what is the best approximation of the solution to the equations that these two lines represent ​

Answer:

The perimeter of △LMN is 8 + [tex]\sqrt{10}[/tex]

Step-by-step explanation:

Step 1: Finding the length of LM

Distance formula  = [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]

here

[tex]x_1[/tex]= 2

[tex]x_2[/tex]= -2

[tex]y_1[/tex]= 4

[tex]y_2[/tex]=1

LM  = [tex]\sqrt{(-2-2)^2 +(1-4)^2}[/tex]

LM  = [tex]\sqrt{(-4)^2 +(-3)^2}[/tex]

LM  = [tex]\sqrt{16 +9)}[/tex]

LM  = [tex]\sqrt{25}[/tex]

LM  = 5

Step 2: Finding the length of MN

Distance formula  = [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]

here

[tex]x_1[/tex]= -2

[tex]x_2[/tex]= -1

[tex]y_1[/tex]=   1

[tex]y_2[/tex]= 4

LM  = [tex]\sqrt{(-1-(-2))^2 +(4 - 1)^2}[/tex]

LM  = [tex]\sqrt{(11+2)^2 +(3)^2}[/tex]

LM  = [tex]\sqrt{1 +9)}[/tex]

LM  = [tex]\sqrt{10}[/tex]

Step 3 : Finding the length of NL

Distance formula  = [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]

here

[tex]x_1[/tex]= -1

[tex]x_2[/tex]= 2

[tex]y_1[/tex]=   4

[tex]y_2[/tex]= 4

NL  = [tex]\sqrt{(2-(-1))^2 +(4 - 4)^2}[/tex]

NL  = [tex]\sqrt{(3)^2 +0}[/tex]

NL  = [tex]\sqrt{9 +0}[/tex]

B  = [tex]\sqrt{9 }[/tex]

NL = 3

Step 4: Finding the perimeter of the triangle

Perimeter =  length of LM +   length of MN +  length of NL

Perimeter = 5 + [tex]\sqrt{10}[/tex] + 3

Perimeter = 8 + [tex]\sqrt{10}[/tex]

Answer:

its D on edg

Step-by-step explanation:

Step-by-step explanation:

The volume of the shell is the volume of the outer sphere minus the volume of the inner sphere.

V = 4/3 π (r+h)³ − 4/3 π r³

V = 4/3 π (r³ + 3r²h + 3rh² + h³) − 4/3 π r³

V = 4/3 π r³ + 4π r²h + 4π rh² + 4/3 π h³ − 4/3 π r³

V = 4π r²h + 4π rh² + 4/3 π h³

If h = 0.1 r:

V = 4π r² (0.1 r) + 4π r (0.1 r)² + 4/3 π (0.1 r)³

V = 0.4π r³ + 0.04π r³ + 0.00133π r³

V = 0.44133π r³

Using the approximation:

V = 4π r² h

V = 4π r² (0.1 r)

V = 0.4π r³

The approximation is reasonable if h is small compared to r.

Answer:

C

Step-by-step explanation:

∠ AFD = ∠ AFC + ∠ CFD

Given ∠ CFA = 90° and

∠ CFD = 90° - ∠ EFD, that is

∠ CFD = 90° - 62° = 28°, thus

∠ AFD = 90° + 28° = 118° → C

Answer:

answer is c. 118

angle AFC+ angleCFD = angle AFD..

[ANGLE AFD =AFC + CFD][ANGLE CFD = 90 -62 ]

Answer:

Volume of the rectangular prism is given by,

[tex]\frac {15}{2x}[/tex] unit .

Step-by-step explanation:

According to the question,

height of the prism = [tex]\frac {5}{2x + 8}[/tex] unit = h (say)

depth of the prism = [tex]\frac {x + 4}{4}[/tex] unit = w (say)

length of the prism = [tex]\frac {12}{x}[/tex] unit = l (say)

So,

the volume of the rectangular prism,

V = lwh

   = [tex]\frac {5}{2x + 8} \times \frac {x + 4}{4} \times \frac {12}{x}[/tex] unit

   =  [tex]\frac {15}{2x}[/tex] unit

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]a-\text{tens digit}\\b-\text{unity digit}\\10a+b-\text{number}\\10b+a-\text{number with reversed digits}\\a+b-\text{sum of digits}\\\\\bold{System\ of\ equations:}\\\\\left\{\begin{array}{ccc}a+b=5\\10b+a=10a+b+27&\text{subtract}\ 10a\ \text{and}\ b\ \text{from both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}a+b=5\\9b-9a=27&\text{divide both sides by 9}\end{array}\right[/tex]

