Based on the calculation, we find that:
(fog)(x) = (15Vx)¹⁵
(gof)(x) = 15V(x¹⁵)
(fog)(x) ≠ (gof)(x)
Function composition can be meant as an operation that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.
To find (fog)(x), we need to substitute g(x) into f(x). This means that we will replace every x in f(x) with 15Vx. So, (fog)(x) = f(g(x)) = f(15Vx) = (15Vx)¹⁵.
Similarly, to find (gof)(x), we need to substitute f(x) into g(x). This means that we will replace every x in g(x) with x¹⁵. So, (gof)(x) = g(f(x)) = g(x¹⁵) = 15V(x¹⁵).
Now, to determine whether (fog)(x) = (gof)(x), we need to compare the two expressions.
(fog)(x) = (15Vx)¹⁵ and (gof)(x) = 15V(x¹⁵). These two expressions are not equal, so (fog)(x) ≠ (gof)(x).
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Given that tangent theta = negative 1, what is the value of secant theta, for StartFraction 3 pi Over 2 EndFraction less-than theta less-than 2 pi?
Negative StartRoot 2 EndRoot
StartRoot 2 EndRoot
0
1
Answer:
Step-by-step explanation:
Since tangent is negative and is equal to the ratio of opposite over adjacent, we can assume that the angle theta lies in either the third or the fourth quadrant, where the x and y coordinates have opposite signs.
In the third quadrant, sine is positive and cosine is negative. Therefore, we have:
tangent theta = opposite/adjacent = -1
sine theta = opposite/hypotenuse > 0
cosine theta = adjacent/hypotenuse < 0
Using the Pythagorean identity, we have:
sin² theta + cos² theta = 1
=> opposite²/hypotenuse² + adjacent²/hypotenuse² = 1
=> opposite² + adjacent² = hypotenuse²
Since we are given that 3π/2 < theta < 2π, we can place the triangle in the third quadrant with a reference angle of π/2. This means that the opposite side is equal to the absolute value of the adjacent side. Let's assume that the hypotenuse is equal to 1, then we have:
opposite/adjacent = -1
=> opposite = -adjacent
opposite² + adjacent² = hypotenuse²
=> adjacent² + (-adjacent)² = 1
=> 2adjacent² = 1
=> adjacent = ±1/√2
Since cosine is negative in the third quadrant, we have:
cosine theta = adjacent/hypotenuse = -1/√2
Finally, we can use the reciprocal identity to find secant:
secant theta = 1/cosine theta = -√2
Therefore, the answer is A. Negative StartRoot 2 EndRoot.
The value of tangent theta is equal to the negative 1. At this value the value of secant theta is [tex]\sqrt{2}[/tex].
What is tangent theta?The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,
[tex]tan\theta=\dfrac{sin\theta}{cos\theta}[/tex]
Given information-
The value of tangent theta is equal to the negative 1.
[tex]tan\theta=-1[/tex]
The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,
[tex]tan\theta=\dfrac{sin\theta}{cos\theta}[/tex]
The value of tangent theta is equal to the negative 1. Thus put the value in above expression as,
[tex]-1=\dfrac{sin\theta}{cos\theta}[/tex]
Simplify it further as,
[tex]-cos\theta=sin\theta[/tex]
When the value of cosine and sine theta is equal, then the angle exist in
4th quadrant with the value of [tex]\dfrac{7\pi }{4}[/tex]. Which extent to the [tex]\sqrt{2}/2[/tex] for the cosine function.
In the trigonometry cosine theta is the reciprocal of the secant theta. Thus,
[tex]\dfrac{1}{sec\theta} =\dfrac{\sqrt{2} }{}[/tex]
[tex]sec\theta=\sqrt{}\dfrac{2}{2}[/tex]
Thus the value of secant theta is [tex]\sqrt{2}[/tex]
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\(f(x)=\frac{1}{x^4}.) a) Evaluate Integral [a=-1,b=4] f(x) dx. b) Find a value of Integral [a=4,b=4] f(x) dx.
