Answer:
To find the range of flight times, you need to find the difference between the shortest and longest flight times. The shortest flight time was on Monday at 314 minutes, and the longest flight time was on Friday at 407 minutes. The range is 407 - 314 = 93 minutes. The correct answer is therefore (b) 93 min.
Step-by-step explanation:
From a rock ledge, the angle of elevation to the top of a tree is 22°. The angle of depression to the base of the tree is 12°.
a) Find the height of the rock ledge, to
the nearest metre.
b) Find the height of the tree, to the
nearest metre.
The height of the rock ledge will be 20.35 meters.
The height of the tree will be 58.75 meters
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The angle of elevation to the top of a tree is 22°.
And, The angle of depression to the base of the tree is 12°.
Now,
Let the height of the rock ledge = x
So, By figure, we get;
⇒ tan 12° = x / 96
⇒ x = 96 × tan 12°
⇒ x = 20.35 meters
And, Let total height of the tree = x + y
= 20.35 + y
Hence, By figure, we get;
⇒ tan 22° = y / 96
⇒ y = 96 × tan 22°
⇒ y = 96 × 0.40
⇒ y = 38.4 meter
Thus, The height of tree = 38.4 meters + 20.35 meters
= 58.75 meters
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To find:-
The height of the rock ledge.Height of the tree .Answer:-
Part A :-
Here we can see that the distance between the rock ledge and the base of the tree is 96m . Also the angle of elevation to the top of the tree from the rock is 22° .
Firstly, we can see that,
[tex]\implies \angle CAD =\angle EDA = 12^o\\[/tex]
This is so because they are alternate interior angles .
Now , in ∆ADE ,
[tex]\implies \tan\theta =\dfrac{p}{b}=\dfrac{AE}{ED}\\[/tex]
[tex]\implies \tan 12^o =\dfrac{AE}{96m} \\[/tex]
[tex]\implies AE = 96\tan12^o m \\[/tex]
[tex]\implies AE = 96 (0.21)m \\[/tex]
[tex]\implies AE = 20.16 \ m \\[/tex]
Hence the height of the rock ledge is 20.16 m.
_______________________________________
Part B :-
Now in ∆ACB , we have;
[tex]\implies \tan\theta =\dfrac{BC}{AC} \\[/tex]
[tex]\implies \tan 22^o =\dfrac{BC}{96m} \\[/tex]
[tex]\implies BC = 96\tan 22^o \ m \\[/tex]
[tex]\implies BC = 96(0.4) m \\[/tex]
[tex]\implies BC = 38.4 \ m \\[/tex]
Now the total height of the tree will be = BC + AE
[tex]\implies h_{tree}= BC + AE \\[/tex]
[tex]\implies h_{tree}=38.4\ m + 20.16 \ m =\boxed{58.56\ m} \\[/tex]
Hence the height of the tree is 58.56m.
and we are done!
Help pls I’ll give extra points
Answer:
1. Gorgeous
2. Tremendous
3. Coarse
4. Crackling
5. Appetizing
Step-by-step explanation:
Those are the only words that make sense in each square.
Answer:
1.) gorgeous
2.) tremendous
3.) crackling
4.) coarse
5.) appetizing
6.) buttery
7.) magnificent
Hope this helps!
What are the x-intercepts of the following graph? On a coordinate plane, a parabola opens down and goes through (negative 2, 0), has a vertex at (0, 4), and goes through (2, 0). a. (0, 2) and (0, -2) c. (2, 0) and (-2, 0) b. (0, 4) d. (1, 0) and (3, 0)
Answer:
C
Step-by-step explanation:
If you read the question carefully, you find that the function goes through (- 2,0) and (2,0)
Where the y value = 0 you have points that are x intercepts. The answer is anything where the y value = 0
The x intercepts are (-2, 0 ) and (2,0)
The answer is C
Answer:
c
Step-by-step explanation
(2, 0) and (-2, 0)
Explain how to write a quadratic equation given the following three points on the graph (5,31) (3,11) (0,11)
Given:
The graph of a quadratic function passes through the points (5,31) (3,11) (0,11).
