Speed in still water= [tex]\sqrt{43}[/tex]miles
Let take the speed in still water be x and the speed of current in the river be y.
The speed of the current in a river= 5 miles
Let the distance be s which is 1.2 miles.
The time(t) difference is 40 minutes.
We have an equation,
[tex]\frac{s}{x-y}[/tex] - [tex]\frac{s}{x+y}[/tex] = t
[tex]\frac{1.2}{x - 5}[/tex] - [tex]\frac{1.2}{x + 5}[/tex] = [tex]\frac{40}{60}[/tex]
1.2 × 60(2 × 5) = 40([tex]x^{2}[/tex] - 25)
x =[tex]\sqrt{43}[/tex]
Therefore the speed in still water is [tex]\sqrt{43}[/tex].
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Question
What value of x makes the equation x+5=2x true?
Answer:
5
Step-by-step explanation:
5+5=2(5)
10=10
Find the perimeter of the figure below, in centimeters.
Write a potential exponential function (y= ab^x) that has a y-intercept of (0,3) and passes through the point (2,48)
Please solve and explain so that I can try and do it on my own too, thank you
A potential exponential function (y = abˣ) that has a y-intercept of (0, 3) and passes through the point (2, 48) is equal to y = 3·4ˣ
What is an exponential function?An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function can be represented by this standard formula:
y = abˣ
Next, we would solve for the value of "a" using y-intercept (0, 3):
y = abˣ
3 = ab⁰
3 = a(1)
a = 3.
Also, we would determine the value of "b" from point (2, 48):
y = abˣ
48 = 3b²
16 = b²
b = √16
b = 4.
Substituting the parameters into the standard formula, we have;
y = 3·4ˣ
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Joseph works in the soft-drink booth at every school baseball game. He earns ⅓ of the total soft drinks sales at each game. At Friday’s game,the total soft drink sales were $79.26. At Saturday’s game, the total soft drink sales were $95.70.How much did Joseph earn by working at the soft ball booth on Friday and Saturday?
Answer:
$58.32
Step-by-step explanation:
x = 1/3(79.26 + 95.70)
x = 1/3(147.96) Divide 147.96 by 3
x = 58.32
Robbie Morse has a $47,500 insurance policy. The annual premium is $987.53. Robbie pays $90.00 monthly.
Calculate the following. (Use a thousands comma where applicable.)
In twelve months, Robbie pays $___
Robbie pays $___ more monthly than he would annually.
To the nearest percent, Robbie pays ___% more by paying monthly than he would paying annually.
Answer: Robbie pay in twelve months $1080 .
$92.47 more Robbie pay and 9.36 %(Approx) Robbie pay.
Step-by-step explanation:
As given
Robbie Morse has a $47,500 insurance policy.
The annual premium is $987.53.
Robbie pays $90.00 monthly.
First find out the Robbie pay in twelve months .
Robbie pay in twelve months = 12 × 90
= $ 1080
Second find out how much more does Robbie pay .
Robbie pay extra = Robbie pay in twelve months - annual premium
= $ 1080 - $987.53
= $92.47
Therefore the $92.47 more Robbie pay .
Third find out the what percentage does Robbie pay .
Formula
Robbies pay more = $92.47
Annual premium = $987.53
Put in the above
Percentage = 9.36 % (Approx)
9.36 %(Approx) Robbie pay.
1. 20 pens cost 300 and 50 pens cost 750
a. is the cost of pens directly proportional to the number of pens
b. calculate the cost of buying 80 pens
ii.) calculate the number of pens if the cost is 1335
You want to buy a sofa that has already been marked down by $ 100 . The furniture store may add the 5% sales tax before applying the additional discount, or it may add the sales tax after applying the additional discount. Which way is better for you, the customer? How much better?
The better way for the customer to buy a sofa is to apply the Sale Tax after the discount.
Let us assume that the marked price of a sofa is $1000.
Now we will first take the sale tax and then the discount on the marked price.
Sale = 1000 × 5/100
= 50
So the price after the sale = 1000 + 50
= 1050
As the discount is $100
Therefore total is to be paid is
1050- 100
i.e., $950
Now we will calculate discount first then the sale tax.
