9. Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale
Answers
tan (theta) = C.O / C.A
Where,
theta: angle
C.O: opposite leg
C.A: adjoining catheto
Substituting values:
tan (25) = x / 5
Clearing x:
x = 5 * tan (25)
x = 2.33
Answer:
x = 2.3
Related Questions
At Martina's auto shop, it takes her 15 minutes to do an oil change and 18 minutes to do a tire change. Let x be the number of oil changes she does. Let y be the number of tire changes she does. Using the values and variables given, write an inequality describing how many oil changes and tire changes Martina can do in at most 3 hours ( 180 minutes).
Answers
You want to know how much she can do in 180 minutes
She can do an oil change in 15 minutes
She can do a tire change in 18 minutes
Based on this information you can make the inequality
[tex]15x + 18y \leq 180[/tex]
The answer is [tex]15x + 18y \leq 180[/tex]
Hope this helps!
It's at most 180 minutes so left side is 'less than or equal to 180'.
what numbers are divisible by 810
Answers
Gina is a tour boat operator and she wants to know the mean age of all the people in her tour group.
She randomly selects 8 people in the group and asks them for their ages. Their responses are 19, 27, 25, 21, 44, 22, 45, and 34.
What is the best estimate of the mean age of all the people in the tour group?
Round to the nearest whole number.
Answers
19 + 27 + 25 + 21 + 44 + 22 + 45 + 34 = 237
237 / 8 = 29.625 = 30 years
Find the 12th term in the following geometric sequence. 0.75, 1.5, 3, 6, . . .
Answers
Answer:
1536
Step-by-step explanation:
Given : A geometric sequence 0.75, 1.5, 3, 6, . . .
To Find:Find the 12th term
Solution:
0.75, 1.5, 3, 6, . . .
First term =a = 0.75
Common difference = [tex]r = \frac{a_3}{a_2} =\frac{a_2}{a_1}=\frac{1.5}{0.75}=\frac{3}{1.5}=2[/tex]
nth term of G.P. = [tex]a_n=a r^{n-1}[/tex]
Where a = First term = 0.75
r = common difference = 2
Substitute n = 12
[tex]a_{12}= 0.75 (2)^{12-1}[/tex]
[tex]a_{12}= 0.75 (2)^{11}[/tex]
[tex]a_{12}= 1536[/tex]
Hence the 12th term in the geometric sequence. 0.75, 1.5, 3, 6, . . . is 1536.
please help asap 50 pts
Answers
Steps:
1. Factor 11 out of 11g
6g^2 + 11 (g) - 35
2. Rewrite 11 as -10 plus 21
6g^2 + (-10 + 21) g - 35
3. Apply the distributive property
6g^2 + (-10g + 21g) - 35
4. Remove parentheses
6g^2 - 10g + 21g - 35
5. Group the first two and the last two terms
(6g^2 - 10g) + (21g - 35)
6. Factor out the greatest common factor from each group
2g (3g - 5) + 7 (3g - 5)
7. Factor out the greatest common factor, 3g - 5
(3g - 5) (2g + 7)
Therefore the answer is A
Answer: A. (3g - 5)(2g + 7)
For these two rules, the second number in the ordered pair is always three times greater than the first number. If the relationship between the two numbers in each ordered pair is the same, the graph will be: Not graph-able A straight line A circle An exponential curve A parabolic curve
Answers
What values for xx and yy make △MNO≅△PRT▵MNO≅▵PRT?
Triangles MNO and PRT
Answers
However, I can help you understand how to solve such problem and you can apply the explanation in the triangles you have.
Now, when writing congruent triangles, the order of the letters is very important. This is because each side/angle in the first triangle is congruent to the corresponding side/angle in the second one.
In the given, we have:
ΔMNO ≈ ΔPRT
This means that:
angle M = angle P
angle N = angle R
angle O = angle T
MN = PR
NO = RT
MO = PT
Now, to get x and y, all you have to do is make use of the above equal angles/sides.
Equate the corresponding angles/sides having the variables x and y and solve for them
Hope this helps :)
A ceo of awesome coolers owns 8 pairs of pants, 10 shirts, 7 ties and 4 jackets. how many different outfits can he wear to the office if he must wear one of each item?
Answers
Refer to the following illustration to answer this Question.
The center of a circle is at (−3, 1) and its radius is 9.
What is the equation of the circle?
Answers
The answer is (x + 3) 2 + (y − 1) 2 = 81
1. Point B lies on line AC. AC = 127, AB is represented by the expression -12x + 11, and BC is represented by the expression -8x - 4. What is the length of AB?
2. Point E lies on line DF. DE is represented by the expression 2x - 8. EF is represented by the expression 2x - 4. If DF = 36 inches, what is the length of DE? What is the length of EF?
