let's recall d = rt, or namely distance = rate * time.
b = speed of the boat in still water
c = speed of the current
when going Upstream, the boat is not really going "b" fast, is really going slower, is going "b - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "b" fast, is really going faster, is going "b + c", because the current is adding its speed to it.
[tex]\begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&82&b-c&2\\ Downstream&106&b+c&2 \end{array}\hspace{5em} \begin{cases} 82=(b-c)2\\\\ 106=(b+c)2 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{82=(b-c)2}\implies \cfrac{82}{2}=b-c\implies 41=b-c\implies \boxed{41+c=b} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{106[~(41+c)+c~]2}\implies \cfrac{106}{2}=41+2c\implies 53=41+2c \\\\\\ 12=2c\implies \cfrac{12}{2}=c\implies \blacksquare~~ 6=c ~~\blacksquare~\hfill \blacksquare~~ \stackrel{41~~ + ~~6}{47=b} ~~\blacksquare[/tex]
For Which distributions is the median the best measure of center?
Select each correct answer
Answer: 6, 6, 9 and 25
Step-by-step explanation:
bbringingbbringingout the data's from the graph and arrangementsarrangingarrangingarrangementsarrangingarranging them serially that's from smallest to biggest biggest, then selecting the middle number if the number of entire entries is an odd number but if it's an even number you take the average of the two middle number
If cos is x=0.25, find sin x
A) sin x ≈ 0.97
B) sin x ≈ 0.75
C) sin x ≈ 0.0625
D) sin x ≈ 0.03
Answer:
In quadrant I, the answer is A. sin(x) ≈ 0.97
A fish is 18 feet below the surface of a lake. The fish swims up 12 feet before diving 45 feet. What equation can be used to find the current depth of the fish in feet?
Numbers are written on the back of calenders that are given out to customers at a grociery store. Each month a number is drawn for a customer to win a gift card. Is it a random sample or a sample and why
Answer:
yo whats your name i think that we are from the same class
Step-by-step explanation:
What areC12, C31, and C22 of matrix C?
Compute the sum to simplify C :
[tex]C = \begin{bmatrix}16-0.5 & 9+0 \\ -3+5 & 0 + 8 \\ 4-3 & -10+14\end{bmatrix} = \begin{bmatrix}15.5 & 9 \\ 2 & 8 \\ 1 & 4\end{bmatrix}[/tex]
Now, [tex]c_{ij}[/tex] is the entry of the matrix in row i and column j, so
[tex]C = \begin{bmatrix}15.5 & \boxed{9} \\ 2 & 8 \\ 1 & 4\end{bmatrix} \implies c_{12} = 9[/tex]
[tex]C = \begin{bmatrix}15.5 & 9 \\ 2 & 8 \\ \boxed{1} & 4\end{bmatrix} \implies c_{31} = 1[/tex]
[tex]C = \begin{bmatrix}15.5 & 9 \\ 2 & \boxed{8} \\ 1 & 4\end{bmatrix} \implies c_{22} = 8[/tex]
12 + 5 + 32 × 10 − 5 =
(12 + 5) + 32 × (10 − 5) =
Add 12 and 5 to get 17.
17 + 32 × 10 − 5Multiply 32 and 10 to get 320.
17 + 320 − 5Add 17 and 320 to get 337.
337−5Subtract 5 from 337 to get 332.
332 ===> Answer
Exercise number 2.(12 + 5) + 32 × (10 − 5)Add 12 and 5 to get 17
17 + 32 (10 − 5)Subtract 5 from 10 to get 5.
17 + 32 × 5Multiply 32 and 5 to get 160.
17+160Add 17 and 160 to get 177.
177 ===> Answer
PLS HELP!!
What is the measure of ZXYZ?
A. 63°
B. 54°
C. 252°
D. 126°
What is the sum of the interior angles of a polygon that has 6 sides
Answer:
720
Step-by-step explanation:
A polygon with 6 angles is called a hexagon
To find the sum of interior angles, we use the following formula:
(n-2)*180 (n is the number of angles)
4*180 = 720
Sin(15) × cos(15) × cos(30)
Answer:
0.2165 to the nearest ten thousandth.
Step-by-step explanation:
Sin(15) × cos(15) × cos(30)
= 0.258819 * 0.965926 * 0.866025
= 0.216506
Using f(x) = 4x + 6 with a domain of {-1, 0, 2), find the range.
A. {10, 6, 15)
B. {2, 14)
C. {-4, 0, 8}
D. {2, 6, 14}
Answer:
D
Step-by-step explanation:
Start by plugging in all the domain values (domain means input) into the function.
f(-1) = 4(-1) + 6 =-4+6=2
f(0) = 4(0) +6=0+6= 6
f(2) = 4(2) +6 = 8+6=14
What is the quotient of (2x4 – 3x3 – 3x2 7x – 3) ÷ (x2 – 2x 1)? 2 x superscript 4 baseline minus 3 x cubed minus eleven-halves 2x2 x – 3 – startfraction 6 over x squared minus 2 x 1 endfraction 2x2 – x 2x2 x – 3
The answer choice which represents the quotient of the polynomials given is; 2x² +x -3.
