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3 years ago

Find the vector equation for the line of intersection of the planes 5x+3y−2z=−45x+3y−2z=−4 and 5x+5z=0

Mathematics

1 answer:

olga_2 [115]3 years ago

8 0

$5x+5z=0\implies x+z=0\implies z=-x$

$5x+3y-2z=7x+3y-2x-2z=7x+3y-2=-4\implies7x+3y=-2$

Letting $x=t$ and $z=-t$ , we have

$7t+3y=-2\implies y=-\dfrac73t-\dfrac23$

so the intersection is given by

$\mathbf r(t)=\left(t,-\dfrac73t-\dfrac23,-t\right)$

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I need help on this question

olga2289 [7]

Hey there!

-1 ¼ • 9

= - (4+1)/4 • 9

= -5/4 • 9

= -(5 × 9)/4

= - 45/4

= - 11.25

Hope it helps ya!

8 0

3 years ago

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A recipe for sugar cookies requires 2 cups of flour for every 2/3 cups of sugar at this rate how many cups of sugar should be us

maks197457 [2]

The answer would be 5/3 or 1 2/3

4 0

3 years ago

Suppose that LMN is isosceles with base LN suppose that M

ira [324]

Given:

In an isosceles triangle LMN, LM=MN.

$m\angle M=(3x+17)^\circ,m\angle L=(2x+36)^\circ$

To find:

The measure of the angles L, M and N.

Solution:

In triangle LMN,

$LM=MN$ (Given)

$m\angle N=m\angle L=(2x+36)^\circ$ (Base angles of an isosceles triangle are equal)

Now,

$m\angle L+m\angle M+m\angle N=180^\circ$

$(2x+36)^\circ+(3x+17)^\circ+(2x+36)^\circ=180^\circ$

$(7x+89)^\circ=180^\circ$

$(7x+89)=180$

On further simplification, we get

$7x=180-89$

$7x=91$

$x=\dfrac{91}{7}$

$x=13$

The value of x is 13. Using this value, we get

$m\angle L=(2(13)+36)^\circ$

$m\angle L=(26+36)^\circ$

$m\angle L=62^\circ$

Similarly,

$m\angle M=(3(13)+17)^\circ$

$m\angle M=(39+17)^\circ$

$m\angle M=56^\circ$

And,

$m\angle N=m\angle L$

$m\angle N=62^\circ$

Therefore, the measure of angles are $m\angle L=62^\circ,m\angle M=56^\circ,m\angle N=62^\circ$ .

5 0

3 years ago

Which facts could be applied to simplify this expression? Check all that apply.

kykrilka [37]

The answer is B, C, and D. Like terms are terms with all the same variable, so 5x and -x are like terms.

C is correct. If we add -x to 5x, we get 4x. The other numbers remain unchanged because they have no like terms.

D is correct. Applying the rule of like terms, which is that like terms are numbers with the same variable, only add together numbers with the same variable.

Hope this helps!

3 0

3 years ago

Read 2 more answers

The figure above shows a square inscribed in a rectangle.

Debora [2.8K]

Answer:

31 units ²

Step-by-step explanation:

Area of a rectangle = length × width

Length = 8 units

Width = 5 units

Area of a rectangle = length × width

= 8 units × 5 units

= 40 units ²

Area of of the blue square = length ²

Length = 3 units

Area of of the blue square = length ²

= (3 units) ²

= 9 units ²

Area of the orange colored part of the figure = Area of a rectangle - Area of of the blue square

= 40 units ² - 9 units ²

= 31 units ²

Area of the orange colored part of the figure = 31 units ²

6 0

2 years ago