The integral of f(x) from a=-1 to b=4 is \(\frac{21}{64}\). The lower and upper limits of integration are the same, the integral is 0.
a) To evaluate the integral of \(f(x)=\frac{1}{x^4}\) from a=-1 to b=4, we need to first find the antiderivative of f(x). The antiderivative of \(\frac{1}{x^4}\) is \(-\frac{1}{3x^3}\). Now we can use the Fundamental Theorem of Calculus to evaluate the integral:
Integral [a=-1,b=4] f(x) dx = \(-\frac{1}{3(4)^3} - (-\frac{1}{3(-1)^3})\)
= \(-\frac{1}{192} + \frac{1}{3}\)
= \(\frac{63}{192}\)
= \(\frac{21}{64}\)
So the integral of f(x) from a=-1 to b=4 is \(\frac{21}{64}\).
b) The integral of f(x) from a=4 to b=4 is 0. This is because the integral of a function over an interval of length 0 is always 0. In other words, if the lower and upper limits of integration are the same, the integral is 0.
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Instructions Use this triangle for problems 1-3
1. what is the value of angle B?
2. What is the length of BC
3. What is the length of AB
Answer:
Q1 Value of angle B = 50°
Q2 BC = 1.3
Q3 AB = 2.57
Step-by-step explanation:
For Part 1
The three angles of a triangle must add up to 180°
Therefore m∠B + 30 + 100 = 180
m∠B + 130 = 180
m∠B = 180 - 30 = 50°
part 2
The law of sines states that, in a triangle, the ratio of each side to the sine of the angle opposite that side must be the same for all sides
We have side AC opposite ∠B
AC = 2 and we found that m∠B = 50° from part 1
The side BC is opposite ∠A which is 30°
Therefore, applying the law of sines
[tex]\dfrac{{AC}}{\sin 50^\circ} = \dfrac{{BC}}{\sin 30^\circ}\\\\\\\dfrac{2}{\sin 50^\circ} = \dfrac{{BC}}{\sin 30^\circ}\\\\[/tex]
Multiplying both sides by sin 30° we get
[tex]\dfrac{2}{\sin 50^\circ} \times \sin 30^\circ =BC\\\\or\\\\BC = \dfrac{2}{\sin 50^\circ} \times \sin 30^\circ[/tex]
Using a calculator to compute the right side we get
BC = 1.30540 ≈ 1.3
part 3
Similarly
[tex]\dfrac{AB}{\sin 100} = \dfrac{2}{\sin50}\\\\AB = \sin 100 \times \dfrac{2}{\sin 50} = 2.57115 \approx 2.57[/tex]
Ammed five practice test to help him prepare for the written drivers permit test this chart shows the number of times he correctly answered the first five questions
Answer:
there is no chart or questions
Step-by-step explanation:
Determine the intervals where the following function is increasing or decreasing. g(x) = 3-1/zx, x<-2 . 4+3/2x, x>-2 Increasing on: (-2,infinity) Decreasing on: (-4,-2)
To determine the intervals where a function is increasing or decreasing, we need to take the derivative of the function and find the critical points. The critical points are where the derivative is equal to zero or undefined.
First, let's take the derivative of the function:
g'(x) = -1/(zx)^2, x<-2 . 3/2, x>-2
Now, let's find the critical points:
-1/(zx)^2 = 0 -> There are no values of x that will make this equation true, so there are no critical points for x<-2.
3/2 = 0 -> There are no values of x that will make this equation true, so there are no critical points for x>-2.
Since there are no critical points, the function is either always increasing or always decreasing. To determine which one it is, we can pick a value of x in each interval and plug it into the derivative:
For x<-2, let's pick x=-3:
g'(-3) = -1/(-3z)^2 = 1/(9z^2) > 0
Since the derivative is positive, the function is increasing on the interval (-infinity, -2).
For x>-2, let's pick x=0:
g'(0) = 3/2 > 0
Since the derivative is positive, the function is also increasing on the interval (-2, infinity).
Therefore, the function is increasing on the entire domain of the function, which is (-infinity, infinity).
