The area of the rectangle is 273 square units.
The task is to find the area of a rectangle where the width of the rectangle is given as 13, and the area as a function of x is provided as A(x) = 2x² - 5x.
To find the area, we need the value of x that corresponds to the width. Since the width is 13, we set x as 13 and substitute it into the area function.
A(13) = 2(13)² - 5(13) = 2(169) - 65 = 338 - 65 = 273 square units.
Thus, the area of the rectangle is 273 square units.
Find the perimeter and the area of the polygon with the given vertices. J (1,2), K (7,2), L (7,8), M (1,8)
Answer : The perimeter and the area of the polygon with the given vertices is, 24 unit and 36 unit² respectively.
Step-by-step explanation :
First we have to calculate the distance of JK, KL, LM and MJ.
Using distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where,
d = distance between the two coordinates
x and y are the coordinates.
To calculate the distance of JK:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{(7-1)^2+(2-2)^2}[/tex]
[tex]d=\sqrt{(6)^2+(0)^2}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]d=6[/tex]
To calculate the distance of KL:
[tex]d=\sqrt{(x_3-x_2)^2+(y_3-y_2)^2}[/tex]
[tex]d=\sqrt{(7-7)^2+(8-2)^2}[/tex]
[tex]d=\sqrt{(0)^2+(6)^2}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]d=6[/tex]
To calculate the distance of LM:
[tex]d=\sqrt{(x_4-x_3)^2+(y_4-y_3)^2}[/tex]
[tex]d=\sqrt{(1-7)^2+(8-8)^2}[/tex]
[tex]d=\sqrt{(-6)^2+(0)^2}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]d=6[/tex]
To calculate the distance of MJ:
[tex]d=\sqrt{(x_4-x_1)^2+(y_4-y_1)^2}[/tex]
[tex]d=\sqrt{(1-1)^2+(8-2)^2}[/tex]
[tex]d=\sqrt{(0)^2+(6)^2}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]d=6[/tex]
The distance of JK, KL, LM and MJ is, 6, 6, 6 and 6.
Now we have to calculate the perimeter of the polygon.
Perimeter of polygon = JK + KL + LM + MJ
Perimeter of polygon = 6 + 6 + 6 + 6
Perimeter of polygon = 24 unit.
Now we have to calculate the area of polygon.
As the distance between the coordinates are equal that means the geometry will be square because in square the all four sides are equal.
Now we have to calculate the area of polygon by using area of square formula.
Area of polygon = Area of square = (side)²
Given: Side = 6
Area of polygon = Area of square = (6)²
Area of polygon = Area of square = 36 unit²
Thus, the area of polygon is, 36 unit²
Rhett decides to build a square room for his movie and music collection. If the area of the room is 9x^2 − 6x + 1 square feet, what is the length of one side of the room?
(3x + 1) feet
(9x − 1) feet
(3x − 1) feet
(9x + 1) feet
Which statement is true about the function f(x)=-√-x
a.The domain of the function is all negative real numbers.
b.The range of the function is all positive real numbers.
c.The domain and range of the function have opposite signs.
d.The domain and range of the function are the same.
Answer: D.The domain and range of the function are the same.
Step-by-step explanation: Given function f(x)=-√-x.
The given function is a square root function and we have minus sign in front of x inside square root.
A square root always defined for positive values or 0.
In order to get a positive number or 0 inside square root, let us solve the inequality:
[tex]-x\geq 0[/tex]
On dividing both sides by -1, the inequality sign would get flip and we get
Domain: [tex]x \leq 0.[/tex]We can see that we have a negative sign in front of square root. So, the value of f(x) would be always a negative number or 0.
Therefore, range would also be :[tex]x \leq 0.[/tex].Therefore, correct option is D option.Answer:
hi thereee, the answer to this question is
d. the domain and range of the function are the same
hope this helps :)
have a good day!
Step-by-step explanation:
i just took the test
Find the side of a square whose diagonal is of the given measure. Given = 12 square root 2ft.
Solve for all values of r 3r/r-5 - 2/r+3=r/r+3
A zoo has 15 emperor penguins. The emperor penguins make up 30% of all the penguins at the zoo. How many penguins live at the zoo?
Answer:
30% = 15
1% = 15/30
= 1/2
100% = 100 x 1/2
= 50
there are 50 penguins in the zoo.
a rock is thrown from the top of a tall building. the distance, in feet, between the rock and the ground x seconds after it is thrown is given by f(x)=-16x62-4x+382 How long after the rock is thrown does it hit the ground
It takes approximately 5.0 seconds for the rock to hit the ground after it is thrown.
Explanation:To find the time when the rock hits the ground, we need to find the value of x when the distance between the rock and the ground is 0. In the given equation, f(x) = -16x^2 - 4x + 382, where f(x) represents the distance between the rock and the ground. We can set this equation equal to 0 and solve for x:
-16x^2 - 4x + 382 = 0
This is a quadratic equation. We can use the quadratic formula to solve for x:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Plugging in the values from the equation, we get:
x = (-(-4) ± sqrt((-4)^2 - 4(-16)(382))) / (2(-16))
This simplifies to:
x = (4 ± sqrt(16 + 24512)) / (-32)
x = (4 ± sqrt(24528)) / (-32)
x ≈ (-4 ± 156.49) / (-32)
Since we're dealing with time, the negative value doesn't make sense in this context. So, we take the positive root:
x ≈ (4 + 156.49) / (-32)
x ≈ 160.49 / (-32)
x ≈ -5.0
Therefore, it takes approximately 5.0 seconds for the rock to hit the ground after it is thrown.
please help ASAP
the vertices of pqr are p(-3, 8), q(-6, -4), and r(1, 1). if you reflect pqr across the x-axis, what will be the coordinates of the vertices of the image p'q'r'?
In which way do REITs resemble mutual friends
REITs resemble mutual funds in that they both allow investors to pool their money to invest in a diversified portfolio. REITs consist of a variety of real estate properties, while mutual funds consist of stocks or bonds. Both provide individuals with an opportunity to invest in a professionally managed portfolio.
Explanation:REITs (Real Estate Investment Trusts) resemble mutual funds in that they both allow investors to pool their money together to invest in a diversified portfolio. Just as mutual funds consist of a variety of stocks or bonds from different companies, REITs consist of a variety of real estate properties such as office buildings, apartments, and shopping centers. Investors buy shares of a REIT and receive a return based on the performance of the real estate portfolio as a whole. Both REITs and mutual funds provide individuals with an opportunity to invest in a professionally managed portfolio without having to directly invest in individual stocks or properties.
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A grocery bag can withstand 300 n of force before it rips apart. how many kilograms of apples can it safely hold?
The grocery bag can handle roughly 30.6 kg of apples safely. This conclusion is drawn based on the concept of forces, weight, and the Physics formula for calculating weight.
Explanation:The subject field for this question is Physics and it relates to the High School level. This question is about the concept in physics known as force, in particular, the force related to weight and how it pertains to carrying capacity.
In physics, force is typically given in units of Newton's (N), named after Sir Isaac Newton. The force exerted by a mass due to gravity is its weight. Specifically, weight is calculated through the formula F = m * g, where F is the force (weight), m is the mass in kilograms, and g is the acceleration due to gravity in m/s² (approximately 9.8 m/s² on Earth).
To find out how many kilograms of apples a bag can hold before it rips, we can use this formula and solve for m (mass). Given that the force the bag can withstand before ripping is 300 N, we have 300 N = m * 9.8 m/s². Isolating m gives us m = 300 N / 9.8 m/s² which is approximately 30.6 kg. Therefore, the bag can safely hold around 30.6 kg of apples.
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Help me in this plz plz
(35 points) Fred played golf and for the past 5 times had a score of 72, 79, 73, 81, and 70. What was his average score? A. 75 B. 77 C. 85 D. 375
The average score of Fred is 75.
What is the average value?The common cost of a characteristic over language is described to be crucial of the feature divided by way of the period of the interval.
calculation:-
a score of 72, 79, 73, 81, and 70.
nu,ber of times = 5
total score = 72+79+ 73+ 81+ 70.
= 375
average score = 375/5
= 75
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The quotient property of radicals requires the indices of the radicals to be the same. Does this mean that it is not possible to write es002-1.jpg as a single radical? Explain.
The radicands are powers of the same base, so they can be written using rational exponents.
Simplify the quotient of the exponential expressions by getting a common denominator and subtracting exponents.
The simplified expression is the 4th root of y
The expression can be written as a single radical by covertong the expression to a rational format such that both the denominator and numerator have the same base as y¼
Numerator = The 4th root of y³ = y¾Denominator = squareroot of y = y½Using indices :
Division sign signifies the powers should be subtracted[tex] \frac{y¾}{y½} = y^{¾ - ½} = y¼[/tex]
Therefore, the expression can be written as a single radical thus y¼
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As a part of their weather unit, Anoki’s science class took a hot air balloon ride. As they passed over a fenced field, the angle of depression of the closer side of the fence was 32°, and the angle of depression of the farther side of the fence was 27°. If the height of the balloon was 800 feet, estimate the width of the field. Round your answer to the nearest foot. 2016_01_25_17_23_501.png The width of the field is about feet
True or false ? A car taking a turn at a constant speed is accelerating.
(60 POINTS)
The measure of angle E, the angle of elevation from point A to point B, is 5(x-2) degrees. The measure of D, the angle of depression from point B to point A is (x + 14) degrees. Find the measure of each angle.
Answer:
measure of angle E equals 20 degrees, measure of angle D equals 20 degrees
Why must bowhunters use broadhead points when hunting big game?
