Answer:
The rate of the boat is 75.17 km/h and the rate of the stream is 17.83 km/h
Step-by-step explanation:
System of Equations
Let's call:
B = speed (rate) of the boat in still water
S = speed (rate) of the stream
The boat travels 172 km in 3 hours when going upstream, that is when the speed of the stream subtracts its own speed. The speed is the distance divided by the time, thus:
[tex]\displaystyle B-S=\frac{172}{3}[/tex]
Multiplying by 3:
3B - 3S = 172 [1]
The boat travels 372 km in 4 hours downstream when the speed of the current adds to its own:
[tex]\displaystyle B+S=\frac{372}{4}=93[/tex]
B + S = 93
Solving for B:
B = 93 - S [2]
Substituting in [1]
3(93 - S) - 3S = 172
Operating:
279 - 3S - 3S = 172
279 - 6S = 172
Subtracting 279:
- 6S = 172 - 279
- 6S = -107
Multiplying by -1 and solving for S:
[tex]S = \frac{107}{6}\approx 17.83\ km/h[/tex]
From [2]:
[tex]B = 93 - \frac{107}{6}[/tex]
[tex]B=\frac{451}{6}\approx 75.17\ km/h[/tex]
Point D is the in center of triangle ABC. Write an expression for the length x in terms of the three side lengths AB, AC, BC.
Hint: Use areas of triangles...A=1/2bh
Answer :
[tex] \underline{ \boxed{x = \frac{2(A_T) }{(AB) + (AC) + (BC)} }}[/tex]
Explanation :
[tex]i \: figured \: it \: out \to \: notice \: that \\ there \: are \:( thre e\: trianges) \: in \: triangle \: ( ABC) \\ and \: they \: all \: have \: the \: same \: height \: = x \\ first \: triangle \: is \: \to \: triangle \: (ABD) \\ second\: triangle \: is \: \to \: triangle \: (ACD) \\ third \: triangle \: is \: \to \: triangle \: (BCD) \\ if \: the \: area \: of \: a \: triangle \: is \: = \frac{1}{2} bh : then \to \\ the \: area \: of \: triangle \: (ABD) = \frac{1}{2} (AB)x \\ the \: area \: of \: triangle \: (ACD) = \frac{1}{2} (AC)x \\ the \: area \: of \: triangle \: (BCD) = \frac{1}{2} (BC)x \\ let \: the \: total \: area \:(A_T) \: be \to \: \frac{1}{2} (AB)x + \frac{1}{2} (AC)x + \frac{1}{2} (BC)x \\ if \to\\ (A_T) = \frac{1}{2} (AB)x + \frac{1}{2} (AC)x + \frac{1}{2} (BC)x \\ then \to \\ (A_T) = \frac{1}{2} \{(AB)x + (AC)x + (BC)x \} \\ x \{(AB) + (AC) + (BC) \} = 2(A_T) \\ x = \frac{2(A_T) }{(AB) + (AC) + (BC)} [/tex]
Expression representing the length 'x' will be, [tex]x=\frac{(AB)(AC)}{AC+BC+AB}[/tex].
In-center of a triangle,In-center of a triangle defines the center of a circle inscribed in the triangles (touching all sides),Perpendicular drawn from in-center to the sides of the are equal in measures (radii of the inscribed circle).Use the hint → Area of the large triangle = sum of the small triangles inside the larger triangle
Area of ΔABC = [tex]\frac{1}{2}(AB)(AC)[/tex]
Area of ΔADC = [tex]\frac{1}{2}(AC)(x)[/tex]
Area of ΔBDC = [tex]\frac{1}{2}(BC)(x)[/tex]
Area of ΔADB = [tex]\frac{1}{2}(AB)(x)[/tex]
Since, Area of ΔABC = Area of ΔADC + Area of ΔBDC + Area of ΔADB
[tex]\frac{1}{2}(AB)(AC)=\frac{1}{2}(AC)(x)+\frac{1}{2}(BC)(x)+\frac{1}{2}(AB)(x)[/tex]
[tex](AB)(AC)=[(AC)+(BC)+(AB)](x)[/tex]
[tex]x=\frac{(AB)(AC)}{AC+BC+AB}[/tex]
Therefore, expression representing the length 'x' will be [tex]x=\frac{(AB)(AC)}{AC+BC+AB}[/tex].
