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2 years ago

What is the solution to the system of equations below?

Mathematics

1 answer:

Burka [1]2 years ago

3 0

Answer:

(x, y) = (-4, -15)

Step-by-step explanation:

You can equate the expressions for y and solve for x.

3/4x -12 = -4x -31

Adding 4x+12 gives ...

(4 3/4)x = -19

(19/4)x = -19

Multiplying by 4/19, we find ...

x = -4

Substituting that into the first equation, we can find y:

y = (3/4)(-4) -12 = -15

The solution is (x, y) = (-4, -15).

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Answer:

x=7, angle a= 45 degrees, angle b= 65 degrees

Step-by-step explanation:

All the angles in a triangle must add up to 180. Subtract 70 from 180, add both angle a and angle b to get 16x-2=110, solve for x, x=7. Substitute x out for 7 in the equations then simplify to get angle a=45 and angle b=65

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3 years ago

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Account A and Account B both have a principal of $1,000 and an annual interest rate of 4%. No additional deposits or withdrawals

postnew [5]

Account A
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3 years ago

Please help!

crimeas [40]

Answer:

The zeros are:

$x =4, x=2, x = 5$

The function has three distinct real zeros.

Hence, option (B) is true.

Step-by-step explanation:

Given the expression

$h\left(x\right)=\left(x-4\right)^2\left(x^2-7x+\:10\right)$

Let us determine the zeros of the function by putting h(x) = 0 and solving the expression

$0=\left(x-4\right)^2\left(x^2-7x+10\right)$

switch sides

$\left(x-4\right)^2\left(x^2-7x+10\right)=0$

$x^2-7x+\:10=\left(x-2\right)\left(x-5\right)$

$\left(x-4\right)^2\left(x-2\right)\left(x-5\right)=0$

Using the zero factor principle

$\mathrm{If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)$

$x-4=0\quad \mathrm{or}\quad \:x-2=0\quad \mathrm{or}\quad \:x-5=0$

$x =4, x=2, x = 5$

Thus, the zeros are:

$x =4, x=2, x = 5$

It is clear that there are three zeros and all the zeros are distinct real numbers.

Therefore,

The function has three distinct real zeros.

Hence, option (B) is true.

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2 years ago

Mr.james runs a petting zoo. he records the number of visitors each week,v, t weeks, after opening the petting zoo. according to

melisa1 [442]

Answer:

$\large \boxed{\text{19 visitors/mo}}$

Step-by-step explanation:

The average rate of change is the change in the number of visitors divided by the change in the number of months.

1. Change in number of visitors

Change in visitors = 182 -125 = 57 visitors

2. Change in number of weeks

Change in time = 5 - 2 = 3 months

3. Average rate of change

$\begin{array}{rcl}\text{Average rate of change} &= &\dfrac{\text{change in visitors}}{\text{change in months}}\\\\&= &\dfrac{\text{57 visitors}}{\text{3 mo}}\\\\& = & \textbf{19 visitors/mo}\\\end{array}\\\text{The average rate of change is $\large \boxed{\textbf{19 visitors/mo}}$}$

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3 years ago