Smalltown has two water filters that clean the town's drinking water. Filter A can filter up to 149.88 gallons of water per minute, and filter B
can filter up to 169.76 gallons of water per minute. About how much water can be filtered by these two filters for Smalltown in 75 minutes?
OA
23.250 gallons
ОВ.
30.000 gallons
Oc.
22,500 gallons
OD
24,000 gallons

Answer:

3√2 units

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, equilateral, scalene, obtuse, acute and right angled triangle.

In a right angled triangle, the hypotenuse is the side with the longest length. Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the square of the remaining two legs

The value of x can be gotten using Pythagoras theorem.

y² = h² + 3²   (1)

x² = h² + 3²   (2)

(3 + 3)² = x² + y² (3)

Substituting y² = h² + 3²  and x² = h² + 3² into equation 3 gives:

(3 + 3)² = (h² + 3²) + (h² + 3²)

36 = h² + h² + 9 + 9

2h² + 18 = 36

2h² = 18

h² = 9

h = 3

Put h = 3, into equation 2 to get the value of x:

x² = 3² + 3²

x² = 9 + 9 = 18

x = √18 = 3√2 units

Answer:

16. 3

17. 12 / 7

18. 24 / 5 ( or ) 4.8

Step-by-step explanation:

16.

2 / ( x - 1 ) = 1

2 = x - 1

x = 2 + 1

x = 3

17.

( x / 3 ) + ( x / 4 ) = 1

LCM ( 3, 4 ) = 12

x / 3 = 4x / 12

x / 4 = 3x / 12

( x / 3 ) + ( x / 4 ) = 1

( 4x / 12 ) + ( 3x + 12 ) = 1

( 4x + 3x ) / 12 = 1

7x / 12 = 1

7x = 12

x = 12 / 7

18.

( x / 3 ) + ( x / 2 ) = 4

LCM ( 3, 2 ) = 6

x / 3 = 2x / 6

x / 2 = 3x / 6

( x / 3 ) + ( x / 2 ) = 4

( 2x / 6 ) + ( 3x / 6 ) = 4

( 2x + 3x ) / 6 = 4

5x / 6 = 4

5x = 24

x = 24 / 5

( or )

x = 4.8

Answer

Part A: The right triangles are smiliar because If the lengths of the hypotenuse and a leg of a right triangle are proportional to the corresponding parts of another right triangle, then the triangles are similar.

Part B: 2z:2x or 2z/2x. You can write z/x as z:x. Then just multiply both sides by the same number to get an equivalent ratio. Let's multiply by 2. then the answer will be: 2z:2x or 2z/2x

Step-by-step explanation:

For the considered two right triangles, the evaluations for sub-parts of the problem are as follows:

Two triangles are similar if two corresponding angles of them are of same measure. It is because when two pairs of angles are similar, then as the third angle is fixed if two angles are fixed, thus, third angle pair also gets proved to be of same measure. This makes all three angles same and thus, those two triangles are scaled copies of each other. Thus, they're called similar.

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]

For the considered case of the specified two right angled triangles, we get the solutions to the parts given in the problem as:

Part 1: The right angled triangles have one angles as of 90 degrees. In the image given, it can be seen that the other angle is of [tex]\alpha[/tex] measures, which is also common in both the triangles.

Thus, two angle pairs in both the given triangles are of same measure. That makes both the specified triangles as a pair of similar triangles.

Part 2: The specified ratio is z/x. From the perspective of angle [tex]\alpha[/tex] , we see that z is serving as hypotenuse, and x is base, thus, the ratio z/x is sec([tex]\alpha[/tex] ) (as sec of an angle is ratio of hypotenuse to base)

Part 3: From the perspective of angle [tex]\alpha[/tex] , the perpendicular is the side 'y' and the base is side with length 'x' (we're considering first triangle here, as we can consider any one of them as both are similar).
Thus, we get tan of [tex]\alpha[/tex] as:

[tex]\tan(\alpha) = \dfrac{y}{x}[/tex]

Part 4: The values of the trigonometric ratios depend only on the angle(as they're functions of angles only) because they are ratio.

If a triangle is right angled, and has a specific angle, then whatever the side be, if that angle along with right angle is kept same, the triangles will be similar . That makes their sides a specific multiple of each other.

a side of one triangle = k times corresponding side of its similar triangle

where k is the scale factor, constant for one pair of similar triangles. Now when we will take their ratio, the value of k cancels out, leaving no difference between first triangle or second triangle, but only caring if they are similar or not(which depends on angles).