[tex]\underline{+\left\{\begin{array}{ccc}a+b=5\\b-a=3\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2b=8\qquad\text{divide both sides by 2}\\.\qquad \boxed{b=4}\\\\\text{Put the value of\ b}\ \text{to the first equation}\\\\a+4=5\qquad\text{subtract 4 from both sides}\\\boxed{a=1}[/tex]

Answer:

Step-by-step explanation:

first we find the slope using the slope formula : (y2 - y1) / (x2 - x1)

(2,-2)....x = 2 and y = -2

(4,1)...x = 4 and y = 1

now sub

slope = (1 - (-2) / (4 - 2) = (1 + 2) / 2 = 3/2

y = mx + b

slope(m) = 3/2

(4,1)...x = 4 and y = 1

now sub and find b, the y int

1 = 3/2(4) + b

1 = 6 + b

1 - 6 = b

-5 = b

so ur equation is : y = 3/2x - 5 <===

Answer:

-2, -1 and 1.

Step-by-step explanation:

x^3 + 2x^2 - x - 2 = 0

x^2(x + 2) - 1(x + 2) = 0   Note the  common factors (x + 2) so we have

(x^2 - 1)(x + 2) = 0

(x - 1)(x + 1)(x + 2) = 0      (x^2 -1 is the difference of 2 squares).

x =  -2, -1 and 1.

Answer:

5 large boxes

3 small boxes

Step-by-step explanation:

Create two equations to represent the problem.

let "a" be the number of small boxes

let "b" be the number of large boxes

20a + 40b = 260    This equation shows the numbers of books

a + b = 8                  This equations shows the number of boxes

Solve the system of equations (solve for a and b). We can solve using the substitution method.

Rearrange a + b = 8 to isolate one of the variables.

a = 8 - b    New equation that represents "a"

Since we know an equation for "a", we can substitute what "a" equals into the other equation. There will only be one variable in the equation, so we can solve by isolating. Isolate by doing reverse operations.

Substitute "a" for 8 - b

20a + 40b = 260

20(8 - b) + 40b = 260     Distribute 20 over the brackets by multiplying

160 - 20b + 40b = 260    Collect like terms (numbers with same variables)

160 + 20b = 260    Start isolating "b". Subtract 160 from both sides

20b = 260 - 160

20b = 100    Divide both sides by 20

b = 5    Number of large boxes

Substitute "b" for 5 in the simplest equation

a + b = 8

a + 5 = 8      Subtract 5 from both sides to isolate "a"

a = 8 - 5    

a = 3      Number of small boxes

Therefore there were 5 large boxes and 3 small boxes sent.

Answer:

s = the number of small boxes

L = the number of large boxes

System of Equations:

25s+40L=250

s+l=7

Step-by-step explanation:

You divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates  of those same 2  points.

Best of Luck to you.

The value of "x" is [tex]\frac{-5}{2}[/tex]

Solution:

Given f(x) = 4x - 6

g(x) = 8x + 4

To find: value of x when f(x) = g(x)

We can equate f(x) and g(x) as per given statement and solve for x

f(x) = g(x)

Substituting the values of f(x) and g(x) in above expression,

4x - 6 = 8x + 4

4x - 8x = 4 + 6

-4x = 10

On solving,

[tex]x = \frac{10}{-4}\\\\x = \frac{-5}{2}[/tex]

Thus value of "x" is [tex]\frac{-5}{2}[/tex]

Answer:

25

Step-by-step explanation:

Given:

32 parks allow camping

43 parks allow playgrounds

10 parks both allow camping and playgrounds

110 total parks

First, we need to add 32, 43, and 10

32 + 43 + 10 = 85

Then, we find the difference of 110 and 85

110 - 85 = 25

Since it isn't a decimal, there is no point in rounding.

Answer: 30 hours

30*0.4 is 12 or 40 percent of 30 is 12

Hope this helps!

The candle burns 12 inch in 30 hour.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into same number of parts.

Given, a candlestick burns at the rate of 0.4 inch per hour.

