Answer:
Rate of Pratap in still water is 4.5 miles/hour and rate of current is 0.5 miles/hour.
Step-by-step explanation:
Pratap Puri rowed 10 miles down a river in 2 hours, but the return trip took him 2.5 hours.
We know that, [tex]Speed = \frac{Distance}{Time}[/tex]
So, the speed of Pratap with the current will be: [tex](\frac{10}{2})miles/hour = 5[/tex] miles/hour
and the speed of Pratap against the current will be: [tex](\frac{10}{2.5})miles/hour = 4[/tex] miles/hour.
Suppose, the rate of Pratap in still water is [tex]x[/tex] and the rate of current is [tex]y[/tex].
So, the equations will be........
[tex]x+y= 5 .............................. (1)\\ \\ x-y=4 .............................. (2)[/tex]
Adding equation (1) and (2) , we will get......
[tex]2x=9\\ \\ x=\frac{9}{2}= 4.5[/tex]
Now, plugging this [tex]x=4.5[/tex] into equation (1), we will get.....
[tex]4.5+y=5\\ \\ y=5-4.5 =0.5[/tex]
Thus, Pratap can row at 4.5 miles per hour in still water and the rate of the current is 0.5 miles/hour.
Pratap's rowing speed in still water is 4.5 miles per hour, and the speed of the current is 0.5 miles per hour.
Explanation:First, we need to understand that Pratap's velocity, or speed, is the sum of his own rowing speed and the speed of the current when he rows downstream, and the difference of his speed and the current when he rows upstream. To find these speeds, we can use the formula for speed, which is distance/time.
When Pratap is rowing downstream (with the current), he covers 10 miles in 2 hours, giving a speed of 10/2 = 5 miles per hour. When rowing upstream (against the current), he covers the same distance in 2.5 hours, giving a speed of 10/2.5 = 4 miles per hour.
Now, if we add these two speeds together and divide by 2, we get the rowing speed of Pratap in still water (since half the time he gets an assist from the current, and half the time he is fighting against it). This is (5+4)/2 = 4.5 miles per hour.
The speed of the current would be the difference between Pratap's rowing speed and the overall speed when he is rowing downstream, which is 5 - 4.5 = "0.5 miles per hour".
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What is the axis of symmetry and vertex for tge function f(x)=3(x-2)
If you distribute the multiplication, your function is written as
[tex] y=f(x)=3x-6 [/tex]
Like every function in the form [tex] y = mx+q [/tex], this function represents a line. A line has no vertex and no axis of symmetry (actually, it is symmetric with respect to every perpendicular line).
find the ratio between a:b for each problem
1.) 2a=9b
2.) 6a-3b=5b
3.) a+b=3b
4.)a/5=b/7
1. 2a=9b first we will divide the both sides with parameter b and get
2(a/b)=9 now we will divide both sides with number 2 and get
a/b=9/2 => a : b = 9 : 2
2. 6a-3b=5b first we will add to both sides number (+3) and get
6a=5b+3b => 6a=8b then divide the both sides with parameter b and get
6(a/b)=8 now we will divide the both sides with number 6 and get
a/b=8/6 if we simplify the fraction we get
a/b=4/3 => a : b = 4 : 3
3. a+b=3b we will add to the both sides parameter (-b) and get
a=3b-b => a=2b then divide the both sides with parameter b and get
a/b=2 => a/b=2/1 => a : b = 2 : 1
4. a/5=b/7 first we will divide the both sides with paremeter b and get
a/(5b)=1/7 now we will multiply the both sides with number 5 and get
a/b=5/7 => a : b = 5 : 7
Good luck!!!
The ratio a:b in the four problems given are 9:2, 4:3, 2:1, and 5:7 respectively. This is achieved by isolating 'a' in each equation and simplifying the resulting expression.
Explanation:Let's find the ratio between a:b for each of the problems you've provided:
In the equation 2a = 9b, divide both sides by 2b to get a:b ratio. This gives a/b = 9/2, which simplifies to the ratio of a:b = 9:2.For the equation 6a - 3b = 5b, first add 3b to both sides to isolate 'a'. This gives 6a = 8b. Dividing by 6b, we get a/b = 8/6, which simplifies to a:b = 4:3.In the case of a + b = 3b, subtract 'b' from both sides, which gives a = 2b. The ratio of a to b is therefore a:b = 2:1.Lastly in the equation a/5 = b/7, cross-multiplication gives 7a = 5b. Dividing both sides by 7b results in a/b = 5/7, which means a:b = 5:7.Learn more about Finding ratios here:https://brainly.com/question/21138916
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(X^2-3)(x^2+3x-1) multiply the polynomials
x^2 - 3(x^2 + 3x - 1)
Distributive property.
