Answer:
Step-by-step explanation:
The equation for the surface consisting of all points P for which the distance from P to the x-axis is twice the distance from P to the yz-plane can be found by using the distance formula in three dimensions.
Let (x, y, z) be a point P on the surface. The distance from P to the x-axis is |x|, and the distance from P to the yz-plane is sqrt(y^2 + z^2). Setting these two distances equal and solving for x, we get:
|x| = 2 * sqrt(y^2 + z^2)
x = 2 * sqrt(y^2 + z^2) if x >= 0
x = -2 * sqrt(y^2 + z^2) if x < 0
This is the equation for a hyperboloid of one sheet. The hyperboloid of one sheet is a three-dimensional surface with two connected components that are mirror images of each other across the x-axis.
A' certain state legislature has senators and representatives. The combined number of senators and representatives is 290. The difference of the numbers is 180. There are more representatives than senators.
How many senators and how many representatives are in this state's legislature?
There are 55 senators and 235 representatives are in this state's legislature.
What do you mean by equation?An equation is a mathematical statement that shows the equality of two expressions. Equations can be used to represent relationships between variables and to solve problems. They are written using an equal sign (=) and can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
For example, the equation 2x + 3 = 7 is an equation that states that the expression on the left side (2x + 3) is equal to the expression on the right side (7). The goal is to find the value of the variable x that satisfies the equation. In this case, x = 2 is a solution to the equation.
Let's call the number of senators in the state legislature "s" and the number of representatives "r". We know the following:
s + r = 290 (the combined number of senators and representatives is 290)
r - s = 180 (the difference of the numbers is 180)
We can use the first equation to solve for one of the variables in terms of the other:
r = 290 - s
Next, we can substitute this expression for r into the second equation:
290 - s - s = 180
Simplifying the left-hand side:
290 - 2s = 180
Adding 2s to both sides:
290 = 180 + 2s
Subtracting 180 from both sides:
110 = 2s
Dividing both sides by 2:
s = 55
So there are 55 senators in the state legislature. To find the number of representatives, we can use the first equation:
r = 290 - s = 290 - 55 = 235
So there are 235 representatives in the state legislature.
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In the figure ABCD is a cyclic find the measure of each angles
The angle relations in a cyclic quadrilateral are discussed above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that ABCD is a cyclic quadrilateral.
A cyclic quadrilateral is a four sided shape that can be inscribed into a circle.
Each vertex of the quadrilateral lies on the circumference of the circle and is connected by four chords.
The opposite angles of a cyclic quadrilateral have a total of 180°.
For a cyclic quadrilateral with successive sides a, b, c, d, semi - perimeter s, and angle A between sides a and d, the angle relations for a cyclic quadrilateral as -
Cosine {A} : [tex]${\displaystyle \cos A={\frac {a^{2}-b^{2}-c^{2}+d^{2}}{2(ad+bc)}}}[/tex]Sine (A) : [tex]$\sin A={\frac {2{\sqrt {(s-a)(s-b)(s-c)(s-d)}}}{(ad+bc)}}[/tex]tan (A/2) : [tex]$\tan {\frac {A}{2}}={\sqrt {\frac {(s-a)(s-d)}{(s-b)(s-c)}}}.[/tex]The angle θ between the diagonals that is opposite sides a and c satisfies -[tex]$\tan {\frac {\theta }{2}}={\sqrt {\frac {(s-b)(s-d)}{(s-a)(s-c)}}}.[/tex]
If the extensions of opposite sides a and c intersect at an angle φ, then -[tex]${\displaystyle \cos {\frac {\varphi }{2}}={\sqrt {\frac {(s-b)(s-d)(b+d)^{2}}{(ab+cd)(ad+bc)}}}}[/tex]
Therefore, the angle relations in a cyclic quadrilateral are discussed above.
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Ahmed ell boxe of pen ($8) and rubber band ($4). Leona ordered a total of 30 carton for $220. How many boxe of pen did Leona order?
By applying the algebra concept, it can be concluded that Leona ordered 25 boxes of pens.
Algebra is a branch of mathematics that uses symbols and mathematical operations, such as addition, subtraction, multiplication, and division to solve problems.
