A cylindrical tank whose diameter is 1.4 metres and height 80 cm is initially empty. Water whose volume is 492.8 litres is poured into the tank. Determine the fraction of the tank filled with water. (4 mark

Answer:

Step-by-step explanation:

For the m it would just be -3 because the equation for slope intercept form is y=mx+b

Answer:

x = -C / (A + b)

Step-by-step explanation:

Without given values for the constants A, b, and C (Assuming they are constants), the best we can do is to isolate the variable x.  Let's proceed to solve for x.

Ax + bx + C = 0

x (A + b) + C = 0

x (A + b) = -C

x = -C / (A + b)

So now, when you get the values of the constants A, b, and C, you can plug those in to solve for variable x.

Cheers.

Answer:

  (4, -3)

Step-by-step explanation:

The system of equations can be described a number of ways. One possible description is "a consistent pair of linear equations in two variables."

Perhaps you want to know the solution to this system of equations. I find it easiest to graph them. The attached graph shows the solution to be ...

  (x, y) = (4, -3)

__

You can also use "elimination" to simplify the system to a single equation in a single variable. Adding 4 times the second equation to 3 times the first will do that.

  3(5x +4y) +4(2x -3y) = 3(8) +4(17)

  23x = 92 . . . . . simplify

  x = 4 . . . . . . . .  divide by 23

Substituting this value into the first equation, we have ...

  5(4) +4y = 8

  5 +y = 2 . . . . . . divide by 4

  y = -3 . . . . . . . . subtract 5

The solution is (x, y) = (4, -3).

Answer:

work shown and pictured

Answer:

  22. The surface area is 1/9 of its original value

  24. The surface area is 120 m^2 less than its original value.

Step-by-step explanation:

22. For similar figures, the surface area is proportional to the square of the linear dimension scale factor. Multiplying all linear dimensions by 1/3 will result in reducing the surface area to (1/3)^2 = 1/9 of its original value.

__

24. As above, the scaled base surface area will be (1/4)^2 = 1/16 of its original value. Since one dimension of the lateral area is multiplied by 4 and the other dimension is multiplied by 1/4, the net effect on that area is multiplication by (1/4)(4) = 1. That is, the lateral area will remain unchanged.

The overall surface area will be reduced by 15/16 of the area of the bases. The area of the bases is (2)(1/2)(8 m)(16 m) = 128 m^2. The changed figure will have a surface area that is 120 m^2 smaller.

Answer:

Step-by-step explanation:

One pump will fill 200l in 20 minutes

So the rate of filling per pump will be 10l/minute (200/20)

Let the number of minutes it will take to fill the 600l be x minutes

Now, since the rate of filling per pump is 10 l/minute

Then in x minute, they would have filled 10l/minute * x = 10x liters

So it is now this 10x liters that will be equal to 600

To find x, we simply divide

10x = 600

x= 600/10

x = 6 minutes

Answer:

94.33

Step-by-step explanation:

add up all numbers then input into a percentage calculator

Percentage of flu vaccine has been given 94.33%

Percentage is defined as ratio expressed as a fraction of 100.

The physician have total 1500 flu injections

300 shots given in September,

450 shots given in October,

and 665 shots given in November,

Total flu vaccine has been given = 300+450+665 = 1415

Percentage of flu vaccine has been given = (1415/1500)×100%

Percentage of flu vaccine has been given = 0.9433×100%

Percentage of flu vaccine has been given = 94.33%

Hence, percentage of flu vaccine has been given 94.33%

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Answer:

2nd statement

3rd statement

4th statement

Step-by-step explanation:

The 2nd statement we know is true since the container was already described with a rectangular pyramid and a rectangular prism.