Bowhunters use broadhead points when hunting big game for their greater cutting surface, penetration, lethality, blood trails, terminal performance, and ethical considerations.
We have,
Bowhunters use broadhead points when hunting big game for several reasons:
- Greater Cutting Surface
Broadhead points have a larger cutting surface area compared to target or field points.
This increased surface area allows for more effective cutting and penetration, which is essential when hunting big game animals that have tough hides, muscles, and bones.
- Penetration and Lethality:
Big game animals often require deep penetration to reach vital organs for an ethical and humane kill.
Broadheads are designed to maximize penetration by creating large wound channels and causing significant tissue damage.
This helps ensure quick and effective kills, minimizing suffering for the animal.
- Blood Trails
- Terminal Performance
- Ethical Considerations
Thus,
Bowhunters use broadhead points when hunting big game for their greater cutting surface, penetration, lethality, blood trails, terminal performance, and ethical considerations.
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Choose the correct simplification of (7x3y3)2.
14x6y6
49x5y5
49x6y6
14x5y5
The correct simplification of (7x3y3)2 = 49x6y6
What is simplification?Simplification is defined as the removal of parentheses in an algebraic expressions in such a way that it would be understood.
From the expression given,
(7x3y3)2 = 2 × 7x × 3y × 3
= 49x6y6
Therefore, the correct simplification of (7x3y3)2 = 49x6y6
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Find the length of both arc AB and arc APB, where
an angle with measure between 90 and 180 is called
An angle with measure between 90° and 180° is called obtuse angle.
The definition of an obtuse angle in geometry states that an angle whose measure is greater than 90° and less than 180° is called an obtuse angle.
So, if the angle measure between 90 degree and 180 degree is obtuse angle.
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Item 20The width of a rectangular room is 60% of its length. The length of the room is 10 feet. What is the area of the room?
Four sides of a octagon each measure 12 cm. The perimeter of the octagon is 70 cm. What is the length of each remaining side, if each remaining side has the same length?
Answer:
It would be 5.5 cm
Step-by-step explanation:
Find the distance between the two points. Round to the nearest tenth if necessary. (10, –4), (5, 8)
169
7
13
16
Two boats on opposite banks of a river start moving towards each other. They first pass each other 1400 meters from one bank. They each continue to the opposite bank, immediately turn around and start back to the other bank. When they pass each other a second time, they are 600 meters from the other bank. We assume that each boat travels at a constant speed all along the journey. Find the width of the river?
Let xx be the width of the river. It is given that, when they have met the first time, boat11 has travelled 14001400 m and boat22, (1400−x)(1400−x) metres.
When they meet for the second time, boat11 has travelled 600+(x−1400)=(x−800)600+(x−1400)=(x−800) m, and boat22, 1400+(x−600)=(x+800)1400+(x−600)=(x+800) m.
Note that, the relationship of the distances each traveled, is the same to both meetings. Thus,
14001400−x=x−800x+80014001400−x=x−800x+800⇒x=?⇒x=?Hope you can take it from here. What transformations change the graph F(x) to the graph g(x)
f(x) = 3x^2
G(x) = 9x^2-4
A. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated DOWN 4 units
B. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated UP 4 units
C. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 1/3 and translated up 4 units
Final answer:
The transformation from f(x) = 3x^2 to g(x) = 9x^2 - 4 includes a vertical stretch by a factor of 3 followed by a vertical translation down by 4 units.
Explanation:
The transformations that change the graph f(x) = 3x2 to the graph g(x) = 9x2 - 4 involve two steps:
A vertical stretch by a factor of 3, which is achieved by multiplying the original function f(x) by 3, yielding 9x2. This transformation changes the original coefficient (3) in front of x2 to a new coefficient (9).
A vertical translation down by 4 units, which is represented by subtracting 4 from the result of the stretch transformation.
Therefore, the correct answer to the student's question is:
A. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated DOWN 4 units.
Combine like terms to simlify the expression: 2/5k—3/5+1/10k
Mr burn's class is taking
a. field trip to the planetarium. The trip will cost $27 for each student. There are 18 students in his class.Use compatible numbers to estimate the total cost of field trip
Answer:
600
Step-by-step explanation:
The answer is 600
How would you solve this?
Choose the option that correctly completes the statement.
The sum of the measures of the interior angles of a quadrilateral is _____ degrees.
270
180
90
360
Answer:
D. 360 degrees.
Step-by-step explanation:
We have been given an incomplete statement. We are asked to complete the given statement using provided options.
Statement:
The sum of the measures of the interior angles of a quadrilateral is _____ degrees.
We know that a quadrilateral is a polygon with 4 vertices.
We can divide a quadrilateral into two triangles by drawing a diagonal. We know that sum of three angles of a triangle is equal to 180 degrees, so sum of angles of two triangles would be 360 degrees.
Therefore, the sum of the measures of the interior angles of a quadrilateral is 360 degrees and option D is the correct choice.