Using ƒ(x) = 3x − 3 and g(x) = -x, find g(ƒ(x)).

Answer:

Speed of boat in still water = 40 mph

Rate of current = 10 mph

Step-by-step explanation:

Let the speed of boat in still water be x & let the speed of the stream be y.

Total Distance = 150 miles

Time taken to travel during upstream = 5 hrs

Speed of the boat during upstream = [tex]\frac{150}{5} = 30\:mph[/tex]

Speed of boat during upstream can be represented as [tex]x - y = 30[/tex] because the boat is moving in the opposite direction of flow of stream.

Time taken to travel during downstream = 3 hrs

Speed of boat during downstream = [tex]\frac{150}{3} = 50\:mph[/tex]

Speed of boat during downstream can be represented as [tex]x+y=50[/tex] because the boat is moving in the same direction of flow of stream.

We got a pair of linear eqns. Let  [tex]x-y=30[/tex] be eqn.1 and [tex]x+y=50[/tex] be eqn.2 . Using substitution method ,

From eqn.1 , [tex]x-y=30[/tex]

[tex]=> x = y + 30[/tex]

Putting 'x' in eqn.2 , [tex]x + y = 50[/tex]

[tex]=> y + 30 + y = 50[/tex]

[tex]=> y + y = 50-30[/tex]

[tex]=> 2y = 20[/tex]

[tex]=> y = \frac{20}{2} = 10\: mph[/tex]

Putting y in eqn.1 ,

[tex]x - 10 = 30[/tex]

[tex]=> x = 30 + 10 = 40 \:mph[/tex]

Hence , the speed of boat in still water is 40 mph and speed of stream is 10 mph

Answer:

The answer will be 10

Step-by-step explanation:

[tex]2\frac{1}{2} = \frac{5}{2}[/tex]

[tex]\frac{5}{2}[/tex] ÷ [tex]\frac{1}{4} = \frac{5}{2} x \frac{1}{4}[/tex] = [tex]\frac{20}{2}[/tex]

[tex]\frac{20}{2} =[/tex] 10 (in its simplest form)

The solution of equation 2 1/2 divided by 1/5 in simplest form is, 5

We have to given that,

To Divide 2 1/2 divided by 1/5 in simplest form.

We can simplify,

⇒ 2 1/2 ÷ 1/4

Change into improper fraction,

⇒ 5/4 ÷ 1/4

⇒ 5/4 × 4/1

⇒ 20/4

⇒ 5

Therefore, The solution of equation 2 1/2 divided by 1/5 in simplest form is, 5

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Answer:

The distance of two points  = 6 √2 = 8.4852

Step-by-step explanation:

Explanation:-

From the graph

Given points are  A ( 4,2) and B ( -2 , -4)  

The distance formula

       = [tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1})^{2} }[/tex]

( x₁ , y₁ ) = ( 4,2 )   and (x₂ , y₂) = ( -2 , -4)

The distance formula

       = [tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1})^{2} }[/tex]

     =[tex]\sqrt{(-2 -(4))^{2} + (-4 - (2))^{2} }[/tex]

  =   [tex]\sqrt{36+36} = \sqrt{72} = 6\sqrt{2}[/tex]

Final answer:-

The distance of two points  = 6 √2 = 8.4852

Answer:

Step-by-step explanation:

r4345456r776i7o7865

Answer:

[tex]\sqrt[3]{54}[/tex] = 3 [tex]\sqrt[3]{2}[/tex]

Step-by-step explanation:

this is the radical after simplifying

Answer:

13.26 * 6 =79.56

Step-by-step explanation:

Answer: is point B

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer is B

Answer:

Hi! The correct answer is 16!

Step-by-step explanation:

~Use the formula (b/2)^2 in order to create a new term to complete the square~

Answer:

the answer is option : c 16

Answer:

Step-by-step explanation:

divide the number then add on

You can solve this using the Quadratic Formula, x =.

a = 1, b = -12, c = 59

x =    Multiply 4 and 1

x =    Multiply 2 and 1

x =    Multiply -4 and 59

x =    Square 12

x =    Subtract

x =    You can't find the square root of negatives, so factor the -92 out.

x =    You can find the square of 4, so take that out.

x =    Split the expression into two parts

x =  (+ or -)    The 2 in the numerator and the 2 in the denominator cancel each other out

x =  (+ or -)    Divide 12 by 2

x = 6 (+ or -)    Now, split the solution into the plus and minus parts.

Answer:

d

Step-by-step explanation:

because it starts off under the water which is -24 then you add a positive 24 to get to sea level

Answer:

the distance above sea level after increasing  24 meters from a depth of 24 meters below sea level

Step-by-step explanation:

equation- -24m + 24m = 0

the answer to the first one is -10 (-5 - 5 - -10)

the answer to the second one is 1,000 (0 + 1,000 = 1,000)

the answer to the third one is 10 ( 20 - 10 = 10)

the answer to the fourth one is 0 (-24 + 24 = 0)

Answer:

me dont know solve it your self HAHAHHH loser

Step-by-step explanation:

Answer:

125

Step-by-step explanation:

First you want to find out the difference between Randy and Phil:

120 - 95 = 25

Then, multiply that by five:

25 × 5 = 125

Hope this helps

Answer:

Davis owns 125 cards

Step-by-step explanation:

120 - 90 =  25 x 5 = 125

Answer:

the answer is x=9

Step-by-step explanation:

Step-by-step explanation:

the answer was x=9 wish you luck on your homework and tests

Answer:

A

Step-by-step explanation:

By triangle inequality,

L < 15+6

15 < L+6

6 < L+15

Solving these, we get 9 < L < 21.

Only 10 falls within the range.

The answer is therefore 10cm i.e. A.

Answer:

3.) 65

Step-by-step explanation:

180-125=55

55+60= 115

a triangle equals 180

180-115=65

The sum of all the angles in a triangle is 180 degrees.

The value of the m∠ACR is 65°.

Option 3 is the correct answer.

The sum of all the angles in a triangle is 180 degrees.

We have,

Line RCBT and ΔABC.

From the diagram, we see that,

In ΔABC,

m∠A + m∠B + m∠C = 180 ___(1)

m∠CBT = 180

m∠CBA + m∠ABT = 180

m∠CBA + 125 = 180

m∠CBA = 180 - 125

m∠CBA = m∠B = 55 ____(2)

m∠BCR = 180

m∠BCA + m∠ACR = 180 ____(3)

From (1) and (2) we get,

m∠A + m∠B + m∠C = 180

60 + 155 + m∠C = 180

m∠C = 180 - 60 - 55

m∠C = 65 ____(4)

From (4) we get,

m∠ACR = 65

Thus,

The value of the m∠ACR is 65°.

Option 3 is the correct answer.

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Answer:

the answer is the option : D

Answer:17

Step-by-step explanation:

Answer:

y>5−2x/3

Step-by-step explanation:

The values of the given function for x=-2, 0 and 5 are -8, -2 and 13 respectively.

The given function is g(x)=3x-2.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Put x=-2 in the given function, we get

g(-2)=3(-2)-2

= -6-2

= -8

Put x=0 in the given function, we get

g(0)=3(0)-2

= -2

Put x=5 in the given function, we get

g(5)=3(5)-2

= 15-2

= 13

Therefore, the values of the given function for x=-2, 0 and 5 are -8, -2 and 13 respectively.

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Answer:

D

Divide both by 3

Step-by-step explanation:

Answer:

Jack took 10 pictures on his bike ride.

Step-by-step explanation:

Given that:

Given measurements of sides are 3 miles and 4 miles

We will find the distance of the new route by using Pythagorean theorem.

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

(3)² + (4)² = c²

9 + 16 = c²

25 = c²

c² = 25

Taking square root on both sides

[tex]\sqrt{c^2}=\sqrt{25}\\c=5[/tex]

The distance of new route = 5 miles

Picture taken per mile = 2

Picture taken on bike ride = 2*5 = 10 pictures

Hence,

Jack took 10 pictures on his bike ride.

Answer: B.

Step-by-step explanation:

Answer:

for seven cabins it should be 14.7 trees, im not sure about 3 cabins, sorry :(

Answer:

3) 6.3

7) 14.7

Step-by-step explanation:

Use ratios to solve the table

10.5/5 = x/3

cross multiply

31.5 = 5x

x = 6.3

10.5/5 = x/7

73.5 = 5x

x = 14.7

Answer:

65 but I not really to sure so A

Answer:

14‏/12‏/2019 — However, we know that the line passes through two known points with x and y coordinates. ... The equation of a curve is y = x^2 + ax + b where a and b are integers. ... x2 (or second order polynomial) graphs are symmetrical about their turning point ... Therefore, we know that the line intercepts the x-axis at (-1,0) and (5,0).

Step-by-step explanation:

Answer:

a = -4, b = 3

Step-by-step explanation:

sorry, im a bit late but hoping to help others that need the answer.

when you complete the square for a quadratic, you r answer can come in the form (x+p)^2+q.

in this form, p is the opposite of the x coordinate.

and q is the same as the y coordinate.

to get p and q from this, we find the opposite of the x coordinate and use the y coordinate we are given, and plug them into this equation.

we get: (x-2)^2+1

lets complete the equation now.

(x-2)^2 = x^2 - 4x + 4, then add the one we left out = x^2 - 4x + 5.

now our equation is in the same format as y=x^2+ax+b so we can just pull out the A and B which gives us:

A = -4

B = 5

if i am wrong please feel free to correct me, ty.

Answer:

11

Step-by-step explanation:

Don't worry I just know

Answer:

slope is -3

Step-by-step explanation:

slope formula m= rise/run= y2-y1/x2-x1

Answer:

I think x=-25

Step-by-step explanation: