Answer: 2748.5 feet
Step-by-step explanation:
Given that the
Height h = 120 feet.
angle of depression = 2.5 degrees
The angle of depression is equal to the angle of elevation.
The base of the observation deck will be achieved by using trigonometry ratio.
Tan Ø = opposite/ adjacent
Opposite = height = 120 feet
Adjacent = base = ?
Substitutes the given parameters into the trigonometry ratio.
Tan 2.5 = 120 / adjacent
Adjacent = 120 / tan 2.5
Adjacent = 2748.452
Therefore, the base of the observation deck is 2748.5 feet
A woman bought some large frames for $10 each and some small frames for $5 each at a closeout sale. If she bought 27 frames for $180, find how many of each type she bought. She bought ____ large frames.
Answer:
Step-by-step explanation:
This is a guessing game. You assume how much there is, and then you check. I was led to the conclusion that there are 9 large frames and 18 small frames.
Answer:
She bought 9 large frames
Step-by-step explanation:
Create a system of two equations and two unknowns (the number of small frames that we call S, and the number of large frames that we call L).
The two equations become:
(a) L + S = 27 (since she bought 27 frames total)
(b) 10 L + 5 S = 180
Now, let's solve for S in the first equation: S = 27 - L
ad use it to replace for S in equation (b):
10 L + 5 (27 - L) = 180
10 L - 5 L + 135 = 180
5 L = 180 - 135
5 L = 45
L = 9
Therefore she bought 9 large frames
PLEASE HELP ME FAST, PLEASE
Answer:
The temperature order are;
(b) 96.62 K = (d) 96.62 K > (a) 48.31 K = (c) 48.31 K = (e) 48.31 K = (f) 48.31 K
Arrangement in order from highest to lowest and alphabetically gives;
(b) ↔ (d) → (a)↔ (c)↔ (e)↔ (f)
Step-by-step explanation:
From the universal gas equation
P×V = N×k×T
Where:
P = Pressure
V = Volume
N = Number of molecules
k = Boltzmann constant = 1.38 × 10⁻²³ J/K
T = temperature
Therefore;
[tex]T =\dfrac{P \times V}{k \times N}[/tex]
Which gives;
(a) When P = 100 kPa = 100,000 Pa, V = 4 L = 0.004 m³, N = 6 × 10²³, we have
100000*0.004/(6*10^(23)*1.38*10^(-23)) = 48.31 K
(b) When P = 200 kPa = 200,000 Pa, V = 4 L = 0.004 m³, N = 6 × 10²³, we have
200000*0.004/(6*10^(23)*1.38*10^(-23)) = 96.62 K
(c) When P = 50 kPa = 50,000 Pa, V = 8 L = 0.008 m³, N = 6 × 10²³, we have
50000*0.008/(6*10^(23)*1.38*10^(-23)) = 48.31 K
(d) When P = 100 kPa = 100,000 Pa, V = 4 L = 0.004 m³, N = 3 × 10²³, we have
100000*0.004/(3*10^(23)*1.38*10^(-23)) = 96.62 K
(e) When P = 100 kPa = 100,000 Pa, V = 2 L = 0.002 m³, N = 3 × 10²³, we have
100000*0.002/(3*10^(23)*1.38*10^(-23)) = 48.31 K
(f) When P = 50 kPa = 50,000 Pa, V = 4 L = 0.004 m³, N = 3 × 10²³, we have
50000*0.004/(3*10^(23)*1.38*10^(-23)) = 48.31 K
FIRST GETS BRAINLLEST What is the perimeter of the track, in meters? Use π = 3.14 and round to the nearest hundredth of a meter.
Answer:
8110
Step-by-step explanation:
80+80+50+50=260
3.14(50)²=7810
7810+260=8110
Which model represents the equation below -4x + (-2) = 3x + (-5)
Answer:
No answer can be found
Step-by-step explanation:
There isn't any model to see as reference.