x^4 + 3x^3 - x^2 - 3x^2 - 9x + 3
Combine like terms.
x^4 + 3x^3 - 4x^2 - 9x + 3
Factor the expression over the complex numbers.
x^2 + 20
Using complex numbers, you can have negative squares, since [tex] i^2=-1 [/tex]
So, you can find the solutions to
[tex] x^2+20=0 \iff x^2 = -20 \iff x=\pm\sqrt{-20}=\pm i \sqrt{20}=\pm 4i\sqrt{5} [/tex]
So, using the factorization [tex] (x-x_1)(x-x_2) [/tex] where [tex] x_{1,2} [/tex] are the roots of the quadratic equation, you have
[tex] x^2+20 = (x-4i\sqrt{5})(x+4i\sqrt{5})[/tex]
This expression can't be further factorized, because all terms have degree 1.
To factor the expression x^2 + 20 over the complex numbers, we can use the quadratic formula or complete the square.
Explanation:To factor the expression x^2 + 20 over the complex numbers, we can use the quadratic formula or complete the square.
Using the quadratic formula, we start by finding the values of x that satisfy the equation x^2 + 20 = 0.
The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a).
In this case, a = 1, b = 0, and c = 20. Substituting these values into the quadratic formula, we get: x = ± √-20.
Since we are factoring over the complex numbers, we can express the solution as: x = ± √20i.
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Find the amount in an account if $3,500 is invested at 6.12% compounded monthly, for 4.5 years
Answer:
4606.48 $
Step-by-step explanation:
Amount invested P = 3500 $
Rate of interest r = 6.12%
Compounding monthly
Monthly rate of interest = 6.12/12 =0.51%
Time = 4.5 years = 4.5 (12) = 54 months
Hence final amount would be
P(1+0.01r)^t
Here r = 0.51 and t = no of months = 54
Hence final amount
= 3500(1.0051)^54
= 3500(1.31613)
=4606.48 $
Thus 3500 if invested now will become 4606.48 in 4.5 years at the rate of interest of 6.12% compounding monthly.
the tax rate is 6.8%
what is the tax on $9.95
round to the nearest hundredth (explain your answer)
The tax on a $9.95 purchase with a 6.8% tax rate, rounded to the nearest hundredth, is approximately $0.68.
Explanation:To calculate the tax on a purchase, you can multiply the purchase amount by the tax rate. In this case, $9.95 is being multiplied by 6.8% (or by 0.068 as a decimal). So, the calculation would look like this: $9.95 * 0.068 = $0.6766. However, the question asks to round to the nearest hundredth. So, the final tax would be approximately $0.68.
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Mary and Joe are trying to save money for a trip this summer. Mary start with $10 and earns $10 each week mowing lawn. Joe already has $20 from birthday gifts and earns five dollars a week pulling weeds. How many weeks will it take for Mary and Joe to have the same amount saved
ANSWERS
Find out the how many weeks will it take for Mary and Joe to have the same amount saved.
To proof
Let us assume that the number of week take for Mary and Joe to have the same amount saved be x.
As given
Mary start with $10 and earns $10 each week mowing lawn.
Joe already has $20 from birthday gifts and earns five dollars a week pulling weeds.
than the equation
10 + 10x = 20 +5x
5x = 10
x = 2 weeks
therefore 2 weeks will it take for Mary and Joe to have the same amount saved.
Hence proved
what is the x-intercept of the line with this equation 8x - 1/3y = 15?
Isolate the x. Note the equal sign. What you do to one side, you do to the other. First, add 1/3y to both sides
8x - 1/3y (+1/3y) = 15 (+1/3y)
8x = 15 + 1/3y
Divide 8 from both sides
(8x)/8 = (15 + 1/3y)/8
x = 15/8 + 1/24y
x = 1/24y + 1.875
x = 1/24y + 1.875 is your answer
hope this helps
Which answer choice best describes f(x) = x - 12?
A. The relationship shows a direct linear variation with a constant variation of-12.
B. The relationship shows a direct linear variation with a constant of variation of 12.
C. The relationship shows a direct linear variation with a constant variation of 1.
D. The relationship does not show a direct linear variation.
D
a direct linear variation equation has the form f(x) = kx
f(x) = x - 12 is not in this form thus does not show a direct linear variation
What is the next term in the sequence?
2, –4, 8, –16, . . .
–24
–32
32
24
The answer is 32 Why?