The 3rd statement is true since the volume for a rectangular prism is,

V=wlh or V=bh    (b=wl)

The volume of a rectangular pyramid is

V=1/3*wlh or V= 1/3*bh     (b=wl)

The 4th statement is true since the formula for the volume of this container is V=wlh+wlh/3. So substitute the values of the rectangular prism and rectangular pyramid and,

V=10*18*12+(18*10*10)/3

V=2160+1800/3

V=2160+600

V=2760

Answer:

137 votes

Step-by-step explanation:

considering an election with 681 votes and 5 candidates up for the election

dividing the votes among'st 5 candidates

= 681 / 5 = 136.2  hence the least number of first-place votes needed by a candidate using the plurality method  would be = 137 votes

136.2 + 136.2 + 136.2 + 136.2 + 136.2 = 681 ( dividing the votes equally )

136 + 136 + 136 + 136+136 = 680

hence the remaining vote = 681 - 680 = 1

least first-place vote = 136 + 1 = 137 votes

Answer:

2/3 x [tex]\sqrt[4]{y^2}[/tex]

Step-by-step explanation:

( 16 x^11 y^8 / 81 x^7 y^6) ^ ( 1/4)

Simplify the expression inside the parentheses

Rewriting the constant

16/81 = 2^4 / 3^4 = (2/3) ^4

Next the x terms

x^11 / x^7

We know that a^b / a^x = a^ ( b-c)

x^ (11-7) = x^4

And finally the y term

y^8/ y^6 = y^( 8-6) = y^2

(  (2/3) ^4 x^4 y^2) ^ ( 1/4)

We know that (ab) ^ c = a^ c * b^c

 (2/3) ^4 ^ 1/4   ( x^4 ^ 1/4   ( y^2) ^ ( 1/4)

We know that a^ b^ c = a^ ( b*c)

(2/3) ^4 ^ 1/4   ( x^4 ^ 1/4   ( y^2) ^ ( 1/4)

( 2/3) ^ ( 4*1/4)  * x^ ( 4*1/4)   * y ^ ( 2 ^ 1/4)

2/3 * x *  y ^ 2/4

2/3x  y ^ 2/4

2/3 x [tex]\sqrt[4]{y^2}[/tex]

━━━━━━━☆☆━━━━━━━

▹ Answer

See below for attached work.

▹ Step-by-Step Explanation

Hope this helps!

CloutAnswers ❁

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Answer:

x = 7

Step-by-step explanation:

4x + 5 = x + 26

4x - x = 26 - 5

3x = 21

x = 21/3

x = 7

Check:

4*7 + 5 = 7 + 26

28 + 5 = 33

Answer:

12

Step-by-step explanation:

The square root of any number is basically asking "what number multiplied by itself will equal this number?"

Usually you memorize these, but there's also a quick way to do it.

We know that [tex]10\cdot10=100[/tex], so the square root must be greater than 10.

We also know that [tex]15\cdot15=225[/tex], so the square root must be less than 15.

A good mid point between these numbers is 13. Let's see what 13 squared is:

[tex]13\cdot13=169[/tex]

So it's a bit less than 13. Let's try 12.

[tex]12\cdot12=144[/tex]

So 12 is the square root of 144.

Hope this helped!

Answer:

[tex]\huge\boxed{\sqrt{144}=12}[/tex]

Step-by-step explanation:

[tex]\begin{array}{c|c}144&2\\72&2\\36&2\\18&2\\9&3\\3&3\\1\end{array}\\\\144=2\cdot2\cdot2\cdot2\cdot3\cdot3=2^2\cdot2^2\cdot3^2\\\\\sqrt{144}=\sqrt{2^2\cdot2^2\cdot3^2}=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt{3^2}=2\cdot2\cdot3=12\\\\\text{Used}\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\sqrt{a^2}=a\\\\\text{for}\ a\ge0,\ b\geq0[/tex]

Plot point F where angle alpha is located.

Triangle ABF has two interior angles x and 80. They add to the exterior angle alpha due to the remote interior angle theorem.

alpha = x+80

Answer:

143.4 mi²

Step-by-step explanation:

Top: 8x6=48

Bottom: 3x8=24

Sides: 3x8=24 and 24

Trapezoids sides: (6+3)/2*2.6=4.5*2.6=11.7 and 11.7

TOTAL: 48+24+24+24+11.7+11.7= 143.4 mi²

Answer:

If the two linear equations have the same slope, the equations represent the same line. Since a line intersects with itself everywhere, there will be an infinite number of solutions.