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Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
We can start from that -5 at the end, which indicates the y -intercept and you may ask how?
If we substitute 0 instead of x, then
[tex]y = \frac{2}{3} . 0 -5\\\\y = -5[/tex]
This will give us the first coordinate, which is ( 0, -5)
After that, let's look at the slope, which is [tex]\frac{2}{3}[/tex] As you might know, the slope is also referred to as rise/run, what do they mean by that is that the first top number tells you how many units you go up and the second one how many units you go right or how many units you go down and go left.
Now, I know this may seem complicated but let's make it clear. Since we know one coordinate, which is ( 0, -5) from that point by knowing the slope we can find a second point; this point is 2 points above and 3 to the right, which tells us that -5 + 2 points above gives us -3 and 3 points on the right gives us a new coordinate: ( 3, -3) And since we now know two coordinates, that is enough to draw the line and have the graph!!!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
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Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
Parallel lines r and s are cut by two transversals, parallel lines t and u. Lines r and s are crossed by lines t and u to form 16 angles. Clockwise from top left, at the intersection of r and t, the angles are 1, 2, 3, 4; at the intersection of s and t, 5, 6, 7, 8; at the intersection of u and s, 9, 10, 11, 12; at the intersection of r and u, 13, 14, 15, 16. How many angles are alternate exterior angles with angle 5?
Answer:
Step-by-step explanation:
The alternate exterior angles with angle 11 are angle 13 and angle 5.Step-by-step explanation: Two angles are called Alternate exterior angles if1. They are on the exterior side of parallel lines and2. Lie on the opposite sides of the transversal line.It is given that r\\ s andt\\ u. From the figure it is noticed that the angle 13 and angle 5 are on the exterior side of parallel lines and they lie on the opposite sides of the transversal line.Therefore alternate exterior angles with angle 11 are angle 13 and angle 5.
Answer:
<5=<16
Step-by-step explanation:
Define - An angle is said to be another angles exterior angle if
1) It on either side of transversal
2) Both the angles r exterior angle
Here <16 is the one and only exterior angle of <5 as it satisfies the rules for the same.
Therefore....
<16 is the exterior angle of <5
there is only 1 exterior angle
Sry dude....but the ans of above guy is wrong
Hope this helps.....
PLS PLS PLS mark my ans as brainliest :)
Murray’s father deposited $6,000 of his savings into two accounts. One account earns 1.5 percent interest, and the other account earns 2.5 percent interest. At the end the year, the interest in the account that earned 2.5 percent was $110.00 more than the other account. Which system represents the amounts of money, x and y, that was put into each account? x + y = 6,000. 0.025 x + 0.015 y = 110. x + y = 6,000. 0.25 x + 0.15 y = 110. x + y = 6,000. 0.025 x minus 0.015 y = 110. x + y = 6,000. 2.5 x minus 1.5 y = 110.
Answer:
x+y=6000
Step-by-step explanation:
0.025x-,0.015y=110
Answer:
x+y=6000
0.025x-,0.015y=110
Step-by-step explanation:
May I please get Brainliest to rank up? Thank you and have an amazing day :D
Tyler needs to get the windows in his new home cleaned. The cleaning company needs to know the total number of window panes before it can tell him how much the job will cost. There are 12 windows, each with four window panes across, and four window panes down. Tyler can find the total number of window panes by multiplying the number of windows by the number of panes in each window. The total number of window panes is an expression with a whole-number exponent. Part A Write an expression with exponents to find the total number of panes in 12 windows.
Answer:
I'm not completely sure but I believe it's (4^2)*12
Step-by-step explanation:
To find the amount of window panes there are, we have to find how much window pains are in each window. So we have a 4 by 4 so that's 16. Since 4 and 4 are the same numbers, we can raise 4 to the power of two to get 16. Then we have to do 16*12 to get the total amount of panes since Panes Per Window multiplied by Number Of Windows equals Total Number Of Panes
Answer:
(4^2)*12
Step-by-step explanation:
Which expression can be used to find the surface area of the following square pyramid?
