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3 years ago

3(x + 4) = 7x - 18 How do I solve it?

Mathematics

1 answer:

aev [14]3 years ago

3 0

Answer:

x = 7.5

Step-by-step explanation:

Step 1:

3 ( x + 4 ) = 7x - 18 Equation

Step 2:

3x + 12 = 7x - 18 Multiply

Step 3:

12 = 4x - 18 Subtract 3x on both sides

Step 4:

30 = 4x Add 18 on both sides

Step 5:

x = 30 ÷ 4 Divide

Answer:

x = 7.5

Hope This Helps :)

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What is the sum of the first 6 terms of this geometric sequence? –4, –16, –64, –256, …

MatroZZZ [7]

$a_1=-4;\ a_2=-16;\ a_3=-64;\ a_4=-256;\ ...\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}\to r=\dfrac{-16}{-4}=4$

The formula of the sum of a geometric sequence:

$S_n=a_1\cdot\dfrac{1-r^n}{1-r}$

We have:

$a_1=-4;\ n=6;\ r=4$

substitute:

$S_6=-4\cdot\dfrac{1-4^6}{1-4}=-4\cdot\dfrac{1-4096}{-3}=-4\cdot\dfrac{-4095}{-3}=-4\cdot1365=-5460$

Answer: C. -5460

6 0

3 years ago

Here are two sets of numbers, a and b. Set a :200,104,100,160. Set b: 270,400,483,300, x. Mean of set a: mean of set b= 3:8. Wor

LenKa [72]

Given:

The given sets are:

Set a : 200, 104, 100, 160.

Set b: 270, 400, 483, 300, x.

Mean of set a: mean of set b= 3:8

To find:

The value of x.

Solution:

Formula for mean:

$Mean=\dfrac{\text{Sum of observations}}{\text{Number of observation}}$

The mean of set of a is:

$Mean=\dfrac{200+104+100+160}{4}$

$Mean=\dfrac{564}{4}$

$Mean=141$

The mean of set of b is:

$Mean=\dfrac{270+400+483+300+x}{5}$

$Mean=\dfrac{1453+x}{5}$

It is given that,

Mean of set a: mean of set b= 3:8

$\dfrac{141}{\dfrac{1453+x}{5}}=\dfrac{3}{8}$

$\dfrac{705}{1453+x}=\dfrac{3}{8}$

$8\times 705=3\times (1453+x)$

$5640=4359
+3x$

Isolate the variable x.

$5640-4359
=3x$

$1281
=3x$

Divide both sides by 3.

$\dfrac{1281}{3}
=x$

$427
=x$

Therefore, the value of x is 427.

3 0

2 years ago

A river discharges 4 × 106 cubic feet of water into the Pacific Ocean each second. There are 86,400 seconds in one day. To find

erik [133]

Answer:

3.456E + 14= $3.456X10^{14$

Step-by-step explanation:

The river discharges $4X10^6$ cubic feet of water into the Pacific Ocean each second.

There are 86,400 seconds in one day.

Amount of water discharges each day

$=4X10^6X86400\\=345600000000\\=3.456X10^{11$

Since this differs from what you have, I will explain the scientific notation.

3.456E + 14 simply means $3.456X10^{14$

The options are not well laid out but you can pick the appropriate option.

8 0

3 years ago

Need help plez and thanks

bulgar [2K]

What do u need help with

8 0

3 years ago

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A radio transmission tower is 170 feet tall. how long should a guy wire be if it is attached 15 feet from the top and is to make

beks73 [17]

The image of the given scenario is attached below.

A right angled triangle is formed, with one angle equal to 27 degrees. The perpendicular side is 155 and we are to find the length of guy wire which makes the hypotenuse of the right angled triangle.

Using the formula of sine, we can write:

$sin(27)= \frac{155}{x} \\ \\ 
x= \frac{155}{sin(27)} \\ \\ 
x=341$

Rounding to nearest whole number, the length of the guy wire that must be attached is 341 feet.

5 0

3 years ago