After answering the presented question, we can conclude that The vector expression of equal magnitude and opposite direction to [tex]\vec{PQ}[/tex] is the same arrow but pointing in the opposite direction: QP vector
What is expression?An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression.
Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form.
They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
To find the vector that starts at [tex]P[/tex] [tex](3,3)[/tex] and ends at [tex]Q(-2,2)[/tex] , we can subtract the coordinates of the starting point from the coordinates of the ending point:
[tex]$\vec{PQ} = \begin{pmatrix} -2 \ 2 \end{pmatrix} - \begin{pmatrix} 3 \ 3 \end{pmatrix} = \begin{pmatrix} -5 \ -1 \end{pmatrix}$[/tex]
So the vector that starts at P(3,3) and ends at [tex]Q(-2,2) is $\vec{PQ} = \begin{pmatrix} -5 \ -1 \end{pmatrix}$.[/tex]
To find the vector of equal magnitude and opposite sense to , we can simply multiply [tex]$\vec{PQ}$[/tex] by [tex]-1:[/tex]
[tex]$-\vec{PQ} = -1 \begin{pmatrix} -5 \ -1 \end{pmatrix} = \begin{pmatrix} 5 \ 1 \end{pmatrix}$[/tex]
So the vector of equal magnitude and opposite sense to [tex]$\vec{PQ}$[/tex] is [tex]$\begin{pmatrix} 5 \ 1 \end{pmatrix}$.[/tex]
Geometrically, we can represent the vectors graphic[tex]$\vec{PQ}$[/tex]ally by drawing them as directed line segments on a coordinate plane. The vector that starts at [tex]P(3,3)[/tex] and ends at [tex]Q(-2,2)[/tex] is represented by the line segment connecting [tex]P[/tex] to [tex]Q[/tex].
Therefore, The vector of equal magnitude and opposite sense to [tex]$\vec{PQ}$[/tex][tex]$\vec{PQ}$[/tex] is represented by the line segment starting at [tex]Q[/tex] and ending at the point R, which is [tex]5[/tex] units to the right and [tex]1[/tex] unit up from [tex]Q[/tex].
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Ava is going on holiday with Fly Away airlines. The maximum weight her suitcase can be is 2020 kg.
When empty her suitcase weighs 33 kg.
The clothes she plans on taking have a combined weight of 55 kg.
Her electrical accessories have a combined weight of 44 kg.
She is also taking 55 hardback books, which each weigh 720720 g.
Finally, the toiletries she is taking have a combined weight of 46004600 g.
How much over the maximum weight will Ava's suitcase be? Give your answer in grams.
As a result, Ava's luggage will weigh 123622200 grams more than the permitted maximum.
What exactly is weight?Weight is the force of gravity that pulls objects toward the core of the Earth. The resulting force that pulls a substance toward Earth is known as gravity. In contrast to gravity force, which occurs among any two masses, this only occurs between Earth as well as a mass.
First, we need to convert all the weights to grams, since the weight limit is given in kilograms and the weights of clothes, electrical accessories, and toiletries are given in grams.
Maximum weight limit = 2020 kg = 2020000 g
Weight of empty suitcase = 33 kg = 33000 g
Weight of clothes = 55 kg = 55000 g
Weight of electrical accessories = 44 kg = 44000 g
Weight of 55 hardback books = 55 x 720720 g = 39639600 g
Weight of toiletries = 46004600 g
Total weight of suitcase and contents = 33000 + 55000 + 44000 + 39639600 + 46004600 = 125642200 g
Amount over maximum weight limit = total weight - maximum weight limit = 125642200 - 2020000 = 123622200 g
Therefore, Ava's suitcase will be over the maximum weight limit by 123622200 grams.
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Question 7
Suppose the graph represents the scale drawing for a fence that Tara is building for a new city dog park. Each unit on the graph represents 12 yards. After studying the scale drawing, Tara decides to build a fence that encloses a smaller area. If Tara dilates rectangle ABCD by a scale factor of 0.75, and fencing costs $6.39 per yard, how much will she spend on fencing?
The total cost to fence the rectangular yard is given as follows:
$1,610.28.
How to obtain the perimeter of a triangle?The perimeter of a rectangle is the total distance around its outer boundary. To find the perimeter of a rectangle, you need to add up the lengths of all four sides.
