A plane ascends at a 28°
angle. When it reaches an altitude of 250 feet, how much ground distance has it covered? Round your answer to the nearest tenth.
(HINT: DRAW THE PICTURE)
Ground distance covered is ft.
(50 points)
Answers
According to trigonometry, the ground distance covered by the plane is approximately 478.7 feet, rounded to the nearest tenth.
What is trigonometry?
The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations.
The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations.
There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc).
The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
To draw a diagram of the situation:
[tex]tan(28°) = opposite / adjacent\\tan(28^{0}) = 250 / x\\x = 250 / tan(28^{0})\\ x= 478.7 ft[/tex]
Therefore, the ground distance covered by the plane is approximately 478.7 feet, rounded to the nearest tenth.
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Related Questions
A card is drawn randomly from a standard 52-card deck. Find the probability of the given event.
(a) The card drawn is 7
Answers
The probabilities for the given events will be a) 1/13 b) 3/13 c) 10/13.
What exactly is probability?
Probability is a measure of the possibility of an event to be occurred. In mathematics, it is defined as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur.
Now,
(a) The probability of drawing a 7 from a standard 52-card deck is 4/52 or 1/13. This is because there are 4 7s in the deck (one in each suit) and a total of 52 cards.
(b) The probability of drawing a face card from a standard 52-card deck is 12/52 or 3/13. This is because there are 12 face cards in the deck (4 jacks, 4 queens, and 4 kings) and a total of 52 cards.
(c) The probability of drawing a non-face card from a standard 52-card deck is 40/52 or 10/13. This is because there are 40 non-face cards in the deck (the 2s through 10s and the aces) and a total of 52 cards.
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Let W1 denote the set of all polynomials f (x) in P(F ) such that in the
representation
f (x)=an xn + an−1 xn−1 + ··· + a1 x + a0 ,
we have ai =0whenever i is even. Likewise let W2 denote the set of
all polynomials g (x) in P(F ) such that in the representation
g (x)=bm xm + bm−1 xm−1 + ··· + b1 x + b0 ,
we have bi =0 whenever i is odd. Prove that P(F )=W1 ⊕ W2 .
Answers
We have shown that P(F) is the direct sum of W1 and W2.
What is a polynomial?
a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
To prove that P(F) is the direct sum of W1 and W2, we need to show two things: first, that every polynomial in P(F) can be written as a sum of a polynomial in W1 and a polynomial in W2, and second, that this decomposition is unique.
Let's begin by showing that P(F) can be written as the direct sum of W1 and W2. Consider an arbitrary polynomial f(x) in P(F). We can write it as a sum of even and odd terms as follows:
f(x) = [f(x) + f(-x)]/2 + [f(x) - f(-x)]/2
The first term on the right-hand side is even, while the second term is odd. Let's define g(x) = [f(x) - f(-x)]/2 and h(x) = [f(x) + f(-x)]/2. Note that g(x) is odd and h(x) is even. Thus, we have expressed f(x) as a sum of an even polynomial h(x) and an odd polynomial g(x).
To show that this decomposition is unique, suppose that f(x) can be written in two ways as a sum of an even polynomial and an odd polynomial:
f(x) = h1(x) + g1(x) = h2(x) + g2(x)
where h1(x) and h2(x) are even polynomials, and g1(x) and g2(x) are odd polynomials. Then we have:
[h1(x) - h2(x)] = [g2(x) - g1(x)]
Since h1(x) - h2(x) is even, and g2(x) - g1(x) is odd, we have:
[h1(x) - h2(x)] = 0 and [g2(x) - g1(x)] = 0
This implies that h1(x) = h2(x) and g1(x) = g2(x), so the decomposition is unique.
Therefore, we have shown that P(F) is the direct sum of W1 and W2.
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Juli is going to launch a model rocket in her back yard. When she launches the rocket, the function h(t)=−16t2+76t
model the height, h, in feet of the rocket above the ground as a function of time, t, measured in seconds. When will the rocket hit the ground? When will the rocket be 70
feet above the ground?
Answers
From given quadratic function we get that the rocket will hit the ground after 4.75 seconds and the rocket will be 70 feet above the ground after 7/2 or 3.5 seconds.
