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3 years ago

Solve the system by substitution. y = 5x y = 9x + 4

Mathematics

1 answer:

SVEN [57.7K]3 years ago

5 0

Answer:

(-1, -5)

Step-by-step explanation:

$\left \{ {{y=5x} \atop {y=9x+4}} \right.$

1. We must calculate x, for that we must substitute y, so we have:

5x=9x+4

2. Now we solve the equation.

5x-9x=4

-4x=4

x=-1

3. Now we must calculate y

y=5x

y=5(-1)

y=-5

And the answer is (-1, -5)

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Find the area of the shape shown below.

DIA [1.3K]

Area = rectangle + triangle
A=(LxW)+(1/2 bh )
A=(20x10)+(1/2x20x4)
A=200+40
A=240

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3 years ago

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. Illustra

Rainbow [258]

Answer:

$x = t$

$y = 1 - t$

$z = 2t$

Step-by-step explanation:

Given

$x=t$

$y=e^{-t}$

$z=2t-t^2$

(0, 1, 0)

The vector equation is given as:

$r(t) = (x,y,z)$

Substitute values for x, y and z

$r(t) = (t,\ e^{-t},\ 2t - t^2)$

Differentiate:

$r'(t) = (1,\ -e^{-t},\ 2 - 2t)$

The parametric value that corresponds to (0, 1, 0) is:

$t = 0$

Substitute 0 for t in r'(t)

$r'(t) = (1,\ -e^{-t},\ 2 - 2t)$

$r'(0) = (1,\ -e^{-0},\ 2 - 2*0)$

$r'(0) = (1,\ -1,\ 2 - 0)$

$r'(0) = (1,\ -1,\ 2)$

The tangent line passes through (0, 1, 0) and the tangent line is parallel to r'(0)

It should be noted that:

The equation of a line through position vector a and parallel to vector v is given as:

$r(t) = a + tv$

Such that:

$a = (0,1,0)$ and $v = r'(0) = (1,-1,2)$

The equation becomes:

$r(t) = (0,1,0) + t(1,-1,2)$

$r(t) = (0,1,0) + (t,-t,2t)$

$r(t) = (0+t,1-t,0+2t)$

$r(t) = (t,1-t,2t)$

By comparison:

$r(t) = (x,y,z)$ and $r(t) = (t,1-t,2t)$

The parametric equations for the tangent line are:

$x = t$

$y = 1 - t$

$z = 2t$

7 0

3 years ago

Please help me !! i do not understand

Oduvanchick [21]

Answer:

Step-by-step explanation:

8 0

3 years ago

100 points gor correct answer Identify the base of a triangle in which h=(3x+15) ft and A=(15x+75) ft^2.

ivolga24 [154]

Answer:

b = 10

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = $\frac{1}{2}$ bh ( b is the base and h the height )

Here h = 3x + 15 and A = 15x + 75, thus

$\frac{1}{2}$ × b × (3x + 15) = 15x + 75

Multiply both sides by 2 to clear the fraction

b(3x + 15) = 30x + 150

Divide both sides by (3x + 15)

b = $\frac{30x+150}{3x+15}$ ← factor numerator and denominator

= $\frac{30(x + 5)}{3(x+5)}$ ← cancel the factor (x + 5) on numerator/denominator

= $\frac{30}{3}$

= 10

7 0

3 years ago

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Find the measure of an angle with measure between 0 and 360 that is conterminal with an angle measuring -800

igomit [66]

Add 720 degrees (which represents two full revolutions around the center) to -800. Result: -80 degrees. This angle is in Quadrant IV.

Subtracting 80 from 360 will give you a positive angle co-terminal with -800 deg. 360 - 80 = ?

5 0

3 years ago

Read 2 more answers