While Brendan is vacationing with his family at the cabin, they take a motorboat on the river. The motorboat travels

18 miles per hour in still water.

1. Let w represent the speed of the river current in miles per hour. Write an expression for how fast the

motorboat is able to go downstream (with the current) Write another expression for how fast the motorboat is

able to go upstream (against the current).

2. The motorboat travels 49 miles upstream in the same time it takes to travel 77 miles downstream. What is the

speed of the current w? Use the Elimination Method to solve.

Answer:

Step-by-step explanation:

Just multiply the first equation by -1 and then add them together to find x. Should look something like

-2x - y = -7

5x + y = 9

--------------------

3x + 0 = 2

x = 2/3

Now back substitute using either equation to find y. I'll use the first:

2(2/3) + y = 7

4/3 + y = 7

y = 7 - 4/3 = 21/3 - 4/3 = 17/3

Answer:

x=2/3

y=17/3

Answer:

x=-9/4, y=-27/4. (-9/4, -27/4).

Step-by-step explanation:

y=7x+9

2y+2x=-18

----------------

simplify 2y+2x=-18 into y+x=-9

------------------

7x+9+x=-9

8x+9=-9

8x=-9-9

8x=-18

x=-18/8

simplify

x=-9/4

y=7(-9/4)+9=-63/4+9=-27/4

Answer:

Step-by-step explanation:

Ratio=3:4

so,the pair of adjacent sides are 3x,4x

Pythagorean theorem,

[tex](3x)^{2}+(4x)^{2}=20^{2}\\9x^{2}+16x^{2}=400\\\\25x^{2}=400\\\\x^{2}=\frac{400}{25}\\\\ x^{2}=16\\\\x=\sqrt{16}\\\\x=4\\\\length=4x=4*4=16cm\\\\breadth=3x=3*4=12cm\\\\Perimeter=2*(l+b)\\\\=2*(16+12)=2*28\\\\=56cm[/tex]

Answer:

srry that was my lil bro

Step-by-step explanation:

Answer:

No, it's not

Step-by-step explanation:

Lets simplify the two fractions to the lowest term

for 5/20 we'll divide the numerator and denominator by 5 (the HCF of the two)

it then becomes 1/4

For 4/12 we'll divide the numerator and denominator by 4 (the HCF of the two)

it then becomes 1/3

1/4 = 0.25

1/3 = 0.33

therefore 5/20 is not equal to 4/12

Answer:

The whole of a fraction

Answer:

it represents the whole fraction

Step-by-step explanation:

because a fraction is one number, like a decimal but stacked kindA

PLEASE MARK BRAINLIEST IF THIS HELPED

Answer: 224 students own a school sweatshirt.

Step-by-step explanation:

40% of 560 means 60% do not have one

0.60 is 60% as a decimal

560 x 0.60 = 336 students without a sweatshirt

560 - 336 = 224

Answer:

  The area is multiplied by 9.

Step-by-step explanation:

The original square has an area of ...

  A = (4 in)² = 16 in²

The larger square has an area of ...

  A = (3·4 in)² = (3²)(4²) in² = 9·16 in² . . . . . 9 times the original area

The area is multiplied by the square of the scale factor: 9.

Answer:

Step-by-step explanation:

to convert degree to radians multiply with π/180

therefore -15° =-(15 ×π/180) = -π/12

Yo sup??

To convert any given angle into radian, just multiply it with π/180

therefore

-15° =-(15 *π/180)

=-π/12

You can also solve this question by applying unitary method.

Hope this helps.

Answer:

0.

Step-by-step explanation:

Using the laws of logarithms:

log81/8 + 2log2/3 - 3log 3/2 + log 3/4​

= log 81/8 + log (2/3)^2 - log (3/2)^3 + log 3/4

= log 81/8 + log 4/9 - log 27/8 + log 3/4

= log 81/8 + log 4/9 - (log 27/8 - log 3/4)

= log (81/8 *  4/9) - log (27/8 * 4/3)

= log 9/2 - log 9/2

= 0.

