The current of Cache Creek has speed 2 mph. It takes a small boat a total of 4 hours to travel 12 miles upstream and 12 miles back. Find the speed of the boat in still water. If your answer is not an integer, round it off to two decimal places.
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
Find the slope of the line that passes through (4, 9) and (6, 10).
Step-by-step explanation:
Slope (m) =ΔYΔX=12=0.5θ =arctan(ΔY)ΔX=26.565051177078°ΔX = 6 – 4 = 2ΔY = 10 – 9 = 1Distance (d) = √ΔX2 + ΔY2 = √5
= 2.2360679774998
Solve y = x + 8 for x.
Answer: y-8= x
Step-by-step explanation:
what number is 40% of 160
Answer: 64
Step-by-step explanation:
Help me pleaseee (you could just tell me the points or something)
Send answers I will check if correct
Step-by-step explanation:
on 1 September they will have same practice day....
What is the solution to 8x-3(2x-4)= 3(x-6
)
Answer:
x = 30
Step-by-step explanation:
8x - 3(2x - 4) = 3(x - 6)
Distribute te -3 on the left, and the 3 on the right
8x - 3(2x - 4) = 3(x - 6)
8x - 6x + 12 = 3x - 18
Simplify
8x - 6x + 12 = 3x - 18
2x + 12 = 3x - 18
Inverse operations
2x + 12 = 3x - 18
-2x -2x
12 = x - 18
+18 +18
30 = x
21. © MP.2 Reasoning Four teams are
tidying the Green trail. They will each
tidy an equal distance. How many miles
does each team tidy?
Answer:
See Explanation (Incomplete Question)
Step-by-step explanation:
The question is incomplete as the distance of the Green tail is not given.
Given
[tex]Teams = 4[/tex]
Required
Determine the distance covered by each
Since each team would cover the same amount of distance, the distance covered by each is the total distance divided by 4.
In other words,
[tex]Each = \frac{Total\ Distance}{4}[/tex]
Assume the total distance of the green tail is 9 miles, the distance by each would be:
[tex]Each = \frac{9}{4}[/tex]
[tex]Each = 2.25\ miles[/tex]
z = -3a + 1
Solve for a
Thanks
Answer:
z-1/-3
Step-by-step explanation:
z-1=-3a
z-1/-3=a
true or false: when you dilate a figure, the coordinates are multiplied by the scale factor
Answer:
True
Step-by-step explanation:
12 / 0.96 please answer this i need it
Answer:
12.5
Step-by-step explanation:
Find the missing side length.
A)
17
B)
19
21
D)
23
Answer:
It's 21
Step-by-step explanation:
12/16 = x/28
cross multiply
16x = 336
divide by 16 on both sides
you get x = 21
I just did a test and got it right
What is the measure of the angle x?
Answer:
30 degrees
Step-by-step explanation:
Brainliest me
Answer:
40
AB=AOB÷2
and AB=ACB
so AB= 80÷2
AB=40
If each cube in the rectangular prism measures 1 cubic centimeter, what is the volume of the prism?
A - 12
B - 24
C - 6
D - 8
Write the decimal expansion for 4/9
Answer:
0.44444444
Step-by-step explanation:
Answer:
the decimal expansion of 4/9 = 0
Step-by-step explanation:
I need help plz help
In 2004, an art collector paid $ for a particular painting. The same painting sold for $ in 1950. Complete parts (a) through (d). a) Find the exponential growth rate k, to three decimal places, and determine the exponential growth function V, for which V(t) is the painting's value, in dollars, t years after 1950.
Answer:
The value of k is 0.149.
Step-by-step explanation:
The complete question is:
In 2004, an art collector paid $84,275,000 for a particular painting. The same painting sold for $27,000 in 1950. Complete part (a) through (d)? (a) Find exponential growth rate k, to three decimal places, and determine the exponential growth function V, for which V(t) is the painting’s value, in dollars, t years after 1950.
Solution:
The exponential growth function can be expressed as follows:
[tex]y=a\cdot e^{kt}[/tex]
y = Final value after t years
a = initial value
It is provided that:
y = $84,275,000
a = $27,000
The value of t from 1950 to 2004 is, t = 54
Compute the value of k as follows:
[tex]y=a\cdot e^{kt}[/tex]
[tex]84,275,000=27,000\times e^{54k}\\\\e^{54k}=\frac{84275000}{27000}\\\\54k=\ln (\frac{84275}{27})\\\\k=\frac{1}{54}\times \ln (\frac{84275}{27})\\\\k=0.149[/tex]
Thus, the value of k is 0.149.
If 3x−y=12, what is the value of
8x/2y?
A) 212
B) 44
C) 82
Answer:
[tex]\frac{8^x}{2^y} 2y=2x^{12}[/tex]
Step-by-step explanation:
Since the numerator and denominator have a common base, this expression can be rewritten as 2(3x−y).
substitute 12 for the exponent, 3x−y and you will get A
Answer:
The answer is A [tex]2^{12}[/tex]
Step-by-step explanation:
Since 2 and 8 are both powers of 2, substituting 23 for 8 in the numerator of
[tex]\frac{8x}{2y}[/tex]
gives you
[tex]\frac{8x}{2y} 2y=2x^{12}[/tex]
Draw a line representing the rise and a line representing the run of the run. State the slope of the line in simplest form.
PLEASE HELP FAST
Which model represents the product Three-fourths times one-third ?
Answer:
the last one yw :)
Step-by-step explanation:
FIRST ONE I WILL MARK BRAINLEST I PROMISE!
