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3 years ago

Given that ABCD is a rhombus, what is the value of x?

Mathematics

1 answer:

Maslowich3 years ago

4 0

Answer:

Step-by-step explanation:

We know that diagonals bisect angles of a rhombus, meaning that they split the angles of two equal parts, that opposite angles are equal, and that the angles of a quadrilateral, such as a rhombus, add up to 360 degrees.

Looking at the drawing I uploaded, and taking into account that diagonals bisect angles of a rhombus, we can say that angle x = y and z = 5x-18

Next, given that opposite angles are equal, we can say that angle B = angle D and angle A = angle C. Therefore,

A+B+C+D= 360 (as the angles of a quadrilateral add up to 360)

A + B + A + B = 360 (plugging in A for C and B for D)

2 ( A + B) = 360

A + B = 180

x + y + z + 5x - 18 = 180 (plugging x+y in for A, and z+5x-18 in for B, as x and y make up A and z and 5x-18 make up B)

x+x+5x-18+5x-18 = 180 (because x=y and z=5x-18)

2(x+5x-18) = 180

divide both sides by 2

x+5x-18=90

6x-18=90

add 18 to both sides

6x=108

divide both sides by 6

x = 18

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dlinn [17]

Answer:

A, B and C

Step-by-step explanation:

Given any three side lengths of a right triangle, the longest side is the hypotenuse.

The side lengths of a right triangle must satisfy the Pythagorean Theorem.

Pythagorean Theorem: $Hypotenuse^2=Opposite^2+Adjacent^2$

Option A: $3, 6, \sqrt{45}$

$(\sqrt{45})^2=3^2+6^2\\45=36+9\\45=45$

True

Option B: 2.5, 6, 6.5

$6.5^2=6^2+2.5^2\\42.25=36+6.25\\42.25=42.25 (TRUE)$

Option C: $4, 8, \sqrt{80}$

$4, 8, \sqrt{80}\\( \sqrt{80})^2=4^2+8^2\\80=16+64\\80=80 (TRUE)$

Since all are true, the side lengths in Options A, B and C forms a right triangle,

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3 years ago

Question 7 of 10

Vsevolod [243]

Answer:

g(x) = –3(x + 6)2 + 48.

Step-by-step explanation:

The graph of f(x) = x2 is shifted right 6 units. The graph of f(x) = x2 is shifted down 48 units. The graph of f(x) = x2 is reflected over the y-axis.

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3 years ago

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Explain why a + b = d. B A C swer

bixtya [17]

Answer:

Explanation below

Step-by-step explanation:

Angles in a Triangle

There are two basic relations of angles we need to recall:

Supplementary angles add up to 180°
Internal angles of a triangle add up to 180°

Note a, b, and c are the internal angles of the triangle. The angle c is what is needed to a+b to complete 180°, thus:

c = 180 - ( a + b )

Also, note c and d are supplementary angles. Again, c is what is needed to d to complete 180°, thus

c = 180 - d

From the two relations above, it follows that:

a + b = d

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3 years ago

Question 13 y-5x= -4

Julli [10]

Which variable are we solving for?

For y:

y= 5x-4/ 13

For x:

x= 13y+4/ 5

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3 years ago

If x^2-x-6 and x^2+3x-18 hacpve a common factor (x-a) then find the value of a.

DedPeter [7]

Answer:

a = 3

Step-by-step explanation:

Factor both expressions

x² - x - 6

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 1)

The factors are - 3 and + 2 , since

- 3 × 2 = - 6 and - 3 + 2 = - 1 , thus

x² - x - 6 = (x - 3)(x + 2)

-----------------------------------

x² + 3x - 18

consider factors of constant term (- 18) which sum to give the coefficient of the x- term (+ 3)

The factors are + 6 and - 3 , since

6 × - 3 = - 18 and 6 - 3 = + 3 , thus

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Both expressions have a common factor of (x - 3)

Compare with (x - a ), then a = 3

3 0

3 years ago

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