We have this information:
The price of a box of pens = $8
The price of a box of rubber bands = $4
Total order = 30 boxes
Total payment = $220
Let p symbolize the number of pens and r symbolize the number of rubber bands. Now we have the following equations:
p + r = 30 ....................... (1)
8p + 4r = 220 ............... (2)
To find the value of p and r, we can do it by simplifying the first equation as follows:
p + r = 30
r = 30 - p
Then we can substitute this value into the second equation:
8p + 4r = 220
8p + 4(30 - p) = 220
8p + 120 - 4p = 220
4p = 220 - 120
= 100
p = 100/4
= 25 boxes of pens
So we can calculate the value of r as well:
r = 30 - p
= 30 - 25
= 5 boxes of rubber bands
Thus, it can be concluded that Leona ordered 25 boxes of pens.
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According to the NCAA, 3. 9% of female high school basketball players go onto play basketball in the NCAA. Of these players, 0. 9% are drafted into the WNBA. If you randomly select one female high school basketball player, what is the probability she will be drafted by a WNBA team?
The probability that a randomly selected female high school basketball player will be drafted by a WNBA team is 0.000351 or approximately 0.04%.
The probability of a female high school basketball player being drafted into the WNBA can be taken as a combination of two probabilities.
The probability that she will play basketball in the NCAA, which is equal to 3.9%, and the probability that she will be drafted into the WNBA given that she plays in the NCAA, which is equal to 0.9%, are both equal.
The probability can be calculated by using the formula:
P(WNBA draft) = P(NCAA) × P(WNBA draft | NCAA)
Where, P(NCAA) = 3.9 ÷ 100 which is equal to 0.039
and, P(WNBA draft | NCAA) = 0.9 ÷ 100 which is equal to 0.009
Hence, by substituting the values in the equation we get
P(WNBA draft) = 0.039 × 0.009
Which is equal to 0.000351 or approximately 0.04%
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there are nine different positions on a baseball team. if a team has 15 players how many different line-ups can the team make? (assume every player can play every position.) the team can make different line-ups. baseball games consist of nine innings. a team wants to change its line-up every inning. if no game goes to extra innings, and a season consists of 66 games, how many complete seasons can the team play without repeating a line-up?
There are 18 seasons and the number of different line-ups the team can make is 24310
A) We are given the team has 17 players and there are 9 different positions in the team.
This is a combination question and thus, the number of different line-ups the team can make is;
C(17, 9) = 24310
B) We are told the basketball games consist of 9 innings.
Thus,
Number of games you can fill = 24310/9 = 2701.1111
And then we are told a season consists of 147 games.
Thus;
The number of complete seasons can the team play without repeating a line-up = 2701.1111/147 ≈ 18 seasons.
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A student is buying single-serve breakfast meals for the next 9 days. The options are meat bowl, vegetarian bowl, cereal bowl, and taco bowl. How many different selections could the student make?
The student has 36 different combinations of breakfast options to choose from (4 options x 9 days).
To determine this:
The student has four different options for breakfast each day for 9 days, so the number of different selections could be calculated as 4 options x 9 days = 36 different selections.
This means that the student has 36 different combinations of breakfast options to choose from, as they can choose one option each day for 9 days. The options are meat bowl, vegetarian bowl, cereal bowl, and taco bowl, and they can choose any combination of these options for their 9 days of breakfast.
For example, they can choose a meat bowl on day 1, a vegetarian bowl on day 2, a cereal bowl on day 3, a taco bowl on day 4, and so on, or they can choose the same option every day, or they can mix and match their options in any combination they like.
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problem 8. (10 pts) for the function find the gradient of at ; find the rate of increase of at the point in the direction ; find the direction of maximum rate of increase at . what is the rate of increase in this direction?
The given function is [tex]f(x,y) = x^2 + y^2[/tex].
