Answer:
45 feet
Step-by-step explanation:
This is a classic right triangle trig problem. We have a reference angle, which is the angle made between the ground and the belt, of 32 degrees. The height up the side of the barn, which is the side across from the reference angle, is 24 feet. Which of our trig ratios relates side opposite to the hypotenuse? It's the sin ratio, so let's set it up and solve for the length of the belt, which is the hypotenuse of the right triangle.
[tex]sin(32)=\frac{24}{x}[/tex]
Doing some algebraic acrobatics that with we get
[tex]x=\frac{24}{sin(32)}[/tex]
Plug that into your calculator in degree mode and you'll get 45.28991. Rounded to the nearest foot is 45 feet.
The length of the conveyor is approximately 45 feet.
The subject of the question is Mathematics, and it deals with determining the length of a conveyor belt that makes an angle with the horizontal. This type of problem involves trigonometry, specifically the use of sine, cosine, or tangent functions to find the length of the hypotenuse of a right-angled triangle.
To find the length of the conveyor belt, we consider the belt as the hypotenuse of a right-angled triangle, with the vertical height of the barn door as the opposite side, and the angle given as the angle between the belt (hypotenuse) and the ground (adjacent side).
The height of the barn door is 24 feet, and the angle between the belt and the ground is 32 degrees. We can use the sine function (sin) since we have the opposite side and need to find the hypotenuse (length of the conveyor belt).
The formula to find the length (L) of the conveyor belt is:
L = height / sin(angle)
L = 24 feet / sin(32 degrees)
L = 24/0.5299
L = 45.29 feet
Pam drove her car 288 miles using a total of 12 gallons. How many gallons would it take for her to drive a total of 156 miles? Gallons
Answer:
6.5 Gallons
Step-by-step explanation:
288 miles / 12 gallons = 24 mpg
156 miles / 24 mpg = 6.5 gallons
2 Points
A football coach is trying to decide: When a team is ahead late in the game,
which strategy is better?
• Play the "regular" defense.
• Play a "prevent" defense that guards against long gains but makes short
gains easier.
The coach reviews the outcomes of 100 games.
Win
Loss
8
Total
50
42
Regular defense
Prevent defense
35
15
50
Total
77
23
100
Compare the probability of winning when playing regular defense with the
probability of winning when playing prevent defense. Draw a conclusion
based on your results.
PREVIOUS
Answer:0.76
0.58
Conclusion you are More likely to win by playing regular defense
Step-by-step explanation:
Probability of winning when playing regular defense is greater than probability of winning when playing prevent defense.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given that,
Taking the strategy of "regular" defense,
P(winning) = 42
P(losing) = 8
Total regular defense games = 50
Taking the strategy of "prevent" defense,
P(winning) = 35
P(losing) = 15
Total regular prevent games = 50
Total games = 100
Probability of winning when playing regular defense = 42 / 50 = 0.84
Probability of winning when playing prevent defense = 35 / 50 = 0.7
Hence, Probability of winning when playing regular defense is greater than probability of winning when playing prevent defense.
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plz help!!!
Select the correct answer.
What is the inverse of the function f(x)=x+1/x?
A.)F^-1(x)=x/x+1
B.)F^-1(x)=1/x-1
C.)F^-1(x)=x-1/x+1
D.)F^-1(x)=x/x-1
we know that f(1)=2 so f^-1(2)=1
so B is correct!
Answer: The correct option is
(B) [tex]f^{-1}(x)=\dfrac{1}{x-1}.[/tex]
Step-by-step explanation: We are given to select the correct expression that is the inverse of the following function :
[tex]f(x)=\dfrac{x+1}{x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Let y denotes f(x). Then,
[tex]y=f(x)~~~~~~\Rightarrow x=f^{-1}(y).[/tex]
Substituting this value in equation (i), we get
[tex]f(x)=\dfrac{x+1}{x}\\\\\\\Rightarrow y=\dfrac{f^{-1}(y)+1}{f^{-1}(y)}\\\\\\\Rightarrow yf^{-1}(y)=f^{-1}(y)+1\\\\\Rightarrow yf^{-1}(y)-f^{-1}(y)=1\\\\\Rightarrow (y-1)f^{-1}(y)=1\\\\\Rightarrow f^{-1}(y)=\dfrac{1}{y-1}\\\\\Rightarrow f^{-1}(x)=\dfrac{1}{x-1}.[/tex]
Thus, the required inverse of the given function is
[tex]f^{-1}(x)=\dfrac{1}{x-1}.[/tex]
Option (B) is CORRECT.