What is quadratic function?
A quadratic function is defined as f(x) = ax² + bx + c, where a, b, and c are constants and x is the independent variable. This function is a second-degree polynomial, which means it has a degree of two.
Now,
To find out when the rocket will hit the ground, we need to find the value of t when h(t) = 0:
-16t² + 76t = 0
Factor out -16t:
-16t(t - 4.75) = 0
So either t = 0 or t = 4.75 seconds. However, we can discard t = 0 because it represents the initial launch and not the impact with the ground. Therefore, the rocket will hit the ground after 4.75 seconds.
To find out when the rocket will be 70 feet above the ground, we need to solve the following equation:
-16t² + 76t = 70
-16t² + 76t - 70 = 0
Dividing both side
8t² - 38t + 35 = 0
Factor the equation:
(4t - 5)(2t - 7) = 0
So either t = 5/4 or t = 7/2. However, we can discard t = 5/4 because it represents a time before the rocket reaches 70 feet. Therefore, the rocket will be 70 feet above the ground after 7/2 or 3.5 seconds.
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please help me find the radius of r
Answers
Step-by-step explanation:
using Pythagoras theorem
Answer:
4² + r² = (2+ r)²
16 + r² = 4 + 4r + r²
12 = 4r
r = 3
Find the estimated standard error for the sample mean for the following samples: (a) n= 9 with SS =1152
Answers
Answer:
To find the estimated standard error for the sample mean, we need to use the formula:
SE = s/√n
where s is the sample standard deviation and n is the sample size.
However, we are not given the sample standard deviation, but we are given the sum of squares (SS). We can use this to find the sample variance (s^2) and then take the square root to find the sample standard deviation.
For a sample size of n = 9, the degrees of freedom (df) are:
df = n - 1 = 9 - 1 = 8
Using the formula for the sample variance:
s^2 = SS/df = 1152/8 = 144
Taking the square root, we find the sample standard deviation:
s = √144 = 12
Now we can find the estimated standard error:
SE = s/√n = 12/√9 = 4
Therefore, the estimated standard error for the sample mean is 4.
Answer:
To find the estimated standard error for the sample mean, we need to divide the sample standard deviation by the square root of the sample size. However, we are given the sum of squares (SS), not the sample standard deviation, so we first need to calculate the sample variance. The formula for the sample variance is: s^2 = SS / (n - 1) where s^2 is the sample variance, SS is the sum of squares, and n is the sample size. Using the given values, we have: s^2 = 1152 / (9 - 1) = 144 Now we can find the estimated standard error: SE = s / sqrt(n) where SE is the estimated standard error, s is the sample standard deviation, and n is the sample size. Since s = sqrt(s^2), we have: SE = sqrt(s^2
5.
What is the width of a rectangle if the area is 2x2-x-6 and the length is 2x + 3?
O-x-1--
O x-2
3
2x+3
O -x + 2
MacBook Air
2x²-1
2
none of the answer choices
Answers
Answer: 2x^2-1/2
Step-by-step explanation:
mulityply this by the given lenght
A circle has an arc of length 17 with central angle 18 degrees. Find the circumference of the circle.
Answers
The circumference of the circle is 340 units.
What is circle ?
In geometry, a circle is a two-dimensional shape consisting of all points that are a fixed distance (called the radius) from a given point (called the center). A circle is a set of points that are equidistant from the center.
Let's use the formula relating the length of an arc to the circumference of a circle:
Length of arc = (central angle / 360) x circumference
Plugging in the given values, we get:
17 = (18/360) x circumference
Simplifying and solving for the circumference, we get:
circumference = 17 x (360/18) = 17 x 20 = 340
Therefore, the circumference of the circle is 340 units.
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(x−a)xa3+(x−a)x−13a2+(x−a)x−23a+(x−a)31=(x−a)xx3
Answers
The solutions to the equation are x = a and x = a/2.
Equation calculation.
