Simplify 7x+42/x^2+13x+42

If m∠RQS=22x-11 and m∠RQT=12x-8, find m∠TQS

Arada [10]

Answer:

∡TQS = 10x -3

Step-by-step explanation:

∡TQS = ∡RQS - ∡RQT

= 22x - 11 - (12x - 8)

= 10x -3

3 0

3 years ago

to find the amount of water that would fill the inside of an aluminum can, which of the following formulas would you use?

Vlad1618 [11]

Answer:

The answer is V = π r 2h

Trust me i just got this question and that was the answer.

Step-by-step explanation:

7 0

3 years ago

Learning Task 4. Solve the problem by applying the sum and product of roots

Delvig [45]

Answer:

Thus, the dimensions of the metal plate are 10 dm and 8 dm.

Step-by-step explanation:

For a quadratic equation:

$x^2+bx+c=0$

The sum of the roots is -b and the product is c. Note the leading coefficient is 1.

We know the perimeter of the rectangular metal plate is 36 dm and its area is 80 dm^2. Being L and W its dimensions, then:

P=2(L+W)=36

A=L.W=80

Note both formulas are closely related to the roots of the quadratic equation, we only need to adjust the data for the perimeter to be exactly the sum of L+W and not double of it.

Thus we use the semi perimeter instead as P/2=L+W=18

The quadratic equation is, then:

$x^2-18x+80=0$

Factoring by finding two numbers that add up to 18 and have a product of 80:

$(x-10)(x-8)=0$

The solutions to the equation are:

x=10, x=8

Thus, the dimensions of the metal plate are 10 dm and 8 dm.

6 0

3 years ago

A sphere has a radius of 11 feet. A second sphere has a radius of 8 feet. what is the difference of the volume of thespheres

Veronika [31]

The difference between the volume of the spheres is 3428.88 cubic feet

Explanation:

Given that one sphere has a radius of 11 feet.

A second sphere has a radius of 8 feet.

Volume of the 1st sphere:

The formula to determine the volume of the sphere is given by

$V=\frac{4}{3} \pi r^3$

Volume of the 1st sphere is given by

$V=\frac{4}{3}(3.14)(11)^3$

$V=\frac{4}{3}(3.14)(1331)$

$V=\frac{16717.36}{3}$

$V=5572.45$

The volume of the 1st sphere is 5572.45 cubic feet.

Volume of the 2nd sphere:

Volume of the 2nd sphere is given by

$V=\frac{4}{3}(3.14)(8)^3$

$V=\frac{4}{3}(3.14)(512)$

$V=\frac{6430.72}{3}$

$V=2143.57$

The volume of the 2nd sphere is 2143.57 cubic feet.

Difference between the volume of the two spheres:

Difference = Volume of the 1st sphere - Volume of the 2nd sphere

= 5572.45 - 2143.57

Difference = 3428.88 cubic feet.

Hence, the difference between the volume of the spheres is 3428.88 cubic feet.

7 0

3 years ago

Solve each system of equations using the elimination method 3x+8y=2 4x-2y=-10

LenaWriter [7]

x = -2

y = 1

let's multiply second equation by 4 to get a common coefficient of y variable.

16x-8y=-40

add the equations

3×+8y=2

16x-8y=-40

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

3x+16x = -38

19x = -38

x = -2

substitute x

3×-2 + 8y = 2

-6 + 8y = 2

8y = 2+6

y = 1

check the answer

-6+8 = 2

-8-2= -20

8 0

3 years ago