To find:
The equation of the quadratic function.
Solution:
A quadratic function is defined as:
[tex]y=ax^2+bx+c[/tex] ...(i)
It is passes through the point (0,11). So, substitute [tex]x=0,y=11[/tex] in (i).
[tex]11=a(0)^2+b(0)+c[/tex]
[tex]11=c[/tex]
Putting [tex]c=11[/tex] in (i), we get
[tex]y=ax^2+bx+11[/tex] ...(ii)
The quadratic function passes through the point (5,31). So, substitute [tex]x=5,y=31[/tex] in (ii).
[tex]31=a(5)^2+b(5)+11[/tex]
[tex]31-11=a(25)+5b[/tex]
[tex]20=25a+5b[/tex]
Divide both sides by 5.
[tex]4=5a+b[/tex] ...(iii)
The quadratic function passes through the point (3,11). So, substitute [tex]x=3,y=11[/tex] in (ii).
[tex]11=a(3)^2+b(3)+11[/tex]
[tex]11-11=a(9)+3b[/tex]
[tex]0=9a+3b[/tex]
Divide both sides by 3.
[tex]0=3a+b[/tex] ...(iv)
Subtracting (iv) from (iii), we get
[tex]4-0=5a+b-3a-b[/tex]
[tex]4=2a[/tex]
[tex]\dfrac{4}{2}=a[/tex]
[tex]2=a[/tex]
Putting [tex]a=2[/tex] in (iv), we get
[tex]0=3(2)+b[/tex]
[tex]0=6+b[/tex]
[tex]-6=b[/tex]
Putting [tex]a=2,b=-6[/tex] in (ii), we get
[tex]y=(2)x^2+(-6)x+11[/tex]
[tex]y=2x^2-6x+11[/tex]
Therefore, the required quadratic equation is [tex]y=2x^2-6x+11[/tex].
WILL MARK BRAINLIEST!!!
Given: square ABCD with a perimeter of 48 units. Find the number of units in BD (in simplest radical form)
Answer:
12√2 units
Step-by-step explanation:
Step-by-step explanation:
perimeter of a square=4side
perimeter= 4s= 48 units
S= 48/4
S = 12 units
digonal BD = S√2
= 12√2 Units
BD = 12√2 Uits
PLEASE HELP WITH EASY FRACTIONS APPRECIATED MUCH!!!
Answer: 3/4 is right
Step-by-step explanation:
In this figure please see attached questions
y2 = 14
y1 = 2
Solution
m = (14 - 2) / (8 - 2)
m = 4 / 4 = 1
Remark
Why is the slope one? I should be 2 shouldn't it? No because there is a common factor to be taken out -- the common factor is 2Answer:
Step-by-step explanation:
y = 2x - 2
x y
2 2
4 6
6 10
8 14
I will use Desmos to get the line.
The slope should be 2
Formula
Slope (m) = ( (y2 - y1) / (x2 - x1) )
Givens
x2 = 8
x1 = 4
y2 = 14
y1 = 6
Solution
m = ( (14 - 6) / ( 8 - 4)
m = 8 / 4
m = 2
How do I even do thissss?
Please provide your question with a math problem in the form of an image or text.
Tell whether the angles are complementary or supplementary. Then find the value of x.
Answer:
Complementary
x = 15
Step-by-step explanation:
Given angles are complementary, because their sum is 90°.Now, let us find the value of x.-> 3x° + 45° = 90°-> 3x° = 90° - 45°-> 3x° = 45°-> x = 45/3-> x = 15ANSWER FAST
q>d, if d=3
Answer:
It depends on what q is.
Step-by-step explanation:
Is d is less than q then q will be greater.
Answer:
q would be anything that’s over 3
Step-by-step explanation:
If d=3, then q>3, so q is any number larger then 3
Two parallel lines are crossed by a transversal.