Find the values of m and b that make the following function differentiable.
f(x) = {x^2, x less than or equal to 2
mx+b, x>2}
thank you so much!!
Both x² and mx + b are differentiable functions of x (they are both polynomials), so if f(x) is also differentiable, we need to pay special attention at x = 2 where the two pieces of f meet.
Continuity means that the limit
[tex]\displaystyle \lim_{x\to2} f(x)[/tex]
must exist.
From the left side, we have x < 2 and f(x) = x², so
[tex]\displaystyle \lim_{x\to2^-} f(x) = \lim_{x\to2} x^2 = 4[/tex]
From the right, we have x > 2 and f(x) = mx + b, so
[tex]\displaystyle \lim_{x\to2^+} f(x) = \lim_{x\to2} (mx+b) = 4m+b[/tex]
It follows that 4m + b = 4.
Differentiability means that the limit
[tex]\displaystyle \lim_{x\to2} \frac{f(x) - f(2)}{x - 2}[/tex]
must exist.
From the left side, we again have x < 2 and f(x) = x². Then
[tex]\displaystyle \lim_{x\to2^-}\frac{f(x)-f(2)}{x-2} = \lim_{x\to2} \frac{x^2-4}{x-2} = \lim_{x\to2} (x+2) = 4[/tex]
From the right side side, we have x > 2 so f(x) = mx + b. Then
[tex]\displaystyle \lim_{x\to2^+}\frac{f(x)-f(2)}{x-2} = \lim_{x\to2} \frac{(mx+b)-(2m+b)}{x-2} = \lim_{x\to2} \frac{mx-2m}{x-2} = \lim_{x\to2}m = m[/tex]
The one-sided limits must be equal, so m = 4, and from the other constraint it follows that 16 + b = 4, or b = -12.
Triangle XYZ is translated 4 units up and 3 units left to yield ?X'Y'Z'. What is the distance between any two corresponding points on ?XYZ and ?X'Y'Z?
Answer:
5 units
Step-by-step explanation:
Let's take point X and X' (it will be the same regardless of the point).
The distance is 3 units to the right then 4 units up.
A direct line will be diagonal and can be found using the pythagorean theorem (refer to visual).
(D: a > 0) 3² + 4² = a² --> 9 + 16 = a² --> a² = 25 --> a = 5
So the distance is 5 units.
When a figure is translated, or moved without rotation or change in size, the distances between corresponding points on the original and new figure remain the same. Therefore, the distance between any two corresponding points on Triangle XYZ and Triangle X'Y'Z' is the same as it was prior to the translation.
Explanation:
In this case, the triangle XYZ is being translated, which means that it is being shifted in the plane. The student has moved the triangle 4 units up and 3 units left. This operation does not alter the size, shape or orientation of the triangle, just its position. Therefore, the distance between any two points on the triangle remains the same before and after the translation. To clarify, if the distance between point X and Y initially is 'd', after the triangle has been translated to yield triangle X'Y'Z', the distance between X' and Y' remains 'd'. This is an important characteristics of translation, a core concept in geometry.
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Please please help me out
Step-by-step explanation:
[tex] { \sin(x) }^{2} + { \cos(x) }^{2} = 1 \\ { \cos(theta) }^{2} = \frac{9}{16} \\ \: { \sin(theta) }^{2} = \frac{6}{16} = \frac{3}{8} \\ \: \sin(theta) = \frac{ \sqrt{3} }{ \sqrt{8} } \\ \sin(theta ) = \frac{ \sqrt{24} }{8}
= \frac{ 2\sqrt{6} }{8} = \frac{ \sqrt{6} }{4}
[/tex]
Answer:
[tex]\frac{\sqrt{7} }{4}[/tex]
Step-by-step explanation:
Using the Pythagorean identity
sin²x + cos²x = 1, then
sinx = [tex]\sqrt{1-cos^2x}[/tex]
sinΘ = [tex]\sqrt{1-(3/4)^2}[/tex]
= [tex]\sqrt{1-\frac{9}{16} }[/tex] = [tex]\sqrt{\frac{7}{16} }[/tex] = [tex]\frac{\sqrt{7} }{4}[/tex]
"How are we ever going to build this bridge?" asks Omkar looking out across the raging river. "Let's start by finding the distance to the big rock on the other side." Melissa replies. Moving 100100100 meters along the river, Melissa looks back and measures the angle between Omkar and the big rock: 33^\circ33 ? 33, degree. Melissa then instructs Omkar to measure the angle between Melissa and the big rock. From his vantage point, Omkar sees an angle of 98^\circ98 ? 98, degree between Melissa and the big rock. What is the distance across the river from Omkar to the big rock? Do not round during your calculations. Round your final answer to the nearest meter.