Answer:
4[1/2(5 x 6)] + 6x6
Step-by-step explanation:
The first part of the expression is 4[1/2(5 x 6)]. This is the formula to find the surface area of the triangles. A regular triangle's area is 1/2(l*w). Since there are four trinagles, you have to multiply the whole expression by 4.
The second part of the equation is finding the surface area of the base which is a square. Since squares have four equal sides, its safe to say that you can use 6 * 6.
Hope that helped!
15 POINTS!!!!!!!
How is a linear function affected by a horizontal shift?
Answer:
horizontal shift can affect the linear function, because it is impossible to distinguish which transformation was applied by looking at the resulting graph.
Step-by-step explanation:
a horizontal shift is a movement left to right along the x-axis, and in equation of a function it's change in the value of x before it's multiplied by the slope.
Answer:
I agree with Lambina and added this answer so she could get brainliest
Step-by-step explanation:
15 POINTS!!!!!!!! How is a linear function affected when a constant is multiplied by x?
Answer:
The Y-intercept changes .
Step-by-step explanation:
Answer:
The y-intercept changes
Step-by-step explanation:
write a system of equations for the problem, and then solve the system. if a plane can travel 340 miles per hour with the wind only 260 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air. please show step by step
Answer:
w = 40 miles per hour
r = 300 miles per hour
Step-by-step explanation:
We add w with the wind and subtract w against the wind
r+w = 340 miles per hour
r - w = 260 miles per hour
Add the two equations together to eliminate w
r+w = 340 miles per hour
r - w = 260 miles per hour
----------------------------------------
2r = 600
Divide by 2
r = 300 miles per hour without the wind
Now find w
r+w = 340
300 + w = 340
Subtract 300
w = 340-300
w = 40 miles per hour
The following data points represent the number of points scored by each player on the Wildcats basketball team last game. ____________________________ 4, 5, 6, 8, 9, 10, 11, 13 (Find the interquartile range (IQR) of the data set.)
Answer:
The answer is 5, TRUST ME
Step-by-step explanation:
I tried the other answer but i got it WRONG.
The interquartile range (IQR) of the data represents the number of points scored by each player is 7.
What is the interquartile range (IQR)?The interquartile range is a measure of variability which can be calculated by dividing data into quartiles.
The formula of IQR = [tex]\rm Q_{3} -Q_{1}[/tex]
The given data is as follows
4, 5, 6, 8, 9, 10, 11, 13
To find the first quartile
[tex]\rm Q_{1}[/tex] = (n + 1)/4 term
= (8+1)/4
= 9/4
To find the Third quartile
[tex]\rm Q_{3}[/tex] = 3(n + 1)/4 term
= 3 (9)/4
= 27/4
The formula of IQR = [tex]\rm Q_{3} -Q_{1}[/tex]
= 27/4 - 9/4
= 28/4
= 7
The interquartile range (IQR) of the data represents the number of points scored by each player on the Wildcats basketball team last game is 7.
Learn more about the interquartile range:
https://brainly.com/question/4135956
b Given: m AB =m BC , m∠x=60°, m∠y=15° Find: m AC
Answer:
105
Step-by-step explanation:
because all the angles added up have to = 180
60+15=75
75-180=105
Can someone help me please
Answer:
No more than ≥
Not under ≤
No less than ≤
maximum ≥
Greater than or equal to ≥
Less than or equal to ≤
Does not exceed ≥
At most ≥
At least ≤
Minimum ≤
Which of the following can prove that figure ABCD is a square?
Answer:
A
Step-by-step explanation:
all sides of square is 90degrees
Since AC and BD is the same, when you join the lines together, it will definitely be a square
what is the second term in the Expansion of (x+y)^5
Answer:
5x+5y
Step-by-step explanation:
The weight of a Great blue heron, a type of bird, can grow to around 4 pounds, but can vary. Let W be a random variable that represents the weight of a Great blue heron. The probability density function of W is given below. Move the left and right sliders so that the area of the blue shaded region represents the probability that a Great blue heron is at least 9 pounds, but no more than 10 pounds.
