4cos^2(−θ) − 3sin(−θ) + 5(−θ)
r = 4cos^2 θ + 3sinθ − 5θ
Since the two equations are not the same, we can conclude that the polar equation does not have polar symmetry about the pole or the polar axis.
Therefore, the answer is "none".
Victor jumped 6 feet high and then 2 more yards. How many yards did he jump in all?
As per the given variables, Victor jumped a total of 4 yards.
Total yards jumped = 6 feet high
Additional yards = 2
A yard is one linear yard. "Yd" is the yard symbol. The standard of measurement has always been derived from either a natural item or a portion of the human body, such as a foot, an arm's length, or the width of a hand.
Converting the initial jump of 6 feet to yards, as the additional distance given is also in yards.
There are 3 feet in a yard, therefore -
6 feet = 6/3
= 2
Thus, Victor jumped 2 yards initially, and then 2 more yards as given in the problem.
Calculating, the total distance Victor jumped in yards -
= 2 + 2
= 4
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Edgar accumulated $7,000 in credit card debt. If the interest rate is 50% per year and he does not make any payments for 5 years, how much will he owe on this debt in 5 years by compounding continuously?
Using the continuously compounded interest formula, the amount of debt owed after 5 years is $ 8988.18
What is continous compounding interest formula?The continuous compounding interest formula is given by P = Peⁿˣ where
P = final amount after time, t, P' = initial amount n = interest rate and x = timeSince Edgar accumulated $7,000 in credit card debt. If the interest rate is 50% per year and he does not make any payments for 5 years, how much will he owe on this debt in 5 years by compounding continuously? To determine that, we use the continuously compounded interest formula.
Given that
P' = $7000n = 50% per year = 0.5 per year andx = 5 yearsSubstituting the values of the variables into the equation, we have that
P = Peⁿˣ
P = $7000e⁰°⁵ ˣ ⁵
P = $7000e⁰°²⁵
P = $7000(1.28)
P = $ 8988.18
So, the amount of debt owed is $ 8988.18
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what is the sum of 14, 12, 8, and 6
Answer:
Step-by-step explanation:
14+12 = 26+8 = 34 + 6 is 40
the answer is 40.
Answer:
[tex]2\sqrt{10[/tex]
Step-by-step explanation:
Add all the numbers together on your calculator
Find the exact value of each of the following:
a)4sin(π/6)+tan(π/4)
b)cos(4π/3) tan(330°)-sin(3π/4)
The exact values for both equations are as follows:
a) 3
b) -√3/2 - √2/2
How to solvea) In order to ascertain the precise value of 4sin(π/6) + tan(π/4), we must first evaluate the trigonometric functions involved: sin(π/6) = 1/2 and tan(π/4) = 1.
Now, by substituting these values in the equation, we get
4(1/2) + 1 = 2 + 1 = 3.
b) To calculate cos(4π/3) tan(330°) - sin(3π/4), it is necessary to convert 330° into radians: (330 * π) / 180 = 11π/6.
After setting this conversion, evaluate the trigonometric functions present: cos(4π/3) = -1/2, tan(11π/6) = √3, and sin(3π/4) = √2/2.
When these values are used within the equation, the result is (-1/2)(√3) - (√2/2) which equals -√3/2 - √2/2.
Ergo, the exact values for both equations are as follows:
a) 3
b) -√3/2 - √2/2
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Jenny is going to design and sell digital greeting cards through CelebrationStock. The online
platform informs Jenny that, based on market research, she will sell -15x + 120 cards in her
first month if she charges x dollars per card.
CelebrationStock will charge Jenny 30% of the amount she charges per card. So, Jenny will
earn 70% of the amount she charges per card, or 0.7x dollars, in profit.
To the nearest dollar, what is the highest price Jenny can charge per card to earn $125 in
profit in her first month?
Answer:
6
Step-by-step explanation:
To find the highest price Jenny can charge to earn $125 in profit, first write an equation.
total profit = profit per card * number of cards
You want to know when Jenny will earn $125 in profit, and the price per card, x, is the variable. The expression 0.7x represents the profit per card.
125=0.7x(–15x+120)
Now, solve for x. Start by writing the equation in standard form
125=0.7x(–15x+120)
125= –10.5x2+84x
0= –10.5x2+84x–125
Now to solve for x, you can use the quadratic formula with a= – 10.5, b=84, and
So, to the nearest dollar, the highest price Jenny can charge per card to earn $125 in profit is $6.0236 or $6.
What is the slope-intercept form of the equation 3x-5y=2
Answer: y = 3/5x - 2/5
Step-by-step explanation: The slope-intercept form is y = mx+b. Hence, solve for y. 3x - 5y = 2.