Because since it's getting added by times 2 for every number the number after 16 would be 32 when doing 16 x 2 and since the last number being -16 was negative the number after it would be positive, also if you want it more straight forward the 32 cannot be negative because when you times a negative with a positive you get a positive. Hope this helps!
Locating Zeros of Polynomial Function:
Approximate the real zeros to the nearest tenth
we are given
[tex]f(x)=2x^4-x^3+x-2[/tex]
we can check each options
option-A:
-1,1
we can plug x=-1 and x=1 and check whethet f(x)=0
At x=-1:
[tex]f(-1)=2(-1)^4-(-1)^3+(-1)-2[/tex]
[tex]f(-1)=0[/tex]
At x=1:
[tex]f(1)=2(1)^4-(1)^3+(1)-2[/tex]
[tex]f(1)=0[/tex]
so, this is TRUE
option-B:
0,1
we can plug x=0 and x=1 and check whethet f(x)=0
At x=0:
[tex]f(0)=2(0)^4-(0)^3+(0)-2[/tex]
[tex]f(0)=-2[/tex]
At x=1:
[tex]f(1)=2(1)^4-(1)^3+(1)-2[/tex]
[tex]f(1)=0[/tex]
so, this is FALSE
option-C:
-2,-1
we can plug x=-2 and x=-1 and check whethet f(x)=0
At x=-2:
[tex]f(-2)=2(-2)^4-(-2)^3+(-2)-2[/tex]
[tex]f(-2)=36[/tex]
At x=-1:
[tex]f(-1)=2(-1)^4-(-1)^3+(-1)-2[/tex]
[tex]f(-1)=0[/tex]
so, this is FALSE
option-D:
-1,0
we can plug x=-1 and x=0 and check whethet f(x)=0
At x=-1:
[tex]f(-1)=2(-1)^4-(-1)^3+(-1)-2[/tex]
[tex]f(-1)=0[/tex]
At x=0:
[tex]f(0)=2(0)^4-(0)^3+(0)-2[/tex]
[tex]f(0)=-2[/tex]
so, this is FALSE
The dashed triangle is a dilation image of the solid triangle. what is the scale factor?
A. 1/4
B. 1/2**
C. 2/3
D. 2?
Will give 25 points. and brainliest.
the table shows realtionships betweeen.....
B. is the graph that fills the requirements
Graph2 with slope of 25 is the graph that shows the relationship on the table.
How to determine the graph of a set of dataTo find the equation of the line passing through points A(3, 75) and B(12, 300) follow these steps:
1. Calculate the slope m:
m = (y₂ - y₁)/x₂ - x₁)
m = (300 - 75)/(12 - 3)
m = 225/9
m = 25.
Graph2 with same slope as the calculated slope is the graph that shows the relationship on the table.
2. Use the point-slope form with one of the points (e.g., A(3, 75)
y - y₁ = m(x - x₁)
y - 75 = 25(x - 3)
3. Simplify the equation:
y - 75 = 25x - 75.
4. Isolate y
y = 25x.
So, the equation of the line passing through points A(3, 75) and B(12, 300) is y = 25x
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What is the probability that a stamp chosen at random is a commemorative or a special delivery stamp?
Definitive: 0.38
Commemorative: 0.16
Semipostal: 0.2
Airmail: 0.08
Special Delivery: 0.18
A) 0.03
B) 0.18
C) 0.16
D) 0.34
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
[tex]P(\text{ getting a commemorative stamp})=0.16[/tex]
and
[tex]P(\text{getting a special delivery stamp})=0.18[/tex]
So, we need to find,
[tex]P(\text{getting either a commemorative or a special delivery stamp})\\=P(\text{getting a commemorative stamp})+P({\text{ getting a special delivery stamp})[/tex]
(∵they are independent events .)
[tex]P(\text{getting either a commemorative or a special delivery stamp})\\=0.16+0.18\\=0.34[/tex]
So, option 'D' is correct.
3 radical 7 - radical 7
= 3
why is this incorrect?
Algebraically, you have to factor the square root of 7 to see why you're wrong:
[tex] 3\sqrt{7}-\sqrt{7} = \sqrt{7}(3-1) = 2\sqrt{7} [/tex]
Conceptually, think that any object - say an apple - represents the square root of seven.
So, you have three apples, and you take away one apple. You have two apples remaining, i.e. [tex] 2\sqrt{7} [/tex]
[tex]3\sqrt{7} - \sqrt{7}[/tex]
Let x represent [tex]\sqrt{7}[/tex], then you can rewrite the expression as 3x - x.