Answer:

A on E2020 (x = -5, x = 2, y = 3)

Step-by-step explanation:

By looking at the equation, we know that the horizontal asymptote can be found by using [tex]y=\frac{a}{b}[/tex], where [tex]a[/tex] and [tex]b[/tex] are the leading coefficients of the variables in the numerator and denominator.

In the equation, [tex]a=3[/tex] and [tex]b=1[/tex]. So, the horizontal asymptote is 3, meaning [tex]y=3[/tex].

To find the vertical asymptotes, we must simplify the denominator by factoring. We will then get [tex](x+5)(x-2)[/tex] in the denominator. So, [tex]x=-5[/tex] and [tex]x=2[/tex].

Therefore, the answer is option A.

Answer:

A Edge 2021

I got 100%

Kara walks A. 3 2/5 miles

Step-by-step explanation:

Step 1; We must calculate how much 2/5 miles is. 2/5 miles equals 0.40 miles. Kara walks this distance times 8 1/2. 8 1/2 times equals 8.5 times. So the distance she walked is the number of loops walked × distance of each loop.

Total distance walked = Number of loops walked × distance of each loop

                                      = 8.5 loops × 0.20 miles = 3.4 miles

Step 2; In order to check which option this is, we must know what values all the given options are equal to

A. 3 2/5 miles equals 3 miles + 2/5 miles = 3 + 0.20 = 3.20 miles.

B 4/85 miles equals 0.047 miles which is lesser than one loops distance.

C. 8 9/10 miles equals 8 miles + 9/10 miles = 8 + 0.90 = 8.90 miles

D. 21 1/4 miles equals 21 miles + 1/4 miles = 21 + 0.25 = 21.25 miles.

So the answer is option A.

The width of the rectangle is 9 cm.

The length of the rectangle is 34 cm.

Step-by-step explanation:

step 1 :

Let width of the rectangle be 'x'

The length of the rectangle = 7 + 3x

step 2 :

Perimeter of the rectangle = 2 (length + width)

⇒ 86 = 2 (7 + 3x + x)

⇒ 86 = 2 (7 + 4x)

⇒ 86 = 14 + 8x

⇒ 72 = 8x

x = 72/8

x = 9

∴ The width of the rectangle is 9 cm

step 3 :

The length of the rectangle = 7 + 3x

                                              = 7 + 3(9)

                                              = 7+27 = 34 cm

Answer:

14.14 in3

Step-by-step explanation:

Answer:

the area of a circle is [tex]\pi[/tex]rsqr

32 x 32 =1024[tex]\pi[/tex]

Step-by-step explanation:

Answer:

A= 1024 x^{2}

Step-by-step explanation:

The sum of the interior angles of the polygon shown is 540 degrees

Solution:

The sum of the measures of the interior angles of a polygon with n sides is:

[tex]Sum = (n -2) \times 180[/tex]

From given figure in question,

Number of sides in polygon = 5 ( which is a pentagon )

Therefore,

n = 5

Thus the sum of measures of interior angles is:

[tex]Sum = (5-2) \times 180\\\\Sum = 3 \times 180\\\\Sum = 540[/tex]

Thus the sum of the interior angles of the polygon shown is 540 degrees

Answer:

[tex]Equation\ of\ line:\ y=\frac{1}{2}x-10[/tex]

Step-by-step explanation:

[tex]Let\ the\ required\ equation\ is\ y=mx+c\\\\where\ m\ is\ the\ slope\ of\ the\ equation\ and\ c\ is\ y-intercept\\\\It\ is\ parallel\ to\ the\ equation\ y=\frac{1}{2}x+3\\\\Hence\ slope\ of\ these\ two\ lines\ will\ be\ same.\\\\Slope\ of\ y=\frac{1}{2}x+3\ is\ \frac{1}{2}\\\\Hence\ slope\ of\ y=mx+c\ is\ \frac{1}{2}\Rightarrow m=\frac{1}{2}\\\\Equation:y=\frac{1}{2}x+c\\\\Line\ passes\ through\ (10,-5).\ Hence\ this\ point\ satisfies\ the\ equation\ of\ line.\\\\-5=\frac{1}{2}\times 10+c[/tex]