Answer:
10 ≥ w ≥ 9 ( ? )
Step-by-step explanation:
the probability that a Great blue heron is at least 9 pounds, but no more than 10 pounds -> w= weight of great blue heron
w is at lest 9 pound's -> w ≥ 9
w is no more than 10 pound's -> w ≥ 10
w ≥ 9 ( + ) w ≥ 10 = 10 ≥ w ≥ 9
A shipping box has dimensions as shown in the diagram. The red, dashed line represents the longest length of item that will fit inside the box. What is the length of the longest item that will fit inside the shipping box? Enter the correct answer in the box by replacing the values of m and n.
Answer:
26.8 in
Step-by-step explanation:
The red dashed line is the hypotenuse of the right triangle with one leg equal to 24 inches and the other leg equal to 12 inches. Its length is given by the Pythagorean theorem:
space diagonal = √(24^2 +12^2) = √(720) = 12√5
space diagonal ≈ 26.83 . . . inches
The length of the longest item that will fit in the box is about 26.83 inches.
im badd i kinda understand but not really understanding it
Answer:
40
Step-by-step explanation:
if you add all the numbers up it becomes 96 and 96 goes Into. 480 5 times so you multiply 5 times the number of giant swallow tails
Answer:
If they are proportional we can expect 40
lol iready
please help i'm doing summer school and i have 2 days
Answer:
a. y < -4x + 4
Step-by-step explanation:
(0, 4) (2, -4)
find the equation of the line.
1. slope: (y² - y¹) / (x² - x¹)
a. (-4 - 4) / (2 - 0) = -8 / 2 = -4
2. y-intercept
a. from the graph, we see it is 4
3. plug it in
a. y = -4x + 4
since this is an equality, we use < > ≤ or ≥
the shaded region is below a dashed line, therefore we use <
y < -4x + 4
Perform all indicated operations, and express each answer in simplest form with positive exponents. Assume that all variables represent positive real numbers. Have to show all work.
Answer:
a. [tex]-( 4\sqrt{3} + 3)[/tex]
b. [tex]x^{\frac{-5}{12}} y^{\frac{31}{24}}[/tex]
c. [tex]\frac{8\sqrt{x} + 8\sqrt{5}}{x - 5}[/tex]
d. [tex]45 + 12\sqrt{5y} + 4 y[/tex]
e. [tex]-(\frac{3}{5x})^{\frac{1}{2}}[/tex]
Step-by-step explanation:
a.
[tex]\sqrt{12} - \sqrt{108} - \sqrt[3]{27}[/tex]
Expand each expression
[tex]\sqrt{4*3} - \sqrt{36 * 3} - \sqrt[3]{3*3*3}[/tex]
Split the first two surds
[tex]\sqrt{4}*\sqrt{3} - \sqrt{36} * \sqrt{3} - \sqrt[3]{3*3*3}[/tex]
[tex]2*\sqrt{3} - 6 * \sqrt{3} - \sqrt[3]{3*3*3}[/tex]
Apply law of indices
[tex]2*\sqrt{3} - 6 * \sqrt{3} - \sqrt[3]{3^3}[/tex]
Apply law of indices
[tex]2*\sqrt{3} - 6 * \sqrt{3} - 3^{3*\frac{1}{3}}[/tex]
[tex]2*\sqrt{3} - 6 * \sqrt{3} - 3^{1}[/tex]
[tex]2*\sqrt{3} - 6 * \sqrt{3} - 3[/tex]
[tex]2\sqrt{3} - 6\sqrt{3} - 3[/tex]
[tex]- 4\sqrt{3} - 3[/tex]
Factorize
[tex]-( 4\sqrt{3} + 3)[/tex]
The expression cannot be further simplified
b.
