What is 25+x= 50 solve for x

which values of x and y are solutions to the open sentence? 4y ≥ 3x 2 a. x = 3, y = 0 b. x = 4, y = 3 c. x = 6, y = 5 d. x = 7,

boyakko [2]

4y ≥ 3x + 2

Plugging in the values in the options, then the required values are when x = 6 and y = 5, then
4(5) ≥ 3(6) + 2
20 ≥ 18 + 2
20 ≥ 20

8 0

3 years ago

There were 20 gallons of gasoline in your car's gas tank. You used 4 gallons and 1 quart. How much gasoline remains in the tank?

Naya [18.7K]

25 gallons and 3 quarts

5 0

3 years ago

Read 2 more answers

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

Help me with this please!!!!!!

castortr0y [4]

Answer:

$\huge\mathcal\red{here's \: your \: solution..} \\ \\ \cos = base \div hypotenuse \: \\ \\ \cos(60) = 1 \div 2 \\ \\ \cos = a \div 14 \\ \\ a \div 14 = 1 \div 2 \\ \\ a = 14 \div2 \\ \\ a = 7 \: cm \\ \\ \huge\mathfrak\green{hope \: it \: helps..}$

4 0

3 years ago

While practicing basketball Jude made 24 baskets in 90 seconds. At this rate how many baskets will he make per hour?

zalisa [80]

Answer:

960 baskets.

Step-by-step explanation:

proportion: 24/1.5=x/60

1.5x=1440

x=960

8 0

3 years ago