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3 years ago

What is the solution of the system of equations c+3d=8 and c=4d-6? Show work plz.

1 answer:

6 0

$\left\{\begin{array}{ccc}c+3d=8\\c=4d-6\end{array}\right\\\\substitute:\\\\(4d-6)+3d=8\\4d+3d-6=8\ \ \ \ /+6\\7d=14\ \ \ \ /:7\\d=2\\\\c=4\cdot2-6=8-6=2\\\\\left\{\begin{array}{ccc}c=2\\d=2\end{array}\right$

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Write the equation of a line in the given form.

Gnom [1K]

Answer:

$y = \frac{1}{4}x - 5$

Step-by-step explanation:

Slope intercept form: y = mx + b

Find slope:

m = (y₂ - y₁) / (x₂ - x₁)

= (-5 - (-4)) / (0 - 4)

= -1 / -4

= 1/4

Find y intercept using anyone of the given points and slope from above:

y = mx + b

$-5 = \frac{1}{4}(0) + b$

b = -5

Now use the above slope and y intercept to create equation of a line:

$y = \frac{1}{4}x - 5$

3 0

3 years ago

a ladder 6m long leans against the wall of house if the foot of the ladder makes an angle 58 degree with tye ground how far is t

Vedmedyk [2.9K]

Answer:

The base of the ladder is 3.2 meters far from the wall.

Step-by-step explanation:

We need to calculate the base of a right triangle. The given information is:

h: hypotenuse = length of the ladder = 6 m

b: is the base =?

θ: is the angle between the hypotenuse and the base = 58°

To find the base we can use the following trigonometric equation:

$cos(\theta) = \frac{b}{h}$

$b = cos(\theta)*h = cos(58)*6 = 3.2 m$

Therefore, the base of the ladder is 3.2 meters far from the wall.

I hope it helps you!

4 0

3 years ago

A fifth-degree polynomial equation with rational coefficients has the roots 3, 8i, and 7- radical 5. Which are also roots of the

Sliva [168]

Using <u>complex numbers and radicals</u>, it is found that the correct option is C.

When a complex number is a root of a polynomial function, it's conjugate also has to be.

Hence, since 8i is a root of the function, -8i is also a root.

The same is valid for radicals, as they are in the $\pm$ format.

Since $7 - \sqrt{5}$ is a root, $7 + \sqrt{5}$ is also a root.

Hence, option C is correct.

For more on <u>complex numbers and radicals</u>, you can check brainly.com/question/25173944

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2 years ago

St 2

Lubov Fominskaja [6]

Answer:

$5.5

Step-by-step explanation:

6 * N (notebook) + 3 * P (pen) = 27

n = 1.5 +P

6 * (1.5 + P) + 3 * P = 27

9 +6p +3p = 27

9p = 18

p (pen): $2

N (notebook): $3.5

combined cost of 1 pen and 1 notebook: $2 + $ 3.5 = $ 5.5

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3 years ago

Write an algebraic rule for the rotation for s (-1,3) s' (-3,-1)

USPshnik [31]

That's the symmetric property

6 0

3 years ago