Answer:
The distance across the river from Omkar to the big rock is 131343149 meters
Step-by-step explanation:
* Lets study the information in the problem
- Let Omkar position is point A
- Let Melissa position is point B
- Let big rock position is C on the other side of the river
* Now we have triangle ABC
- The distance between Omkar and Melissa is 100100100 meters
along the river
- The angle between Omkar and the big rock is angle BAC
∴ m∠BAC = 33°
- The angle between Melissa and the big rock is angle ABC
∴ m∠ABC = 98°
- The big rock is at angle C
* Now we can find the distance between Omkar and the big rock
by finding the length of side AC in the triangle
- By using the sine rule
∵ sin A/BC = sin B/AC = sin C/AB
∵ AB = 100100100 meters
∵ m∠ABC = 98°
- Lets find m∠C
∵ In any triangle the sum of the measures of the interior angles is 180°
∴ m∠A + m∠B + m∠C = 180°
∵ m∠A = 33° , m∠B = 98°
∴ 33° + 98° + m∠C = 180° ⇒ add
∴ 131° + m∠C = 180° ⇒ subtract 131 from both sides
∴ m∠C = 49°
- Now lets use the sine rule
∵ sin ABC/AC = sin C/AB
∴ sin 98/AC = sin 49/100100100 ⇒ by using cross multiplication
∴ AC = (sin 98 × 100100100) ÷ sin 49 = 131343148.8
∴ AC ≅ 131343149 meters
* The distance across the river from Omkar to the big rock is
131343149 meters
Answer:
The distance across the river from Omkar to the big rock is 72 meters.
Step-by-step explanation:
Using the given information draw as triangle as shown below.
According to angle sum property, the sum of interior angles of a triangle is 180°.
In triangle ABC,
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]98^{\circ}+33^{\circ}+\angle C=180^{\circ}[/tex]
[tex]131^{\circ}+\angle C=180^{\circ}[/tex]
[tex]\angle C=180^{\circ}-131^{\circ}=49^{\circ}[/tex]
The measure of angle C is 49°.
Sine formula:
[tex]\frac{a}{\sin a}=\frac{b}{\sin b}=\frac{c}{\sin c}[/tex]
Using sine formula in triangle ABC, we get
[tex]\frac{AC}{\sin B}=\frac{AB}{\sin C}[/tex]
[tex]\frac{AC}{\sin 33^{\circ}}=\frac{100}{\sin 49^{\circ}}[/tex]
[tex]AC=\frac{100}{\sin 49^{\circ}}\times \sin 33^{\circ}[/tex]
[tex]AC=\frac{100}{0.7547}\cdot0.544639[/tex]
[tex]AC=72.166[/tex]
[tex]AC\approx 72[/tex]
Therefore the distance across the river from Omkar to the big rock is 72 meters.
Over the summer, for every 14 Okra seeds Dana planted, 9 plants grew. If he planted 182 seeds how many grew into plants
Answer:
117
Step-by-step explanation:
182/14=13
13x9=117
How do you solve for the quotient of (x^-1) - 1 ÷ x - 1?
[tex]\bf x^{-1}-1\div x-1\implies \implies \cfrac{1}{x}-1\div x-1\implies \cfrac{\frac{1}{x}-1}{~~x-1~~}\implies \cfrac{~~\frac{1-x}{x}~~}{\frac{x-1}{1}} \\\\\\ \cfrac{1-x}{x}\cdot \cfrac{1}{x-1}\implies \cfrac{-(\begin{matrix} x-1 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix})}{x}\cdot \cfrac{1}{\begin{matrix} x-1 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\implies -\cfrac{1}{x}\implies -x^{-1}[/tex]
If f(x) and its inverse function, f^-1(x), are both plotted on the same coordinate plane, where is their point of intersection?
