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3 years ago

Is (4,9) a solution to this system of inequalities? y < x + 3 and y > 2x + 1

Mathematics

1 answer:

Setler79 [48]3 years ago

7 0

No

Put (4,9) in equation 1

Mark brainliest please

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If 20 divided by 5 = 4 Then 20 divided by 5.5=4.?

ahrayia [7]

Answer:

Step-by-step explanation:

20 divided by 5.5 is a decimal 3.63

3 0

3 years ago

HELP PLZ i need help with this math side i just need b,c,d a =4x+2y=16

tino4ka555 [31]

Answer:

Please check the explanatio.

Step-by-step explanation:

Solving Part b)

We know that the slope-intercept form of the equation line is

$y=mx+b$

where m is the slope and b is the y-intercept

Given the equation

$4x+2y=16$

Re-writing the equation in the slope-intercept form

$4x+2y=16$

$y=-2x+8$

Here, m=-2 and b=8

Thus, the equation in the slope-intercept form will be:

$y=-2x+8$

Solving Part c)

As you sold two pounds of cheddar cheese.

i.e. y=2

substituting y=2 in the slope-intercept form of the line equation

$y=-2x+8$

$2=-2x+8$

Subtract 8 from both sides

$-2x+8-8=2-8$

$-2x=-6$

Divide both sides by -2

$\frac{-2x}{-2}=\frac{-6}{-2}$

$x=3$

You sold 3 pounds of swiss cheese.

Solving Part d)

$y=-2x+8$

putting x=2.5 in the equation

$y=-2x+8$

$2=-2\left(2.5\right)+8$

$2=3$

The sides are not equal

FALSE

Thus, x=2.5 does not make any sense in the context of the problem.

6 0

2 years ago

Jaime has 8/10 of a candy bar left over. He wants to split it into 1/3 pieces.

Valentin [98]

Answer:

2 pieces.

Step-by-step explanation:

To identify how many pieces he can split with 8/10 of a candy bar, divide 8/10 by 1/3.

Divide 8/10 by 1/3:

$\frac{8}{10} / \frac{1}{3}=$

Find the Ricipricol, then flip the sign:

$\frac{8}{10} (\frac{3}{1} )=$

Multiply:

$\frac{8}{10} (\frac{3}{1})=\frac{24}{10} =\frac{2.4}{1}$

2.4 represents how many pieces of chocolate he can make with 8/10 of a candy bar.

However, 2.4 pieces can't be made, therefore he can only make 2 full pieces.

6 0

2 years ago

Find the two intersection points

bogdanovich [222]

Answer:

Our two intersection points are:

$\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)$

Step-by-step explanation:

We want to find where the two graphs given by the equations:

$\displaystyle (x+1)^2+(y+2)^2 = 16\text{ and } 3x+4y=1$

Intersect.

When they intersect, their x- and y-values are equivalent. So, we can solve one equation for y and substitute it into the other and solve for x.

Since the linear equation is easier to solve, solve it for y:

$\displaystyle y = -\frac{3}{4} x + \frac{1}{4}$

Substitute this into the first equation:

$\displaystyle (x+1)^2 + \left(\left(-\frac{3}{4}x + \frac{1}{4}\right) +2\right)^2 = 16$

Simplify:

$\displaystyle (x+1)^2 + \left(-\frac{3}{4} x + \frac{9}{4}\right)^2 = 16$

Square. We can use the perfect square trinomial pattern:

$\displaystyle \underbrace{(x^2 + 2x+1)}_{(a+b)^2=a^2+2ab+b^2} + \underbrace{\left(\frac{9}{16}x^2-\frac{27}{8}x+\frac{81}{16}\right)}_{(a+b)^2=a^2+2ab+b^2} = 16$

Multiply both sides by 16:

$(16x^2+32x+16)+(9x^2-54x+81) = 256$

Combine like terms:

$25x^2+-22x+97=256$

Isolate the equation:

$\displaystyle 25x^2 - 22x -159=0$

We can use the quadratic formula:

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

In this case, a = 25, b = -22, and c = -159. Substitute:

$\displaystyle x = \frac{-(-22)\pm\sqrt{(-22)^2-4(25)(-159)}}{2(25)}$

Evaluate:

$\displaystyle \begin{aligned} x &= \frac{22\pm\sqrt{16384}}{50} \\ \\ &= \frac{22\pm 128}{50}\\ \\ &=\frac{11\pm 64}{25}\end{aligned}$

Hence, our two solutions are:

$\displaystyle x_1 = \frac{11+64}{25} = 3\text{ and } x_2 = \frac{11-64}{25} =-\frac{53}{25}$

We have our two x-coordinates.

To find the y-coordinates, we can simply substitute it into the linear equation and evaluate. Thus:

$\displaystyle y_1 = -\frac{3}{4}(3)+\frac{1}{4} = -2$

And:

$\displaystyle y _2 = -\frac{3}{4}\left(-\frac{53}{25}\right) +\frac{1}{4} = \frac{46}{25}$

Thus, our two intersection points are:

$\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)$

6 0

3 years ago

Bruce's hourly wage increased from $15.50 to $18.60. What ratr of increase does this represent?

Galina-37 [17]

Answer:

New price 3.10

Step-by-step explanation:

5 0

3 years ago