9514 1404 393
Answer:
boat speed: (7t -95)/(6t² -110t +500)
stream speed: (37t -345)/(6t² -110t +500)
Step-by-step explanation:
The relation between time, speed, and distance is ...
time = distance/speed
The boat speed (b) is added to the stream speed (s) going downstream. The stream speed is subtracted going upstream. The given relations tell us ...
25/(b-s) +44/(b+s) = t
15/(b-s) +22/(b+s) = 5
This gives us 2 equations in 3 unknowns, so we can only provide a solution in terms of one of the unknowns. Since we are asked for the speeds, they will be provided in terms of t.
Subtracting the first equation from 2 times the second gives ...
2(15/(b-s) +22/(b+s)) -(25/(b-s) +44/(b+s)) = 2(5) -(t)
5/(b-s) = 10 -t
5/(10 -t) = b -s
Substituting for b-s in the second equation gives ...
15/(5/(10-t)) +22/(b+s) = 5
30 -3t +22/(b+s) = 5
22/(b+s) = 3t -25
22/(3t -25) = b+s
Adding the equations for the sum and difference of speeds, we get ...
(b-s) +(b+s) = 5/(10-t) +22/(3t -25)
2b = (5(3t -25) +22(10 -t))/((10-t)(3t-25)) = (95 -7t)/((10-t)(3t-25))
b = (7t -95)/(6t² -110t +500)
Subtracting the equations for sum and difference of speeds, we get ...
(b+s) -(b-s) = 22/(3t -25) -5/(10 -t)
2s = (22(10-t) -5(3t -25))/((10-t)(3t-25))
s = (37t -345)/(6t² -110t +500)
__
The speed of the boat in still water is (7t -95)/(6t² -110t +500) km/h.
The speed of the stream is (37t -345)/(6t² -110t +500) km/h.
__
Note that these solutions only make sense for values of t between 25/3 and 345/37, approximately 8.33 < t < 9.32. For t=9 hours, the boat speed is 8 km/h and the stream speed is 3 km/h.
angle A and angle B are complementary angles. If m angle A = (6x – 8)° and m
angle B = (5x + 21)°, then find the measure of angle B.
Answer: B = 56 degrees
Step-by-step explanation: Complementary angles add up 90 degrees. So we will set both of the equations equal to 90 degrees and then solve from there.
6x+8+5x+21=90
1. Simplify 5x + 6x and 21 - 8
11x+13=90
2. Subtract 13 from both sides.
11x=90-13
3. Simplify 90-13 to 77.
11x=77
4. Divide both sides by 11.
x = 77/11
5. Simplify 77/11 to 7
x=7
Now we have to take the value of x and substitute it back into B = (5x+21)
1. Substitute
B = (5(7)+21)
B = 35 +21
B = 56
HOPE THIS HELPS :)
Ana spends 0.45 of her homework time reading. What is 0.45 as a percent? Explain.
Answer:
45%
Step-by-step explanation:
someone please help me
Answer:
A. 20ft
Step-by-step explanation:
Answer:
d. 98.5
Step-by-step explanation:
Triangles:
5 x 4 = 20/2 = 10
Circle:
5² x 3.14 = 78.5
Add both of them 98.5
Solve for x. round your answer to the nearest tenth
Trigonometry
Answer:
[tex]\displaystyle x \approx 16.5[/tex]
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 EqualityTrigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] tanθ = opposite over adjacentStep-by-step explanation:
Step 1: Define
Angle θ = 70°
Opposite Leg = x
Adjacent Leg = 6
Step 2: Solve for x
Substitute in variables [tangent]: [tex]\displaystyle tan70^\circ = \frac{x}{6}[/tex][Multiplication Property of Equality] Isolate x: [tex]\displaystyle 6tan70^\circ = x[/tex]Rewrite: [tex]\displaystyle x = 6tan70^\circ[/tex]Evaluate: [tex]\displaystyle x = 16.4849[/tex]Round: [tex]\displaystyle x \approx 16.5[/tex]Please help have only an hour please use picture
Answer:
The answer is C. n = 3
Step-by-step explanation:
I got this answer by using the butterfly method. I multiplied 3 and 2 and got 6. Then take 6 and divide it by 2 and you get 3.
So therefore, n = 3
Please mark brainliest if this helped.
