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JulijaS [17]
4 years ago
10

Use the system of equations to answer the questions.

Mathematics
1 answer:
Mrac [35]4 years ago
3 0

Answer:

the value of x and y is 3 and -1 respectively.

Step-by-step explanation:

from the question

let

2x + 3y = 3........................ equation 1

y = 8 - 3x.............................. equation 2

put y = 8 - 3x in equation 1

2x + 3y = 3........................ equation 1

2x + 3 ( 8 - 3x) = 3

2x + 24 - 9x = 3

24 - 7x = 3

24  = 3 + 7x

24 -3 = 7x

21 = 7x

divide both sides by 7

x = 3

put x = 3 in equation 2

y = 8 - 3x.............................. equation 2

y = 8 - 3 ( 3)

y = 8 -9

y = -1

therefore the value of x and y is 3 and -1 respectively.

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The circumference of a circle is 15π ft. What is the area, in square feet? Express your answer in terms of π.
DerKrebs [107]

Answer:

  • Area of the circle is 56.25π square feet.

Step-by-step explanation:

<u>Given that</u>:

  • The circumference of a circle is 15π ft.

<u>To Find</u>:

  • What is the area, in square feet?

<u>We know that</u>:

  • Circumference of a circle = 2πR
  • Area of a circle = πR²

Where,

  • Radius is denoted as R.

<u>Finding the radius of the circle</u>:

Circumference of a circle = 15π

⟶ 2πR = 15π

⟶ 2πR = 2π × 7.5

Cancelling 2π.

⟶ R = 7.5

∴ Radius of the circle = 7.5 ft.

<u>Finding the area of the circle</u>:

⟶ Area = πR²

⟶ Area = π(7.5)²

⟶ Area = π × 7.5 × 7.5

⟶ Area = π × 56.25

⟶ Area = 56.25π

∴ Area of the circle = 56.25π ft.²

7 0
3 years ago
Which expression is equivalent to third- 32^3/5 ​
lara [203]

Answer:

Step-by-step explanation:

(-32)^3/5 =((-32)^1/5)^3 = (-2)^3 = -8. QED

6 0
3 years ago
If 115 steps = 1 mln and 2 steps = 5 feet what is the ratio of feet to minutes?​
Tanya [424]

Answer:

55

Step-by-step explanation:

7 0
4 years ago
1. The sum of two consecutive integers is at least 23. What is the smallest value that will make the statement true?
Volgvan

Answer:

1- 11+ 12 = 23

2- -7 + -6 = -13

7 0
3 years ago
Read 2 more answers
MN is a diameter of a circle with centre ' O ' . If BD = CD , prove that ∠OAD = ∠OCD
Varvara68 [4.7K]

Answer:

\sf \: Proved \: \angle \: OAD  \:  =  \angle \: OCD

Step-by-step explanation:

<em>Given:</em>

Mn is diameter of circle having centre O

and BD = OD,

<em><u>To prove that:</u></em>

<u>\angle \: OAD  \:  =  \angle \: OCD</u>

<em>Solution:</em>

Join the points O and B and draw OB,

On joining the line,

in ∆OCD and ∆OBD,

OC =OB → (Radius of same circle)

BD =CD → (from given)

OD =OD → (Common side in both the triangles)

Hence ∆OCD and ∆OBD are congruent from SSS property.

so we can say that,

\angle \: OBD  \:  =  \angle \: OCD

Consider above prove as statement A

Corresponding angles of congruent traingle.

in ∆ OAB,

OA = OB (radius of same circle)

hence ∆OAB is an isosceles traingle.

We know that opposite angle of isosceles traingle are always equal. hence,

\angle \: OBD  \:  =  \angle \: OAB \\ \angle \: OAB  \:  =  \angle \: OAD (same \: angles) \\ \angle \: OBD  \:  =  \angle \: OAD

Consider above prove as statement B

From Statement A & B we can say that

\angle \: OAD  \:  =  \angle \: OCD

<em>Thanks for joining brainly community!</em>

5 0
2 years ago
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