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2. Are these ratios equal? 6:10 and 5:20
Answer:
No
Step-by-step explanation:
Think of it like this. 6/10 is 60% and 5/20 is 25%. These two values aren't the same.
A bag of dog food says that it now contains 20% more. Originally, it came with 63 ounces of dog food. How much dog food does the bag come with now? Set up the double number line to show that 63 ounces is 100%.
Answer:
75.6 ounces
Step-by-step explanation:
Step one.
Given data
we are told that the original quantity of food is 63 ounces
and the increase is in food is by 20%
Step two:
let us find the increase in ounces
=20/100*63
=0.2*63
=12.6 ounces
Hence the amount of food in the bag now is
=12.6+63
=75.6 ounces
Find g(x), where g(x) is the translation 2 units right of f(x)=|x|.
n
Which expression is represented by the model?
+
+
+
X-3
X+ 3
ОО
-X-3
-X+3
Plz hurry
3(b + 3) = 2a + 27
SHOW STEPS FOR BRAINLIEST
Answer:
[tex]3(b + 3) = 2a + 27 \\ 3b + 9 = 2a + 27 \\ \boxed{- 2a + 3b= 18}[/tex]
hope this helps.
The base of a traingular field is twice its altitude , If the cost of levelling the field , at the rate of rupess 10 per m2 is rupees 4,000 , find it base and altitude
Answer:
Base=40m and
Altitudes=20m
Step-by-step explanation:
Area of the field can be calculated as
Area= total cost / rate
Where total cost= 4,000 rupees
Rate= 10 per m2
Area of the field= 4000/10
= 400m^2
Let the altitudes be denoted as "x metre"
Then the base = 2x
Area= 1/2bh
Where b= base
h= altitudes
Then if we substitute we have
400m^2= 1/2× x × 2x
400= x^2
x= √400
x=20m
Then altitudes = 20m
the base = 2x= 2×20=40m
Hence, it base and altitude are 40m and 20m respectively.
would this angle be name angle CUE or CUT ?
Answer:
[tex]\huge\boxed{\angle\text{CUE}}[/tex]
Step-by-step explanation:
We can model what both readings of this angle would be. Angle names are usually formed by taking the two lines that form to intersect this angle at a vertice, and these 3 make up the name.
Angle ∠CUT would be formed by the lines CU and UT. We can see that this is not the case, as the angle is formed by lines CU and CE.
Since they intersect at point U, that means the angle name would be CUE.
Hope this helped!
Write the equation of the line in fully simplified slope-intercept form.
Which of the following is true about the order of operations?
1. Multiplication comes before division.
2. Addition and subtraction are done from left to right.
3. Addition and subtraction are done before multiplication and division.
4. Exponents are the first operation to be completed.
Answer:
2
Step-by-step explanation:
Multiplication comes before division. To add or subtract we can do from left to right by thousand, hundred, or any respective place value thus options (1) and (2) are correct.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
Subtraction = Minus of any two or more numbers with each other called subtraction.
Using the PEMDAS rule,
Parenthesis = 1st
Exponents = 2nd
Multiplication = 3rd
Divide = 4th
Addition = 5th
Subtraction = 6th
Suppose an addition,
120 + 320
Now add from left to right,
100 + 300 = 400
20 + 20 = 40
Now, 400 + 40 = 440
Thus, adding from left to right is true.
Hence "Multiplication comes before division. To add or subtract we can do from left to right by thousand, hundred, or any respective place value ".