To find the gradient of f at the point (x0, y0), we take the partial derivatives of f with respect to x and y:
[tex]$$\nabla f(x0,y0) = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}\right) = \left(2x0, 2y0\right)$$[/tex]
The rate of increase of $f$ at the point (x0, y0) in the direction (u,v) is given by the dot product of the gradient and the direction vector:
[tex]$$\nabla f(x0,y0) \cdot (u,v) = 2x0u + 2y0v$$[/tex]
The direction of maximum rate of increase at (x0, y0) is the direction of the gradient, which is (2x0,2y0). The rate of increase in this direction is the length of the gradient vector, which is given by:
[tex]$$||\nabla f(x0,y0)|| = \sqrt{(2x0)^2 + (2y0)^2} = 2\sqrt{x0^2 + y0^2}$$[/tex]
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A and B are oppoite vertice of a regular ix-ide hape, the point C and D are the midpoint of two oppoite ide. The area of the regular ix-ided hape i 60. Determine the product of the length of the line AB and CD!
The product of AB and CD in a regular hexagon with an area of 60 is (40 / √3) / 2.
To find the product of the length of AB and CD in a regular hexagon, we have to initially calculate the length of one side of the hexagon and later use that information to find the length of AB and CD.
Let us say that the length of one side of the hexagon = s.
W.k.t the area of the hexagon = 60, so we can use the formula for the area of a regular hexagon:
Area = (3 * √3) / 2 * [tex]s^2[/tex]
Making this equal to 60 and solving s:
60 = (3 * √3) / 2 * [tex]s^2[/tex]
120 = 3 * √3 * [tex]s^2[/tex]
40 = √3 * [tex]s^2[/tex]
(40 / √3) = [tex]s^2[/tex]
Taking the square root of both sides:
s = (40 / √3)^(1/2)
Now that we found the length of one side of the hexagon, So we can use that to find the length of AB and CD.
AB = the length of one side of the hexagon times the square root of 3, CD = the length of one side of the hexagon divided by 2.
So,
AB = s * √3
CD = s / 2
Now, we can find the product of AB and CD by multiplying them together:
AB * CD = s * √3 * s / 2
AB * CD = (s^2 * √3) / 2
AB * CD = (40 / √3) / 2
So the product of AB and CD in a regular hexagon with an area of 60 is equal to (40 / √3) / 2.
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The sum of the squares of three positive numbers in an ap is 155. The sum of the numbers is 21. Find the number
In how many ways can 8 persons be seated at a round table if 2 particular persons must not sit next to each other?A 40320B 5040C 3600D 720
The total number of arrangements possible if A and B must not sit together:
= 3600
Now, According to the question:
The no. of circular arrangements of n distinct items = (n-1)!
If A,B,C,D,E,F,G and H are the 8 persons to be seated around the table and A,B the 2
particular persons who must not sit together.
The total no.of circular arrangements for 8 persons = (8-1)! = 7! = 5040 --(1)
The no. of circular arrangements possible if A and B were to sit together = 6! (considering A and B as a single pair).
But, A and B can interchange their positions.
Hence, the no. of arrangements =6!×2=720×2=1440−−−−>(2)
So, the total number of arrangements possible if A and B must not sit together, = (1) - (2)
= 5040-1440
= 3600
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How to convert cups to pounds?
To convert cups to pounds, you can use the following conversion factor 1 cup = 0.5 pounds
How to convert cups to pounds?A cup is a unit of volume commonly used in cooking and baking recipes, while a pound is a unit of weight.To convert from cups to pounds, you need to know the density of the substance you are measuring.The conversion factor of 1 cup to 0.5 pounds assumes that you are measuring a substance with a density of 8 ounces per cup. This is a commonly used conversion factor for substances such as sugar, flour, or butter.If you are measuring a different substance with a different density, the conversion factor may be different.To convert from cups to pounds, simply multiply the number of cups by the conversion factor of 0.5.For example, 2 cups of sugar is equal to 2 x 0.5 = 1 pound of sugar.It's important to keep in mind that this conversion is an approximation and may not be completely accurate for all substances.If you need a more precise conversion, it's best to consult a reference or use a conversion calculator.To learn more about cups and pounds refer:
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don't quite understand. can someone explain pls?
The two column proof showing that m∠AKG = m∠HKB is as below and explained.
How to interpret two column proof?A two-column proof is defined as a geometric proof consists of a list of statements, and the reasons that we know those statements are true.
The two column proof showing the vertical angles are explained below.