Thus, the trigonometric functions depend only on angles.

Learn more about similar triangles here:

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Answer:

Answer:

Step-by-step explanation:

Answer:

[tex]x=1\frac{2}{9} +1\frac{1}{9}y[/tex]

Step-by-step explanation:

x - 3y + 8x - 7y = 5 + 6

9x - 10y = 11

9x - 10y + 10y = 11 + 10y

9x = 11 + 10y

9x ÷ 9 = 11 + 10y ÷ 9

[tex]x=1\frac{2}{9} +1\frac{1}{9}y[/tex]

Answer:

x = -1

y = -2

Step-by-step explanation:

x - 3y = 5     ----------------(I)

8x - 7y = 6 ----------(II)

Multiply equation (I) by (-8) and then add the two equations

(I)*(-8)     -8x + 24y = -40

(II)           8x   - 7y   = 6    {Now add and x will be eliminated}

                       17y = -34     {Divide both sides by 17}

                           y = -34/17

y = -2

Plugin  y  =-2 in equation (I)

x - 3*(-2) = 5

x  + 6 = 5         {Subtract 6 from both sides}

     x = 5 - 6

x = - 1

Answer:

answer 2)  24[tex]\sqrt{5}[/tex]

Step-by-step explanation:

after the dilation pt D is (8,-32)

after the dilation pt E is (-16,16)

if you use the distance formula for these two points you get [tex]\sqrt{2880}[/tex] which simplifies to 24[tex]\sqrt{5}[/tex]

Answer:

84

Step-by-step explanation:

m∠CMT=101-54=47

m∠PMA=37, So

m∠PMA+m∠CMT=47+37=84

The sum of the angle ∠PMA + ∠CMT will be 84 so option (D) will be correct.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

In other words, the angle is the measurement of the angular distance. For instance, we have a meter and an inch for linear motion, but we don't have a measurement for angular rotation, therefore the angle is helpful in determining angular rotation.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

The Angle of description has given below

∠CMT=101-54=47

∠PMA=37, means

∠PMA+∠CMT = 47+37 = 84 hence, 84 will be the correct answer.

For more about the angle

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Answer:

1/125

Step-by-step explanation:

5^-3

We know that a^-b = a/a^b

1/5^3

1/125

Answer:

[tex] \displaystyle {5}^{ - 3} = \boxed{\frac{1}{ 125} }[/tex]

Step-by-step explanation:

we would like to evaluate the following expression:

[tex] \displaystyle {5}^{ - 3} [/tex]

recall that,

[tex] \displaystyle {x}^{ - n} = \frac{1}{ {x}^{n} } [/tex]

let x be 5 thus substitute:

[tex] \displaystyle {5}^{ - 3} = \frac{1}{ {5}^{3} } [/tex]

simplify:

[tex] \displaystyle {5}^{ - 3} = \boxed{\frac{1}{ 125} }[/tex]

Answer:

-4.68

Step-by-step explanation:

i hope this helps

0.12 - 4.8 = -4.68

Answer:

4.68

Step-by-step explanation:

[tex]y = \frac{x - 8}{3} [/tex]

then change y and x place

[tex]x = \frac{y - 8}{3} [/tex]

now find y

[tex]y = 3x + 8[/tex]

so inverse function is f(×)=3x+8

Answer:

x = 4 and y = -6

Step-by-step explanation:

Solve by elimination by multiplying the first equation by -2:

-8x - 6y = 4

8x + 3y = 14

Add them together and solve for y:

-3y = 18

y = -6

Plug in -6 as y into one of the equations and solve for x:

8x + 3y = 14

8x + 3(-6) = 14

8x - 18 = 14

8x = 32

x = 4

So, the solution is x = 4 and y = -6

Answer:

x = 4​

y = -6

Step-by-step explanation:

4x + 3y = -2

8x + 3y = 14​

Multiply the second equation by -1

4x + 3y = -2

-8x - 3y = -14

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

-4x       = -16

Divide by -4

-4x/-4 = -16/-4

x = 4​

4x+3y = -2

4*4 +3y = -2

16 +3y = -2

3y = -2-16

3y = -18

y = -6

Answer:

see explanation

Step-by-step explanation:

(14)

tan F = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{GH}{FH}[/tex] = [tex]\frac{12}{5}[/tex]

(15)

sin G = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{FH}{FG}[/tex] = [tex]\frac{5}{13}[/tex]

Using simple mathematical operations we know that Sunita's truly hourly wage is $38.

