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3 years ago

Find the measures of the interior angles please

Mathematics

1 answer:

sweet [91]3 years ago

8 0

Solution:

X°+68°+(x-24)°=180°

Or,2x°-24°=180°

Or,x=180°

now by puttin' the value of x we get,

<A=180°

<B=68°

<C=156°

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Let T be the plane-2x-2y+z =-13. Find the shortest distance d from the point Po=(-5,-5,-3) to T, and the point Q in T that is cl

GaryK [48]

Answer:

d=10u

Q(5/3,5/3,-19/3)

Step-by-step explanation:

The shortest distance between the plane and Po is also the distance between Po and Q. To find that distance and the point Q you need the perpendicular line x to the plane that intersects Po, this line will have the direction of the normal of the plane $n=(-2,-2,1)$ , then r will have the next parametric equations:

$x=-5-2\lambda\\y=-5-2\lambda\\z=-3+\lambda$

To find Q, the intersection between r and the plane T, substitute the parametric equations of r in T

$-2x-2y+z =-13\\-2(-5-2\lambda)-2(-5-2\lambda)+(-3+\lambda) =-13\\10+4\lambda+10+4\lambda-3+\lambda=-13\\9\lambda+17=-13\\9\lambda=-13-17\\\lambda=-30/9=-10/3$

Substitute the value of $\lambda$ in the parametric equations:

$x=-5-2(-10/3)=-5+20/3=5/3\\y=-5-2(-10/3)=5/3\\z=-3+(-10/3)=-19/3\\$

Those values are the coordinates of Q

Q(5/3,5/3,-19/3)

The distance from Po to the plane

$d=\left| {\to} \atop {PoQ}} \right|=\sqrt{(\frac{5}{3}-(-5))^2+(\frac{5}{3}-(-5))^2+(\frac{-19}{3}-(-3))^2} \\d=\sqrt{(\frac{5}{3}+5))^2+(\frac{5}{3}+5)^2+(\frac{-19}{3}+3)^2} \\d=\sqrt{(\frac{20}{3})^2+(\frac{20}{3})^2+(\frac{-10}{3})^2}\\d=\sqrt{\frac{400}{9}+\frac{400}{9}+\frac{100}{9}}\\d=\sqrt{\frac{900}{9}}=\sqrt{100}\\d=10u$

7 0

3 years ago

Factor -12x^6-60x^5-75x^4

lesya [120]

-12x^6 - 60x^5-75x^4.......GCF = 3x^4
3x^4(-4x^2 - 20x - 25)
3x^4(-2x - 5)(2x + 5) <==

6 0

3 years ago

If (x + 2) is a factor of x3 − 6x2 + kx + 10, k =

ch4aika [34]

Answer:

The value of k is -11

Step-by-step explanation:

If (x+2) is a factor of x3 − 6x2 + kx + 10:

Then,

f(x)=x3 − 6x2 + kx + 10

f(-2)=0

f(-2)=(-2)³-6(-2)²+k(-2)+10=0

f(-2)= -8-6(4)-2k+10=0

f(-2)= -8-24-2k+10=0

Solve the like terms:

f(-2)=-2k-22=0

f(-2)=-2k=0+22

-2k=22

k=22/-2

k=-11

Hence the value of k is -11....

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3 years ago

The table below shows the linear relationship between the number of people at a picnic and the total cost of the picnic.

REY [17]

Wheres the table at bro post a pic

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3 years ago

Read 2 more answers

today at Allison's cupcake and cookie budget for her party at $105 if you would like to have at least 40 cupcakes and cookies co

Sati [7]

Answer:

a ≤ b + 5

a + b ≥ 40

2.5 a + 1.5 b ≤ 105

Step-by-step explanation:

3 0

3 years ago