The distance of plane from the starting point is 69.46 km.
Given that the plane first flies 35 km in the direction N30W and then 60 km in the direction N60E.
We have to find the distance of plane from starting point.
We have to use pythagoras theorem in this which says that the square of hypotenuse is equal to sum of squares of the base and perpendicular.
[tex]H^{2} =P^{2} +B^{2}[/tex]
From the figure we can say that P=35 km .and B=60 km
In this we have to find the value of H when P=35 and B=60
[tex]H^{2} =35^{2} +60^{2}[/tex]
[tex]H^{2}[/tex]=1225+3600
[tex]H^{2}[/tex]=6946
H=69.46
Hence the distance of plane from starting point is 69.46 km.
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Write the first five terms of the sequence. an = n 2 + 2 2, 3, 6, 11, 18 3, 6, 9, 12, 15 3, 6, 11, 18, 27
The first five terms of the sequence will be 3, 6, 11, 18, 27. Then the correct option is C.
What are sequence and series?A sequence is a list of elements that have been ordered sequentially, such that members come either before or after.
The equation will be given below.
[tex]\rm a_n = n^2+2[/tex]
Then the first five terms of the sequence will be
For n = 1, we have
a₁ = 1² + 2
a₁ = 3
For n = 2, we have
a₂ = 2² + 2
a₂ = 6
For n =3, we have
a₃ = 3² + 2
a₃ = 11
For n = 4, we have
a₄ = 4² + 2
a₄ = 18
For n = 5, we have
a₅ = 5² + 2
a₅ = 27
Then the sequence will be 3, 6, 11, 18, 27.
Then the correct option is C.
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Can someone help me pls
Answer:
(d) x = (5±√53)/2
Step-by-step explanation:
The given quadratic equation is in standard form, so the coefficients are readily identified. The solution is given by the quadratic formula based on those coefficients.
Quadratic formulaThe solution to the quadratic equation ax² +bx +c = 0 is given by the formula ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
ApplicationThe given equation has coefficients a = 1, b = -5, c = -7, so the solutions given by the formula are ...
[tex]x=\dfrac{-(-5)\pm\sqrt{(-5)^2-4(1)(-7)}}{2(1)}=\dfrac{5\pm\sqrt{25+28}}{2}\\\\\boxed{x=\dfrac{5\pm\sqrt{53}}{2}}[/tex]
help me please i give you brainly
Answer:
the answer is false .
Step-by-step explanation:
Given that a= 3, b= -2 and c= -4, evaluate the following expression. 3a-b/2c + 3a-c/c-b
The value of the given algebraic expression is -63/8.
To evaluate an algebraic expression, we substitute the values of the variables in the expression, and then follow the rules of solving a numeral expression.
In the question, we are asked to evaluate the algebraic expression:
{(3a - b)/2c} + {(3a - c)/(c - b)}, given the values of a = 3, b = -2, and c = -4.
To evaluate the expression {(3a - b)/2c} + {(3a - c)/(c - b)}, given the values a = 3, b = -2, and c = -4, we substitute these values in the expression and solve as follows:
{(3(3) - (-2))/2(-4)} + {(3(3) - (-4))/((-4) - (-2))}
= {(9 + 2)/(-8)} + {(9 + 4)/(-4 + 2)}
= {-(11/8)} + {-(13)(2)}
= -(11/8) - (13/2)
= -(11/8) - (52/8)
= -(63/8).
Thus, the value of the given algebraic expression is -63/8.
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5.
AMNOP is a square-based pyramid where the volume of pyramid is
392 cm³ and the height is 6 cm. Find the each side of the base area of pyramid.
The length of each side of the base of the pyramid is 14 cm
Volume of a pyramidFrom the question, we are to determine the length of each side of the base of the pyramid
The volume of a square-based pyramid is given by
V = 1/3(b²h)
Where V is the volume
b is the length of the base
and h is the height
From the given information,
V = 392 cm³
h = 6 cm
Putting the parameters into the equation, we get
392 = 1/3(b²× 6)
392 = b² ×2
b² = 392/2
b² = 196
b = √196
b = 14 cm
Hence, the length of each side of the base of the pyramid is 14 cm
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help me pls
4/3(6/4/5)
Answer:
0.4
Step-by-step explanation:
4/3(1.5/5)
4/3(0.3)
1.33333333333(0.3)
0.4
5. How many 6-digit numbers can be formed from the digits 0,1,3,5,7 and 9 which are divisible by 10 and no digit is repeated?
