In his motorboat, Bill Ruhberg travels upstream at top speed to his favorite fishing spot, a distance of 264 mi, in 6 hr. Returning, he finds that the trip downstream, still at top speed, takes only 5.5 hr. Find the rate of Bill's boat and the speed of the current. Let x = the rate of the boat in still water and y = the rate of the current.
Answer:
The values are [tex]x = 46 miles /hr [/tex]
[tex]y = 4 \ miles / hr[/tex]
Step-by-step explanation:
From the question we are told that
The distance covered is d = 264 miles
The time taken is [tex]t_1 = 6 hours[/tex]
The time taken for the return trip is [tex]t_2 = 5.5 \ hours[/tex]
Generally during the trip toward fishing spot , the velocity is mathematically represented as
[tex]v_t = \frac{d}{t_1 } = x - y[/tex]
=> [tex]v_t = \frac{264}{6 } = x - y[/tex]
=> [tex]x - y = 44 \cdots 1 [/tex]
Generally during the return trip , the velocity is mathematically represented as
[tex]v_r = \frac{d}{t_2} = x+ y[/tex]
=> [tex]v_r = \frac{264}{5.5} = x+ y[/tex]
=> [tex]48 = x+ y\cdots 2[/tex]
add equation 1 and 2
[tex]2x = 92[/tex]
=> [tex]x = 46 miles /hr [/tex]
substituting this into equation 1
[tex] 46 - y = 44 \cdots 1 [/tex]
=> [tex]y = 4 \ miles / hr[/tex]
Ryan and his brother are at a carnival. They separate from each other at the ferris wheel at 1:00 PM, and they agree that they will each meet back at the ferris wheel from time to time to see whether the other is ready to leave. Ryan checks the ferris wheel every 15 minutes. His brother checks in every 24 minutes. At what time will they meet at the ferris wheel again. (Hint: Don't forget you're looking for a time)
Answer:
3:00pmStep-by-step explanation:
The idea hear is to find the least common multiples of 15 and 24
Given that they separated at exactly 1:00pm
the multiples are
15= 15,30,45,60,75,90,105,120
24= 24, 48,72,96,120
the multiples common is 120
Therefore they will meet in 120minute, which is 2 hours time \
hence the time will be 3:00pm
What is the slope of a line perpendicular to the line whose equation is
6x - 5y = -40. Fully reduce your answer.
Answer:
Slope = - 5/6
Step-by-step explanation:
Step 1:
y = mx + b Slope Intercept Form
Step 2:
6x - 5y = - 40 Equation
Step 3:
- 5y = - 6x - 40 Subtract 6x on both sides
Step 4:
y = 5/6x - 80 Divide 5 on both sides
Step 5:
m = Slope
Answer:
Slope = - 5/6
Hope This Helps :)
3y + 8 = I 7
Also can you show me the written steps?
which polynomial function has zeros when x= -2, 3/4, 5
Answer: f(x)=(x+2)(4x-3)(x-5)
Step-by-step explanation:
Alg2.2.5 practice 2
Polynomial function has zeros when x=[tex]-2, \frac{3}{4} , 5[/tex] is
[tex]4x^3-15x^2-31x+30[/tex]
Given :
polynomial function has zeros when x= -2, 3/4, 5
Lets write the zeros in factor form
If 'a' is a zero , then factor is (x-a)
The given zeros are [tex]-2, \frac{3}{4} , 5[/tex]
lets write all the three zeros in factor form
[tex](x-(-2)) (x-\frac{3}{4})(x-5)\\(x+2)(4x-3)(x-5)[/tex]
Now multiply the parenthesis to get the polynomial
[tex]\left(x+2\right)\left(4x-3\right)\left(x-5\right)\\\left(4x^2+5x-6\right)\left(x-5\right)\\4x^2x+4x^2\left(-5\right)+5xx+5x\left(-5\right)-6x-6\left(-5\right)\\combine \; like \; terms\\4x^3-15x^2-31x+30[/tex]
polynomial function has zeros when x= -2, 3/4, 5 is
[tex]4x^3-15x^2-31x+30[/tex]
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What is P in 3 +
p=8
Btw thanks for the help ❤️
Answer:
5
Step-by-step explanation:
find the equation of the line shown
how do you do this ?
