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2 years ago

20 increased by twice Greg's savings Use the variable g to represent Greg's savings.

Mathematics

2 answers:

Pie2 years ago

7 0

Answer:

2g+20

Step-by-step explanation:

Sophie [7]2 years ago

4 0

40g
20 + 20=40
Sorry if I’m wrong

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The difference between the roots of the equation 3x2+bx+10=0 is equal to 4 1 3 . find b.

inna [77]

Given that the difference between the roots of the equation $3x^2+bx+10=0$ is $4 \frac{1}{3} = \frac{13}{3}$ .

Recall that the sum of roots of a quadratic equation is given by $- \frac{b}{a}$ .

Let the two roots of the equation be $\alpha$ and $\alpha + \frac{13}{3}$ , then

$\alpha + \alpha + \frac{13}{3} =2 \alpha + \frac{13}{3} =- \frac{b}{a} =- \frac{b}{3} \\ \\ i.e.\ \ 2 \alpha + \frac{13}{3}=- \frac{b}{3}$ . . . (1)

Also recall that the product of the two roots of a quadratic equation is given by $\frac{c}{a}$ , thus:

$\alpha \left( \alpha + \frac{13}{3} \right)= \alpha ^2+ \frac{13}{3} \alpha = \frac{c}{a} = \frac{10}{3} \\ \\ i.e.\ \ \alpha ^2+ \frac{13}{3} \alpha=\frac{10}{3}$ . . . (2)

From (1), we have:

$2 \alpha =- \frac{b}{3} - \frac{13}{3} \\ \\ \Rightarrow \alpha =- \frac{b}{6} - \frac{13}{6}$

Substituting for alpha into (2), gives:

$\left(- \frac{b}{6} - \frac{13}{6}\right)^2+ \frac{13}{3} \left(- \frac{b}{6} - \frac{13}{6}\right)= \frac{10}{3} \\ \\ \Rightarrow \frac{b^2}{36} + \frac{13b}{18} + \frac{169}{36} - \frac{13b}{18} - \frac{169}{18} = \frac{10}{3} \\ \\ \Rightarrow \frac{b^2}{36} - \frac{289}{36} =0 \\ \\ \Rightarrow \frac{b^2}{36} = \frac{289}{36} \\ \\ \Rightarrow b^2=289 \\ \\ \Rightarrow b=\pm\sqrt{289}=\pm17$

5 0

3 years ago

A class has 10 boys and 15 girls. What is the ratio of boys to girls

enyata [817]

10:15

10 to 15

10/15

Hope this helps

6 0

3 years ago

The rule for Function A is y= -2/3x

Rom4ik [11]

Answer:

Both functions have negative rates of change

Function B has a greater rate of change than Function A

Step-by-step explanation:

we know that

Function A

The rule for Function A is

$y=-\frac{2}{3}x$

This is the equation of a proportional relationship (the line passes through the origin)

The slope is equal to $m=-\frac{2}{3}$

Function B

Find the equation of the function B

we have the points (-2,0) and (0,-2)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{-2-0}{0+2}$

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

$m=-1$

The equation of the function B in slope intercept form is equal to

$y=mx+b$

we have

$m=-1\\b=-2$

substitute

$y=-x-2$

Verify each statement

Option 1) Both functions have negative rates of change

The statement is true

Because, the rate of change is the slope of the linear equation

Function A ----> $m=-\frac{2}{3}$

Function B ----> $m=-1$

Option 2) Both functions have the same rate of change.

The statement is false (see the explanation)

The rate of change are different ( m=-2/3 and m=-1)

Option 3) When graphed, Function A and Function B are parallel

The statement is false

When graphed, Function A and Function B are intersecting lines, because their slopes are different

Option 4) Function B has a greater rate of change than Function A

The statement is true

Remember that the rate of change can be either positive (increasing function) or negative (decreasing function). To find out which function has a greater rate of change, compare the absolute value of their slopes

therefore

1 > 2/3

6 0

3 years ago

(5 - 3i) + (6 + 5i)

Ad libitum [116K]

Answer:

11+2i=9

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Find the area of the figure below

icang [17]

Answer:

324

Step-by-step explanation:

Simplify it

3 0

3 years ago