What is the quotient of the polynomial division?According to the task content, the quotient of the polynomial division; (2x4 – 3x3 – 3x2 7x – 3) ÷ (x2 – 2x 1) is required;
Hence, it follows from long division of polynomials that the required quotient is; 2x² +x -3.
Read more on quotients of polynomials;
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Answer:
D: 2x² +x -3
Step-by-step explanation:
whats the answer to this. In circle K with m \angle JKL= 144m∠JKL=144 and JK=6JK=6 units, find the length of arc JL. Round to the nearest hundredth.
The length of arc JL is 24.46 units see attachment for diagram.
What is an arc?An arc is a part of the circumference of a circle that meets two radii of a circle to form a sector.
Analysis:
From bigger triangle, if we bisect 144, the line meets JL at 90°.
To find AL,
sin 72 = AL/6
AL = 6 sin 72 = 5.71
To find the angle at O
∠O = 2∠K ( twice angle at circumference is equal to angle at center)
∠O = 2 (144) = 288°
For smaller right-angled triangle,
sin 144 = AL/OL
sin 144 = 5.71/OL
OL = radius of circle = 5.71/0.587 = 9.73 unit
length of arc JL = ∅/360 x 2πr
= 144/360 x 2 x 3.142 x 9.73 = 24.46 units
In conclusion, the length of arc JL is 24.46 units
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Round 381,726 to the nearest thousand
PLEASE HELP MI AMOR ILL LOVE YOU FORVER I SWEAR
Answer:
x = 8
z = 65
Step-by-step explanation:
Through various rules, we are able to assert: (6x + 67)° = 115°.
Now, we want to solve for x:
6x + 67 = 115
6x = 48
x = 8
We know that z° is equal to the complement of (6x + 67)°, and together these must sum to 180°. Therefore, we can simply take 180° - 115° to find that z° = 65°.
simplify PLEASE HELP ASAP
Answer:
[tex]0 < x < 6[/tex]
Step-by-step explanation:
This question asks to solve an inequality which can be written as:
[tex]\sqrt{x^2-6x+9} < 3[/tex]
Solve for x:
[tex]\sqrt{x^2-6x+9} < 3\\x^2-6x+9 < 9\\x^2-6x < 0\\x(x-6) < 0[/tex]
From here we can deduce that the inequality is [tex]0[/tex] when:
[tex]x = 0[/tex] or [tex]x = 6[/tex]
We can write the solution as:
[tex]0 < x < 6[/tex]
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's evaluate ~
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {x}^{2} - 6x + 9 } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {x}^{2} - 3x - 3x+ 9 } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {x}^{}(x - 3) - 3(x - 3) } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ (x - 3)(x - 3) } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ (x - 3) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: { (x - 3) {}^{} } [/tex]
Now, we have been given that value of x :
[tex]\qquad \sf \dashrightarrow \:x < 3[/tex]
So, let's plug the value of x as 3 in the given expression ~
[tex]\qquad \sf \dashrightarrow \:3 - 3[/tex]
[tex]\qquad \sf \dashrightarrow \:0[/tex]
Therefore, we can conclude that :
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {x}^{2} - 6x + 9 } < 0[/tex]
Value of the expression should be less than 0
kite EFGH is graphed on the coordinate plane. three of its verticies are E(1,6), F(3,5), and G(4,-3). what are the coordinates of the fourth vertex, H?
The coordinates of the fourth vertex, H is; (-6.056, 7.302)
How to find the Coordinates of a Kite?
A kite has 4 sides and we know that a pair of diagonally opposite angles of a kite are said to be congruent.
We are given the coordinates of its' vertices as;
E(1,6), F(3,5), and G(4,-3).
The two diagonals are perpendicular;
Slope of EG = (-3 - 6)/(4 - 1)
Slope of EG = -9/5
Equation of line passing through G is;
y = mx + c
-3 = -9/5(4) + c
-15 = -36 + 15c
c = 51/15 = 17/5
y = (-9/5)x + 17/5 ------(1)
Equation of line passing through F is;
y = mx + c
6 = (5/9)(1) + c
54 = -9 + 9c
c = 7
y = (5/9)x + 7 -----(2)
Solving eq 1 and eq 2 simultaneously gives;
x = -1.528 and y = 6.151
If (a, b) are coordinates of vertex H, then;
(a + 3)/2 = -1.528 and (b + 5)/2 = 6.151
Thus;
a = -6.056 and b = 7.302
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Using the image above, what is the measure of Angle L? Round to the nearest hundredth
Answer:
you can approximate it to 61°
You buy milk that contains 180 calories per 2 cups. use a ratio table to find the number of calories in 16 cups.
Mark brainlist to whoever answers first
Answer:
The reflection over the y-axis means that we just multiply the x-value of the coordinates by -1. So we take (4, 0) and get the x-value of 4 and multiply it by -1 which gives us (-4, 0) which is option C.
Which equation is graphed here?
y−1=−13(x−1)
y−1=−13(x+1)
y+4=3(x−1)
y−4=−3(x+1)
Number graph ranging from negative four to four on the x and y axes. A line is drawn on the graph that passes through (negative one, four) and (one, negative two).
