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3 years ago

a line is perpendicular to y=-2x+5 and intersects the point (-4,2). what is the equation of this perpendicular line?

Mathematics

1 answer:

german3 years ago

6 0

Answer:

y = 1/2x + 4

Step-by-step explanation:

If the line is perpendicular to y = -2x + 5 then the new line has a slope of 1/2.

So solve for b: using y = mx + b

2 = 1/2(-4) + b

2 = -2 + b

4 = b

Put it all together

y = 1/2x + 4

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Elza [17]

Answer:

3(n-8)

Step-by-step explanation:

5 0

3 years ago

Please show work and thank youuu

Assoli18 [71]

Answer: $6\sqrt{3}$

======================================================

Explanation:

Method 1

We can use the pythagorean theorem to find x.

$a^2+b^2 = c^2\\\\6^2+x^2 = 12^2\\\\36+x^2 = 144\\\\x^2 = 144-36\\\\x^2 = 108\\\\x = \sqrt{108}\\\\x = \sqrt{36*3}\\\\x = \sqrt{36}*\sqrt{3}\\\\x = 6\sqrt{3}\\\\$

-----------------------------------

Method 2

Use the sine ratio to find x. You'll need a reference sheet or the unit circle, or simply memorize that sin(60) = sqrt(3)/2

$\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(60^{\circ}) = \frac{x}{12}\\\\\frac{\sqrt{3}}{2} = \frac{x}{12}\\\\x = 12*\frac{\sqrt{3}}{2}\\\\x = 6\sqrt{3}\\\\$

-----------------------------------

Method 3

Similar to the previous method, but we'll use tangent this time.

Use a reference sheet, unit circle, or memorize that tan(60) = sqrt(3)

$\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(60^{\circ}) = \frac{x}{6}\\\\\sqrt{3} = \frac{x}{6}\\\\x = 6\sqrt{3}\\\\$

-----------------------------------

Method 4

This is a 30-60-90 triangle. In other words, the angles are 30 degrees, 60 degrees, and 90 degrees.

Because of this special type of triangle, we know that the long leg is exactly sqrt(3) times that of the short leg.

$\text{long leg} = (\text{short leg})*\sqrt{3}\\\\x = 6\sqrt{3}\\\\$

The short leg is always opposite the smallest angle (30 degrees).

3 0

2 years ago

87 ÷ 4 how many are in each group? are there any left over?

german

87 ÷ 4 = 21 remainder3

7 0

4 years ago

What is the y intercept of (-6, -5) when the slope is -2/3?

Alecsey [184]

X must be increased by 6 to get its value to be 0. Then the corresponding change in y will be (-2/3)*6 = -4. That value added to -5 makes it -9.

The y-intercept will be -9.

6 0

3 years ago

Maxis taking a cross-country road trip. Gas prices vary as the friends travel across the US from $4 dollars per gallon on the ea

Alex787 [66]

Answer:

The quantity of fuel bought at $4 is 40.84 gallons

The quantity of fuel bought at $3 is 116.699 gallons

The quantity of fuel bought at $5 is 17.505 gallons

Step-by-step explanation:

Here we have

Gas used on East coast = X gallons

Gas consumed in the mid-US = Y gallons

Gas consumed in the West coast = Z gallons

Where Y = 2×(X + Z)..........(1)

4·X + 3·Y + 5·Z = 515.........(2)

X + Y + Z = 150..................(3)

Therefore substituting for Y in equation (3) we have

X + 2×(X + Z) + Z = 150

3·X + 3·Z = 150

X = (150 - 3·Z)/3 = 50 - Z

Therefore, equation (2) becomes;

4·(50 - Z) + 3·(2×((50 - Z) + Z)) + 5·Z = 515

200 - 4·Z + 300 -6·Z + 6·Z + 5·Z = 515

500 + 2·Z = 515

Z = 15

X = 50 - Z = 50 - 15 = 35

Y = 2×(X + Z) = 2×(35 + 15) = 2 × 50 = 100

(b) Whereby the bought 174 gallons based on the same ratio as in part (a), we have;

Ratio in part (a) is given as follows;

Proportion of Z gallons = 15/150 = 1/10

Proportion of X gallons = 35/150 = 7/30

Proportion of Y gallons = 100/150 = 2/3

Therefore the proportion of 174 gallons that was consumed in the East coast, X gallons = (7/30)×174 = 203/5 gallons = 40.6 gallons

The proportion of 174 gallons that was consumed in the mid-US, Y gallons = (2/3)×174 = 116 gallons

The proportion of 174 gallons that was consumed in the West coast, Z gallons = (1/10)×174 = 87/5 gallons = 17.4 gallons

Based on price of per gallon, we have

The proportion of $515 that was consumed in the East coast on X gallons = $4 ×35 = $140

Proportion = 140/515= 28/103

The proportion of $515 that was consumed in the mid-US on Y gallons = $3 ×100= $300

Proportion = 300/515= 60/103

The proportion of $515 that was consumed in the West coast on Z gallons = $5 ×15= $75

Proportion = 75/515= 15/103

Therefore, the quantity of fuel bought at $4 = ((28/103) × 601)/4 = 40.84 gallons

The quantity of fuel bought at $3 = ((60/103) × 601)/3 = 116.699 gallons

The quantity of fuel bought at $5 = ((15/103) × 601)/5 = 17.505 gallons.

5 0

3 years ago