Answer:
Step-by-step explanation:
Their point of intersection, assuming there is one, will be somewhere on the line y = x. This line, y = x, is the line of symmetry between a function and its inverse. So if the two do in fact intersect, it will be at some point on that line
the time in minutes for each of Sam's phone calls this week are shown in the list
Answer:
Where's the list?
What is the exact value of sin 60° ?
Enter your answer, as a simplified fraction, in the box.
$$
Answer:
The exact value of [tex]\sin(60\degree)[/tex] is [tex]\frac{\sqrt{3} }{2}[/tex].
Step-by-step explanation:
Recall that [tex]\sin(60\degree)[/tex] is a special angle that can be obtained using an equilateral triangle.
The right triangle obtained using one of the lines symmetry was used to find the exact value of [tex]\sin(60\degree)[/tex] using SOH-CAH-TOA
The exact value of [tex]\sin(60\degree)[/tex] is [tex]\frac{\sqrt{3} }{2}[/tex].
If he randomly chooses two students, one at a time, what is the probability that they are both girls?
Answer:
B) 15/91
Step-by-step explanation:
Probability of a girl as first choice is ...
number of girls / total number of students = 6/14 = 3/7
Probability of a girl as second choice (given a girl as first choice) is ...
number of girls / remaining number of students = 5/13
Then the probability of the two events is the product of their individual probabilities:
(3/7)·(5/13) = 15/91 . . . . . matches choice B
A parallelogram has vertices (5, 0), (3, -3), (-4, -3), and (-2, 0). What is the approximate perimeter of the parallelogram?
Check the picture below.
so the top and bottom segments are simply 7 units, we can read that off the grid. Let's find the length of the other two segments, "c".
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{2}\\ b=\stackrel{opposite}{3}\\ \end{cases} \\\\\\ c=\sqrt{2^2+3^2}\implies c=\sqrt{13} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perimeter of the parallelogram}}{7+7+\sqrt{13}+\sqrt{13}}\qquad \approx \qquad 21.21[/tex]
Answer:
C: 30 units
Step-by-step explanation:
on edge 2021! hope this helps!!~ d=(´▽｀)=b
Please help me out please!!!!!!!!!
Answer:
Do Addition
Step-by-step explanation:
x=76+78
x= 154
Answer:
x = 77°
Step-by-step explanation:
The measure of x is half the sum of the measures of the arcs intercepted by the angle and it's vertical angle, that is
x = 0.5 × (78 + 76)° = 0.5 ×154° = 77°
What is the value of coefficient c in this quadratic equation?
5x2 + 6x + 7 = 2(x + 2)
A.
7
B.
4
C.
3
D.
-3
E.
3/5
Answer:
C 3
Step-by-step explanation:
5x^2 + 6x + 7 = 2(x + 2)
Distribute the 2
5x^2 + 6x + 7 = 2x + 4
Subtract 2x from each side
5x^2+6x-2x +7 = 2x-2x+4
5x^2 + 4x + 7 = 4
Subtract 4 from each side
5x^2 +4x+7-4 = 4-4
5x^2 +4x+3 = 0
This is in the form ax^2 + bx +c where c is 3
Answer:
C. 3Step-by-step explanation:
[tex]ax^2+bx+c=0\\\\5x^2+6x+7=2(x+2)\qquad\text{use the distributive property}\\\\5x^2+6x+7=2x+4\qquad\text{subtract}\ 2x\ \text{and 4 from both sides}\\\\5x^2+4x+\boxed{3}=0[/tex]
Help! Find the value of x to the nearest hundredth
Question 9:
cos x = 10/36
Take the inverse on both sides.
arccos(cos x) = arccos(10/36)
x = 73.8723797868
x = 73.87
Question 10:
tan 89 = x
57.2899616308 = x
57.29
Help, please. Time sensitive.
What are the solutions to the system of equations?
{y=x2−3x−y=1
Solve the system by graphing.
a. (0, −3) and (0, −1)
b. (1, −2) and (−2, 1)
c. (2, 1) and (−1, −2)
d. (1, 2) and (−2, −1)
Answer:
c. (2, 1) and (−1, −2)
Step-by-step explanation:
Assuming you intended y=x²-3 and x-y=1, you can graph the parabola and the straight line (rewrite x-y=1 as y = x-1).
You can then see the intersections at x=-1, y=-2 and x=2, y=1.
The values given in the table below are the coordinates of points on a line.
What is the slope of this line?
Answer:
slope = 5
Step-by-step explanation:
To calculate the slope m use the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (1, 3) and (x₂, y₂ ) = (2, 8) ← ordered pairs from the table
m = [tex]\frac{8-3}{2-1}[/tex] = 5
The slope of a line can be calculated using the formula (y2-y1) / (x2-x1) using any two points on the line. The result you get from this calculation is the slope of the line.
Explanation:To find the slope of a line from a set of coordinates, you need two points from the line. Let's consider these two points as (x1, y1) and (x2, y2). The formula for the slope is (y2-y1) / (x2-x1). This formula shows the change in y-values divided by the change in x-values, often referred to as 'rise over run'.
If, for instance, from your table the two points are (3,4) and (5,8), substitute these values into the formula: Slope = (8-4) / (5-3) = 4/2 = 2. So the slope of the line is 2.
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Koen is training for a track meet. Last month, he ran for four and a half hours. He averaged a speed of six miles per hour. How many miles did Koen run?
Hopefully I read the question right, if not I'm sorry
Koen ran for 4 and a half hours, which is also 4.5 hours
Since he averaged a speed of 6 mph, I multiply the number of hours by speed each hour, which is 4.5*6
4.5*6=27
Koen ran 27 miles.
Answer:
38 miles
Step-by-step explanation:
study island
The volumes of two similar solids are 1728 m³ in 343 m³. The surface area of the larger solid is 576 m². What is the surface area of the smaller solid
A. 196 m²
B. 76 m2
C. 1372 m²
D. 392 m²
Answer:
A. 196 m²
Step-by-step explanation:
The two similar solids have volumes 1728 m³ and 343 m³.
The ratio of their side lengths is :
[tex]\sqrt[3]{1728}:\sqrt[3]{343}[/tex]
This simplifies to:
[tex]12:7[/tex]
If the surface area of the larger solid is 576 m², then the surface area of the smaller solid is given by:
[tex]\frac{7^2}{12^2}\times 576=196[/tex]
The correct answer is A
98 POINTS! QUESTION + ANSWERS IN PHOTO! Use squared identities to simplify the following equation....
2sin^2xcos^2x
Using trig functions we know:
sin^2(x) = 1- cos(2x)/2
cos^2(x) = 1 + cos(2x) /2
Now we have:
2sin^2xcos^2x = 2 * 1- cos(2x)/2 * 1 + cos(2x) /2
Simplify to: (1- cos(2x) * 1+cos(2x))/2
Difference of squares is (a-b) (a+b) = a^2 -b^2
(1- cos(2x) * 1+cos(2x))/2 = 1^2 -cos^2(x)/2 *1^2 +cos^2(x) /2
Multiply to get 1-cos(4x) /4
The answer is D.
The sum of the digits of a two-digit number is 13. The units digit is one more than twice the tens digit. Find the number, and...
The sum of the digits of a three-digit number is 6. The hundreds digit is twice the units digit, and the tens digit equals to the sum of the other two. Find the number.
Answer:
1)49
2)231
Step-by-step explanation:
1)
4+9=13
4*2=8
8+1=9
2)
2+3+1=6
2+1=3
1*2=2
Answer:
#1. 49 #2. 231
Step-by-step explanation:
#1. 4 x 2 + 1 =
8 + 1 =
9
add 40 + 9 = 49
#2. x + 2x + (x + 2x) = 6
6x = 6
x = 1
2x = 2
x + 2x = 3
(2 x 100) + (3 x 10) + 1 or 231.
Can I get Brainliest☺☺☺☺
help please with this question
Let f(x)=x^2-6x-27. enter the x-intercepts of the quadratic function in the boxes.
Step-by-step explanation:
0 = x² - 6x - 27
a = 1, b = -6, c = -27 Factor using AC method.
ac = (1)(-27) = -27
Factors of -27 that add up to -6 are -9 and 3.
Therefore:
0 = (x - 9) (x + 3)
x = -3, x = 9
The x-intercepts are (-3, 0) and (9, 0).
Cherry is paid $72.00 for working six hours in a library. If the amount paid is proportional to the number of hours worked, what is the constant of proportionality?