Answer: C n=3
Step-by-step explanation:
First croas multiply the 2 and 3 to get one side
then you multiply 2n and move it to the other side so it can equal
2n=6
2n/2=6/2
n=3
The cost of renting a car is represented by C=8.5h+25.5, where C is the cost in dollars and h is the number of hours rented.
If Peter rents a car and pays a cost of $85, how many hours did he rent it for?
Use the distance formula to find the distance between each pair of points. round to the nearest tenth of neccessary.
Answer:
1). 4.2 2). 7.65 3). 14.14
Step-by-step explanation:
1). √(y2 - y1)² + (x2 - x1)²
√[-1 - (-4)]² + [-3 - (-6)]²
√(3)² + (3)²
√9 + 9
√18
= 4.2
2). √(2.5 - 1)² + ( -4 - 3.5)²
√(1.5)² + (-7.5)²
√(2.25) + (56.25)
√58.5
= 7.65
3).√(5 - (-5)² + (-5-5)²
√(10)² + (-10)²
√(100) + (100)
√200
= 14.14
PLZ HELP NEED BY TODAY!!
Step-by-step explanation:
Given 5x + 8 = 118 (vertically opposite angles)
[tex]5x + 8 = 118 \\ 5x = 118 - 8 \\ 5x = 110 \\ x = 110 \div 5 \\ = 22[/tex]
Which of these is an example of due process?
a search without good reason
a prejudiced jury
a cruel punishment
a fair trial
Answer:
A fair trial.
Answer:
Step-by-step explanation: a search without good reason
Which is a number that can be written as a fraction in the form ?
Rational Numbers: Any number that can be written in fraction form is a rational number. This includes integers, terminating decimals, and repeating decimals as well as fractions. An integer can be written as a fraction simply by giving it a denominator of one, so any integer is a rational number.
Hope this helps!
Solve the equation for the interval [0, 2pi). 2sin^2x = sin x
A) 0, pi, pi/6, 5pi/6
B) pi/6, 5pi/6
C) pi/3, 2pi/3
D) pi/2, 3pi/2, pi/3, 2pi/3
Answer:
A
Step-by-step explanation:
We want to solve the equation:
[tex]2\sin^2(x)=\sin(x)[/tex]
For the interval [0, 2π).
First, we can move all the terms to one side. Start off by subtracting sin(x) from both sides:
[tex]2\sin^2(x)-\sin(x)=0[/tex]
We can factor:
[tex]\sin(x)\left(2\sin(x)-1\right)=0[/tex]
By the Zero Product Property:
[tex]\sin(x)=0\text{ or } 2\sin(x)-1=0[/tex]
Solve for each case:
[tex]\displaystyle \sin(x)=0\text{ or } \sin(x)=\frac{1}{2}[/tex]
Use the unit circle to solve:
[tex]\displaystyle x=\left\{0, \frac{\pi}{6},\frac{5\pi}{6}, \pi\right\}[/tex]
Hence, our answer is A.
*Please note that we should not simply divide both sides by sin(x) to acquire 2sin(x) = 1. The problem with the operation is that we are dividing by sin(x), yet we do not know what the value of x is. Thus, one or more values of x may result in sin(x) = 0, and we cannot divide by 0. Hence, we are required to subtract and then factor, unless the question specifically states that sin(x) ≠ 0.
Find x. PQR = MNR ...............
Answer:
x = 55
Step-by-step explanation:
<QRP = <NRM because of vertical angles
To find <NRM:
x + 35 + 90 = 180
x + 125 = 180
x = 55
<NRM = 55
<QRP or x = 55
find the unit price to the nearest tenth of one cent. 12-ounce can of cola for 60 cents
Answer:
1 ounce is 0.05
Step-by-step explanation:
The sophomore class needs a combined total of 216 medium and large t-shirts for field day. The number of medium t-shirts needed is three times the number of large t-shirts needed. Based on this information, would it be reasonable for the sophomore class to order 72 large t-shirts and 144 medium t-shirts? A. No, because the number of medium t-shirts is not 3 times the number of large t-shirts B. No, because the number of large t-shirts is not 3 times the number of medium t-shirts C. Yes, because the total number of t-shirts is 216 D. Yes, because the number of large t-shirts is of the total number of t-shirts
For a beverage, Lisa mixes cups of lemonade to cups of iced tea in a ratio of 2:5. Which of the following best describes the amount of lemonade to iced tea?
