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3 years ago

Use the substitution method to solve the system of equations. Then check your solution.

Mathematics

1 answer:

Goshia [24]3 years ago

7 0

1. a=2 b=-3
2.
3.x=10 y=14
4.
I'll do the rest in 5 mins

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Which set(s) of points show x in DIRECT PROPORTION to y?

vredina [299]

Answer: OPTION D.

Step-by-step explanation:

For this exercise it is important to remember that:

1. Direct proportion equations have the following form:

$y=kx$

Where "k" is the constant of proportionality.

2. The graph of Direct proportions is an straight line that passes through the origin.

Observe the picture attached.

If you join the points G, C and A, you get a straight line that passes through the origin,

If you join the points F, G and H, you also get a straight line that passes through the origin,

Therefore, the sets of points show "x" in Direct proportion to "y", are:

$\{F, G, H\}$ and $\{{G, C, A}\}$

5 0

3 years ago

Read 2 more answers

Find the constant of proportionality k. Then write an equation for the relationship between x and y

ExtremeBDS [4]

Question:

Find the constant of proportionality k. Then write an equation for the relationship between x and y

$\begin{array}{ccccc}x & {2} & {4} & {6} & {8} \ \\ y & {10} & {20} & {30} & {40} \ \ \end{array}$

Answer:

(a) $k = 5$

(b) $y = 5x$

Step-by-step explanation:

Given

$\begin{array}{ccccc}x & {2} & {4} & {6} & {8} \ \\ y & {10} & {20} & {30} & {40} \ \ \end{array}$

Solving (a): The constant of proportionality:

Pick any two corresponding x and y values

$(x_1,y_1) = (2,10)$

$(x_2,y_2) = (6,30)$

The constant of proportionality k is:

$k = \frac{y_2 - y_1}{x_2 - x_1}$

$k = \frac{30-10}{6-2}$

$k = \frac{20}{4}$

$k = 5$

Solving (b): The equation

In (a), we have:

$(x_1,y_1) = (2,10)$

k can also be expressed as:

$k = \frac{y- y_1}{x- x_1}$

Substitute values for x1, y1 and k

$5 = \frac{y- 10}{x- 2}$

Cross multiply:

$y - 10 = 5(x - 2)$

Open bracket

$y - 10 = 5x - 10$

Add 10 to both sides

$y - 10 +10= 5x - 10+10$

$y = 5x$

6 0

3 years ago

Is 12.89 a irrational number

shtirl [24]

12.89 can be written as 1289/100, hence its a rational number.

5 0

3 years ago

I need to know The value of f(1/2)

Lostsunrise [7]

$\huge\boxed{\textsf{a.)}\ 10}$

Substitute $\frac{1}{2}$ for $x$ .

$f\left(\frac{1}{2}\right)=5\cdot4^\frac{1}{2}$

Use $a^\frac{m}{n}=\sqrt[n]{a^m}$ .

$\begin{aligned}f\left(\frac{1}{2}\right)&=5\cdot\sqrt[2]{4^1}\\&=5\cdot\sqrt[2]{4}\\&=5\cdot2\\&=\boxed{10}\end{aligned}$

7 0

2 years ago

Answer choices: A: y=x B: y=1/4x -2 C: y= -x + 7/4 D: y= 7/4x -2

Nuetrik [128]

Answer:

b: y=1/4x -2

Step-by-step explanation:

It says the answer in the question. the slope on the graph is really just 1 though.

5 0

2 years ago