I need help finding the intersection of the line and plane​

Answer:

See below.

Step-by-step explanation:

So we have the two functions:

[tex]f(x)=8x-5\text{ and } g(x)=9-2x[/tex]

And we want to find:

[tex](f\circ g)(x)\text{ and } (g\circ f)(x)[/tex]

1)

Recall that:

[tex](f\circ g)(x)[/tex]

is the same as:

[tex]=f(g(x))[/tex]

Thus, we can substitute g(x):

[tex]=f(9-2x)[/tex]

And substitute that into f(x):

[tex]f(x)=8x-5\\f(9-2x)=8(9-2x)-5[/tex]

Distribute:

[tex]=72-16x-5[/tex]

Subtract and simplify:

[tex]=67-16x\\=-16x+67[/tex]

Thus:

[tex](f\circ g)(x)=-16x+67[/tex]

2)

Similarly:

[tex](g\circ f)(x)=g(f(x))[/tex]

Substitute f(x):

[tex]g(f(x))=g(8x-5)[/tex]

Substitute:

[tex]g(8x-5)=9-2(8x-5)[/tex]

Distribute:

[tex]=9-16x+10[/tex]

Simplify:

[tex]=-16x+19[/tex]

Therefore:

[tex](g\circ f)(x)=-16x+19[/tex]

Answer:

A set of all positive integers between 7 and 43.

Step-by-step explanation:

If a triangle is given with the sides a, b, c, triangle is possible when,

a + b > c

a + c > b

b + c > a

Following the same rule in a triangle having side lengths 18, 25 and l unit.

18 + 25 > l    ⇒ l < 43

18 + l > 25    ⇒ l > 7

25 + l > 18    ⇒ l > -7

Therefore, length of the third side of the triangle will be,

7 < l < 43  (A set of positive integers between 7 and 43)

Answer: n> or equals to 3

Step-by-step explanation:

Find explanation on the attachment

Answer:

$125

Step-by-step explanation:

Given the following :

Number of desks sold = 3

Amount of rent paid = $4

Amount paid to carpenter = 1/2 of revenue

Amount left = $185.50

At what price did Ryan sell each desk?

If Rayee gave half of his revenue to the carpenter and then had $185.50 left,

The his revenue before paying the carpenter will be twice what he has left ($185.50 * 2) = $371

Hence, total revenue from the sale of 3 desk= ($371 + rent) = (371 + 4) = $375

Then each desk cost :

$375 / 3 = 125

$125

Answer:

Step-by-step explanation:

Multiply by x^2 on both sides

9x^2+27x+8=0

Factor.

The answers are -1/3, -8/3

Answer:

y = 1.5x

Step-by-step explanation:

Cost of pineapples:

x pounds of pineapple will cost:

This function is represented as:

Answer:

to what?

Step-by-step explanation:

Answer:

The domain of a function is the set of all possible inputs for the function.  The range of a function is the set of all possible outputs for the function.

Step-by-step explanation:

Answer:

1151.25

Step-by-step explanation:

You would divide $27,630 by 12 months.

You would then have her monthly salary. Since there are 4 weeks in a month, she has two pay periods. You would divide her monthly salary (2302.5) by two weeks, to get $1151.25

Answer:

see below (I hope this helps!)

Step-by-step explanation:

Alternate exterior angles are congruent so we know that ∠2 ≅ ∠ 7. Vertical angles are also congruent so ∠7 ≅ ∠6. Consecutive interior angles are supplementary so we know that ∠6 and ∠4 are supplementary. Now, we can use the Transitive Property (this states that if a = b and b = c then a = c) to compare ∠2 and ∠4. In this case, a = ∠2, b = ∠7 and c = ∠6 so we know that ∠2 ≅ ∠6 and since ∠6 is supplementary to ∠4, we can use the Transitive Property again to conclude that ∠2 and ∠4 are supplementary.

3^4*5^4 = (3*5)^4 = 15^4

Raise this to the exponent -3 and we get

(3^4*5^4)^(-3) = (15^4)^(-3) = 15^(4*(-3)) = 15^(-12)

The last step is to use the rule

x^(-k) = 1/( x^k )

So,

15^(-12) = 1/( 15^12 )

It seems like Tania multiplied all the exponents to get 4*4*(-3) = 16*(-3) = -48, but you only multiply the inner and outer exponents together as I did when I went from (15^4)^(-3) to 15^(-12)

Answer:

please mark my answer brainliest

Step-by-step explanation:

Answer:

[tex]x - (-8) = 3[/tex]

[tex]x = -5[/tex]

Step-by-step explanation:

Equation

[tex]x - -8 = 3[/tex]

Solving (a): Using Parenthesis

The equation can be rewritten by putting -8 in a parenthesis as follows;

[tex]x - (-8) = 3[/tex]

Solving (b): The correct answer

[tex]x - (-8) = 3[/tex]

Start by opening the bracket

[tex]x + 8 = 3[/tex]

Subtract 8 from both sides

[tex]x + 8 - 8 = 3 - 8[/tex]

[tex]x = 3 - 8[/tex]

[tex]x = -5[/tex]

Hence, the correct solution is [tex]x = -5[/tex]

Answer:

Step-by-step explanation:

5). y = 4 - x²

   Table for the points on this function will be,

   x          -2          -1          0           1           2

   y           0          3          4           3           0

  Therefore, Domain of the function will be: (-∞, ∞)

  And Range of the function will be : (-∞, 2]

7). [tex]y=2+\sqrt{x-1}[/tex]

    This function is defined from the values of x ≥ 1

   Table for the input-output values of this function is,

   x        1          2         5         10          17  

   y        2         3         4          5           6  

   Therefore, Domain of the function will be: [1, ∞)

   And Range of the function : [2, ∞)

Answer:

I thought it would be 24

Answer: [tex]\sqrt{66}[/tex]

Step-by-step explanation:

The Pythagorean Theorem says that a^2 + b^2 = c^2  where a and b are the two legs.  

