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3 years ago

9

Find the missing Side of the triangle

1 answer:

sammy [17]3 years ago

3 0

Answer:

2√15

Step-by-step explanation:

Use the Pythagorean theorem.

2² + x² = 8²

x² + 4 = 64

x² = 60

x² = 4 * 15

x = 2√15

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What is the equation of the line (in slope-intercept form) that passes through the point (5,−1) and is parallel to the line y=2x

tatyana61 [14]

Answer:

<h2>y = 2x - 11</h2>

Step-by-step explanation:

$\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================$

$\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\==========================$

$\text{We have the equation of a line:}\ y=2x-7\to m_1=2.\\\\\text{The slope of a parallel line:}\ m_2=m_1=2.\\\\\text{We have the equation:}\\\\y=2x+b\\\\\text{Put the coordinates of the point (5, -1) o the equation:}\\\\-1=2(5)+b\\-1=10+b\qquad\tex\text{subtract 10 from both sides}\\-11=b\to b=-11\\\\\text{Finally:}\\\\y=2x-11$

5 0

3 years ago

The weekly cost of food for a family of four using the moderate cost plan in the United States increased at a relatively constan

Mila [183]

Answer:

Part a) The weekly cost of food for a family of four in 1997 was $153.09

Part b) $y=4.83x+153.09$

Part c) $\$215.88$

Step-by-step explanation:

Part a. What was the weekly cost of food for a family of four in 1997?

Let

y ---->the weekly cost of food for a family of four

x ---> the number of years since 1997

we know that

The linear equation in point slope form is equal to

$y-y1=m(x-x1)$

In this problem we have a linear function between variable x and variable y

In 2004, the weekly cost of food for a family of four was $186.90

so

In the year 2004

The value of x is equal to

x=2004-1997=7 years

we have

$point\ (7,186.90)$

$m=\$4.83\ per\ year$

substitute

$y-186.90=4.83(x-7)$ ----> equation in point slope form

Remember that the year 1997 is when the value of x is equal to zero

so

For x=0

$y-186.90=4.83(0-7)$

solve for y

$y=4.83(-7)+186.90$

$y=153.09$ -----> y-intercept or initial value

therefore

The weekly cost of food for a family of four in 1997 was $153.09

Part b. Write an equation that gives the weekly cost of food for a family of four as a function of the number of years since 1997

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-intercept or initial value

we have

$m=\$4.83\ per\ year$

$b=\$153.09$ ----> initial value in 1997

substitute

$y=4.83x+153.09$

Part c. Find the weekly cost of food for a family of four in 2010 assuming the same rate of increase

In the year 2010

x=2010-1997=13 years

substitute in the linear equation

$y=4.83(13)+153.09=215.88$

5 0

3 years ago

1/7 divided by blank equals 14

kherson [118]

Answer:

1/98

Step-by-step explanation:

Step 1: Translate statement into equation.

$\frac{1}{7}/x = 14$
$\frac{1}{7x}=14$

Step 2: Multiply both sides by 7x.

$\frac{1}{7x} * 7x = 14 * 7x$
$1 = 98x$

Step 3: Divide both sides by 98.

$\frac{1}{98} =\frac{98x}{98}$
$x = \frac{1}{98}$

Step 4: Check if solution is correct.

$\frac{1}{7}/\frac{1}{98}$
$\frac{1}{7}*98$
$14$

Therefore, the answer is 1/98.

3 0

2 years ago

98 POINTS!!<br><br> need fast help on this one pleaseeee

Gekata [30.6K]

Answer:

39047

Step-by-step explanation:

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3 years ago

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Romashka [77]

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3 years ago