As marked price is $1000 and discount is $100
So price after discount = $1000- $100
= $900
Now we will apply the sale tax on the discount price which is 5%
Sale price = 900 × 5/100
=45
Total price to be paid = 900 + 45
= $945
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Solve this math problem
Answer:
X = 32
Step-by-step explanation:
X/4 = 8
To solve for x, multiply each side by 4
X/4*4 = 8*4
X = 32
PLEASE ANSWER THIS AS QUICK AS U CAN.VERY QUICK PLS!
6t ÷ 9
I hope this helps!
Answer: 6t
Step-by-step explanation:
there are 6 t's so yea it's the 6th work for me -_-
what is the name of a line drawn across two parallel lines?
Answer:transversal
Step-by-step explanation:
b) Estimate the value of √97.5 + 1.96
The correct answer is 11.834.
Decimal Fraction Math refers to the mathematical expression of a fraction or mixed number where the denominator is a power of 10, such as 10, 100, or 1000, etc. Mathematical operations can be performed on fractions more easily when they are expressed in decimal form.
From 0 to 9, single-digit numerals are read exactly as they are written. However, when two numerals are involved, the left digit implies 10 times what the right digit indicates. In the number 24, that is, 4 is 4 and 2 is 20. Together, they make 24.
The rightmost digit of a three-digit number has the same meaning as the middle one, which is ten times the digit, and the leftmost digit, which is 100 times the digit.
√97.5 + 1.96
= 9.874 + 1.96
= 9874/1000 + 1960/1000
= 11834/1000
= 11.834
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Find the greatest integer that is less than the value of the logarithm. Use your calculator to check your answers.
log (1.3x10⁷)
The greatest integer that is less than the value of the logarithm log(1.3 x 10⁷) is 7.
The given logarithmic expression is log(1.3 x 10⁷)
Use the product rule of the logarithm logₐ(X.Y) = logₐ(X) + logₐ(Y), to get
log(1.3 x 10⁷)
= log(1.3) + log(10⁷)
= log(1.3) + 7 log(10) (Using the power rule of the logarithm logₐ(Xⁿ) = n logₐ(X))
= log(1.3) + 7 (Since log(10) = 1)
≈ 7.113 (approximate value)
We know that, log(1) = 0 and log(10) =1. And the logarithm is an increasing function.
So, log(1.3) is very close to 0 and strictly less than 1.
Therefore, the greatest integer that is less than the value of the logarithm log(1.3 x 10⁷) is 7.
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1537x242 multiply by multi digit
Diana and Joby wrote the following proofs to prove that vertical angles are congruent. Who is correct? Please explain why as well to get Brainly.
O Diana is correct, but Joby is not.
O Both Diana and Joby are correct.
O Neither Diana nor Joby is correct.
O Joby is correct, but Diana is not.
The proof that is correct about vertical angles being congruent is; Joby's proof
How to prove that vertical angles are congruent?Vertical angles are defined as the angles formed when two lines meet each other at a point. They are always equal to each other and as such they are congruent.
Now, from the given image, we see that four angles are formed which are; ∠1, ∠2, ∠3, ∠4
Now, according to vertical angle theorem, we can say that;
∠2 = ∠4 and ∠1 = ∠3
Thus, we can conclude that vertical angles are congruent by the vertical angle theorem
Thus, we conclude that Joby's proof is correct.
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Find an equation for the perpendicular bisector of the line segment whose endpoints
are (7,5) and (-1,9).
Check the picture below.
keeping in mind that perpendicular lines have negative reciprocal slopes, and that we also know that the line is a perpendicular bisector, namely it cuts that segment into two equal halves as you can see in the picture, so it really passes through the midpoint of that segment, so let's get the slope of that green segment
[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{7}}} \implies \cfrac{4}{-8}\implies -\cfrac{1}{2}[/tex]
so for the perpendicular bisector that'd be
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{-1}\implies 2}}[/tex]
now let's check for the midpoint of the green segment
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{7}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -1 +7}{2}~~~ ,~~~ \cfrac{ 9 +5}{2} \right) \implies \left(\cfrac{ 6 }{2}~~~ ,~~~ \cfrac{ 14 }{2} \right)\implies (3~~,~~7)[/tex]
so we're really looking for the equation of a line whose slope is 2 and that it passes through (3 , 7)
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 2}(x-\stackrel{x_1}{3}) \\\\\\ y-7=2x-6\implies {\LARGE \begin{array}{llll} y=2x+1 \end{array}}[/tex]
How do I solve these types of questions? Any hints or help will be appreciated
Step-by-step explanation:
ATTACHED ARE THE SOLUTIONS !!!!
