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2 years ago

I need help i need the statement and reason

Mathematics

1 answer:

Marina86 [1]2 years ago

6 0

For number one
S: supplement.
R: angle1+angle8 =18
#2
S: supplement
R: angle 3+ angle 6=180

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Nine fewer than half a number is five more than four times the number. Define a variable, write an equation, and solve to find t

nignag [31]

N = the number

0.5n - 9 = 4n + 5
(0.5n - 0.5n) - 9 = (4n - 0.5n) + 5
-9 = 3.5n + 5
(-9 - 5) = 3.5n + (5 - 5)
-14 = 3.5n
-14/3.5 = 3.5n/3.5
-4 = n

The number is -4.

3 0

3 years ago

Solve the system algebraically. Check your work.

Luden [163]

answer.

Answer:

x=2 and y=0 is the required result.

Step-by-step explanation:

We have been given system of equations:

5x+2y=105x+2y=10 (1)

And 3x+2y=63x+2y=6 (2)

We will use elimination method:

Multiply 1st equation by 3 and 2nd equation by 5 we get:

15x+6y=3015x+6y=30 (3)

15x+10y=3015x+10y=30 (4)

Now subtract (4) from (3) we get:

-4y=0−4y=0

y=0y=0

Now, put y=0 in (1) equation:

5x+2(0)=105x+2(0)=10

5x=105x=10

x=2x=2

Hence, x=2 and y=0

8 0

3 years ago

I need help pls is only 1 question

Yanka [14]

Answer:

$T = 1300$

Step-by-step explanation:

Given

$Radius, r = 9\ in$

$Height, h = 14\ in$

See attachment

Required

Determine the total surface area, T

T is calculated using:

$T = 2\pi r(r + h)$

Substitute values for r and h

$T = 2\pi * 9(9 + 14)$

$T = 2\pi * 9(23)$

Remove bracket

$T = 2\pi * 9*23$

$T = 2\pi * 207$

Take $\pi = 3.14$

So, we have:

$T = 2 * 3.14 * 207$

$T = 1299.96$

$T = 1300$ --- approximated.

Hence, the surface area is 1300 square inch

4 0

2 years ago

The surface area of a cylinder is increasing at a rate of 9 pi square meters per hour. The height of the cylinder is fixed at 3

Alekssandra [29.7K]

Answer:

$9\pi \text{ cubic meters per hour}$

Step-by-step explanation:

Since, the surface area of a cylinder,

$A= 2\pi r^2 + 2\pi rh$ ................(1)

Where,

r = radius,

h = height,

If $A= 36\pi\text{ square meters}, h = 3\text{ meters}$

$36\pi = 2\pi r^2 + 2\pi r(3)$

$18 = r^2 + 3r$

$\implies r^2 + 3r - 18=0$

$r^2 + 6r - 3r - 18 = 0$ ( by middle term splitting )

$r(r+6)-3(r+6)=0$

$(r-3)(r+6)=0$

By zero product property,

r = 3 or r = - 6 ( not possible )

Thus, radius, r = 3 meters,

Now, differentiating equation (1) with respect to t ( time ),

$\frac{dA}{dt}= 4\pi r\frac{dr}{dt} +2\pi(r\frac{dh}{dt} + h\frac{dr}{dt})$

∵ h = constant, ⇒ dh/dt = 0,

$\frac{dA}{dt} = 4\pi r \frac{dr}{dt} +2\pi h \frac{dr}{dt}$

We have, $\frac{dA}{dt}=9\pi\text{ square meters per hour}, r = h = 3\text{ meters}$

$9\pi = 4\pi (3) \frac{dr}{dt}+2\pi (3)\frac{dr}{dt}$

$9\pi = (12\pi + 6\pi )\frac{dr}{dt}$

$9\pi = 18\pi \frac{dr}{dt}$

$\implies \frac{dr}{dt} =\frac{1}{2}\text{ meter per hour}$

Now,

Volume of a cylinder,

$V=\pi r^2 h$

Differentiating w. r. t. t,

$\frac{dV}{dt}=\pi ( r^2 \frac{dh}{dt}+h(2r)\frac{dr}{dt})=\pi ((3)(6) (\frac{1}{2})) = 9\pi \text{ cubic meters per hour}$

6 0

3 years ago

I’m so confused please help , this is 100 points

sesenic [268]

Answer:

m`1 = 43` 2,3

m<2 1/12*

and m <3 = 1,3/2

Step-by-step explanation:

6 0

2 years ago

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