Answer: Increasing on: (-infinity, infinity) Decreasing on: None
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PLEASE HELP IM TIMED!
The value for the function f(g(-2)) is obtained as f(g(-2)) = 0.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The graph for the function y = f(x) is given.
The graph for the function y = g(x) is given.
We need to evaluate the function f(g(-2)).
From the graph of y = g(x) the value for g(-2) is obtained as -
g(-2) = 1
So, now we have -
f(g(-2)) = f(1)
From the graph of y = f(x) the value for f(1) is obtained as -
f(1) = 0
Therefore, the value is obtained as 0.
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Dierks made $13.50 per hour. He got a new job in which he made 8% more. How much did her her make per hour at his new job?
Answer: $14.58
Step-by-step explanation:
13.50 x .08 = 1.08
13.50 + 1.08 = 14.58
(1 point) Determine whether the following matrices are in echelon form, reduced echelon form or not in echelon form.
a. Reduced echelon form [100 010 000 -10-100]
b. Not in echelon form [ -8000 -4200 -8110 -9101 -8130]
c. Reduce echelon form [11 10 -4 -10]
d. Echelon form [ 100 001 000 -502]
The given matrices are checked and their status is mentioned in the following list below :a. Reduced echelon form [100 010 000 -10-100] b. Not in echelon form [ -8000 -4200 -8110 -9101 -8130] c. Reduce echelon form [11 10 -4 -10] d. Echelon form [ 100 001 000 -502] Echelon form and reduced echelon form of matrices
The Matrix A is in the reduced echelon form if and only if the following conditions are satisfied:All rows having 0s are at the bottom of the matrix.There must be no 0 rows in the matrix.In each row of the matrix containing the leading nonzero element, all entries above and below the leading entry are 0.
The leading coefficient of a nonzero row is always strictly to the right of the leading coefficient of the row above it.In each column containing a leading coefficient, all other entries are zero.
For a matrix to be in echelon form, it must fulfill the following conditions : All rows containing all zero elements are located at the bottom of the matrix. All leading coefficients in any nonzero row are always strictly to the right of the leading coefficient in the row above it.
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The diameter of a circle is 10 ft. Find its area to the nearest whole number.
When the diameter οf the is 10 feet, then the area οf the circle is 78.54 ft².
What is circle?A circle is created in the plane by each pοint that is a specific distance frοm anοther pοint (center). Hence, it is a curve made up οf pοints that are separated frοm οne anοther by a defined distance in the plane. Mοreοver, it is rοtatiοnally symmetric abοut the centre at every angle. Every pair οf pοints in a circle's clοsed, twο-dimensiοnal plane are evenly spaced apart frοm the "centre." A circular symmetry line is made by drawing a line thrοugh the circle. Mοreοver, it is rοtatiοnally symmetric abοut the centre at every angle.
The circle's diameter is specified as 10 feet. Since we already knοw that the circle's diameter is twice its radius, we can calculate its radius as fοllοws:
diameter = radius / 2 = 10 / 2 = 5 feet
Area οf circle = πr²
π5²
= π5 × 5
= 78.54 ft²
The size οf the circle is 79 square feet when the answer is rοunded tο the next whοle number.
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The area of the circle to the nearest whole number is 79 square feet.
What is the diameter?
In geometry, the diameter of a circle is defined as the longest straight line segment that can be drawn between any two points on the circle, passing through the center of the circle. It is twice the length of the radius of the circle.
The formula for the area of a circle is A = πr^2, where r is the radius of the circle.
Given that the diameter of the circle is 10 feet, we can find the radius by dividing the diameter by 2:
radius = diameter / 2 = 10 ft / 2 = 5 ft
Now we can use the formula to find the area of the circle:
A = πr^2
= π(5 ft)^2
= 25π square feet
To get the answer to the nearest whole number, we can use the approximation π ≈ 3.14:
A ≈ 25 × 3.14
≈ 78.5
Therefore, the area of the circle to the nearest whole number is 79 square feet.