We can simplify the left-hand side of the equation using the common denominator of x^3:
(x-a)x/x^3 + (x-a)(-1)/(3a^2 x^3) + (x-a)(-2)/(3a x^3) + (x-a)(1)/(x^3)
= [(x-a)x^2 - (x-a)/(3a^2) - 2(x-a)/(3a) + (x-a)x]/x^3
= [(x^3 - a^3)/x^2 - (1/(3a^2))(x-a) - (2/(3a))(x-a)]/x
= [(x^2 + ax + a^2)(x-a)/(x^2 a^2) - (x-a)/(3a^2) - (2/3)(x-a)/a]/x
= (x^2 + ax + a^2)/(x^2 a^2) - 1/(3a^2) - 2/(3a)/x
= (3x^2 + 3ax + 3a^2 - x^2 a - ax^2 - a^3)/(3a^2 x^2)/x
= (2x^2 + 3ax + 3a^2 - ax^2 - a^3)/(3a^2 x^2)/x
= (x^2 + 3ax + 3a^2 - a^3)/(3a^2 x^2)/x
Now, we can see that the expression on the right-hand side is:
(x-a)/(x^3)
Multiplying both sides by x^3, we get:
(x-a)x = (x^2 + 3ax + 3a^2 - a^3)/3a^2
Multiplying both sides by 3a^2, we get:
(x-a)3a^2x = x^2 + 3ax + 3a^2 - a^3
Expanding (x-a)(3a^2)x, we get:
3a^2x^2 - 3a^3x = x^2 + 3ax + 3a^2 - a^3
Moving all terms to one side, we get:
2x^2 - 3ax + 2a^2 = 0
This is a quadratic equation, and we can solve for x using the quadratic formula:
x = [3a ± sqrt((9a^2 - 8a^2)/4)]/4
x = [3a ± a]/4
x = a or x = 2a/4 = a/2
Therefore, the solutions to the equation are x = a and x = a/2.
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( Need Help Please and thank you! )
Answers
Answer:
( x - 5 )
Hope this helps!
Step-by-step explanation:
[tex]2x^{2} -7x-15[/tex] can factor into ( 2x + 3 ) ( x - 5 ).
( 2x + 3 ) ( x - 5 ) = ( cross multiply ) : [tex]2x^{2} -10x + 3x - 15[/tex] = [tex]2x^{2} -7x-15[/tex].
How do I find the value for f(x)=6+3x
Answers
Answer: To find the value of f(x) for a given value of x, you need to substitute that value of x into the equation and simplify.
For example, if you want to find f(2), you would substitute x=2 into the equation:
f(x) = 6 + 3x
f(2) = 6 + 3(2)
f(2) = 6 + 6
f(2) = 12
Therefore, f(2) = 12.
Step-by-step explanation:
The value of f(x) is 18 given that the value of x is substituted as 4. The expression is usually solved with substitution method.
How to solve the expression?To find the value of f(x) for a given value of x, you need to substitute that value of x into the equation for f(x) and solve for f(x).
For example, if you want to find the value of f(x) when x = 4, you would substitute x = 4 into the equation for f(x) as follows:
f(4) = 6 + 3(4)
Simplifying the expression on the right-hand side:
f(4) = 6 + 12
f(4) = 18
Therefore, the value of f(x) when x = 4 is 18.
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Sea=4x⁵-x³+7 y b(x)=2x⁵+x²
Al dividir a entrar b podemos encontrar polinomios únicos, conciente de que y resuido r que satisfacen la ecuación
Donde de r(x) es menor que el grado de b(c)
Cuál es la conciente de que (x)
Y el resuido de r(x)
Answers
En resumen, al dividir Sea=4x⁵-x³+7 entre b(x)=2x⁵+x², obtenemos un cociente de 2x³-x² y un residuo de -2x²+7.
Para encontrar los cocientes y el residuo al dividir Sea=4x⁵-x³+7 entre b(x)=2x⁵+x², debemos realizar la división larga de polinomios. El procedimiento es similar a la división larga de números enteros:
2x³ -x² +0x +0
---------------------------------
2x⁵ | 4x⁵ +0x⁴ -x³ +0x² +0x +7
4x⁵ +0x⁴
-------------
0x⁴ -x³
0x⁴ +0x³
-------------
-x³ +0x²
-x³ +0x²
-------------
0x² +0x
0x² +0x
------------
7
2x⁵ +x²
--------
-2x² +7
Por lo tanto, el cociente de la división es 2x³-x², y el residuo es -2x²+7. Es importante notar que el grado del residuo (grado 2) es menor que el grado del divisor b(x) (grado 5), como se requiere en la definición de la división de polinomios.
