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3 years ago

Write the equation of a line that passes through the point (1,4) and has a slope of 9.

Mathematics

1 answer:

Kryger [21]3 years ago

4 0

Answer:

y=9x-5

Step-by-step explanation:

You want to find the equation for a line that passes through the point (1,4) and has a slope of 9.

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

To start, you know what m is; it's just the slope, which you said was 9. So you can right away fill in the equation for a line somewhat to read:

y=9x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(1,4). When x of the line is 1, y of the line must be 4.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: b is what we want, the 9 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specifically passes through the point (1,4).

So, why not plug in for x the number 1 and y the number 4? This will allow us to solve for b for the particular line that passes through the point you gave!.

(1,4). y=mx+b or 4=9 × 1+b, or solving for b: b=4-(9)(1). b=-5.The equation of the line that passes through the point (1,4) with a slope of 9

y=9x-5

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What is a simple way to solve for the sum and difference of 2 cubes? For example, 27+64<img src="https://tex.z-dn.net/?f=x%5E3"

salantis [7]

Answer:

(3 + 4x)(9 - 12x + 16x²) = 0

(4m - 1)(16m² + 4m + 1) = 0

Step-by-step explanation:

Here we have to solve the sum of two cubes which is $27 + 64x^{3}$

Now, the equation is $27 + 64x^{3} = 0$

⇒ 3³ + (4x)³ = 0

⇒ (3 + 4x)[3² - 3(4x) + (4x)²] = 0

⇒ (3 + 4x)(9 - 12x + 16x²) = 0

So, (3 + 4x) = 0 or (9 - 12x + 16x²) = 0

Therefore, from the above two relation we can solve for x.

One root will be $- \frac{3}{4}$ and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation.

Again, we have to solve the difference of two cubes which is $64m^{3} - 1$

Now, the equation is $64m^{3} - 1 = 0$

⇒ (4m)³ - 1³ = 0

⇒ (4m - 1)[(4m)² + 4m(1) + 1²] = 0

⇒ (4m - 1)(16m² + 4m + 1) = 0

So, (4m - 1) = 0 or (16m² + 4m + 1) = 0

Therefore, from the above two relation we can solve for m.

One root will be $\frac{1}{4}$ and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation. (Answer)

8 0

3 years ago

OOOO

lbvjy [14]

Step-by-step explanation:

Given bi-quadratic equation is:

$x^4+95x^2 -500=0$

Substituting $x^2=a,$ given bi-quadratic equation reduces in the form of following quadratic equation:

$a^2 +95a -500=0\\$

Let us factorize the above quadratic equation:

$a^2 +95a -500=0\\\therefore\: a^2 +100a -5a-500=0\\\therefore\: a(a +100) -5(a+100)=0\\\therefore\: (a +100)(a -5)=0\\\therefore\: (a +100)=0\:\: or \:\: (a -5)=0\\\therefore\: a = - 100\:\: or \:\: a = 5\\\\CASE\: (1)\:\\When\: a = - 100 \implies x^2 = - 100\\\therefore x=\pm \sqrt{-100}\\$

Since square root of a negative number cannot be found, so:

$x \neq \pm \sqrt{-100}\\$

$CASE\: (2)\:\\When\: a =5 \implies x^2 =5\\\therefore x=\pm \sqrt{5}\\$

3 0

3 years ago

Please help!!!! i don’t understand any of this and really need it.

astraxan [27]

Answer:

B) 3.2 mi

Step-by-step explanation:

1. The midpoints: midpoint formula = ((x₁ + x₂)/2, (y₁+ y₂)/2)

upper = ((6 + -4)/2, (8 + 0)/2) --> (1, 4)

lower = ((-8 + 2)/2, (3 + -5)/2) --> (-3, -1)

2. Distance: distance formula = √((x₁ - x₂)² + (y₁ - y₂)²)

√((1 + 3)² + (4 + 1)²) = √(16 + 25) = √41 ≈ 6.403... ≈ 6.4

3. Scale: 6.4 * 0.5 mi = 3.2 mi

5 0

3 years ago

A bucket was 7/10 full with water. After Vick washed the car, the bucket wad only 3/10 full. What fraction of the water in the b

Phoenix [80]

Hey there!

Vick had 7/10 bucket of water. . . .

She used some of the water and now has 3/10 left . . .

Subtracts the numbers 7 and 3 to solve this:

7 - 3 = 4 <----

The correct answer to your question should be 4/10 of a bucket.

Vick used 4/10 of the bucket to wash the car.

Hope this helps you.
Have a great day!

3 0

3 years ago

Factor the expression below using the greatest common factor 6p3- 2p2 - 8p

miss Akunina [59]

Answer:

The Factor of expression using the greatest common factor is $2p(3p^2- p-4)$