And 12 inch candle takes time to burn

= division of a 12 with a time taken to burn by ine candle

= 12 / 0.4

= 30 hour

Therefore, the candle burns 12 inch in 30 hour.

To learn more about the division;

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The solution is price of 1 slice of pizza  is $ 1.75 and price of 1 bottle of water is $ 1.25

Solution:

Let "p" be the price of 1 slice of pizza

Let "b" be the price of 1 bottle of water

Given that Abby bought two slices of pizza and  three bottles of water for $7.25

So we can frame a equation as:

two slices of pizza x price of 1 slice of pizza  + three bottles of water x price of 1 bottle of water = $ 7.25

[tex]2 \times p + 3 \times b = 7.25[/tex]

2p + 3b = 7.25 ------- eqn 1

Cameron bought four slices of pizza and  one bottle of water for $8.25

So we can frame a equation as:

four slices of pizza x price of 1 slice of pizza  + one bottles of water x price of 1 bottle of water = $ 8.25

[tex]4 \times p + 1 \times b = 8.25[/tex]

4p + 1b = 8.25 ----- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "p" and "b"

Multiply eqn 1 by 2

4p + 6b = 14.5 ----- eqn 3

Subtract eqn 2 from eqn 3

4p + 6b = 14.5

4p + 1b = 8.25

( - ) ------------------

5b = 6.25

b = 1.25

Substitute b = 1.25 in eqn 1

2p + 3b = 7.25

2p + 3(1.25) = 7.25

2p + 3.75 = 7.25

2p = 3.5

p = 1.75

Summarizing the results:

price of 1 slice of pizza  = $ 1.75

price of 1 bottle of water = $ 1.25

Answer:

y - 2 = x + 3

y = x + 5

-x + y = 5 standard form

Answer:

Step-by-step explanation:

Given, ∠1≅∠2, ∠3≅∠4 and AP≅DP,

        ∠1≅∠2(given)

     ⇒m∠1=m∠2(definition of congruent angles)

         180°=180°(Reflexive)

      ⇒m∠[tex]ABP+[/tex]m∠1=m∠[tex]DCP[/tex]+m∠2

          But  m∠1 =m∠2 (definition of congruent angles)

     ⇒m∠[tex]ABP+[/tex]m∠1=m∠[tex]DCP[/tex]+m∠1

        m∠[tex]ABP+[/tex]=m∠[tex]DCP[/tex] ( If equals are subtracted from equals, the remainders are equal)

Therefore, Δ[tex]ABP=[/tex]Δ[tex]DCP[/tex] (by AAS criteria)

condition are:

Answer:

Exact Form: 5/2

Decimal Form: 2.5

Mixed Number Form: 2 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

7x -5y = -18

Making y as subject

-5y = -7x - 18

Dividing through by -5

y = -7/-5x - 18/-5

y = 7/5x + 18/5

Slope m = 7/5

Intercept b = 18/5

Answer:

The width of both rectangles are [tex]\frac{36}{l},\frac{21}{L}[/tex].

Step-by-step explanation:

Given : The area of one rectangle is 36 square  feet. The area of a second rectangle is  21 square feet. The rectangles have the  same width and the dimensions are  whole numbers.

To find : What is the width of  both rectangles?

Solution :

According to question, the two rectangles have the same widths but they have different lengths.

Let the width of both rectangle be 'w'

Let the length of one rectangle be 'l'

Let the length of second rectangle be 'L'

The area of the rectangle is [tex]\text{Area}=\text{Length}\times \text{Width}[/tex]

The area of one rectangle,

[tex]36=l\times w[/tex]

[tex]w=\frac{36}{l}[/tex]

The area of second rectangle,

[tex]21=L\times w[/tex]

[tex]w=\frac{21}{L}[/tex]

The width of both rectangles are [tex]\frac{36}{l},\frac{21}{L}[/tex].

Answer:

x= 9

Step-by-step explanation:

Please see attached picture for full solution.

3.1 is already in standard form.

Answer:

  -0.75

Step-by-step explanation:

The table values listed for the left side expression and the right side expression are closest together when the value of x is -0.75.

__

A graphing calculator shows the expressions both have a value near -0.658 when x ≈ - 0.775. The closest table value to x = -0.775 is x = -0.75.

Answer: x = -0.75

            -0.72   -0.65

Step-by-step explanation:

Consider the equation below.

