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3 years ago

What is the area of this rhombus?

Mathematics

2 answers:

sasho [114]3 years ago

4 0

Answer:

22.5

Step-by-step explanation:

9 times 5 = 45

45/2 = 22.5

ioda3 years ago

3 0

Answer:

90 m²

Step-by-step explanation:

$A=\frac{pq}{2}$

10 · 18

180

180 ÷ 2

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There are 38 tables at the fifth grade picnic at a local park. There will be 182 students attending the picnic. The parents were

dmitriy555 [2]

Answer:

274 parents

Step-by-step explanation:

38 tables times 12 per table

38*12=456

456-182=274

5 0

3 years ago

Solve for x(one solution,no solution,or infinite solutions) -2(3x+-1)=-6x-1

shtirl [24]

Answer: 0= -3 No solution

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

If x+y=12 and xy=15,find the value of (x^2+y^2)

Mice21 [21]

Answer: $x^2+y^2=\dfrac{105\pm 18\sqrt6}{2}$

<u>Step-by-step explanation:</u>

EQ1: x + y = 12 --> x = 12 - y

EQ2: xy = 15

Substitute x = 12-y into EQ2 to solve for y:

(12 - y)y = 15

12y - y² = 15

0 = y² - 12y + 15

↓ ↓ ↓

a=1 b= -12 c=15

$.\ y=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\.\quad =\dfrac{-(-12)\pm \sqrt{(-12)^2-4(1)(15)}}{2(1)}\\\\\\.\quad =\dfrac{12\pm \sqrt{144-120}}{2}\\\\\\.\quad =\dfrac{12\pm \sqrt{24}}{2}\\\\\\.\quad =\dfrac{12\pm 2\sqrt{6}}{2}\\\\\\.\quad =6\pm \sqrt{6}$

Now, let's solve for x:

$xy=15\\\\x(6\pm\sqrt6)=15\\\\x=\dfrac{15}{6\pm\sqrt6}\\\\\\x=\dfrac{15}{6\pm\sqrt6}\bigg(\dfrac{6\pm\sqrt6}{6\pm\sqrt6}\bigg)=\dfrac{6\pm \sqrt6}{2}$

Lastly, find x² + y² :

$y^2=(6\pm \sqrt6)^2\quad \rightarrow \quad y^2=36\pm 12\sqrt6 +6\quad \rightarrow \quad y^2=42\pm 12\sqrt6$

$x^2=\bigg(\dfrac{6\pm \sqrt6}{2}\bigg)^2\quad \rightarrow \quad x^2=\dfrac{42\pm 12\sqrt6}{4}\quad \rightarrow \quad x^2=\dfrac{21\pm 6\sqrt6}{2}$

$x^2+y^2=\dfrac{21\pm 6\sqrt6}{2}+42\pm 12\sqrt6\\\\\\.\qquad \quad = \dfrac{21\pm 6\sqrt6}{2}+\dfrac{84\pm 24\sqrt6}{2}\\\\\\. \qquad \quad = \dfrac{105\pm 18\sqrt6}{2}$

5 0

3 years ago

What is the value of x in the solution to the following system of linear equations? Y=3x+2 y=x-4

omeli [17]

Answer:-3

Step-by-step explanation:

y=3x+2................(1)

y=x-4......................(11)

Subtract (11) from (1)

y-y=3x-x+2-(-4)

0=2x+2+4

0=2x+6

Collect like terms

0-6=2x

-6=2x

Divide both sides by 2

-6/2=2x/2

-3=x

x=-3

5 0

3 years ago

Factor the following equation to find its zeros. y = x² - 36

alukav5142 [94]

Answer:

x = 6, x = - 6

Step-by-step explanation:

Given

y = x² - 36

To find the zeros let y = 0, that is

x² - 36 = 0 ← x² - 36 is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

x² - 36 = 0

x² - 6² = 0

(x - 6)(x + 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 6 = 0 ⇒ x = - 6

3 0

3 years ago