[tex]-5=-5+c\\\\c=-10[/tex]

[tex]Equation\ of\ line:\ y=\frac{1}{2}x-10[/tex]

Answer:

The correct option is the last option d.) y = negative 3 plus-or-minus StartRoot 5 x + seven-halves EndRoot

Step-by-step explanation:

the given equation is [tex]5y + 4 =(x+3)^{2} + \frac{1}{2}[/tex]

Therefore we can write [tex]5y\hspace{0.1cm} = (x+3)^{2} + \frac{1}{2} - 4 \hspace{0.3cm} \Rightarrow \hspace{0.2cm} 5y = (x+3)^{2} - \frac{7}{2} \hspace{0.3cm} \Rightarrow \hspace{0.3cm} y = \frac{(x+3)^{2}}{5} - \frac{7}{10}[/tex]

To find the inverse of the above function let us replace x with y and y with x.

Therefore we get

[tex]x = \frac{(y+3)^{2}}{5} - \frac{7}{10}[/tex]

Now we write the above equation with only y on the Left hand side and we will obtain the inverse of the given function

[tex]y = \pm \sqrt{5 (x + \frac{7}{10} )} \hspace{0.1cm} - \hspace{0.1cm} 3 \hspace{0.1cm} \Rightarrow\hspace{0.1cm} y = \pm \sqrt{5x + \frac{7}{2} } - \hspace{0.1cm} 3 \hspace{0.1cm}[/tex]

Therefore the correct option is the last option d.) y = negative 3 plus-or-minus StartRoot 5 x + seven-halves EndRoot , [tex]y = \pm \sqrt{5x + \frac{7}{2} } - \hspace{0.1cm} 3 \hspace{0.1cm}[/tex]

Answer:

y = negative 3 plus-or-minus StartRoot 5 x + seven-halves EndRoot

Step-by-step explanation:

Answer:

x-6

Step-by-step explanation:

Answer:

x - 30

Step-by-step explanation:

[tex]3(x - 6) + (4x + 12) - 6x \\ 3x - 18 + 4x + 12 - 6x \\ 3x + 4x - 6x - 18 - 12 \\ x - 30[/tex]

Answer:

A(x1,y1) and B(x2,y2)

Step-by-step explanation:

you take two points your start and your stop and put them into the equations and solve

Answer:

Step-by-step explanation:

I would be happy to answer them but I do not see the 3 questions.

Answer:

m<B=m<K=100

m<A=m<J=133

m<L=m<C=41

m<M=m<D=86

Step-by-step explanation:

Since [tex]ABCD\cong JKLM[/tex], the corresponding angles are congruent.

This implies that:

[tex]m\angle A=133=m\angle J[/tex]

m<L=41=m<C

m<M=86=m<D

The sum of angles in a quadrilateral is 360 degrees.

m<B+133+41+86=360

m<B+260=360

m<B=360-260

m<B=m<K=100

Answer: You're given one leg. Because you know both legs are equal, you know the length of both the legs.

Step-by-step explanation:

You're given the hypotenuse. Divide the hypotenuse by the square root of 2 to find the legs (which are equal).

Answer:

55m+63

Step-by-step explanation:

6m+7(7m+9)

6m+49m+63

55m+63

Answer:

W= -2

Step-by-step explanation:

Simply the expression: 9(w – 4) – 7w = 5(3w – 2)

First step: 9w -36-7w = 15w-10

Second step: 2w-36=15w-10

Third step:-36+10=15w-2w

Fourth step:-26=13w

Fifth step: w=[tex]\frac{-26}{13}[/tex]

Six step: w=-2

Answer:

-2=w

Step-by-step explanation:

9(w-4) - 7w= 5(3w-2)

9w-36-7w= 15w - 10

2w-36=15w-10

- 2w      -2w

-36=13w-10

+10         +10

-26= 13w

-2=w

Answer:

1655

Step-by-step explanation:

Note the common difference d between consecutive terms of the sequence

d = - 1 - (- 4) = 2 - (- 1) = 5 - 2 = 8 - 5 = 3

This indicates the sequence is arithmetic with sum to n terms

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

Here a₁ = - 4, d = 3 and n = 90, thus

[tex]S_{90}[/tex] = [tex]\frac{90}{2}[/tex] [ (2 × - 4) + (89 × 3) ] = 45(- 8 + 267) = 45 × 259 = 1655

Answer:D

Step-by-step explanation:

It will take them 6 hours to travel 300 miles. How I got my answer: 160 divided by 3.2 = 50 miles per hour, 300 divided by 50 = 6 hours. Hope I could help! :D

Answer:

t = 6hrs

Step-by-step explanation:

Speed = distance/time

Speed at 160miles in 3.2hrs will be = 160/3.2= 50

At the constant speed of 50, time taken to travel 300miles

Is speed = distance / time

50 =300/t

Cross multiply

50t =300

Divide both sides by 50

t = 300/50

t = 6hrs

Answer:

[tex]E(p)=51,450p+346,920[/tex]

Step-by-step explanation:

The function

[tex]m(p) = 175p + 1,180[/tex]

gives the mass of the car as a function of the number of passengers in it.

And the function

[tex]E(m) = 9.8m*h[/tex]

gives the potential energy of the car as a function of the car's mass.

Now if the height of the ramp is 30 meters, we have

[tex]E(m) =9.8m*(30)[/tex]

[tex]E(m) =294m[/tex]

And to find the potential energy as a function of the number of passengers, we just substitute [tex]m(p)[/tex] into [tex]E(m)[/tex] to get:

[tex]E(m(p))=294(175p+1180)[/tex]

[tex]\boxed{ E(p)=51,450p+346,920}[/tex]

which gives the potential energy as a function of the number of passengers.

Answer:

its A on edge2021

Step-by-step explanation:

Answer:

Angles: 40.9°, 99.05°, 40.05°

Step-by-step explanation:

Triangles

When we are given the lengths of the 3 sides of a triangle, we can easily compute all the internal angles by using the cosine's law or formula. Being x,y and z the sides of a triangle, and \alpha, \beta , \gamma the three opposite angles respectively, then

[tex]x^2=y^2+z^2-2yzcos\alpha[/tex]

[tex]y^2=x^2+z^2-2xzcos\beta[/tex]

[tex]z^2=x^2+y^2-2xycos\gamma[/tex]

We have x=5.9, y=8.9, z=5.8, then from

[tex]x^2=y^2+z^2-2yzcos\alpha[/tex]

We solve for [tex]\alpha[/tex]

[tex]\displaystyle cos\alpha=\frac{y^2+z^2-x^2}{2yz}[/tex]

[tex]\displaystyle cos\alpha=\frac{8.9^2+5.8^2-5.9^2}{2\times 8.9\times 5.8}[/tex]

[tex]cos \alpha=0.756[/tex]

[tex]\alpha=40.9 ^o[/tex]

Similarly

[tex]\displaystyle cos\beta=\frac{x^2+z^2-y^2}{2xz}[/tex]

[tex]\displaystyle cos\beta=\frac{5.9^2+5.8^2-8.9^2}{2\times 5.9\times 5.8}[/tex]

[tex]cos\beta=-0.157[/tex]

[tex]\beta=99.05^o[/tex]

Finally

[tex]\displaystyle cos\gamma=\frac{5.9^2+8.9^2-5.8^2}{2\times 5.9\times 8.9}[/tex]

[tex]cos\gamma=0.765[/tex]

[tex]\gamma=40.05^o[/tex]

Answer:

Answer is D

Step-by-step explanation:

Answer:

(sqrt(5))/4

Step-by-step explanation:

Simplify the following:

sqrt(5/16)

sqrt(5/16) = (sqrt(5))/(sqrt(16)):

(sqrt(5))/(sqrt(16))

sqrt(16) = sqrt(2^4) = 2^2:

(sqrt(5))/(2^2)

2^2 = 4:

Answer: (sqrt(5))/4