A boat can travel 28 miles up a river in the same amount of time it takes to travel 36 miles down the same river. If the current is traveling at 2 miles per hour, what is the speed of the boat in still water?

The solution to this equation is p = -6

First degree equation is a mathematical expression and sentence, which is defined by having only one unknown. Its representation is given by: ax+b=0.

— To solve this expression, let's eliminate these square root symbols:

√-5p = √24-p

-5p = 24 - p

— Move the p term before the positive sign equality, thus also shifting the 24th term:

-5p = 24 - p

-5p + p = 24

-4p = 24

— Finally, let's divide the second to the first term of this equation:

-4p = 24

p = 24 ÷ (-4)

p = -6

Therefore, the correct result of this expression will be p = -6

The velocity of a particle when it moves on a straight line along the x-axis will be V= 42 m/s

Velocity is defined as the ratio of the distance moved by the object in a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.  

Here we have a displacement function:-

F(t)=3t⁴-5t³+6t-7

So to find out the velocity we will differentiate the above equation with respect to t.

d(F(t)/dt=12t³-15t²+6

V=12t³-15t²+6

Put the value of t=2 seconds

V=12x(2x2x2)-15x(2x2)+6

V=42 meters per second

Hence the velocity of a particle when it moves on a straight line along the x-axis will be V= 42 m/s

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Answer:

[tex]\sqrt{65}[/tex]

Step-by-step explanation:

[tex]a^{2}+b^{2}=c^{2}[/tex]

[tex]4^{2} +7^{2} =c^{2}[/tex]

[tex]16+49=c^{2}[/tex]

[tex]65=c^{2}\\\sqrt{65}=c[/tex]

Answer:

65

Step-by-step explanation:

Answer:

c) 5

Step-by-step explanation:

we know that,

alpha + beta = -b/a

here, we are given that alpha is L and beta is M (roots of the quadratic equation)

therefore,

L+M = -b/a

L+M = -(-40)/8

L+M = 40/8

L+M = 5

HOPE IT HELPS!!

PLEASE MARK BRAINLIEST... ♡

Answer:

L + M are 5.122 and -0.122 so I am assuming the answer you want is 5 or c.

Step-by-step explanation:

SOME OF THIS I NEEDED TO RESEARCH BECAUSE I FEEL LIKE THIS IS OUT OF MY DEPTH BUT I GUESS HERE YOU GO

STEP

1

:

Equation at the end of step 1

 (23x2 -  40x) -  5  = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  8x2-40x-5

The first term is,  8x2  its coefficient is  8 .

The middle term is,  -40x  its coefficient is  -40 .

The last term, "the constant", is  -5

Step-1 : Multiply the coefficient of the first term by the constant   8 • -5 = -40

Step-2 : Find two factors of  -40  whose sum equals the coefficient of the middle term, which is   -40 .

     -40    +    1    =    -39

     -20    +    2    =    -18

     -10    +    4    =    -6

     -8    +    5    =    -3

     -5    +    8    =    3

     -4    +    10    =    6

     -2    +    20    =    18

     -1    +    40    =    39

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

2

:

 8x2 - 40x - 5  = 0

STEP

3

:

Parabola, Finding the Vertex:

3.1      Find the Vertex of   y = 8x2-40x-5

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 8 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C ,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   2.5000  

Plugging into the parabola formula   2.5000  for  x  we can calculate the  y -coordinate :

 y = 8.0 * 2.50 * 2.50 - 40.0 * 2.50 - 5.0

or   y = -55.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = 8x2-40x-5

Axis of Symmetry (dashed)  {x}={ 2.50}

Vertex at  {x,y} = { 2.50,-55.00}

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-0.12, 0.00}

Root 2 at  {x,y} = { 5.12, 0.00}

Solve Quadratic Equation by Completing The Square

3.2     Solving   8x2-40x-5 = 0 by Completing The Square .

Divide both sides of the equation by  8  to have 1 as the coefficient of the first term :

  x2-5x-(5/8) = 0

Add  5/8  to both side of the equation :

  x2-5x = 5/8

Now the clever bit: Take the coefficient of  x , which is  5 , divide by two, giving  5/2 , and finally square it giving  25/4

