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2 years ago

Determine whether each ordered pair is a solution to the inequality x+y>6. Select all solutions.

Mathematics

1 answer:

Juli2301 [7.4K]2 years ago

7 0

Answer:

B. (6,1)

C. (7,3)

D. (9,9)

Step-by-step explanation:

In a coordinate pair, the first number is x and the second number is y.

A. -7 + -4 = -11 -11 is less than 6. -11<6

B. 6 + 1 = 7 7 is greater than 6. 7>6

C. 7 + 3 = 10 10 is greater than 6. 10>6

D. 9 + 9 = 18 18 is greater than 6. 18>6

E. 2 + -8 = -6 -6 is less than 6. -6<6

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3 years ago

Use the quadratic formula to solve for the roots in the following equation. 4x 2 + 5x + 2 = 2x 2 + 7x – 1

Natali5045456 [20]

Answer:

So, The roots are $x= \frac{1+\sqrt{5}i}{2} \,\, and \,\,x= \frac{1-\sqrt{5}i}{2}$

Step-by-step explanation:

$4x^2 + 5x + 2 = 2x^2 + 7x - 1$

We need to solve the equation to find the roots using quadratic formula.

The quadratic formula is:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Rearranging the above equation:

$4x^2 -2x^2+ 5x-7x + 2+1 =0$

$2x^2 -2x + 3 =0$

Where a =2 , b=-2 and c =3 Putting values in quadratic equation and solving:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(2)(3)}}{2(2)}\\x=\frac{2\pm\sqrt{4-24}}{4}\\x=\frac{2\pm\sqrt{-20}}{4}\\\sqrt{-20} \,\,can\,\,be\,\, written\,\, as\,\, 2\sqrt{-5}\\ x=\frac{2\pm2\sqrt{-5}}{4}\\x=\frac{2+2\sqrt{-5}}{4} \,\, and \,\, x=\frac{2-2\sqrt{-5}}{4}\\x=\frac{2(1+\sqrt{-5})}{4} \,\, and \,\, x=\frac{2(1-\sqrt{-5})}{4}\\ x=\frac{1+\sqrt{-5}}{2} \,\, and \,\, x=\frac{1-\sqrt{-5}}{2}\\As \,\,we\,\, know\,\, \sqrt{-1} = i \\$

$x= \frac{1+\sqrt{5}i}{2} \,\, and \,\,x= \frac{1-\sqrt{5}i}{2}$

So, The roots are $x= \frac{1+\sqrt{5}i}{2} \,\, and \,\,x= \frac{1-\sqrt{5}i}{2}$

6 0

3 years ago

The lower supports are and the area of the two supports is square meters. The upper arch can be decomposed as one semicircle wit

Galina-37 [17]

Answer:

The lower supports are Congruent Rectangles and the area of the two supports is 24 square meters.

The upper arch can be decomposed as one semicircle with radius 6 meters minus a semicircle with radius 3 meters.

The area of the archway is (13.5 π + 24) square meters.

Step-by-step explanation:

See attachment for the firgure,

In order to determine the area of archway = The area of upper support + area of lower support.

As given, the lower support are two congruent rectangles consists of dimension 3 m × 4 m

Therefore, the area of lower support can be written as,

The area of lower support = 3 × 4 + 3 × 4 = 12 + 12 = 24 square m.

Now, the upper support arch can be decomposed as the two concentric semi circles having radius 3 m and 6 m,

Hence, the area of the upper support = Area of semi circle having radius i.e 6 m - Area of semi circle having radius i.e 3 m

=> π6²/2 - π3²/2= 27π/2= 13.5π square m

Therefore, the area of the archway = (13.5 π + 24) square meters

4 0

3 years ago

Which one of these is a rational number

alekssr [168]

D is the ans. Square root of 49 equals to 7

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2 years ago

Read 2 more answers

PLEASE HELP ME ASAP

pickupchik [31]

lol we have the same question on our test besides i’m in middle school Answer: idfk

Step-by-step explanation: don’t ask me i’m failing math

7 0

2 years ago