help quick plz i will make u a brainllest

Extract the normal vectors from the given planes:

[tex]-2x+y+z+2=0\implies\vec n_1=(-2,1,1)[/tex]

[tex]x+y-3z+1=0\implies\vec n_2=(1,1,-3)[/tex]

(which are unique up to their signs, meaning either [tex]\vec n_1[/tex] or [tex]-\vec n_1[/tex] are valid choices for the normal vector)

The third plane must be perpendicular to both these given planes, which means it would be parallel to both [tex]\vec n_1[/tex] and [tex]\vec n_2[/tex], which in turn means its own normal vector [tex]\vec n_3[/tex] should be perpendicular to both [tex]\vec n_1[/tex] and [tex]\vec n_2[/tex].

Enter the cross product:

[tex]\vec n_3=\vec n_1\times\vec n_2=(-4,-5,-3)[/tex]

or (4, 5, 3), which also works.

The given plane passes through (-1, 1, 4), so its equation is

[tex](x+1,y-1,z-4)\cdot\vec n_3=0[/tex]

Simplify:

[tex](x+1,y-1,z-4)\cdot(4,5,3)=0[/tex]

[tex]4(x+1)+5(y-1)+3(z-4)=0[/tex]

[tex]\boxed{4x+5y+3z=13}[/tex]

Answer:

a) 280°

b) Ans - (D) P is North East of Q

Answer:

V= -2000t + 20000

Step-by-step explanation:

Let m be the slope of our function :

Let's check :

Answer:

a) 1.84m

b) 42.53°

Step-by-step explanation:

First, look though the diagram provided by the question.

And use the formula: [tex]\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}[/tex]

Based on Additional Mathematics Form 4 (Dual Language Programme) KSSM from Malaysia

To find the length of AD

[tex]\frac{AD}{sin 67}=\frac{2}{sin 90}[/tex]

[tex]AD=\frac{2}{sin 90} * sin 67[/tex]

AD= 1.84 m

Find the angle C

[tex]\frac{sin 90}{2.5}=\frac{sin C}{1.84}[/tex]

sin C=[tex]\frac{sin 90}{2.5} * 1.84[/tex]

= 0.736

[tex]sin^{-1} (0.736)=47.39[/tex] degree

So, we have the value of AD and the value of angle C. Now , we can solve the the angle of CAD.

Same as the first question use the formula of sine rule and you will get the answer.

[tex]\frac{sin 90}{2.5}=\frac{sin ACD}{1.69}[/tex]

[tex]sinA = \frac{sin90}{2.5} * 1.69[/tex]

=0.676

=42.53°

So, the answer of the angle of CAD is 42.53°

Check the answer:

90°+47.39°+42.53°

=179.92°

=180°(rounded off)(Proved)

That is all from me. I hope you will understand my solution.

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where m is the slope

c is the y intercept

Equation of the line using point ( -1 , 2) and slope 3/2 is

Hope this helps you

Answer:

Option A is the correct option

Step-by-step explanation:

[tex] \frac{2 {x}^{2} - 10x - 28}{6x} \times \frac{6}{x - 7} [/tex]

Factor out 2 from the expression

[tex] \frac{2( {x}^{2} - 5x - 14)}{6x} \times \frac{6}{ x - 7} [/tex]

Weite -5x as a difference

[tex] \frac{2( {x}^{2} + 2x - 7x - 14)}{x} \times \frac{1}{ x - 7} [/tex]

Factor out

[tex] \frac{2(x(x + 2) - 7(x + 2))}{x} \times \frac{1}{x - 7} [/tex]

Factor X+2 from the expression

[tex] \frac{2(x + 2)(x - 7)}{x} \times \frac{1}{x - 7} [/tex]

Reduce the expression with x-7

[tex] \frac{2(x + 2)}{x} [/tex]

Distribute 2 through the parentheses

[tex] \frac{2x + 4}{x} [/tex]

Hope this helps...

Answer:

2070

Step-by-step explanation:

Multiply 230 people by 9 ferries, if each ferry is used once.

Answer:

106

Step-by-step explanation:

given: 5t + 76

If t = 6, we substitute t=6 into the equation and solve:

5t + 76

= 5(6) + 76

= 30 + 76

= 106

Hi there! Hopefully this helps!

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Answer: 106.

First, we need to evaluate.

(Note: when a letter and a number are close to together [5t] it means to multiply)

So if "t" = 6 we rewrite the problem like this:

5(6) + 76.

5 x 6 = 30.

Now we rewrite the problem again.

30 + 76 = 106.