Answers
Since AB + BC = AC
Then
-12x + 11 - 8x -4 = 127
-20x + 7 = 127
X = -6
Ab would then equal 83
What is 5.1 x 10^-1 as an ordinary number?
Answers
so its 5.1 * 0.1 = 0.51
Answer:
0.51
Step-by-step explanation:
10^1=divide by 10
5.1/10=0.51
The center of a circle is at (2, −5) and its radius is 12.
What is the equation of the circle?
(x−2)2+(y+5)2=144
(x+2)2+(y−5)2=144
(x+2)2+(y−5)2=24
(x−2)2+(y+5)2=24
Answers
The equation of the circle is given by (x-h)^2 + (y-k)^2 = r^2 where (h,k) represent the center of the circle and r represents the radius
From the question , we have been given (h,k) = (2,-5) and r =12
(x-2)^2 + (y-(-5))^2 = 12^2
The two minuses in the second term cancel out and give a plus. (-*- = +)
(x-2)^2 + (y+5)^2 = 144
So, the equation of the circle is:
(x-2)^2 + (y+5)^2 = 144 (Option A)
Brainliest for correct answer!
Which strategy can be used to solve this problem? Dan has dogs named Chester and Ally. Together the two dogs weigh 40 pounds. Chester weighs 4 pounds more than Ally. How much does Ally weigh? A. Write a number sentence. Let p represent the amount that Ally weighs. (4 + 40) ÷ 2 = p B. Guess and test. Guess that Ally weighs 20 pounds. Add 4 to 20 to find out how much Chester weighs (24). Add Chester's and Ally's weights (44). Ask if the sum is more or less than 40. Revise your guess so it is 19 and test your answer again. Repeat the process until you have the correct answer. C. Draw a diagram. Draw 40 dots to represent how much the two dogs weigh altogether. Divide the dots into 2 equal groups and then divide one of the groups by 4.
Answers
C = weight of Chester
A = weight of Ally
From the information given,
Both dogs weigh 40 pounds. Therefore,
C + A = 40 --- (1)
In addition, Chester weighs 4 pounds more than Ally. Therefore,
C = A + 4 ---- (2)
Substituting for C from equation (2) in equation (1);
A + 4 + A = 40
2A + 4 = 40
2A = 40 -4 = 36
2A = 36
A = 36/2
A = 18 pounds
Therefore, Ally weighs 18 pounds.
write this as an equation in point-slope form Please answer as quickly as possible. 50 pts!!!!!
m=-3, (-2,1)
Answers
The answer is: " y − 1 = - 3(x + 2) " .
__________________________________________________________
Explanations:
__________________________________________________________
Note: The "point-slope form" of the equation of a line is:
→ " y − y₁ = m(x −x₁) " .
We are given the slope, m" , is: " - 3 " ;
We are given a point on the line [on the graph that is represented by this equation]; with the coordinates: " (-2 , 1) " ;
→ which is in the format: " (x₁ , y₁) " ;
→ As such: " x₁ = -2 " ; " y₁ = 1 " ;
_____________________________________________________
As aforementioned, the equation of a line in "point-slope form" ; is:
_________________________________________________________
→ " y − y₁ = m(x − x₁) " ;
in which:
→ "(x₁ , y₁) " represents the coordinates of a given point on the [line of the graph represented by the equation] ; AND:
→ " m " = the slope of the line [represented by the equation] " ;
We proceed by substituting our known values for "m" ; "y₁" ; and "x₁" :
→ " y − 1 = - 3(x − (-2) ) " ;
_______________________________________________________
→ Rewrite as:
_______________________________________________________
→ " y − 1 = - 3(x + 2) " ;
→ which is our answer; since it is written in "point-slope form" .
_______________________________________________________
Describe the number of solutions for each system of equations graphed
below
Answers
1- In case we are dealing with system of equations, the solution would be the point of intersection of the two graphs
2- In case we're dealing with only one equation, the solution would be the points of intersection of the graph with the x-axis
Graph (a):
The graph is for a system of equations (two lines). Therefore, the solution would be the point of intersection of the two lines.
From the graph, we can note that there is only one point of intersection between the two lines (-3,-1). Therefore, the system of equations has only one solution
Graph (b):
The graph is for a system of equations (two lines). Therefore, the solution would be the point of intersection of the two lines.
From the graph, we can note that the two lines are parallel. This means that they will never intersect. Therefore, the system of equations has no solutions
Graph (c):
The graph is for a single line. Therefore, the solution(s) would be the point(s) that make the overall equation equal to zero, i.e. point(s) of intersection with the x-axis.
From the graph, we can note that the line intersects with the x-axis only once at point (2,0). This means that the line has only one solution.
Hope this helps :)
A fire truck has a ladder that can extend to 60 feet in length. the ladder can be safely raised to a maximum angle of 75o with the horizontal. disregarding the height of the fire truck itself, which is closest to the maximum height that the ladder can safely reach?