3x - x = 2x. Now replace "x" with [tex]\sqrt{7}[/tex] and you get 2[tex]\sqrt{7}[/tex].
The reason 3 is incorrect is because you are supposed to perform the operation (+, -, x, ÷) with the coefficients, not with the variable or radical.
What is the area of a triangle whose vertices are R(−4, 2) , S(1, 2) , and T(−5, −4) ?
Enter your answer in the box.
________ units²
That triangle has a horizontal base with y=2. The length of that base is RS=1-(-4)=1+4=5. The height of the triangle is the vertical distance from line y=2 to T(-5,-4). That height is 2-(-4)=2+4=6. The area of the triangle is base * height/2 = 5*6/2= 15
The answer is 15 units ^2
Answer:
The answer is 15 units².
Step-by-step explanation:
I am a hundred percent sure. I did the math and got it right on my test.
HELPP!!! Will give Brainliest!!!
What is the local maximum value of the function? (Round answer to the nearest thousandth.) g(x) = 3x^3 + 3x^2 - 30x + 24
Answer:
The answer is 72.578 :))
Step-by-step explanation:
I got it right in my exam
A family of 2 adults and 3 children go to a play. Admission cost $8 per adult and $5 per child what expression would show the total admission cost for the family
answer=2X8+3X5=16+15=31
Which rule describes the x-coordinates in the translation below?.
x + 0
x + 6
x – 6
x + 2
Answer:
A) x + 0
Step-by-step explanation:
In triangle ABC, the coordinates are: A(1, -1), B(1, -5) and C(4, -5)
In triangle A'B'C', the coordinates are: A(1, -5), B(1, 1) and C(4, 1)
Look at the x-coordinates in both the triangles remains the same because the triangles are reflected over x-axis, therefore, only the y-coordinate changes.
Therefore, the rule for x-coordinates = x + 0
Answer: A) x + 0
Hope this will helpful.
Thank you.
Answer:a
Step-by-step explanation:
∠C and ∠D are vertical angles with m∠C=−3x+58 and m∠D=x−2 . What is m∠D ? Enter your answer in the box
∠C and ∠D are vertical angles
so <C = <D because vertical angles are equal
Substitute
−3x + 58 = x−2
Solve for x
Subtract x from both sides
-4x + 58 = - 2
Subtract 58 from both sides
-4x = - 60
Divide both sides by -4
x = 15
<D = x−2 = 15 - 2 = 13
Answer
<D = 13°
Answer:
The measure of angle D is 13°
Step-by-step explanation:
-3x+58=x-2
+3x to each side
58=4x-2
Add 2 to each side
60=4x
Divide each side by 4
X=15
Now substitute that in:
-3(15)+58=13
(15)-2=13
The measure of angle D is 13°
What is the quadratic equation of the curve of best fit shown below
A store decreased its price on a computer by $56 to $355. What was the original price?
A. $299
B. $411
C. $301
D. $421
The original price of the computer was $411. This was found by adding the reduction amount to the final price, i.e., $355 + $56.
Explanation:This question is concerned with a simple arithmetic operation. It's provided that the price of the computer was reduced by $56 to $355. The original price should thus be the markdown plus the final price.
Performing this calculation:
Add the amount of reduction ($56) to the current price ($355).
The solution is:
$355 (final price) + $56 (reduction) = $411 (original price)
Therefore, the original price of the computer was $411
So, option D is ($411) correct .
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Bart lives 6 blocks from his grandparents. Melinda lives 8 blocks farther from her grandparents as Bart does . How many blocks does Melinda live from her grandfathers
Given that Bart and Melinda are grand children and Bart lives
6 blocks from his grand parents.
Also given that Melinda lives 8 blocks farther from her grandparents as Bart does .
This means Melinda lives 6+8 = 14 blocks from her grand father house
This question involves addition because farther as Bart does means , Melinda lives 8 +6 hence we get 14
Answer is: Melinda lives 14 blocks from her grandfathers
4/|p|+12=14.
Can you solve with the absolute value of p as a denominator?
Need help asap please! Which equation matches the graph shown?
A.Y=x^2-6x+2
B.Y=2x^2-4x+2
C.Y=x^2-2x+1
D.Y=-2x^2+4x-2
Answer:
The correct option is A.
Step-by-step explanation:
The vertex form of a parabola is
[tex]y=a(x-h)^2+k[/tex] ..... (1)
Where, (h,k) is vertex and a is a constant.
From the given graph it is clear that the vertex of the graph is (3,-7) and y-intercept is (0,2).