Answer:
y=1/2x+0.5
Step-by-step explanation:
The slope is 1/2, which you can see by looking at the change of y/x. The y intercept is 0.5, which can be seen on the y axis.
Which points lie on the line y= -1/2x +4?
A) (-2,5) and (2,3)
B) (0,6) and (1,4)
C) (-2,5) and (4,3)
D) (-2,3) and (0,2)
Which answer choice is the equation of a line that passes through the points (1.-3) and (-1,3)? A) y = -1/3
B) -3y = x + 1
C) y = 3x
4) 3x + y = 0
Question #1
first, you need to find the slope. Use the formula: m=(y₂-y₁)/(X₂-X₁). Plug in x and y values. once you have found the slope, use point-slope form;
(y-y₁)=m(x-x₁). Again, plug in x and y values. Simplify the equation. Do that with the coordinate pairs, to see which one matches y=-1/2x+4. The answer though is A, (-2,5) and (2,3).
Question #2
Do the same thing, find the slope using the formula, and then use point-slope form. After that, find the matching equation and that's the answer. I am confused though because the right equation would be [tex]y=-3x[/tex], but that's not one of the answers.
For a school art project, Kali has 604 square tiles measuring 1 inch on each side. She plans to use the tiles to completely cover the box in the shape of a rectangular prism shown below. (FORMULA: Surface Area = 2lw + 2lh + 2wh) Which statement about Kali's tiles is true? Group of answer choices Kali needs 476 more tiles to completely cover the box. Kali needs 104 more tiles to completely cover the box. Kali will have 534 tiles left after completely covering the box. Kali will have 250 tiles left after comp
Answer:
Kali needs 104 more tiles to completely cover the box.
Step-by-step explanation:
Length of box = 20 in
Breadth of box = 6 in
Height of box= 9 in
Total surface area of box = 2lw + 2lh + 2wh
Total surface area of box = 2(20)(6) + 2(20)(9) + 2(6)(9)
Total surface area of box = 708 sq. in.
Side of tile = 1 in
Area of 1 tile = [tex]Side^2 = 1^2 = 1 sq. in[/tex]
Area of 604 tiles = 604 sq. in.
Area remain uncovered = 708 - 604 = 104 sq.in.
So, Kali needs 104 more tiles to completely cover the box.
Write the quotient as a power
Answer:
a^20
Step-by-step explanation:
a^21-a^1
a^20
Solve:
x/4 - x/8 = 5
Answer:
x=40
Step-by-step explanation:
x/4 - x/8
LCM of 4,8=8
x/4x2/2 - x/8=5
2x/8 - x/8 =5
x/8=5
transpose
x=5x8
x=40
hope this helps
please mark as brainliest
i will make you brainlliest whoever answers this right and will give you points Please help me i am having a hard time
Evaluate 14 + (-8) ÷ 2 · -3.
26
-9
-30
15
14 + (-8) / 2 x -3
Follow order of operations: divide and multiply from left to right:
-8/2 = -4 x -3 = 12
Now you have 14 + 12
The answer is 26
Answer:
26
Step-by-step explanation:
14+(-8) ÷ 2 (-3)
14+ (-4)(-3)
14+12
26
Which equation shows a proportional relationship between x and y?
y = 16
y = 7x
y=−7x−2
y = 9x + 1
The equation that shows a proportional relationship is y = 7x.
How to find the equation that is proportional?Two variables have a proportional relationship if all the ratios of the variables are equivalent.
In other words, a proportional relationship is one in which two quantities vary directly with each other.
