All categories

3 years ago

1. Solve by graphing y = 3x – 5 y = -2x + 5

Mathematics

1 answer:

wariber [46]3 years ago

7 0

Answer:

Slope = 0.333/2.000 = 0.167

x-intercept = 5/-1 = -5.00000

y-intercept = 5/6 = 0.83333

Step-by-step explanation:

Step 1 :

Equation of a Straight Line

1.1 Solve 6y-x-5 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 6y-x-5 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 5/6 so this line "cuts" the y axis at y= 0.83333

y-intercept = 5/6 = 0.83333

Calculate the X-Intercept :

When y = 0 the value of x is 5/-1 Our line therefore "cuts" the x axis at x=-5.00000

x-intercept = 5/-1 = -5.00000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 0.833 and for x=2.000, the value of y is 1.167. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 1.167 - 0.833 = 0.333 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 0.333/2.000 = 0.167

Geometric figure: Straight Line

Slope = 0.333/2.000 = 0.167

x-intercept = 5/-1 = -5.00000

y-intercept = 5/6 = 0.83333

Processing ends successfully

plz mark me as brainliest :)

You might be interested in

The intersection of roads M and N creates a 41.4 degree angle. What are the complimentary and supplementary angles of this inter

astra-53 [7]

Complimentary means 90 degree angle so 90-41.4= the complimentary angle which is 48.6. Supplementary means 180 degrees so 180-41.4= the supplementary angle which is 138.6..

5 0

3 years ago

A directed line segment begins at F(-8, -2), ends at H(8, 6), and is divided in the ratio 8 to 2 by G. What are the coordinates

I am Lyosha [343]

Given:

A directed line segment begins at F(-8, -2), ends at H(8, 6), and is divided in the ratio 8 to 2 by G.

To find:

The coordinates of point G.

Solution:

Section formula: If a point divide a line segment with end points $(x_1,y_1)$ and $(x_2,y_2)$ in m:n, then the coordinates of that point are

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Point G divide the line segment FH in 8:2. Using section formula, we get

$G=\left(\dfrac{8(8)+2(-8)}{8+2},\dfrac{8(6)+2(-2)}{8+2}\right)$

$G=\left(\dfrac{64-16}{10},\dfrac{48-4}{10}\right)$

$G=\left(\dfrac{48}{10},\dfrac{44}{10}\right)$

$G=\left(4.8,4.4\right)$

Therefore, the coordinates of point G are (4.8, 4.4).

4 0

2 years ago

What is the percent decrease if the number of student is 80 and now its 64.

Neporo4naja [7]

Answer:

Step-by-step explanation:

When you do 64/80 you get 0.8 which means that the percent decrease is .2

8 0

3 years ago

Read 2 more answers

Can anyone pls help me with this, I don't even know where to start? I can also give Brainliest

svetoff [14.1K]

The interior angles of a parallelogram will always equal 360. The interior angles of a triangle are 180 if it is a equilateral triangle then the angles are 60 degrees each. You know 2 sides of parallelogram. The 100 degree and 90 degree. You can find the one opposing the x because it’s on a straight line and a straight line is 180 degrees if a triangle is 60 degree angle then the opposing angle to complete the straight line must be 180-60 so you get 120. You now know 3 sides. 120, 90 and 100
They should add up to be 360 so you can set up an equation like so
120+90+100+x=360
And x = 50

6 0

3 years ago

Read 2 more answers

The sodium content of a popular sports drink is listed as 200 mg in a 32-oz bottle. Analysis of 20 bottles indicates a sample me

julia-pushkina [17]

Answer:

The sample does not contradicts the manufacturer's claim.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 200 mg

Sample mean, $\bar{x}$ = 211.5 mg

Sample size, n = 20

Alpha, α = 0.05

Sample standard deviation, s = 18.5 mg

a) First, we design the null and the alternate hypothesis for a two tailed test

$H_{0}: \mu = 200\\H_A: \mu \neq 200$

We use Two-tailed t test to perform this hypothesis.

b) Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$ Putting all the values, we have

$t_{stat} = \displaystyle\frac{211.5 - 200}{\frac{18.5}{\sqrt{20}} } = 2.7799$

c) Now,

$t_{critical} \text{ at 0.05 level of significance, 19 degree of freedom } = \pm 2.0930$

Since, the calculated t-statistic does not lie in the range of the acceptance region(-2.0930,2.0930), we reject the null hypothesis.

Thus, the sample does not contradicts the manufacturer's claim.

d) P-value = 0.011934

Since the p-value is less than the significance level, we reject the null hypothesis and accept the alternate hypothesis.

Yes, both approach the critical value and the p-value approach gave the same results.

4 0

3 years ago