Answers
[tex]sin\left(75^{\circ} \right)=\frac{h}{60}[/tex]
[tex]h=60\cdot sin\left(75^{\circ} \right)=58\:feet[/tex]
The maximum height that the ladder can safely reach is closest to 58 feet.
Final answer:
Using trigonometry and the sine function, the maximum height that the ladder can reach when raised to a 75-degree angle with a length of 60 feet is approximately 58 feet.
Explanation:
To determine the maximum height that a fire truck ladder can safely reach when it is extended to 60 feet in length and raised to a maximum angle of 75 degrees with the horizontal, we would use trigonometry, specifically the sine function. The sine of an angle in a right triangle is equal to the opposite side (height in this case) divided by the hypotenuse (the length of the ladder).
Therefore, the maximum height (h) can be calculated using the formula:
h = Ladder Length × sin(Angle)
Where:
Ladder Length is 60 feet
Angle is 75 degrees
Plugging in our values we get:
h = 60 feet × sin(75 degrees)
Using a calculator, we find that:
sin(75 degrees) is approximately 0.9659.
Therefore:
h ≈ 60 feet × 0.9659
h ≈ 57.95 feet
The maximum height the ladder can safely reach when disregarding the height of the fire truck itself is approximately 58 feet.
A survey of 1,000 people was done by New York Times. 80% of the people did not know the name of their representative in Congress. How many of the 1,000 people knew the name of the Congressman?
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which of the following are examples of exponential decay
1) the population of a florida is increasing by 43% each year
2) the pesticide DDT has half life if 15 years
3) March madness has 64 teams in the bracket. Each round half the teams are eliminated
4) after an antibiotic is added to culture of bacteria, the number of bacteria is reduced by half every three hours
5) a tree frog population doubles every three weeks
Answers
B)
C)
D)
A pizza has a circumference of 16 pie and the slices are cut at 24 degree angles.
a. What is the length of the crust of one slice of pizza?
b. What is the area of one slice?
c. If the radius was doubled what would be the area of one slice of te similar pizza?
Answers
What is the probability of getting a number greater than or equal to 2 when rolling a number cube number 1 to 6
Answers
The probability of rolling a number that is equal to or greater than 2 is a 5/6 chance. It is a 5/6 chance because there are 6 numbers on a dice and the total amount of numbers from 2 to 6 is 5 numbers (2, 3, 4, 5, 6).
I hope this helps!
the probability of getting a number greater than or equal to 2 when rolling a fair number cube is [tex]\( \frac{5}{6} \).[/tex]
When rolling a fair number cube (also known as a fair six-sided die), each face has an equal probability of showing up. Since there are 6 faces numbered 1 to 6, the probability of getting any specific number (including 2) on a single roll is [tex]\( \frac{1}{6} \)[/tex], assuming the die is fair.
To find the probability of getting a number greater than or equal to 2, we can count the favorable outcomes (rolling a number 2, 3, 4, 5, or 6) and divide by the total possible outcomes (which is 6 for a fair six-sided die).
Favorable outcomes: 2, 3, 4, 5, 6 (total of 5 numbers)
Total possible outcomes: 6 numbers
So, the probability of getting a number greater than or equal to 2 when rolling a fair number cube is [tex]\( \frac{5}{6} \).[/tex]
Determine whether quantities vary directly or inversely and find the constant of variation. A teacher grades 25 students essays in 4 hours. Assuming he grades at the same speed, how long will it take him to grade 35 essays?
Answers
To determine whether quantities vary directly or inversely, let's first define the variables:
Let x be which student essays had been graded.
Let y be the time taken to grade those essays.
In this case, it seems that the time taken to grade essays varies inversely with the number of essays graded. This means that as the number of essays increases, the time taken to grade them decreases, assuming the grading speed remains constant.
So, we can set up an equation using the constant of variation: xy = k
where the variation in the ratio is designated by k.
Given that the teacher grades 25 essays in 4 hours, we can use this information to find the constant of variation:
25 × 4 = k
k = 100
Now that we have the constant of variation, we can use it to find the time it takes to grade 35 essays:
35y = 100
y = (100/35)
y ≈ 2.857
So, it will take approximately 2.857 hours to grade 35 essays.
To determine if quantities vary directly or inversely, we compare how changes in one quantity affect the other.
Here, as the number of essays increases, the time taken to grade them decreases, indicating an inverse relationship.
Using the formula for inverse variation, xy = k, where x is the number of essays and y is the time taken, we find the constant of variation by substituting values: 25 × 4 = k, which gives k=100.
With the constant, we can find the time to grade 35 essays: 35y = 100.
Solving for y, we get y ≈ 2.857 hours. Therefore, it will take approximately 2.857 hours to grade 35 essays.