There are 120 6-digit numbers that can be formed
How to determine the combination of digits?The digits are given as:
0,1,3,5,7 and 9
Since the number must be divisible by 10.
Then the number must end in 0
The other 5 digits can take any of the 0,1,3,5,7.
So, the number of combination is:
Count = 5! * 1
Expand
Count = 5 * 4 * 3 *2 * 1 * 1
Evaluate
Count = 120
Hence, there are 120 6-digit numbers that can be formed
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hi who know how to do this 3 question?,I will mark brainlest for good answer.
Answer:
its answer is 36
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What is the decimal expansion of the following fraction? 1/5
Answer:
0.2
Step-by-step explanation:
Answer:
0.2
Step-by-step explanation:
1 divided by 5 = 0.2
1. Please answer the question on exponential growth or decay. Round to
the nearest whole number or penny if the question is concerning money if
necessary.
A country pledges to reduce its annual
CO₂ emissions by 2% per year. If the
emissions in 2022 are 4,200 Mt (metric
megatons), what are the maximum
allowable emissions in the year 2031?
The maximum value of allowable emissions in the year 2031 is equal to 3,502.
How to calculate the maximum value?In order to determine the maximum value of allowable emissions in the year 2031, we would use an exponential function which also relates to compound interest as follows:
A = P(1 - r)^t
For the time, we have:
Time, t = 2031 - 2022
Time, t = 9
Substituting the given parameters into the formula, we have;
A = 4,200(1 - 0.02)^9
A = 4,200(0.98)^9
A = 4,200 × 0.8338
A = 3501.7 ≈ 3,502.
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heeelpp mee please !!!!!
Answer:
210 yd²
Step-by-step explanation:
If we rotate the shape we get a right angle triangle with a hypotenuse of 29 yd :
The area of a right angle triangle is given by the formula :
A = [tex]\frac{ab}{2}[/tex]
Substituting the 2 values given in diagram gives us :
A = [tex]\frac{(20)(21) }{2}[/tex] = 420÷2 = 210
Our units will be yd² as we are dealing with area
HALP
x =x=x, equals
^\circ
∘
Answer:
90°+x = 180°(angles on a straight line)x=180°-90°x=90°THERE ARE A LOT OF WAYS TO WORK THE ANSWER OUT BUT THAT ONE IS SIMPLE AND EASY TO UNDERSTANDStep-by-step explanation:
HOPE THIS HELPS!!Please help me with Algebra 2 questions (2).
#8: Simplify the expressions. Assume all variables are positive.
#11: Solve the equation.
8. The simplified form of the expression is [tex]- 5 x^{\frac{4}{5}}y^{3}[/tex]
11. The value of x is 4
Simplifying an expressionFrom the question, we are to simplify the give expression
The given expression is
[tex]y^{3}\sqrt[5]{32x^{4} } - 7\sqrt[5]{x^{4}y^{15} }[/tex]
[tex]y^{3} (32x^{4} )^{\frac{1}{5} } - 7(x^{4}y^{15} )^{\frac{1}{5}[/tex]
[tex]y^{3} \times 32^{\frac{1}{5} } x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{\frac{15}{5}}[/tex]
[tex]y^{3} \times 2^{5 \times} ^{\frac{1}{5} } \times x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{3}[/tex]
[tex]y^{3} \times 2 \times x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{3}[/tex]
[tex]2 x^{\frac{4}{5} } y^{3} - 7 x^{\frac{4}{5}}y^{3}[/tex]
[tex]= - 5 x^{\frac{4}{5}}y^{3}[/tex]
11. [tex]\frac{1}{2}(5x+7 )^{\frac{2}{3} } =\frac{9}{2}[/tex]
Multiply both sides by 2
[tex]2 \times \frac{1}{2}(5x+7 )^{\frac{2}{3} } =2 \times \frac{9}{2}[/tex]
[tex](5x+7 )^{\frac{2}{3} } =9[/tex]
Multiply both sides by a power of 3/2
[tex](5x+7 )^{\frac{2}{3} \times {\frac{3}{2} } } =9^{\frac{3}{2} }[/tex]
[tex](5x+7 )=3^{2 \times} ^{\frac{3}{2} }[/tex]
[tex]5x+7 =3^{3}[/tex]
[tex]5x+7 =27[/tex]
[tex]5x =27-7[/tex]
[tex]5x = 20[/tex]
[tex]x = \frac{20}{5}[/tex]
x = 4
Hence,
8. The simplified form of the expression is [tex]- 5 x^{\frac{4}{5}}y^{3}[/tex]
11. The value of x is 4
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help me please 10 points!!
