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katen-ka-za [31]

3 years ago

10

Type the correct answer in the box. Use numerals instead of words.

2 answers:

Art [367]3 years ago

8 0

Answer: The y-intercept of the line is 6

Step-by-step explanation:

The equation of the line in the form $y = mx + b$ is called "Slope-Intercept form", where "m" is the slope of the line and "b" is the y-intercept.

Knowing that the line passes through the point (10,1) and has a slope of -0.5, we can identify that:

$x=10\\y=1\\m=-0.5$

Then, we can substitute values into the equation $y = mx + b$ and solve for "b".

$1=(-0.5)(10)+b\\\\1=-5+b\\\\1+5=b\\\\b=6$

Therefore, the y-intercept of the line is 6 .

Karo-lina-s [1.5K]3 years ago

7 0

Answer:

6

Step-by-step explanation:

A line that passes through the point (x,y), with a y-intercept of b and a slope of m, can be represented by the equation $y = mx + b$ .

If a line has the slope of -0.5, then m=-0.5 and the equation of the line is

$y=-0.5x+b$

This line passes throughthe point (10,1), then the coordinates of this point satisfy the equation of the line:

$1=-0.5\cdot 10+b\\ \\1=-5+b\\ \\b=1+5\\ \\b=6$

and the equation of the line is

$y=-0.5x+6$

Since b=6, the y-intercept of the line is 6.

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Convert the decimal to a fraction in simplest form:

Shkiper50 [21]

Answer:

Decimal 0.333 to a fraction in simplest form is: $\frac{333}{1000}$

Step-by-step explanation:

Given the decimal

$0.333$

Multiply and divide by 10 for every number after the decimal point.

There are three digits to the right of the decimal point, therefore multiply and divide by 1000.

Thus,

$0.333=\frac{0.333\cdot \:\:1000}{1000}$

$=\frac{333}{1000}$ ∵ 0.333×1000 = 333

Let us check if we can reduce the fraction $\frac{333}{1000}$

For this, we need to find a common factor of 333 and 1000 in order to cancel it out.

But, first, we need to find the Greatest Common Divisor (GCD) of 333, 1000

<u>Greatest Common Divisor (GCD) : </u>

The GCD of a, b is the largest positive number that divides both a and b without a remainder.

Prime Factorization of 333: 3 · 3 · 37

Prime Factorization of 1000: 2 · 2 · 2 · 5 · 5 · 5

As there is no common factor for 333 and 1000, therefore, the GCD is 1.

Important Tip:

As GCD is 1, therefore the fraction can not be simplified.

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4 0

3 years ago

Match each series with the equivalent series written in sigma notation

PIT_PIT [208]

Answer:

$3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n$

$4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n$

$2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n$

$3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n$

Step-by-step explanation:

Given

See attachment for complete question

Required

Match equivalent expressions

Solving (a):

$3 + 12 + 48 + 192 + 768$

The expression can be written as:

$3 \to 3*4^{0$ --- 0

$12 \to 3 * 4^{1$ ---- 1

$48 \to 3 * 4^{2$ --- 2

$192 \to 3 * 4^{3$ ---- 3

$768 \to 3 * 4^{4$ ---- 4

For the nth term, the expression is:

$Term = 3 * 4^{n$ ---- n

So, the summation is:

$3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n$

Solving (b):

$4 + 32 + 256 + 2048 + 16384$

The expression can be written as:

$4 \to 4 * 8^0$ --- 0

$32 \to 4 * 8^1$ ---- 1

$256 \to 4 * 8^2$ --- 2

$2048 \to 4 * 8^3$ ---- 3

$16384 \to 4 * 8^4$ ---- 4

For the nth term, the expression is:

$Term \to 4 * 8^n$ ---- n

So, the summation is:

$4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n$

Solving (c):

$2 + 6 + 18 + 54 + 162$

The expression can be written as:

$2 \to 2 * 3^0$ --- 0

$6 \to 2 * 3^1$ ---- 1

$18 \to 2 * 3^2$ --- 2

$54 \to 2 * 3^3$ ---- 3

$162 \to 2 * 3^4$ ---- 4

For the nth term, the expression is:

$Term \to 2 * 3^n$ ---- n

So, the summation is:

$2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n$

Solving (d):

$3 + 15 + 75 + 375 + 1875$

The expression can be written as:

$3 \to 3 * 5^0$ --- 0

$15 \to 3 * 5^1$ ---- 1

$75 \to 3 * 5^2$ --- 2

$375 \to 3 * 5^3$ ---- 3

$1875 \to 3 * 5^4$ ---- 4

For the nth term, the expression is:

$Term \to 3 * 5^n$ ---- n

So, the summation is:

$3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n$

5 0

3 years ago