Substitute h=3 and k=-7 in equation (1).
[tex]y=a(x-3)^2-7[/tex]
The y-intercept is (0,2). So, substitute c=0 and y=2 in the above equation to find the value of a.
[tex]2=a(0-3)^2-7[/tex]
[tex]2+7=a(3)^2[/tex]
[tex]9=9a[/tex]
Divide both sides by 9.
[tex]1=a[/tex]
The value of a is 1.
Substitute a=1, h=3 and k=-7 in equation (1).
[tex]y=1(x-3)^2-7[/tex]
[tex]y=x^2-6x+9-7[/tex]
[tex]y=x^2-6x+2[/tex]
The equation of the parabola is [tex]y=x^2-6x+2[/tex].
Therefore the correct option is A.
1. Solve. 3(h – 4) = –1/2(24 – 6h)
2. Solve for x. ax + bx = –c
A license plate has six characters. Three characters are letters, two characters are numbers (0-9), and one character is a letter or a number. The letters and numbers can repeat. Note: there are 26 letters in the alphabet. How many different license plates can be made? Answer plates what is the probability of getting a plate with abc123 or 123abc? P(abc123 or 123abc) = answer (enter as a reduced fraction using / for the fraction bar.)
The number of different license plates that can be made is 63,273,600 and the probability of getting a plate with abc123 or 123abc is 1/2,808,000.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
A license plate has six characters. Three characters are letters, two characters are numbers (0-9), and one character is a letter or a number.
Total letters = 26
Total numbers = 10
As the repetitions are allowed.
Number of ways = 26×26×26×10×10×(26+10)
N=63,273,600 Ways
P(abc123 or 123abc) = P(abc123)+P(123abc) - P(abc123 and 123abc)
The intersection of abc123 and 123abc is zero because both license plates are not possible at a time
P(ABC123 or 123ABC)=P(ABC123)+P(123ABC)
[tex]\rm P=\dfrac{1}{26}\dfrac{1}{25}\dfrac{1}{24}\dfrac{1}{10}\dfrac{1}{9}\dfrac{1}{8} + \dfrac{1}{10}\dfrac{1}{9}\dfrac{1}{8}\dfrac{1}{26}\dfrac{1}{25}\dfrac{1}{24}[/tex]
P= 2/5616000
or
P = 1/2,808,000
Thus, the number of different license plates that can be made is 63,273,600 and the probability of getting a plate with abc123 or 123abc is 1/2,808,000.
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Given a function where one x-intercept of a parabola is (-4,0), what will be the new x-intercept if h is increased by 6?
(2, 0) would be the new x - intercept.
The equation of a parabola can be written in vertex form as:
y = a(x - h)² + k
Here, h represents the x-coordinate of the vertex. The x-intercepts of the parabola are the points where the parabola crosses the x-axis (i.e., where y = 0).
Given that one x-intercept is at (-4, 0), we know that x-intercepts are symmetrically located around the vertex. If the vertex's x-coordinate h is increased by 6, the entire parabola shifts horizontally to the right by 6 units.
Since the x-intercept is affected by the shift in the vertex:
Before the shift: one of the x-intercepts is at -4.
After the shift by h, the new x-intercept will be located 6 units to the right of the original intercept.
Therefore, the new x-intercept will be at:
-4 + 6 = 2
Which expression represents a quadratic expression in complete factored form?
A.)(2x+4)(x-3)
B.)(x-1)(3x-9)
C.)(x+4)(x-3)
D.)(x-2)+(x+3)
Answer: C
Step-by-step explanation:
A) not completely factored because 2 can be factored out of 2x + 4
B) not completely factored because 3 can be factored out of 3x - 9
C) CORRECT
D) not factors because the terms are added instead of multiplied
Thus, (x - 2) + (x + 3) is not a quadratic equation. Then A, B, and C are the quadratic equation.
What is a Quadratic equation?It is a polynomial of maximum power 2. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
Which expression represents a quadratic expression in complete factored form?A. (2x + 4)(x - 3)
On multiplying
2x² - 2x -12
B. (x - 1)(3x - 9)
On multiplying
3x² -12x + 9
C. (x + 4)(x - 3)
On multiplying
x² + x - 12
D. (x - 2) + (x + 3)
On multiplying
2x + 1
Thus, (x - 2) + (x + 3) is not a quadratic equation. Then A, B, and C are the quadratic equation.
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Analyze the diagram below and complete the instructions that follow.
Find AEB.
2x+50=7x
50 = 5x
x = 10
2(10) + 50
20 + 50
= 70 degrees