100 POINTS+BRAINLIEST 8TH GRADE MATH PT 2: Word problem involving algebraic equations on them-As usual please explain the steps simply and some things to remember. answers for points will be reported :))
Answers
Answer:
[tex]\sf a. \quad \dfrac{21}{10+x}+\dfrac{21}{10-x}=5[/tex]
Step-by-step explanation:
Formula for calculating speed:
[tex]\boxed{\sf Speed=\dfrac{Distance}{Time}}[/tex]
Therefore:
[tex]\boxed{\sf Time=\dfrac{Distance}{Speed}}[/tex]
Given values:
x = the current (in mph)Speed = 10 mphDistance = 21 milesTotal time = 5 hoursIf the boat is traveling downstream, the current (x mph) will be pushing the boat faster, and so the boat's speed will increase by x mph.
Therefore, the expression for the time it takes for the boat to travel downstream is:
[tex]\sf Time\:(downstream)=\dfrac{21}{10+x}[/tex]
If the boat is traveling upstream, the current (x mph) will be pushing against the boat and so the boat's speed will decrease by x mph.
Therefore, the expression for the time it takes for the boat to travel upstream is:
[tex]\sf Time\:(upstream)=\dfrac{21}{10-x}[/tex]
Therefore, if the total time it takes to travel downstream and upstream is 5 hours:
[tex]\implies \sf \dfrac{21}{10+x}+\dfrac{21}{10-x}=5[/tex]
To solve for x:
[tex]\implies \sf \dfrac{21}{10+x}+\dfrac{21}{10-x}=5[/tex]
[tex]\implies \sf \dfrac{21(10-x)}{(10+x)(10-x)}+\dfrac{21(10+x)}{(10-x)(10+x)}=5[/tex]
[tex]\implies \sf \dfrac{21(10-x)+21(10+x)}{(10+x)(10-x)}=5[/tex]
[tex]\implies \sf21(10-x)+21(10+x)=5(10+x)(10-x)[/tex]
[tex]\implies \sf 210-21x+210+21x=5(100-10x+10x-x^2)[/tex]
[tex]\implies \sf 420=500-5x^2[/tex]
[tex]\implies \sf 5x^2=80[/tex]
[tex]\implies \sf x^2=16[/tex]
[tex]\implies \sf x=\pm4[/tex]
Therefore, the rate of the current is 4 mph.
Related Questions
Jonathan is driving to his grandma’s house. Jonathan’s car is going 75 mph and he has to go 340 miles still. Brighton, Jonathan’s cousin, is leaving his house and is traveling 70 mph and has to go 320 miles. Who gets to grandma’s house first? How long did it take him?
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Answer: Jonathan will get to his grandma's house first because his car is going 5 mph faster than Brighton's. It will take Jonathan 4 hours and 48 minutes to get to his grandma's house.
Answer: Johnathan will get it in 4.53 hours. Jonathon's cousin will take 4.57 hours.
Step-by-step explanation:
340/75=4.53
320/70=4.57
Could someone please help?It means alot :)
Answers
Answer: H
Step-by-step explanation:
help me pls this is really hard
Answers
Answer:
31.40 inches
Step-by-step explanation:
Circumference of circle is 2πr where r is radius. We know that r is 5 inches as shown in the image. Therefore:
[tex] \displaystyle{C = 2 \times 3.14 \times 5}[/tex]
Evaluate
[tex] \displaystyle{C = 10 \times 3.14} \\ \\ \displaystyle{C = 31.40}[/tex]
Therefore, the circumference of circle is 31.40 inches
pls help its two questions aleks!!!.
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Answer:
GCF of 18 and 3 is 3
Step-by-step explanation:
use GCF to factor 18+3
I wasn't fully sure on this question sorry :(
Expand the expression 3(n + 7)
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Answer:
3n + 21
Explanation:
you just times 3 with the numbers in the brackets
3n+3•7
3n+21
Explanation: Numerical factors in this term have been multiplied.
(2n²•n³•3n¹)²
(y•4y²)³
(4b³•b)²
(3s²•s³)²
(3r²•2r³)³
Simplify the exponents. Please show me how to do the step by step?? I'm not sure how to solve these when they have parentheses
Answers
(2n²•n³•3n¹)²
First, simplify inside the parentheses. We multiply the coefficients and exponents. The coefficients: 2×3=6. and the exponents: 2×3×1=6. All together that gives: [tex](6n^6)^2[/tex]Then multiply the inside of the parentheses by itself since it's the exponent is 2. Therefore we end with [tex]36n^12[/tex]
(y•4y²)³
Same approach. Multiply the inside which gives [tex]4y^3[/tex] Then calculate that to the power of 3.
[tex]4y^3[/tex]×[tex]4y^3[/tex]×[tex]4y^3[/tex]=[tex]64y^9\\[/tex]
(4b³•b)²
[tex]=(4b^4)^2\\=4b^4\cdot4b^4\\=16b^8[/tex]
(3s²•s³)²
[tex]=(3s^5)^2\\=3s^5\cdot3s^5\\=9s^{10}[/tex]
(3r²•2r³)³
[tex]=(6r^5)^3\\=6r^5\cdot6r^5\cdot6r^5\\=216r^{15}[/tex]
Hope that helped. Let me know if you have any further questions!
