To determine the missing side and how much longer the trip was compared to the shortest route, we can use the Pythagorean theorem.
The helicopter flew 6 miles north and 9 miles east, forming a right triangle. Let's denote the missing side as 'd', which represents the straight-line distance (the shortest route) between the starting point and the ending point.
According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the known sides are 6 miles (the north side) and 9 miles (the east side). Let's calculate the missing side 'd' using the Pythagorean theorem:
d^2 = 6^2 + 9^2
d^2 = 36 + 81
d^2 = 117
d ≈ √117
d ≈ 10.8 miles (rounded to the tenths place)
The shortest route (the hypotenuse 'd') is approximately 10.8 miles.
To find how much longer the actual trip was compared to the shortest route, we subtract the shortest route from the actual distance:
Actual distance - Shortest route = Extra distance
The actual distance traveled in this case is 6 miles north + 9 miles east, which equals 15 miles. So, the extra distance is:
15 miles - 10.8 miles = 4.2 miles (rounded to the tenths place)
Therefore, the helicopter's trip was approximately 4.2 miles longer than if it had taken the shortest route.
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OK this is another question which I need help on please please help if you can. CAUSED ME MUCH DISTRESS
Answer:
15 = 2x - 3y
Step-by-step explanation:
We have the two points P1(3,-3) and P2(9,1).
First, calculate the slope between those points:
slope [tex]= \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-3)}{9 - 3} = \frac{4}{6} = \frac{2}{3}[/tex]
Now simply move 3 steps from (3,-3) towards the y-axis to get the intersection with the y-axis (each step reduces x by 1 and applies the slope to the y-value):
(3,-3)
---> (2, -3 - (2/3)) = (2,-3 2/3)
---> (1, (-3 2/3) - 2/3) = (1, -4 1/3)
---> (0, (-4 1/3) - 2/3) = (0,-5)
This tells us, that our line intersects the y-axis at (0,-5).
The general form of a line is f(x) = <SLOPE> * x + <Y-VALUEATXEQUALSZERO>.
In our case: f(x) = y = (2/3)x -5.
To get it into the correct form, we simply subtract y from both sides and get:
0 = (2/3)x - y - 5
To get only integers just multiply everything with 3 and add 15 and get:
15 = 2x - 3y, which fulfils the form asked for in the problem.
Help!!!!!!!!!!!!! BRAINLIST WILL BE REWARDED
Answer:
135
Step-by-step explanation:
supplementary angles: either of two angles whose sum is 180°.
180 - 45 = 135
The 28 students in Mrs. Colby's class will share 98 slices of
pizza equally
How many slices will each student get?
Answer:
3 1/2 slices each
Step-by-step explanation:
98/28=3.5
Answer:
Every student will get 3 to 4 slices of pizza
Step-by-step explanation:
This is because you need to divided 98 with he 28 student, which you will get 3.5. That is the correct answer, but the question asked equally, so each student will get 3 to 4 slices of pizza.
Hope this helped
Solve for a
djəН
12
a =
✓ [?]
10
a
Pythagorean Theorem: a2 + b2 = c2
Enter
Answer:
a=[tex]\sqrt{44}[/tex]
Step-by-step explanation:
A^2+B^2=C^2
Substitute the values for what you know so:
a^2+10^2=12^2
Simplify:
a^2+100=144
-100 -100
------------------------
A^2=44
A=[tex]\sqrt{44}[/tex]
The bill at the restaurant was $18.79 estimate the amount to leave as a $10 tip. A. $2.00 B. $3.00 C. $9.00 D. $21.00
Answer: The correct option is A: $2.00
Step-by-step explanation:
The question should be:
"The bill at the restaurant was $18.79 estimate the amount to leave as a 10% tip. A. $2.00 B. $3.00 C. $9.00 D. $21.00"
The general case is:
When we have a quantity A (where A is the 100%) the X% of A is:
(X%/100%)*A
In this problem, we have a bill of $18,79 and we want to leave a 10% tip.
Then $18,79 is the 100% we want to see how much is the 10% of $18,79
If we use the above equation we get:
Tip = (10%/100%)*$18,79 = $1,879
The option that approaches the best to this amount is option A, $2.00
Then the tip should be $2
The correct option is A.
