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3 years ago

Given that ABCD is a rhombus, find the value of x. (X+14)

Mathematics

1 answer:

Kay [80]3 years ago

6 0

Answer:

option B. $x=38^o$

Step-by-step explanation:

we know that

1) The two diagonals of a rhombus are perpendicular

2) The sum of the interior angles in any triangle must be equal to 180 degrees

Let

O ----> the intersection point of the diagonals of the rhombus

In the right triangle OAD

$x^o+(x+14)^o+90^o=180^o$

solve for x

$x^o+(x+14)^o=90^o$

$2x=90^o-14^o$

$2x=76^o$

$x=38^o$

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igomit [66]

Answer:

Step-by-step explanation:

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2 years ago

X^2+y^2=25 find the distance of point (x,y) from origin

storchak [24]

Answer:

Step-by-step explanation:

The radius is 5.

All I do was think of the center-radius form a circle

(x-h)^2+(y-k)^2=r^2

x^2 + y^2 =25

(x-0)^2+(y-0)^2=5^2

The center is (0,0) and the radius is 5.

So a point on the circle (x,y) has a distance of 5 from the center

and the center's case here is (0,0).

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2 years ago

2. Given: -2x =4y +62(2y+3) =3x -5What is the solution (x,y)?I

Andrews [41]

this is a 2x2 system of equations.

Let:

-2x = 4y + 6 (1)

and

2(2y+3) = 3x - 5 (2)

Let's rewrite (1) as:

2x + 4y = -6 (1)

and (2) as:

3x - 4y = 11 (2)

Now, from (1)

Let's solve for x:

2x + 4y = -6

Subtract 4y from both sides:

2x + 4y - 4y = -6 - 4y

2x = -6 - 4y

Divide both sides by 2:

2x/2 = (-6 - 4y)/2

x = -3 - 2y (3)

Replacing (3) into (2)

3x - 4y = 11

3(-3 - 2y) - 4y = 11

Using distributive property:

-9 - 6y - 4y = 11

Add like terms:

-10y - 9 = 11

Add 9 to both sides:

-10y - 9 + 9 = 11 + 9

-10y = 20

Divide both sides by -10:

(-10y)/-10 = 20/-10

y = -2

Finally, replace the value of y into (3)

x = -3 - 2y

x = -3 - 2(-2)

x = -3 + 4

x = 1

Therefore the solution is :

x= 1 and y=-2

(x,y) = (1,-2)

7 0

1 year ago

Law of sines: 2.2 units 2.4 units 3.0 units 3.3 units

Arada [10]

Answer:

$RS=2.4\ units$

Step-by-step explanation:

<em>The complete question is </em>

What is the length of line segment RS? Use the law of sines to find the answer. Round to the nearest tenth.

see the attached figure to better understand the problem

step 1

Find the measure of angle S

Applying the law of sines

$\frac{QS}{sin(R)}=\frac{QR}{sin(S)}$

substitute the given values

$\frac{3.1}{sin(80^o)}=\frac{2.4}{sin(S)}$

Solve for sin(S)

$sin(S)=\frac{sin(80^o)}{3.1}(2.4)$

$S=sin^{-1}[sin(80^o)}{3.1}(2.4)]$

$S=49.68^o$

step 2

Find the measure of angle Q

Remember that the sum of the interior angles in any triangle mut b equal to 180 degrees

$m\angle Q+m\angle R+m\angle S=180^o$

substitute the given values

$m\angle Q+80^o+49.68^o=180^o$

$m\angle Q+129.68^o=180^o$

$m\angle Q=180^o-129.68^o$

$m\angle Q=50.32^o$

step 3

Find the length of segment RS

Applying the law of sines

$\frac{QS}{sin(R)}=\frac{RS}{sin(Q)}$

substitute the given values

$\frac{3.1}{sin(80^o)}=\frac{RS}{sin(50.32^o)}$

$RS=\frac{3.1}{sin(80^o)}{sin(50.32^o)}$

$RS=2.4\ units$

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3 years ago

Michael's teacher bought a box of 124 crayons for the art class to share. The crayons cost $21.08 with tax included. What was th

Marizza181 [45]

Well, that would be $0.17 per crayon with tax. The answer with out tax depends on where they were bought. Tax where I live would be 7%, making the crayons' shelf price $19.60, that would be $0.15 per crayon.

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3 years ago