[tex](\frac{x^{\frac{-3}{4}}y^{\frac{2}{3}}}{x^{\frac{-1}{3}}y^{\frac{-5}{8}}})[/tex]
Expand the expression
[tex](\frac{x^{\frac{-3}{4}} * y^{\frac{2}{3}}}{x^{\frac{-1}{3}} * y^{\frac{-5}{8}}})[/tex]
Apply the following law of indices;
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
[tex]x^{{\frac{-3}{4} - \frac{-1}{3}}} * y^{{\frac{2}{3} - \frac{-5}{8}}}}[/tex]
[tex]x^{{\frac{-3}{4} + \frac{1}{3}}} * y^{{\frac{2}{3} + \frac{5}{8}}}}[/tex]
Add the exponents
[tex]x^{\frac{-9+4}{12}} * y^{{\frac{16+15}{24}}}}[/tex]
[tex]x^{\frac{-5}{12}} * y^{{\frac{31}{24}}}}[/tex]
[tex]x^{\frac{-5}{12}} y^{\frac{31}{24}}[/tex]
The expression cannot be further simplified
c.
[tex]\frac{8}{\sqrt{x} - \sqrt{5}}[/tex]
Rationalize the denominator
[tex]\frac{8}{\sqrt{x} - \sqrt{5}} * \frac{\sqrt{x} + \sqrt{5}}{\sqrt{x} + \sqrt{5}}[/tex]
[tex]\frac{8(\sqrt{x} + \sqrt{5})}{(\sqrt{x} - \sqrt{5})(\sqrt{x} + \sqrt{5})}[/tex]
Simplify the numerator
[tex]\frac{8\sqrt{x} + 8\sqrt{5}}{(\sqrt{x} - \sqrt{5})(\sqrt{x} + \sqrt{5})}[/tex]
Simplify the denominator by difference of two squares
[tex]\frac{8\sqrt{x} + 8\sqrt{5}}{\sqrt{x}^2 - \sqrt{5}^2}[/tex]
[tex]\frac{8\sqrt{x} + 8\sqrt{5}}{x - 5}[/tex]
The expression cannot be further simplified
d.
[tex](3\sqrt{5} + 2\sqrt{y})^2[/tex]
Expand the expression
[tex](3\sqrt{5} + 2\sqrt{y})(3\sqrt{5} + 2\sqrt{y})[/tex]
Open the bracket
[tex]3\sqrt{5} (3\sqrt{5} + 2\sqrt{y})+ 2\sqrt{y}(3\sqrt{5} + 2\sqrt{y})[/tex]
Open both brackets
[tex]3\sqrt{5} *3\sqrt{5} + 3\sqrt{5}*2\sqrt{y}+ 2\sqrt{y}*3\sqrt{5} + 2\sqrt{y}*2\sqrt{y}[/tex]
[tex](3\sqrt{5} *3\sqrt{5}) + (3\sqrt{5}*2\sqrt{y})+ (2\sqrt{y}*3\sqrt{5}) + (2\sqrt{y}*2\sqrt{y})[/tex]
Multiply each expression in the bracket
[tex](3*3\sqrt{5*5}) + (3*2\sqrt{5*y})+ (2*3\sqrt{5*y}) + (2*2\sqrt{y*y})[/tex]
[tex](9\sqrt{25}) + (6\sqrt{5y})+ (6\sqrt{5y}) + (4\sqrt{y^2})[/tex]
Solve like terms
[tex](9\sqrt{25}) + (12\sqrt{5y}) + (4\sqrt{y^2})[/tex]
Take square root of 25 and y²
[tex](9 * 5) + (12\sqrt{5y}) + (4 * y)[/tex]
[tex](45) + (12\sqrt{5y}) + (4 y)[/tex]
Remove the brackets
[tex]45 + 12\sqrt{5y} + 4 y[/tex]
The expression cannot be further simplified
e.
[tex]-\sqrt{\frac{3}{5x}}[/tex]
This expression can not be simplified; However, it can be rewritten, by applying law of indices as
[tex]-(\frac{3}{5x})^{\frac{1}{2}}[/tex]
Which relation is a function? Coordinate grid with graph of a vertical line at x equals 3. A coordinate grid with graph of a curve that increases through the third quadrant through the origin and exits the first quadrant A coordinate grid with the graph of a circle centered at the origin and passing through the point begin ordered pair 2 comma 1 end ordered pair. A coordinate grid containing a U shape with arrows on both ends that opens to the right. The bottom portion of the U passes through the origin.
Answer:
the answer is "A coordinate grid containing a U shape with arrows on both ends that opens to the right. The bottom portion of the U passes through the origin"
I took the test. Good luck!
A function is a coordinate grid containing a U shape with arrows on both ends that opens to the right, and in which the bottom portion of the U passes through the origin.
A function is a rule that connects outputs to each value. The relationship between value and output is often described with a mathematical formula, where the value is represented by one or more variables, alternatively by a table or graphically by a graph, a relationship diagram or an arrow diagram.
An important property of functions is that they are deterministic (that is, consistent, so that each value always gives the same value). This means that the function can be seen as a machine, which systematically delivers output values as soon as input values are inserted.
Learn more in https://brainly.com/question/23505310
The number of members of an online community increases each month. The
function M(t) = N(1 + ) represents the number of members at month t, where
Nis the initial number of members and ris the rate of increase. Select the
correct statement.
O A. Nincreases each month.
B. The initial value is (1 + r).
C. The function is linear.
D. The value of Mis a product of Nand a factor that does not depend
on N.
Answer:
Option D.
Step-by-step explanation:
Note: The given function is incomplete. Consider the given function as [tex]M(t)=N(1+r)^t[/tex].
The number of members at month t is
[tex]M(t)=N(1+r)^t[/tex]
where,
N is the initial number of members.
r is the rate of increase.
t is number of months
Here, N is constant. So, option A is incorrect.
N is initial value and (1+r) is growth factor. So, option B is incorrect.
The given function is an exponential function.
The value of M is a product of N and a factor that does not depend on N.
Therefore, the correct option is D.
I NEED HELP :_( Which of the following points is in the solution set of y > -x∧2 + 5? (0, 5) (2, 4) (1, 3)
Answer:
[tex]\huge\boxed{(2;\ 4)}[/tex]
Step-by-step explanation:
We have
[tex]y>-x^2+5[/tex]
Put the coordinates of the given points and check the inequality:
For (0; 5) → x = 0; y = 5
[tex]5>-0^2+5\\5>0+5\\5>5\qquad\bold{FALSE}[/tex]
For (2; 4) → x = 2, y = 4
[tex]4>-2^2+5\\4>-4+5\\4>1\qquad\bold{TRUE}[/tex]
For (1; 3) → x = 1, y = 3
[tex]3>1^2+5\\3>1+5\\3>6\qquad\bold{FALSE}[/tex]
Answer:
y>-x²+5
taking(0, 5)
5>-0²+5
5>5 false
taking 2,4
4>-2²+5
4>-4+5
4>1 true
taking 1,3
3>-1²+5
3>6false
so 2,4 is your answer
Please answer both questions
Answer:
36 and 24
Step-by-step explanation:
Answer:
Part a : 20 units², Part d : 12 units²
Step-by-step explanation:
We are given that the side lengths of each square is 6 units. In this case we can calculate the area of the triangles, subtracting from the area of the outer square, such that we calculate the remaining, area of the shaded region / inscribed square.