La respuesta a la pregunta "cuál es la conciente de que (x)" no es clara, ya que no está claro lo que se está pidiendo. Podría ser una pregunta incompleta o una cuestión mal redactada.
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The British telecom tower is about 3/7 the height of the empire state building write two different numerical expressions to model the height of the British telecom tower
Answers
1. H × (3/7) and 2. H - (4/7)H are two different numerical expressions to model the height of the British telecom tower.
What are the expressions?
Let H be the height of the Empire State Building. Then, the height of the British Telecom Tower can be modeled using the following expressions:
1. H × (3/7)
This expression finds 3/7 of the height of the Empire State Building, which represents the height of the British Telecom Tower.
2. H - (4/7)H
This expression finds the remaining height after taking away 3/7 of the height of the Empire State Building.
Simplifying, we get (3/7)H, so subtracting this from H gives (4/7)H, which represents the height of the Empire State Building above the height of the British Telecom Tower.
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(b) During a housing boom the price of houses increased over an 18 month period. A house that cost 240000 at the start of the period had a sale value of 276000 at the end of the period. What was the average rate of change in the price per month?
Answers
After answering the presented question, we can conclude that As a result, the average monthly rate of change in price during the housing bubble was $2,000.
What is average rate?The term "average rate" can have different meanings depending on the context in which it is used. In general, it refers to the amount of change that occurs over a certain period of time, divided by the length of that time period. Here are a few examples of how the term might be used in different fields.
The average monthly rate of change in price can be estimated by dividing the total price change by the number of months:
(final price - beginning price) / number of months = average rate of change
The beginning price was $240,000, the final price was $276,000, and the time duration was 18 months in this example. Hence, using these data, we can calculate the average rate of change as:
(276000 - 240000) / 18 = 36000 / 18 = 2000 Average rate of change
As a result, the average monthly rate of change in price during the housing bubble was $2,000.
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y^2-16/4y-16/y+4/16y is
Answers
Answer: 4y^2y-80+y^2/4y
Step-by-step explanation:
what is the correct order
Answers
The correct order will be:
Length of the blue segment. - 12 units
Length of the green segment (circumference of the base) - 18 units
Length of the orange segment. - 24 units
Area of one base. - 452.4 unit²
Area of the rectangle. - 2,261.9 unit².
What is a cylinder?A cylinder is a three-dimensional shape that consists of two parallel circular bases that are connected by a curved surface. The bases are usually identical in size and shape and are located on opposite ends of the cylinder. The curved surface that connects the bases is in the form of a rectangle that has been wrapped around the cylinder, creating a tube-like shape.
Area of one base = r² = 3.142 × 12 × 12 = 452.448 = 452.4 unit².
Area of the rectangle = 2πr (h + r) = 2 × 3.142 × 12 (18 + 12) = 2,261.9 unit².
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What is the total area, in square feet, of the shaded sections of the trapezoid below? 100 points if you get the ANSWER CORRECT
Answers
Answer: 44.64ft^2
Step-by-step explanation:
Triangle 1:
A = 1/2 x 5.3 x 7.2
A = 19.08
Triangle 2:
A = 1/2 x 7.1 x 7.2
A = 25.56
25.56 + 19.08 = 44.64
Total area of triangles = 44.64ft^2
10 men can complete a job in 14 days, How long will it take 4 men to finish the same Job if they work at the same rate?
Answers
Well:
You put 10 over 14 is equal to x (? #of days) over 4 cross multiply so now it’s 10x =(14•4) or 56. Divide both sides by 10 to get x by itself and you get an answer of:
5.6
pls help this is due in 20 mins
Answers
The quadratic function's equation, when given the numbers in the table, can be found to be f(x) = x^2 - 5x + 6.
How to find the quadratic function's equation ?We are given a table of values and need to find the quadratic function in standard form: f(x) = ax^2 + bx + c. Let's use the points (-6, 72), (-4, 42), and (-3, 30).
