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4 years ago

Find, to four significant digits, the distance between the graphs of 2x-3y+4=0 and 2x-3y+15=0.

1 answer:

4 0

In analytical geometry, we can find the linear distance between two parallel lines by determining the coefficients of the variables and the constants. The general equation for a linear equation is: Ax + By = C.

Line 1: 2x - 3y = -4
Line 2: 2x - 3y = -15

In this case, A=2 and B=-3. The constants are C₁ = -4 and C₂ = -15. The distance follows this formula:

d = |C₁ - C₂|/(√(A²+B²)
d = |⁻4 - ⁻15|/(√(2²+⁻3²)
d = 3.051 units

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If m∠DEF = (5x−8)°. Which equation would you use to find the value of x?

dimulka [17.4K]

Answer:

5x-8=90

Step-by-step explanation:

Thale’s Theorem

5x-8=90

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3 years ago

Angela says that 6.25 is 1/100 the value of 625. Write an explanation to support Angela's statement.

gladu [14]

Answer:

6.25 times 100 will equal to 625. When you multiply by 100, you can move the decimal two spaces to the right since there are two zeros, and you get 625.

Step-by-step explanation:

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3 years ago

Read 2 more answers

Julian fully simplifies this polynomial and then writes it in standard form. 4x2y2 – 2y4 – 8xy3 + 9x3y + 6y4 – 2xy3 – 3x4 + x2y2

Rasek [7]

4x²y² - 2y⁴ - 8xy³ + 9x³y + 6y⁴ - 2xy³ - 3x⁴ + x²y²

= 5x²y² +4y⁴ - 10xy³ + 9x³y - 3x⁴ combined like terms

= -3x⁴ + 9x³y + 5x²y² - 10xy³ + 4y⁴ descending exponent order based on "x"

If Julian wrote his list in descending order based on "y", then the order would be reversed.

Answer: 4y⁴

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4 years ago

Read 2 more answers

Part A

ira [324]

Answer:

Part A)

scientific notation ------> $2.56*10^{11}\ bits$

standard notation -----> $256,000,000,000\ bits$

Part B)

scientific notation ------> $5.12*10^{11}\ bits$

standard notation -----> $512,000,000,000\ bits$

Part C)

scientific notation ------> $1.28*10^{11}\ bits$

standard notation -----> $128,000,000,000\ bits$

Part D)

scientific notation ------> $6.4*10^{10}\ bits$

standard notation -----> $64,000,000,000\ bits$

Part E)

scientific notation ------> $3.2*10^{11}\ bits$

standard notation -----> $320,000,000,000\ bits$

Step-by-step explanation:

we know that

$1\ Gigabyte=1*10^{9}\ bytes$

$1\ byte=8\ bits$

therefore

$1\ Gigabyte=8*10^{9}\ bits$

Part A

Theresa and her brother, Ruben, are getting phones that each have 32 gigabytes of storage. How many bits of storage come with each phone? Type your answer in both scientific and standard notation

we know that

Each phone have 32 gigabytes of storage

using proportion

$\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{32}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=32*8*10^{9}\\ \\x=256*10^{9}\ bits\\ \\x=2.56*10^{11}\ bits$

scientific notation ------> $2.56*10^{11}\ bits$

standard notation -----> $256,000,000,000\ bits$

Part B

Theresa’s parents, Cal and Julia, are getting phones that each have 64 gigabytes of storage. How many bits of storage come with each phone? Type your answer in both scientific and standard notation.

we know that

Each phone have 64 gigabytes of storage

using proportion

$\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{64}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=64*8*10^{9}\\ \\x=512*10^{9}\ bits\\ \\x=5.12*10^{11}\ bits$

scientific notation ------> $5.12*10^{11}\ bits$

standard notation -----> $512,000,000,000\ bits$

Part C

Because they are getting four new phones, the family also gets two free tablets. Each tablet has 16 gigabytes of storage. How many bits of storage come with each tablet?

we know that

Each tablet have 16 gigabytes of storage

using proportion

$\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{16}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=16*8*10^{9}\\ \\x=128*10^{9}\ bits\\ \\x=1.28*10^{11}\ bits$

scientific notation ------> $1.28*10^{11}\ bits$

standard notation -----> $128,000,000,000\ bits$

Part D

Theresa talked her parents into getting SD cards for her phone and her brother’s phone. Inserting an SD card into a phone gives it more storage. They both get 8-gigabyte SD cards. How many bits of storage come with each SD card? Type your answer in both scientific and standard notation

we know that

Each SD card have 8 gigabytes of storage

using proportion

$\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{8}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=8*8*10^{9}\\ \\x=64*10^{9}\ bits\\ \\x=6.4*10^{10}\ bits$

scientific notation ------> $6.4*10^{10}\ bits$

standard notation -----> $64,000,000,000\ bits$

Part E

With their plan, the family also gets access to storage on the cloud. They can store a total of 40 gigabytes on the cloud. How many bits of storage do they get on the cloud? Type your answer in both scientific and standard notation

we know that

The cloud have 40 gigabytes of storage

using proportion

$\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{40}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=40*8*10^{9}\\ \\x=320*10^{9}\ bits\\ \\x=3.2*10^{11}\ bits$

scientific notation ------> $3.2*10^{11}\ bits$

standard notation -----> $320,000,000,000\ bits$

3 0

4 years ago

Which probability formulas are always true for any events A and B.

zhenek [66]

P(A U B) = P(A) + P(B) - P(A and B)

P(A | B) = P(A and B) / P(B)

6 0

3 years ago