Area of Outer Square ( Same in all Cases ) = 6 [tex]*[/tex] 6 = 36 units²,
Area of Common Triangles ( 4 Triangles ) = 1 / 2 [tex]*[/tex] Base [tex]*[/tex] Height = 1 / 2 [tex]*[/tex] 2 [tex]*[/tex] ( 6 - 2 ) = 1 / 2 [tex]*[/tex] 2 [tex]*[/tex] 4 = 4,
4 [tex]*[/tex] 4 = 16 units²
Area of inscribed Square = 36 units² - 16 units² = 20 units²
For this second case the inscribed shape is not a square, but it can be calculated through a similar approach,
Area of Outer Square ( Same in all Cases ) = 6 [tex]*[/tex] 6 = 36 units²,
Area of Common Triangles ( 2 Triangles ) = 1 / 2 [tex]*[/tex] Base [tex]*[/tex] Height = 1 / 2 [tex]*[/tex] 4 [tex]*[/tex] 6 = 2 [tex]*[/tex] 6 = 12,
12 [tex]*[/tex] 2 = 24 units²
Area of inscribed shape = 36 units² - 24 units² = 12 units²
Plz help me 8+x^2-11
Answer:
-3 + x^2
Step-by-step explanation:
8+x^2-11
First combine the like terms.
so..
8-11 = -3
= -3 + x^2
but we don't know the value of x so we just leave it as it is.
And they both are not like terms so we cant solve them together so you stop there
Hope that helped!
Answer:
x^2 - 3Step-by-step explanation:
Simplify the numbers for you to get
x^2 stays the same
-11 = 8 = -3
Please help me find x!!!!
Answer:
x = 56
Step-by-step explanation:
Well if both lines are straight that means that 118 is on both sides,
180 - 118 = 62
So angle E and F are both 62.
So we do 62 *2 = 124.
180 - 124 = 56
x = 56
Thus,
angle x is 56.
Hope this helps :)
An ant needs to travel along a 20cm × 20cm cube to get from point A to point B. What is the shortest path he can take, and how long will it be (in cm)?
Answer:
48.28 cm
Step-by-step explanation:
The shortest distance would be to travel diagonally to the top-right corner, and then travel along the edge to B,
Diagonal = 20^2+20^2=c^2
400+400=c^2
800=c^2
square root of 800=c
c=28.28
Edge = 20
Total: 20+20.28=48.28 cm
Sid is packing crushed ice into a cone-shaped cup. The cone has a height of 5 in. Its base has a diameter of 4 in. What is the volume of the cone? StartFraction 20 Over 3 EndFraction pi inches cubed 20 pi inches cubed StartFraction 80 Over 3 EndFraction pi inches cubed 80 pi inches cubed
Answer:
20 over 3 pi inches cubed
Step-by-step explanation:
The formula for the volume of a cone is 1/3πr² · h
1. Set up the equation
1/3π2² · 5
2. Solve
1/3π(4)(5)
20/3π in.³
Answer:
20 over 3 pi inches cubed
Step-by-step explanation:
height - 5 in
diameter - 4 in
radius - 2 in (half of diameter)
V = [tex]\pi r^{2} \frac{h}{3}[/tex]
V = [tex]\pi (2)^{2} \frac{5}{3}[/tex]
V = [tex]\pi (4)\frac{5}{3}[/tex]
V = [tex]\pi (\frac{20}{3} )[/tex]
V = [tex]\frac{20}{3} \pi[/tex] in³
The volume of the cone is 20 over 3 pi inches cubed.
Hope that helps.
Amanda is ordering an ice cream dessert. She must order a size, a flavor of ice cream, and a topping. There are 2 sizes, 1 flavor, and 6 toppings to choose from. How many different ice cream desserts could she order?
Answer: 12
Step-by-step explanation:
Order requirement:
Size ; flavor and topping
Available variety:
Size = 2
Flavor = 1
Toppings = 6
Number of different ice-cream desserts which can be ordered :
Since one of each of size, topping and flavor must be selected :
(Number of available flavors * number of Toppings available * number of sizes available)
1 * 6 different Toppings = 6 varieties
6 varieties * 2 different sizes = 12 varieties
Therefore, there are 12 different variety of ice-cream dessert she can order.