Horizontal and parallel lines b and c are cut by transversal a. At the intersection of lines b and a, the bottom right angle is 50 degrees. At the intersection of lines c and a, the top left angle is y degrees.
What is the value of y?
The value of y is 130°
What are corresponding angles?The angles occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.
Given here:
Horizontal and parallel lines b and c are cut by transversal a. At the intersection of lines b and a, the bottom right angle is 50 degrees. At the intersection of lines c and a, the top left angle is y degrees.
Thus the angle adjacent to the 50-degree angle will be 130
but this angle corresponds to the angle y thus y=130 as corresponding angles are equal when a transversal intersects two parallel lines
Hence, The value of y is 130°
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Y=6(1.02)^x growth or decay?
Answer:
(Exponential) Growth
Step-by-step explanation:
Given that the growth rate is greater than 1, this is exponential growth where the growth rate is 2%.
----------------------------------------------------------------------
Step-by-step explanation:
nzkaoavdvsoasb xzakoakaidbzbsva
Answer:
See attached
Step-by-step explanation:
Solution is below
Simplify the difference. (2w2 – 8w – 8) – (5w2 + 3w – 5)
Answer:
-3w2-11w-3
Step-by-step explanation:
take w2 and w as variables. you can substitute it as w2=y and w=X then expand brackets
2y-8x-8-5y-3x+5
note that the signed changed at the second part because it was expanded with the minus sign which is basically like -1, so it changes the signs
then you collect like terms:
2y-5y-8x-3x-8+5= -3y-11x-3
now put substitute back w2=y and w=X
-3w2-11w-3
if it won't be a problem solving with w2 and w, then you skip the substitution part and solve the same
Help asap PLSSS!! I’d really appreciate it. Thank you!!
The value of x and y in equations 17x - y = 40 and 2x + 4y = 50 are x = 3 and y = 11.
What is equation ?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
17x - y = 40 ⇒ (1)
2x + 4y = 50 ⇒ (2)
(1)* 4
68x - 4y = 160
Adding equation (1) and (2)
68x - 4y = 160
2x + 4y = 50
⇒ 70 x = 210
x = 3
Substituting the value of x in equation (1)
17*3 - y = 40
51 - y = 40
-y = 40 - 51
-y = -11
y = 11
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When 4 is added to five times a number the sum is 34. Find the number. *
Answer:
let the number be 'x'
now,
4+5x=345x=34-4x=30/5x=6so, the number is 6.
hope it helps
stay safe, healthy and happy.
I thought of a number, added 26 to it, and then divided the result by 20.what is my number?
Answer:
Step-by-step explanation:
14 MAY BE
. This line plot shows how many miles Maya walked this week.
Answer:
60.5 or 60 1/2
Step-by-step explanation:
7 (2)
8.5 (1)
9 (1)
9.5 (2)
10 (1)
14 + 8.5 + 9 + 19 + 10
60.5
7 time a number , increased by 4
Answer:
7 times a number increased by 4 times the number
Let a number and the number be an arbitrary variable. Let's call it x. We have an algebraic expression. Let's take it in pieces:
7 times a number: 7x
4 times the number: 4x
The phrase increased by means we add 4x to 7x:
7x + 4x
Simplifying, we get: (7 + 4)x
11x
Step-by-step explanation:
Find the slope of the line 6x - 2y = -16
Answer:
The slope is 3
Step-by-step explanation:
Lydia used 1/3 pound of peppers and 1/10 pound of cheese to make 3 pizzas. If Lydia uses the same recipe to make 1 pizza, how much cheese is needed?
Answer: Lydia used 1/3 pound of peppers and 1/10 pound of cheese to make 3 pizzas, which means that she used 1/3 / 3 = 1/9 pound of peppers and 1/10 / 3 = 1/30 pound of cheese per pizza.
If Lydia uses the same recipe to make 1 pizza, she will need 1/9 pound of peppers and 1/30 pound of cheese. Therefore, the amount of cheese needed is 1/30 pound.
Step-by-step explanation:
Give the following number
in Base 10.
