Answer:
The speed of the boat in calm water is 12.8 miles per hour.
Step-by-step explanation:
While going downstream the speed of the boat is "x + 2", where x is the speed in calm water, while going upstream the speed of the boat is "x - 2". He made a trip that had two legs, each with a distance of 50 miles, therefore, the sum of the times it took him to complete each leg must be equal to the total time of the trip.
[tex]speed = \frac{distance}{time}\\\\time = \frac{distance}{speed}[/tex]
For the upstream:
[tex]time_{up} = \frac{50}{x - 2}[/tex]
For the downstream:
[tex]time_{d} = \frac{50}{x + 2}[/tex]
The sum of each of these times must be equal to "8 h", therefore:
[tex]8 = time_{up} + time_{d}\\\\8 = \frac{50}{x - 2} + \frac{50}{x + 2}\\\\8 = \frac{50*(x+2) + 50*(x - 2)}{(x-2)*(x+2)}\\\\8*(x-2)*(x+2) = 50*x + 100 + 50*x - 100\\\\8*(x^2 - 4) = 100*x\\\\8*x^2 - 100*x - 32 = 0\\\\x^2 - 12.5*x - 4 = 0\\\\x_{1,2} = \frac{-(-12.5) \pm \sqrt{(-12.5)^2 - 4*(1)*(-4)}}{2}\\\\x_{1,2} = \frac{12.5 \pm \sqrt{156.25 + 16}}{2}\\\\x_{1,2} = \frac{12.5 \pm \sqrt{172.25}}{2}\\\\x_{1,2} = \frac{12.5 \pm 13.124}{2}\\\\x_1 = 12.812\\\\x_2 = -0.312[/tex]
Since the speed can't be negative in this context, the only possible answer is 12.812 mph.
Answer:
12.8
Step-by-step explanation:
Find an equation of the line containing the given pair of points.
(4,1) and (12,7)
Answer:
y= 3/4x-2
Step-by-step explanation:
y2-y1/x2-x1
7-1/12-4
m=6/8
m=3/4
now solve for b (y-intercept)
plug in any y or x from any point
7=3/4(12)+b
7=36/4+b
7=9+b
7=9+b
subtract nine on both sides
-2=b
thats how u get ur equation
find the area of the shape attached
Answer:
Radius x radius x 3.14 / 2 = area of semicircle
5 x 5 x 3.14 = 78.5
don't divide because there is two semicircle
22-10=12
12 x 10 = 120
120 + 78.5 = 198.5 cm squared
Step-by-step explanation:
Find the value of x in the triangle... Then classify the triangle as acute, right or obtuse
34°, acute
134°, obtuse
44°, right
54°, acute
Answer:
x = 44
right
Step-by-step explanation:
The sum of the angles in a triangle add to 180
90+ 46+x = 180
Combine like terms
136+x = 180
Subtract 136 from each side
136+x-136=180-136
x =44
Since we have a 90 degree angle it is a right triangle
HELPPP
Lane has a gift card worth $300 for a local entertainment store. Movies cost $20 each and
newly released video games cost $50 each. In order to use the gift card, Lane must purchase at
least seven items. Which is a combination of movies and newly released video games that
Lane could purchase using his gift card?
A 01 movie and 6 video games
B2 movies and 4 video games
C6 movies and 5 video games
D8 movies and 1 video game
Answer:
D) 8 movies and 1 video game
Step-by-step explanation:
We are given that Lane has a gift card worth $300 for a local entertainment store.
Cost of 1 movie = $20
Cost of 1 video game = $50
In order to use the gift card, Lane must purchase at least seven items
A) 01 movie and 6 video games
Cost of 1 movie = $20
Cost of 6 video game = [tex]50 \times 6 = 300[/tex]
Total cost = 300+20 = 320
Since Lane has a gift card worth $300 , So Lane could not purchase 01 movie and 6 video games using his gift card
B) 2 movies and 4 video games
We are given that she must purchase at least seven items
So, She could not buy 2 movies and 4 video games
C)6 movies and 5 video games
Cost of 6 movie = [tex]20 \times 6 =120[/tex]
Cost of 5 video game = [tex]50 \times 5= 250[/tex]
Total cost = 250+120=370
Since Lane has a gift card worth $300 , So Lane could not purchase 06 movie and 5 video games using his gift card
D) 8 movies and 1 video game
Cost of 8 movie = [tex]20 \times 8 =160[/tex]
Cost of 1 video game = 50
Total cost = 160+50=210
So, she could purchase 8 movies and 1 video game
A seller has a house that is 2100 ft2. The neighborhood comps show the line
of best fit to be y = 0.074x + 50.48. What is a fair price for this house?