Add  25/4  to both sides of the equation :

 On the right hand side we have :

  5/8  +  25/4   The common denominator of the two fractions is  8   Adding  (5/8)+(50/8)  gives  55/8

 So adding to both sides we finally get :

  x2-5x+(25/4) = 55/8

Adding  25/4  has completed the left hand side into a perfect square :

  x2-5x+(25/4)  =

  (x-(5/2)) • (x-(5/2))  =

 (x-(5/2))2

Things which are equal to the same thing are also equal to one another. Since

  x2-5x+(25/4) = 55/8 and

  x2-5x+(25/4) = (x-(5/2))2

then, according to the law of transitivity,

  (x-(5/2))2 = 55/8

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-(5/2))2   is

  (x-(5/2))2/2 =

 (x-(5/2))1 =

  x-(5/2)

Now, applying the Square Root Principle to  Eq. #3.2.1  we get:

  x-(5/2) = √ 55/8

Add  5/2  to both sides to obtain:

  x = 5/2 + √ 55/8

Since a square root has two values, one positive and the other negative

  x2 - 5x - (5/8) = 0

  has two solutions:

 x = 5/2 + √ 55/8

  or

 x = 5/2 - √ 55/8

Note that  √ 55/8 can be written as

 √ 55  / √ 8

Solve Quadratic Equation using the Quadratic Formula

3.3     Solving    8x2-40x-5 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     8

                     B   =   -40

                     C   =   -5

Accordingly,  B2  -  4AC   =

                    1600 - (-160) =

                    1760

Applying the quadratic formula :

              40 ± √ 1760

  x  =    ——————

                     16

Can  √ 1760 be simplified ?

Yes!   The prime factorization of  1760   is

  2•2•2•2•2•5•11

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 1760   =  √ 2•2•2•2•2•5•11   =2•2•√ 110   =

               ±  4 • √ 110

 √ 110   , rounded to 4 decimal digits, is  10.4881

So now we are looking at:

          x  =  ( 40 ± 4 •  10.488 ) / 16

Two real solutions:

x =(40+√1760)/16=5/2+1/4√ 110 = 5.122

or:

x =(40-√1760)/16=5/2-1/4√ 110 = -0.122

Answer:

In the explanation

Step-by-step explanation:

AB = line segment

ABC = angle

AB = line segment

CD = intersecting line

AC = line segment

AB = line segment

EBC = angle

BC = line segment

Answer:

48, 110,140

Step-by-step explanation:

Question 1

V= 4 * (6+6)

V=4 * 12

V= 48

Question 2

V= 11 * 10

V= 110

Question 3

V= (7 + 7) *10

V= 14 * 10

V= 140

Answer: C. 30:1

Step-by-step explanation:

A ratio of x:y is created by taking the number of x and the number of y, plugging them in, and reducing if necessary. In this problem, x is orange trees and y is cherry trees. There are 30 orange trees and only 1 cherry tree, so the ratio is 30:1. It cannot be reduced.

Answer:

864 ft3

Step-by-step explanation:

length = 12 ft

width = 8 ft

depth = 9 ft

Volume = ? = length * width * depth

The relative frequency table is:

Class         Frequency  Relative frequency

40 - 50         4                     0.1

50 - 60          6                     0.15

60 - 70           11                     0.18

70 - 80            9                     0.23

80 - 90              7                    0.18

90 - 100             3                   0.08

The relative frequency measures how often a value appears relative to the sum of the total values. The class width is 10. The class width is the difference between the upper and lower boundary (e.g. 100 - 90).

Frequency is the number of times the numbers in the class interval appear in the data set. Relative frequency is the frequency of a class interval divided by the total frequency of the data set.