Statement 1: Segment GH Intersects Segment AB at K
Reason 1: Given
Statement 2: m∠AKG + m∠GKB = 180°
m∠GKB + m∠HKB = 180°
Reason 2: Definition of supplementary angles
Statement 3: m∠AKG + m∠GKB = m∠GKB + m∠HKB
Reason 3: Substitution property
Statement 4: m∠AKG = m∠HKB
Reason 4: Subtraction property
Now, supplementary angles are defined as angles that sum up to 180 degrees and that is why m∠AKG + m∠GKB = 180° and m∠GKB + m∠HKB = 180°
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The ratio of the circumference of the sun to the earth is given as 109:1. What will be the ratio of the diameter of the earth to the sun?
a. Data insufficient
b. 1:109
c. 40:3
d. 109:1
The Sun's diameter is 864,000 miles. 864,000 x 108 = 93,000,000 kilometers separate the earth from the sun. This is equivalent to 109 times the size of Earth.
What is the Sun's diameter in relation to the Earth's diameter?The Sun's diameter is 1,391,000 kilometers, or 864,400 miles. This is equivalent to 109 times the size of Earth. About 333,000 times as much as Earth's weight is that of the Sun.The diameter of 108 Earths is equivalent to the diameter of the Sun. The Sun's diameter is 864,000 miles. 864,000 x 108 = 93,000,000 kilometers separate the earth from the sun. This is equivalent to 109 times the size of Earth.The Sun's diameter is 864,000 miles. 864,000 x 108 = 93,000,000 kilometers separate the earth from the sun. This is equivalent to 109 times the size of Earth.The Sun's diameter is 1,391,000 kilometers, or 864,400 miles. This is equivalent to 109 times the size of Earth.To learn more about Sun's diameter refer to:
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Option is not mentioned, The ratio of the diameter of the earth to the sun is di = 1.8 × 10-3m.
What is the ratio of the Sun's diameter to that of the Earth's?The Sun is 1,391,000 kilometres (864,400 miles) across. It is the same as Earth being 109 times its size. The Sun's mass is roughly 333,000 times that of the Earth.
The Sun's diameter is equal to the diameter of 108 Earths. The Sun is 864,000 kilometres across. The earth is 93,000,000 kilometres from the sun, or 864,000 times 108 kilometres. It is the same as Earth being 109 times its size.
The Sun is 864,000 kilometres across. The earth is 93,000,000 kilometres from the sun, or 864,000 times 108 kilometres. It is the same as Earth being 109 times its size.
The Sun is 1,391,000 kilometres (864,400 miles) across. This is the same as 109 times the size of Earth. .
The angle of reflection is θ.
D is the distance between the mirror's centre and the sun's centre, where d is the sun's diameter. d/D the equation is equal to 0.009
Angle of incidence = angle of reflection according to the rules of reflection. Consequently, θ2 = θ, = θ, d D The ratio tan θ;=0.009 tan θ =0.009 is another option.
We will assume that because the sun is far away from the mirror, the image will form at the mirror's focus. Therefore, distance OB = f, where f is the concave mirror's focal length
The focal length of a spherical concave mirror is equal to half of its radius of curvature. Given that the radius of the curveturer is 0.4 m, f= 42 = 0.4 m 2 = 0.2 m.
Taking into account the image's diameter as d2, tan 0, di f tan 0 di 0.2 = Taking the value of tan from above, 0.009 di 0.2 = di 0.009 x 0.2 = As a result, the image's diameter is d; = 0.0018m di = 1.8 × 10-3m.
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simplify each expression by adding or subtracting {5a2+5-a} + {6-2a+4a4}
Answer:
4a⁴ + 5a² - 3a + 11
Step-by-step explanation:
5a² + 5 - a + 6 - 2a + 4a⁴
Combine like terms.
5a² + 11 - 3a + 4a⁴
4a⁴ + 5a² - 3a + 11
Answer:
4a⁴ + 5a² - 3a + 11
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The expression is,
→ (5a² + 5 - a) + (6 - 2a + 4a⁴)
Let's simplify the expression,
→ (5a² + 5 - a) + (6 - 2a + 4a⁴)
→ 5a² + 5 - a + 6 - 2a + 4a⁴
→ (4a⁴) + (5a²) + (-a - 2a) + (5 + 6)
→ 4a⁴ + 5a² + (-3a) + (11)
→ 4a⁴ + 5a² - 3a + 11
Therefore, this is the answer.
Line G has a slope of 5/4. Line H is perpendicular to line G, what is the slope of line g.
Answer:
-4/5
Step-by-step explanation:
Since Line H is perpendicular to Line G, its slope is the negative reciprocal of the slope of Line G.
Line G: m = 5/4
Line H: m = -4/5
EASY POINTS, WILL GIVE BRAINLIEST TO FIRST ANSWER
Which equation represents the graph?
A. y equals negative one third times x minus 1
B. y = −3x − 1
C. y equals negative one third times x plus one third
D. y equals negative 3 times x plus one third
Answer:
B. y = -3x -1
Step-by-step explanation:
Is this one because of the part of maths that studies the way in which words and the groups they form are combined to express meanings, as well as the relationships that are established between all these units. A set of rules defining the correct sequences of the elements of a programming science and maths formulas.
Find the slope of a line parallel to the line whose equation is x + 2y = -14. Fully
simplify your answer.
Answer:
So first solve the equation given
X+2y=-14
-x -x
-----------------
2y=-x-14
---- ---------
2 2
y=- 1/2x-7
this would be your parallel line equation because y=-1/2x-7
Parallel lines have the same slope
Perpendicular lines have a negative reciprocal slope (so -2 would be positive 1/2)
Hope this helps!
Please leave a comment if I made a mistake, I will correct it!
A bag contains 5 black pencils and 3 yellow pencils. What is the
probability of drawing 1 black pencil and 2 yellow pencils without
replacement?
The probability of drawing 1 black pencil and 2 yellow pencils without replacement is 0.035714.
The probability of drawing 1 black pencil and 2 yellow pencils without replacement can be calculated by multiplying the individual probabilities of drawing each pencil.
The first step is to calculate the probability of drawing a black pencil which is 5/8. Then, the probability of drawing the first yellow pencil is 4/7 and the probability of drawing the second yellow pencil is 3/6.
To find the probability of drawing all three pencils, you multiply these three probabilities together:
5/8 × 4/7 × 3/6 = 0.035714.
This result represents the probability of drawing 1 black pencil and 2 yellow pencils in that order without replacement.
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this was a question on my homework assignment from school but I don't know how to solve this without the height of the cone from top to bottom.
Answer: [tex]\sqrt{585}[/tex] units or [tex]3\sqrt{65}[/tex] units
Step-by-step explanation:
The formula for volume of a cone is π[tex]r^{2}[/tex][tex]\frac{h}{3}[/tex]. You can find the height by plugging in 72π for volume and 3 for radius.
diameter = radius x 2, so 6/2=3 units for radius.
72π = π([tex]3^{2}[/tex])([tex]\frac{h}{3}[/tex])
72=9*[tex]\frac{h}{3}[/tex]
8 = [tex]\frac{h}{3}[/tex]
h = 24 units
The formula for slant height is [tex]\sqrt{{r}^2 + {h}^2 }[/tex]
Plug in 3 for r and 24 for h. You should get [tex]\sqrt{(9+576)}[/tex]=[tex]\sqrt{585}[/tex] or 3[tex]\sqrt{65}[/tex] as your answer.
1)The time (in minutes) that it takes a mechanic to change oil has an exponential distribution with mean 20.
a) Find P(X < 25), P(X > 15), and P(15 < X < 25)
b) Find the 40th percentile
a) P(X<25) = 0.7135 P(X>15) = 0.4724 P(15<X<25)=0.1859 and The 40th percentile is : 10.2165
What is exponential distribution?The exponential distribution is a continuous probability distribution used in probability theory and statistics that frequently addresses the amount of time until a certain event occurs. It refers to a system in which things proceed continuously and separately at such an average speed that is constant.
Let X = The time (in minutes) that it takes a mechanic to change oil
We have,
X = Exp (mean = 20)
The distribution function of X is: F(x) = P (X < x) = 1 - e{-x/20}
a) Consider, P (X < 25) = F(25)
= 1 - e{-25/20}
= 0.7135
Consider, P( X > 15)
= 1 - P (X < 15)
= 1 - 1 - e{-15/20}
= 0.4724
Consider, P(15 < X < 25)
= P (X < 25) - P (X < 15)
= 1 - e{-25/20} - 1 - e{-15/20}
= 0.1859
Hence,
P(X<25) = 0.7135 P(X>15) = 0.4724 P(15<X<25)=0.1859
b) We want to find x such that P(X<x) =0.40
Consider, P (X < x) = 0.40
1 - e{-x/20} = 0.40
x = 10.2165
Hence, The 40th percentile is : 10.2165
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If I paid $625 interest on $5000 that I borrowed at 5%, how many years did I borrow it? *Remember, I = P x R x T help fast
below is a sketch of the region bounded by the line y=4−2x, the line y=0, and the line x=0
[tex]y = 4-2x , y = 0 , x = 0[/tex] The region is a triangle with the upper right corner at (2, 4).
1. Start by drawing the three lines: the line [tex]y=4−2x[/tex], the line y=0, and the line x=0.
2. Find the coordinates of the upper right corner of the region. To do this, we need to find the point where the two lines y=4−2x and x=0 intersect. We can solve this by setting y=4−2x and x=0, which gives us the point (0, 4). This is the upper right corner of the region.
3. The region is a triangle with the upper right corner at (2, 4).
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Zach’s car travels 21 miles on 1 gallon of gas. Write an equation to represent the relationship between the gas Zach’s car uses and the distance he travels. Then solve the equation to see how far Zach travels on a trip if he uses 16 gallons of gas
The equation to see how far Zach travels is y = 21x and Zach traveled 336 miles using 16 gallons of gas.
What is the equation to see how far Zach travels on a trip?Number of miles traveled Zach's car traveled= 21 miles
Quantity of gallons used = 1 gallon
y = kx
Where,
x = total gallons used
k = unit rate of miles per gallon
y = Number of miles traveled
So,
21 = k × 1
21 = k
y = 21x
Hence,
if he uses 16 gallons of gas
y = kx
y = 21 × 16
y = 336 miles
In conclusion, Zach's car traveled 336 miles.
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a rectangle is formed by placing two identical squares side by side the perimeter of each square is 24 cm what is the area of the entire rectangle
The area of the rectangle is 72 cm^2.
How to determine the area of the rectangleLet's call the side length of each square s.
Since the perimeter of each square is 24 cm, then each side measures 24 cm / 4 = 6 cm.
So the length of the rectangle is 2s = 2 * 6 cm = 12 cm.
And the width of the rectangle is s = 6 cm.
Therefore, the area of the rectangle is A = l * w = 12 cm * 6 cm = 72 cm^2.
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The area of the rectangle is 72 square centimeters.
How to find the area of the rectangle?The rectangle is formed by placing two identical squares side by side the perimeter of each square is 24 cm.
Remember that for a square of sidelength S, the perimeter is P = 4*S
Then the sidelength of the squares is
24cm = 4*S
24cm/4 = 6cm = S
When we place these two squares together, we will have a rectangle of 6cm by 12cm, and the area is the product of the dimensions, then the area is:
A = 6cm*12cm = 72cm²
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Find the horizontal asymptote of f of x equals quantity x squared plus 3x plus 6 end quantity over quantity x squared plus 1.
The horizontal asymptote will be y = 2
What is Horizontal asymptote?
A graph's horizontal asymptote is a horizontal line y = b along which the graph approaches as the inputs approach or ∞ or –∞. A graph's slant asymptote is a slanted line y = mx + b along which the graph approaches the line as the inputs approach or ∞ or –∞
What is Square?
A square is a regular quadrilateral, which implies it has four equal sides and angles. It can alternatively be defined as a rectangle having two neighboring sides of identical length.
f (x) = [tex]\frac{2x^{2}+3x+6 }{x^{2} +1}[/tex]
Here degree of numerator = degree of denominator
Hence the equation of horizontal asymptote y = 2/1
=2
Hence the equation of horizontal asymptote y=2
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The horizontal asymptote will be y = 2
What is Horizontal asymptote?
