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3 years ago

Find the exact value of x.

Mathematics

2 answers:

Anna007 [38]3 years ago

5 0

It would probably be 7.2111

oksian1 [2.3K]3 years ago

4 0

Answer:

The exact value of x will be $\sqrt{52}$ or 7.2111

Step-by-step explanation:

Hope this Helped

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Help quick ❗️❗️ Which sequence of transformations will change did your PQRS to figure P’Q’R’S’?

babymother [125]

Answer:

Counterclockwise rotation about the origin by 90° followed by reflection over the Y-axis ⇒ answer (D)

Step-by-step explanation:

* Lets revise the reflection and the rotation of a point

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

- If point (x , y) rotated about the origin by angle 90° counter clockwise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 90° clockwise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180°

∴ Its image is (-x , -y)

* There is no difference between rotating 180° clockwise or

anti-clockwise around the origin

- In our problem

# The vertices of the original figure are:

P(1 , -3) , Q (3 , -2) , R (3 ,-3) , S (2 , -4)

# The vertices of the image are:

P' (-3 , 1) , Q' (-2 , 3) , R' (-3 , 3) , S' (-4 , 2)

∵ x and y are switched

∴ The figure is rotated about origin by 90°

∵ The signs of the x-coordinates and the y-coordinates

didn't change

∴ The rotation is followed by reflection, to know about which

axis we must to find the images after the rotation

∵ P (1 , -3) ⇒ after rotation 90° counter clockwise is (3 , 1)

∵ Q (3 , -2) ⇒ after rotation 90° counter clockwise is (2 , 3)

∵ R (3 , -3) ⇒ after rotation 90° counter clockwise is (3 , 3)

∵ S (2 , -4) ⇒ after rotation 90° counter clockwise is (4 , 2)

* The images are P' (-3 , 1) , Q' (-2 , 3) , R' (-3 , 3) , S' (-4 , 2)

- The sign of x-coordinates of all of them changed

∴ The rotation followed by reflection over the y-axis

* The answer is ⇒ Counterclockwise rotation about the origin

by 90° followed by reflection over the Y-axis

7 0

3 years ago

I’ll mark you thank youuu

pentagon [3]

Answer:

y = 1/5x + 32/5

Step-by-step explanation:

3 0

3 years ago

Two problems here I need solved! I need every step, so please have that with your answers!!

Free_Kalibri [48]

QUESTION 1

We want to solve,

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x^{2}-6x+8}$

We factor the denominator of the fraction on the right hand side to get,

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x^{2}-4x - 2x+8}.$

This implies
$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x(x-4) - 2(x - 4)}.$

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{(x-4)(x - 2)}$

We multiply through by LCM of
$(x-4)(x - 2)$

$(x - 2) + x(x-4) = 2$

We expand to get,

$x - 2 + {x}^{2} - 4x= 2$

We group like terms and equate everything to zero,

${x}^{2} + x - 4x - 2 - 2 = 0$

We split the middle term,

${x}^{2} + - 3x - 4 = 0$

We factor to get,

${x}^{2} + x - 4x- 4 = 0$

$x(x + 1) - 4(x + 1) = 0$

$(x + 1)(x - 4) = 0$

$x + 1 = 0 \: or \: x - 4 = 0$

$x = - 1 \: or \: x = 4$

But
$x = 4$
is not in the domain of the given equation.

It is an extraneous solution.

$\therefore \: x = - 1$
is the only solution.

QUESTION 2

$\sqrt{x+11} -x=-1$

We add x to both sides,

$\sqrt{x+11} =x-1$

We square both sides,

$x + 11 = (x - 1)^{2}$

We expand to get,

$x + 11 = {x}^{2} - 2x + 1$

This implies,

${x}^{2} - 3x - 10 = 0$

We solve this quadratic equation by factorization,

${x}^{2} - 5x + 2x - 10 = 0$

$x(x - 5) + 2(x - 5) = 0$

$(x + 2)(x - 5) = 0$

$x + 2 = 0 \: or \: x - 5 = 0$

$x = - 2 \: or \: x = 5$

But
$x = - 2$
is an extraneous solution

$\therefore \: x = 5$

7 0

3 years ago

Write an equation in slope-intercept form for a line that passes through the

Anvisha [2.4K]

Answer:

y=(1/2)x+4

Step-by-step explanation:

you have 2 points but in order to find slope intercept you need slope so,

(y2-y1)/(x2-x1)

(-1+4)/(8-2)=1/2 =slope

slope intercept:

y-y1=m(x-x1)

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

y-2=(1/2)x+2

y=(1/2)x+4

3 0

3 years ago

Absolute value to find distance

qaws [65]

Answer:

Step-by-step explanation:

The distance between two any points <em>a</em> i <em>b</em> is |a-b| as we don't know which of them is larger number.

So:

a=-2 and b=1 means distance |-2-1| = |-3| = 3

{If we know the value of given points we can subtract the smaller one from the larger. It also works: -2<1, so the distance would be 2-(-1)=2+1=3}

6 0

3 years ago