Answer:

80º and 100º

Step-by-step explanation:

Answer:

[tex] \frac{13}{47} [/tex]

Step-by-step explanation:

There are 47 boys

13 picked karting

Answer:

2688 $ will be added. Therefore, the cost will be 44688 $.

Step-by-step explanation:

6.4% of 42000$ (a) / 100%=2688 $ (b).

a + b = 44688 $.

Answer:

Hello!

~~~~~~~~~~~~~~~~~~~~

Expanded form of  (5a/3 -2b/5)^3 =

[tex]\frac{125a^3}{27} - \frac{10a^2b}{3} + \frac{4ab^2}{5} - \frac{8b^3}{125}[/tex]

Step-by-step explanation: You have to Simplify the expression.

Hope this helped you. Brainliest would be nice!

Answer:

Answer:

7% of 33= 2.1

2% of 640= 12.8

15% of 470=70.5

7/9 of 51= 119/3

.52 of 62= 32.24

Answer:

1) 2.31

2) 12.8

3) 72

4) 44.625

5) 32.24

Step-by-step explanation:

7% of a number is simply 0.07*the number.

7/8 is just .875*the number

Hope it helps <3

Answer:

you need 36cups of flour

Step-by-step explanation:

3 cups of flour = 8 ounces of water

x cups of flour = 96 ounces of water

96*3 =8x

288 =8x

288/8=36

x=36

Answer:

108

Step-by-step explanation:

Add the sides of the triangle

5+3+4 = 12 then look for the height

which is 9

12*9 is 108

Answer:

22

Step-by-step explanation:

x-1 is a midsegment.

According to the Triangle midsegment theorem, x-1 is half of the third side (42)

x-1 = 42/2

x-1 = 21

x= 22

or

2x-2=42

2x=44

x=22

Hope this helps!

If you look at the top sides and bottom sides of both figures, this means that they are the same or similar.

In this figure, they are similar because one side is half of the other.

So... divide the longer length in half and solve for x.

42 / 2 = 21

x - 1 = 21

x - 1 + 1 = 21 + 1

x = 22

Therefore, the answer is C.

Best of Luck!

Answer:

hope its helpful to uh.......

Answer:

Step-by-step explanation:

The no of different ways in which these restaurants can be visited

= ¹⁵P₁₅

= 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

= 1.30 x 10¹²

b ) Each combination takes 1 week and 50 weeks in  a year to work

No of years to take to try all the combination

= 1.30 x 10¹² / 50

= 2.615 x 10¹⁰ years .

Answer:

Plan II

Step-by-step explanation:

A certain county has 1,000 farms.

Corn is grown on 100 of these farms but on none of the others.

Since corn is grown on only 100 of these farms, the population of interest is the 100 farms on which corn is grown.

Therefore, a better method for estimating the total farm acreage of corn for the county is Plan II.

a) Identify the 100 corn-growing farms.

b) Sample 20 corn-growing farms at random.

c) Estimate the mean acreage of corn for corn-growing farms in a confidence interval.

d) Multiply both ends of the interval by 100 to get an interval estimate of the total.

Answer:

7t^2 + 3t + 6

Step-by-step explanation:

The computation of the expression is shown below:

The function describes the manufacturing cost of product A.

a(t) = 5t + 2

Likewise for product B, the manufacturing cost function is

b(t) = 7t^2 - 2t + 4

So if we combined these two, the equation would be presented below

= a(t) + b(t)

= 5t + 2 + 7t^2 - 2t + 4

= 7t^2 + 3t + 6

Hence, the correct option is D

Step-by-step explanation:

1, vertical- axis intercept is the water at the beginning

3, she should have included the y-intercept and x-intercept of the linear function

Answer:

1261.68

Step-by-step explanation:

1350 = the increased watch price= 107% of the original

1350= 1.07x

1261.68224299

Check:

7% of 1261.68224299 is 88.317757

1261.68224299 + 88.317757 = 1349.9 = 1350

Round:

1261.68224299  

To the penny= to the hundreth= 1261.68

Answer:

The answer is below

Step-by-step explanation:

We must first define the concepts a little:

We have that when the sides are congruent that is to say that they have the same direction and the same size and also the two opposite sides are parallel, the angles will be the same.

Now, in an isosceles triangle, two angles are congruent, because their two sides are congruent.

Answer:

9

Step-by-step explanation:

x2 + 3

(3)2 + 3

6 + 3

9

Answer:

12.

Step-by-step explanation:

x = 3; x^2 + 3.

(3)^2 + 3 = 3 * 3 + 3 = 9 + 3 = 12

Hope this helps!

Answer:

C

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Here b = 19 and h = 16 , thus

A = 0.5 × 19 × 16 = 152 yd² → C

Answer:

i think its wht u need...