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3 years ago

What is the slope of the line represented by the equation 4x+8y=4

2 answers:

8 0

Rearrange the formula so that its in the form of y=mx+b
so it would be:
8y= -4x + 4
then divide by 8:
y= -4/8 x + 4/8:
Simplify:

y= -1/2x + 1/2

the slope is -1/2

Juliette [100K]3 years ago

6 0

The slope is 1.000/2.000=-0.500

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What is the value of x? O 2 03 06 07 "Е

Svet_ta [14]

Ima pretty sure it’s 06

6 0

2 years ago

What is the factorization of 729^15+1000?

igomit [66]

Answer:

The factorization of $729x^{15} +1000$ is $(9x^{5} +10)(81x^{10} -90x^{5} +100)$

Step-by-step explanation:

This is a case of factorization by sum and difference of cubes, this type of factorization applies only in binomials of the form $(a^{3} +b^{3} )$ or $(a^{3} -b^{3})$ . It is easy to recognize because the coefficients of the terms are perfect cube numbers (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).

Let's solve the factorization of $729x^{15} +1000$ by using the sum and difference of cubes factorization.

1.) We calculate the cubic root of each term in the equation $729x^{15} +1000$ , and the exponent of the letter x is divided by 3.

$\sqrt[3]{729x^{15}} =9x^{5}$

$1000=10^{3}$ then $\sqrt[3]{10^{3}} =10$

So, we got that

$729x^{15} +1000=(9x^{5})^{3} + (10)^{3}$ which has the form of $(a^{3} +b^{3} )$ which means is a sum of cubes.

Sum of cubes

$(a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})$

with $a= 9x^{5}$ y $b=10$

2.) Solving the sum of cubes.

$(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )$

$(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)(81x^{10}-90x^{5}+100)$

8 0

2 years ago

Solve the system of equations: y = x + 2 y = x2 + 5x + 6 HELP PLZ

soldier1979 [14.2K]

Answer:

x=2(twice)

y=0(twice)

Step-by-step explanation:

This question can be solved using substitution method

So let's solve

y=x+2....(1)

y=x2+5x+6....(2)

Substitute (1) into(2)

X+2=x2+5x+6

Collect like terms

X2+5x-x+6-2=0

X2+4x+4=0

X2+2x+2x+4=0

X(x+2)+2(x+2)=0

(X+2)(x+2)=0

X+2=0

Substrate 2 from both sides

X=-2

X+2=0

X=-2

Let's substitute the value of x into (1)

y=x+2

y=-2+2

Y=0(twice)

6 0

3 years ago

An athletic field is a 48 yd-by-96 yd rectangle, with a semicircle at each of the short sides. A running track 20 yd wide surr

MA_775_DIABLO [31]

The distance would be equal to 2 times the longest side of the rectangle plus twice the shortest side multiplied by pi / 2 for the semicircle, that is:

longest side 96 and shortest 48

D = 2 * (96) + 2 * (1/2) * pi * 48

D = 192 + pi * 48

This shorter side, which starts at 48, will expand each time by two more in proportion to 20 of the running track between 8 than the number of divisions, that is, 2 * (20/8) = 5

In other words, there are 8 distances, like this:

D1 = 192 + 3.14 * 48 = 342.72 yd

D2 = 192 + 3.14 * (48 + 5) = 358.42 yd

D3 = 192 + 3.14 * (48 + 10) = 374.12 yd

D4 = 192 + 3.14 * (48 + 15) = 389.82 yd

D5 = 192 + 3.14 * (48 + 20) = 405.52 yd

D6 = 192 + 3.14 * (48 + 25) = 421.22 yd

D7 = 192 + 3.14 * (48 + 30) = 436.92 yd

D8 = 192 + 3.14 * (48 + 35) = 452.62 yd

6 0

2 years ago

Original: $110 New: $59 %Decrease:__________

Lemur [1.5K]

Answer:

46.36%

Step-by-step explanation:

Original: 110

New: 59

Percent Decrease: x

110 - 59 = 51

51/110 ≈ 46.3636... ≈ 46.36%

-Chetan K

3 0

2 years ago

Read 2 more answers