Answer:
6.61 mph
Step-by-step explanation:
Speed of current; c = 2 mph
Total time to travel upstream and back; t = t1 + t2 = 4 hours
Let x represent speed of the boat in still water
Then the actual speed of the boat when going upstream is x - 2, and the actual speed when going downstream downstream is x + 2.
We know that; distance = speed x time, Thus;
For the upstream trip;
12 = (x - 2)t1
t1 = 12/(x - 2)
For the downstream trip;
12 = (x + 2)t2
t2 = 12/(x +2)
Adding both equations, we have;
t1 + t2 = (12/(x - 2)) + (12/(x +2))
4 = (12/(x - 2)) + (12/(x +2))
Multiply through by (x - 2)(x + 2)
4(x - 2)(x + 2) = 12(x + 2) + 12(x - 2)
4x²- 16 = 12x + 24 + 12x - 24
4x² - 16 = 24x
4x² - 24x - 16 = 0
Using quadratic formula, we have;
x ≈ 6.61 mph
What is an equation of the line that passes through the points (0, -1) and (6, 1)? Put your answer in fully reduced form
2 with the exponent of 2 ⋅(45÷9) - 3
i need the answer
please answer see the image below
Answer:
49.73Step-by-step explanation:
total area = area of rectangle - area of circle
= (13 x 6) - (π 3²)
= 78 - 28.274
= 49.73 sq. units
Match the reasons to the statements given.
Given:
ABCD
EF contains T
Prove:
ET = FT
Answer:
The reasons and the statements are given as follows;
1. Parallelogram ABCD [tex]{}[/tex] Given
2. BT = TD [tex]{}[/tex] Diagonals of parallelogram bisect each other
3. ∠1 = ∠2 [tex]{}[/tex] Vertically opposite angles
4. BC ║ AD [tex]{}[/tex] Definition of parallelogram
5. ∠3 = ∠4 [tex]{}[/tex] If lines are parallel then alternate interior
angles are equal
6. Triangle BET congruent to Triangle DFT by ASA
7. ET = T_F [tex]{}[/tex] CPCTE
Step-by-step explanation:
Statement [tex]{}[/tex] Reason
1. Parallelogram ABCD The given quadrilateral
2. BT = TD Based on the properties of a parallelogram, the parallelogram diagonals bisect each other
3. ∠1 = ∠2 Vertically opposite angles formed by two intersecting lines are equal
4. BC ║ AD By definition, the opposite sides of a parallelogram are parallel
5. ∠3 = ∠4 Based on the property of equality of the alternate interior angles of two parallel lines
6. Triangle BET congruent to Triangle DFT by Angle-Side-Angle rule of congruency
7. ET = T_F by Congruent Parts of Congruent Triangles are Equal, CPCTE, postulate.
The reasons that matches the statements in the two-column proof is shown in the table attached in the image below.
Recall:
Based on the, CPCTE Theorem, if two triangles are congruent, all its corresponding sides and angles of both triangles are therefore congruent together.The ASA Congruent Theorem justifies that two triangles are congruent if they have two pairs of congruent angles and a pair of included sides that are also congruent.Given parallelogram ABCD, and also, we know that EF contains T, to prove that ET = FT, establish that:
ΔBET ≅ ΔDFT by the ASA Congruence Theorem, then demonstrate that ET = FT by the CPCTE Theorem.
Therefore, the reasons that matches the statements in the two-column proof is shown in the table attached in the image below.
Learn more about ASA Congruence Theorem on:
https://brainly.com/question/3168048
Trevor went to the pet store to get a new pet fish. Unfortunately, the selection at the store wasn't very good. Exactly 90% of the fish at the store were goldfish. Trevor wanted any fish, but a goldfish. If there are 140 fish at the store, then how many fish could Trevor choose from?
Answer: 14 fish
explanation: 90% of 140= 126 (if u use a proportion or multiply 0.9x140).
140-126=14
Answer: He has 14 other fish to choose from in the store
Step-by-step explanation:
90% ÷ 100 = .9
.9 × 140 = 126
140 - 126 = 14
please answer the image below
Answer:
301.593Step-by-step explanation:
surface area = 2πrh + 2πr²
where r = 4 km radius
h = 8 km
plugin values into the formula
surface area = 2πrh + 2πr²
= 2π (4) 8 + 2π (4)²
= 201.062 + 100.531
= 301.593 km²
Solve the equation
2/3x-6=9
Answer: 2/3-6=9 is equal to = − 2(2x+6)
Answer:
x = 45 over 2 or 22.5
Step-by-step explanation:
ADD 6 to both sides of the equation SimplifyMultiply 3 by the same value to eliminate fraction denominatorsSimplifyDivide 2 by both sides of the equation by the same termSimplifywhat is the factterd form for the eqaution 3x^2+8x+4
Answer:
(3x+2)(x+2)
Step-by-step explanation:
1 Split the second term in 3{x}^{2}+8x+43x
2
+8x+4 into two terms.