Therefore, a proportional relationship can be represented as y = kx.
where
k = constant of proportionalitythe variables are x and yTherefore, y varies directly as x in a proportional relationship.
Hence, the equation that shows proportional relationship is y = 7x as 7 is the constant of proportionality. y and x are the variables.
learn more on proportional relationship here: brainly.com/question/20213987
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Answer:
y = 7x
Step-by-step explanation:
the proportional relationship is y = 7x as 7 is the constant of proportionality. y and x are the variables.
help asap i need this todayy
PLEASE HELP!! Brainliest to first answer
Part A: An archer shoots an arrow into the sky where the motion of the arrow can be modeled by the equation() = −5^2 + 20 + 4. Where t is time in seconds and f(t) is height in feet. Find how long it will take the arrow to hit the ground using an algebraic method. Round to the nearest tenth if necessary. Show all of your reasoning used with this algebraic method.
Part B: Using the information in Part A, find how high the arrow will go at its maximum height, and how long it takes for this to occur using an algebraic method. Show all of your reasoning used with this algebraic method. Round to the nearest tenth if necessary.
Answer:
The arrow will take 4.19 seconds to hit the ground
The arrow will go 24 feet to reach its maximum height and it takes 2 seconds to reach this height
Step-by-step explanation:
The quadratic function is f(t) = -5t² + 20t + 4, where
f(t) is the height in feet
t is the time in seconds
If the arrow hit the ground that means h(t) = 0
→ Substitute h(t) by 0 and use the quadratic formula to find t
∵ h(t) = 0
∴ 0 = -5t² + 20t + 4
→ Switch the two sides
∴ -5t² + 20t + 4 = 0
→ Multiply all terms by -1 to make the coefficient of t² positive
∴ 5t² - 20t - 4 = 0
→ The quadratic formula is [tex]t=\frac{-b+-\sqrt{b^{2}-4ac}}{2a}[/tex] , where
a is the coefficient of t²b is the coefficient of tc is the numerical term∵ a = 5, b = -20, c = -4
∴ [tex]t=\frac{-5+-\sqrt{(-20)^{2}-4(5)(-4)}}{2(5)}[/tex]
∴ [tex]t=\frac{-5+-\sqrt{400+80}}{10}[/tex]
→ Find the values of t in decimal
∴ t = 4.19 seconds OR t = -0.19 ⇒ refused because it is negative
∴ The arrow will take 4.19 seconds to hit the ground
The graph of this quadratic function is a parabola with maximum vertex (h, k), where
h = [tex]\frac{-b}{2a}[/tex]k = f(h)To find the maximum height and the time taking for this to occur find h and k where k is the maximum height and h is the time for this to occur
∵ f(t) = -5t² + 20t + 4
∵ a = -5 and b = 20
∴ h = [tex]-\frac{20}{2(-5)}=-\frac{20}{-10}=2[/tex]
∴ The time for the maximum height is 2 seconds
→ Now use it to find k
∵ k = f(h)
∴ k = f(2)
∵ f(2) = -5(2)²+ 20(2) + 4
∴ f(2) = -5(4) + 40 + 4
∴ f(2) = -20 + 40 + 4
∴ f(2) = 24
∴ k = 24
∴ The maximum height is 24 feet
The arrow will go 24 feet to reach its maximum height and it takes 2 seconds to reach this height
Evaluate the function for f(-9 if (x) = 3/5 x + 8
A. 67/5
B. -67/5
C. -13/5
D. 13/5
Answer:
D
Step-by-step explanation:
f(-9) = 3/5(-9) + 8 = 13/5
For a school fund-raiser, students sold T-shirts with the school logo for $14. PLEASE HELP!
They sold sweatshirts with the school logo for $20.
They sold 233 pieces of clothing and raised $3,748.
How many of each type of shirt did they sell at the fund-raiser?
Let x = the number of T-shirts sold.
Let y = the number of sweatshirts sold.
