The area of a square pond is 1000m2.A path of uniform width is surrounded outside the pond and its area is 369m2.find the outer length of the path​

Answer:

[tex]y=\frac{\frac{16}{3}(x+1)(x+6)}{(x-1)(x-4)}[/tex]

Step-by-step explanation:

Because x=1 and x=4 are the solutions to x-1=0 and x-4=0, then we have (x-1)(x-4) in the denominator.

Because (-1,0) and (-6,0) are the solutions to x+1=0 and x+6=0, then we have (x+1)(x+6) in the numerator.

Now we have [tex]y=\frac{a(x+1)(x+6)}{(x-1)(x-4)}[/tex] where we plug in (0,8) to solve for a:

[tex]y=\frac{a(x+1)(x+6)}{(x-1)(x-4)}[/tex]

[tex]8=\frac{a(0+1)(0+6)}{(0-1)(0-4)}[/tex]

[tex]8=\frac{6a}{4}[/tex]

[tex]32=6a[/tex]

[tex]\frac{32}{6}=a[/tex]

[tex]\frac{16}{3}=a[/tex]

Therefore, the equation for the rational function is [tex]y=\frac{\frac{16}{3}(x+1)(x+6)}{(x-1)(x-4)}[/tex]

Answer:  infinitley many solutions

Step-by-step explanation:

Answer:

The answer is A.15c+3

Step-by-step explanation:

Answer:

b = 161, m = 111

Step-by-step explanation:

b + m = 272

m + 50 = b

Substitute

m + 50 + m = 272

2m = 222

m = 111

Plug in for m

b + 111 = 272

b = 161

Answer:

4.25 sq. ft

Step-by-step explanation:

l = 24

w = 0.5

h = 12

SA = 2lw + 2lh + 2wh

2*(12*0.5 + 24*0.5 + 12*24) = 612 sq. in = 4.25 sq. ft

Answer:

x-1

correct me if im wrong

Answer:

B. 8 x 10^3

Step-by-step explanation:

1.6 x 10^5 / 0.2 x 10^2

= 160 000 / 20

= 8 000

You can write this as 8 x 10^3

Answer:

3 years

Step-by-step explanation:

$3000(.021)=$63 per year.

189/63=3 years.

A linear model that best fits the overall pattern of points is given by the

regression line of the data.

Reasons:

a. Points on the graph are;

(6, 218),

The slope, b, regression line equation is given by the following formula;

[tex]b = \mathbf{\dfrac{\sum \left(x_i - \overline x\right) \times \left(y_i - \overline y\right) }{\sum \left(x_i - \overline x\right )^2 }}[/tex]

The regression line equation is; [tex]\overline y = b \cdot \overline x + a[/tex]

Where;

[tex]\overline x[/tex] = 18.732

[tex]\overline y[/tex] = 187.24

[tex]\sum \left(x_i - \overline x\right) \times \left(y_i - \overline y\right)[/tex] = -4926.59

[tex]\sum \left(x_i - \overline x\right )^2[/tex] = 792.3944

Therefore;

[tex]b = \dfrac{-4926.59}{792.3944 } \approx -6.2173[/tex]

[tex]a = \overline y - b \cdot \overline x[/tex]

Which gives;

a = 187.24 - (-6.2173) × 18.732 ≈ 303.70

The equation of the line is therefore; [tex]\overline y = \mathbf{-6.2173 \cdot \overline x + 303.70}[/tex]

Using the above regression line equation, the linear model of the scatter

plot can be drawn as presented in the graph created with MS Excel.

b. The slope of the line is b = -6.2173

c. The relationship between price per serving and sodium per serving is

as follows;

When the price per serving increases by 1 cent, the sodium per serving

decreases by 6.2173 mg.

Learn more about the regression line formula here:

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Option A

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if any doubt leave a comment

Answer:

x=2 and XM=11

Step-by-step explanation:

because M is the midpoint of the line, you know that both XM and ZM are equal and you know an expression for the lengths of both of these.

set these expressions equal and solve:

4x+3=3x+5 so by subtracting the 3x from the right side, moving it over to the left and subtracting 3 from the left side to move it over to the right, you get:

x=2

then to find XM, plug in this value of x to get XM=11

4(2)+3=11

Answer:

A: 437.1 cm³

Step-by-step explanation:

You find the area of the prism by the base of the prism & height multiplied together.

Here, the base of the prism is a triangle.

All the triangles sides are given, so lets lave them: A:8, B:8, and C:10.

Using SSS, we can find the area, which is ≈ 31.1.

If we multiply that number by 14.

We get he area of the prism.

Depending on how your rounded, the area of the prism is:

≈437.2, which is close enough to know that the asswer is A: 737.1 cm³

Hope this helped <3

It's probably 52 or 40.

Answer: why do they have so many cars what are you trying to ask and what does Mario have to do with this?

Step-by-step explanation:

please change your question.

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

Work Shown:

x = number of windows purchased

The cost expression is 145.50x+3150 because the "145.50x" portion represents the $145.50 per window charge, then we tack on the fixed fee of $3150. Set this cost expression equal to the total charge ($5769) and solve for x.

[tex]145.50x+3150 = 5769\\\\145.50x = 5769-3150\\\\145.50x = 2619\\\\x = 2619/(145.50)\\\\x = 18\\\\[/tex]

They bought 18 windows.

Answer:

13 miles is the greatest whole number of miles she can go.

Step-by-step explanation:

37-3=34

$5 for 2 miles

34/5 = 6 remainder 4

that is 12 miles. But since she still has 4 dollars left, she can go another mile. so, 12 +1 = 13

hope this helps :)

Answer:

Tyler's - (-5 - 3y) + (3y) = -5

Han's - (x) + (-5 - x) = -5

Step-by-step explanation:

If we are going to use Tyler's first step then we would use x = - 5 - 3y and substitute it in the original simultaneous equation x + 3y = -5, becoming (-5 - 3y) + (3y) = - 5 giving an exact answer of - 5.

But if we are using Han's first step then we will still substitute into the original simultaneous equation but in 3y. It would become

x + (-5 - x) = - 5 which also gives us an exact answer of -5.

Thus proving that both first steps show the same solution of -5.

Heyy!!

2x2 + 7x - 4 = 0

4x + 7x - 4 = 0

11x - 4 = 0

11x = 4

x = 4/11

Answer:200 minutes or 3 hours and 20 minutes

Step-by-step explanation:

multiple 5 and 40 and you’ll get the answer 200

Answer:

200 minutes which is 3 hours and 20 minutes.

Step-by-step explanation:

FIrst you multiply 5 x 40 which equals 200

To find out how many hours there are in 200 minutes, you divide it by 60.

200 divided by 60 = 3.3...

3 hours. The remander is 20 minuites and there you have it.

Answer:

40x --14

Step-by-step explanation:

Multiply 9 and 2 to get 18

Use distribute property

Multiply 8 by 5x -15

Subtract 32 from 18 = -14

The answer it 9300 so 9296 round to is 9300

[tex]\huge\textbf{Hey there!}[/tex]

[tex]\huge\boxed{\mathsf{6\times(-24)\div (-4)}}\\\huge\boxed{= \mathsf{\dfrac{6(-24)}{-4}}}\\\huge\boxed{\mathsf{= \dfrac{\bold{-144}}{-4}}}\\\huge\boxed{\mathsf{\dfrac{-144\div-4}{-4\div-4}}}\\\huge\boxed{= \mathsf{\dfrac{\bold{36}}{1}}}\\\huge\boxed{\mathsf{= 36\div1}}\\\huge\boxed{\mathsf{= 36}}\\\\\\\huge\text{\bf Therefore, your answer is: \boxed{\mathsf{36}}}\huge\checkmark[/tex]

[tex]\huge\text{\bf Good luck on your assignment and enjoy}\\\huge\text{\bf your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Box B i think.