3{x}^{2}+6x+2x+43x
2
+6x+2x+4
2 Factor out common terms in the first two terms, then in the last two terms.
3x(x+2)+2(x+2)3x(x+2)+2(x+2)
3 Factor out the common term x+2x+2.
WILLL GIVE BRAINLEAST Name a positive or negative number to represent each situation.
1. depositing $85 in a bank account ____
I think the answer would be +85 or just 85 because deposit means to add something so I am pretty sure it would be +85.
x + 1 - x = 1
Solve this equation
Please help
Answer:
x=1
Step-by-step explanation:
1+1-1=1
1+1=2
2=1=1
Answer:
[tex]x=Any\ real\ number[/tex]
Step-by-step explanation:
[tex]x+1-x=1\\1=1\\As\ x\ just\ gets\ canceled\ x\ can\ take\ any\ real\ values.[/tex]
Please Help I am having one of those dumb moments.
Answer: Which of the following equations is an example of inverse variation between the values x and y?
Explanation: C
you answer 24 questions on a 100 point test correctly and earn 96%.
There are 25 questions in total, each question is worth 4 points.
Your friend earns a grade of 76%on the same test. How many questions did your friend answer correctly?
Answer:
19
Step-by-step explanation:
He gets 6 wrong and 19 correct
Use 3 for pi. I will give brainliest to whoever answers correctly
Answer:
where is the 3
Step-by-step explanation:
What is the lease common multiple of 6 and 15
Answer:
It would be 30.
Step-by-step explanation:
One number is three less than a second number. Six times the first is 6 more than 3 times the second. Find the numbers.
Step-by-step explanation:
Given,
x = y - 3
Also,
6(y - 3) = 3y + 6
6y - 18 = 3y + 6
6y - 3y = 6 + 18
3y = 24
y = 24/3
y = 8
x = 8 - 3
x = 5
Therefore, the first number is 5 and the second number is 8.
If alice earns 56% more than wallaceAlice's salary is how many times Wally's salary?
Answer:
Alice's salary is 1.56 times Wally's salary
Step-by-step explanation:
Let Wally's salary = x
Alice's salary = x + 56% of x
= x + 0.56x
= 1.56x
= 1.56 * Wally's salary
Answer:b
Step-by-step explanation:
please answer the question below
Answer:
The rate of change in the submarine's elevation is 26.0 feet per second.
Step-by-step explanation:
She begins 151 feet below sea level
Thus, her initial point is y₁ = 151 feet below sea level
i.e. at t₁=0 seconds, y₁ = 151 feet below sea level
After descending for the 3 seconds, she is 229 feet below sea level.
Thus, her second point is y₂ = 229 feet below sea level after 3 seconds
i.e. at t₂=3 seconds, y₂ = 229 feet below sea level
The rate of change is basically the slope. Thus, the rate of change can be obtained by taking the slope.
slope = rate of change = (y₂ - y₁)/(t₂ - t₁)
= (229 - 151) / (3 - 0)
= 78/3
= 26.0
Therefore, the rate of change in the submarine's elevation is 26.0 feet per second.
Function f is defined by the equation f(x)=x2
What is f(3)
Find the perimeter of a rhombus whose diagonals are
30cm and 34cm
a non rh
rhombus whose
diagonals
are
Answer:
Rhombus Side = sqr root [(34 / 2)^2 + (30 / 2)^2]
Rhombus Side = sqr root [17^2 + 15^2]
Rhombus Side = sqr root [289 + 225}
Rhombus Side = sqr root [514]
Rhombus Side = 22.6715680975
Rhombus Perimeter = side * 4 = 90.68627239 cm
Step-by-step explanation:
Makayla borrows $15200. Some is from her friend at 5% annual interest, 2 times as much as that from her bank at 8% , and the remainder from her insurance company at 4%. She pays a total of $968 in interest for the first year. How much did she borrow from each source?
