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2 years ago

Find the sum of the first 3 terms of a geometric sequence with a=96 and r=1/4 the sum is____.

1 answer:

3 0

For Geometric sequence, the next term is multiplied by the common ratio.

Common ratio, r = 1/4

1st term, a = 96

2nd term = ar = 96*1/4 = 24

3rd term = ar² = 96*(1/4)*(1/4) = 6

Sum of the first three terms = 96 + 24 + 6 = 126

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A triangle has a base of 3⅖ inches and an area of 5⅒ square inches. Find the height of the triangle. Show your reasoning

N76 [4]

Answer: 3 in.

Step-by-step explanation:

Given

The base of the triangle is $3\frac{2}{5}\ inches$

The area of the triangle is $5\frac{1}{10}\ inches^2$

Solve mixed fraction

Base is

$=3\dfrac{2}{5}\\\\=\dfrac{17}{5}\ in.$

Area is

$=5\dfrac{1}{10}\\\\=\dfrac{51}{10}\ in.^2$

The area of the triangle is given by

$\Rightarrow \text{Area A=}\dfrac{1}{2}\times \text{base}\times \text{height}$

Insert the values to get the height

$\Rightarrow \dfrac{51}{10}=\dfrac{1}{2}\times \dfrac{17}{5}\times \text{height}\\\\\Rightarrow \text{height}=3\ in.$

8 0

2 years ago

Can someone help me solve this equation 5-x=12

RSB [31]

In order to solve you get x by itself:
5-x=12
-5 -5
-x=7
divide by negative 1

7 0

2 years ago

Write an inequality that represents the following:

Scilla [17]

Answer:

The maximum number of hours can be spend on work is 4 hours

Step-by-step explanation:

Given as :

The fixed charge of an auto shop = $100

The labor charge of auto shop = $175 per hour

The maximum money to be spend = $800

Let The maximum number of hours can be spend on work = n hours

<u>According to question</u>

The maximum money to be spend = fixed charge of an auto shop + labor charge of auto shop per hour × maximum number of hours

Or, $800 = $100 + $175 × n

Or, $175 × n = $800 - $100

Or, $175 × n = $700

∴ n = $\frac{700}{175}$

i.e n = 4

So, The maximum number of hours can be spend on work = n = 4 hours

Hence, maximum number of hours can be spend on work is 4 hours Answer

6 0

3 years ago

Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.

koban [17]

Answer:

Rise is a vertical line from 0 to 4

Run is a horizontal line from 0 to 4

Slope of a line is called the gradient.

Additional information:

Gradient =rise/run

= 4/4

= 1

Y=mx +c

Y=1x +4

Y= x+4

But the slope show a negative correlation, so gradient will be negative & it's y = - x + 4.

BTW the rise and run could also be from 4 on the y-axis and down to the 4 on the x-axis.

So, there is two possible triangles you could make.

As a result, the rise is a straight line going up or down ( vertical ) and the run is a straight line going across from left to right (horizontal).

7 0

2 years ago

Tamara is creating a model of a rectangle. She has ab26 inches of yellow ribbon to use for the border of the rectangle. She want

soldi70 [24.7K]

Answer:

Step-by-step explanation:

Step one:

given data

we are told that the border/perimeter of the yellow ribbon is 26in

let the width be x

W=x

and the lenght

L=x+3

Step two:

Required

The expression for the perimeter to find the dimensions of the yellow ribbon given the above condition.

we know that the perimeter of a rectangle is given as

P=2L+2W

26=2(x+3)+2x---------This is the expression required

26=2x+6+2x

26=4x+6

26-6=4x

20=4x

divide both sides by 4

x=20/4

x=5in

The width is 5in

The length is

L=x+3

L=5+3

L=8in

4 0

3 years ago