F16 = [? ]10
The next decimal number should be changed to hexadecimal. Your final response may contain up to six fractional digits. In decimal 386210, subscript 10 to F16.
How do you write a number in base 10?F16 is 001000011000.1111. 218. F716 is 001000011000.111101112. 710 = (h0)16 = 716 is how the hexadecimal number is represented. It is necessary to add a 1 to the left and modify the number for both to 0. In base-2, the numeral 15 is represented as 1111, and the number 16 is represented as 10000. The greatest value in base-16 is the letter F, in a similar vein. such that 10 is the new value.
Binary 10 equals 1010, thus. Dividing 10 by 2 successively until the quotient equals 0 will yield the decimal to binary equivalent. By writing the remainder in each division step from bottom to top, it is possible to determine the binary equivalent.Base-16 is the definition given to hexadecimal. There are many powers of 16 in each place value in the number. The hexadecimal numbers are: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. 10 through 15 are represented, accordingly, by the letters A through F.
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Manuel's small dog eats
1
8
bag of dog food in 1 month. His large dog eats
5
8
bag of dog food in 1 month.
How many bags do both dogs eat in 6 months?
Answer:
I wanna say 348?? maybe.... I think
How to solve Mathematics techniques
Answer:
you can add them
Step-by-step explanation:
classify the angles below as acute, right, obtuse or straight
Answer:
Obtuse - over 90°
Acute - less than 90°
Right - 90°
Straight - 180°
1. Obtuse
2. Acute
3. Right
Find the area of the polygon.
19 ft
14 ft
3 ft
4 ft
4 ft
3. Selecting three desserts from eight possible choices on a menu. How
many choices are there if you determine a 1st, 2nd and 3rd rank. What are
the possible outcome? Show all evidence of understanding.
Answer:
56 possible outcomes
Step-by-step explanation:
Order does not matter in this case, so we will find all the possible combinations:
8 nCr 3 = 8! / ((8 – 3)! 3!) = 40320 / 720 = 56
Therefore, there are 56 possible outcomes.
Complete the square for the expression. Then factor the trinomial.
x2 - 6x
Expression:
Factored form:
Expression: x² - 6x + 9
Factored form: (x - 3)²
Using the concept of factorization.
What is factorization?The breaking or breakdown of an entity (such as an integer, a matrix, or even a polynomial) into such a combination of some other unit, or factors, whose multiplication yields the original number, matrix, etc., is known as factorization or factoring in mathematics.
Similarly to this, factoring is a very useful technique in algebra that is utilized at all levels. Additionally, to, of course, simplify complex expressions, it offers a standard way for solving quadratic equations. Graphing functions also makes advantage of it.
Factor the expression, put each factor equal to 0, and then solve each equation to solve a quadratic equation by factoring. To do this, rearrange all terms on one side of the equation such the other side equals 0.
Given that,
x² - 6x
Now, to find the value of c = (b/2)²
divide the coefficient of x by 2.
So, divide 6 by 2 we get: ( -1.3)²
Next, multiply -1 by 3: (-3)²
Now, raise -3 to the power of 2, we get: 9
So, the expression becomes: x² - 6x + 9
Factorized form: (x - 3) (x -3)
or we can write (x - 3)²
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A new car costs $40,000. The value of the car depreciates by 20% per year.
a. Create a formula to determine the value of the car t years from now.
b.when will the car be worth 25,000? Round to 2 decimal places.
Answer:
i think A
Step-by-step explanation:
correct me if I wrong k
Please help…. The table below shows the amount of money Linda spends for a craft demonstration
to get the equation of any straight line, we simply need two points off of it, let's use those ones in the picture below.
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{32})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{53}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{53}-\stackrel{y1}{32}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{8}}} \implies \cfrac{ 21 }{ 7 } \implies 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{32}=\stackrel{m}{ 3}(x-\stackrel{x_1}{8}) \\\\\\ y-32=3x-24\implies {\Large \begin{array}{llll} y=3x+8 \end{array}}[/tex]