Answer:
The 3 problem
Step-by-step explanation:
Answer:
The answer is C) x+y = 233, 14x + 20y = 3748
Step-by-step explanation:
x(number of t-shirts sold) + y(number of sweatshirts sold) = 233 (total number of pieces of clothing sold)
14x (14 is the cost of each t-shirt and since x = number of t-shirts sold then it is 14x or 14 multiplied by number of t-shirts sold) + 20y (20 is the cost of each sweatshirt and since y = number of sweatshirts sold then it is 20y or 20 multiplied by number of sweatshirts sold) = 3748 (total of money raised)
Determine the given equation is a linear equation write yes or no. If yes, write the equation in standard form.
7n - 8m = 4 - 2m.
Use Standard form
Answer:
The equation is linear. Standard form:
7n - 6m - 4 =0
Step-by-step explanation:
Linear Equations
The linear equations are identified because all terms form a polynomial of degree 1 or zero (no variable).
The standard form of a linear equation is:
ax+by+cz+d=0
where x, y, z are the variables, and a,b,c are constants.
The equation:
7n - 8m = 4 - 2m
Is linear, both variables have an exponent of 1 and there is an independent term. Moving all terms to the left side:
7n - 8m - 4 + 2m =0
Simplifying:
7n - 6m - 4 =0
(25,-14) (-3,7)
determine the slope
What role does Geometric formulas have in our lives??
What are both of these shaded as?
Answer:
1 whole and 15/100= 1.15
Step-by-step explanation:
The first box is 1 whole, in total there are 100 squares. All u need to do is count the number of squares
Corresponding angles?
Helo im trying to pass
Answer:
Corresponding angles are
1 and 3
or 5 and 7
or 2 and 4
or 6 and 8
Step-by-step explanation:
Help me solve this problem please
Option C, a = (w - 4b )/7 is the correct answer
w = 7a + 4b
7a = w - 4b
a = (w- 4b )/7
which equation matches the graph
A.y=4/3x+6
B.y=3/4x+6
C.4y-3x=12
D.3x-4y=12
Answer:
B. y=3/4x+6
Step-by-step explanation:
tttttttttttttt
Answer: B
Step-by-step explanation: the y-intercept is always the b in the equation y=mx+b. in this case it’s 6. Then you look at the rise and the run. its 3/4 because you go up 3 units, and to the right 4 units, to get to the next coordinate point.
7. Which number is not a perfect square?
A. 81
C. 169
B. 125
D. 289
Answer:
B. 125
Step-by-step explanation:
square roots:
81 = 9
169 = 13
125 = 11.180..
289 = 17
Someone pls help me!!! (7th grade math work) will mark as Brainliest
SHOW WORK PLSSSSKSKSKS
Answer:
J. 42 = x 57 100Step-by-step explanation:
last year won 57 games
this year won 15 games
the difference is 57 - 15 = 42,
this means it drops 42 / 57 = 0.73 (100%) ≈ 73%
therefore, the percentage decrease from the given choices is: J
42 = x
57 100
choose the graph of the translated parent function f(x)=cos(x) where it is translation 3 units up
Answer:c
Step-by-step explanation:move up 3 units on the y axis and create the graph
⚠️⚠️ What’s the coordinate numbers for A and B ⚠️⚠️
PLEASEE I WANNA FINISH
Answer:
A (-2,-3) B (3,-3)
Step-by-step explanation:
I took math in high school
Answer:
The coordinate numbers are A (-2,-3) B(3,-3)
what is 5280 divided by 60
Answer:
88
Step-by-step explanation:
n-4=20
What is the answer.?
Answer:
n=24
Step-by-step explanation:
add 4 to both sides
Answer:
n =24Step-by-step explanation:
[tex]n-4=20\\\\\mathrm{Add\:}4\mathrm{\:to\:both\:sides}\\n-4+4=20+4\\\\Simplify\\\\n = 24[/tex]