All categories

3 years ago

If m ABC = 118°, solve for x.

Mathematics

1 answer:

ziro4ka [17]3 years ago

6 0

Given:

m∠ABC = 118°

m∠DAC = (9x - 33)°

m∠CAB = (2x + 7)°

To find:

The value of x.

Solution:

Sum of the adjacent angles in a parallelogram = 180°

m∠ABC + m∠CAB + m∠DAC = 180°

118° + 9x° - 33° + 2x° + 7° = 180°

92° + 11x° = 180°

Subtract 92° from both sides.

92° + 11x° - 92° = 180° - 92°

11x° = 88°

Divide by 11° on both sides.

x = 8

The value of x is 8.

You might be interested in

PLS TRY TO ANSWER ASAP.

Harrizon [31]

Answer:

0.075 m/min

Explanation:

You need to use derivatives which is an advanced concept used in calculus.

1. Write the equation for the volume of the cone:

$V=\dfrac{1}{3}\pi r^2h$

2. Find the relation between the radius and the height:

r = diameter/2 = 5m/2 = 2.5m

h = 5.2m

h/r =5.2 / 2.5 = 2.08

3. Filling the tank:

Call y the height of water and x the horizontal distance from the axis of symmetry of the cone to the wall for the surface of water, when the cone is being filled.

The ratio x/y is the same r/h

x/y=r/h

y = x . h / r

The volume of water inside the cone is:

$V=\dfrac{1}{3}\pi x^2y$

$V=\dfrac{1}{3}\pi x^2(2.08)\cdot x\\\\\\V=\dfrac{2.08}{3}\pi x^3$

4. Find the derivative of the volume of water with respect to time:

$\dfrac{dV}{dt}=2.08\pi x^2\dfrac{dx}{dt}$

5. Find x² when the volume of water is 8π m³:

$V=\dfrac{2.08}{3}\pi x^3\\\\\\8\pi=\dfrac{2.08}{3}\pi x^3\\\\\\ 11.53846=x^3\\ \\ \\ x=2.25969\\ \\ \\ x^2=5.1062$ m²

6. Solve for dx/dt:

$1.2m^3/min=2.08\pi(5.1062m^2)\dfrac{dx}{dt}$

$\dfrac{dx}{dt}=0.03596m/min$

7. Find dh/dt:

From y/x = h/r = 2.08:

$y=2.08x\\\\\\\dfrac{dy}{dx}=2.08\dfrac{dx}{dt}\\\\\\\dfrac{dy}{dt}=2.08(0.035964m/min)=0.0748m/min\approx0.075m/min$

That is the rate at which the water level is rising when there is 8π m³ of water.

4 0

3 years ago

Find the average rate of change for the given function from x=-1 to x=4

loris [4]

I believe the slope is 0 because it they are both horizontal lines? I may be wrong though.

6 0

3 years ago

Identify the fraction as proper, improper, or mixed 17/18

Citrus2011 [14]

This is a proper fraction because the numerator is smaller than the denominator, making it proper.

If it were improper the numerator would be larger than the denominator. If it were a mixed fraction there would be a WHOLE number and a fraction, for example 5 1/2.

I hope this helps! <3

6 0

3 years ago

Help plz just answer

Rom4ik [11]

Answer:

c 42

Step-by-step e

xplanation:

5 0

3 years ago

WILL GIVE BRAINLIEST FOR CORRECT ANSWER +80 points

Salsk061 [2.6K]

Answer:

2,375 joules I think............

6 0

3 years ago

Read 2 more answers