Step-by-step explanation:
a)=
y = 70 + 41 (exterior angle is equal to sum of its opposite interior angles)
so, y = 111°
Now,
y = x + 58° ((exterior angle is equal to sum of its opposite interior angles)
or. 111° - 58° = x
so, x = 53°
b)=
x = 180° - 127° (linear pair of x is corresponding to 127)
so, x = 53°
Now,
y = 83° (y is vertically opposite to angle that is corresponding to 83)
c)= x = 47° (alternate angles)
y = 47 + 32 (exterior angle is equal to sum of its opposite interior angles)
so, y = 79°
d)= other angle = 180-45-45 = 90
Using the formula:-
sinA/a = sinB/b = sinC/c
or, sin45/3 = sin45/y
or, 1/√2/3 = 1/√2/y
or, y = 3
Now,
sinC/c = sinA/a
or, sin90/x sin45/3
or, 1/x = 1/√2/3
or, 1/x = 1/3√2
so, x = 3/√2
Complete the identities.
1+cot²θ=
Answer:
[tex]\csc ^2(\theta)[/tex]
Step-by-step explanation:
Using Pythagorean identity,
[tex]\mathrm{1+\cot ^2(x)=\csc ^2(x)}\\\mathrm{=\csc ^2(\theta)}[/tex]
Answer:
1 + cot² θ = sec² θ
Step-by-step explanation:
1 + cot²θ =
I know this identity to be true:
sin² θ + cos² θ = 1
Divide both sides by sin² θ.
sin² θ / sin² θ + cos² θ / sin² θ = 1 / sin² θ
1 + cot² θ = sec² θ
What is the best description of the relationship in the scatterplot below?
A) Positive linear association
B) Negative linear association
C) Nonlinear association
D) No association
Find the coordinate of point X such that the ratio of MX to XJ is 1:1
The coordinates of the midpoint are:
x = (A + C) / 2
y = (B + D) / 2
Where (A, B) and (C, D) are the coordinates of the points M and J.
What is the midpoint of a line?The midpoint is the middle point of a line segment and it is equidistant from both endpoints.
We have,
M_______X_______J
MX : XJ = 1 : 1
The formula for finding the coordinates of the midpoint is:
x = (a + c ) / 2
y = ( b + d ) / 2
(x, y) = coordinates of the midpoint.
Where (a, b) and (c, d) are the coordinates of the two endpoints.
We can consider,
M = (A, B)
J = (C, D)
X = (x, y)
Thus the coordinates of the midpoint X are:
x = (A + C) / 2
y = (B + D) / 2
Where (A, B) and (C, D) are the coordinates of the points M and J.
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Write each equation in logarithmic form.
5⁻³ = 1/125
The logarithmic form of 5⁻³ = 1/125 is , [tex]log_5(\frac{1}{125} ) =-3[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_aN = x[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms :
[tex]log a + log b = log a.b[/tex][tex]log a - log b = log \frac{a}{b}[/tex][tex]log a^x = x loga[/tex][tex]log_aa=1[/tex][tex]log_a1=0[/tex]According to statement,
5⁻³ = 1/125
as, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_aN = x[/tex]
Here,
a= 5, x= -3, N = 1/125
therefore logarithmic form is : [tex]log_5(\frac{1}{125} ) =-3[/tex]
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Graph the coordinates of the triangle in the coordinate plane. Multiply each coordinate by a scale factor of 3 (k=3). Then, graph the new triangle. How are the triangles related?
The two triangles are similar triangles and the graph of the triangles are attached
Graph the coordinates of the triangle in the coordinate plane.The complete question is added as an attachment
The coordinates of the triangle are given as
A (0, 3), B (3, 3) and C (3, -1)
So, we enter the above coordinates in a graphing calculator
See attachment for the graph of the triangle
Multiply each coordinate by a scale factor of 3 (k=3).
Here, we have
A' 3 * (0, 3), B' 3 * (3, 3) and C' 3 * (3, -1)
This gives
A' (0, 9), B' (9, 9) and C' (9, -3)
Next, we enter the above coordinates in a graphing calculator
See attachment for the graph of the triangle
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Create a division problem, we’re both the divisor in division are decimals. Call Sean must be a whole number greater than one.
