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3 years ago

What is the answer to 5(p+6)=8p

Mathematics

2 answers:

motikmotik3 years ago

7 0

$5(p+6)=8p \\ 5p+30=8p \\ 30=3p \\ \boxed{p=10}$

Alekssandra [29.7K]3 years ago

4 0

$5\left( p+6 \right) =8p\\ \\ 5p+30=8p\\ \\ 8p-5p=30$

$\\ \\ 3p=30\\ \\ \frac { 1 }{ 3 } \cdot 3p=\frac { 1 }{ 3 } \cdot 30\\ \\ p=10$

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spayn [35]

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6 0

3 years ago

How do you solve x for (x+5)^3/2 = ( x-1)^3

malfutka [58]

Answer:

x = 6 (2^(1/3) + 2^(2/3)) + 7 or x = 6 (-2)^(1/3) ((-1)^(1/3) - 2^(1/3)) + 7 or x = 6 (-2)^(1/3) ((-2)^(1/3) - 1) + 7

Step-by-step explanation:

Solve for x:

1/2 (x + 5)^3 = (x - 1)^3

Expand out terms of the right hand side:

1/2 (x + 5)^3 = x^3 - 3 x^2 + 3 x - 1

Subtract x^3 - 3 x^2 + 3 x - 1 from both sides:

1 - 3 x + 3 x^2 - x^3 + 1/2 (x + 5)^3 = 0

Expand out terms of the left hand side:

-x^3/2 + (21 x^2)/2 + (69 x)/2 + 127/2 = 0

Bring -x^3/2 + (21 x^2)/2 + (69 x)/2 + 127/2 together using the common denominator 2:

1/2 (-x^3 + 21 x^2 + 69 x + 127) = 0

Multiply both sides by 2:

-x^3 + 21 x^2 + 69 x + 127 = 0

Multiply both sides by -1:

x^3 - 21 x^2 - 69 x - 127 = 0

Eliminate the quadratic term by substituting y = x - 7:

-127 - 69 (y + 7) - 21 (y + 7)^2 + (y + 7)^3 = 0

Expand out terms of the left hand side:

y^3 - 216 y - 1296 = 0

Change coordinates by substituting y = z + λ/z, where λ is a constant value that will be determined later:

-1296 - 216 (z + λ/z) + (z + λ/z)^3 = 0

Multiply both sides by z^3 and collect in terms of z:

z^6 + z^4 (3 λ - 216) - 1296 z^3 + z^2 (3 λ^2 - 216 λ) + λ^3 = 0

Substitute λ = 72 and then u = z^3, yielding a quadratic equation in the variable u:

u^2 - 1296 u + 373248 = 0

Find the positive solution to the quadratic equation:

u = 864

Substitute back for u = z^3:

z^3 = 864

Taking cube roots gives 6 2^(2/3) times the third roots of unity:

z = 6 2^(2/3) or z = -6 (-1)^(1/3) 2^(2/3) or z = 6 (-2)^(2/3)

Substitute each value of z into y = z + 72/z:

y = 6 2^(1/3) + 6 2^(2/3) or y = 6 (-1)^(2/3) 2^(1/3) - 6 (-1)^(1/3) 2^(2/3) or y = 6 (-2)^(2/3) - 6 (-2)^(1/3)

Bring each solution to a common denominator and simplify:

y = 6 (2^(1/3) + 2^(2/3)) or y = 6 (-2)^(1/3) ((-1)^(1/3) - 2^(1/3)) or y = 6 (-2)^(1/3) ((-2)^(1/3) - 1)

Substitute back for x = y + 7:

Answer: x = 6 (2^(1/3) + 2^(2/3)) + 7 or x = 6 (-2)^(1/3) ((-1)^(1/3) - 2^(1/3)) + 7 or x = 6 (-2)^(1/3) ((-2)^(1/3) - 1) + 7

7 0

3 years ago

Read 2 more answers

Find the area of the triangle to the nearest tenth . Pleaseeee help

tigry1 [53]

Answer:

15.8 cm²

Step-by-step explanation:

Please see attached photo for diagram.

We'll begin by calculating the angle A. This can be obtained as follow:

B = 56°

C = 78°

A =?

A + B + C = 180 (Sum of the angle in triangle)

A + 56 + 78 = 180

A + 134 = 180

Collect like terms

A = 180 – 134

A = 46°

Next, we shall determine the value of b by using the sine rule. This can be obtained:

Side opposite angle C (c) = 7.2 cm

Angle C = 78°

Angle B = 56°

Side opposite angle B (b) =?

b/Sine B = c/sine C

b/Sine 56 = 7.2/Sine 78

Cross multiply

b × Sine 78 = 7.2 × Sine 56

Divide both side by Sine 78

b = 7.2 × Sine 56 / Sine 78

b = 6.1 cm

Finally, we shall determine the area of the triangle. This can be obtained as follow:

Side opposite angle C (c) = 7.2 cm

Side opposite angle B (b) = 6.1 cm

Angle A = 46°

Area (A) =?

A = ½bcSineA

A = ½ × 6.1 × 7.2 × Sine 46

A = 15.8 cm²

Therefore, the area of the triangle is 15.8 cm²

4 0

3 years ago

Romeo paid $380.75 in car repairs. The sales tax rate is 10%. Which of the following is a reasonable estimate of the tax Romeo

xxMikexx [17]

Answer:

ADD THE TEN PERCENT IT WOULD BE 418.82

Step-by-step explanation:

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5 0

2 years ago

Express the function graphed on the axes below as a piecewise function.<br><br> Please helppp!

Scilla [17]

It has multiple functions but it should be close to the middle

3 0

3 years ago