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Help me please
What is the slope of the line?
answers for both boxes please
Answer:
5 for the green box and 9 for the purple one
Step-by-step explanation:
Answer:
(2,1)
Step-by-step explanation:
2x - 2y = 2
5x + 2y = 12
2x + 5x = 7x
-2y + 2y = 0
2 + 12 = 14
7x = 14
7x/7 = 14/7
x = 2
2x - 2y = 2
2(2) - 2y = 2
4 - 2y = 2
-2y = 2 - 4
-2y = -2
-2y/-2 = -2/-2
y = 1
Please help, this is called Writing Equations
Answer:the answer is C
Step-by-step explanation:
George has 52 coins in quarters and nickels. He has a total of $3.60. How many quarters does he have?
there are 36 quarters.
Let the number of nickels be x
Let the number of quarters be y
Value Value
Type Number of of
of of EACH ALL
coin coins coin coins
-------------------------------------------
nickels x $0.05 $0.05x
quarters y $0.25 $0.25y
-------------------------------------------
TOTALS 52 ----- $3.60
The first equation comes from the second column.
x + y = 11
The second equation comes from the last column.
0.05x + 0.25y = 3.60
Get rid of decimals by multiplying every term by 100:
5x + 25y = 360
So we have the system of equations:
x+y=52
5x+25y=360
We solve by substitution. Solve the first equation for y:
x + y = 52
y = 52 - x
Substitute (52 - x) for y in 5x + 25y = 360
5x + 25(52 - x) = 360
5x + 1300 - 25x = 360
-20x + 1300 = 360
-20x = -940
x = = 5 the number of nickels.
Substitute in y = 52 - x
y = 52 - (5
y = 47 quarters.
The number of quarters is 52-x or 52-5 or 47 quarters.
You are kayaking at a pace of 63 feet every 12 seconds. Your friend's pace is 21 feet every 2 seconds. Are you and your friend kayaking at the same pace? If not, who is faster?
Answer:
Your friend is kayaking faster.
Step-by-step explanation:
The way to approach this answer is by putting one of them in terms of the other. So that both are in terms of the same time. If you kayak 63 feet in 12 seconds how many feet do you kayak in 2 seconds? Simply divide by 6. 63/6 = 12/6. So, in 2 seconds (12/2) you kayak 10.5 feet (63/6). But your friend kayaks 21 feet in the same time... so he's going faster.
The formula for the area, A, of a regular polygon in terms of the perimeter of the polygon, p, and the length of the apothem, a, is:
img2
Upper A = one-half a p. A polygon with 5 sides has an apothem with measure a.
What is the equivalent equation when solving for p?
Answer:
2
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
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Solve for x:
2x + y = -2
4x + y = -8
Answer:
x = -3
Step-by-step explanation:
2x + y = -2
4x + y = -8
2x + y = - 2
y = -2x - 2
4x + y = - 8
y = -4x - 8
y = -2x - 2
y = -4x - 8
-2x - 2 = -4x - 8
4x - 2x = 2 - 8
2x = -6
2x/2 = -6/2
x = -3
To check just use da graph ;w;
The x is -3
Answer:
Step-by-step explanation:
x= −1 −y/2
x= 4 −8−y/4
If two equations have the same slope but different y intercepts, what type of lines will they make if you draw them on the same graph
PLEASE HELP!! THANK U
Answer:
The answer will be two parallel lines.
Step-by-step explanation:
This occurs due to the fact that they have the same slope, so they will never cross each other.
What is the smallest rotational symmetry of a rhombus?
What decimal is equivalent to 4/15
Hey there!
In order for you to find out the decimal form a fraction, just simply DIVIDE the NUMERATOR (TOP number) from the DENOMINATOR (BOTTOM number) and you should be able to find out your answer!
Formula:
NUMERAATOR / DENOMINATOR = ANSWER
NUMERATOR ➡️ 4
DENOMINATOR ➡️ 15
4 / 15 = answer
4 / 15 = 2.667
POSSIBLE ANSWER: 2.667 ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
How is 80.106 written in expanded form?
Plzzzz answer asap
Answer:
[tex]80.106= 8 * 10 + 0 * 1 * 0.1 + 6 * 0.001[/tex]
Given:
80.106
Required:
Write in expanded form
First, we need the place value of each digit:
Next, we multiply each digit by its place value, to give the expanded form;[tex]8- > Tens- > 10\\0- > Units- > 1\\1- > Tenths- > 0.1\\0- > Hundreds- > 0.01\\6- > Thousands- > 0.001[/tex]
[tex]80.106= 8 * 10 + 0 * 1 * 0.1 + 6 * 0.001[/tex]
PLEASE HELP WILL MARK BRAINLIEST!!!!