For every 2 cups of lemonade, there are 3 cups of iced tea.
For every 2 cups of lemonade, there are 5 cups of iced tea.
For every 3 cups of lemonade, there are 2 cups of iced tea.
For every 5 cups of lemonade, there are 2 cups of iced tea.
Answer:
Answer 2 would be true.
Step-by-step explanation:
Because our ratio is 2:5 (or 2 to 5 for easier understanding) we know that every 2 cups we use of lemonade, we pair with 5 cups of tea.
Answer:
The answer is B
Step-by-step explanation:
For every 2 cups of lemonade, there are 5 cups of iced tea.
What is the value of x?
Answer:
x = 64
Step-by-step explanation:
2x = 128
x = 64
Answer:
hi
Step-by-step explanation:
i think so
128⁰+2x⁰=180⁰
2x⁰=180⁰-128⁰
2x⁰=52⁰
x=52/2
x=26⁰
hope it helps
have a nice day
Find m
A) 70°
C) 42°
B) 145°
D) 130°
Answer:
42 degrees
Step-by-step explanation:
Angles E and G are equal. Therefore, 8x - 6 = 7x, and x = 6.
Then the measure of angle G must be 7(6), or 42 degrees.
What is the height of the cylinder in the diagram? Round your answer to the nearest whole number.
Answer:
8 is the height
Step-by-step explanation:
please mark this answer as brainlest
What is a equivalent expression to z+z+z+z
Please help me do this
Answer:
∠ U = 60°
Step-by-step explanation:
The tangent- tangent angle U is half the difference of its intercepted arcs
minor arc VT = 120° , then
major arc VT = 360° - 120° = 240°
Then
∠ U = [tex]\frac{1}{2}[/tex] (240 - 120)° = [tex]\frac{1}{2}[/tex] × 120° = 60°
Reese is selling lemonade at the parade. He gets to keep 50% of the money he collects. A large lemonade is
$5.00 and a small lemonade is $2.00.
The expression represents 50%
of the money he collects
.0.50(5l + 2s)
Use the Distributive Property to expand the expression.
Answer:
.5(5I)+.5(2s)
Step-by-step explanation:
CHOOSING BRAINLIEST ( SCREENSHOT PROVIDED )
Find the missing number to complete the linear equation that gives the rule for this table.
x | y
0 | 0
1 | 25
2 | 50
3 | 75
Answer:
y= 25
i think
Step-by-step explanation:
HELLO!! I NEED HELP! Please show full Solutions. I will mark brainliest for the best answer. Thank you and god bless.
Multiply. Write your answer as a fraction in simplest form.
−1(45)=
asap
Answer:
-9/20
put 45 over 100, then divide them both by 5.
............................
Answer:
Thaey are proportional
Step-by-step explanation:
find the missing side lenght of the triangle below
Answer:
12
Step-by-step explanation:
5^2 + x^2 = 13^2
x = 12
Answer:
12
Step-by-step explanation:
Use Pythagorean theorem
[tex]a^2 +b^2 =c^2[/tex]
c= always hypotenuse/ longest side/ side across from right angle = 13
a= 5
[tex]5^2+b^2=13^2[/tex]
[tex]25+b^2=169[/tex]
Subtract 25 from 169
[tex]b^2= 144[/tex]
Square root both sides
b= 12
--------
it's also a special triangle known as a 5, 12, 13 triangle
Jen collects stamps. The first month she added 25 stamps. Six months later, she doubled in number to a total of 98. How many stamps did she have to start her collection?
Answer:
49
Step-by-step explanation:
help help help help help
A=√18-√8+√50
Write A in the form m√2 where m is an integer
Answer:
6√2
Step-by-step explanation:
A=3√2-2√2+5√2
A=6√2
Answer:
6√2
Step-by-step explanation:
A=√18-√8+√50 = √9√2 - √4√2 + √2√25, or A = (√2)(3 - 2 + 5) = 6√2
1.-28 -20 help me plsss
If you mea. 1 . -28 - 20 then the answer is going to be
[tex]1. - 48[/tex]
but if you mean -28 -20 the the answer is going to be
[tex] - 48[/tex]
please help me i don’t know te anser
A=b h................
Answer:
A = 20
Step-by-step explanation:
A = bh
b = 4
h = 5
4 × 5 = 20