Step-by-step explanation:
A certain ferry moves up and down a river between Town A and
B. It takes the ferry two hours to travel to Town A and only an
hour and thirty minutes to return to Town B. If the current is 5mph
how far apart are the two cities?
Answer: 60 miles
Step-by-step explanation:
Given
It takes ferry 2 hours to travel to town A and only [tex]1.5\ hr[/tex] to travel back to town B.
Speed of current is [tex]u=5\ mph[/tex]
Suppose the speed of the ferry is [tex]v[/tex] mph
Distance traveled in both the cases is same, but it took more time traveling to city A that is, ferry is moving upstream and downstream for returning time.
[tex]\Rightarrow 2(v-5)=1.5(v+5)\\\Rightarrow 2v-10=1.5v+7.5\\\Rightarrow 0.5v=17.5\\\Rightarrow v=35\ mph[/tex]
Distance between the towns is [tex]2\times (35-5)=60\ \text{miles}[/tex]
Answer:
The distance between the two towns is 60 miles.
Step-by-step explanation:
Let the distance between A and B is d.
A to B , t = 2 hour
B to A , t' = 1.5 hour
Speed of current, u = 5 mph
Let the speed of ferry is v.
distance = speed x time
d = (v - 5) x 2 = (v + 5) x 1.5
2 v - 10 = 1.5 v + 7.5
0.5 v = 17.5
v = 35 mph
So, the distance is
d = (35 - 5) x 2 = 60 miles.
The table below represents a linear function f(x), and the equation represents a function g(x): X) -1, 0, 1 F(x) -5, -1, 3 G(x)=4x+3
Part A. Write a sentence to compare the slope of the two functions and shows the steps you used to determine the slope of f(x) and g(x)
Part B which functions has greater y-intercept. Justify
Answer:
(a) g(x) has a greater slope
(b) g(x) has a greater y intercept
Step-by-step explanation:
Given
[tex]x \to -1,0,1[/tex]
[tex]f(x) \to -5,-1,3[/tex]
[tex]g(x) = 4x + 3[/tex]
Solving (a): Compare the slopes
Slope (m) is calculated as:
[tex]m =\frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, for f(x), we have:
[tex]m =\frac{-1- 0}{-5- -1}[/tex]
[tex]m =\frac{-1}{-4}[/tex]
[tex]m =\frac{1}{4}[/tex]
For g(x), we have:
Assume [tex]g(x) = mx + c[/tex] then the slope is m
Compare the above to [tex]g(x) = 4x + 3[/tex]
Then the slope of g(x) is 4
g(x) has a greater slope
Solving (b): Function with greater y intercept
Here we set [tex]x= 0[/tex]
From the table of f(x)
[tex]f(x) = -1[/tex] when [tex]x = 0[/tex]
From [tex]g(x) = 4x + 3[/tex]
[tex]g(0) = 4 * 0 + 3[/tex]
[tex]g(0) = 3[/tex]
Hence:
g(x) has a greater y intercept
I really need some help with this question also.
A) 2/5
B) 3/5
C) 11/25
D) 14/25
Expand the following using the Binomial Theorem and Pascal’s triangle (2x − 3y)^4
Answer:
Step-by-step explanation:
Binomial Expansion:
[tex](2x-3y)^4 \\\\= 4C_0(2x)^4 (-3y)^0 + 4C_1(2x)^3 (-3y)^1 + 4C_2(2x)^2(-3y)^2 \\\\+ 4C_3(2x)^1 (-3y)^3 + 4C_4(2x)^0 (-3y)^4\\\\=16x^4 + 4(8x^3)(-3y) + 6(4x^2)(9y^2) + 4(2x)(-27y^3) + 81y^4\\\\=16x^4 - 96x^3y + 216x^2y^2-216xy^3 +81y^4[/tex]
Pascal's Triangle:
Zero row 1
First row 1 1
Second row 1 2 1
Third row 1 3 3 1
Fourth row 1 4 6 4 1
Evaluate the price wise function ag the indicated value from the domain:
A. f(-3)=-1/2
B. f(-3)=-1/3
C.f(-3)=4
D.f(-3)=9
How many solutions are there to the equation below? 9(x – 4) = 9x – 33
Answer:
no solution
Step-by-step explanation:
Multiplicar:
a. (– 6) (– 7) =
b. – 12 x – 5 =
c. (+ 10) (– 6) =
d. (– 15) (+ 5) =
e. (+ 11) (+6) =
f. (– 3) (– 5) (– 6) =
g. (– 8) (+6) (-3) =
h. (- 5) (+ 3) (+9) =
Answer:
a. 42
b. -12x-5
c. -60
d. -75
e. 66
f. -90
g. 144
h. -135
Which integers could you add to −18 to get a sum that is greater than 5?