A. $205.88
B. $206.00
C. $176,000
D. $206,000
The fair price for the house is $205.88.
The correct answer is option A.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
To find the fair price for the house, we can use the equation of the line of best fit provided:
y = 0.074x + 50.48
where y represents the price of the house and x represents the square footage of the house.
We can substitute 2100 for x to find the price of the house.
y = 0.074(2100) + 50.48
y = 155.4 + 50.48
y = 205.88
Therefore,
The fair price for the house is $205.88.
Learn more about equations here:
https://brainly.com/question/17194269
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help also I did some of it just not 3 and 4 and 6which is 2.5 ×__=80,1×__=32,3×__=96
Answer:
the answer is 32
Step-by-step explanation: divide the product by the number that is being mutiplied
How should the decimal point in 6.8 be moved to determine the product of 6.8
and 100?
()) two places to the left
1)) three places to the right
<)) three places to the left
()) two places to the right
The correct answer is two places to the right
The following information should be considered:
For each and every 0 you have to move the decimal one place. And since the 100 is positive you move the decimal to the right.Learn more: https://brainly.com/question/17429689?referrer=searchResults
Find the slope of the line through the points (13, 14) and (0, −1)
Answer:
[tex] \frac{15}{13} [/tex]
Step-by-step explanation:
gradient= [tex] \frac{y1 - y2}{x1 - x2} [/tex]
Thus, slope of line
[tex] = \frac{14 - ( - 1)}{13 - 0} \\ = \frac{14 + 1}{13} \\ = \frac{15}{13} [/tex]
what is measurement of angle 2 and 11
Answer:
Angle 2 = 40 degrees Angle 11 = 60 degrees
Step-by-step explanation:
Start by using angle 1 to find angle 2
angle 1 is 140 + 2 is unknown = 180 degrees
140 + x = 180
-140 -140
x = 40
Angle 2 is 40 degrees
Now add together angles 2 and 9 to find the measure of angle 11
40 + 80 + x = 180
120 + x = 180
-120 -120
x = 60
Angle 11 is 60 degrees
Answer:
Angle #2 = 40 degrees Angle #11 = 60 degrees
Step-by-step explanation:
.
Helllp fast please someone
Answer: -10
Step-by-step explanation:
-4 - 6 = -10
how to solve x - 7 = -13
Answer:
x = -6
Step-by-step explanation:
to solve this you can just add 7 to both sides of the equation.
x -+7 = -13
+7 +7
x = -6
this works because since it puts the x by itself, the other side of the equation is then equal to x and typically in equations with variables you solve for the variables.
hope it helps!
Please help! I don’t understand
the correct answer is B
The answer is definitely B
A taxi driver charges a flat rate of $3.50 plus an additional $1.65 per mile. If Mohammad wants to spend, at most, $60, how far can he travel in the taxi cab? Round your answer to the nearest mile.
Answer:
11.6 should be your answer!
Step-by-step explanation:
Im so sorry if its wrong!
Hope this helps!!
( > .< )
Answer:
34 miles
Step-by-step explanation:
3.50 + 1.65m <60
1.65m< 60-3.50
1.65m<56.5
1.65m/1.65< 56.5/1.65
m<34.24242424
m<34
graph {x | x > 4} {x | x < -2} on a number line
Answer:
Step-by-step explanation:
well,
you mark an arrow to the left side of # line with open circle on -2
then,
you mark an arrow to the right side of # line with open circle on 4
Easy 50 points. Graph solutions with picture.
Answer:
(-1,-4)
Step-by-step explanation:
The system of equations are given on a graph. The lines cross at coordinate (-1,-4). This would the the solution of the equations.
The system's solution should be (-1,-4).
Answer:
-1,-4Step-by-step explanation:
The equation of lines shows the two points
and it cross in the coordinates(-1,-4)
so
solution is( -1,-4)
Interpret the average rate of change of -14/3 that
you found previously. What does this mean in
terms of the waterslide, from x = 0 to x = 15?
