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mr Goodwill [35]

3 years ago

12

Determine the slopes of the following equation using their intercepts

1 answer:

Olin [163]3 years ago

8 0

Answer:

yo slide me that number ong

Step-by-step explanation:

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4x+25=57<br>valor de x por favor

sukhopar [10]

Answer:

4x=8

Step-by-step explanation:

4x=32

32/4=8

8 0

3 years ago

Read 2 more answers

19. There were 20 drinks in a cooler.

ella [17]

For this case we have that the complete question is:

There were 20 drinks in a cooler. Joey drank 15% of the drinks. Sandra drank 1/5 of the drinks. Hannah drank 1/4 of the drinks. Tammy drank 30% of the drinks. How many drinks are left in the cooler? a 0 b 2 c 5 d 9

We propose a rule of three:

20 ---------> 100%

x ------------> 15%

Where the variable "x" represents the amount of drinks equivalent to 15%.

$x = \frac {15 * 20} {100}\\x = 3$

So, Joey drank 3 drinks.

On the other hand, we have that Sandra drank $\frac {1} {5}$ of the drinks:

$20 * \frac {1} {5} = \frac {20} {5} = 4$

Thus, Sandra drank 4 drinks.

In addition, Hannah drank $\frac {1} {4}$ of the drinks:

$20 * \frac {1} {4} = 5$

So Hannah drank 5 drinks.

Finally, Tammy drank 30% of the drinks:

20 ---------> 100%

y ------------> 30%

Where the variable "y" represents the amount of drinks equivalent to 30%.

$y = \frac {30 * 20} {100}\\y = 6$

So Tammy drank 6 drinks.

Adding up we have:

$3 + 4 + 5 + 6 = 18$

So: $20-18=2$

Thus, 2 drinks remain in the refrigerator.

Answer:

Option B

5 0

3 years ago

Use Lagrange multipliers to find the maximum and minimum values of (i) f(x,y)-81x^2+y^2 subject to the constraint 4x^2+y^2=9. (i

sp2606 [1]

i. The Lagrangian is

$L(x,y,\lambda)=81x^2+y^2+\lambda(4x^2+y^2-9)$

with critical points whenever

$L_x=162x+8\lambda x=0\implies2x(81+4\lambda)=0\implies x=0\text{ or }\lambda=-\dfrac{81}4$

$L_y=2y+2\lambda y=0\implies2y(1+\lambda)=0\implies y=0\text{ or }\lambda=-1$

$L_\lambda=4x^2+y^2-9=0$

If $x=0$ , then $L_\lambda=0\implies y=\pm3$ .
If $y=0$ , then $L_\lambda=0\implies x=\pm\dfrac32$ .
Either value of $\lambda$ found above requires that either $x=0$ or $y=0$ , so we get the same critical points as in the previous two cases.

We have $f(0,-3)=9$ , $f(0,3)=9$ , $f\left(-\dfrac32,0\right)=\dfrac{729}4=182.25$ , and $f\left(\dfrac32,0\right)=\dfrac{729}4$ , so $f$ has a minimum value of 9 and a maximum value of 182.25.

ii. The Lagrangian is

$L(x,y,z,\lambda)=y^2-10z+\lambda(x^2+y^2+z^2-36)$

with critical points whenever

$L_x=2\lambda x=0\implies x=0$ (because we assume $\lambda\neq0$ )

$L_y=2y+2\lambda y=0\implies 2y(1+\lambda)=0\implies y=0\text{ or }\lambda=-1$

$L_z=-10+2\lambda z=0\implies z=\dfrac5\lambda$

$L_\lambda=x^2+y^2+z^2-36=0$

If $x=y=0$ , then $L_\lambda=0\implies z=\pm6$ .
If $\lambda=-1$ , then $z=-5$ , and with $x=0$ we have $L_\lambda=0\implies y=\pm\sqrt{11}$ .

We have $f(0,0,-6)=60$ , $f(0,0,6)=-60$ , $f(0,-\sqrt{11},-5)=61$ , and $f(0,\sqrt{11},-5)=61$ . So $f$ has a maximum value of 61 and a minimum value of -60.

5 0

3 years ago

Does anyone know this?

lana66690 [7]

Answer:

Δ HGI ≅ ΔEDF

Step-by-step explanation:

Given:

Δ DEF ≅ Δ GHI

From the given congruence statement we can figure out the corresponding sides that are congruent.

The arrangement shows:

$D\rightarrow G\\E\rightarrow H\\F\rightarrow I$

So the rearranged statement can be written as:

ΔEDF ≅ Δ HGI

or

∴ Δ HGI ≅ ΔEDF

8 0

3 years ago

.A ladder is leaning against a wall. The top of the ladder is 4 feet above the ground

Scorpion4ik [409]

Step-by-step explanation:

The ladder forms a triangle with the wall and ground.

The side of the triangle opposite of the 60° angle is 4 feet.

To find the length of the ladder (the hypotenuse), use sine.

sine = opposite / hypotenuse

sin 60° = 4 / L

L = 4 / sin 60°

L = 4 / (√3 / 2)

L = 8 / √3

L = 8√3 / 3

L ≈ 4.619 feet

To find the distance from the wall, use tangent.

tangent = opposite / adjacent

tan 60° = 4 / x

x = 4 / tan 60°

x = 4 / √3

x = 4√3 / 3

x ≈ 2.309 feet

8 0

3 years ago