Answer:
9
Step-by-step explanation:
Answer:
i think its negative 9 because The absolute value of −9 is 9
Step-by-step explanation:
have a great day!
1/√10. Rationalise the denominator and simplify
Answer:
√10/10
Step-by-step explanation:
Multiply the numerator and denominator by the conjugate.
Hope this helps!! Please consider marking brainliest! Have a good one!!
Answer:
√10 / 10
Step-by-step explanation:
1/√10
To rationalize the denominator we need to get rid of any √ in the denominator. we do this by multiplying both sides by the square root:
1/√10 * √10/√10 = √10 / 10
Two factory workers win the in-house raffle with a prize of £240. Monika and Robert share the prize money in a ratio of 3:5. How much does Monika get?
Answer:
Monika gets £90
Step-by-step explanation:
Let us use the ratio method to solve this question
∵ Monika and Robert are Two factory workers
∵ They win the in-house raffle with a prize of £240
∵ Monika and Robert share the prize money in a ratio of 3: 5
→ That means the total of the ratio is equivalent to the value of the prize
∵ The total of the ratio = 3 + 5 = 8
→ By using the ratio method
→ Monika : Robert : Total
→ 3 : 5 : 8
→ x : y : 240
→ By using the cross multiplication
∵ x × 8 = 3 × 240
∴ 8x = 720
→ Divide both sides by 8
∵ [tex]\frac{8x}{8}[/tex] = [tex]\frac{720}{8}[/tex]
∴ x = 90
∵ x represents the share of Monika
∴ Monika gets £90
The scatter plot shows the average monthly outside temperature and the monthly
electricity cost
Based on the scatter plot, what is the best prediction for the electricity cost if the
temperature for the month is 21°C?
$450
$500
$600
$700
Answer:
600 is the answer
Step-by-step explanation:
I literally just took the test! Hope dis helps.
Answer:
600
Step-by-step explanation:
I took this test on USA test prep and got this question it correct
can you substarct in any order?
Answer:
No
Step-by-step explanation:
In subtracting, you must start with the larger number
Find the distance between C (-1,7) and D (-8,-3). Please provide a thorough explanation, thank you!
Answer:
[tex]d=\sqrt{149}\approx12.21[/tex]
Step-by-step explanation:
To find the distance between any two points, we can use the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
We have the two points (-1, 7) and (-8, -3).
Let (-1, 7) be (x₁, y₁) and let (-8, -3) be (x₂, y₂). Substitute:
[tex]d=\sqrt{(-8-(-1))^2+(-3-7)^2}[/tex]
Evaluate:
[tex]d=\sqrt{(-8+1)^2+(-10)^2}[/tex]
Evaluate:
[tex]d=\sqrt{(-7)^2+(-10)^2}[/tex]
Square:
[tex]d=\sqrt{49+100}[/tex]
Add:
[tex]d=\sqrt{149}\approx12.21[/tex]
This cannot be simplified. Hence, the distance between (-1, 7) and (-8, -3) is √(149) or approximately 12.21 units.
10. Which is the best estimate of the product of
13 and 49?
A 60
© 500
® 400
0 600
Alan travels eight and two thirds kilometers to get to school. He ran one and ten elevenths kilometers and walked the rest. How many kilometers were left to walk?
six and two thirty thirds kilometers
five and twenty five thirty thirds kilometers
six and twenty five thirty thirds kilometers
six and twenty thirty thirds kilometers
please help will give brainlyest
Answer: I am pretty sure its C i hope this helps :D
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
A quadrilateral has two angles that measure 110° and 140°. The other two angles are in a ratio of 5:6. What are the measures of those two angles?
Tara and Levi are trying to decide between homeowners insurance policies offered by two different agencies. AAA Insurance has offered to insure their home for an annual premium of $0.38 per $100 with a $500 deductible. Thompson’s Insurance has offered to insure the same home for an annual premium of $0.26 per $100 with an deductible of $1,000. Insurance Company Annual Premium (per $100) Deductible AAA Insurance $0.38 $500 Thompson's Insurance $0.26 $1,000 The house Tara and Levi purchased is valued at $425,000. Which of the following statements accurately describes the difference between the two plans? a. AAA Insurance is cheapest if Tara and Levi experience an incident that results in severe damage or loss to their home. b. AAA Insurance would be cheapest if Tara and Levi can avoid any incidents that result in severe damage or loss to their home. c. Thompson’s Insurance is cheaper even if Tara and Levi experience an incident that results in severe damage or loss to their home. d. Thompson’s will be more expensive whether or not Tara and Levi experience an incident that results in severe damage or loss to their home.
Answer: C
- Thompson’s insurance is cheaper even if Tara and Levi experience an incident that results in severe damage or loss to their income
Step-by-step explanation: I literally just got finished with the test, hope this helps.
Thompson’s Insurance is cheaper even if Tara and Levi experience an incident that results in severe damage or loss to their home.
Given are the information,
House valued at $425,000
AAA Insurance: $0.38 per 100 with a $500 deductible
425,000 / 100 = 4,250
4,250 x 0.38 = 1,615 annual premium
Thompson’s insurance: $0.26 per 100 with a $1000 deductible
425,000 / 100 = 4,250
4,250 x 0.26 = 1,105 annual premium
The difference we can see are :
If an incident occurs that results in damage or loss to their home, the couple shall shell out 500 before AA Insurance can take over payment for expenses.
On the other hand, the couple will shoulder 1,000 before Thompson’s insurance take over payment for expenses in the event there is an incident that results in damage or loss to their home.
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