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Please help I will give you 5 stars 20 points and a heart its urgent
7x - 4y = -8
X + 2y = -14
Step-by-step explanation:
First of all sorry for the bad hand writing
so rn I'm using elimination method which I try to eliminate y by multiple number 2 equation with 2
in order to find x
I know my explanation is quite confusing but any way goodluck n hope u understand
HELP PLS HURRY...............................................................................
Answer:
C) - 1/10--------------------------------
Given two points:
[tex](-3, -7/2}) \ and \ (2, -4)[/tex]Find the slope of the line containing these points.
Slope equation:
[tex]m=(y_2-y_1)/(x_2-x_1)[/tex]Substitute coordinates and find the slope:
[tex]m=(-4-(-7/2))/(2-(-3))=(-4+7/2)/(2+3)=(-1/2)/5=-1/10[/tex]Answer:
-1/10
Step-by-step explanation:
To find:-
The slope of the line passing through the points (-3,-7/2) and (2,-4) .Answer:-
We are here given two points and we are interested in finding out the slope of the line passing through the points. Slope can be calculated by using;
[tex]:\implies \sf \boxed{\pink{\sf m =\dfrac{y_2-y_1}{x_2-x_1}}} \\[/tex]
where ,
(x1,y1) and (x2,y2) are the coordinates of the two points.Also , we can write the coordinate (-3,-7/2) as (-3,-3.5) .
So on substituting the respective values, we have;
[tex]:\implies \sf m =\dfrac{-3.5- (-4)}{-3-2} \\[/tex]
[tex]:\implies \sf m = \dfrac{-3.5+4}{-5} \\[/tex]
[tex]:\implies \sf m =\dfrac{0.5}{-5} \\[/tex]
[tex]:\implies \sf m = \dfrac{1}{2(-5)}\\[/tex]
[tex]:\implies \sf m =\dfrac{1}{-10} \\[/tex]
[tex]:\implies \sf \pink{ m =\dfrac{-1}{10}} \\[/tex]
Hence the slope of the line is -1/10 .
In excerpt from baby mammoth mummy: frozen in time What does the narrator think of Sky's view of women? Use two details from the story to
port your response.
The narrator's thoughts on Sky's view of women is that the view is confusing and hypocritical.
What does the narrator think of sky's view ?The narrator thinks that Sky's perspective on women is unexpected, perplexing, absurd, and at odds with the person Sky appears to be. She is taken aback by Sky's refusal to perform any chores he views as falling under the purview of women.
The narrator is even more shocked that when Sky observes her "struggling with a bucket of water," he advises her not to fill the bucket all the way up rather than offering to assist her.
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The sum of four times a number x and another number y is 65. The difference of five times the number x and three times y is 94. What is the value of y?
The value of y is -3. The equation formed from the question is 4x + y = 65 and 5x -3y = 94.
First, we will solve for x
Multiplying the 4x + y = 65 equation by 3 we get
12x +3y =195
Now solving both the equation
The variable y gets cancelled because of having the same value
∴ 17x = 289
x= 17
Now putting the value of x in equation 4x + y = 65 to get the value of y
4*17 +y =65
68 +y = 65
y= -3
Now putting the value of x in equation 5x -3y = 94 to get the value of y
5*17 -3y =94
85 -3y =94
-3y = 94-85
y= -3
Therefore, the value of y is -3
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Jimmy is paying for a meal with group of friends. They received great service, so he is giving a 20% tip. The meal came to 166.60 before sales tax. How much will he leave as a tip?
Tip=$
Jimmy will leave a $33.32 tip for the great service.
What is the total of the cost?
Whole cost is the sum of all expenditures made to generate a certain level of production; when this total cost is divided by the amount produced, average or unit cost is discovered.
To calculate the tip, we need to first find 20% of the total cost of the meal (before sales tax):
20% of 166.60 = 0.20 x 166.60 = 33.32
Therefore, Jimmy will leave a $33.32 tip for the great service.
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How many real solutions are there to the equation 2(x-1)^(2)(2x+3)(x+5)^(3)=.001?