In this care leg 1 is 4 and leg two is the square root of 50. So we will square them to find c which is the hypotenuse.

4^2 + [tex]\sqrt{50} ^2[/tex]  = C^2

16 +  50 = c^2

  66 = c^2

    c =[tex]\sqrt{66}[/tex]  

Answer:

Median

Step-by-step explanation:

A line that goes from the vertex of a triangle to the midpoint of the opposite side is a median.

Answer:

x=-3

Step-by-step explanation:

5x+7+3x=-8+3x

Combine like terms

8x+7 = 3x-8

Subtract 3x from each side

8x+7-3x = 3x-8-3x

5x+7 = -8

Subtract 7 from each side

5x+7-7 = -8-7

5x = -15

Divide each side by 5

5x/5 = -15/5

x = -3

Answer:

Root 37

Step-by-step explanation:

All of the others are square numbers so they have no decimal numbers. Root 37 = 6.08...... making it an irrational number.

Greetings from Brasil...

We will pass the - 2 to the 1st member

2 + [1/(X + 7)] = 15/(5(X + 7))

simplifying the numerator and denominator of the 2nd member

2 + [1/(X + 7)] = 3/(X + 7)

solving the sum of the 1st member

(2X + 15)/(X + 7) = 3/(X + 7)

product of the means by extremes

(2X + 15) · (X + 7) = 3 · (X + 7)

2X² + 15X + 14X + 105 = 3X + 21

2X² + 29X - 3X + 105 - 21 = 0

solving this 2nd degree equation

Δ = b² - 4.a.c

Δ = 26² -  4 . 2 . 84

Δ = 676 - 4. 2 . 84

Δ = 4

X' = (-26 + √4)/2.2     X'' = (-26 - √4)/2.2

X' = -24 / 4     X'' = -28 / 4

Answer:

x = 0

Step-by-step explanation:

First, distribute the -4 to the parentheses:

-4 + 3x = 2x - 4(1 - 3x)

-4 + 3x = 2x - 4 + 12x

Then, add like terms:

-4 + 3x = 14x - 4

Solve for x:

3x = 14x

0 = 11x

0 = x

Answer:

x=0

Step-by-step explanation:

We are given the following equation and asked to solve. We must solve for x by isolating x on one side of the equation.

-4 + 3x= 2x-4(1-3x)

First, distribute the -4. Multiply each term inside the parentheses by -4.

-4+3x=2x + (-4*1) + (-4*-3x)

-4+3x= 2x -4 + (-4*-3x)

-4+3x= 2x-4+12x

Combine like terms on the right side of the equation. The terms 2x and 12x can be added.

-4+3x= (12x+2x)-4

-4+3x=14x-4

Next, subtract 3x to both sides of the equation.

-4+3x-3x=14x-3x-4

-4= (14x-3x)-4

-4= 11x-4

Next, add 4 to both sides of the equation.

-4+4=11x-4+4

-4+4=11x

0=11x

Finally, divide both sides of the equation by 11.

0/11= 11x/11

0/11=x

0=x

The solution to the equation -4 + 3x= 2x-4(1-3x)  is x=0

Answer:

(no solutions exist)

Step-by-step explanation:

Hey, your question is incomplete so, plz write complete question to get the required answer

When we use an exponent of 1/2, it is the same as a square root. The more general rule is

[tex]\sqrt{x} = x^{1/2}[/tex]

In this case, we plug in x = 10.

The use of a fractional exponent is handy when you want to deal with things like cube roots on a calculator. This is because

[tex]\sqrt[3]{x} = x^{1/3}[/tex]

Many calculators don't have a button labeled [tex]\sqrt[3]{}[/tex] but they have the button [tex]x^y[/tex] to allow fractional exponents.

Let the width be x.

Then,length = 2x + 3

Area of rectangle = 560 [ Given ]

⇒ l × b = 560

⇒ ( 2x + 3 ) x = 560

⇒ 2x² + 3x - 560 = 0

⇒ 2x² + 35x - 32x - 560 = 0

⇒ x ( 2x + 35 ) - 16 ( 2x + 35 ) = 0

⇒ ( x - 16 ) = 0 and ( 2x + 35 ) = 0

⇒ x = 16 and x = -35/2 [ Ignore negative number ]

★ Width = x = 16 cm

★ Length = 2x + 3 = 2 × 16 + 3 = 32 + 3 = 35 cm

Answer:

3(3 +4n)

OR

9 + 12n

Step-by-step explanation:

9 + 12n

Factorize it

3(3 +4n)

OR

The answer is the same.

Since we can't add a number with a number and letter. So in that case the answer is ;

9 + 12n.

Thanks !!!!

Answer:

6x3−2x2−11x+4

Step-by-step explanation:

the numbers after the x are squared

Answer:

80%

Step-by-step explanation:

Total area is the area of two circles. Each circle if accepted as a unit, in total it equals to 2 units.

Shaded area:

Percentage of shaded area compared to total:

Answer: 80% of all region is shaded

Answer:

A hypothesis is a limited explanation of a phenomenon; a scientific theory is an in-depth explanation of the observed phenomenon. A law is a statement about an observed phenomenon or a unifying concept, according to Kennesaw State University. ... However, Newton's law doesn't explain what gravity is, or how it works.

Step-by-step explanation:

Answer:

law is federal

Step-by-step explanation:

ik