Answer:
23
Step-by-step explanation:
-18+(18+5) = 5,
so adding any integer that is greater than (18+5)=23 will give a sum that is greater than 5.
Answered by GAUTHMATH
Find each measure
Please help me
Answer:
19) 100
20) 360 - 90 = 270
21) 360- 125 = 235
22) 45
Step-by-step explanation:
Central angles and the arcs they create are congruent.
HELP HELP HELPPPP PLEASEEE
Directions: Determine if segments AB and CD are parallel, perpendicular, or neither.
AB formed by (-2, 13) and (0, 3)
CD formed by (-5, 0) and (10, 3)
Given:
AB formed by (-2,13) and (0,3).
CD formed by (-5,0) and (10,3).
To find:
Whether the segments AB and CD are parallel, perpendicular, or neither.
Solution:
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
AB formed by (-2,13) and (0,3). So, the slope of AB is:
[tex]m_1=\dfrac{3-13}{0-(-2)}[/tex]
[tex]m_1=\dfrac{-10}{2}[/tex]
[tex]m_1=-5[/tex]
CD formed by (-5,0) and (10,3). So, slope of CD is:
[tex]m_2=\dfrac{3-0}{10-(-5)}[/tex]
[tex]m_2=\dfrac{3}{10+5}[/tex]
[tex]m_2=\dfrac{3}{15}[/tex]
[tex]m_2=\dfrac{1}{5}[/tex]
Since [tex]m_1\neq m_2[/tex], therefore the segments AB and CD are not parallel.
[tex]m_1\times m_2=-5\times \dfrac{1}{5}[/tex]
[tex]m_1\times m_2=-1[/tex]
Since [tex]m_1\times m_2=-1[/tex], therefore the segments AB and CD are perpendicular because product of slopes of two perpendicular lines is always -1.
Hence, the segments AB and CD are perpendicular.
Answer:
AB is perpendicular to CD.
Step-by-step explanation:
AB formed by (-2, 13) and (0, 3)
CD formed by (-5, 0) and (10, 3)
Slope of a line passing through two points is
[tex]m= \frac{y''-y'}{x''- x'}[/tex]
The slope of line AB is
[tex]m= \frac{3- 13}{0+2} = -5[/tex]
The slope of line CD is
[tex]m'= \frac{3 -0 }{10+5} = \frac{1}{5}[/tex]
As the product of m and m' is -1 so the lines AB and CD are perpendicular to each other.
In general, a gallon of paint can cover 400 square feet. Muhanmmad needs to cover a 21 foot by 17 foot wall and a circular area with a 5 foot radius. How many gallons will he have to buy?
Answer:
1.1 gallons of paint
Step-by-step explanation:
The wall measures;
21 foot by 17 foot
Thus, area of wall = 21 × 17 = 357 ft²
Circular area has a radius of 5 ft.