Complete Question:
Determine whether quantities vary directly or inversely and find the constant of variation. A teacher grades 25 students' essays in 4 hours. Assuming he grades at the same speed, how long will it take him to grade 35 essays?
Anyone know what the answer is?
Answers
If an arithmetic series has a1 equals=44, d equals 5, and n=24, what is sn?
Answers
In an orienteering competition, Jada walks 70 degrees north of west for 200 meters. She then walks due east for 90 meters. How far and at what bearing is Jada from her starting point?
Answers
c²=a²+b²-2abCos C
a=200, b=90, C=70°
thus plugging in our values we get:
c²=200²+90²-2×200×90×cos70
c²=40000+8100-36000(0.3420)
c²=35788
hence
c=189.1772 m'
therefore the distance Jada is from the starting point is 189.1772 m
Answer:
N55.0679°W
Step-by-step explanation:
Check the attachment for detailed explanation.
Use the graphs of f(x) =2/x and g(x)=1/-3-x to determine the solutions to f(x) = g(x).
A) (-2, -1)
B) (-2, 1)
C) (2, -1)
Answers
f(x) =2/x
and
g(x)=1/(-3-x)
we know that
the solutions to f(x) = g(x) is the intersection of both graphs
the intersection of both graphs is the point (-2,-1)
the answer is the option
A) (-2, -1)
see the attached figure
QUICK QUESTION PLEASE. help.
The length of a rectangle is six times its width. If the perimeter of the rectangle is 112 ft, find its area.
Answers
2l+2w=112
l=6w
2(6w)+2w=112
12w+2w=112
14w=112
w=8
l=48
A=384 ft^2
The area of the rectangle will be 384 ft². Square feet and other similar units are used to measure area.
What is the area?The space filled by a flat form or the surface of an item is known as the area.
The number of unit squares that cover the surface of a closed-form is the figure's area.
Let the length of a rectangle is,l and the width of a rectangle be,w
Given condition;
l=6w
The perimeter of the rectangle = 112 ft,
⇒2l+2w=112
According to condition;
2(6w)+2w=112
12w+2w=112
14w=112
w=8
The length of a rectangle is;
l=6w
l=48
Area of rectangle = length × width
A =lw
A=6 × 48 ft
A=384 ft^2
Hence the area of the rectangle will be 384 ft².
To learn more about the area, refer to the link;
https://brainly.com/question/11952845
#SPJ2
The perimeter of a rectangle is 108 inches. the rectangle is 34 inches long. how wide is it?
Answers
[tex] \frac{108 - 34 - 34}{2} [/tex]
= 20 inches
In a rectangle, there are 2 similar length measurements & 2 similar width measurements
How can operations of polynomials be used to create new polynomial models? Provide real world examples of when it is necessary to add, subtract, multiply, or compose polynomials to get a new polynomial that model real situations.
Answers
Answer with explanation:
When we add, subtract or multiply or in some cases division is done between two or more Polynomials then we can get new polynomials.
This can be explained in following way
[tex]1.\rightarrow (x^3+x^2+3x+4) +(x^4+5x+6)\\\\=x^4+x^3+x^2+8x+10\\\\2.\rightarrow (x^3+x^2+3x+4) -(x^4+5x+6)\\\\=-x^4+x^3+x^2-2x-2\\\\3.\rightarrow (x+2)\times x^2\\\\=x^3+2x^2\\\\4.\rightarrow \frac{x^3+2x^2}{x}\\\\\rightarrow x^2+2x[/tex]
Real world Situation
There is a large enclosed room .We want to place bulbs in ceiling.To do that,we draw few straight lines that is Linear polynomial columnwise and then we have drawn Linear polynomial Row wise.The point of intersection of these lines gives the points where the bulbs should be fixed.Now ,if we join these points where the bulb is placed we will get a new polynomial.
Hadmids will start at 11:00A.M., but the players must arrive at the field three-quarters of an hour early to warm up. The game must end by 1:15 P.M. Hadmid say he has to be at the field at 9:45 A.M is hadmid correct? Explain your answer.
Answers
A plane intersects a double-napped cone such that the plane intersects both nappes through the cone's vertex. which terms describe the degenerate conic section that is formed? select each correct answer. degenerate parabola pair of intersecting lines point line degenerate hyperbola degenerate ellipse
Answers
pair of intersecting lines
degenerate hyperbola
Answer with explanation:
It is given that, a plane intersects a double-napped cone such that the plane intersects both Nappes through the cone's vertex.It also depends on how thick or thickness of the plane:
1.We can surely say that degenerate hyperbola will be formed,whatever be the thickness of Plane.
2. Two parallel lines=pair of intersecting lines ,because both ,A double napped cone and Plane is three dimensional shape.Instead of intersecting lines ,two parallel lines which we call pair of intersecting lines, will be formed.