There are 2 real solutions to the equation [tex]2(x-1)^(2)(2x+3)(x+5)^(3)=.001.[/tex]
To find the real solutions, we can use the zero product property. This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero. In this case, we can set each of the factors equal to zero and solve for x:
[tex]2(x-1)^(2)=02x+3=0(x+5)^(3)=0[/tex]
Solving each of these equations gives us the following solutions:
[tex]x=1x=-3/2x=-5[/tex]
However, we need to check each of these solutions to see if they satisfy the original equation. Plugging each solution back into the equation gives us:
[tex]2(1-1)^(2)(2(1)+3)(1+5)^(3)=.0012(-3/2-1)^(2)(2(-3/2)+3)(-3/2+5)^(3)=.0012(-5-1)^(2)(2(-5)+3)(-5+5)^(3)=.001[/tex]
The first and third solutions do not satisfy the equation, but the second solution does. Therefore, there are 2 real solutions to the equation [tex]2(x-1)^(2)(2x+3)(x+5)^(3)=.001.[/tex]
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helloo!! i need help figuring out the like terms in this list. thanks! :)
The like terms on the list are given as follows:
[tex]\sqrt{2}, -3\sqrt{2}, 5\sqrt{2}, \sqrt{50}[/tex]
What are like terms?Like terms are terms that share these two features:
Same letters. (algebraic variables).Same exponents.If two terms are like terms, then they can be either added or subtracted.
In the case the terms are roots, they have the same root.
The square root of 50 is given as follows:
[tex]\sqrt{50} = \sqrt{2 \times 25} = 5\sqrt{2}[/tex]
Hence the like terms are given as follows:
[tex]\sqrt{2}, -3\sqrt{2}, 5\sqrt{2}, \sqrt{50}[/tex]
There are no terms with 3 or 5 on the root, hence the other two terms have no like terms.
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Classify the polygon. Be as specific as possible.
Quadrilateral JKLM with JK = 10, KL = 7, ML = 10, and JM = 7
We can say that JKLM is an isosceles trapezoid, since the non-parallel sides (JK and ML) are congruent.
What is Polygon?A polygon is a closed plane figure with three or more straight sides that meet at the vertices. It is formed by connecting line segments endpoint-to-endpoint with each segment intersecting exactly two others.
The given quadrilateral JKLM has four sides, and its opposite sides are parallel.
Furthermore, since all four sides have different lengths, it is not a parallelogram.
Also, since no angles or sides are congruent, it is not a kite or a rhombus.
Therefore, the most specific classification for this quadrilateral would be a trapezoid, which is a quadrilateral with one pair of parallel sides.
To be more specific, we can say that JKLM is an isosceles trapezoid, since the non-parallel sides (JK and ML) are congruent.
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EN UNA SUSTRACCION QUE SUCEDE CON LA DIFERENCIA SI SOLO EL MINUENDO AUMENTA 10 UNIDADES
The solution of the given problem of unitary comes out to be the difference grows in the same proportion that we grow the minute.
What is an unitary method?The data collected from this nanosection must be multiplied by two in order to complete the task using the unitary technique. In essence, the color portions of both the unit method are either skipped or the indicated entity is set when a wanted item shows. For forty pens, a variable charge of Inr ($1.01) could have been required. It's possible that one country will have total influence over the approach taken to accomplish this.
Here,
The difference in a sustraction is equal to the remainder of the minute less the sustrancing.
The remainder between the new minuendo and the sustraendo will be greater than the previous remainder if the minuendo increases by just 10 units.
For instance, the difference is 15 if the remainder is
=> 25 – 10.
If we only increase the minimum by 10 units,
we will have
=>35 – 10 and the new difference will be 25.
In other words, the difference grows in the same proportion that we grow the minute.
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Complete question:
If in a subtraction, the minuend increases by 10 units, how much does the difference increase?
In a garment factory, a women work b hours a day and produce c articles each day. If
d women are released, how many hours a day will the remaining women have to work
to produce c articles each day? (There’s an attached photo to this !)
The equation (bd)/(b-d) = c can be used to determine how many hours a day the remaining women must work in order to produce the same number of articles each day, when some of the women have been released.