The divisions problem are:
3234 ÷ 19.611945 ÷ 0.054068 ÷ 0.37424 ÷ 0.824629 ÷ 0.1117.9056 ÷ 1.9What are decimals?A decimal is a number that consists of a whole and a fractional part.
Given:
we have the condition as divisor in division are decimals
So, we know in division we have main two parts: Dividend and Divisor.
we have to take the divisor as decimals.
So let us take the example
4068 / 0.03
So, for solving it we can proceed as
4068 * 100 /3
= 1356 * 100
=135600
Similarly, there many like
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There are 8 players on a tennis team. The team is planning to play in a doubles tournament. How many different groups of players of 2 players can the coach make, if the position does not matter?
Answer:
I think the answer is 4 not sure though
Answer:
28 is the answer!
I got it right, look at the pic!!
is this number rational or irrational
Answer: rational
explain
WILL GIVE U BRAINLIEST NEED HELP PLEASE
Find the ratio of 5 hours to 25 minutes.
Answer:
1:12
Step-by-step explanation:
You have to convert both value to the same measurement, so you gonna find how many minutes is in 5 hours which is (300 minutes) then you put 25/300 then cancel out
Solve. Check for extraneous solutions. √3 x+7=x-1
x = 6 is the extraneous solution of the equation
The equation given is
[tex]\sqrt{3x + 7}[/tex] = x -1
To find the Extraneous solution we need to square on both sides of the equation
[tex](\sqrt{3x + 7} )^{2}[/tex] =[tex](x - 1)^{2}[/tex]
3x + 7 = [tex]x^{2}[/tex] --2x + 1
[tex]x^{2}[/tex] - 5x - 6 = 0
[tex]x^{2}[/tex] - 6x + x - 6 = 0
x(x - 6) +1(x -6) =0
(x-6)(x+1) = 0
x = -1, 6
Now we need to put the value of x in the equation
x = -1
[tex]\sqrt{(3 * -1) + 7}[/tex] = -1 -1
[tex]\sqrt{4}[/tex] = -2
2≠ -2
Now put
x = 6
[tex]\sqrt{3 * 6 + 7}[/tex] = 6 -1
[tex]\sqrt{25}[/tex] = 5
5=5
Therefore we get to know that x = -1 is the extraneous solution and x = 6 is the solution of the equation
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ASAP PLEASE HELP IF RIGHT ANSWER WILL GIVE BRAINLIEST, 10 POINTS, AND 5 STAR OVERALL!!!! IF WRONG ANSWER OR INVALID WILL REPORT, PLEASE, PLEASE, PLEASE!!
The value of y when we make y the subject of the formula in 5x - 5y = 40 will be B. y = -3x - 8
How to illustrate the information?It should be noted that an equation is simply used to show the relationship that exists between the variables that are given.
In this situation, the equation given s
is illustrated as:
-15x - 5y = 40
Divide through by -5
-3x - y = 8
Then make y the subject of the formula
y = -3x - 8
Therefore, value of y when we make y the subject of the formula in 5x - 5y = 40 will be y = -3x - 8.
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Draw the image of Quadrilateral ABCD translated -2 units horizontally and 5 units vertically. Label the image points using prime notation. (in other words Rule: (x, y) --> (x-2, y+5) )
The image of Quadrilateral ABCD after transformation is shown in graph with coordinates A' (0, 2), B' (2, 4), C' (5, 4) and D' (4, 3).
What is Transformation?
Transformation is the act or process of changing completely.
The rule of transformation is given as;
(x, y) --> (x-2, y+5)
Now, The coordinates of Quadrilateral ABCD are;
A (2, -3) , B (4, -1), C (7, -1) and D (6, -2)
Apply the rule of transformation to find the coordinates of the image of Quadrilateral ABCD as;
A' (2-2, -3+5) = (0, 2)
B' (4-2, -1+5) = (2, 4)
C' (7-2, -1+5) = (5, 4)
D' (6-2, -2+5) = (4, 3)
Hence, The coordinates of image of Quadrilateral ABCD are;
A' (0, 2), B' (2, 4), C' (5, 4) and D' (4, 3).
And, The image of Quadrilateral ABCD after transformation is shown in graph.
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Expand each logarithm.
log 4 √47/5²
The value of logarithmic expression log 4 √47/5² is log (47/25)^1/4.
By considering the given logarithmic expression
log 4 √47/5²
log 4 √47/25
log (47/25)^1/4
The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.
Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).
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