If a rectangle has length l and width w, then its perimeter P is given by the equation presented as follows:
P = 2l + 2w
Considering the scale factor of 0.75, the distance represented by each unit on the graph is given as follows:
0.75 x 12 = 9 yards.
Hence the dimensions of the rectangle are given as follows:
Length of 8 x 9 = 72 yards.Width of 6 x 9 = 54 yards.The perimeter of the fence is then given as follows:
2 x (72 + 54) = 252 yards.
It costs $6.39 per yard, hence the total cost to fence the yard is given as follows:
252 x 6.39 = $1,610.28.
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[tex]8x ^{2} y + 12xy - 16xz[/tex]
Factorize the expression
The factοrs οf the expressiοn is 4x(2xy+3y-4z).
What is factοrizatiοn?Tο factοrise an algebraic statement, we first identify the terms' highest cοmmοn factοrs and then arrange the terms intο grοups in accοrdance with thοse grοups. In plain English, factοrizatiοn is the prοcess thrοugh which an algebraic expressiοn gets expanded in the οppοsite directiοn.
Here the given expressiοn is ,
=> [tex]8x^2y+12xy-16xz[/tex]
Nοw factοrizing the given expressiοn then,
=> 4×2×x×x×y+4×3×x×y-4×4×x×z
=> 4x(2xy+3y-4z)
Hence the factοrs οf the expressiοn is 4x(2xy+3y-4z).
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work out the product of 1 and 3/3 and 1 and 2/6 give your answer in its simplest form
Answer:
To multiply 1 3/3 by 1 2/6, we can first convert these mixed numbers to improper fractions, then multiply them together, and finally simplify the result to its simplest form.
1 3/3 can be written as 4/3 (since 1 whole and 3/3 is equivalent to 4/3)
1 2/6 can be written as 8/6 (since 1 whole and 2/6 is equivalent to 8/6)
Now, we can multiply these two fractions together:
4/3 x 8/6 = (4 x 8) / (3 x 6) = 32/18
To simplify this fraction, we can divide the numerator and denominator by their greatest common factor, which is 2:
32/18 = (2 x 16) / (2 x 9) = 16/9
Therefore, the product of 1 3/3 and 1 2/6 is 16/9, or 1 and 7/9 in mixed number form, in its simplest form.
Determine which expression is equivalent to
3
4
−
x
(
1
2
−
5
8
)
+
(
−
3
8
x
)
4
3
−x(
2
1
−
8
5
)+(−
8
3
x).
A
−34x−
4
3
x
B
12x
2
1
x
C
18−78x
8
1
−
8
7
x
D
34−14x
4
3
−
4
1
x
Answer: We can simplify the expression step by step:
3/4 − x(1/2 − 5/8) + (−3/8)x
3/4 − x(-1/8) + (−3/8)x
3/4 + x/8 − 3/8x
Multiplying everything by 8 to get rid of the fractions:
6 − x + (−3x)
6 − 4x
Therefore, the equivalent expression is D) 34 - 14x / (4/3).
Step-by-step explanation:
The entry fee to East Egg Hunt Event is $7.00. Each ride requires a ticket that cost $2.00. Cassie spent a total of $45.00. How many tickets Cassie Purchase?
Answer: 19 tickets
Step-by-step explanation: $45 - $7 = 38 38 divided by $2 = 19 tickets
Find the length of side x to the nearest tenth.
Given:-
A right angled triangle is given to us .Two angles are 60° and 30° , longest side is x and another side is "2" .To find:-
The value of x .Answer:-
In the given right angled triangle, we may use the trigonometric ratios. We can see that the measure of the longest side is "x" which is hypotenuse and it needs to be find out. The perpendicular in this case is "2" .
We may use the ratio of sine here as , we know that in any right angled triangle,
[tex]\implies\sin\theta =\dfrac{p}{h} \\[/tex]
And here , p = 2 and h = x , so on substituting the respective values, we have;
[tex]\implies \sin\theta = \dfrac{2}{x} \\[/tex]
Again here angle is 60° . So , we have;
[tex]\implies \sin60^o =\dfrac{2}{x} \\[/tex]
The measure of sin45° is √3/2 , so on substituting this we have;
[tex]\implies \dfrac{\sqrt3}{2}=\dfrac{2}{x} \\[/tex]
[tex]\implies x =\dfrac{2\cdot 2}{\sqrt3}\\[/tex]
Value of √3 is approximately 1.732 . So we have;
[tex]\implies x =\dfrac{4}{1.732} \\[/tex]
[tex]\implies \underline{\underline{\red{\quad x = 2.31\quad }}}\\[/tex]
Hence the value of x is 2.31 .