Answer:
104m²
Step-by-step explanation:
we can find the area of a trapezoid from its bases and height in the following formula:
[tex]A=\frac{a + b}{2}h[/tex]
where...
A: area
a: one base
b: other base
h: height
here, we can see that our two bases are 9 and 17, and that our height is 8.
Now, let's plug these values into our formula:
a: 9
b: 17
h: 8
[tex]A=\frac{a + b}{2}h[/tex]
[tex]A=\frac{9 + 17}{2}8[/tex]
Now, we can simplify:
[tex]A=\frac{9 + 17}{2}8[/tex]
[tex]A=\frac{26}{2}8[/tex]
A = 13 · 8
A = 104
so, the area of this trapezoid is 104m²
(note: we write area as squared / in square units)
hope this helps! have a lovely day :)
help me pls and if u can explain too.
Part 1
The gradient of the line is [tex]\frac{11-1}{-3-2}=-2[/tex], so the equation is [tex]y=-2x+5[/tex].
This means the system is
[tex]y=-2x+5\\\\y=ax^2 +b[/tex]
Part 2
Substituting in the coordinates (-3,11) and (2,1) into the equation of the parabola,
[tex]11=9a+b\\\\1=4a+b[/tex]
Subtracting the equations, we get 10=5a, and thus a = 2
Substituting a = 2 back into the system, we get b = -7
Part 3
The equation of the parabola is [tex]y=2x^2 - 7[/tex], and the turning point is at [tex]x=0[/tex]. Therefore, the value of y is -7
(b) In the figure, AABC and ACDE are equilateral triangles. Prove that: AD = BE.
i have sent the picture of the figure also please send the solution fast
Since both the given triangles are equilateral, their interior angles are each measure 60°.
Consider triangles ADC and BEC.
We have:
AC = BC (given)DC = EC (given)ACD = ACB + BCD = 60 + BCD (angle addition)ECB = ECD + BCD = 60 + BCD (angle addition)According to above, two sides and the included angle of triangles ADC and BEC are congruent by ASA.
Therefore AD = BE as corresponding sides of congruent triangles, hence proved.
GEOMETRY)
Fill in the blanks:
How many degrees is arc PA?
How many degrees is angle PRA?
Line PR is a diameter of the circle. How many degrees is arc PAR?
How many degrees is arc AR?
(The picture is below and Q is the one above the circle and A at the bottom of the circle)
Part 1
By the inscribed angle theorem, arc PA measures 62 degrees.
Part 2
Angles inscribed in the same arc are congruent, so angle PRA measures 31 degrees.
Part 3
Diameters form semicircles, and the arc of a semicircle measures 180 degrees, so arc PAR measures 180 degrees.
Part 4
Subtracting arc PA from arc PAR, we get arc AR measures 118 degrees.
A scuba diver is 50 ft below sea level. Which of the following best describes this situation?
1. |50|
2. -50
3. +50
4. ±50
Answer:
-50
Explanation:
At sea level would be 0 so anything above would be a positive number and anything below a negative number.
HELPS I NEED THE ANSWER PLSSSSSSSSSSSS!
Answer:
5.5x+7.146 (the six is repeating)
Step-by-step explanation:
Answer:
5.5x + 7.25
Step-by-step explanation:
5.5(x+6.5)-(x+9.5)-(19-x) Convert the fractions to decimal
5.5x+35.75 -x - 9.5 - 19 +x Expand
(5.5x - x + x) +(35.75 - 9.5 - 19) Group like terms
5.5x + 7.25 Combine like terms
Ms. johnson uses a statistics program to analyze all the data collected by her students during a lab experiment about acceleration due to gravity. the program reports =31.5 and . what is the variance of the data? round to the nearest tenth.
Since the variance is the square of the standard deviation, the variance here is 6.3.
