Find the 12th term of the given explicit geometric formula. f(n) =3(2)^ n-1

How many solutions does this linear system have? y = y equals StartFraction 2 over 3 EndFraction x plus 2.x+ 2 6x – 4y = –10

Ira Lisetskai [31]

Answer:

The system has one solution

Step-by-step explanation:

we have the system of equations

$y=\frac{2}{3}x+2$ ----> equation A

$6x-4y=-10$ ----> equation B

Solve the system by substitution

substitute equation A in equation B

$6x-4(\frac{2}{3}x+2)=-10$

$6x-\frac{8}{3}x-8=-10$

Solve for x

Multiply by 3 both sides to remove the fraction

$18x-8x-24=-30$

Combine like terms

$10x=-30+24$

$10x=-6$

$x=-\frac{6}{10}$

Simplify

$x=-\frac{3}{5}$

Find the value of y

$y=\frac{2}{3}(-\frac{3}{5})+2$

$y=-\frac{6}{15}+2$

$y=\frac{24}{15}$

Simplify

$y=\frac{8}{5}$

The solution of the system is the point $(-\frac{3}{5},\frac{8}{5})$

therefore

The system has one solution

4 0

3 years ago

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I got 13.7 is that correct

Ghella [55]

Answer:

The answer to your question is 10.5 in

Step-by-step explanation:

Data

First triangle

height = x

base = 7 in

Second triangle

height = 12 in

base = 8 in

Process

1.- Use proportions to solve this problem, relates the sides of a triangle with the same sides of the other triangle.

$\frac{x}{7} = \frac{12}{8}$

2.- Multiply both sides by 7

$7\frac{x}{7} = \frac{7(12)}{8}$

3.- Simplify

x = $\frac{84}{8}$

4.- Result

x = 10.5 in

3 0

3 years ago

A coin bank contains only quarters and dimes. The total value of the coins in the bank is $8.80. If the dimes were quarters and

masha68 [24]

Answer:

18 dimes

Step-by-step explanation:

Let the number of dimes be d and quarters be q

The value is $8.80 = 880¢, so:

10d + 25q = 880 ⇒ 2d + 5q = 176

If the dimes were quarters and the quarters were dimes, the coins' total value would be $7.30 or 730¢

25d + 10q = 730 ⇒ 5d + 2q = 146

Now we have 2 equations. Solving the system by elimination, subtract 5 times the second equation from twice the first equation:

2(2d + 5q) - 5(5d + 2q) = 2(176) - 5(146)
4d - 25d = -378
-21d = -378
d = -378/-21
d = 18

8 0

3 years ago

Suppose that G(x) = F(x) - 7. Which statement best compares the graph of G(x) with the graph of F(x)?

fiasKO [112]

The graph of g(x) is just the graph of f(x) shifted down vertically 7 units

8 0

3 years ago

Write an equation that gives the proportional relationship of the graph.

viktelen [127]

The required equation is: $y= 7x$

Option C is correct.

Step-by-step explanation:

The proportional relationship can be found using the equation: $y=k\,x$

where x and y are the points and k is the constant of proportionality.

We need to find k.

From the graph given, we can locate points x and y:

x=5, y= 35 then k would be:

$y=kx\\k=y/x\\k=35/5\\k=7$

x=10, y=70 then k would be:

$y=kx\\k=y/x\\k=70/10\\k=7$

For each values of x and y, the constant of proportionality k is 7

So, the required equation is: $y= 7x$

Option C is correct.

Keywords: Proportional Relationship

Learn more about Proportional Relationship at:

#learnwithBrainly

6 0

4 years ago

Read 2 more answers