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Using algebraic expressions, the value of x in the diagram given is calculated as: x = 4

An algebraic equation is an equation that has an unknown variable (i.e. x) and digits, which can be used to solve a problem.

Algebraic expression for Mat A is: 4x + 3

Algebraic expression for Mat B is: 2x + 11

We would have the following algebraic equation:

4x + 3 = 2x = 11

Solve for the value of x

4x - 2x = 11 - 3

2x = 8

x = 8/2

x = 4

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3x + 2y=-10 equation 1

y=-x -4 equation 2

use the substitution method of elimination to get the answer to the question.

*using substitution

substitute equation 2 in one and we get

3x +2(-x-4)=-10

3x- 2x-8=-10

x=-2 and y=-2

Answer:

B

Answer:  Choice A

(-2, -2)

=============================================================

Explanation:

I'll use the substitution method to solve this system.

Replace y in the first equation with -x-4. This is because y = -x-4 is mentioned in the second equation.

So,

3x + 2y = -10

3x + 2( y ) = -10

3x + 2( -x-4 ) = -10 .... substitution

3x - 2x - 8 = -10

x - 8 = -10

x = -10+8

x = -2

Then use this to find y

y = -x-4

y = -(x) - 4

y = -(-2) - 4

y = 2 - 4

y = -2

We have x = -2 and y = -2 pair up together

They form the ordered pair solution (x, y) = (-2, -2)

This shows why Choice A is the answer.

Another way to see this is to graph each equation given using a tool like Desmos. It's a free graphing app.

See below.

The two lines intersect at (-2, -2) which is the solution.

Answer:

y - 5 = 3(x + 7)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = 3 and (a, b ) = (- 7, 5 ) , then

y - 5 = 3(x - (- 7) ) , that is

y - 5 = 3(x + 7)

Answer:

Cos 0 = 15/17

Step-by-step explanation:

.................................................

The supplement of each interior angle has measure

180° - 165° = 15°

and so

n = 360°/15° = 24

since the exterior angles add up to 360° and are all congruent.

Answer:

24 trillion miles. The nearest-known exoplanet is a small, probably rocky planet orbiting Proxima Centauri – the next star over from Earth. A little more than four light-years away, or 24 trillion miles.

The number of miles in 4.25 light-years will be 24.986 × 10¹² miles.

Conversion means to convert the same thing into different units.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The nearest-known exoplanet from the earth is 4.25 light-years away.

We know that 1 lightyear = 5.879 × 10¹² miles.

Then the number of miles in 4.25 light-years will be

⇒ 4.25 light-years

⇒ 4.25 × 5.879 × 10¹² miles

⇒ 24.986 × 10¹² miles

The number of miles in 4.25 light-years will be 24.986 × 10¹² miles.

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Step-by-step explanation:

(6+r)^2 = 81 + r^2

36 + 12r+ r^2 = 81 + r^2

12r = 81-36 = 45

r = 15/4 = 3.75

The value of [tex]\sin \beta[/tex] in the given triangle ABC is [tex]\dfrac{4}{5}[/tex]. Option D is correct.

Trigonometric ratios are the ratio of sides of a right angled triangle. There are 6 types of trigonometric ratios: sin, cos, tan, cosec, sec, and cot.

Sine trigonometric ratio is the ratio of perpendicular (side opposite to the angle) to the hypotenuse.

In the given figure, the side opposite to the angle [tex]\beta[/tex] is AC = 4 and the hypotenuse is AB = 5.

So, the sine ratio will be equal to,

[tex]\sin \beta=\dfrac{4}{5}[/tex]

Therefore, the value of [tex]\sin \beta[/tex] in the given triangle ABC is [tex]\dfrac{4}{5}[/tex]. Option D is correct.

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Step-by-step explanation:

because the distance from O to the other 3 points is the same. each bisector provides a line of points with equal distance to the 2 end points of its base line.

where these 2 bisectors intersect, is the point that has the same distance to all end points.