Answer:
The length of side x to the nearest tenth is 2.3.
Step-by-step explanation:
From inspection of the given right triangle, we can see that the interior angles are 30°, 60° and 90°. Therefore, this triangle is a 30-60-90 triangle.
A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : √3 : 2. Therefore, the formula for the ratio of the sides is b: b√3 : 2b where:
b is the shortest side opposite the 30° angle.b√3 is the side opposite the 60° angle.2b is the longest side (hypotenuse) opposite the right angle.We have been given the side opposite the 60° angle, so:
[tex]\implies b\sqrt{3}=2[/tex]
Solve for b by dividing both sides of the equation by √3:
[tex]\implies b=\dfrac{2}{\sqrt{3}}[/tex]
The side labelled "x" is the hypotenuse, so:
[tex]\implies x=2b[/tex]
Substitute the found value of b into the equation for x:
[tex]\implies x=2 \cdot \dfrac{2}{\sqrt{3}}[/tex]
[tex]\implies x=\dfrac{4}{\sqrt{3}}[/tex]
[tex]\implies x=2.30940107...[/tex]
[tex]\implies x=2.3\; \sf (nearest\;tenth)[/tex]
Therefore, the length of side x to the nearest tenth is 2.3.
HELPPP ASAP IM AWARDING 80 POINTS!!!!
A cylindrical candle has a radius of 4 cm and a height of 10.4 cm.
What is the exact surface area of this candle?
32.0π cm²
83.2π cm²
91.2π cm²
115.2π cm²
Answer:
D) 115.2π cm².
Step-by-step explanation:
The surface area of a cylinder can be calculated using the formula:
Surface Area = 2πr² + 2πrh
where r is the radius and h is the height of the cylinder.
In this case, r = 4 cm and h = 10.4 cm. Substituting these values in the formula, we get:
Surface Area = 2π(4)² + 2π(4)(10.4)
Surface Area = 2π(16) + 2π(41.6)
Surface Area = 32π + 83.2π
Surface Area = 115.2π
Therefore, the exact surface area of the candle is 115.2π cm².
The answer is (D) 115.2π cm².
Answer: The answer is D, 115.2π cm²
Step-by-step explanation: When we use the formula of 2πrh+2πr2=2·π·4·10.4+2·π·42 to get the surface area, which equals 361.91
We can divide this by pi to get 115.2π cm²
Hope this helped!
I need some help please
Answer:
question where is the question?
Use the distributive property to multiply the expression 9(7m+2)
Answer:
63m+18
Step-by-step explanation:
9*7m is 63m and 9*2 is 18
Combine them and you get 63m+18!
Solve for x. Round to the nearest tenth.
x =
Roderick earns an interest of $30 per year for every $500 deposited in his savings account calculate the interest earned if he has $1,250 in his account
Answer:
1250/500
=2.5
Multiplied by interest rate (30)
2.5 times 30
= $75.00
Step-by-step explanation:
Hope I helped.
BRAINLIEST PLEASE!!!Roderick earns an interest of $30 per year for every $500 deposited in his savings account. This means that the interest rate per $500 deposit is:Interest rate per $500 = $30/$500 = 0.06 or 6%To calculate the interest earned on Roderick's savings account, we first need to determine how many $500 deposits he has. We can do this by dividing his total savings by $500:Number of $500 deposits = $1,250/$500 = 2.5
the sum of two numbers is 30. The difference between the two numbers is 15. what are the two numbers?
ALGEBRA HW!! I WILL GIVE BRAINLYEST
please answer both questions parts.
The table of original value and rounded values are
x y
0.2 0
0.5 1
0.9 1
1.08 1
1.49 1
1.72 2
2.3 2
2.94 3
The graph is attached
How to make the graphThe graph is made in a cartesian coordinate by tracing the point of intersection of the two points
The table is represented as ordered pair as (original value, rounded value) for the given x and y values:
(0.2, 0), (0.5, 1), (0.9, 1), (1.08, 1), (1.49, 1), (1.72, 2), (2.3, 2), (2.94, 3)
The graph is a scattered plot and its attached
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Express using algebra.
24% of z
Answer: 0.24z
Step-by-step explanation: If you make 24% a decimal you will get 0.24. Then you make your equation 0.24z or 0.24 x z .