3^(-x) - 3 = 4^x - 1

consider the values of x  = 1.75, -1.5, -1.25, -1, -0.75,-0.5,-0.25

 x         3^(-x) -3                 4^x - 1

-1.75  3.83                 -0.91

-1.5          2.19                -0.88

-1.25         0.95                    -0.82

-1          0                      -0.75

-0.75 -0.72                     -0.65

-0.5          -1.27                     -0.50

-0.25 -1.68                     -0.29

The bold values when x = -0.75 gives -0.72 and -0.65 is the approximate solution to the equation

by approximation -0.72 when rounded off = -0.7

and -0.65 when rounded off = -0.7

Option D

Money earned by Marty is $ 16.72

Solution:

Given that, Marty started a lawn mowing business

He kept track of his expenses and earnings in a table

Lawn Mower = - $49.99

Gasoline = - $8.79

Moyer's yard = $ 40

Griffen's yard = $ 35.50

To find: Money earned by Marty

Total money earned = lawn mower + gasoline + moyers yard + griffens yard

Total money earned = -49.99 - 8.79 + 40 + 35.50

Total money earned = -58.78 + 40 + 35.50

Total money earned = -18.78 + 35.50 = 16.72

Thus money earned by Marty is $ 16.72

Answer: Stephanie is the fastest

Step-by-step explanation:

Here we have to find who runs faster:

Liz:

[tex]8 ft/s[/tex]

Katie:

[tex]\frac{350 ft}{31 s}=11.29 ft/s[/tex]

Stephanie:

[tex]\frac{1 mile}{388 s}. \frac{5280 ft}{1 mile}=\frac{5280 ft}{388 s}=13.60 ft/s[/tex]

Noah:

[tex]\frac{541 ft}{1 min}. \frac{1 min}{60 s}=9.01 ft/s[/tex]

As we can see after comparing, Stephanie is the fastest, since she travels more distance in less time.

Final answer:

After calculating that each person bought an average of 4 pounds of cookie dough last year, and using the average predicted sales of 650 people for this year, the math club should prepare approximately 2600 pounds of cookie dough.

Explanation:

The question is asking for an estimation of how many pounds of cookie dough the math club will need to sell this year, given that they predict selling to more people than last year. To calculate this, we need to find the average amount of cookie dough sold per person last year and then multiply that by the predicted number of people for this year.

Last year, the math club sold 2,080 pounds of cookie dough to 520 people. Thus, each person bought an average of
2080 pounds ÷ 520 people = 4 pounds per person.

This year, they are predicting sales to between 630 and 670 people. We will use the average of these two numbers for a better estimation, which is (630 + 670) ÷ 2 = 650 people.

Now, we multiply the average amount of dough per person by the estimated number of people:

4 pounds per person × 650 people = 2600 pounds.

Therefore, the math club should prepare approximately 2600 pounds of cookie dough for this year's fundraiser.

Answer: 28.08%

Step-by-step explanation: To find the percent increase, we divide the amount of change by the original number.

The amount of change is the difference between the two numbers which in this case is 561,000 - 438,000 and the original number is 438,000.

561,000 - 438,000 is 123,000 so we are left with 123,000 divided by 438,000 which is 0.2808. Finally, since our problem is asking us for a percent, we write 0.2808 as a percent by moving the decimal point two places to the right to get 28.08%.

So when the population changes from 438,000 to 561,000, it has increased by 28.08%.

Answer:

x - 0, 1

y - 2, 15/7

I'm assuming we factor...

The answer is (2a + c)(4a^2 - 2ac + c^2.)

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(The question that got me to Ace rank!)

Answer:

(2a + c)(4a² - 2ac + c²)

Step-by-step explanation:

8a³ + c³ ← is a sum of cubes and factors in general as

a³ + b³ = (a + b)(a² - ab + b²)

Given

8a³ + c³

= (2a)³ + c³

= (2a + c)((2a)² - 2ac + c²), that is

= (2a + c)(4a² - 2ac + c²)

True!

The Cartesian coordinate system is formed by two perpendicular axes, which are the x-axis and y-axis. In this problem, we are given two lines:

[tex]x=4 \ and \ y=5[/tex]

Since the x and y-axes are perpendicular, then the lines [tex]x=4 \ and \ y=5[/tex] are also perpendicular.

Cartesian coordinate system: https://brainly.com/question/2141683

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