Answer:

62

Step-by-step explanation:

If B = 94, then it'd be 94 - (8*4)

94 - 32

62

The correct probability expression is (a) P(a) = three-fifths

Using the data in the complete question, we have:

n(A) = 3

n(U) = 5

The probability of A is then calculated using:

P(A) = n(A)/n(U)

This becomes

P(A) = 3/5

Hence, the correct probability expression is (a) P(a) = three-fifths

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Answer:

It’s A my friend

Step-by-step explanation:

i did the quiz

yw :)

hope i helped/ made life easier

In the observation of Rachel the experimental probability of the next car which comes in is red is 5/12 and the experimental probability of the next car which comes in is not red is 7/12.

Experimental probability of an event is the ratio of number of favorable outcome which appeared while conducting an event to the total number of outcome of that event is occurred.

Rachel found that 20 out of 48 cars that entered a parking lot were red. In this observation, the probability of a car to be red is,

[tex]P=\dfrac{20}{48}\\P=\dfrac{5}{12}[/tex]

Thus, the experimental probability that the next car that comes in is red is 5/12.

The experimental probability that the next car that comes in is not red is,

[tex]P^{-1}=1-\dfrac{5}{12}\\P^{-1}=\dfrac{12-5}{12}\\P^{-1}=\dfrac{7}{12}[/tex]

Hence, In the observation of Rachel, the experimental probability of the next car which comes in is red is 5/12 and the experimental probability of the next car which comes in is not red is 7/12.

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The greatest number of pieces will be 12 where each piece will have a different length and the length of each piece is a whole number, in inches and the remaining piece length will be 12 in(90 - 78).

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

The total length of the wood = 90 in

We have to cut it into the greatest number of pieces, where each piece will have a different length and the length of each piece is a whole number, in inches.

We can cut it like:

1 in, 2 in, 3 in, 4 in, and so on

The above shows the arithmetic sequence,

The sum of the n natural number is given by:

[tex]\rm S_n = \dfrac{n(n+1)}{2}[/tex]

[tex]\rm 90 = \dfrac{n(n+1)}{2}[/tex]

After solving, we will get a quadratic equation:

n² + n -180 = 0

After solving, we will get:

n = 12.92 and n = -13.92(term can not be negative)

n = 12 (taking whole number)

Thus, the greatest number of pieces will be 12 where each piece will have a different length and the length of each piece is a whole number, in inches and the remaining piece length will be 12 in(90 - 78).

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We will see that:

h(g(g(x)) = -78 + 24x

Which means that the statement is false.

Here we have that:

g(x) = 13 - 2x

h(x) = 6x

Now we want to find the composition of functions:

h(g(g(x))

First, let's find g(g(x)) = 13 - 2*g(x) = 13 - 2*(13 - 2x) = 13 - 26 + 4x

g(g(x)) = -13 + 4x

Now let's evaluate h(x) in that:

h(g(g(x)) = 6*g(g(x)) = 6*(-13 + 4x) = -78 + 24x

This is not equal to what we have in the question, so we conclude that the statement is false.

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Answer:

the second one

Step-by-step explanation:

Answer:

371/999

Step-by-step explanation:

all repeating numbers like that just go over nines. Two repeating? Over 99. Four repeating? Over 9,999

Answer:

-5 5/6

Step-by-step explanation:

convert 2/3 into 4/6 and when u subtract a positive from a negative u add it instead  

Answer:

It’s B

Step-by-step explanation:

they are a linear pair, when added up,the equal 180, so u would subtract 56 from 180 to get the answer.

ur wlcm :)

brainliest please?

Answer:

1/428 or 0.00233644859% chance

Step-by-step explanation:

Simply because there is only one page 45 use 428 as your denominator and then divide 1 by 428!

Answer: 1/428

Step-by-step explanation: There are 428 pages so that is the denominator. 45 is only one page so 1 is the numerator. Therefore it is a 1 in 428 chance that you would land on 45. Hope this helped!