On a coordinate plane, a line goes through (1, negative 1) and (4, 2). A point is at (2, 5). What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2, 5)? y + 5 = x + 2 y − 2 = x − 5 y − 5 = −(x − 2) y + 2 = −(x + 5)

9514 1404 393

Answer:

Step-by-step explanation:

A) Your scientific or graphing calculator can tell you the product:

  (3.9×10^33 erg/s)(1.55×10^7 s) = 6.045×10^40 ergs

__

B) 10^2 mm is 100 mm, about 4 inches, so 1.8×10^2 mm is about 7 inches. This is somewhat larger than the diameter of a human hair (and about the same size as the diameter of a human head).

1.8×10^-2 mm = 18 μm is a more reasonable estimate of hair diameter

(The range of hair diameters is reportedly about 17 to 181 μm, so the given dimension is on the low end.)

Answer:

1)B

2)G

3)B

4)F

5)D

Answer:

2,391 paid altogether. The interest Rate was another 391 dollars.

Step-by-step explanation:

Answer:

Integer, Rational number, Real number

Step-by-step explanation:

Answer:

With? I dont see an image if you attached one

Step-by-step explanation:

Answer:

y=-3x+5

bring (4,-7) in other three lines

you will know that it is unreasonable that

-7=-14

-7=-17

-7=14

The equation for the line perpendicular to the line represented by the equation  [tex]y= \ \frac{1}{3} x-2[/tex]  that passes through the point [tex](4,-7)[/tex] will be  [tex]y=-3x+5[/tex].

Equation for the perpendicular line, the perpendicular lines have opposite-reciprocal slopes.

Now,

The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

Equation of a perpendicular line   [tex]y=mx-b[/tex]

Here, [tex]m=[/tex] slope

So,

We have

     [tex]y= \ \frac{1}{3} x-2[/tex]  

Here,

[tex]m = \frac{1}{3}[/tex]

As mentioned above, we have to find the slope of perpendicular,

i.e.

 (slope of perpendicular)  [tex]m[/tex] [tex]=-3[/tex]      

So,

     [tex]y=mx-2[/tex]

[tex]y=(-3)x-b[/tex]

We have

Point [tex](4,-7)[/tex] through which line passes. i.e.

[tex]x=4[/tex]

[tex]y=(-7)[/tex]

Therefore,

    [tex]-7=(-3)*4-b[/tex]

⇒  [tex]b=7-12[/tex]

    [tex]b=(-5)[/tex]

So, Equation of a perpendicular line,

 [tex]y=-3x+5[/tex]

So, Equation of a perpendicular line,  [tex]y=-3x+5[/tex] which is derived from  [tex]y=mx-b[/tex] .

Hence, we can say that the equation for the line perpendicular to the line represented by the equation  [tex]y= \ \frac{1}{3} x-2[/tex]  that passes through the point [tex](4,-7)[/tex] will be  [tex]y=-3x+5[/tex].

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Answer:

point slope form

Step-by-step explanation:

hi! we can use point slope form:

y-y1=m(x-x1)

where m is the slope, x1 is the x-coordinate of the given point, and y1 is the y-coordinate of the given point.

example:

slope is 4

ordered pair is (2,3)

y-3=4(x-2)

y-3=4x-8

y=4x-5

hope this helps!

Answer:

12

Step-by-step explanation:

Answer:

Ratio of the lengths = 1 : 16 and 1 : 15.71

Ratio of the Area = 1 : 251.29

Step-by-step explanation:

Model = 1/2in and 1/6in.

Actual = 2/3ft and 2/9ft.

1 ft = 12 inches

2/3 ft = 8 inches

2/9 ft = 2.67 inches

Model = 0.5 inches and 0.17 inches

Actual = 8 inches and 2.67 inches

Ratio

0.5 : 8 and 0.17 : 2.67

= 0.5 / 8 and 0.17 / 2.67

= 1 / 16 and 1 / 15.71

= 1 : 16 and 1 : 15.71

Area of the tile in the model = length × width

= (0.5 × 0.17) inches

= 0.085 inches

Area of the actual tile = length × width

= (8 × 2.67) inches

= 21.36 inches

Ratio of the area

0.085 : 21.36

= 0.085 / 21.36

= 1 : 251.29

Answer:

Ah thank you, you too from me.

Answer:

B

Step-by-step explanation:

8th graders IQR-5

9th graders IQR-8

So, 8th Graders IQR is 3 less than 9th Graders IQR

Answer:

3.15 10^-4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hope this helps! <3

Answer:

here is a hint

Step-by-step explanation:

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Compare slope of an equation and slope of a line on graph and compare y-intercepts.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

For linear equation,

Compare slope of an equation and slope of a line on graph and compare y-intercepts.

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Therefore, compare slope of an equation and slope of a line on graph and compare y-intercepts.

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Answer:

Constraints are restrictions (limitations, boundaries) that need to be placed upon variables used in equations that model real-world situations. ... Constraints then become necessary to allow the mathematical model to realistically represent the situation. hope this helps!

