Solve this system of equations using substitution.

Gabriela's monthly take-home pay is $2800, and her monthly rent is $700. If both her monthly take-home pay and her rent increase

ruslelena [56]

Gabriela spends about 30% of her take home pay on rent.

5 0

3 years ago

Read 2 more answers

The dimensions of a rectangular garden were 4m by 5m. Each dimension was increased by the same amount the garden then had an are

pogonyaev

The dimension of new garden is 7 meter by 8 meter

Solution:

The dimensions of a rectangular garden were 4m by 5m

Length = 4 m

Width = 5 m

Each dimension was increased by the same amount the garden then had an area of 56 square meter

Let "x" be the amount of increase

Then,

Length = 4 + x

Width = 5 + x

Also, given that,

New area = 56 square meter

The area of rectangle is given as:

$Area = length \times width$

Substituting the values we get,

$56 = (4+x)(5+x)\\\\56 = 20 + 4x + 5x + x^2\\\\x^2 + 9x + 20 - 56 = 0\\\\x^2 + 9x -36=0$

Let us solve the above equation by quadratic formula

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Using the above formula,

$\text{For } x^2+9x-36 \text{ we get , }$

a = 1 and b = 9 and c = -36

Substituting the values of a = 1 ; b = 9 ; c = -36 in above quadratic formula we get,

$x = \frac{-9\pm \sqrt{9^2-4\cdot \:1\left(-36\right)}}{2\cdot \:1}\\\\x = \frac{-9\pm \sqrt{81+144}}{2}\\\\x = \frac{-9 \pm 15}{2}$

We get two solutions,

$x = \frac{-9+15}{2} \text{ or } x = \frac{-9-15}{2}\\\\x = 3 \text{ or } x = -12$

Since dimension cannot be negative, ignore x = -12

Thus solution is x = 3

Length = 4 + x = 4 + 3 = 7

Width = 5 + x = 5 + 3 = 8

Thus dimension of new garden is 7 meter by 8 meter

5 0

3 years ago

Which expression is equivalent to pq? p+q p-a p/q pq

sveta [45]

Answer:

pq are being multiplied together.the answer is D. pq. Hope it helps

5 0

3 years ago

Find the length of side x in simplest radical form with a rational denominator

lions [1.4K]

Answer: 5/2

Explanation:

According to 30-60-90 triangle rule:

The side opposite of 30 degree is equal to half of the hypotenuse and the hypotenuse here is 5 so therefore x = 5/2

4 0

3 years ago

Here is a graph of the function y, both continuous and differentiable. For approximately what values of x between -5 and 5 is th

Law Incorporation [45]

From the graph you can determine the first derivative by looking at the turning points. These are where the first derivative is zero.

$y' = x(x-2)(x+2)(x-5)(x+5) \\ \\ y' = x^5 -29x^3 +100x$

Take derivative to get 2nd derivative and set equal to zero:
$y'' = 5x^4 -87x^2 +100 = 0$

Solve for x:
$x^2 = \frac{87 \pm \sqrt{87^2 -2000}}{10} \\ \\ x = \pm 1.11, \pm 4.02$

7 0

4 years ago