Answer:
On average, the slide drops 14 feet for every 3 feet of horizontal distance.
On average, the slide drops about 4.7 feet for every 1 foot of horizontal distance.
On average, the slide drops 14 feet for every 3 feet of horizontal distance. On average, the slide drops about 4.7 feet for every 1 foot of horizontal distance.
What is the average rate of change?It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
It is given in the question that Interprets the average rate of change of -14/3 that you found previously.
On average, the slide drops 14 feet for every 3 feet of horizontal distance. On average, the slide drops about 4.7 feet for every 1 foot of horizontal distance.
To know more about the average rate of change follow
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Can someone please help me find the slope of the line!!!!! Extra Points and Braniest will be given!!!
Answer:
(3,12)
Step-by-step explanation: The slope is rise over run so the rise is x and run run is the y
is a diameter of circle O. If m∠ACB = 30°, what is m∠DBA? A. 30° B. 50° C. 60° D. 70° E. 90°
Every triangle equals 180 degrees, and we're trying to find the angle of DBA. So, we can identify DAB as a 90 degree angle to start. Then we can identify that ACB = ADB, meaning ADB is 30 degrees. With that information, we have this equation:
DBA = 180 - 90 - 30
DBA = 60
The measure of the angle ∠DBA will be 60°. Then the correct option is C.
What is a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
The diagram is given below.
BD is the diameter of circle O. If m∠ACB = 30°.
We know that the central angle is double the angle at the periphery that was subtended by the same chords.
∠AOB = 2∠ACB
∠AOB = 2 x 30
∠AOB = 60°
We know that the triangle AOB is an equilateral triangle, in which each angle will be 60°.
Thus, the measure of the angle ∠DBA will be 60°.
Then the correct option is C.
More about the circle link is given below.
https://brainly.com/question/11833983
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A water trough is 8 m long and has a cross-section in the shape of an isosceles trapezoid that is 40 cm wide at the bottom, 100 cm wide at the top, and has height 60 cm. If the trough is being filled with water at the rate of 0.1 m3/min how fast is the water level rising when the water is 30 cm deep?
Answer:
1.785 cm / min
Step-by-step explanation:
We have to the following equation:
V = A * L
The volume is equal to the area times the length, now, if we derive with respect to time we have:
dV / dt = dA / dt * L
Now, the area of a trapezoid is:
A = (Upper base + Lower base) / 2 * height
Now we have:
Upper base = 40 + h
Lower base = 40
Replacing we have:
A = (40 + h + 40) / 2 * h
A = (h ^ 2) / 2 + 40 * h
Now, we derive and we are left:
dA / dt = d [(h ^ 2) / 2 + 40 * h] / dh * dh / dt
dA / dt = (h + 40) * dh / dt
we replace dA / dt:
dV / dt = [(h + 40) * dh / dt] * L
We have that dV / dt is equal to 0.1 m ^ 3 / min, we know that 1m ^ 3 is equal to 10 ^ 6 cm ^ 3, therefore:
dV / dt = 10 ^ 5 cm ^ 3 / min
in addition L is equal to 8 m or what is equal to 800 cm, and also h at the required moment is 30 cm
we replace everything and we have:
10 ^ 5 = 800 * (30 +40) * dh / dt
dh / dt = 10 ^ 5/56000
dh / dt = 1.785 cm / min
the diameter of a circle is 5 ft. Find the circumference to the nearest tenth(urgent)
Answer:
15.71
Step-by-step explanation:
To find the radius, half the diameter because r x 2 = diameter. 5/2 = 2.5
Put in circumference formula C=2πr
c=2 x 3.14 x 2.5
c= 2 x 7.85
c=15.7
Put the value into the circle circumference formula C=2πr
which of these can be rewritten as an exact answer without the square root symbol? √4 √125 √0.6 √12.35 Thank you :)
Answer:
[tex]\sqrt{4}[/tex]
Step-by-step explanation:
Because
→ [tex]\sqrt{4}[/tex] is equal to 2
→ [tex]\sqrt{125}[/tex] is equal to [tex]5\sqrt{5}[/tex] or 11.18033989
→ [tex]\sqrt{0.6}[/tex] is equal to [tex]\frac{\sqrt{15} }{5}[/tex] or 0.7745966692
→ [tex]\sqrt{12.35}[/tex] is equal to 3.514256678
Answer:
√4
Step-by-step explanation:
√4 = 2
The other ones can only be approximated:
√125 = 5√5 ≈ 11.18033
√0.6 ≈ 0.774597
√12.35 ≈ 3.51426
Need help with #12 pls explain
please need help I will be MARKING as BRIANILIST. thank you so much.
