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2 years ago

Consider the system of equations.

Mathematics

2 answers:

lidiya [134]2 years ago

5 0

Answer:

A. (4, -4)

Step-by-step explanation:

Equation form x = 4, y = −4

Yuri [45]2 years ago

5 0

Answer:

Option A

Step-by-step explanation:

5x + 2 y = 12 -----------(I)

5x - 2y = 28 ------------(II)

Add equation (I) & (II). So, y will be eliminated and we will get the value of x

(I) 5x + 2y = 12

(II) 5x -2y = 28 {Now add}

10x = 40

x = 40/10

x = 4

Plugin x = 4 in equation (I)

5*4 + 2y = 12

20 + 2y = 12

2y = 12 - 20

2y = -8

y = -8/2

y = -4

You might be interested in

What are the potential solutions of log4x+log4(x+6)=2?

lions [1.4K]

The potential solutions of $log_4x+log_4(x+6)=2$ are 2 and -8.

<h3>Properties of Logarithms</h3>

From the properties of logarithms, you can rewrite logarithmic expressions.

The main properties are:

Product Rule for Logarithms - $log_{b}(a*c)=log_{b}a+log_{b}c$
Quotient Rule for Logarithms - $log_{b}(\frac{a}{c} )=log_{b}a-log_{b}c$
Power Rule for Logarithms - $log_{b}(a^c)=c*log_{b}a$

The exercise asks the potential solutions for $log_4x+log_4(x+6)=2$ . In this expression you can apply the Product Rule for Logarithms.

$log_4x+log_4(x+6)=2\\ \\ x*(x+6)=4^2\\ \\ x^2+6x=16\\ \\ x^2+6x-16=0$

Now you should solve the quadratic equation.

Δ= $b^2-4ac=36-4*1*(-16)=36+64=100$ . Thus, x will be $x_{1,\:2}=\frac{-6\pm \:\sqrt{100} }{2\cdot \:1}=\frac{-6\pm \:10}{2}$ . Then:

$x_1=\frac{-6+10}{2}=\frac{4}{2} =2\\ \\ \:x_2=\frac{-6-10}{2}=\frac{-16}{2} =-8$

The potential solutions are 2 and -8.

Read more about the properties of logarithms here:

brainly.com/question/14868849

4 0

2 years ago

what would the phrase "three times the sum of a number and 4" look like as a variable expression? 3(3x 4) 3x 4 3x−4 3(x 4)

rosijanka [135]

It would be
(X + 3) times 3

6 0

2 years ago

Read 2 more answers

(a) Find a vector parallel to the line of intersection of the planes −4x+2y−z=1 and 3x−2y+2z=1.

valentinak56 [21]

Find the intersection of the two planes. Do this by solving for z in terms of x and y ; then solve for y in terms of x ; then again for z but only in terms of x.

-4x + 2y - z = 1 ==> z = -4x + 2y - 1

3x - 2y + 2z = 1 ==> z = (1 - 3x + 2y)/2

==> -4x + 2y - 1 = (1 - 3x + 2y)/2

==> -8x + 4y - 2 = 1 - 3x + 2y

==> -5x + 2y = 3

==> y = (3 + 5x)/2

==> z = -4x + 2 (3 + 5x)/2 - 1 = x + 2

So if we take x = t, the line of intersection is parameterized by

r(t) = ⟨t, (3 + 5t )/2, 2 + t⟩

Just to not have to work with fractions, scale this by a factor of 2, so that

r(t) = ⟨2t, 3 + 5t, 4 + 2t⟩

(a) The tangent vector to r(t) is parallel to this line, so you can use

v = dr/dt = d/dt ⟨2t, 3 + 5t, 4 + 2t⟩ = ⟨2, 5, 2⟩

or any scalar multiple of this.

(b) (-1, -1, 1) indeed lies in both planes. Plug in x = -1, y = 1, and z = 1 to both plane equations to see this for yourself. We already found the parameterization for the intersection,

r(t) = ⟨2t, 3 + 5t, 4 + 2t⟩

3 0

2 years ago

I REALLY NEED AN ANSWER FAST! Which statement about the diagram is true?

Marina86 [1]

Answer:

Step-by-step explanation:

To keep it short, refer to triangle exterior angle theorem.

Edit: If you want the full explanation,

A isn't the answer. The triangle exterior angle states that the measure of the 2 triangle interior add up to the the exterior angle of the other interior angle within the triangle.

Meaning that

measure of angle 1 equal the measure of 3 and 4 combined.

B. is wrong they are equal to each other because angle 2 is equal to angle 2

angle 1 is equal to angle 3 and 4

So they are equal

C.Wrong unless it a 30 60 90 triangle or 45 45 90 triangle, C is wrong

D. is right since measure of angle 4 and angle 3 add up to angle 1, angle 4 would be lesser than angle 1.

3 0

3 years ago

Read 2 more answers

HELP ME OUT PLEASE!!!

ANTONII [103]

Answer:

D) y= 4x - 1

Step-by-step explanation:

We are basically trying to see which of the equations provided are true on both sides of the equal sign when you plug in the x and y values.

Let's start!

Choice A:

plug in 0 for x and -1 for y

-1 = 4(0)

And you are left with...

-1 = 0

This equation is false! Therefore it does not match the function in the table

Choice B:

plug in the values again

-1 = 0 + 1

-1 = 1

False!

Choice C:

-1 = 0 + 5

-1 = 5

False!

Lastly...Choice D:

-1 = 4(0) -1

Multiply 4 and 0 which is 0, so you are left with...

-1 = -1

This equation is true!!

So your answer is D

Hope this helps :D

7 0

2 years ago