The four mathematical operations are functions that change one number into another by taking input values, or numbers, as inputs.

They include addition, subtraction, multiplication, and division.

So, she works nine hours a day, after all.

She worked 162 hours total over the course of 18 days, or 18 x 9 hours.

Also, it is understood that she gets one paid day off for every 18 hours worked.

She is therefore paid for nine hours each day.

She is compensated for a total of 19 x 9 = 171 hours.

She receives hourly pay of $36,

Her total compensation is 171 divided by 36, or $6156.

Actual wages = Total amount she was paid/Total hours she worked

= 6156/612

= 38

Therefore, using simple mathematical operations we know that Sunita's truly hourly wage is $38.

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Answer:

I believe the answer is 1

Answer:

Step-by-step explanation:

X=-6

Answer:

the correct answer will be

x=-6

Answer:

[tex]x=2.[/tex]

Step-by-step explanation:

[tex]\text{Since Pythagoras Theorem, we have}\\10^2=x.(x+48)\\\Rightarrow x^2+48x=100\\\Rightarrow x^2+48x-100=0\\\Rightarrow x^2 -2x+50x-100=0\\\Rightarrow x.(x-2)+50.(x-2)=0\\\Rightarrow (x-2).(x+50)=0\\\Rightarrow x=2 \: \text{or} \: x=-50.\\\text{Since x is positive}\\\text{Therefore}, x=2.[/tex]

[tex]\\ \rm\Rrightarrow 10^2=x(x+48)[/tex]

[tex]\\ \rm\Rrightarrow 100=x^2+48x[/tex]

[tex]\\ \rm\Rrightarrow x^2+48x-100=0[/tex]

[tex]\\ \rm\Rrightarrow x^2+50x-2x-100=0[/tex]

[tex]\\ \rm\Rrightarrow x(x+50)-2(x+50)=0[/tex]

[tex]\\ \rm\Rrightarrow (x+50)(x-2)=0[/tex]

[tex]\\ \rm\Rrightarrow x=-50,2[/tex]

Distance must be positive

Answer: Here are the first four with how to.

Answer:

30.

3×4=12

12×5=60

60÷2=30

Answer:

5.95cm

Step-by-step explanation:

Given data

Area of base of cone= 120π cm^2

Volume of cone= 240π cm^3

Area of base= Area of circle

Area= πr^2

120π= πr^2

120= r^2

r= √120

r= 10.9

r= 11cm

Let us find the height of the cone

The expression for the volume of cone is given as

V= 1/3πr^2h

240π= 1/3π*11^2*h

240= 1/3*121*h

240= 40.33h

divide both sides by 40.33

h=240/40.33

h= 5.95cm

Hence the height of the cone is 5.95cm approx

Answer:

1,501.47 ft

Step-by-step explanation:

the vertical distance above the ground =

1922 × tan 38° = 1,922 × 0.7812

= 1,501.47 ft

Answer:

1501.63ft is required answer m

Answer:

[tex]slope = \frac{4}{1} = 1 \\ y - intercept = 3 \\ \therefore \: \: y = 4x + 3[/tex]

[tex]\displaystyle\bf x-2=0 =>\boxed{ x=2 \quad ; y=-3 }[/tex]

Answer: I would pick black socks too because there are 8 pair of black socks with 4 pairs of white socks and 8 is > greater than 4.

Okay, so...

If there are 8 black socks + 4 white socks, then it = 12 socks totall. the fract Would Be 8/12 but if you simplify it, its 4/6, if you simplify it one more time you final answer is.....

You will have a 2/3 chance of picking a black sock.

Answer:

2 1/2

Step-by-step explanation:

5/8 ÷ 1/4

5/8 x 4/1

SIMPLIFY (if you want; if you dont, you can always multiply like normal but i find this way easier)

5/2 x 1/1 = 5/2 = 2 1/2

Answer:

8 questions

Step-by-step explanation:

100-2(8)=84

100-16=84

Answer:

[tex]\frac{15}{17}[/tex]

Step-by-step explanation:

Have a nice day