The hypotenuse of a right triangle measures 15 cm and one of its legs
measures 5 cm. Find the measure of the other leg. If necessary, round to the
nearest tenth.
Answer:
[see below]
Step-by-step explanation:
Use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
'c' will be the hypotenuse.
The hypotenuse is 15 cm. One of the legs is 5 cm.
[tex]5^2+b^2=15^2\\\\25 + b^2 = 225\\\\25-25+b^2=225-25\\\\b^2=200\\\\\sqrt{b^2}=\sqrt{200}\\\\ b=14.1421356237..., -14.1421356237[/tex]
14.1421356237 ≈ 14.1
The other leg should be about 14.1 cm.
Hope this helps.
The length of the other leg is 14.14 cm rounded to two decimal places.
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
Given, The hypotenuse of a right triangle measures 15 cm, and one of its legs measures 5 cm.
We know,
Hypotenuse² = Base² + Adjacent².
Therefore,
15² = 5² + Adjacent².
Adjacent = √(225 - 25).
Adjacent = √200.
Adjacent = 14.14.
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someone please help!!
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Quadratic formula.
Since we know that, for
[tex]a {x}^{2} + bx + c = 0[/tex]
For this quadratic equation, the formula is :
[tex] \frac{ - b - + \sqrt{ {b}^{2} } - 4ac }{2a} [/tex]
so we apply it here,
so we get as,
[tex] \frac{ - 5 + - \sqrt{25 - 24} }{6} [/tex]
option C is correct.
Answer:..........
Step-by-step explanation:
6 times the difference of d and 5
Answer:
6(d - 5)
Step-by-step explanation:
Answer:
d-30
Step-by-step explanation
6*5 the do d- that which is d-30
Plz help me!!
Can someone tell me how to get the answer as well plz? Thank you
The hypotenuse of a right triangle measures 15 cm and one of its legs
measures 5 cm. Find the measure of the other leg. If necessary, round to the
nearest tenth
Answer:
√200 or 14.1
Step-by-step explanation:
Pythagoras' Theorem: a²+b²=c²
Rearrange to get b² (one of the smaller sides): c²-a²=b²
225-25=200
√200 = 14.1
Answer:
14.1 I hope this helps! Brainliest please!
Step-by-step explanation:
So we use the Pythagorean theorem which is a squared + b squared = c squared. C is the hypotenuse. So we do:
15 squared - 5 sqaured = b squared
225 - 25 = b squared
200 = b squared
14.1 = b
If f(x) = 12 – 2 and g(x) = x + 3, find all values of x, to the nearest tenth, for
which f(x) = g(x).
Answer:
x=7
Step-by-step explanation:
f(x) =g(x)
12-2=x+3
10=x+3
10-3=x
x=7
simplify the expression
16+(-5)-2/5j-4/5j+6
Answer:
17 - 6j / 5
Step-by-step explanation:
Expand the polynomial: (2x+3)^2
Answer:
4x^2+12x+9
Step-by-step explanation:
(2x+3)^2=(2x+3)(2x+3)=4x^2+12x+9
what is the degree of the polynomial ? 6x^3y^5+8y^6
Answer:
degree 8
Step-by-step explanation:
The degree of a polynomial is determined by the largest exponent of the variable in the polynomial.
6x³[tex]y^{5}[/tex] ← has degree 3 + 5 = 8
8[tex]y^{6}[/tex] ← has degree 6
Thus the polynomial is of degree 8
Suppose an ordered pair is not a solution of y > x + 10. Must it be a solution to y < x + 10? Explain. 50 points!!!!
Answer:
I think when u substitute the order pair for x and y Into the equation the y is gonna be les than the x + 10
Step-by-step explanation:
K so am confused abt ur question but here
example (2,5)
y < x + 10
substitute 2 for x and 5 for y
5 < 2 + 10
5 < 12
y is less than x + 10
PLEASE HELP ME!!!!!!!!!!!!
Rosa is selling juice and cookies for a fundraiser. She earns $2 for every cookie and $3 for every bottle of juice. She wants to earn at least $24 from all the sales. Let x represent the number of cookies sold and y represent the number of bottles of juice sold. What does the slope of this inequality represent? 2x + 3y ≥ 24
Answer:
The slope is 2. It represents the price of the cookies.
Step-by-step explanation:
The slope is 2 because its in frount of the x and 2 is the price of the cookies.
Si: a + b + c = 18
hallar: abc + bca + cab
Answer:
abc + bca + cab
abc(1+1+1)
3×18
54
Answer:
54
Step-by-step explanation:
a + b + c = 18
abc + bca + cab = ???
18 / 3 = 6
a = ? = 6
b = ? = 6
c = ? = 6
(6 + 6 + 6) + (6 + 6 + 6) + (6 + 6 + 6)
(18) + (18) + (18)
abc + bca + cab = 54
H E L P pls and thank you :)
The estimate obtained from a sample of which size is likely to be closest to the actual parameter value of a population?
A. 84
B.112
C.12
D.184
Answer:
184 D
Step-by-step explanation:
A sample size of 184, is more likely to provide an estimate closest to the actual parameter value of the population.
Option D is the correct answer.
What is the population parameter?It is typically unknown and can only be estimated using sample data.
The goal of statistical inference is to use the information in a sample to make inferences or d
A population parameter is a numerical value that describes a characteristic of a population, such as the mean or standard deviation.
We have,
The estimate obtained from a larger sample size is likely to be closer to the actual parameter value of a population.
This is because a larger sample size reduces the effects of sampling variability and random errors, resulting in a more accurate estimate of the population parameter.
Thus,
A sample size of 184, is more likely to provide an estimate closest to the actual parameter value of the population.
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At the student store, pencils are sold in either packs of three or packs of eight.
Without opening any packages, which numbers of pencils is it possible to buy?
Which numbers are impossible?
Answer
4, 7, 5, 10, 13, .......
Step-by-step explanation:
the only numbers that are impossible to get are the non-multiples of 3 and 8
and the numbers that 8 and 3 do not add up to and the multiples of 8 and 3 do not add up to
Which properties were used to prove that the expressions 7x+4-x-2 and 6x+2 are equivalent?
Answer:
12
Step-by-step explanation:
12
The graph of a liner function is shown on the coordinate grid. what is the slope of the graph of this function?
A-7/3
B-3/7
C- -7/3
D- -3/7
Answer: C -7/3
Step-by-step explanation: Slope is rise over run, rise/run, and your line means your slope will be negative. So, you will first count straigt down from your firt point until you reach the line of the second point, which is 7. Next, you would count/run to the point, which is 3. Rise/run = -7/3. I hope this helps :)
Allison sells apples at the market. On a given day, the ratio of red delicious to Macintoshes to granny smiths sold is 4:3:2. If her truck can carry 180 bushels of apples, how many bushels of granny smiths should she include? *
Answer:
40
Step-by-step explanation:
80+60+40=180
There is 20 more of each type of apple
Samaia buys two water bottles and three bags of chips for $9.45. Abdullah goes to the same store and buys four water bottles, as Samaia, and five bags of chips, same as ones Samaia bought, for $14.75. Which choice below accurately represents a system of equations, w for water bottles and c for chips, for this scenario? Each water bottle is same price and each bag of chips is same price. * A) 3w + 2c = 9.45 AND 5w + 4c = 14.75 B) 2w + 3c = 9.45 AND 4w + 5c = 14.75 3) 2w + 3c = 14.75 AND 4w + 5c = 9.45 D) 5c + 9w = $24.20
Answer:
B) 2w + 3c = 9.45 AND 4w + 5c = 14.75
Step-by-step explanation:
Let us represent:
Number of water bottles = w
Number of bag of chips = c
Hence:
Samaia buys two water bottles and three bags of chips for $9.45.
2w + 3c = 9.45......Equation 1
Abdullah goes to the same store and buys four water bottles, as Samaia, and five bags of chips, same as ones Samaia bought, for $14.75.
4w + 5c = 14.75......Equation 2
Which choice below accurately represents a system of equations, w for water bottles and c for chips, for this scenario?
Option B) 2w + 3c = 9.45 AND 4w + 5c = 14.75 is the correct option.
Madison was working at a store in the mall. She earns 7% commission for each sale that she makes. Last month, she sold a total of $1,450. How much commission did she earn?
