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Sedbober [7]
3 years ago
10

Two perpendicular lines have opposite y-intercepts. The equation of one of these lines is y = mx + b. Express the x-coordinate o

f the intersection point of the lines in terms of m and b.
Mathematics
1 answer:
Fofino [41]3 years ago
6 0

Answer:

x = -2bm/(m²+1)

Step-by-step explanation:

One line has equation

... y = mx + b

The slope of the perpendicular line is the negative reciprocal of the slope of the original line. The perpendicular line with the opposite y-intercept has equation

... y = (-1/m)x - b

The point of intersection is where the x- and y-values are equal, so ...

... mx + b = (-1/m)x - b

... (m +1/m)x = -2b . . . . . . . add 1/m - b to both sides

... (m²+1)x = -2bm . . . . . . . multiply by m

... x = -2bm/(m²+1) . . . . . . divide by the coefficient of x

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A loan for $1,200 has an annual interest rate of 5.2%. There is a $15 processing fee to receive the loan. The loan’s APR is .
Charra [1.4K]

<u>Answer: </u>

A loan for $1,200 has an annual interest rate of 5.2%. There is a $15 processing fee to receive the loan. The loan’s APR is 5.2%

<u>Solution: </u>

Since full form of APR is Annual Percentage Rate and it is defined as rate of interest for whole year which means it is same as annual interest rate. Also processing fee is totally different component.

So APR = annual interest rate ----- eqn 1

Given that a loan of $1200 has an annual interest rate of 5.2% .

So by using eqn 1 we can say APR = annual interest rate = 5.2%

Hence APR for a loan of $1200 is 5.2%

6 0
3 years ago
Belinda builds a rectangular prism that is 2 cubes​ long, 3 cubes​ wide, and 2 cubes tall. Each dimension of​ April's rectangula
zepelin [54]

Answer:

96 cubes vol.

Step-by-step explanation:

the volume of Belinda's prism =

2×3×2 = 12 cubes vol.

Each dimension of April's rectangular prism is twice as many cubes as Belinda's prism.

the volume of April's prism =

(2×2)×(2×3)×(2×2)= 4×6×4= 96 cubes vol.

so,

the volume of April's prism = (2)³ times the volume of Belinda's prism

4 0
3 years ago
The sum of the three angles of a triangle is 180°. Two angles of a triangle measure 15 and 73. Of x is the third angle, set up a
Agata [3.3K]

Answer:

The measure of the third angle is 92°

Step-by-step explanation:

We first have to make an equation that represents this equality. To do it we simply have to add the values ​​that give us with x and this will result in 180 °

15° + 73° + x = 180°

once we have the equation what we have to do is solve x, so we will pass all the terms that are adding to x by subtracting 180

x = 180° - 73° - 15°

now that we have cleared the x we ​​only have to perform the indicated operation and we will obtain the value of x

x = 92°

The measure of the third angle is 92°

8 0
3 years ago
7. A fish tank hold 100 gallons of water and is losing water at a rate of 1 gallons per hour. A second fish tank
djverab [1.8K]

Answer:

B

Step-by-step explanation:

the first fish tank has 100 gallons of water and 1 gallon is removed every hour which makes 100-h

the second tank has 40 gallons in it and 2 gallons are added every hour which makes 40+2h

after 20 hours the second tank will have more gallons than the first tank

this means that 40+2h would be greater than 100-h since it's also asking you "After how many hours will the first tank  have less water than the second?"

4 0
3 years ago
Twice the difference of a number and 16 is the same as three times a number less than 18
Maksim231197 [3]

Answer:

Step-by-step explanation:

Let x be the "number."

"twice the difference of a number and 16" can be written as:  

2(x-16)

"is the same as three times a number less than 18" can be written as:

= 3(x<18)

I wonder if this was meant to say "is the same as three times a number less  18," instead of "less than 18."  If so, we would have:

=3(x-18)

1.  Using the sentence as written:  2(x-16) = 3(x<18)

2.  Using the sentence as amended:  2(x-16) = =3(x-18)

 Going with this interpretation:  

 2(x-16) = 3(x-18)

2x - 32 = 3x - 54

x = 22

4 0
2 years ago
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