All categories

2 years ago

3(x - 1) - 8 = 4(1+x) + 5

Mathematics

2 answers:

valina [46]2 years ago

7 0

Answer:

x= 20

Step-by-step explanation:

Step 1- Distribute into the parenthesis.

3x-1(3)-8= 1(4)+4x+5

Step 2- Multiply

3x-3-8= 4+4x+5

Step 3- Add.

3x-3-8= 4x+9

Step 4- Subtract 3x to both sides to move the variable to one side.

3x-11= 4x+9

-3x -3x

Step 5- Subtract 9 to both sides.

-11= 1x+9

-9 -9

-20= x

Exchange the signs.

20= x

Maurinko [17]2 years ago

3 0

Answer:

x = -20

Step-by-step explanation:

3(x - 1) - 8 = 4(1+x) + 5

3x - 3 -8 = 4 + 4x + 5

3x - 11 = 9 + 4x

-x = 20

x = -20

You might be interested in

Mr.Richard has an orchard of length and breadth 280m and 200m respectively. He wants to fence it with 4 rounds of barbed wire. F

sesenic [268]

Answer:

$109.71

Step-by-step explanation:

first we find the perimeter

=2(280+200)

=2×480

=960m

now we multiply it by 4 as he wants it 4 times around

960×4

3840

now we find the fencing cost

since 35 per meter we divide it by 35

3840/35

=$<u>109.71</u>

8 0

2 years ago

What are the zeros of the function?

cluponka [151]

The function is:

f ( x ) = x² - x - 72

This is a quatdratic function. So we can find the zeroes of the function with the formula:

x 1/2 = ( - b +/- √(b² - 4 ac) ) / ( 2a )

And we have: a = 1, b = - 1 and c = - 72

x 1/2 = ( 1 +/- √((-1)² - 4 · 1· ( - 72 )) ) / 2

x 1/2 = ( 1 +/- √( 1 + 288 ) ) / 2

x 1/2 = ( 1 +/- √289 ) / 2

x 1/2 = ( 1 +/- 17 ) / 2

x 1 = ( 1 - 17 ) 2 = - 16 / 2 = - 8

x 2 = ( 1 + 17 ) / 2 = 18 / 2 = 9

Answer: The zeroes are - 8 and 9.

7 0

2 years ago

Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.

FromTheMoon [43]

Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:

$\rho = \sqrt{x^{2}+y^{2}+z^{2}}$

$\phi = cos^{-1}\frac{z}{\rho}$

For angle θ:

If x > 0 and y > 0: $\theta = tan^{-1}\frac{y}{x}$ ;

If x < 0: $\theta = \pi + tan^{-1}\frac{y}{x}$ ;
If x > 0 and y < 0: $\theta = 2\pi + tan^{-1}\frac{y}{x}$ ;

Calculating:

a) (4,2,-4)

$\rho = \sqrt{4^{2}+2^{2}+(-4)^{2}}$ = 6

$\phi = cos^{-1}(\frac{-4}{6})$

$\phi = cos^{-1}(\frac{-2}{3})$

For θ, choose 1st option:

$\theta = tan^{-1}(\frac{2}{4})$

$\theta = tan^{-1}(\frac{1}{2})$

b) (0,8,15)

$\rho = \sqrt{0^{2}+8^{2}+(15)^{2}}$ = 17

$\phi = cos^{-1}(\frac{15}{17})$

$\theta = tan^{-1}\frac{y}{x}$

The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = $\frac{\pi}{2}$

c) (√2,1,1)

$\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}}$ = 2

$\phi = cos^{-1}(\frac{1}{2})$

$\phi$ = $\frac{\pi}{3}$

$\theta = tan^{-1}\frac{1}{\sqrt{2} }$

d) (−2√3,−2,3)

$\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}}$ = 5

$\phi = cos^{-1}(\frac{3}{5})$

Since x < 0, use 2nd option:

$\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }$

$\theta = \pi + \frac{\pi}{6}$

$\theta = \frac{7\pi}{6}$

Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:

$r=\sqrt{x^{2}+y^{2}}$

Angle θ is the same as spherical coordinate;

z = z

Calculating:

a) (4,2,-4)

$r=\sqrt{4^{2}+2^{2}}$ = $\sqrt{20}$

$\theta = tan^{-1}\frac{1}{2}$

z = -4

b) (0, 8, 15)

$r=\sqrt{0^{2}+8^{2}}$ = 8

$\theta = \frac{\pi}{2}$

z = 15

c) (√2,1,1)

$r=\sqrt{(\sqrt{2} )^{2}+1^{2}}$ = $\sqrt{3}$

$\theta = \frac{\pi}{3}$

z = 1

d) (−2√3,−2,3)

$r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}}$ = 4

$\theta = \frac{7\pi}{6}$

z = 3

5 0

2 years ago

Sarah is making 4 batches of granola bars. She adds 7/8 cup peanuts. Her measuring cup holds 1/8 cup. How many times must Sarah

Naya [18.7K]

Answer:

Sarah is making 4 batches of granola bars. She needs 7/8 cup peanuts to each batch and her measuring cup holds 1/8 cup.

Thus, if one cup holds then to make , Sarah will have to measure = 7 times for one batch of granola bars.

Therefore, for making 4 batches of granola bars, Sarah must measure 1/8 cup peanuts 7 x 4=28 times.Step-by-step explanation:

3 0

2 years ago

4% of what days is 56 days

leva [86]

The answer would be 14 because 4x__=56 ? 4 x14 =56

6 0

2 years ago

3(x - 1) - 8 = 4(1+x) + 5​

3(x - 1) - 8 = 4(1+x) + 5