Solve the right triangle (tan,sin,cos)
The value of the trigonometric functions for the right triangle is tan(29) = 0.518. cos(29) = 0.838. sin (29) = 0.435.
What are basic trigonometric functions?The sine, cosine, and tangent trigonometric ratios are the three most important ones. These are their definitions:
Sine (sin) is the proportion of a right triangle's hypotenuse to the length of the side that faces an angle.
The length of the side next to an angle in a right triangle divided by the length of the hypotenuse is known as the cosine (cos).
In a right triangle, the tangent (tan) is the ratio between the lengths of the sides that face each other and the angle.
These ratios are used in trigonometry to connect the angles and sides of right triangles, and they may be used to a number of triangle- and other geometric shape-related problems.
In the given triangle using the sum of interior angle of triangle we have:
180 - 90 - 29 = 61
The measure of the third angle is 61 degrees.
Now, tan(61) = XZ/XY
XZ = XY * tan(61)
XZ = 18 * 1.927 = 34.686
Now, using the Pythagoras theorem we have:
ZY² = XZ² + XY²
ZY² = 34.686² + 18²
ZY² = 1712.3996
ZY = 41.38
Now, the value of:
sin(29) = opposite/hypotenuse = XY/ZY = 18/41.388 = 0.435
cos(29) = adjacent/hypotenuse = XZ/ZY = 34.686/41.388 = 0.838
tan(29) = opposite/adjacent = XY/XZ = 18/34.686 = 0.518
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what is the perimeter for a 141 by 234
Step-by-step explanation:
the width is 23.5ft and the length is 47ft
A company is focus testing a new type of fruit drink. The focus group is 47% male. Of the responses, 40% of the males and 54% of the females said they would buy the fruit drink. Find the ratio of males who would buy the drink to females who would buy the drink. Round to the nearest ten thousandth if necessary.
Answer: the ratio of males who would buy the drink to females who would buy the drink is approximately 0.6560.
Step-by-step explanation:
Let's assume that there are 100 people in the focus group. Then, the number of males in the focus group is 47 and the number of females is 53.
Out of 47 males, 40% said they would buy the fruit drink, which is 0.4 x 47 = 18.8 males (rounded to the nearest whole number). Out of 53 females, 54% said they would buy the fruit drink, which is 0.54 x 53 = 28.62 females (rounded to the nearest whole number).
The ratio of males who would buy the drink to females who would buy the drink is:
18.8/28.62 = 0.6560 (rounded to the nearest ten-thousandth)
Therefore, the ratio of males who would buy the drink to females who would buy the drink is approximately 0.6560.
6 2/5 subtract 2 9/10
Answer: 9 3/10
Step-by-step explanation:
6 + 2/5 + 2 + 9/10= 6 + 2 = 8 = 2/5 + 9/10= 4/10 + 9/10= 13/10= 1 3/10= 8 + 1 + 3/10= 9 3/10
A dilation centered at the origin maps the point (4,6) to the point (5/2,15/4). What is the scale factor of the dilation
We may be confident that this is the correct scale factor because both equation equations yield the same value of k. As a result, the dilatation has a scale factor of 5/8 and is centered at the origin.
What is equation?An equation is a statement in mathematics that states the equality of two expressions. An equation has two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine which variable(s) must be changed in order for the equation to be true. Simple or complex equations, regular or nonlinear equations, and equations with one or more elements are all possible. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are employed in a variety of mathematical disciplines, including algebra, calculus, and geometry.
Let (x,y) be a point on the plane and k be the dilation scale factor centred at the origin. The image of (x,y) under dilation is thus given by (kx, ky).
The dilation is given as (4,6) to (5/2,15/4). That is to say:
[tex]k(4) = 5/2 \sk(6) = 15/4\\k = 5/8 \sk = 5/8[/tex]
We may be confident that this is the correct scale factor because both equations yield the same value of k. As a result, the dilatation has a scale factor of 5/8 and is centered at the origin.
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Please Help! A picture is 60cm wide and 1.8 meter long.The ratio of its width to its perimeter in the lowest term is?
Answer:
60:61.8 OR 10:10.3
Step-by-step explanation:
Cant be simplified - unless your in advanced classes. If so
10:10.3
Answer:
Step-by-step explanation:
1/3 or 0.3 or 33.333333% or 3^-1 or 3.333333 x 10^-1
Pls answer today and fast!!!! Use the tools below to make a triangle with angle measures or 60 degrees, 40 degrees, and 80 degrees.