What is an equation?An equation is an expression used to relate two or more quantities, usually by using mathematical operators such as addition, subtraction, multiplication and division. An equation typically has an equal sign (=) as its central element, with the left and right sides of the equation representing the two sides of the equation.
The answer to this question can be determined by using the following equation: (bd)/(b-d) = c. This equation is a simple ratio that takes into account the number of hours the women work per day (b), the number of women released (d), and the number of articles produced each day (c).
For example, if a factory had 10 women working 8 hours a day and produced 100 articles each day, and 5 of those women were released, then the equation (8 x 5) / (8-5) = 100 would determine that the remaining women must work 12.5 hours per day in order to produce the same number of articles.
In conclusion, the equation (bd)/(b-d) = c can be used to determine how many hours a day the remaining women must work in order to produce the same number of articles each day, when some of the women have been released.
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L.8 Solve polynomial equations ZCH Solve using the quadratic formula. -9h^(2)+6h+4=0
The solutions to the given polynomial equation are x = (1 + √5)/(3) and x = (1 - √5)/(3).
To solve the given polynomial equation using the quadratic formula, we need to first identify the values of a, b, and c. In this case, a = -9, b = 6, and c = 4. The quadratic formula is given by:
x = (-b ± √(b^(2) - 4ac))/(2a)
Plugging in the values of a, b, and c into the formula, we get:
x = (-(6) ± √((6)^(2) - 4(-9)(4)))/(2(-9))
Simplifying the equation, we get:
x = (-6 ± √(36 + 144))/(-18)
x = (-6 ± √180)/(-18)
x = (-6 ± 6√5)/(-18)
x = (1 ± √5)/(3)
Therefore, the solutions to the given polynomial equation are x = (1 + √5)/(3) and x = (1 - √5)/(3).
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Which equation calculates the number of 13
-foot pieces that can be cut from a piece of wood that is 7
feet long?
CLEAR CHECK
13÷7=121
7÷13=121
13÷7=21
7÷13=21
Answer:
2
Step-by-step explanation:
Select the correct answer
Answer:
6
Step-by-step explanation:
simplified and I got 6 because square root of 80 is that
√8=√2x2x2
Im Not Sure If You Needed This Or Not
Giving 50 POINTS. Im really struggling please no guesses or wrong answers. thank you! appreciate it
Look at the picture.
<, > - dotted line
≤, ≥ - solid line
x > a, x ≥ a - to the right of a
x < a, x ≤ a - to the left of a
y > a, y ≥ a - up from a
y < a, y ≤ a - down from a
What is the highest number of degrees (as a whole number) an image can rotate without returning to it's exact original position?
please answer in __°!
Answer:
359°
Step-by-step explanation:
When an image is rotated by a multiple of 360 degrees, it returns to its original position because it has completed one full revolution. However, if the image is rotated by any angle less than 360 degrees, it will not return to its exact original position.
For example, if an image is rotated by 45 degrees, it will not return to its exact original position, but will instead be in a new and unique position. If the image is then rotated by another 45 degrees, it will again be in a new and unique position, and so on.
Therefore, the highest number of degrees an image can rotate without returning to its exact original position is 359 degrees.
Answer: 359 degrees
Step-by-step explanation:
If you rotate any object exactly 360 degrees, it returns to it's original position. Remember that phrase "360 no-scope?" It involves spinning until you're back where you started; try doing it right now. You'll be back where you were. But this question wants to know how far you can rotate an object without it being back where it was. I would usually say 359.999999999, but it's a whole number answer, so we'll stick with 359. Hope this helps!
6 time the quantity of a number minuse 5 is 90
Answer:
6(x)-5=90
Step-by-step explanation:
Move all terms that don't contain x to the right side and solve.
Exact Form:
x=95/6
Decimal Form:
x=15.83
Mixed Number Form:
x= 15 5/6
tbh i don't know if this is right
In a video game each player earns 5 pts for reaching the next level and 15 pts for each coin collected. Make a table to show the relationship between the num of coins collected c and total pts p graph the ordered pairs and analyze the graph
Table showing relation of points and coins is as in the solution, graph is straight line p = 15c+5, drawn and attached below. y-intercept is (0,5).
