What is the answer to this question?

Evelyn and Meredith were paddling at a rate of [tex]\frac{3+\sqrt{493}}{11}mph[/tex] which is equivalent to 2.29mph approximately.

Step 2: See attached picture

Step 3: In this case we only have different variables, there is the rate at which Evelyn and Meredith were paddling, the rate at which they moved when rowing upstream, the rate at which they moved when rowing downstream, the time it took them to paddle upstream and the time it took them to paddle downstream.

v = rate at which Evelyn and Meredith were paddling.

[tex]v_{up}[/tex]= velocity at which they were moving when paddling upstream.

[tex]v_{down}[/tex]= velocity at which they were moving when paddling downstreamstream.

[tex]t_{up}[/tex]= time it took them paddling upstream.

[tex]t_{down}[/tex]= time it took them paddling downstream

Se attached picture for the table.

Step 4: Building this equation will require us to combine different equations into a single one. Let's start with the equation for the final rate at which they paddled when rowing upstream.

[tex]v-2=v_{up}[/tex]

When rowing upstream, the current will drag the kayak, so we subtract it from the rate at which they were rowing.

Let's find the final rat at which they moved when rowing downstream.

[tex]v+2=v{down}[/tex]

next, the problem tells us it took them 3 hours and 40 minutes to row up and down the channel so we can convert it into just hours like this:

[tex]40min*\frac{1hr}{60min}=\frac{2}{3}hr[/tex]

[tex]3hr+\frac{2}{3}hr=\frac{11}{3}hr[/tex]

so now we can build our equation for time.

[tex]t_{up}+t_{down}=\frac{11}{3}[/tex]

We also know that the rate is built by dividing the distance over the time it took them to travel the distance, so:

[tex]v_{up}=\frac{1}{t_{up}}[/tex]

[tex]v_{down}=\frac{1}{t_{down}}[/tex]

If we solved each of those equations for their respective times, we would end up with the following:

[tex]t_{up}=\frac{1}{v_{up}}[/tex]

[tex]t_{down}=\frac{1}{v_{down}}[/tex]

so we can now combine all the equations together so we get:

[tex]t_{up}+t_{down}=\frac{11}{3}[/tex]

[tex]\frac{1}{v_{up}}+\frac{1}{v_{down}}=\frac{11}{3}[/tex]

[tex]\frac{1}{v-2}+\frac{1}{v+2}=\frac{11}{3}[/tex]

So this equation models the problem.

Step 5: We can solve this equation by multiplying everything by the LCD

In this case the LCD is:

3(v-2)(v+2)

so, when doing the respective multiplications we end up with:

[tex]\frac{3(v-2)(v+2)}{v-2}+\frac{3(v-2)(v+2)}{v+2}=\frac{11(3)(v-2)(v+2)}{3}[/tex]

We can now simplify to get:

3(v+2)+3(v-2)=11(v+2)(v-2)

We can now do the respective multiplications to get:

[tex]3v+6+3v-6=11(v^{2}-4)[/tex]

and we can further simplify:

[tex]6v=11v^{2}-44[/tex]

Step 5: So we can now solve it by using the quadratic formula, first, we need to rewrite the equation in standard form:

[tex]11v^{2}-6v-44=0[/tex]

So we can now use the quadratic formula:

[tex]v=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}[/tex]

we substitute:

[tex]v=\frac{-(-6) \pm \sqrt{(-6)^{2}-4(11)(-44)}}{2(11)}[/tex]

and simplify:

[tex]v=\frac{6 \pm \sqrt{36+1936}}{22}[/tex]

[tex]v=\frac{6 \pm \sqrt{1972}}{22}[/tex]

[tex]v=\frac{6 \pm \sqrt{4(493)}}{22}[/tex]

[tex]v=\frac{6 \pm 2\sqrt{493}}{22}[/tex]

[tex]v=\frac{3 \pm \sqrt{493}}{11}[/tex]

this gives us two possible results:

[tex]v=\frac{3 + \sqrt{493}}{11}[/tex] and [tex]v=\frac{3 - \sqrt{493}}{11}[/tex]

Step 6: We only pick the first result since it's the positive result. We don't take the second one because a negative result represents the kayak moving in the opposite direction which is not how the situation was modeled.

For further information, take a look at the following link:

https://brainly.com/question/12919292?referrer=searchResults

Answer:

80°

Step-by-step explanation:

Triangle ABC and CYZ are similar so the angles would also be same

Answer:

Luis’s, because he flipped the inequality sign when he subtracted

Step-by-step explanation:

Given:

7.2b + 6.5 > 4.8b – 8.1.

Amelia started by subtracting 7.2b from both sides to get 6.5 > –2.4b – 8.1.

Amelia:

7.2b + 6.5 - 7.2b > 4.8b – 8.1 - 7.2b

6.5 > -2.4b - 8.1

Correct

Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1.

7.2b + 6.5 - 4.8b > 4.8b – 8.1 - 4.8b

2.4b + 6.5 > -8.1

Incorrect

Shauna started by subtracting 6.5 from both sides to get 7.2b > 4.8b – 14.6

7.2b + 6.5 - 6.5 > 4.8b – 8.1 - 6.5

7.2b > 4.8b - 14.6

Correct

Clarence started by adding 8.1 to both sides to get 7.2b + 14.6 > 4.8b.

7.2b + 6.5 + 8.1 > 4.8b – 8.1 + 8.1

7.2b + 14.6 > 4.8b

Correct

Answer:

m<TSU = 65

Step-by-step explanation:

As one can see, the measure of angle (RST) is (90) degrees. This is indicated by the box around the angle. As a general rule, when there is a box around an angle, the angle measure if (90) degrees. It is also given that the measure of angle (RSU) is (25) degrees. As per the given diagram, the sum of the measures of angles (RSU) and (UST) is (RST). Therefore, one can form an equation and solve for the measure of angle (UST).

(RSU) + (UST) + (RST)

Substitute,

25 + (UST) = 90

Inverse operations,

25 + (UST) = 90

UST = 65

(<UST) is another way of naming angle (TSU).

Answer:

∠ TSU = 65°

Step-by-step explanation:

∠ RST = 90°

∠ RSU + ∠TSU = ∠ RST , that is

25° + ∠ TSU = 90° ( subtract 25° from both sides )

∠ TSU = 65°

Answer:

height ≈ 30 ft

Step-by-step explanation:

The situation is modelled by a right triangle.

let h be the height of the totem pole, then

tan50.1° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{25}[/tex] ( multiply both sides by 25 )

25 × tan50.1° = h , then

h ≈ 30 ft ( to the nearest foot )

Answer:

ok from looking at this equation we can we that every it goes 1 up and on over so

-x+2

Hope This Helps!!!

Answer:

Simplify the expression.

36a to the power of 7 then - 156a to the power of 4 then -15a to the power of3

for the to be parallel both the angle must be equal

so 7x - 20 = 3x + 20 - > 4x = 40⁰

x = 10⁰

Answer:

2

Step-by-step explanation:

→ The radius of a circle is square root the 4

2

Answer:

It's an identity

Step-by-step explanation:

The answer is an identity

I identity are composed by sin^2 and cos^2

Tan^2 can be simplified into those two sin n cos

Answer:

4:1

Step-by-step explanation:

Answer:

{x| x = -7, -6, 2, 11, 3}

Step-by-step explanation:

domain of a relation is the set of values of that act as input

so answer:-

{x| x = -7, -6, 2, 11, 3}

domain is taken as x

Answer:

x = 42.5

Step-by-step explanation:

A triangle inscribed inside of a circle using the diameter of the circle as it's hypotenuse is a right triangle ( a 90 degree triangle ) where the angle opposite of the hypotenuse is the 90 degree angle ( angle C )

Hence angle C = 90

If angle C = 2x + 5

Then 2x + 5 = 90

Notice that we just created an equation that we can use to solve for x

We now solve for x algebraically

2x + 5 = 90

Step 1 subtract 5 from both sides

2x + 5 - 5 = 90 - 5

Outcome: 2x = 85

Step 2 divide both sides by 2

2x/2 = 85/2

Outcome: x = 42.5

Answer:

A'(2,2) B'(3,4) C'(1,4) O'(Q,2)

Answer:

∆a = 1/2

Step-by-step explanation:

parabolas cross the x-axis at (-4, 0) and (6, 0)

y = a(x + 4)(x - 6)

At the y-intercept x = 0

y =  a(0 + 4)(0 - 6)

y = -24a

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

y-intercept of the first parabola is (0,–12)

-12 = -24a

a = 1/2

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

y-intercept of the second parabola is (0, -24)

-24 = -24a

a = 1

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

What is the positive difference between the a values

∆a = 1 - 1/2

∆a = 1/2

Answer:

This system of equations has no solution since the first one says:

x

2

−

y

=

8

while the second one gives us:

x

2

−

y

=

−

(

y

−

x

2

)

=

−

0

=

0

and  

8

≠

0

Step-by-step explanation:

Answer:

$843.67

Step-by-step explanation:

We can use a proportion to solve this problem:

12 : 100 = x : 896

x =(896 * 12)/100 = $107,52

896 - 107.52 = $788,48 (price of the computer after the discount)

7 : 100 = x : 788,48

x = (788,48 * 7)/100 = $55,1936

788.48 + 55,1936 = 843,6736 = $843.67 (final price)

The equation is:

3n - 3 = 2n + 19

=> 3n - 2n = 19 + 3

=> n = 22

So, the answer is 22.