Move 5y to the right side and move 2 to the left. 3x - 2 = 5y. Divided 5 for all sides: 3/5x - 2/5 = y. Hence, writing in slope-intercept form is y= mx + b, y = 3/5x - 2/5.
pls help quickly!!
Factor completely
3zy²x + y²x - 12zx - 4x
Select one:
a. x (3z + 1) (y + 2)(y-2)
b. None of these.
c.xy (3z + 1)(y-2)
d. x (3z + 1) (4z-3)
e. x (3z-1) (y + 2)²
Several trusses are needed to build the frame of the shed roof. Each roof truss is 16 inches apart, as measured from the centers of the beam widths.
The roof could be constructed so that the ridgeline of the roof is parallel to the longest dimension of the shed (first picture below) or it could be constructed so that the ridgeline of the roof is parallel to the shortest dimension of the shed (second picture below).
The number of roof trusses that would be needed for the longest length is 2
Calculating the number of roof trusses that would be neededThe longest lengths from the question are given
Longest lengths = 28 and 22
Next, we expand the lengths of the roof trusses
This is to calculate the greatest common factor (GCF) of the lengths
So, we have
28 = 2 * 2 * 7
22 = 2 * 11
Multiplying the common factors gives the GCF
So, we have
GCF = 2
This means that the number of roof trusses that would be needed for the longest length is 2
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PLS HELP ME WITH THIS QUESTION PLS
PLS SHOW YOUR WORKING OUT
The value of p is -3/2, the value of q is -1/(t+1), and the value of r is 2.
How did we get these values?Let the first term of the arithmetic series be a, and the common difference be d = 3. Then, we have:
a = 2t + 1
n-th term = a + (n-1)d = 2t + 1 + 3(n-1) = 3n + (2t - 2)
(Notice that the second equation can be found by substituting the expression for a into the formula for the n-th term and simplifying.)
We also know that the n-th term is given by (14t - 5), so we can equate the two expressions:
3n + (2t - 2) = 14t - 5
Simplifying and solving for n, we get:
n = (12t + 3)/3 = 4t + 1
So, the n-th term can also be expressed as:
3n + (2t - 2) = 3(4t + 1) + (2t - 2) = 14t - 5
Simplifying, we get:
14t - 5 = 14t - 5
This confirms that our expressions for the first term, common difference, and n-th term are all consistent with each other.
Now, we can use the formula for the sum of an arithmetic series to find the sum of the first n terms:
S_n = (n/2)(2a + (n-1)d) = (n/2)(4t + 4t + 1 + 3n - 3) = (3/2)n^2 + (5/2)t - 3n/2 + 1/2
We want to rewrite this expression in the form p(qt - 1)^r. To do this, we can try to complete the square in the n term, like this:
S_n = (3/2)[n^2 - 2n(t+1) + (t+1)^2] + (5/2)t - (3/2)(t+1)^2 + 1/2
S_n = (3/2)[n - (t+1)]^2 - (1/2)(t+1)^2 + (5/2)t + 1/2
Let u = n - (t+1), so that:
S_n = (3/2)u^2 - (1/2)(t+1)^2 + (5/2)t + 1/2
We want to rewrite this in the form p(qt - 1)^r, so let's try to match the terms:
p = -3/2
q = -1/(t+1)
r = 2
Therefore, the value of p is -3/2, the value of q is -1/(t+1), and the value of r is 2.
Note that the assumption that t is greater than 0 was not necessary for the derivation of the sum formula, but it is necessary for the existence of the arithmetic series (since otherwise the first term would be negative).
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The text format of the question in the picture:
22. The first term of an arithmetic series is (2t + 1) where t is > 0 The nth term of this arithmetic series is (14t - 5)
The common difference of the series is 3
The sum of the first n terms of the series can be written as p(qt - 1)^r where p, q and r are integers.
Find the value of p, the value of q and the value of r Show clear algebraic working.
An office manager needs to cover the front face of a rectangular box with a label for shipping. The vertices of the face are (–5, 8), (3, 8), (–5, –4), and (3, –4). What is the area, in square inches, of the label needed to cover the face of the box?
96 in2
48 in2
40 in2
20 in2
The area, in square inches, of the label needed to cover the face of the box is 96 in².
Option A is correct.
How do we calculate?We must first determine the length and breadth of the rectangle before multiplying them together to determine the area of the rectangular face.
The distance between the x-coordinates of two opposite points determines the length of the rectangle:
length equals 3 - (-5) = 8.
The distance between the y-coordinates of the same two opposite points determines the rectangle's width:
width = 8 + (-4) = 12
In conclusion, the rectangle's size is: 8 × 12 = 96 square inches is the area formula.
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