For point (-6, 72):
72 = a(-6)^2 + b(-6) + c
For point (-4, 42):
42 = a(-4)^2 + b(-4) + c
For point (-3, 30):
30 = a(-3)^2 + b(-3) + c
Let's use the elimination method.
1 - 3) 42 = 27a - 3b
2 - 3) 12 = 7a - b
b = 7a - 12
Substitute this expression for b into the first equation:
42 = 27a - 3(7a - 12)
42 = 27a - 21a + 36
6 = 6a
a = 1
Now that we know a = 1, let's find b:
b = 7(1) - 12
b = -5
Finally, let's find c by substituting a and b into any of the original equations. We'll use the first one:
72 = 36(1) - 6(-5) + c
72 = 36 + 30 + c
6 = c
So, the quadratic function in standard form is:
f(x) = x^2 - 5x + 6
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A camera's normal price is $460. Buying it duty free reduces the price by 25%. Find the actual selling price of the camera.
Answers
The actual selling price of the camera after the 25% discount is $345.
What is selling price?The amount received by the buyer is the selling price of a product or service. Although the seller sets the price, a number of variables affect how the seller arrives at that particular figure. Depending on the seller's discretion, different customers may pay different prices for the same good or service.
If the normal price of the camera is $460, a 25% reduction in price would be:
25% of $460 = 0.25 x $460 = $115
This means the reduction in price when buying the camera duty-free is $115.
So the actual selling price of the camera after the discount is:
$460 - $115 = $345
Therefore, the actual selling price of the camera after the 25% discount is $345.
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Cual es el valor de x ? 5 ( x - 56 ) = -3 ( x + 2 ) + 1
Answers
Answer:
Step-by-step explanation:
[tex]\frac{275}{8}=34,375[/tex]
i need help asap i have to finish
Answers
Answer: (D) 12 to 4
Step-by-step explanation:
First, we will find the number of people waiting in line for each activity.
➜ Bumper cars is 12
➜ Slingshot is 4
Next, we will create our ratio. This is asking for Bumper cars to Slingshot, so Bumper cars is first with Slingshot second.
➜ 12 to 4
whats 2+2? i rlly need to know
Answers
Answer:
4
Step-by-step explanation:
2+2 = 4
The answer is 2+2 = 4.
Fond the sum 2/5 + 3/6
Answers
To add 2/5 and 3/6, we need to find a common denominator for the two fractions. The smallest number that both 5 and 6 divide into evenly is 30. So, we can convert the two fractions to have a denominator of 30:
2/5 = 12/30 3/6 = 15/30
Now, we can add the two fractions by simply adding their numerators (since they have the same denominator):
12/30 + 15/30 = 27/30
We can simplify the fraction by reducing it to the lowest terms. Both the numerator and denominator have 3 as a factor, so we can divide them both by 3:
27/30 = (3 x 9) / (3 x 10) = 9/10
Therefore, the sum 2/5 + 3/6 is equal to 9/10.
please help me i really need it please
Answers
Answer: First one (top left)
Step-by-step explanation:
Answer:
One in the top left corner
Hope this helps!
Step-by-step explanation:
find the equation of circle with center (0,5)and a point on the circle (2,4)
Answers
The equation of the circle with center (0, 5) and a point on the circle (2, 4) is x² + (y - 5)² = 5
Define circleIn geometry, a circle is a closed two-dimensional shape that is formed by a set of points that are equidistant from a fixed point called the center. The distance between any point on the circle and the center is called the radius.
The equation of a circle with center (h, k) and radius r is given by:
r²=(x - h)² + (y - k)²
In this case, the center of the circle is (0, 5) and a point on the circle is (2, 4). The radius of a circle, which is the separation between its centre and any point on the surface, may be calculated using the following formula:
r = √((2 - 0)² + (4 - 5)²) = √(5)
Now we can substitute the values of the center and the radius into the equation of the circle:
(x - 0)² + (y - 5)² = (√(5))²
Simplifying, we get:
x²+ (y - 5)² = 5
As a result, the circle's equation with its centre (0, 5) and a point on it (2, 4) is:
x² + (y - 5)² = 5
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Analyze the diagram below and complete the instructions that follow.
Find sin 45°.
A.