Answer:

IK≅WY

Step-by-step explanation:

Answer:

a. 42

b. -12x-5

c. -60

d. -75

e. 66

f. -90

g. 144

h. -135

Answer:

cuadradas 777,2 unidades

Step-by-step explanation:

Answer:

67.7

Step-by-step explanation:

i just took the quiz

Answer:

45 x 56=

2520 and

5 x 7=35*8=280*9=2520

2520=2520

Hope This Helps!!!

60 percent

Step-by-step explanation:

Covert 3/5th into percentage so the answer will be 60.

The equation will be:

25 + d = t

where t is total money

Answer:

Step-by-step explanation:

each die has numbers 1-6 thus there are 36 (6*6) possible outcomes

a) 18 of the 36 are even = 1/2 = .5 = 50%

b) (1,2) and (2,1) are the only 3's 2/36 = 1/18 = .055

c) there are 10 combos that are LESS THAN 6 (2,3,4,5)

   10/36 = .277 = 27.7%

2 3 4 5 6 7

3 4 5 6 7 8

4 5 6 7 8 9

5 6 7 8 9 10

6 7 8 9 10 11

7 8 9 10 11 12

Answer:

B. b = 3a + 2

Step-by-step explanation:

We can write the equation in slope-intercept form as b = ma + c, where,

m = slope/rate of change

c = y-intercept/initial value

✔️Find m using any two given pair of values, say (2, 8) and (4, 14):

Rate of change (m) = change in b/change in a

m = (14 - 8)/(4 - 2)

m = 6/2

m = 3

✔️Find c by substituting (a, b) = (2, 8) and m = 3 into b = ma + c. Thus:

8 = 3(2) + c

8 = 6 + c

8 - 6 = c

2 = c

c = 2

✔️Write the equation by substituting m = 3 and c = 2 into b = ma + c. Thus:

b = 3a + 2

Answer:

(g ￮ f )(- 5) = - 6

Step-by-step explanation:

Evaluate f(- 5), then substitute the value obtained into g(x)

f(- 5) = - 2(- 5) - 7 = 10 - 7 = 3 , then

g(3) = - 4(3) + 6 = - 12 + 6 = - 6

Answer:

[tex](gof)(-5)=-6[/tex]

Step-by-step explanation:

One is given the following information;

[tex]f(x)=-2x-7\\g(x)=-4x+6[/tex]

One is asked to find the following,

[tex](g o f)(-5)[/tex]

The expression ([tex]gof[/tex]) is another way to denote ([tex]g(f(x))[/tex]), in essence, substitute function (f) into function (g) in place of parameter (x). The simplify to find the resulting function;

[tex]g(f(x))\\=-4(-2x-7)+6\\=(-4)(-2x)+(-4)(-7)+6\\=8x+28+6\\=8x+34[/tex]

One is asked to evaluate the function ([tex]gof[/tex]) for (-5). Substitute (-5) into the function and simplify to evaluate;

[tex](gof)(-5)=8x+34\\=8(-5)+34\\=-40+34\\=-6[/tex]

Answer:

Step-by-step explanation:

x is greater than minus 3. You have everything right but the graph. The arrowhead goes the other way. Around -3 is as small as x gets.

0====0====0====0====0

-3       -2      -1        O       1

O------------------------------->

Answer:

80 ft

Step-by-step explanation:

Let the height of the light house be x feet.

[tex] \therefore \: \frac{128}{8} = \frac{x}{5} \\ \\ x = \frac{128 \times 5}{8} \\ \\ x = \frac{640}{8} \\ \\ x = 80 \: feet[/tex]

Answer:

1) f(x)<x+4

f(x)>-x-3

f(x)<5

[tex]ANSWER: (-3,4)[/tex]

2)2.5>0+2

2.5<0+3

2.5<0+5

[tex]ANSWER: (0,2.5)[/tex]

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

HOPE IT HELPS

HAVE A GREAT DAY!!