What is the inverse of y = 2x

Ray UW is the angle bisector of AngleVUT.

tester [92]

Answer:

AngleWUT =38°, option 2

Step-by-step explanation:

We have three rays passing through U. A ray is set extend in one direction with one fixed point.

We have UW ray bisecting VUT.As the ray bisects the angle between VUW and WUT would be same .

Given angles are (4x+6)° and (6x-10)°.

As these angles are equal

$4x+6=6x-10$

$2x=16$

$x=8$

AngleWUT = (6x – 10)°

and x is 8 so on substituting AngleWUT =38°.

5 0

3 years ago

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Find the standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8

Gekata [30.6K]

First, let $(x,y)$ be a point in our parabola. Since we know that the focus of our parabola is the point (0,8), we are going to use the distance formula to find the distance between the two points:
$\sqrt{(x-0)^{2}+(y-8)^{2}}$

Next, we are going to find the distance between the directrix and the point in our parabola. Remember that the distance between a point (x,y) of a parabola and its directrix, $y=c$ , is: $|y-c|$ . Since our directrix is y=-8, the distance to our point will be:
$|y-(-8)|$
$|y+8|$

Now, we are going to equate those two distances, and square them to get rid of the square root and the absolute value:
$\sqrt{(x-0)^{2}+(y-8)^{2}}=|y+8|$
$(\sqrt{(x-0)^{2}+(y-8)^{2}})^{2}=|y+8|^{2}$
$(x-0)^{2}+(y-8)^{2}=y+8$

Finally, we can expand and solve for $y$ :
$x^2+y^2-16y+64=y^2+16y+64$
$x^{2}-16y=16y$
$32y=x^{2}$
$y= \frac{1}{32} x^2$

We can conclude that t<span>he standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8 is </span> $y= \frac{1}{32} x^{2}$

3 0

3 years ago

Which number can each term of the equation be multiplied by to eliminate the fractions before solving? 6 –3/4x +1/3 =1/2 x + 5

irga5000 [103]

Answer:

The number is 12.

Step-by-step explanation:

Given: $6-\dfrac{3}{4}x+\dfrac{1}{3}=\dfrac{1}{2}x+5$

We need to find a number multiply to each term to get rid of fraction.

We will find LCD of denominator.

First we see the numbers at denominator

Denominators are 4,3,2

Now, we will find the LCD of 2,3, and 4

Factor of 2: 2x1

Factor of 3: 3x1

Factor of 4: 2x2x1

LCD = 2x2x3 = 12

If we multiply by 12 to each term to eliminate the fraction.

Simplest equation:

$12\cdot 6-12\cdot \dfrac{3}{4}x+12\cdot \dfrac{1}{3}=12\cdot \dfrac{1}{2}x+12\cdot 5$

$72-9x+4=6x+60$

Hence, The number is 12.

5 0

3 years ago

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URGENT!!!! The area of a rectangular floor is 80 square feet. The length of the floor is 2 feet less than the width of the floor

KatRina [158]

Answer:

The width of the floor is 10 ft.

Step-by-step explanation:

First, you have to form expressions of width and length in terms of w. With the given information :

width = w ft

length = (w - 2) ft

Given that the area of rectange is A = length × width so you have to subtitute the expressions and value into the formula :

A = l × w

80 = (w - 2) × w

w(w - 2) = 80

w² - 2w = 80

w² - 2w - 80 = 0

(w + 8)(w - 10) = 0

w + 8 = 0

w = -8 (rejected)

w - 10 = 0

w = 10

3 0

2 years ago

Given: // CDAB , ∠≅∠ DB and ≅ EDBF . Prove: Δ ABF ≅ Δ CED

SCORPION-xisa [38]

Given: line segment AB // to line segment CD, ∠B ≅∠D and line segment BF ≅ to line segment ED. Prove: Δ ABF ≅ Δ CED.

Follow the matching numbers on the statement versus reason chart.

Statement:

1. line segment AB // to line segment CD.

2. ∠B ≅∠D

3. line segment BF ≅ to line segment ED.

4. ∠A ≅∠C

5. Δ ABF ≅ Δ CED

Reason:

1. Given

2. Given

3. Given

4. Alternate interior angles are congruent.

5. Corresponding parts of congruent triangles are congruent.

4 0

3 years ago