Answer:
Amount borrowed from friend = 4000
From Bank = 8000
From insurance = 3200
Step-by-step explanation:
Given that:
Amount borrowed = $15200
Let amount borrowed from friend = x
x at 5% = 0.05x
From Bank = 2x at 8% = 0.08*2x = 0.16x
From insurance = 15200 - (x + 2x) at 4%
From insurance = 15200 - 3x at 4% ; (15200 - 3x)* 0.04 = 608 - 0.12x
Interest paid in first year = $968
Simple interest = principal * rate * time
968 =
968 = (0.05x + 0.16x + 608 - 0.12x)
968 - 608 = 0.05x + 0.16x - 0.12x
360 = 0.09x
x = 360 / 0.09
x = 4000
Hence,
Amount borrowed from friend = 4000
From Bank = 2x = 4000 * 2 = 8000
From insurance = 15200 - (4000 + 8000) = 3200
Which is the correct equation to find the value of X?
Answer:
The answer would be X=12
Answer:
8x-17 = 5x+19
Step-by-step explanation:
Assuming the two lines that are slightly horizontal are parallel and a straight line cuts through it, both angles should be corresponding angles and they are equal. Thus, 8x-17 = 5x+19.
A person is studying the relationship between temperature and mental ability. So,
she devised a test in which a group of 10 mice are timed as they run through a maze
which leads to food and water. The researcher repeats the test 3 times with each
group to see how much they improve and she uses three groups.
• Group 'A', does the test under normal room temperature of 76°F.
• Group 'B', does the test in the cold at a temperature of 45°F.
• Group 'C', does the test under a hot temperature of 105°F.
How would you most correctly describe Group 'A' in a statistical study?
Answer:
Group A is a Control Group
Step-by-step explanation:
60% of the shakes at The Shake Shop have protein powder in them. There are 30 shakes on the menu. How many shakes have protein powder in them?
Answer:
18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
Brainliest if you can help and provide an answer plus explanation :)
Q: How much money would you save on 10 pounds of blueberries at the less expensive fruit stand? (Hint: Find the cost of 10 pounds of blueberries for each, A and B, then subtract the values.) Remember to explain your reasoning!
Answer:
According to my...calculations, you would save $20.
Step-by-step explanation:
You have to find the ratio/the rate of change, then you multiply it to get to ten pounds. You do the same for the other line. Then you just subtract it.
A= 2 pounds for $12
B= 1 pound for $4
Multiply the two to get to 10, and whatever the number is (5) you multiply 12 by it as well. For B, you multiply by 10. You get $60, for A. $40 for B.
The amount saved would be $20.
What does -3/8 x 3/5 x -5/6 equal
It equals 3/16 because I first multiplied the first to fractions together and I know that negative times a positive is negative so we would get a negative and I also multiplied the 2 to get -9/40 and then multiplied -5/6 to -9/40 to get the answer of 3/16!
Joe's grandma lives 36 blocks up the street from Joe. On Saturday, Joe
rode his bike two-thirds of the way to his grandma's house and then realized he
forgot the present he was going to give her. Joe rode back to his house, got the
present, and rode all the way to his grandma's house. Then he rode straight home.
How many blocks did Joe ride in all? Use labeled sketches, numbers, or words to
solve this problem. Show all your work.
Answer:
108 blocks.
Step-by-step explanation:
Joe's grandmother lives 36 blocks away from Joe.
Joe rode two thirds of the way to the house is 2/3 * 36= 24 blocks.
Then he rode back to his house (1 - 2/3) * 36= 12 blocks.
Then Joe rode back to grandma's house= 36 blocks.
Then he rode straight home= 36 blocks.
Total number of blocks he rode is 24+12+36+36= 108 blocks.
-2 1/4 x 6 8/9 please help
Answer:
Step-by-step explanation:
Convert mixed fraction to improper fraction and then multiply
[tex]-2 \frac{1}{4}=- \frac{2*4+1}{4} = -\frac{9}{4}\\\\6 \frac{8}{9}= \frac{6*9+8}{9} = \frac{62}{9}\\\\-2\frac{1}{4}* 6\frac{8}{9} = \frac{-9}{4} * \frac{62}{9}\\\\= \frac{-31}{2}\\\\= -15 \frac{1}{2}[/tex]
34 x 21
22 x 41
17 x 66
59 x 5
which pair factor ONLY contains composite numbers ?
Answer:
The last option
can we still reduce 4/5 to the lowest term?
Answer:
no as both terms cannot be futher divided.
What is 3/7 - 1/4? .....
Answer:
Exact Form: 5/28
Decimal Form: 0.17857