Answer:

x = 3

y = -1

Step-by-step explanation:

Based on the fact that our have two variables and two equations, I'm going to assume you are trying to find the values of x and y.

For these two equations, let's first find the value of x using the equation elimination method.

We're going to eliminate the y variable by multiplying the first equation by 2 and then adding that new equation to the second equation.

7x - y = 22 ==> 14x - 2y = 44

4x + 2y + (14x - 2y) = 10 + (44)

18x + 0y = 54

x = 3

Now we plug the value of x back into one of the equations to find the value of y.

7x - y = 22

7(3) - y = 22

-y = 22 - 21

y = -1

So our values are as follows:

x = 3

y = -1

Cheers.

Answer:

(i) a1/a2 =/ b1/b2

(ii) a1/a2=b1/b2 =/ c1/c2

(iii) a1/a2=b1/b2=c1/c2

Step-by-step explanation:

=/ means not equal to.

graphical repesentation of

1.intersecting lines

2.coincident lines

3.parallel lines

a1/a2 and next two slots is basically dividing the coefficents if each equation.

for eg. 1. a1/a2= 2/4=1/2 and so on.

parallel lines are inconsistent whereas intersecting and coincident lines are consistent.

Answer:

The equivalent expression for this equation is x²¹ × y⁻²¹

Step-by-step explanation:

When you are multiplying exponents that are in parentheses, you multiply the exponential numbers together. So, for this problem, we will multiply the exponents together so we can get our final equivalent expression.

(x⁻³ × y³)⁻⁷

So, we will multiply -3 by -7 and we will also multiply 3 by -7 because those are our exponential numbers.

x²¹ × y⁻²¹

So, this is the final expression that is equivalent to our equation.

The expression (x⁻³.y³)⁻⁷ is equivalent to x ²¹ . y ⁻²¹.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

The given expression is,

(x⁻³.y³)⁻⁷

To find the solution for the expression,

Simplify the power terms,

x⁽⁻³ˣ⁻⁷⁾ . y ³ˣ⁻⁷

x ²¹ . y ⁻²¹

The simplified form of the expression (x⁻³.y³)⁻⁷ is x ²¹ . y ⁻²¹.

Hence, option (A) is correct.

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Answer:

this glizzy

Step-by-step explanation:

blow this glizzy u madd u wrong answer

Answer:

  4

Step-by-step explanation:

Sometimes when evaluating polynomials, it is easier if you write them in Horner form:

  (y +5)y -2

For y = -6, this is ...

  (-6 +5)(-6) -2 = (-1)(-6) -2 = 6 -2 = 4

The value of your expression is 4.

Answer:

[tex]\huge\boxed{Area = 24\ square\ units}[/tex]

Step-by-step explanation:

Area of parallelogram = Base * Height

Where Base = 6 , Height = 6

Area = 6 * 4

Area = 24 square units

Answer:

24 square units

Step-by-step explanation:

the area formula is A=bh

b=6

h=4

A=4*6

A=24

Answer:

Step-by-step explanation:

4^5 is equivalent to 4^2*4*3, which, in turn, is equivalent to:

16*64 = 1024.

Also:  

8*128 = 1024, and

4*256 = 1024, and so on.

Answer:

B = 31, C = 11

Step-by-step explanation:

Let B be the number of Black printer ink cartridges and C be the number of color printer ink cartridges.

42 were sold in total, hence,

B+C= 42 ------------(1)

Also, its given that

14.99 B+20.99C= 695.58 ------(2)

Multiplying (1) by 20.99,

14.99 B+14.99 C= 629.58 ------(3)

Now, subtracting (3) from (2),

14.99 B+20.99C= 695.58

14.99 B+14.99 C= 629.58

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

6 C = 66

C= 66/6

C = 11

We know, B+ C= 49

Hence B = 42- 11 = 31

B = 31

Hence, number of Black printer ink cartridges = 31 and color printer ink cartridges = 11 .

Answer:

The length of the bridge is 72 cm

Step-by-step explanation:

In order to find the length of bridge, we have to apply distance formula which is D = S × T where S represents speed and T is time :

[tex]d = s \times t[/tex]

[tex]let \: s = 18,t = 4[/tex]

[tex]d = 18 \times 4[/tex]

[tex]d = 72 \: cm[/tex]

The length of the bridge is 11 cm .

When an object moves in a straight line at a steady speed, we can calculate its speed if we know how far it travels and how long it takes. This equation shows the relationship between speed, distance traveled and time taken:

Speed is distance divided by the time taken.

For example, a car travels 30 kilometers in 2 hours.

Its speed is 30 ÷ 2 = 15km/hr.

Formula used :

Distance  = Speed * Time

Time = Distance / Speed

Speed = Distance / Time

According to the question

Length of train = 61 cm

Speed of train = 18 cm/s

Time taken to cross the bridge = 4 seconds

In this length traveled by train = length of train + Length of bridge

( as time given is to completely cross platform )

Therefore,

length traveled by train = 61 + Length of bridge

formula used

Distance  = Speed * Time

61 + Length of bridge =  18 * 4

61 + Length of bridge = 72

Length of bridge  = 72 - 61

Length of bridge  = 11 cm

Hence, the length of the bridge is 11 cm .

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Answer:

18

Step-by-step explanation:

HOPE I HELPED

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DESPERATELY TRYING TO LEVEL UP

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JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

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Answer:

third option

Step-by-step explanation:

Given

3 [tex]\left[\begin{array}{ccc}-2&5\\1&0\\\end{array}\right][/tex]

Multiply each element in the matrix by 3

= [tex]\left[\begin{array}{ccc}3(-2)&3(5)\\3(1)&3(0)\\\end{array}\right][/tex]

= [tex]\left[\begin{array}{ccc}-6&15\\3&0\\\end{array}\right][/tex]  

Answer:

C.

Step-by-step explanation:

Answer:

I think C is the answer .

Step-by-step explanation:

If (x-6) and (x-1) are the factors of function f then remainder of function f is 0.

(x-6)(x-1) = 0

Either,

x-6 = 0

x = 6

and

x-1 = 0

x = 1

so 6 and 1 are the zeros or roots of function f.

Answer:

the answer is 1 and 6 :D

Step-by-step explanation:

Answer:

MC = 45

Step-by-step explanation:

Δ ABH and Δ MCH are similar and the ratios of corresponding sides are equal, that is

[tex]\frac{AB}{MC}[/tex] = [tex]\frac{AH}{MH}[/tex] , substitute values

[tex]\frac{54}{MC}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )

6MC = 270 ( divide both sides by 6 )

MC = 45

Answer:

How much did she sell it

Answer:

B, C, E

Step-by-step explanation:

I just took the test

Answer:

i dont know if im correct but

Step-by-step explanation:

B, C, and E are the right ones hope it helps

Answer:

Step-by-step explanation:

(x-4) (x+10)  ⇒ (x+a)(x+b)=x²+(a+b)x+ab

a=-4 , b=10

x²+(-4+10)x+-4(10)

x²+6x-40

(3x+4) (3x +5)

3(x+4/3) *3(x+5/3)  ⇒ identity : (x+a)(x+b)=x²+(a+b)x+ab  

a=4/3    b=5/3

3*3=9

9[x²+(4/3 +5/3)x+4/3(5/3)]

9[x²+9/3 x+20/9]

9x²+27x+20

(-3a +5b +4c)^2  ⇒  

suitable identity is (a+b+c)²= a² + b² + c² + 2ab + 2bc + 2ca

a=-3a , b=5b , c=4c

9a²+25b²+16c²- 30ab +40bc - 24ca