Step-by-step explanation:

Ratio of total circles to total shapes is 4 : 7

An equation is an expression that shows the relationship between two or more variables and numbers.

There are 8 triangles and 6 circles. The ratio of total circles to total shapes is given by:

Ratio of total circles to total shapes = 8 circles : (8 + 6) shapes

Ratio of total circles to total shapes = 8 : 14 = 4 : 7

Find out more about equation at: https://brainly.com/question/2972832

Answer:

Step-by-step explanation:

Let first odd number = a, second odd number = a +2, third odd number = a + 4

a + a + 2 + a + 4 = 987

3a + 6 = 987

3a = 981

a = 327

First odd number = a = 327

Second odd number = a + 2 = 329

Third odd number = a + 4 = 331

[tex]\huge\textbf{Hey there!}[/tex]

[tex]\mathbf{4(3.5 - 1.5) - \dfrac{1}{2}}\\\\\mathbf{\rightarrow 4(2) - \dfrac{1}{2}}\\\\\mathbf{\rightarrow 8 - \dfrac{1}{2}}\\\\\mathbf{\rightarrow \dfrac{15}{2} \approx 7.5 \approx \boxed{\bf 7 \dfrac{1}{2}}}\\\\\\\\\huge\boxed{\textbf{Therefore, your answer is: \boxed{\mathsf{Option \ B. \ 7 \dfrac{1}{2}}}}}\huge\checkmark[/tex]

[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]

[tex]\huge \bf {Question}:—[/tex]

[tex] \boxed{\bf \: 4(3.5 - 1.5) - 1/2}[/tex]

[tex]\bf\huge Solution:—[/tex]

[tex] \sf \longmapsto \: 4*(3.5-1.5)-1/2[/tex]

[tex] \boxed{\bf \: Convert \: 1/2 \: i nto \: Decimal:—}[/tex]

[tex]\sf \longmapsto \: 4*(3.5-1.5)-0.5[/tex]

[tex] \boxed{\bf \: Subtract \: 3.5-1.5 :—\: (2 \: is \: the \: result)}[/tex]

[tex]\sf \longmapsto \: 4*(2) - 0.5[/tex]

[tex] \boxed{\bf Multiply \: 4 \: and \: 2:—(8 \: is \: the \: result)}[/tex]

[tex]\sf \longmapsto8-0.5[/tex]

[tex] \boxed{\bf \: Simply \: Subtract:—}[/tex]

[tex]\sf \longmapsto7.5[/tex]

[tex]\boxed{\bf Convert \: to \: Fraction, \: And \: Fraction\:to\:Mixed \:Fraction:—}[/tex]

[tex]\sf\longmapsto 15/2[/tex]

[tex] \boxed{\bf \: Mixed \: Fraction:—}[/tex]

[tex]\boxed{\sf\longmapsto 7 \dfrac{1}{2} }[/tex]

________________________________

[tex]\boxed{\bf Solving \: in \: another \: way:—}[/tex]

[tex]\sf \longmapsto4*2-1/2[/tex]

[tex]\sf \longmapsto4*(2)-1/2[/tex]

[tex]\sf \longmapsto8-1/2[/tex]

[tex]\sf \longmapsto \: 15/2[/tex]

[tex] \boxed{\bf \: Mixed \: Fraction:—}[/tex]

[tex]\boxed{\sf \longmapsto \: 7 \dfrac{1}{2} }[/tex]

________________________________

[tex] \boxed{\bf \: \: Answer \: i s \: Option \: B}[/tex]

[tex] \boxed{\huge\sf \: (B) \: \bf \: 7\dfrac{1}{2}} [/tex]

Answer:

11.1%

Step-by-step explanation:

Increase = 20 - 18

= 2

% increase= increase/initial price × 100

= 2/18 × 100

11.1%

Answer:

2/8

Step-by-step explanation:

Answer: 4oz

Step-by-step explanation: