A water tank is 2/3 full. 40 litres of water are taken from the tank. The tank is now 1/2 full. How many litres does the tank hold when full?

Answer:

Note that

0.16666...is equivalent to 1/6

Step-by-step explanation:

We can use the sum of fractions to write out the decimal:

For this particular question, we can see that

0.16666...is the fraction 1/6, therefore

the given decimal

2.16666...=2+1/6=13/6

Answer: (3,4)

Step-by-step explanation:

To find the midpoint, you want to use the formula [tex]m=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]. Since we are given the two points, we can plug them in and solve.

[tex]m=(\frac{-1+7}{2} ,\frac{9+(-1)}{2} )[/tex]            [add numerator]

[tex]m=(\frac{6}{2} ,\frac{8}{2} )[/tex]                          [divide]

[tex]m=(3,4)[/tex]

Now, we know that the midpoint is (3,4).

Answer: not sure if that is a b but i beleive it is so

bh+hr=25

move all terms to the left side and set equal to 0. then set each factor equal to zero.

h= [tex]\frac{25}{b+r}[/tex]

isolate the variable by dividing each side by factors that dont

contain the variable.

r=[tex]\frac{25}{h}-b[/tex]

x=[tex]\frac{r-h}{y}[/tex]

isolate the variable by dividing each side by factors that dont

contain the variable.

h=-xy+r

solve for r by simplifieng both sides of the equation, then isolating the variable.

r=xy+h

Answer:

1A. h = 25/(b + r)

1B. r = 25/h - b

2A. h = r - xy

2B. r = xy + h

Step-by-step explanation:

1. bh + hr = 25

A. h(b + r) = 25

h = 25/(b + r)

B. h(b + r) = 25

b + r = 25/h

r = 25/h - b

2. x = (r - h)/y

A. xy = r - h

h + xy = r

h = r - xy

B. xy = r - h

r = xy + h

Answer:

c

Step-by-step explanation:

just because sorry, I'm new but please don't rate this bad but I do know the awnser

Answer: [tex]b=13/8[/tex]

Cross multiply

[tex](13)*(1)=8*b\\13=8b[/tex]

Flip the equation

[tex]8b=13[/tex]

Divide both sides by 8

[tex]8b/8=13/8\\b=13/8[/tex]

Answer:

70

Step-by-step explanation:

because 70 times 6 equals 420

Answer:

Step-by-step explanation:

x = -5

-5 < -4  and if x<-4 then  f(x) = - 2x - 8

so:

    f(-5) = - 2(-5) - 8 = 10 - 8 = 2

Answer:

-300

Step-by-step explanation:

if the whale is at the serface 0 and it goes 300ft down its -300

Answer:

-3

Step-by-step explanation:

6x take 4x equals 2x

So it'll be 2x+4=-2

Then you do - 2 take 4 which is - 6

So then it is 2x=-6

-6÷2=-3

Hope this helps you :)

Answer:

x=-3

Step-by-step explanation:

6x+4=4x-2

Subract the x on the right side on both sides

Equation should now be:

2x+4=-2

Now subtract the 4 from both sides

The equation is now:

2x=-6

Now all you have to do is divide the x on both sides

Your answer is now x=-3

Answer:

100, 110, 105

Step-by-step explanation:

Answer:

100,105,110

Step-by-step explanation:

Answer:

H stays G  -2,-4    F -5,-3  are the new points

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The rate of change in function f(x) from x = a to x = b is (f(b) - f(a))/(b - a).

rate of change = (7 - 3)/(2 - 0) = 4/2 = 2

Answer:

rate of change = 2 unit rise per 1 unit run

Step-by-step explanation:

The rate of change of two points on a graph is represented by the slope of a line connecting the two points.

here we are given the coordinates of the two points, hence we can simply apply the slope formula for a line given two points (see attached)

for points (0,3) and (2,7)

x₁ = 0, y₁ = 3, x₂ = 2, y₂ = 7

substituting these into the formula

rate of change

= slope, m

= (y₂-y₁) / (x₂-x₁)

= (7 - 3) / (2 - 0)

= 4 / 2

= 2

Answer:

AC = 23

Step-by-step explanation:

Assuming A, B, and C are on a line with B in the middle...

We know that AB + BC = AC. Travelling from A to C is the same as travelling from A to B, then B to C, as B is on the way between A and C.

Knowing this, we can set up this equation and add the 2 numbers we know:

AC = AB + BC

AC = 11 + 12

AC = 23

Answer:

$42

Step-by-step explanation:

12*3=36+6=42

Answer:

C. 51,84

Step-by-step explanation:

the volume of the triangular prism is 1/2*3.2*5.4*6

Answer:

C

Step-by-step explanation:

The volume (V) of the triangular prism is calculated as

V = Al ( A is the area of the triangular end, l is the length )

A = [tex]\frac{1}{2}[/tex] bh ( b is the base, h the perpendicular height )

Here b = 5.4 and h = 3.2 , thus

A = 0.5 × 5.4 × 3.2 = 8.64 cm² , then

V = 8.64 × 6 = 51.84 cm³ → C

Answer: Yes [tex]\angle FDE[/tex] is one possible angle name

Another name is [tex]\angle EDF[/tex]

When it comes to naming an angle this way, all we need to worry about is the vertex point. This is where the angle hinges (think of a door or a pair of scissors). In this case, the hinge or vertex point is at point D. The vertex is always the middle letter of any three-letter sequence. The order of the other two points does not matter.

This is why saying "angle FDE" is the same as "angle EDF".

Answer: 4 shirts x 3 pairs of pants x 4 ties = 4 x 3 x 4=48

so there are 48 possibilities (option 3)

Answer:

12 people like to watch football

Step-by-step explanation:

The results are that 98 like to watch basketball, 12 like to watch football, and 2 dislike both.

Total number of residents = 100

Basketball (B) = 98

Football(F) = 12

Number of residents that like basketball and football = ( B ∩ F)

2 dislike both

n ( B ∪ F) - People that dislike it = n(B) + n ( F ) - n ( B ∩ F)

100 - 2 = 98 + 12 - n ( B ∩ F)

98 = 110 - n ( B ∩ F)

n ( B ∩ F) = 110 - 98

= 12

Therefore, 12 people like both Football and Basketball

How many like to watch football?

From the above question, we can see that the total number of people that like to watch football = 12 people

Answer:

x=6

Step-by-step explanation:

A midpoint is the middle point of a line segment, therefore it is equal distances from both ends of the segment.

This means that PQ and QR have the same length. So all we have to do is set each value equal to each other, and then solve for X.

[tex]3x+14=7x-10\\3x+24=7x\\24-4x\\x=6[/tex]

Answer:

x=-0.4

Step-by-step explanation:

ok you have to visualize this line

P                         Q                           R

O---------------------O-----------------------O

        3x+14                    7x-10

so to make the equation of PR you would add PQ and QR together.

3x+14+7x-10

add your like terms

10x+4

solve for x

10x+4=0

subtract 4 from each side

10x=-4

divide both sides by 10

x=-2/5       fraction

x=-0.4       decimal

Answer:

Step-by-step explanation:

I'm just going to go out on a limb here and assume that those are a set of poorly made parenthesis. This, then, would be your equation:

[tex]x+\frac{x}{7}+\frac{1}{11}(x+\frac{x}{7})=60[/tex]

The first thing to do is distribute through the parenthesis to get:

[tex]x+\frac{x}{7}+\frac{x}{11}+\frac{x}{77}=60[/tex]

Next is to get rid of the denominators by multiplying by the LCM of 77:

[tex]77(x+\frac{x}{7}+\frac{x}{11}+\frac{x}{77}=60)[/tex] which gives you:

77x + 11x + 7x + x = 4620 and

96x = 4620 so

[tex]x=\frac{385}{8}[/tex]

Answer:

x = 35°, Angle 1 = 145°, Angle 2 = 35°

Step-by-step explanation:

In a trapezoid, the angles on the same leg are supplementary, meaning they add up to 180°. That means Angle 2 plus Angle 1 equals 180°. Therefore:

[tex](4x+5)+x=180^{\circ}\\5x+5=180^{\circ}\\5x=175^{\circ}\\x=35^{\circ}[/tex]

Therefore, x = 35°, Angle 2 = 35°, and Angle 1 =

[tex]4x-5^{\circ}\\4(35^{\circ})+5^{\circ}\\140^{\circ}+5^{\circ}=145^{\circ}[/tex]

To ensure our answers make sense, we verify they equal 180°:

[tex]145^{\circ}+35^{\circ}=180^{\circ}[/tex]

Answe

x = 35°, Angle 1 = 145°, Angle 2 = 35°

Step-by-step explanation:

Step-by-step explanation:

In a trapezoid, the angles on the same leg are supplementary, meaning they add up to 180°. That means Angle 2 plus Angle 1 equals 180°. Therefore:

Therefore, x = 35°, Angle 2 = 35°, and Angle 1 =

To ensure our answers make sense, we verify they equal 180°:

Answer:

70feet

Step-by-step explanation:

during the

1st sec it travels 28 ft

2nd sec =28-7=21ft

3rd sec= 21-7=14ft

4th sec= 14-7= 7ft

last sec=7-7=0ft, at this point the car stops.

so altogether it travels 28+21+14+7+0= 70 feet

[tex]f(0)=3(0)+1[/tex]

[tex]f(0)=1[/tex]

[tex]g(1)=\frac{4(1)+2}{3}[/tex]

[tex]g(1)=\frac{4+2}{3}[/tex]

[tex]g(1)=\frac{6}{3}[/tex]

[tex]g(1)=2[/tex]

Hope this helps.

頑張って!

Answer:

math

Step-by-step explanation:

Answer:

(no global maxima found)

Step-by-step explanation:

Find and classify the global extrema of the following function:

f(x) = 4 x^4 - 2 x^3 + x - 5

Hint: | Global extrema of f(x) can occur only at the critical points or the endpoints of the domain.

Find the critical points of f(x):

Compute the critical points of 4 x^4 - 2 x^3 + x - 5

Hint: | To find critical points, find where f'(x) is zero or where f'(x) does not exist. First, find the derivative of 4 x^4 - 2 x^3 + x - 5.

To find all critical points, first compute f'(x):

d/( dx)(4 x^4 - 2 x^3 + x - 5) = 16 x^3 - 6 x^2 + 1:

f'(x) = 16 x^3 - 6 x^2 + 1

Hint: | Find where f'(x) is zero by solving 16 x^3 - 6 x^2 + 1 = 0.

Solving 16 x^3 - 6 x^2 + 1 = 0 yields x≈-0.303504:

x = -0.303504

Hint: | Find where f'(x) = 16 x^3 - 6 x^2 + 1 does not exist.

f'(x) exists everywhere:

16 x^3 - 6 x^2 + 1 exists everywhere

Hint: | Collect results.

The only critical point of 4 x^4 - 2 x^3 + x - 5 is at x = -0.303504:

x = -0.303504

Hint: | Determine the endpoints of the domain of f(x).

The domain of 4 x^4 - 2 x^3 + x - 5 is R:

The endpoints of R are x = -∞ and ∞

Hint: | Evaluate f(x) at the critical points and at the endpoints of the domain, taking limits if necessary.

Evaluate 4 x^4 - 2 x^3 + x - 5 at x = -∞, -0.303504 and ∞:

The open endpoints of the domain are marked in gray

x | f(x)

-∞ | ∞

-0.303504 | -5.21365

∞ | ∞

Hint: | Determine the largest and smallest values that f achieves at these points.

The largest value corresponds to a global maximum, and the smallest value corresponds to a global minimum:

The open endpoints of the domain are marked in gray

x | f(x) | extrema type

-∞ | ∞ | global max

-0.303504 | -5.21365 | global min

∞ | ∞ | global max

Hint: | Finally, remove the endpoints of the domain where f(x) is not defined.

Remove the points x = -∞ and ∞ from the table

These cannot be global extrema, as the value of f(x) here is never achieved:

x | f(x) | extrema type

-0.303504 | -5.21365 | global min

Hint: | Summarize the results.

f(x) = 4 x^4 - 2 x^3 + x - 5 has one global minimum:

Answer: f(x) has a global minimum at x = -0.303504

Answer:

18

Step-by-step explanation:

9+9=18 bam solved it

Answer:

Substitute x with six in the equation and solve as normal.

Step-by-step explanation:

The format here is a bit weird, but it basically means x is six.

Answer:

p(x)=x2 - 3x + 8

p(4) =(4)2 - 3(4) + 8

= 16 - 12 + 8

= 4+8

= 12

p(-2)= (-2)2 - 3(-2) + 8

= 4+6+8

=18

Answer: 86.6ft closer to the ground.

Step-by-step explanation:

The diameter of the wheel is 200ft

Then the radius, half of the diameter, is: r = 200ft/2 = 100ft.

Initially, the seat is at the same level that the center of the wheel.

And the distance between the center of the wheel and the bottom is the radius.

Then the initial position is at an angle of 0° from the x-axis. (where the (0,0) of this axis coincides with the center of the wheel=

Now, the wheel rotates 60°. (downwards, so we actually could use -60° measuring from the positive x-axis)

And thinking in this as a triangle rectangle, where the opposite angle is 60°, we can calculate the displacement in the vertical direction as:

y = sin(-60°)*R

y = sin(-60°)*100ft = -86.6ft

So the seat is 86.6ft closer to the ground.

The seat is [tex]86.6feet[/tex] closer to the ground

The seat will be closer by the height it drops when the Ferris wheel turns downwards by [tex]60^{\circ}[/tex].

The height, and the radius of the Ferris wheel form the opposite and the hypotenuse of a [tex]60^{\circ}[/tex] right-angled triangle. Since the diameter of the Ferris wheel is 200feet, the radius will be 100feet. So we have

[tex]sin60^{\circ}=\frac{opp}{hyp}=\frac{h}{100}\\\\h=100\times sin60^{\circ}\\=100\times 0.8660\\=86.6[/tex]

So the seat is [tex]86.6feet[/tex] closer to the ground

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