Convert the units of weight.

The measure of angle P is five less than four times the measure of angle Q. Of angle P and angle Q are supplementary angles, fin

Andru [333]

Answer:

m∠P=140°

Step-by-step explanation:

Given:

∠P and ∠Q are supplementary angles.

The measure of angle P is five less than four times the measure of angle Q.

To find m∠P

Solution:

The measure of angle P can be given as:

A) $m\angle P=4(m\angle Q-5)$

And

B) $m\angle P+ m\angle Q=180$ [Definition of supplementary angles]

Substituting equation A into B.

$4(m\angle Q-5)+ m\angle Q=180$

Solving for $m\angle Q$

Using distribution:

$4m\angle Q-20+ m\angle Q=180$

Simplifying by combining like terms.

$5m\angle Q-20=180$

Adding 20 to both sides.

$5m\angle Q-20+20=180+20$

$5m\angle Q=200$

Dividing both sides by 5.

$\frac{5m\angle Q}{5}=\frac{200}{5}$

$m\angle Q=40$

Substituting $m\angle Q=40$ in equation B.

$m\angle P+ 40=180$

Subtracting both sides by 40.

$m\angle P+ 40-40=180-40$

$m\angle P=140$

Thus, we have:

m∠P=140° (Answer)

7 0

3 years ago

Suppose z equals f (x comma y ), where x (u comma v )space equals space 2 u plus space v squared, y (u comma v )space equals spa

barxatty [35]

$z=f(x(u,v),y(u,v)),\begin{cases}x(u,v)=2u+v^2\\y(u,v)=3u-v\end{cases}$

We're given that $f_x(6,1)=3$ and $f_y(6,1)=-1$ , and want to find $\frac{\partial z}{\partial v}(1,2)$ .

By the chain rule, we have

$\dfrac{\partial z}{\partial v}=\dfrac{\partial z}{\partial x}\dfrac{\partial x}{\partial v}+\dfrac{\partial z}{\partial y}\dfrac{\partial y}{\partial v}$

and

$\dfrac{\partial x}{\partial v}=2v$

$\dfrac{\partial y}{\partial v}=-1$

Then

$\dfrac{\partial z}{\partial v}(1,2)=\dfrac{\partial z}{\partial x}(6,1)\dfrac{\partial x}{\partial v}(1,2)+\dfrac{\partial z}{\partial y}(6,1)\dfrac{\partial y}{\partial v}(1,2)$

(because the point $(x,y)=(6,1)$ corresponds to $(u,v)=(1,2)$ )

$\implies\dfrac{\partial z}{\partial v}(1,2)=3\cdot2\cdot2+(-1)\cdot(-1)=\boxed{13}$

4 0

3 years ago

Use distribute property and simplify<br> Help me please

stellarik [79]

Answer:

104

155

180

Step-by-step explanation:

an easy way is to solve what is in the parenthesis then multiply by the outside number

but if you need to use the distributive property:

1. 4 x (20 - -6)

(4 x 20) - (4 x -6) = 80 - -24 = 80 + 24 = 104

2. -5 x (24 - -7)

(-5 x 24) - (-5 x -7) = -120 - 35 = 155

3. 12 x (-30 + 45)

(12 x -30) + (12 x 45) = -360 + 540 = 180

5 0

3 years ago

Read 2 more answers

Three oblique pyramids have the same regular square base. Which one has a volume of 15 cubic units if the area of the bases are

deff fn [24]

Answer:

The one which has a height of 3 units. H=3

Step-by-step explanation:

Well, the volume of pyramid is equal to the area of base multiply by the height of pyramid and divide by 3. Writing as a formula it can be expressed as V=(A*H)/3 where V is volume of pyramid, A is area of base and H is the height of pyramid. If V=15 cubic units and A=15 square units, H should be equal to 3 (to be cancelled out by 3. Please look at formula above) in order to make V=15.

8 0

2 years ago

Read 2 more answers

Becky and luke bought the same kind of pencils and erasers . Becky spent $1.45 for 2 pencils and 3 erasers . Luke spent $2.65 fo

ivann1987 [24]

Answer: the cost of each pencil is $0.5

the cost of each eraser is $0.15

Step-by-step explanation:

Let x represent the cost of one pencil.

Let y represent the cost of one eraser.

Becky spent $1.45 for 2 pencils and 3 erasers. This means that

2x + 3y = 1.45- - - - - - - - - -1

Luke spent $2.65 for 5 pencils and 1 eraser. This means that

5x + y = 2.65- - - - - - - - - -2

Multiplying equation 1 by 1 and equation 2 by 3, it becomes

2x + 3y = 1.45

15x + 3y = 7.95

Subtracting, it becomes

- 13x = - 6.5

x = - 6.5/- 13

x = 0.5

Substituting x = 0.5 into equation 2, it becomes

5 × 0.5 + y = 2.65

2.5 + y = 2.65

y = 2.65 - 2.5

y = 0.15

6 0

3 years ago