Which price is equivalent to $1.50 for 1 pound of apples?
Answer: $3.00 for 2 pounds of apples
Step-by-step explanation:
Answer:
A: 6 pounds of Apples for 9$
9/6=1.5=$1.50 per pound
Step-by-step explanation, no need to.
what is the volume of this figure ?
A) 3x2x6
B)6x8x2
C)8x2x3
D)3x2x8x6
Answer:
Step-by-step explanation:
since the hypotenuse of 6 cm is shorter than the base of 8 cm there is something wrong with this drawing. The box can't be square so maybe answer C is good but.. since this box isn't a right angled box.. we really don't know. This is a bad question b/c it's making the appearance of being a right angle but it can not be. Like an Escher drawing.. not possible irl
The volume of the rectangular prism is 8×2×3 cubic in or 48 cubics in option (B) 8×2×3 cubic in is correct.
What is a rectangular prism?It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape. It is also called a cuboid.
The missing height of the rectangular prism is 3 cm
It is given that:
The rectangular prism is shown in the picture with dimensions.
As we know, the volume of the rectangular prism is given by:
V = length×width×height
Length = 2 cm
Width = 8 cm
Height = 3 cm
The volume of this figure:
V = 2×8×3
Or
The volume of this figure V = 8×2×3 cubic in
Thus, the volume of the rectangular prism or the volume of the figure is 8×2×3 cubic in or 48 cubics in option (B) 8×2×3 cubic in is correct.
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1. The list of ordered pairs represents a function: (12,6) (3,1) (2,-2) (5,10) (-8,-4) ( _, _)
Which of the following could be the missing ordered pair?
A. (2,1)
B. (12,7)
C. (-8,8)
D. (-3,-4)
2. Rita works at a gym where she gets paid $450 each week plus $15.50 for any new gym membership she sells. If y represents the total pay per week and x represents the number of new memberships sold, which of the following equations represents a higher rate per membership sold.
A. y =31/3x + 500
B. y =15x + 425
C. y =33/2x + 425
D. y =15.05x +475
Answer:
1. D
2. y = 15.50x + 450
Step-by-step explanation:
1. Since it is a function, the missing pair can't repeat input values with different output, therefore only option D is unique so is the correct choice.
2. x > (y - 450)/ 15.50
i) Rita gets paid $450 per week.
ii) She gets $15.50 for every new membership she sells.
iii) let y represent the total pay per week.
iv) let x represent the number of new memberships sold.
v) the equation representing total pay is y = 15.50x + 450.
vii) therefore the equation that represents a higher rate of membership sold is given by x > (y - 450)/ 15.50
2.1834 around you to the nearest hundredth
Answer:
2.18 I think this is the answer sorry if it's not-
Answer:
2,1044 is the correct answere
A grocery store determined that an increase in the price of milk does not imply that customers will buy more or less milk. What can we conclude?
A. There is no correlation between the price of milk and the amount of milk bought.
B. There is a correlation between the price of milk and the amount of milk bought. There may or may not be causation, but further studies would need to be done in order to study this.
C. There is a correlation between the price of milk and the amount of milk bought. However, there is no causation.
Use the figure to find the measures of the numbered angles. ∠5 = ∠6 =
Answer:
∠ 5 = 49°, ∠ 6 = 131°
Step-by-step explanation:
∠ 5 and 49° are corresponding angles and are congruent, then
∠ 5 = 49°
∠ 5 and ∠ 6 are adjacent angles and are supplementary, sum to 180° , that is
∠ 6 + ∠ 5 = 180°
∠ 6 + 49° = 180° ( subtract 49° from both sides )
∠ 6 = 131°
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Vertical stretch by a factor of 6, reflected about the x-axis, horizontally
translated 8 units to the left, vertically translated up 9 units:
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