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Tresset [83]
3 years ago
6

the graphs of 2x+3Y=5 and 3x+y=18 contain two sides of a triangle. a vertex of the triangle is at the intersection of the graphs

. what are the coordinates of the intersection?
Mathematics
1 answer:
Artemon [7]3 years ago
5 0

Answer:

(7, - 3 )

Step-by-step explanation:

Solve the 2 equations simultaneously to find intersection.

Given the equations of the sides

2x + 3y = 5 → (1)

3x + y = 18 → (2)

Multiplying (2) by - 3 and adding to (1) will eliminate the y- term

- 9x - 3y = - 54 → (3)

Add (1) and (3) term by term

(2x - 9x) + (3y - 3y) = (5 - 54) and simplifying gives

- 7x = - 49 ( divide both sides by - 7 )

x = 7

Substitute x = 7 into (1) or (2) for corresponding value of y

Substituting in (2)

21 + y = 18 ( subtract 21 from both sides )

y = - 3

Point of intersection = (7, - 3 )

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Please include work!
geniusboy [140]

Answer:

x = ± 4

y = - 2

Step-by-step explanation:

y = 0.5x² - 10 ------------------------(I)

y = -x² + 14   ------------------------(II)

Substitute the y value in equation (II)

    0.5x² - 10  = -x² + 14           {Add x² to both sides}            

0.5x² + x² -10 = 14                  {combine like terms}

       1.5x² - 10 = 14                   {Add 10 to both sides}

               1.5x² = 14 + 10

                1.5x² = 24         {Divide both sides by 1.5}

               1.5x²/1.5 = 24/1.5

                       x² = 16

                      x = ±4

Substitute x = 4 in (I)

y = 0.5 * 4² - 10

 = 0.5*16 - 10

 = 8- 10

y = -2

Substitute x = -4 in (I)

y = 0.5 * (-4)² - 10

 = 0.5*16 - 10

 = 8- 10

y = -2

5 0
3 years ago
Mary wants to buy a new house but needs money for the down payment. Her parents agree to lend her money at an annual rate of 2%,
lukranit [14]

Answer:

a) Simple interest paid = $360

b) Total repayment amount = $6360

Step-by-step explanation:

It is given that:

Principal, P = $6000

Rate of interest, R = 2%

Time, T = 3 years

<em>(a) Total interest paid</em>:

<u>Formula</u> for Simple Interest is given as:

S.I. = \dfrac{P \times R \times T}{100}

Putting the values of P, R and T to find out Simple Interest:\\\Rightarrow S.I. = \dfrac{6000 \times 2 \times 3}{100}\\\Rightarrow S.I. = \$360

<em>(b) Total repayment amount</em>:

We know that formula for total amount is given as:

<em>Amount = Principal + Simple Interest</em>

Amount = 6000 + 360 = $6360

So, total repayment amount = $6360

So, the answers are:

a) Simple interest paid = $360

b) Total repayment amount = $6360

3 0
3 years ago
Find the values of x and y. lines that appear to be tangent are tangent
Ket [755]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The value of  y  =  122^o

The value of  x = 61^o

Step-by-step explanation:

Generally the total angle that make up a circle is

      \theta _T = 360

From the diagram we see that

    \theta _T  =  y^o + 238^o

=>    y^o  =  360  -238

       y^o  =  122^o

Generally angle that is formed as a result of interception of a chord and a tangent is equal to the intercepted arc divided by 2

 This implies that

           x =  \frac{y}{2}

substituting values

          x =  \frac{122}{2}

          x = 61^o

4 0
3 years ago
The probability of pulling an orange is 2 out of 5 if I 20 times how many of them would be orange
telo118 [61]
The answer would be 8.
4 0
2 years ago
What are the zeros of the polynomial function f(x)=x(x-4)(x+9)? HELP NEEDED!!!!
Kipish [7]

Answer: 0, 4, -9

Set the equation equal to zero.

x(x - 4)(x + 9) = 0

Solve for x by setting each factor equal to zero.

The factors in the equation are x, (x - 4), and (x + 9).

  • x = 0
  • (x - 4) = 0

        x = 4

  • (x + 9) = 0

        x = -9

The zeros of the function are 0, 4, and -9.

7 0
3 years ago
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