Three lines meet at a point. Set up and solve an equation to find the value of r.
Answers
Answer:
57
Step-by-step explanation:
1. Carl makes a punch using the following recipe:
Give two other recipes that would taste exactly the same.
2. Look at the following recipes. Would each pair (a and b) taste the same? If not, which punch would taste more like plain juice? Use proportional reasoning, ratios, and graphs to help. Explain your reasoning for each.
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Answer: 1 purple, 1 and a half green, and 4 purple and 6 green.
Step-by-step explanation:
I'm not sure exactly what the question is, but if I thought of it correctly then it should be correct.
68% = Fraction what is it?
Answers
Answer: 17/25
Step-by-step explanation:
The Leonard family uses up a 1/2 gallon jug of milk every 3 days. At what rate do they drink milk?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
Answers
Answer: 1/8 a gallon per day
Step-by-step explanation: 1/2 / 3 = 1/8
I don't do the PLES HELP PLES HELP ASAP stuff I just need help
I need to maintain my A in algebra
Answers
Answer:
Step-by-step explanation:
Step 1) find the rise over run
rise: 2
run: 3
Step 2) put this into slope intercept form (y=mx+b)
B is the y intercept, which is -5 in this case
final answer: y = 2/3x -5
run is 3:))))
Picture 1: is the function described by the points linear or nonlinear?
Picture 2: which table could be a partial set of values for a linear function?
Picture 3: is this function linear or nonlinear?
Picture 4: select linear or nonlinear to correctly classify each function.
Picture 5: a function is represented by values in the table. The function represented in the table is linear or is not linear.
Answers
Answer:
1) Linear
2) Top left
3) Nonlinear
4) Nonlinear
5) Linear
Step-by-step explanation:
1
There is a constant rate of change of 3. As the y changes by 3, the x changes by 1
2
The constant rate of change is 2
3
No constant rate of change
4
nonlinear The [tex]x^{2}[/tex] tells us that it will not be linear
5
linear
Can be written the in the slope intercept form
'y = -8x + 13
Can you solve this for me? Thank you! :>
Answers
Answer:
h < 40
Step-by-step explanation:
Less than is <
Greater than is >
Less than or equal to is ≤
Greater than or equal to is ≥
h < 40
help me please!!!!!!!
Answers
Answer:
Area=5+17 divided by 2x4 which equals 44 squared cm
Step-by-step explanation:
to find the area of a trapezoid you have to add the length of the top base and the bottom base divided by 2 multiplied by the height (A=base A+ base B divided by 2 times the height)
please hurry
Determine if the table shows a proportional relationship.
x 18.6 54.3 58.8
y 6.2 18.1 19.6
Yes, it is proportional because all y over x ratios are equivalent to one third.
Yes, it is proportional because all y over x ratios are equivalent to one fourth.
No, it is not proportional because 18.6 over 6.2 does not equal 18.1 over 54.3.
No, it is not proportional because 18.1 over 54.3 does not equal 58.8 over 19.6.
Answers
Which expression is equivalent to this expression?
3/4 (4h – 6)
A)3h – 9/2
B)4h + 9/2
C)3h – 6
D)4h + 6
Answers
Answer:
A) 3h-9/2
Step-by-step explanation:
3/4(4h-6)
3h-18/4
3h-9/2
———————
3/4 X 4 = 3
3h - 18/4
3h - 9/2
The width of a rectangle is 4.25x-6.5 feet and its length is 6.5x+9 feet. Find the perimeter of the rectangle.
The perimeter of the rectangle is __ feet.
Answers
Answer:
15.5y+9ft if im not wrong
Step-by-step explanation:
solve the equation for y: y + 7 = 5/4 (x + 16)
Answers
To solve the equation for y, we need to get y by itself on one side of the equation.
The first step is to get rid of the fraction on the right side of the equation by multiplying both sides by 4:
4y + 28 = x + 16
Then, we need to move the x term to the left side of the equation by subtracting x from both sides:
4y + 28 - x = 16
Then, we need to move the constant term 28 to the left side of the equation by subtracting 28 from both sides:
4y - x = -12
Finally, we have the equation in the form y = (1/4)x - 3, so the solution for y is y = (1/4)x - 3
It is important to note that in this solution we have used the distributive property and followed the order of operations to get to the final result, if you don't follow this steps you might get a different result.
STEPS FOR SOLVING LINEAR EQUATIONy+7=45(x+16)Use the distributive property to multiply 45 by x+16.y+7=45x+20Swap sides so that all variable terms are on the left hand side.45x+20=y+7Subtract 20 from both sides.45x=y+7−20Subtract 20 from 7 to get −13.45x=y−13Divide both sides of the equation by 45, which is the same as multiplying both sides by the reciprocal of the fraction.4545x=45y−13Dividing by 45 undoes the multiplication by 45.x=45y−13Divide y−13 by 45 by multiplying y−13 by the reciprocal of 45.x=54y−52SOLVE FOR Yy=45x+13
A builder buys 12.4 acres of land to develop a new set of walking trails and baseball fields.
