A garden that is 14 feet by 17 feet will have a pedestrian pathway on the border, making the combined area of the garden and the border 311 square feet what is the width of the pathway

Answer:

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24x3=72

And 10% of 24 is 2.4

So $74.04

Answer: 80

Step-by-step explanation:

100 ----- x

30 ------ 24

V

10// ----- x

3// ------ 24

V

3 · x = 24 · 10

3x = 240

x = 240/3

x = 80

Answer:

20

Step-by-step explanation:

f(x) = 30

30 = 1.8x -5.4

35.4 = 1.8x

x = 35.4/1.8

x = 19.666

Answer:

Price = 20, Amount = 14

Step-by-step explanation:

A = Amount of Mangoes

P = Price for 1 Mango

P = A + 6

280 = P * A

insert A+6 for P

280 = (A+6) * A

280 = 6A + A²

280=1*a^2+6*a  | Vertausche beide Seiten der Gleichung.

1*a^2+6*a=280  | quadratische Ergänzung: ergänze auf beiden Seiten (3)^2

1*a^2+6*a+(3)^2=3^2+280  | Rechne 3 hoch 2 aus.

1*a^2+6*a+(3)^2=9+280  | addiere 9 und 280

1*a^2+6*a+(3)^2=9+280  | Fasse die rechte Seite mit Hilfe der binomischen Formel zusammen.

1*(1*a+(3))^2=289  | Auf beiden Seiten Quadratwurzel ziehen.

1*a+(3)=+-*289^0.5  

1*a_1+(3)=289^0.5  

1*a_1+3=289^0.5  | Ziehe die Wurzel aus 289

1*a_1+3=17  | -3

1*a_1=14  

The total number of mangoes bought by Kumar are 14.

"An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values is called mathematical equation. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc."

We have,

Total amount for mangoes(P) =  280

Price of one mango is equal to 6 more than the total number of mangoes (A) i.e., P = A+6

By using mathematical equation from the question

P×A = 280.....(1)

Substitute P = A+6 in equation (1)

⇒ (A+6) × A = 280

⇒[tex]A^{2}+6A =280[/tex]

Add [tex]3^{2}[/tex] on both sides of above equation

⇒[tex]A^{2}+6A+3^{2} = 280+3^{2}[/tex]

⇒[tex]A^{2}+2.(1)(3A)+3^{2} =289[/tex]          (∵ [tex](a+b)^{2} = a^{2}+2ab+b^{2}[/tex])

⇒[tex](A+3)^{2} =289[/tex]

⇒[tex]A+3 = \sqrt{289}[/tex]

⇒[tex]A=17-3[/tex]

⇒[tex]A=14[/tex]

Hence, The total number of mangoes bought by Kumar are 14.

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Answer:

12 - p

Step-by-step explanation:

12 - p

Answer:

Answer:

Total amount ÷ number of person's

Step-by-step explanation:

for example:- there are four persons and the total amount they have to pay is ₹2000

Now,

contribution of each person = total amount ÷no.of persons

= ₹(2000 ÷4)

=₹500

Step-by-step explanation:

Answer:

8:21

Step-by-step explanation:

Answer:

If [tex]r = 1.006[/tex], then it means that dependent variables increases by a factor of 1.006 per decade.

Step-by-step explanation:

Mathematically speaking, the function represents an exponential equation, whose form is:

[tex]f(t) = a_{o}\cdot r^{k\cdot t}[/tex] (1)

Where:

[tex]t[/tex] - Independent variable.

[tex]r(t)[/tex] - Dependent variable.

[tex]a_{o}[/tex] - Initial value.

[tex]k[/tex] - Convergence ratio.

[tex]r[/tex] - Increase rate.

If [tex]r = 1.006[/tex], then it means that dependent variables increases by a factor of 1.006 per decade.

Answer:

35.18576

Step-by-step explanation:

use eqation E

Answer:

If the angle is in radians...

Area of sector =½r²¢

Where ¢ is theta.

Since Our angle is degree

We use

Area of Sector = ¢/360 x πr²

¢=theta

radius = Diameter/2

radius = 16/2 = 8m

Area = 126/360 x π x 8²

= 112π/5

=70.37

Answer:

+ or > depending on what you mean exactly

Step-by-step explanation:

-7x<6-9

-7x<-3

x>3 (remember to flip the sigh)

the sign is the > symbol , or positive, not sure what you mean really

Answer:

x = 15

Step-by-step explanation:

20^2 + x^2 = 25^2

400 + x^2 = 625

subtract each side 400

it results to 225

square root 225, to equals this -->

X = 15

Answer:

15

Step-by-step explanation:

Step-by-step explanation:

If A [4 3 ] is a singular matrix find the

[a 3 ] value of 'a'.

a=4

Answer: C

Step-by-step-explanation: Given

- (12x + 8) ≤ - 2x + 11 ← distribute parenthesis on left side

- 3x - 2 ≤ - 2x + 11 ( add 3x to both sides )

- 2 ≤ x + 11 ( subtract 11 from both sides )

- 13 ≤ x , thus

x ≥ - 13

Since x can equal - 13 then a solid circle at - 13 represents the solution

Since x greater than - 13 then the arrow is facing to the right of - 13 on the number line.