Answer: Choice D
y-4 = -3(x+1)
========================================================
Explanation:
Let's first find the slope of the line through (-1,4) and (1,-2)
[tex](x_1,y_1) = (-1,4) \text{ and } (x_2,y_2) = (1,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - 4}{1 - (-1)}\\\\m = \frac{-2 - 4}{1 + 1}\\\\m = \frac{-6}{2}\\\\m = -3\\\\[/tex]
The slope is -3, which tells us that the answer must be choice D.
Choices A,B, & C can be eliminated because choices A and B have a slope of -13, while choice C has a slope of 3.
Refer to the point-slope format [tex]y-y_1 = m(x - x_1)[/tex] where m is the slope and [tex](x_1,y_1)[/tex] is a point the line goes through.
Find the area of a circle with a radius of 9. Leave the answer in terms of π.
Answer:
A = 81π units²
Step-by-step explanation:
the area (A) of a circle is calculated as
A = πr² ( r is the radius ) , then
A = π × 9² = 81π units²
PLEASE HELP ASAP!!!
(k12 students appreciated!!)
What are the zeros of the function?
ƒ(x)= x^3+x^2-6x
Answer: x = 0, x = -3, x = 2
Step-by-step explanation:
f(x) = x^3 + x^2 - 6x
f(x) = 0
x^3 + x^2 - 6x = 0
x(x^2 + x - 6) = 0
x = 0 or
x^2 + x - 6 = 0
D = b^2 - 4ac = 1 - 4*(-6) = 25
x = (-b - sqrt(D))/(2a) = (-1 - 5)/2 = -3 or
x = (-b + sqrt(D))/(2a) = (-1 + 5)/2 = 2
I need to know this asap
Answer:
Output: 3
Step-by-step explanation:
(x, y)
(Input, Output)
(2, 3)
Last question!!! please solve this problem using the pythagorean theorem, and give me the right answer and I will give you brainliest. :)
======================================================
Explanation:
Draw out a right triangle as you see below.
Let's use the pythagorean theorem to find 'a'
[tex]a^2 + b^2 = c^2\\\\a = \sqrt{c^2 - b^2}\\\\a = \sqrt{(9.9)^2 - (7.3)^2}\\\\a = \sqrt{44.72}\\\\a \approx 6.6873\\\\a \approx 6.7\\\\[/tex]
Marcus states that the polynomial expression 3x3 – 4x2y y3 2 is in standard form. ariel states that it should be y3 – 4x2y 3x3 2. explain which student is correct and why.
The correct student is Marcus because the power of the polynomial decreases till 0
How to determine the correct student?The polynomial expressions are given as:
Marcus: 3x³ - 4x²y + y³ + 2
Ariel: y³ - 4x²y + 3x³ + 2
The standard form of a polynomial with the variable x is:
P(x) = ax³ + bx² + cx + d
This means that the power of the polynomial decreases till it gets to 0
Using the above form as a guide, the correct student is Marcus.
Marcus is correct because the power of the polynomial decreases till it gets to 0
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NEED HELP PLEASE ANSWER ASAP!
Answer:
(2) Graph 2
Step-by-step explanation:
Question 40
| 2x + 3 | > 7It means the absolute value has to be greater than 7At x = -5 and x = 2, the absolute value is 7So, the numbers between them won't be includedThe points have an open dotx < -5 and x > 2(2) Graph 2Determine why the triangles are congruent. Choose from SSS, SAS, ASA, AAS, and HL. If the triangles are not congruent type NC.(Use all capitals in your answer)
Answer:
Step-by-step explanation:
The triangular prism below has a base area of 31 units^2
and a volume of 310 units^3
Find its height.
The height of the given triangular prism.
Solution:[tex]h = \frac{V}{ A_{B}}[/tex]
[tex]h = \frac{310}{31} [/tex]
[tex]\large\boxed{\sf{h=10 \: units}}[/tex]
Therefore, the height of the given triangular prism is 10 units.
h= 310/31
h= 10 units
hope this helps
Find uv.
v
u
640
10
w
write your answer as an integer or as a decimal rounded to the nearest tenth.
uv =
The value of uv to the nearest tenth or as an integer is 3.1 units
How to find side of a right triangle?uv is the adjacent side of the right triangle.
uv can be found using trigonometric ratios as follows:
Therefore,
tan 63 = opposite / adjacent
Hence,
tan 63 = 6 / adjacent
cross multiply
uv tan 63 = 6
divide both sides by tan 63
uv = 6 / tan 63
uv = 6 / 1.96261050551
uv = 3.05716906145
uv = 3.1 units
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can someone help me with this thank you
10+5h = 25
thank you thank you thank you
Answer:
h=3
Step-by-step explanation:
Here's the explanation
Move 10 to the other side
5h=25-10
5h=15
h=15/5
h=3
10+5h=25
10+5h-10=25-10
5h=15
[tex]\frac{5h}{5}=\frac{15}{5}[/tex]
h=3
the answer is 3