Part A
The builder plans to use 0.25 of the land for baseball fields. How many acres will the builder use for the baseball fields?
_____ acres
Part B
The builder buys a second property that has 0.6 times as many acres as the first property. How many acres of land are in the second property?
_____ acres
Please explain your steps and what you did. Thank you!
Answers
Answer:
a. 3.1 acres
b. 7.44 acres
Step-by-step explanation:
a.
0.25 can also be written as 25%
to find 25% of 12.4 do:
25/100 * 12.4 (cross multiply by 4)
= 25/25 * 3.1
= 1 *3.1
= 3.1
b.
0.6 * 12.4
= 7.44
What is the volume of the following rectangular prism? Volume = 1 3/4 and 1/2
I NEED HELP ASAP
Answers
Answer:
Hi! I'm in middle school as well and I had this same question.
Step-by-step explanation:
I believe the answer is 7 1/3 or 7.333333
If it isn't, I am deeply sorry
In September, the demand for pizza on the boardwalk reduces, therefore Manco and Manco reduced their prices from $4 to $3.75 per slice. Describe this change as a percentage.
A-1.07% decrease
B-93.75% decrease
C-6.25% decrease
D-67% decrease
Answers
Answer:C
Step-by-step explanation:
400 / 6.25 = 25
12x-14=-2 two step eqautions
Answers
[tex]12x-14=-2[/tex]
Add 14 to both sides:
[tex]12x-14+14=-2+14[/tex]
[tex]12x=12[/tex]
Divide both sides by 12:
[tex]\dfrac{12x}{12} =\dfrac{12}{12}[/tex]
[tex]\fbox{x = 1}[/tex]
12x =12
x= 1
Julia has $80. She wants to purchase a nail paint set for $16 and earrings. She spends the rest of the money on earrings. Each pair of earrings costs $8. Write an inequality for the number of pairs of earrings she can purchase.
Answers
after the nail set is bought, she will have 80-16 left, that is 64. If each pair of earrings costs 8 dollars, then she can buy 64/8 =8: She can buy 8 pairs of earrings.
If the question is interpreted that she doesn't spend all her money, then we could say, if we must that if y=number of earrings she can buy then
Your answer is y≤8
The image of a trapezoid is shown.
An isosceles trapezoid with a short base of 3 meters and a height of 6.2 meters. The portion of the large base from the left vertex to the perpendicular is 4 meters. The portion of the large base from the right vertex to the perpendicular is 7 meters.
What is the area of the trapezoid?
20.2 m2
43.4 m2
33.4 m2
86.8 m2
Answers
Answer:
the answer is b
Step-by-step explanation:
because it is b
Mrs. Valentino spends $63 at Target. This is 45% of the money she brings to the store. How much money does Mrs. Valentino bring to Target?
Answers
Answer: $140
Step-by-step explanation:
$63/45%
÷ 9 both sides
$7/5%
x 20 both sides
$140/100%
=$140
Maggie wants to purchase 3 items that cost a total of $256. The sales tax in her area is 9.5%. What would her total cost be?
Answers
Answer: The answer is $280.32
Step-by-step explanation:
Determine P(not blue) if the spinner is spun once. 12.5% 25% 37.5% 62.5%
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Answer:
the spinner did not spin once because it only went to 62.5% around not 100% around
Step-by-step explanation:
it never reaches 100% thus it could not spin around fully
Please help. This is almost overdue :-(
Answers
I believe this is $24.25
Total paid = $296
Number of tickets = 16
Cost per tickets = 296/16 = $18.5
This cost excludes the $5.75 saved due to the group.
Original price = $18.5 + $5.75 = $24.25
Answer:
Step-by-step explanation:
I believe this is $24.25
Total paid = $296
Number of tickets = 16
Cost per tickets = 296/16 = $18.5
This cost excludes the $5.75 saved due to the group.
Original price = $18.5 + $5.75 = $24.25
In a recent year, 18.9% of all registered doctors were female. If there were 43,100 female registered doctors that year, what was the total number of registered doctors? Round your answer to the nearest whole number.
Answers
well, the total is "x", which oddly enough is the 100%.
now, we know that 18.9% of "x" is 43100, what the dickens is "x"?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 43100& 18.9 \end{array} \implies \cfrac{x}{43100}~~=~~\cfrac{100}{18.9} \\\\\\ 18.9x=4310000\implies x=\cfrac{4310000}{18.9}\implies x\approx 228042[/tex]
The whole decimal is 2,280.42328
You have to divide 43,100 by 18.9
Have a great day and good luck with math!
PLEASE HELP ME
This figure is made from a square and part of a circle. What is the perimeter of the figure to the nearest whole number unit?
A. 48
B. 54
C. 61
D. 64