Thus;
Area of circle = πr² = π × 5² = 78.54 ft²
Total area covered = 357 + 78.54 = 435.54 ft² ≈ 436 ft²
A gallon of paint can cover 400 ft²
Thus gallons Muhammad would need = 436/400 = 1.09 gallons ≈ 1.1 gallons
Brainly to whomever somehow solves for g & k. I WILL REPORT SCAMS AND UNHELPFUL/ UNRELATED ANSWERS.
Answer:
g = 48
k = 18
Step-by-step explanation:
h / 10 = 60 / 12
h / 10 = 5
h = 5 x 10
h = 50
40 / h = g / 60
40 / 50 = g / 60
4 / 5 = g / 60
g = ( 60 x 4 ) / 5
= 12 x 4
g = 48
90 / k = 60 / 12
90 / k = 5
k = 90 / 5
k = 18
product of -2/3 and 5 2/4?
Answer: [tex]-\frac{11}{3}[/tex]
Step-by-step explanation:
[tex]-\frac{2}{3} *5\frac{2}{4} \\\\\\=-\frac{2}{3} *5\frac{1}{2} (5\frac{1}{2} =\frac{5*2}{2} +\frac{1}{2} =\frac{10+1}{2} =\frac{11}{2})\\\\\\=-\frac{2}{3} *\frac{11}{2} =-\frac{11}{3}[/tex]
What is the answer to this question
Answer:
B - Congruent : SAS
Step-by-step explanation:
We are given that there are two sides that are congruent and one angle is congruent and it is in the order Side Angle Side.
Solve the inequality -10w _< 20
Step-by-step explanation:
-10w< 20w< 20/-10w< -2hope it helps
stay safe healthy and happy...What is the equation of the
following line written in slope-Intercept form?
Answer:
y = -7x - 11
Step-by-step explanation:
Question 5 can I have as much as you can do please
Answer:
x = 12
Step-by-step explanation:
The sum of angles in a triangle is 180°
Thus,
(x + 20) + (10x) + (x + 16) = 180°
Collect like terms
x + 10x + x + 20 + 16 = 180°
12x + 36 = 180°
12x = 180 - 36
12x = 144
Divide both sides by 12
x = 144 ÷ 12
x = 12
Substitute the value of x into the question
Therefore,
x + 20 = 12 + 20
= 32°
10x = 10(12)
= 120°
x + 16 = 12 + 16
= 28°
What percent did the price drop
Answer:
10%
Step-by-step explanation:
You have the correct answer. Nice job!
17:56 Dawn is trying to find out how much weight she can push across the room. She is really trying to find her __________.
pls help im begging u..
identify the unit rate shown in the graph
Choices:
A. 1/3 mile per hour
B. 3 hours per mile
C. 3 miles per hour
D. 4 miles per hour
The answer is C or 3 miles per hour
how is it 3?:
there is a point at 6 and another at 3 all we do is 6 - 3 = 3
A client has two refrigerators, one in the kitchen and one in the basement.The former is new and efficient. The latter is 30 years old and uses 120Kwh/month. If this client pays 0.15/kwh
Incomplete question: we assume figures to explain further
Answer and explanation:
Given that client pays $0.15/kwh
If old fridge is inefficient and consumes 120kwh/month
And new fridge is efficient and therefore consumes 50kwh/month
For the old fridge, client will be paying
120×0.15= $18 per month on electricity charges
For the new fridge, client will be paying
50×0.15= $7.5 per month on electricity charges
the median of 2,8,6,10,4,12
Answer: 6
Step-by-step explanation: 6 is a median
Hey there!
To find your mean you have to put the numbers from descending (least/decreasing) to ascending (greater/increasing) order
Median is also understood as the “middle number”
2, 8, 6, 10, 4, 12
= 2, 4, 6, 8, 10, 12
Based on that information, you have in your new data set you have 2 pairs in the middle (6 & 8), so you’ll have to total/average of the number. We have to DIVIDE them by 2 because it’s 2 numbers
6 ends the descending set and 8 starts the ascending set
Median = 6 + 8 / 2
6 + 8 = 14
= 14/2
= 7
Answer: therefore your MEDIAN is most likely 7
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
What is the value of x?