Step-by-step explanation:

Answer: Constraints are restrictions (limitations, boundaries) that need to be placed upon variables used in equations that model real-world situations. Constraints then become necessary to allow the mathematical model to realistically represent the situation

Answer:

ad bc

Step-by-step explanation:

Answer: for part a the answer is aed and bec.

Step-by-step explanation:

Answer:

Y = 10

Step-by-step explanation:

As, Y / X = 125/25

125/25 = 5

Therefore, y = 5x

So when x = 2

Y = 5x

So, Y = 5x2

Therefore, Y = 10

[y] will be equivalent to 10, if [x] is equal to 2

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

Given is the value of [y] varies directly with [x] and y = 125 when x = 25.

Using the formula for direct proportionality -

y₁/x₁ = y₂/x₂

125/25 = y₂/2

y₂ = (125 x 2)/25

y₂ = 5 x 2

y₂ = 10

Therefore, [y] will be equivalent to 10, if [x] is equal to 2

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Answer:

Lili's CD be worth at the end of 3 years is $2714.23

Step-by-step explanation:

Lili deposit $2500 at the Annual percent rate 2.75% and for 3 years compounded quarterly.

Let's use formula

A = p[tex](1+\frac{r}{n} )^{n*t}[/tex]

From the given information

p=2500

r =0.0275

t=3

n=4

Plug in these values into the formula

A=2500[tex](1+\frac{0.0275}{4})^{4*3}[/tex]

Simplify the right side of the equation,

A=$2714.23

Answer:

Unit rate miles per day is, 3

Step-by-step explanation:

Unit rate are defined as the rate are expressed as quantity of 1 such that 2 miles per hour or 5 km per hour.

As per the given statement: A construction crew built 1/2 miles of road in 1/6 days

by unit rate definition;

After substituting the given values we have

⇒  

or

Therefore, unit rate miles per day is, 3

Step-by-step explanation:

hhhthhg

Answer:

Maximum price = GH¢85

Step-by-step explanation:

Let p be the number of times she raises the price as well as the number of times 10 less plates are sold

Revenue, R = number of plates sold * price sold

R = (300 - 10p)(20 + 5p)

R =  6000 + 1500p - 200p - 50p²

R = 6000 + 1300p - 50p²

50p² - 1300p - 6000 = 0

p² - 26p - 120 = 0

finding the axis of symmetry, p = -b/2a

p = -(-26)/2*1

p = 13

Maximum price = 13 * 5 + 20 = GH¢85

Number of plates sold = 300 - 10 * 13 = 170 plates

Maximum revenue = GH¢85 * 170 = GH¢14,450

Answer:

The answer is "More accurately is the left hand".

Step-by-step explanation:

In the given-question when we look at the given equation and see its given graph. This graph offers a much more reliable right hand because it has a smaller distance than that of the left. That being said, the left hand never surpassed the target, again and again, that's why the above given choice is correct.

Answer:

m=(c-0.15)/0.26

Step-by-step explanation:

c=0.41+0.26m-0.26

0.26m=c-0.15

m=(c-0.15)/0.26

Answer:

12 over 27 = 4 over 9

Step-by-step explanation:

12 over (12 + 15) = 12 over 27 = 4 over 9

Answer:

I believe it would be 5/2

Answer:

Step-by-step explanation:

Let's solve for w.

s=a+lw

Step 1: Flip the equation.

lw+a=s

Step 2: Add -a to both sides.

lw+a+−a=s+−a

lw=−a+s

Step 3: Divide both sides by l

[tex]\frac{lw}{l} =\frac{-a+s}{l}[/tex]

Answer:

Step-by-step explanation:

If she has 84 candles and 48 holders, we can write out the factors of both values as shown

For candles

84 = 2×2×3×7

84 = 12×7

For 48

48 = 2×2×2×2×3

48 = (2×2)×(2×2×3)

48 = 4×12

48 = 12×4

From both factors, we can are that 12 common to both of them. This means that the maximum number of gift boxes Ariana can pack is 12

The other factors will give the amount of scented candles and candle holders that each box will have. This means that each box will have 7scented candles and 4 holders.

Given:

Area of rectangle = [tex]6n^4+20n^3+14n^2[/tex]

Width of the rectangle is equal to the greatest common monomial factor of [tex]6n^4, 20n^3,14n^2[/tex].

To find:

Length and width of the rectangle.

Solution:

Width of the rectangle is equal to the greatest common monomial factor of [tex]6n^4, 20n^3,14n^2[/tex] is

[tex]6n^4=2\times 3\times n\times n\times n\times n[/tex]

[tex]20n^3=2\times 2\times 5\times n\times n\times n[/tex]

[tex]14n^2=2\times 7\times n\times n[/tex]

Now,

[tex]GCF(6n^4, 20n^3,14n^2)=2\times n\times n=2n^2[/tex]

So, width of the rectangle is [tex]2n^2[/tex].

Area of rectangle is

[tex]Area=6n^4+20n^3+14n^2[/tex]

Taking out GCF, we get

[tex]Area=2n^2(3n^2+10n+7)[/tex]

We know that, area of a rectangle is the product of its length and width.

Since, width of the rectangle is [tex]2n^2[/tex], therefore length of the rectangle is [tex](3n^2+10n+7)[/tex].