In Exercise 3, one equation relating the times Eric spends running and walking to reach the goal of covering 1600 meters is 200x + 80y=1600. Suppose Eric runs and walks for a total of 12 minutes to reach his goal.

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[tex]y=-x+5~~~~~.....(i)\\\\x-y=1~~~~~~.....(ii)\\\\\\(i)-(ii):\\\\~~~~~y-x+y=-x+5-1\\\\\implies 2y=4\\\\\implies y= \dfrac 42\\\\\implies y=2\\\\\text{Substitute y=2 in eq (ii):}\\ \\~~~~ x-2 = 1\\\\\implies x= 1+2\\\\\implies x = 3\\\\\\\text{Hence,}~~ (x,y) = (3,2)[/tex]

Answer:

See below

Step-by-step explanation:

sf = s0 + v0 t  + 1/2 at^2

        1  + (-3)t + 1/2 (.2t) t^2           ( weird acceleration value)

s =  1 -3t + .1 t^3           You will need a 't' value to determine the position

Answer:

[tex]derivative n thof \: sin2x [/tex]

Answer:

The function is C(d) = 0.69d+25.95. The equation will be 0.69(57)+2595.

for the last question 0.69d+25.95 = 57, so 0.69d = 31.05, so d is 45

The max distance you can drive with 120 dollars is 45 miles.

Answer:

7/x < 8y

Step-by-step explanation:

7/x < 8y

The student T distribution would be used since we don't know the population variance (by extension the population standard deviation).

However, if n > 30, then the student T distribution is going to look very similar to the standard normal Z distribution. It won't be a perfect match, but it'll be close enough that it's more simple to use the Z distribution. With the Z distribution, you only have one set of values and you don't have to worry about the degrees of freedom.

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"f" varies inversely with "L"}}{f=\cfrac{k}{L}}\qquad \textit{we also know that} \begin{cases} f=\stackrel{lbs}{20}\\ L=\stackrel{ft}{1.5} \end{cases} \\\\\\ 20=\cfrac{k}{1.5}\implies 30=k~\hfill \boxed{f=\cfrac{30}{L}} \\\\\\ \textit{when L = 6, what is "f"?}\qquad f=\cfrac{30}{6}\implies f=5[/tex]

Answer:

  32 pounds

Step-by-step explanation:

Pounds of potatoes can be found by multiplying pounds of onions by 5 1/3:

  (5 1/3)(6 pounds) = 32 pounds

The restaurant bought 32 pounds of potatoes.

Answer: If I did it correctly it should be 150.8

Step-by-step explanation:

The formula for the volume of a cylinder is height x π x (diameter / 2)2, where (diameter / 2) is the radius of the base (d = 2 x r), so another way to write it is height x π x radius2.

Hope this helps!

Answer:

B

Step-by-step explanation:

2/6  x  d   = 388

d = 388 x 6/2 = 1164 m

Answer:

The total distance covered in miles is B, 1164 miles.

Step-by-step explanation:

Since we know that 2/6 of his total trip distance is 388 miles we can do 388 / 2/6 = 1164. Therefore, his total trip distance is 1164 miles.

Answer:

[tex]x = 52[/tex]

Step-by-step explanation:

Step 1:  Create an expression

[tex]2x + 76 = 180[/tex]

Step 2:  Subtract 76 from both sides

[tex]2x + 76 - 76 = 180 - 76[/tex]

[tex]2x = 104[/tex]

Step 3:  Divide both sides by 2

[tex]\frac{2x}{2} = \frac{104}{2}[/tex]

[tex]x = 52[/tex]

Answer: [tex]x = 52[/tex]

Answer:

x = 52

Step-by-step explanation:

the 2 inside angles add up to 180 degress since they lie on the same side on the transversal line. so we set the eqaution up:

2x+76=180

2x=104

x=54

Answer:

x=1 y=2

Step-by-step explanation:

Isolate x for 4x -y =2: x=2+y/4

Substitute x= 2+y/4

(2+13y/4) +3y=7

simplify 2+13y/4) =7

Isolate y for 2+13y/4) =7: y=2

Forx= 2+y/4

Substitute y =2

x=2+2/4

x=1

Answer:

see explanation

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

(3, 4 ) → (3, - 4 )

(3, 1 ) → (3, - 1 )

(5, 1 ) → (5, - 1 )

Answer:

Points would be (3,-1) (5,-1) (3,-4)

Step-by-step explanation:

So its asking for a reflection on the x-axis, which means you simply take the shape and move the points to the same spot on the other side of the boldest horrizontal line, or in other words, you can just add a negative to the y variable in the points, because the rule is (x,-y).

Answer:

180

Step-by-step explanation:

This is 180 because the specific angles in a triangle will unless an irregularly shaped triangle will equal up to 180.

Answer:

it is 57

Step-by-step explanation:

Answer:

A. √57

Step-by-step explanation:

√47 would be off the number line because it's below the number 7

√65 would be past 8 but the red dot comes before the number 8

√72 would be past 8 as well and it would be past √65 but the dot is before number 8

This leaves our answer as √57 beause the square root of 57 is 7.549 (etc.) which is between the numbers 7 and 8, while also being slightly higher than 7.5 :)

Have a good day!

Answer:

It's a fraction

Step-by-step explanation:

You have to figure out the meaning of the letters and find what goes on top

Answer:

Step-by-step explanation: yes, we belive that they start young with pyromania.  They may see as something powerful

Answer:

3

Step-by-step explanation:

((7x-4)^2) - (7x-4)(7x-4) + 3

(7x-4)(7x-4) is 7x-4^2

So its (7x-4)^2 - (7x-4)^2 + 3

(7x-4)^2 cancel out.

Answer is 3

Answer:

1.33 hours(If it doesn't let you type that in, just do 1 hour for rounding purposes)

Step-by-step explanation:

First, we take the 350 gal variable and divide that by 4.39, we now get 79.73

Now, we convert that into hours(60mins per hour), so 79.73 divided by 60.

We get 1.33, which is your answer!

[tex]\text{Given that,}\\\\f(x) = \dfrac x{1- \ln (x-1)}\\\\\\f'(x)=\dfrac{(1- \ln(x-1))-x\cdot \left(0-\dfrac 1{x-1} \right)}{(1- \ln(x-1))^2}\\\\\\~~~~~~~~= \dfrac{(x-1)(1- \ln(x-1))+x}{(x-1)(1-\ln(x-1))^2}\\\\\\~~~~~~~~= \dfrac{x-x\ln(x-1)-1+\ln(x-1)+x}{(x-1)(1-\ln(x-1))^2}\\\\\\~~~~~~~~= \dfrac{2x-1-(x-1)\ln(x-1)}{(x-1)(1-\ln(x-1))^2}\\[/tex]

[tex]\text{domain f(x):} ~\{x|x > 1, x\neq e+1 \}[/tex]

Answer:

yes

Step-by-step explanation:

yes

each input (x) has exactly one output (y)

in other words

it passes the vertical line test

Answer:

1992

Step-by-step explanation:

60x38=2280

32x9=288

2280-288=1992

Hope it helps!

Answer:

trigonometric function whose value for the complement of an angle is equal to the value of a given trigonometric function of the angle itself the sine is the cofunction of the cosine.

Answer:

Step-by-step explanation:

Answer:

[tex]\large\lim_{x\rightarrow 1} f\left( x\right)=8[/tex]

Step-by-step explanation:

[tex]\lim_{x\rightarrow 1} \frac{f\left( x\right) -8}{x-1} =10[/tex]

[tex]\lim_{x\rightarrow 1} f\left( x\right) -8=10\times \lim_{x\rightarrow 1}\left( x-1\right)[/tex]

[tex]\lim_{x\rightarrow 1} f\left( x\right) -8=10\times\left( (1)-1\right)[/tex]

[tex]\lim_{x\rightarrow 1} f\left( x\right) -8=10\times\left( 0\right)=0[/tex]

[tex]\lim_{x\rightarrow 1} f\left( x\right) -8=0[/tex]

[tex]\lim_{x\rightarrow 1} f\left( x\right) =8[/tex]

Step-by-step explanation:

the length and the width of a rectangle create a right-angled triangle, with the diagonal being the Hypotenuse of that triangle (the baseline, opposite of the 90° angle).

so, we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse.

so, we have here

diagonal² = 40² + 9² = 1600 + 81 = 1681

diagonal = sqrt(1681) = 41 in