Which of the following is equivalent to the expression below?<br> 4x + 3(2x - 1)

Frank's paper airplane glided 78.9 m. Sarah's plane glided 85 m. How many more centimeters did Sarah's plane glide? 1 m= 100 cm

Olegator [25]

Answer:

610 cm

Step-by-step explanation:

78.9 x 100 = 7890 cm 85 x 100 = 8,500 cm

8,500 - 7890 = 610 cm

4 0

2 years ago

A 5-lb bag of apples costs $4.50, and an 8-lb bag of the same type of apples costs $7.52. Greg found the unit price, which is th

Sedaia [141]

Answer:

4 cents

Step-by-step explanation:

4.50 divide by is .9 and 7.52 divide by 8 is .94

3 0

3 years ago

What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?

Trava [24]

Answer:

$\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}$

Step-by-step explanation:

The explicit formula for a geometric sequence:

$a_n=a_1r^{n-1}$

$a_n$ - n-th term

$a_1$ - first term

$r$ - common ratio

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}$

We have

$a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...$

The common ratio:

$r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}$

<h2>It's not a geometric sequence.</h2>

If $a_3=-\dfrac{1}{16}$ then the common ratio is $r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}$

Put to the explicit formula:

$a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}$

Put $a_n=\dfrac{1}{1024}$ and solve for <em>n </em>:

$-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1$

$\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6$

5 0

3 years ago

Can someone help me with this right answer only and please explain it too

sineoko [7]

Answer:

g(6) = 71

f(11) = 62

Step-by-step explanation:

Let's solve g(6) first

Plug 6 into x

g(6) = 2(6)^2 - 1

g(6) = 2(36) - 1

g(6) = 72 - 1

g(6) = 71

Now let's solve f(11)

f(11) = 5(11) + 7

f(11) = 55 + 7

f(11) = 62

<em>Thus, out answers are 71 and 62 respectively</em>

5 0

3 years ago

Identify the effect on the graph of replacing f(x) by f(x - h)

Tresset [83]

Given:

Replace f(x) by f(x - h).

To find:

The effect on the graph of replacing f(x) by f(x - h).

Solution:

Horizontal shift is defined as:

If the graph f(x) shifts h units left, then f(x+h).

If the graph f(x) shifts h units right, then f(x-h).

Where, h is a constant that represents the horizontal shift.

In the given problem f(x) is replaced by f(x - h) and we need to find the effect on the graph.

Here, we have x-h in place of x.

Therefore, the graph of f(x) shifts h units right to get the graph of f(x-h).

4 0

3 years ago

Which of the following is equivalent to the expression below? 4x + 3(2x - 1) - 4x