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2 years ago

How do I solve to get the answer for: 2t + 8 ≥ −4(t + 1)

Mathematics

1 answer:

Rzqust [24]2 years ago

4 0

2t + 8 ≥ -4t - 4
2t+4t ≥ -8-4
6t ≥-12
t ≥ -12/6
t ≥ -2

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Learning Task 3. Find the equation of the line. Do it in your notebook.

Wewaii [24]

Answer:

1) The equation of the line in slope-intercept form is $y = 5\cdot x +9$ . The equation of the line in standard form is $-5\cdot x + y = 9$ .

2) The equation of the line in slope-intercept form is $y = \frac{2}{5}\cdot x +\frac{14}{5}$ . The equation of the line in standard form is $-2\cdot x +5\cdot y = 14$ .

3) The equation of the line in slope-intercept form is $y = 3\cdot x +4$ . The equation of the line in standard form is $-3\cdot x +y = 4$ .

4) The equation of the line in slope-intercept form is $y = 2\cdot x + 6$ . The equation of the line in standard form is $-2\cdot x +y = 6$ .

5) The equation of the line in slope-intercept form is $y = \frac{5}{6}\cdot x -\frac{7}{6}$ . The equation of the line in standard from is $-5\cdot x + 6\cdot y = -7$ .

Step-by-step explanation:

1) We begin with the slope-intercept form and substitute all known values and calculate the y-intercept: ( $m = 5$ , $x = -1$ , $y = 4$ )

$4 = (5)\cdot (-1)+b$

$4 = -5 +b$

$b = 9$

The equation of the line in slope-intercept form is $y = 5\cdot x +9$ .

Then, we obtain the standard form by algebraic handling:

$-5\cdot x + y = 9$

The equation of the line in standard form is $-5\cdot x + y = 9$ .

2) We begin with a system of linear equations based on the slope-intercept form: ( $x_{1} = 3$ , $y_{1} = 4$ , $x_{2} = -2$ , $y_{2} = 2$ )

$3\cdot m + b = 4$ (Eq. 1)

$-2\cdot m + b = 2$ (Eq. 2)

From (Eq. 1), we find that:

$b = 4-3\cdot m$

And by substituting on (Eq. 2), we conclude that slope of the equation of the line is:

$-2\cdot m +4-3\cdot m = 2$

$-5\cdot m = -2$

$m = \frac{2}{5}$

And from (Eq. 1) we find that the y-Intercept is:

$b=4-3\cdot \left(\frac{2}{5} \right)$

$b = 4-\frac{6}{5}$

$b = \frac{14}{5}$

The equation of the line in slope-intercept form is $y = \frac{2}{5}\cdot x +\frac{14}{5}$ .

Then, we obtain the standard form by algebraic handling:

$-\frac{2}{5}\cdot x +y = \frac{14}{5}$

$-2\cdot x +5\cdot y = 14$

The equation of the line in standard form is $-2\cdot x +5\cdot y = 14$ .

3) By using the slope-intercept form, we obtain the equation of the line by direct substitution: ( $m = 3$ , $b = 4$ )

$y = 3\cdot x +4$

The equation of the line in slope-intercept form is $y = 3\cdot x +4$ .

Then, we obtain the standard form by algebraic handling:

$-3\cdot x +y = 4$

The equation of the line in standard form is $-3\cdot x +y = 4$ .

4) We begin with a system of linear equations based on the slope-intercept form: ( $x_{1} = -3$ , $y_{1} = 0$ , $x_{2} = 0$ , $y_{2} = 6$ )

$-3\cdot m + b = 0$ (Eq. 3)

$b = 6$ (Eq. 4)

By applying (Eq. 4) on (Eq. 3), we find that the slope of the equation of the line is:

$-3\cdot m+6 = 0$

$3\cdot m = 6$

$m = 2$

The equation of the line in slope-intercept form is $y = 2\cdot x + 6$ .

Then, we obtain the standard form by algebraic handling:

$-2\cdot x +y = 6$

The equation of the line in standard form is $-2\cdot x +y = 6$ .

5) We begin with a system of linear equations based on the slope-intercept form: ( $x_{1} = -1$ , $y_{1} = -2$ , $x_{2} = 5$ , $y_{2} = 3$ )

$-m+b = -2$ (Eq. 5)

$5\cdot m +b = 3$ (Eq. 6)

From (Eq. 5), we find that:

$b = -2+m$

And by substituting on (Eq. 6), we conclude that slope of the equation of the line is:

$5\cdot m -2+m = 3$

$6\cdot m = 5$

$m = \frac{5}{6}$

And from (Eq. 5) we find that the y-Intercept is:

$b = -2+\frac{5}{6}$

$b = -\frac{7}{6}$

The equation of the line in slope-intercept form is $y = \frac{5}{6}\cdot x -\frac{7}{6}$ .

Then, we obtain the standard form by algebraic handling:

$-\frac{5}{6}\cdot x +y =-\frac{7}{6}$

$-5\cdot x + 6\cdot y = -7$

The equation of the line in standard from is $-5\cdot x + 6\cdot y = -7$ .

6 0

2 years ago

Jay sells 10 packs of apples for 80p. He wants to make £75 at the end of the year. How many packs of apples does he need to sell

ipn [44]

Answer:

937.5 packs of apples

Step-by-step explanation:

Note that:

100p = £1

80p = x

Cross Multiply

100x = 80p × £1

x = 80/100

x = £0.8

Jay sells 10 packs of apples for 80p.

Hence:

£0.8 = 10 packs of apples

£75 = x

Cross Multiply

£0.8 × x = £75 × 10 Packs

x = £75 × 10 Packs/£0.8

x = 937.5

Therefore, to make £75 at the end of the year, he has to sell 937.5 packs of apples

3 0

2 years ago

Let x^2+18x=44 . What values make an equivalent number sentence after completing the square?

Lostsunrise [7]

To find the final term to compete the square you need to divide the 'x' term by 2 then square it

$x^2 +18x + = 44+ \\ x^2+18x+( \frac{18}{2} )^2=44+( \frac{18}{2} )^2 \\ x^2+18x+9^2=44+9^2 \\ x^2+18x+81=44+81 \\ (x+9)^2=125$ - equivalent equation

6 0

3 years ago

Read 2 more answers

Find the sine of angle S. Reduce the answer to the lowest terms.

NeX [460]

Answer:

$\sin e\text{ S = }\frac{3}{5}$

Explanation:

Here, we want to get the value of sine S

The sine of an angle is the ratio of the opposite side to the hypotenuse side

The hypotenuse side is the side that faces the right angle which is the small box. It is the longest side of the triangle and it measures 10

The opposite is the side that faces the angle which is 6

We have the sine as:

$\frac{6}{10}\text{ = }\frac{3}{5}$

8 0

8 months ago

What is the box-and-whiskers plot used to show?

12345 [234]

The whole idea of that kind of graph is that they allow you to view the complete distribution of data while also being able to see first and third quartiles, the median, and the minimums and maximums.

5 0

2 years ago