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2 years ago

Write the equation in slope-intercept form that contains the following point and is perpendicular to the given line

Mathematics

1 answer:

Len [333]2 years ago

8 0

Answer:

y = 1/4 x -3

Step-by-step explanation:

y = -4x + 3;

the slope of this equation is -4

we want the slope perpendicular to this

take the negative reciprocal

- (-1/4) = 1/4

so the slope of our line will be 1/4

we have the slope and a point so we can use point slope form

y-y1 = m (x-x1)

y--2 = 1/4(x-4)

y+2 = 1/4 (x-4)

we need to change it to slope intercept form (y=mx+b)

distribute

y+2 = 1/4 x -1/4*4

y+2 = 1/4x -1

subtract 2 from each side

y +2-2 = 1/4 x -1-2

y = 1/4 x -3

the slope is 1/4 and the y intercept is -3

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What is an expression for the distance between the origin and a point P(x,y)

kirza4 [7]

Answer:

$d = \sqrt{ {x}^{2} + {y}^{2} }$

Step-by-step explanation:

Distance between origin (0, 0) and point (x, y) is given as:

$d = \sqrt{ {(x - 0)}^{2} + {(y - 0)}^{2} } \\ \\ \red{ \bold{ d = \sqrt{ {x}^{2} + {y}^{2} } }}$

5 0

2 years ago

John looked at his bank account and noticed that he had $2,029.90 in his account. All that he could remember is that he created

Over [174]

We will have that for the previous year, he had in the account:

$m_{y6}=2029.90-\frac{2029.90\cdot6}{100}\Rightarrow m_{y6}=1908.106$

For the year previous to that one, he had:

$m_{y5}=1908.106-\frac{1908.106\cdot6}{100}\Rightarrow m_{y5}=1793.61964$

For the previous year to that, he had:

$m_{y4}=1793.61964-\frac{1793.61964\cdot6}{100}\Rightarrow m_{y4}=1686.002462$

For the year previous to that one, he had:

$m_{y3}=1686.002462-\frac{1686.002462\cdot6}{100}\Rightarrow m_{y3}=1584.842314$

For the second year that the money was in the account, there was:

$m_{y2}=1584.842314-\frac{1584.842314\cdot6}{100}\Rightarrow m_{y2}=1489.751775$

And the orinial ammount of money that was in the account was:

$m_{y1}=1489.751775-\frac{1489.751775\cdot6}{100}\Rightarrow m_{y1}=1400.366669$

From this, we know that Jhon had originally $1400.37 in the bank account.

6 0

2 months ago

The family wants to determine if they can drive to the national park using Just one tank of gas in their car. Determine whether

Nataliya [291]

Answer:

The Fullers can reach the national park

Step-by-step explanation:

The complete question is

The Fuller family wants to drive to a national park. Some information about their trip is given in the table below.

Distance to national park 515 miles

Car’s gas tank capacity 20 gallons

Average gas mileage for car 26 miles per gallon

The family wants to determine if they can drive to the national park using just one tank of gas in their car. Determine whether the Fullers can reach the national park. Show your work or explain your answer.

we know that

The Average gas mileage for the car is 26 miles per gallon

That means

With 1 gallon the car runs 26 miles

using a proportion

Find out how many miles the car runs with 20 gallons (one tank of gas)

$\frac{26}{1}\ \frac{miles}{gallon}=\frac{x}{20}\ \frac{miles}{gallons}\\\\x=26(20)\\\\x=520\ miles$

Compare with the distance to the national park

$520\ miles>515\ miles$

therefore

The Fullers can reach the national park

7 0

2 years ago

Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonome

ratelena [41]

Answer:

$x = 0.175\cdot (1-\cos 4\cdot \theta)$

Step-by-step explanation:

Let use the following trigonometric identities:

$\sin^{2}\theta = \frac{1-\cos 2\cdot \theta}{2} \\\cos^{2}\theta = \frac{1+\cos 2\cdot \theta}{2}$

Then, the equation is simplified by substituting its components:

$x = 1.40\cdot \left(\frac{1-\cos 2\cdot \theta}{2} \right)\cdot \left(\frac{1+\cos 2\cdot \theta}{2} \right)$

$x = 0.35\cdot (1-\cos^{2}2\cdot \theta)$

$x = 0.35\cdot \sin^{2}2\cdot \theta$

$x = 0.35\cdot \left(\frac{1-\cos 4\cdot \theta}{2} \right)$

$x = 0.175\cdot (1-\cos 4\cdot \theta)$

7 0

3 years ago

Read 2 more answers

Solve for x 0°<x<360 3cos2x +sinx=1

BartSMP [9]

Step-by-step explanation:

3cos2x +sinx=1

3(1-2sin²x)+sinx=1

3-6sin²x+sinx=1

sinx(-6sinx+1)=1

either

sinx=1

sinx=sin(90)

:.x=90

-6sinx+1=1

-6sinx=1-1

sinx=0/-6

sinx=sin0,sin180

:.x=0,180and90

8 0

2 years ago