Answer:
101.50
Step-by-step explanation:
Answer:
$101.50
Step-by-step explanation:
7% of 1450 = 0.07 × 1450 = 101.5
HELP
will give brainliest
Answer:
y= 3x+2
I hope this helped :)
PLEASE HELP ILL MARK BRAILIEST!!!
P.S please show how you figured it out
Answer:
I think that the answer is either B or C
Step-by-step explanation:
I concluded to this answer simply by looking at where the lines were placed.
Remember that if a line is not touching, but next to another line, they are parallel to each other? Well, that doesn't change here. since, {m angle 1} and {m angle 2} added together equal 180, I would believe that the answer is C, but I may be wrong.
Well, I hope that helps :)
What is the equation of the line that passes through the point (-5, -4) and has a
slope of -3/5
Answer:
y=-3/5x-7
Step-by-step explanation:
y-y1=m(x-x1)
y-(-4)=-3/5(x-(-5))
y+4=-3/5(x+5)
y=-3/5x-15/5-4
y=-3/5x-3-4
y=-3/5x-7
1, 3, 9, 27, ... What's the pattern rule and the next three numbers?
Answer:
multiply by three
Step-by-step explanation:
Step-by-step explanation:
1 x 3 = 3 x 3 = 9 x 3 = 27
=> Pattern rule = [tex]3^{n-1}[/tex]
=> The next three numbers = 81 , 243 , 729
What is the value of x in the matrix equation below?
=======================================================
Explanation:
The -2 outside the first matrix multiplies to every item inside that first matrix.
So the x updates to -2x in the upper left corner.
That -2x adds to the 3 in the upper left corner of the second matrix. The sum -2x+3 must be equal to the value in the upper left corner of the third matrix.
Everything is focused on the upper left corner.
So we must solve -2x+3 = x
Doing so leads to...
-2x+3 = x
3 = x+2x
3 = 3x
3x = 3
x = 3/3
x = 1
A cylinder has a volume of 48π cm3 and height h. Complete this table for volume of cylinders with the same radius but different heights.
height (cm) volume (cm3)
h 48π
2h ? answer in pi
5h ? answer in pi
h/2 ? answer in pi
h/5 ? answer in pi
Answer:
(i) For [tex]2\cdot h[/tex], the volume is [tex]96\pi[/tex] cubic centimeters.
(ii) For [tex]5\cdot h[/tex], the volume is [tex]240\pi[/tex] cubic centimeters.
(iii) For [tex]\frac{h}{2}[/tex], the volume is [tex]24\pi[/tex] cubic centimeters.
(iv) For [tex]\frac{h}{5}[/tex], the volume is [tex]9.6\pi[/tex] cubic centimeters.
Step-by-step explanation:
The volume of the cylinder ([tex]V[/tex]), measured in cubic centimeters, is defined by the following formula:
[tex]V = \pi\cdot r^{2}\cdot h[/tex] (1)
Where:
[tex]r[/tex] - Radius, measured in centimeters.
[tex]h[/tex] - Height, measured in centimeters.
From statement, we understand that volume of the cylinder is directly proportional to its height. That is:
[tex]V \propto h[/tex]
[tex]V = k\cdot h[/tex] (2)
Where [tex]k[/tex] is the proportionality constant, measured in square centimeters.
In addition, we eliminate this constant by constructing the following relationship:
[tex]\frac{V_{2}}{V_{1}} = \frac{h_{2}}{h_{1}}[/tex]
[tex]V_{2} = \frac{h_{2}}{h_{1}} \cdot V_{1}[/tex] (3)
Based on (3) and knowing that [tex]V_{1} = 48\pi[/tex], we calculate the volumes for each height ratio:
(i) For [tex]2\cdot h[/tex], the volume is [tex]96\pi[/tex] cubic centimeters.
(ii) For [tex]5\cdot h[/tex], the volume is [tex]240\pi[/tex] cubic centimeters.
(iii) For [tex]\frac{h}{2}[/tex], the volume is [tex]24\pi[/tex] cubic centimeters.
(iv) For [tex]\frac{h}{5}[/tex], the volume is [tex]9.6\pi[/tex] cubic centimeters.