A graph's horizontal asymptote is a horizontal line y = b along which the graph approaches as the inputs approach or ∞ or –∞. A graph's slant asymptote is a slanted line y = mx + b along which the graph approaches the line as the inputs approach or ∞ or –∞
What is Square?
A square is a regular quadrilateral, which implies it has four equal sides and angles. It can alternatively be defined as a rectangle having two neighboring sides of identical length.
f (x) = [tex]\frac{2x^{2} +3x+6}{x^{2} +1}[/tex]
Here the degree of numerator = degree of the denominator
Hence the equation of horizontal asymptote y = 2/1
=2
Hence the equation of horizontal asymptote y=2
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Which would cause a shift in the supply curve?
The supply curve shifts as a result of every factor but a change in market price. The movement along the supply curve and the change in price are correlated.
What is meant by supply curve?The supply curve can change depending on a number of variables, such as shifts in production costs (such as raw material and labor prices), advancements in technology, the level of competition and the number of sellers/producers, as well as the regulatory and tax environment.
Although a shift in the quantity supplied or along the supply curve for a given commodity or service is frequently brought about by a change in price, the supply curve itself does not alter as a result.
Input prices, weather conditions, technological advancements, as well as governmental taxes, regulations, and subsidies, can all modify the supply curve for goods and services, resulting in a different quantity being delivered for a given price.
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Kevin's bank offered him a 4. 5% interest rate for his mortgage. If he purchases 3 points, what will be his new rate?
The new interest rate for his mortgage would be 3.75%.
The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also gets additional income in terms of the recipient, known as interest, taking into account the time value of money.
Purchasing a point simply implies negotiating for a lower rate of interest, which involves paying 1% of the loan in lieu of 1% interest reduction.
A point implies a reduction in interest rate by 0.25% while 3 points would reduce the interest rate by 0.75%(0.25%*3)
New interest rate=4.5%-0.75%=3.75%
Thus, The new interest rate for his mortgage would be 3.75%.
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at a point on the ground 50 meters from the foot of a tree, the angle of elevation of the top of the tree is 48 degrees. find the height of the tree to the newest hundredth of a meter.
When measured from a position on the ground 50 meters away from a tree, the height of the tree is 55.5 meters to the nearest hundredth of a meter.
what is trigonometry ?The association between triangle line angle lengths and angles is examined in the mathematics discipline known as trigonometry. The application of geometry in astronomical inquiry gave rise to the area's first appearance in the 18th century, roughly in the third centuries BC. Exact approaches mathematics focuses on certain right triangle and how they could be applied to operations. In trigonometry, there are six well-known trigonometric functions. They are identified by their various names and buzzwords: sine, cosine, parallel, cotangent, hyperbolic tangent, and cosecant (csc). Trigonometry is the study of the properties of triangles, particularly of right triangles. The features of all geometric forms are studied in geometry.
given
Base = 50, Elevation Angle = 48
An angle's opposite or adjacent side is its tan.
Tan (48),
height/distance, = 50*tan (48),
height, or 55.5 feet.
When measured from a position on the ground 50 meters away from a tree, the height of the tree is 55.5 meters to the nearest hundredth of a meter.
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PLEASE HELP!!!! I WILL GIVE BRAINLIEST
Answer:
Below
Step-by-step explanation:
Work your way through this to make sure you understand:
The 'b' part at the bottom means you have to make SURE that BOTH of the answers actually WORK In the equation.... ONE MAY not...you have to try them both to see if one is 'extraneous' (which means 'does not work')
Find sn for the arithmetic series where a1=5 , An= -13 , n=10
The sum of the first 10 terms of the arithmetic sequence is given as follows:
-40.
How to obtain the sum of an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The sum for the first n terms of an arithmetic sequence is given by the equation presented as follows:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
In which:
[tex]a_1[/tex] is the first term.[tex]a_n[/tex] is the nth term.The parameters for this problem are given as follows:
[tex]n = 10, a_1 = 5, a_n = -13[/tex]
Hence the sum is given as follows:
S = 5 x (5 - 13)
S = -40.
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