What is table?A table has records (rows) and fields (columns). Fields have different data types. as Text, Numbers, Dates, and Hyperlinks. record: It contains certain data, such as information about specific employees or products.
Given,
In a video game, player earns 5 points for reaching next level
15 points are for each coin collected
when player has 1 coin, number of points
= 15 + 5
= 20
when player has 2 coin, number of points
= 2(15) + 5
= 35
Equation for c coins, number of points
p = 15c + 5
Table can be created as follows:
Coins(c) Points()
0 5
1 15
2 35
3 50
4 65
5 80
6 95
7 110
8 125
Graph is a straight line, y-intercept is (0,5).
Hence, table of the relationship of points and coins is
Coins 0 1 2 3 4 5 6 7 8
Points 5 15 35 50 65 80 95 110 125
Graph of the data is an straight line p = 15c + 5, (0,5) is y-intercept.
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Write the correct postulate, theorem, property, or definition that justifies the statement below the diagram.
Given: ∠MRS ≅ ∠MRO
In the given figure the equation m∠MRS + m∠MRO = 180° is the postulate describing the linear pair of angles.
What is an angle?The English word "angle" derives from the Latin word "angulus," which means "corner." The vertex and the two rays are referred to as the sides of an angle, respectively, and are the shared termini of two rays.
It is given that -
∠MRS ≅ ∠MRO
Now, what that means is that ∠MRS is congruent to ∠MRO.
Thus, to understand this concept of equality or congruence, we can prove it since from the given image, we see that -
m∠MRS = m∠MRO = 90°
Since they are both right angles then we can say that the correct theorem is the definition of a right angle triangle.
m∠MRS + m∠MRO = 180°
It is seen that the angles form a linear pair and lie on the same plane.
Therefore, the correct postulate is linear pair.
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A hot air balloon is 520m from the ground. A building is 450m tall. If the angle of elevation from the top of the building to the hot air balloon is 10, find the horizontal distance from the balloon to the building in meters
Answer: The horizontal distance from the hot air balloon to the building is approximately 2533.39 meters.
Step-by-step explanation:
We can use trigonometry to solve this problem. Let's draw a diagram to visualize the situation!!
=== begin diagram ===
B (balloon)
/|
/ |
/ | 520m
/ |
/θ |
/ |
/______|___ C (ground)
A D
=== end diagram ===
In the diagram, we have a hot air balloon at point B that is 520m from the ground at point C. We also have a building at point D that is 450m tall. The angle of elevation from point D to point B is 10 degrees (angle θ).
We want to find the horizontal distance between point B and point D (distance AB in the diagram).
To do this, we can use the tangent function:
tan(θ) = opposite/adjacent
In this case, the opposite side is the height of the building (450m) and the adjacent side is the horizontal distance we want to find (AB). We can rearrange the formula to solve for AB:
AB = opposite/tan(θ)
AB = 450m / tan(10°)
AB ≈ 2533.39m
Therefore, the horizontal distance from the hot air balloon to the building is approximately 2533.39 meters.
Mav has $560 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.She buys a new bicycle for $425.05.
She buys 4 bicycle reflectors for $15.19 each and a pair of bike gloves for $15.79.
She plans to spend some or all of the money she has left to buy new biking outfits for $29.20 each.
Write and solve an inequality which can be used to determine
�
o, the number of outfits Mav can purchase while staying within her budget.
Answer:
Inequality:
29.2x + 501.60 ≤ 560
Answer:
She may buy up to 2 reflectors.
Step-by-step explanation:
She can spend up to $560, so the total expense has to be less than or equal to $560.
total expense ≤ 560
All items she buys have a price and a number of items except for the outfits which have a price but an unknown number.
Let x = number of outfits.
total expense = $425.05 + 4 × $15.19 + $15.79 + x × $29.20
total expense = 29.2x + 501.60
Inequality:
29.2x + 501.60 ≤ 560
29.2x ≤ 58.4
x ≤ 2
She may buy up to 2 reflectors.