An angle is a geometric figure formed by two rays or line segments that share a common endpoint, called the vertex. Angles are measured in degrees or radians and are typically denoted by symbol ∠ followed by the name of the vertex, like ∠ABC.
What is the Angle?The size of angle is determined by amount of rotation needed to bring one of rays or line segments into coincidence with others.
Angles can be acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (exactly 180 degrees), or reflex (greater than 180 degrees).
Angles are fundamental to geometry and have many applications in physics, engineering, and other fields.
This is because the sum of the angles in a triangle must always be 180°, and 40° + 60° + 80° = 180°.
However, the angles do not satisfy the conditions of the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Therefore, It is not possible to construct a triangle with angle measures of 40°, 60°, and 80°.
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Ruggiero Brothers Oil has an R85 000 liability it must pay four years from today. The company is opening a savings account, so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today, and then deposit an additional R16 000 each year for the next four years, starting one year from today. The account pays a 6% rate of return. How much does the firm need to deposit today?
Answer:
Step-by-step explanation:
To determine the amount that Buggiero Brothers Oil must deposit today in order to have enough money to pay the R85 000 liability four years from today, we can use the present value formula:
Present Value (PV) = Future Value (FV) / (1 + r)^n
where:
- FV is the future value, which is R85 000
- r is the annual interest rate, which is 6%
- n is the number of years until the liability needs to be paid, which is 4
To calculate the future value of the annual deposits of R16 000, we can use the future value of an annuity formula:
FV = PMT x [(1 + r)^n - 1] / r
where:
- PMT is the annuity payment, which is R16 000
- r is the annual interest rate, which is 6%
- n is the number of years of the annuity, which is 3 (since the first payment is made one year from today)
Plugging in the numbers:
FV = R16 000 x [(1 + 0.06)^3 - 1] / 0.06
FV = R61 719.56
Therefore, the total future value that Buggiero Brothers Oil will have in four years, including the initial deposit and the annual payments, will be:
FV = R85 000 + R61 719.56
FV = R146 719.56
Plugging in the numbers to the present value formula:
PV = R146 719.56 / (1 + 0.06)^4
PV = R116 442.12
Thus, Buggiero Brothers Oil needs to deposit R116 442.12 today to have enough money to pay the R85 000 liability four years from today, assuming a 6% rate of return.
Find the value of angle ZOX
using the image below
Answer: 64°
Step-by-step explanation:
Had this problem and got it right
what is the successor of -34
The successor of -34 is -33 using the formula "n+1".
What is a successor?A phrase that follows or is right after a specific number, term, or value is known as a successor.
The successor of n is "n+1" if n is a number (and n belongs to any whole number).
The terms just after, immediately after, and next number/next value are also used to describe a successor.
As is common knowledge, integers are collections of numbers that range from negative infinity to positive infinity.
The integers are.........., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,.................. The preceding and following numbers will also be negative integers if the provided number is a negative integer.
So, the successor of -34:
= -34 + n
= -34 + 1
= - 33
Therefore, the successor of -34 is -33 using the formula "n+1".
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Cyndi is making a mixture of cashews and peanuts the cashews are $7 per pound and $3 a pound for peanuts. Cyndi wants 20 pounds of the mixture which will cost $5.40 per pound .. what's the system and how much would she need to equal $108
The amounts of each substance needed to obtain a mixture of 20 pounds at a price of $5.4 per pound is given as follows:
Cashews: 12 pounds.Peanuts: 8 pounds.How to obtain the amounts?The amounts are obtained by a system of equations, for which the variables are given as follows:
Variable x: amount of cashews.Variable y: amount of peanuts.The mixture has a total of 20 pounds, hence:
x + y = 20.
y = 20 - x.
The total cost of the mixture is of $108, as 108/20 = 5.4, hence:
7x + 3y = 108
Replacing the second equation into the first, the value of x is given as follows:
7x + 3(20 - x) = 108
4x = 48
x = 12.
Then the value of y is given as follows:
y = 20 - 12
y = 8.
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Which measurements could create more than one triangle?
A.
A triangle with sides measuring 50 mm and 35 mm and a nonincluded angle measuring 25°
B.
A triangle with sides measuring 5 cm, 10 cm, and 15 cm
C.