Then the graph representing the solution is C

Answer:

B) [tex]y=x-5[/tex]

Step-by-step explanation:

Because [tex]g(x)=\frac{x^2-3x-5}{x+2}[/tex] simplifies to [tex]x-5+\frac{5}{x+2}[/tex], we only care about the quotient, which will be our oblique asymptote equation. Therefore, the oblique asymptote for the function will be [tex]y=x-5[/tex]. See the attached graph for a visual.

Answer:

B

Step-by-step explanation:

Did it rn

Answer:

x ^2 y √ 3 y

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Answer:

120(1/3)^n-1

This is the correct answer for sure.

Answer:

i think its d

Step-by-step explanation:

Answer:

6,079.42

Step-by-step explanation:

FV   =   P (1  +  r / n)^Yn

P is the starting principal, r is the annual interest rate, Y is the number of years invested, and n is the number of compounding periods per year. FV is the future value, meaning the amount the principal grows to after Y years.

Answer:

0

Step-by-step explanation:

-3c-11+14c=-14c-11

                  +14c

-3c-11+28c = -11

                  +11

-3c+28c = 0

25c=0

divide both sides by 25

c=0

Answer:

c=0

Step-by-step explanation:

-3c-11+14c=-14c-11

Combine like  terms

-11c -11 = -14c -11

Add 11 to each side

-11c-11+11 = -14c -11+11

-11c = -14c

Add 14c to each side

-11c+14c = -14c+14c

3c =0

Divide by 3

3c/3 = 0/3

c =0

Given:

Radius of a cylinder = 2 cm

Height of the cylinder = 10 cm

To find:

The surface area of the cylinder.

Solution:

The total surface area of the cylinder is:

[tex]A=2\pi rh+2\pi r^2[/tex]

Where, r is the radius and h is the height of the cylinder.

Putting [tex]r=2[/tex] and [tex]h=10[/tex] in the above formula, we get

[tex]A=2\pi (2)(10)+2\pi (2)^2[/tex]

[tex]A=40\pi +2\pi (4)[/tex]

[tex]A=40\pi +8\pi [/tex]

[tex]A=48\pi [/tex]

Therefore, the surface area of the cylinder is [tex]48\pi [/tex] square cm and its approximate value is 150.8 square cm.

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

Explanation:

We can apply the remote interior angle theorem. Some math books or teachers may refer to this as the "exterior angle theorem". They're the same idea just with different names.

According to that theorem, the interior angles x and 53 add up to the exterior angle 158

x+53 = 158

x = 158-53

x = 105

This theorem only works if neither interior angle is adjacent to the exterior angle. Hence the "remote" part.

----------

If you wanted a slightly longer approach, then let y be the missing angle that isn't marked in the diagram. Angle y is adjacent to the 158 degree angle.

We can find y by noting how 158 and y are supplementary

158+y = 180

y = 180-158

y = 22

Then we use the fact that adding three angles of any triangle always gets us 180 degrees

x+y+53 = 180

x+22+53 = 180

x+75 = 180

x = 180-75

x = 105

Effectively, this example helps reinforce why the remote interior angle theorem is true.

Answer:

107 in ²

Step-by-step explanation:

Surface area of the triangular prism = bh + L(s1 + s2 + s3)

Where,

b = 2 in.

h = 8 in.

s1 = 8.2 in.

s2 = 2 in.

s3 = 8 in.

L = 5 in.

Substitute

Surface area = 2 × 8 + 5(8.2 + 2 + 8)

Surface area = 16 + 5(18.2)

Surfaces area = 16 + 91

Surface area = 107 in ²

Answer:

[tex]f(x)^{-1}=\frac{x-1}{2}[/tex]

Step-by-step explanation:

start by replacing f(x) for y:

y = 2x + 1

switch y and x:

x = 2y+1

solve for x by first subtracting 1 from both sides:

2y = x-1

divide 2 from both sides:

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

replace y with [tex]f(x)^{-1}[/tex]:

[tex]f(x)^{-1}=\frac{x-1}{2}[/tex]

Answer:

the third side is 4.

Step-by-step explanation:

Using  Pythagorean theorem of a^2 + b^2 = c^2 for right triangles, substitute

the numbers to show ([tex]\sqrt{65})^{2}[/tex] + [tex]b^{2}[/tex] = [tex]9^{2}[/tex] and solve for b. The square root and square cancel each other out, so you get 65 + [tex]b^{2}[/tex] = 81.

Subtract 65 from both sides to get [tex]b^{2}[/tex] = 16.

Then take the square root of both sides to get b = [tex]\sqrt{16}[/tex] which equals 4.

Answer:

24 feet

Step-by-step explanation:

The given parameters of the blueprint are;

The length of each grid square on the blueprint = 10 feet

The total distance in feet around the garden, P = 4 + 2 + 2 + 4 + 6 + 6 = 24

The total distance in feet around the garden = 24 feet

Answer:

15a^5 b^15

Step-by-step explanation:

_____________

Answer:

the first and third option

Step-by-step explanation:

In the initial recipe, the ratio of tomato sauce to chile sauce is 1 : 3/2

To make it spicier this ratio has to be higher than the initial ratio

Ratio in the first option : 1/2 : 1 = 1 : 2

option 2 : if both recipes are double, the proportion of ingredients remain the same

oprion 3 : 1 : 3

option 4 : 1 : 1

option 5 : 1 : 5/3