0 14
0 17
O 27
O 34
PLEASE HELP
Question 4 (True/False Worth 4 points)
(0701)
True or False?
is a solution to the inequality 12+2 < 12
True
O False
please help me, i suck at this
Answer:
(5, -5)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Coordinates (x, y)Terms/CoefficientsSolving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
2x - 3y = 25
5x + 3y = 10
Step 2: Solve for x
Elimination
Combine two equations: 7x = 35[Division Property of Equality] Divide 7 on both sides: x = 5Step 3: Solve for y
Substitute in x [1st Equation]: 2(5) - 3y = 25Multiply: 10 - 3y = 25[Subtraction Property of Equality] Subtract 10 on both sides: -3y = 15[Division Property of Equality] Divide -3 on both sides: y = -5Answer:
(5,-5)
Step-by-step explanation:
Hi there!
We are given this system of equations:
2x-3y=25
5x+3y=10
and the question asks to solve it by elimination
To solve by elimination, we will add the equations together to clear one variable, solve for the variable that wasn't cleared, then use the value of the variable that wasn't cleared to solve for the variable that was cleared earlier
Before we clear a variable, the coefficients in front of the variable that we want to clear need to be opposites (ex. if we wanted to clear x, the coefficients of x in the systems have to be -2 and 2, as that would equal 0).
In this case, the coefficients in front of y in the equations are -3 and 3 respectively. That equals 0, so y would be cleared if we added the equations together
so we don't have to multiply or divide by anything prior to clearing
Let's add the equations together. Remember that y will be cleared, as (-3y+3y=0)
2x-3y=25
+
5x+3y=10
______________
7x+0=35
subtract 0 from both sides
7x=35
divide both sides by 7
x=5
we found the value of x
now we need to find the value of y
substitute 5 as x into either one of the equations to solve for y
if we were to do it into 2x-3y=25 for instance,
2(5)-3y=25
multiply
10-3y=25
subtract 10 from both sides
-3y=15
divide both sides by -3
y=-5
So the answer is x=5, y=-5, or as point (5,-5)
Hope this helps! :)
What is the value of the expression below
(-64)^2/3
Answer:
16
Step-by-step explanation:
[tex](-64)^2/3[/tex]
64 = [tex]2^{6}[/tex]
[tex]2^{6} ^{\frac{1}{3} } ^{2}[/tex]
[tex]2^{ 2^{2} }[/tex]
[tex]2^{4}[/tex]
16
Using the unit circle, what is the exact value of tan pi/6?
Answer:
1/root(3)
Step-by-step explanation:
the steps are in the pic above.
The value of tan pi/6 is 0.5773502.
What are trigonometric functions?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.
Given that, what is the exact value of tan pi/6,
To find the value of tan π/6 using the unit circle:
Rotate ‘r’ anticlockwise to form pi/6 angle with the positive x-axis.
The tan of pi/6 equals the y-coordinate(0.5) divided by the x-coordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.
Hence, the value of tan pi/6 = y/x = 0.5774 (approx)
Learn more about trigonometric functions click;
https://brainly.com/question/6904750
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A circular garden is surrounded by a circular path of 7m width.If the area of path is 770m²,find the area of the garden without path.
help me this question ⁉️
Answer:
Answer:
Radius of the circular garden
= 210 sq
=105m
Radius of the region covering the garden and the path =105m+7m
=112m
Area of the region between two concentric circles
with radius of outer circle R, and inner circle r =π(R sq−r sq)
Hence, the area of the path
=π(112sq−105 sq)= 7/22
(12544−11025)
= 33418/7
=4774m sq
HOPE THIS WILL HELP YOU MATE
find the area of the rectangle whose dimensions are 9cm and 8cm.
Answer:
72 cm²
Step-by-step explanation:
Area = 9(8) = 72
..............