A triangle with sides measuring 8 cm and 12 cm and an included angle measuring 85°
D.
A triangle with sides measuring 5 inches, 7 inches, and 9 inches
Answer:
D. A triangle with sides measuring 5 inches, 7 inches, and 9 inches. This is because the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In option A, the side lengths satisfy this condition since 50 + 35 > 25. In option B, the side lengths do not satisfy this condition since 5 + 10 < 15. In option C, the side lengths satisfy this condition since 8 + 12 > 85. In option D, the side lengths do not satisfy this condition since 5 + 7 < 9, 7 + 9 > 5, and 5 + 9 > 7.
Your firm is considering adding a product line. The accounting department has determined that the cost
function for this new product will be C(x) = 55x + 3500 and the revenue function will be R(x) = 80x,
where x is the number of units sold. Additionally, the sales department has determined that you reasonably
can expect to sell around 164 units. You must decide whether to go ahead with the new product line.
Find the break-even quantity:
Find the profit function: P(x) =
Make your decision:
O Proceed with the product line: the products are profitable and we can reasonably expect to meet
our break-even quantity.
Cancel the product line: the quantity needed to break even is more than our firm can reasonably
expect to sell.
O Cancel the product line: producing these products is not profitable.
Submit Question
the profit function is positive, producing 164 units of the new product line would yield a profit of $600.
We should proceed with the product line since it is profitable and we can reasonably expect to meet our break-even quantity.
To find the break-even quantity, we need to set the cost function equal to the revenue function and solve for x:
C(x) = R(x)
55x + 3500 = 80x
25x = 3500
x = 140
Therefore, the break-even quantity is 140 units.
To find the profit function, we subtract the cost function from the revenue function:
P(x) = R(x) - C(x)
P(x) = 80x - (55x + 3500)
P(x) = 25x - 3500
Now we can evaluate the profit function at different values of x to see if producing these products is profitable or not.
If we plug in x = 164, the expected sales quantity, we get:
P(164) = 25(164) - 3500
P(164) = 4100 - 3500
P(164) = 600
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Help asap will give brainiest
Use the image to determine the line of reflection.
4
3
2
1
0
?
Ty
5
-6
-7
-8
-9
-10
1
2
B
A
A
3₂
Α',
В'
4
E
5
E
6
с
Reflection across x = 6
D'
Reflection across the x-axis
Reflection across y = -3
C₁
Reflection across the y-axis
Answer: D
Step-by-step explanation: so if we look at the picture, youll notice 2 things right off the bat, firstly, the top shape goes over the y axis, so that wont work, secondly, the shapes are on the same side of the x axis (the positive side) so that wouldnt work, the last thing we now have to look at is making the shapes even, essentially if you were to flip one shape over a certain distance, the mirrored shape needs to be the same distance you flipped the first shape. In this case, if we flip shape 1, over -3, the other shape will be 6 spaces away from the 1st shape, because you need to also move the second shape 3 spaces away from where you flipped the first shape.
side note: reflecting over the x axis or y axis, means the line of reflection is equal to 0 on either the y axis or x axis
To try to make this less confusing, another way to find the reflection is by evenly counting the shapes to the middle, how-ever many squares/spaces it takes for both shapes to reach the center of the two in this case, is how many spaces they are reflected.
The image undergoes a reflection at y=-3, Option D is correct.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.
Reflections are congruence transformations that generate a mirror image of an object, without changing its size or shape.
In the given figure the above image is original and it is flipped to form the image which is below the x axis.
In this case, if we flip shape 1, over -3, the other shape will be 6 spaces away from the 1st shape, because you need to also move the second shape 3 spaces away from where you flipped the first shape.
Hence, the image undergoes a reflection over y axis which is at y=-3.
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The following data indicate the scores of some students in a competition. Which a box plot represents the data?
100 points!!!!!
The correct answer to the given question is graph D
How to solveGiven a set of data points, we are tasked with identifying the correct box plot representation.
We begin by arranging the data in ascending order, which gives us 12, 17, 21, 23, 24, 28, and 29 points.
Next, we use the properties of a box plot to eliminate incorrect representations.
The left end of the whisker should correspond to the smallest data point, and the right end to the largest.
Among the given graphs, only one satisfies this condition.
The middle point is identified as the fourth data point, which is 23.
Finally, we determine the lower and upper lines of the box to be 17 and 28, respectively.
The only graph that satisfies all conditions is graph D.
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