Answer:
A
Step-by-step explanation:
15:60
Simplify the ratio.
15/15:60/15
1:4
Answer:
1:4
Step-by-step explanation:
The answer is 1:4 because 15:60 simplified is 1:4
Simplify 1/4(8x+16)+4x.
Answer:
6x+4
Step-by-step explanation:
First thing to do is distribute 1/4 into the parenthesis. So 1/4 times 8x and 16. Which will give you 2x and 4. Then add like terms which will be 2x + 4x which is 6x. Then you have the 4 left over so your new equation is 6x+4.
Answer:
[tex]\fbox{\begin{minipage}{3em}6x + 4\end{minipage}}[/tex]
Step-by-step explanation:
[tex]A= \frac{1}{4} (8x + 16) + 4x[/tex]
Apply associate property:
[tex]A = \frac{1}{4} *8x + \frac{1}{4} *16 + 4x[/tex]
Simplify the first two components:
[tex]A = 2x + 4 + 4x[/tex]
Rearrange the components:
[tex]A = 2x + 4x + 4[/tex]
Simplify:
[tex]A = 6x + 4[/tex]
Hope this helps!
:)
The coordinate grid shows points a through k. Which points are solutions to the system of inequalities 2x+y 8 please help this is my last resort
Answer:
The points that verify the system of inequalities are:
point E, pointF, and point G.
Step-by-step explanation:
Please see the attached image that illustrates the boundary lines in your system of inequalities.
The boundary line for the inequality [tex]2x+y<10[/tex] is depicted in green, while the boundary line for the inequality [tex]2x-4y>8[/tex] is depicted in red.
By solving for y in each inequality, we understand which half-plane should be considered for the inequality:
First inequality (green boundary line) :
[tex]2x+y<10\\y=10-2x[/tex]
This means that we are to consider the points below the green boundary line.
Second inequality (red boundary line) :
[tex]2x-4y >8\\2x-8>4y\\y<\frac{1}{2} x-2[/tex]
This means we have to consider the points below the red boundary line.
Recall as well that both conditions we arrived at have to be satisfied by the points that are solutions of both inequalities.
From the image, we can see that there are only three points that reside at the same time below the green and the red boundary lines. These points are: point E, pointF, and point G.
On the other hand, we have two points that lie on a boundary line (point J and H), but they should be ignored, since the system of inequalities contain just inequality symbols < or >, and not the "equal" sign.
Translate the following sentence into an equation. Five times a number less than eighteen is equal to thirteen.
Answer:
5(n<18)=13
Step-by-step explanation:
Five times a number less than eighteen is equal to thirteen
5 (n < 18 = 13
HELP! WILL GIVE BRAINLIEST TO BEST ANSWER!!! BE VERY DETAILED PLEASE <3 Examine your selected object and the construction you made from 1.08. Which transformations (translations, reflections, or rotations) are present in the constructions?
Answer:
It's Rotated I believe
Step-by-step explanation:
what is -5+11y-3=25? will mark brainliest!!
Step-by-step explanation:
-5 +11y -3 = 25
11y = 25 + 5 + 3
11y = 33
y = 33/11
y = 3
i need help please thanks
Answer:
66 units
Step-by-step explanation:
just addition
Answer:
66 units
Step-by-step explanation:
The perimeter of a two dimensional object is all of its sides added together:
6+14+10+17+4+3+8+4=
20+10+17+4+3+8+4=
30+17+4+3+8+4=
47+4+3+8+4=
51+3+8+4=
54+8+4=
62+4=
66 units
What is the shape of the cross section of the figure that is parallel to the triangular bases? A triangular prism.
a parallelogram that is not a rectangle
a rectangle
a triangle that must have the same dimensions as the bases
a triangle that may not have the same dimensions as the bases
Answer:
AStep-by-step explanation:
a parallelogram that is not a rectangle
Hope this helpsAnswer:
A
Step-by-step explanation:
I did it on the quiz