112
B. √√√2
L
45°
Answers
Answer:
it was c
Step-by-step explanation:
because on my fraction test I got the same answer and it was right
Answer:
C
Step-by-step explanation:
because it
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Hudson sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
80 visitors purchased no costume.
32 visitors purchased exactly one costume.
3 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase more than one costume as a percent to the nearest whole number.
Answers
The probability that the next person will purchase more than one costume as a percent to the nearest whole number is 3%
.Out of the total 80 + 32 + 3 = 115 visitors, 80 did not purchase any costumes and 32 purchased exactly one costume. This means that the remaining 3 visitors purchased more than one costume.
Therefore, the probability that the next person will purchase more than one costume is 3/115, which is approximately 0.0261.
To express this as a percentage to the nearest whole number, we need to multiply by 100 and round to the nearest integer. Thus, the answer is:
0.0261 × 100 ≈ 3%
Therefore, the probability that the next person will purchase more than one costume is approximately 3%.
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The diameter of the semicircle with center $O,$ shown below, is 4 units. What is the area of the shaded region?
Answers
the area of the right-angled triangle with adjacent and opposite sides of 2 units is 2 square units.
what is right-angled triangle ?
A right-angled triangle is a type of triangle that has one angle measuring exactly 90 degrees (a right angle). This angle is formed by the intersection of two sides of the triangle, which are called the legs or catheti, and it is opposite to the longest side of the triangle, which is called the hypotenuse. The hypotenuse is always opposite the right angle.
In the given question,
The area of a right-angled triangle is given by the formula:
Area = 1/2 x base x height
where the base and height are the two perpendicular sides of the triangle.
In this case, the adjacent side and opposite side of the right-angled triangle are both 2 units.
Let's call the hypotenuse of the triangle 'c'. Then, by the Pythagorean theorem, we have:
c² = 2² + 2²
c² = 8
c = √(8) = 2.8284 (rounded to 4 decimal places)
Now, we can use the trigonometric ratios to find the base and height of the triangle. In this case, we can use the tangent ratio:
tan(theta) = opposite/adjacent
tan(theta) = 2/2
tan(theta) = 1
theta = tan⁻¹(1) = 45 degrees
Therefore, the base and height of the triangle are:
base = adjacent x tan(theta) = 2 x tan(45) = 2 x 1 = 2
height = opposite x tan(theta) = 2 x tan(45) = 2 x 1 = 2
Now we can use the area formula to find the area of the triangle:
Area = 1/2 x base x height
Area = 1/2 x 2 x 2
Area = 2 square units
Therefore, the area of the right-angled triangle with adjacent and opposite sides of 2 units is 2 square units.
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3(x-2) + 7x= 1/2 (6 x-2)
Answers
Simplify the right side of the equation by distributing the 1/2 :
3(x-2)+7x=1/2(6x-2)
3x-6+7x=3x-1
Combine like terms on both sides of the equation:
10x-6=3x-1
Add 6 to both sides of the equation:
10x=3x+5
Subtract 3x from both sides of the equation
7x=5
Finally, divide both sides of the equation by 7:
X=5/7
Therefore the solution is x=5/7.
Explaination:
First you remove the parentheses and rewrite. That leaves you with
3x - 6 + 7x = 1/2 * 2(3x - 1)
Then simplify the expression
3x - 6 + 7x = 3x - 1
Then cancel the equal terms on both sides
6- + 7x = -1
Then move the constant to the right
7x = -1 + 6
Add -1 + 6
7x = 5
Finally, divide it out!
x = 5/7
Answer the following questions with 2 complete sentences for each question.
1) What do you notice about the picture?
2) What do you wonder about the image?
3) What is the information in the picture trying to tell you?
Answers
1. The picture depicts the circle theorem
2. I wonder how the circle theorem fully apply to the image
3. The informed is that the angle between a radius and a tangent at the point of contact is a right angle.
Circle theoremThe angle between a radius and a tangent at the point of contact is a right angle.
Suppose FGC
Then FC is the hypothenuse of triangle FGC
So, FC greater than FG
FC greater than FB+BG
FC greater than FC+BG (impossible)
This is the case on either side of C along the tangent
So, the shortest distance between F and the tangent is FC
When the distance between a point and a line is minimum, the angle between them is right angled.
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