A commonly used measure of dispersion is the standard deviation, which is simply the square root of the variance. Therefore, we just raise the standard deviation to the power of 2 to get the answer. We do as follows:
s = √v
(2.5)² = (√v)²
v = 6.25 = 6.3
So, Since the variance is the square of the standard deviation, the variance here is 6.3.
DISCLAIMER: The question was incomplete. Please find the full content below.
Question
Ms. Johnson uses a statistics program to analyze all the data collected by her students during a lab experiment about the acceleration due to gravity. The program reports a mean of 31.5 and a standard deviation of 2.5. What is the variance of the data?
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Answer: D). 6.3
Step-by-step explanation:
A loaded 8-sided die is loaded so that the number 4 occurs 3/10 of the time while the other numbers occur with equal frequency. what is the expected value of this die
Answer:
4.4
Step-by-step explanation:
The sum of the probabilities of all possible outcomes is 1.
As the die is loaded so that the number 4 occurs 3/10 of the time, and the other numbers occur with equal frequency, then the probability of numbers 1, 2, 3, 5, 6, 7 and 8 being rolled is 1/10.
Create a probability distribution table for X, where X is the score on the loaded 8-sided die:
[tex]\begin{array}{ | c | c | c | c | c | c | c | c | c |}\cline{1-9}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\\cline{1-9} & & & & & & & &\\ \text{P}(X=x) & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{3}{10} & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{1}{10}\\& & & & & & & &\\\cline{1-9}\end{array}[/tex]
Add a product row and a totals column:
[tex]\begin{array}{ | c | c | c | c | c | c | c | c | c | c |}\cline{1-10}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 &\text{Total} \\ \cline{1-10} &&&&&&&&& \\ \text{P}(X=x) & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{3}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & 1\\ &&&&&&&&&\\ \cline{1-10} &&&&&&&&&\\\text{Product} & \frac{1}{10} & \frac{2}{10} & \frac{3}{10} & \frac{12}{10} & \frac{5}{10} & \frac{6}{10} & \frac{7}{10} & \frac{8}{10} & \frac{44}{10} \\ &&&&&&&&&\\\cline{1-10}\end{array}[/tex]
(The Product is row is the product of the score on the die and its probability).
The expected value (EV) is the sum of the product of each outcome and its probability.
Therefore, the expected value (EV) of this die is 44/10 = 4.4
7
Solve the system of inequalities by graphing.
2x + 5y < 25
y < 3x-2
5x - 7y < 14 DUE NOW
The solution to the inequality 2x + 5y < 25, y < 3x-2 and 5x - 7y < 14 is the dark triangular region shown in the graph.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Inequality shows the non equal comparison of two or more numbers and variables.
The solution to the inequality 2x + 5y < 25, y < 3x-2 and 5x - 7y < 14 is the dark triangular region shown in the graph.
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Find m/HFG if m/EFG = 2x + 52, m/EFH = 21°, and
m/HFG = x + 31.
Answer:
31°
Step-by-step explanation:
Given Angle EFG = Angle EFH + Angle HFG (based on the diagram)
[tex]2x+52 = 21 + (x+31)\\2x+52 = 21+x+31\\2x+52=x+52\\2x-x+52=52\\x+52=52\\x=52-52\\x=0[/tex]
From here we can see the value of x is non-existent.
Substitute x to find Angle HFG.
x+31 = 0 + 31 = 31°
I have $230 and I’m at a bookstore. I love books, so I want to buy as many as I can. The books I want to buy each cost $17. At most, how many books can I buy and still have at least $25 left for dinner?
Answer:
12 books
Step-by-step explanation:
Lets set aside $25 for dinner first.
Amount left = $230 - $25 = $205
Number of books able to buy = amount left ÷ cost per book
= $205 ÷ $17
= 12.058 books
Of course, you cant buy .058 books , that wont make sense, so you take the highest possible WHOLE number, which in this case, is 12 books.
Alice, Bob, and Carol were riding their bikes along the same path at different speeds. Alice's speed was twice Bob's speed, and Carols' speed was one-third that of Alice's speed. What was Carol's speed, in miles per hour, if Bob's speed was 9 miles per hour
Carol's speed is computed to be 6 miles/hour, solved using the equation (3x)/2 = 9.
We assume Carol's speed to be x miles/hours.
Carol's speed is given to be one-third of Alice's speed.