Answer:
She's being paid six hours per hour
Step-by-step explanation:
She's being paid six hours per hour
72/6 = 6
Solve the equation identify extraneous solutions
Answer:
Step-by-step explanation:
The goal to solving any equation is to have x = {something}. That means we need to get the x out from underneath that radical. It's a square root, so we can "undo" it by squaring. Square both sides because this is an equation. Squaring both sides gives you
[tex]x^2=-3x+40[/tex]
Get everything on one side of the equals sign and set the quadratic equal to 0:
[tex]x^2+3x-40=0[/tex]
Throw this into the quadratic formula to get that the solutions are x = 5 and -8. We need to see if only one works, both work, or neither work in the original equation.
Does [tex]5=\sqrt{-3(5)+40}[/tex]?
[tex]5=\sqrt{-15+40}[/tex] and
[tex]5=\sqrt{25}[/tex]
and 5 = 5. So 5 works. Let's try -8 now:
[tex]-8=\sqrt{-3(-8)+40}[/tex] and
[tex]-8=\sqrt{24+40}[/tex] so
[tex]-8=\sqrt{64}[/tex]
-8 = 8? No it doesn't. So only 5 works. Your choice is the third one down.
Which of the following points is a solution to the system of linear inequalities?
{y≤2x-5
y>-3x
A.
(1, 1)
B.
(–2, 2)
C.
(5, 3)
D.
(–4, 4)
Answer:
C. (5, 3)
Step-by-step explanation:
this point is within the answer area... look below at the graph of both linear inequalities
For this case we have the following system of inequations:
[tex]y\leq2x-5\\y> -3x[/tex]
We must replace each of the points and verify that the inequalities are met:
Point A: (1,1)
[tex]1 \leq2 (1) -5\\1 \leq2-5\\1 \leq-3[/tex]
It is not fulfilled!
Point B: (-2,2)
[tex]2 \leq2 (-2) -5\\2 \leq-4-5\\2 \leq-9[/tex]
It is not fulfilled!
Point C: (5,3)
[tex]3 \leq2 (5) -5\\3 \leq10-5\\3 \leq5[/tex]
Is fulfilled!
[tex]3> -3 (5)\\3> -15[/tex]
Is fulfilled!
Point D: (-4,4)
[tex]4 \leq2 (-4) -5\\4 \leq -8-5\\4 \leq -13[/tex]
It is not fulfilled!
Thus, the point that is the solution of inequalities is:
(5,3)
ANswer:
(5,3)
Please help me out please
Answer:
48 ft³
Step-by-step explanation:
The volume (V) of the pyramid is
V = [tex]\frac{1}{3}[/tex] area of base × perpendicular height (h)
Calculate h using the right triangle formed by a segment from the vertex to the midpoint of the base and across to the slant face ( the hypotenuse )
Using Pythagoras' identity on the right triangle then
h² + 3² = 5²
h² + 9 = 25 ( subtract 9 from both sides )
h² = 16 ( take the square root of both sides )
h = [tex]\sqrt{16}[/tex] = 4
area of square base = 6² = 36, hence
V = [tex]\frac{1}{3}[/tex] × 36 × 4 = 12 × 4 = 48 ft³
PLEASE HELP ME! PLEASE!!
Which scale factors produce an expansion under a dilation of he original image?
Choose all answers that are correct.
a)-0.75
b)-2
c)0.75
d)2
Which scale factors produce a contraction under a dilation of he original image?
Choose all answers that are correct.
a)-1.8
b)-0.8
c)1.8
d)0.8
Answer:
1. 0.75
2. -0.8
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First when looking at dialations, ignore the negative signs. They do not affect the expansion or contraction.
An expansion is any number greater than 1 and a contraction is any number less than 1.
Expansion: b) -2 and d) 2
Contraction: b) - 0.8 and d) 0.8
Solve for x. Round your answer to 2 decimal places.
Answer:
x = 29.91
Step-by-step explanation:
Cos (53) = 18/x
x = 18 / Cos(53)
x = 18/ 0.6018
x = 29.91
For this case we have that by definition of trigonometric relations of a rectangular triangle, that the cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle. Then, according to the figure we have:
[tex]cos (53) = \frac {18} {x}[/tex]
Clearing x:
[tex]x = \frac {18} {cos (53)}\\x = \frac {18} {0.60181502}\\x = 29,9095226969[/tex]
Rounding:
[tex]x = 29.91[/tex]
Answer:
29.91