Then Alice's speed is three times Carol's speed, that is, Alice's speed = 3x miles/hour.
Alice's speed is given to be twice Bob's speed.
Then Bob's speed is half of Alice's speed, that is, Bob's speed = (3x)/2 miles/hour.
But, Bob's speed is given to be 9 miles per hour.
Therefore, we get the equation:
(3x)/2 = 9.
To find Carol's speed, we solve this equation as follows:
(3x)/2 = 9,
or, {(3x)/2}*2 = 9*2 {Multiplying both sides by 2},
or, 3x = 18 {Simplifying},
or, 3x/3 = 18/3 {Dividing both sides by 3},
or, x = 6 {Simplifying}.
Therefore, Carol's speed is computed to be 6 miles/hour, solved using the equation (3x)/2 = 9.
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URGENT PLEASE ANSWER THESE ASAP
Answer:
(b) 25 muffins
(c) 38 muffins
Step-by-step explanation:
Given:
A cookie cost $0.80 A muffin costs $1.60buy 200 treatsspend $200 or lessForming system of linear equations:
muffins (m) + cookies (c) = 200 treats
1.60m + 0.80c = $200
Solve by Substitution:
m + c = 200
1.6m + 0.8c = 200
using m + c = 200, solve for m by subtracting c:
m + c - c = 200 - c
m = 200 - c
we can now plug in m tot he second equation,
1.6(200 - c) + 0.8c = 200
320 - 0.8c = 200
320 - 320 - 0.8c = 200 - 320
-0.8c = -120
-0.8c/-0.8 = -120/-0.8
c = 150
plug c back in to find m,
m = 200 - c
m = 200 - 150
m = 50
(b) if you buy 200 cookies, then how many muffins?
we use this equation as we want to stay in the price limit: 1.6m + 0.8c = 200
c = 200 so 1.6m + 0.8(200) = 200
1.6m + 0.8(200) = 200
1.6m + 160 = 200
1.6m = 200 - 160
1.6m = 40
1.6m/1.6 = 40/1.6
m = 25
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Some families spend their incomes according to budget plans. If a family used the plan
below as a basis, about how much would it spend for clothing?
Shelter.
Food
Clothing
Operation
Savings
Other Expenses.
$525
Monthly
Income
.26%
.28%
7%
. 10%
. 9%
20%
100%
O $35.75
O $36.75
O $53.20
$75.00
O none of these
Using proportions, it is found that the family would spend $36.75 on clothing.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The family has a budget of $525, and spends 7% of it in clothing, hence the amount is given by:
A = 0.07 x 525 = $36.75.
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if a researcher counting how many seconds each bystander helps a stranger struggling to pick up a heavy box fan varying amounts of time but i 10 seconds and 15 seconds equally as much in the data. all the restaurant under 10 seconds. this means the data are
The mean of the data about researcher counting of seconds each by stander helps a stranger struggling to pick up a heavy box fan varying amounts of time is 11.67 seconds.
Given if a researcher counting how many seconds each by stander helps a stranger struggling to pick up a heavy box fan varying amounts of time but is 10 seconds and 15 seconds equally as much in the data. all the restaurant under 10 seconds.
We have to calculate mean of the data.
Mean is the sum of numbers divided by total numbers included.
Mean=∑X/n
where n is the numbers.
Mean =(10+15+10)/3
=35/3
=11.67
Hence mean of the data about researcher's counting is 11.67.
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−6i⋅(6−2i)=minus, 6, i, dot, left parenthesis, 6, minus, 2, i, right parenthesis, equals Your answer should be a complex number in the form a+bia+bia, plus, b, i where aaa and bbb are real numbers.
The solution to the given product is:
-6i*(6 - 2i) = -12 - 36i
How to solve the given expression?
Here we want to solve:
-6i*(6 - 2i)
Here the thing that you need to remember is that i² = -1.
Expanding the product, we get:
-6i*(6 - 2i) = (-6i)*6 + (-6i)*(-2i)
= -36i + (6i)*(2i) = -36i + 12i² = -36i - 12
Then we conclude:
-6i*(6 - 2i) = -12 - 36i
That is the solution to the given expression.
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You walk into a room. 2 dogs, 4 horses 1 giraffe and a duck on the bed. 3 chickens flying over a chair. How many legs are on the floor?.
Answer:
8+16+2=28
Step-by-step explanation: