The length of the rectangular fence is 4 feet greater than its width. The perimeter of the fence is less than 42 feet. What is the range of the lengths of the fence?

Answer:

Step-by-step explanation:

The length of each side corresponds to the sizes of each angle respectively.

To determine the length of each side, we would apply sine rule which is expressed as

a/sinA = b/SinB = c/SinC

The diagram of the triangle is shown in the attached photo. The longest side is c. If the shortest side is 10 cm less than the longest side, it means that the length of the shortest side is c - 10

Therefore,

c/Sin75 = (c - 10)/Sin45

c/0.966 = (c - 10)/0.707

Cross multiplying, it becomes

c × 0.707 = 0.966(c - 10)

0.707c = 0.966c - 9.66

0.966c - 0.707c = 9.66

0.259c = 9.66

c = 9.66/0.259

c = 37.3 cm

The shortest side is

37.3 - 10 = 27.3 cm

Applying the sine rule again,

b/Sin60 = 37.3/Sin75

b/0.866 = 37.3/0.966

Cross multiplying, it becomes

0.966b = 0.866 × 37.3

b = 32.3018/0.966

b = 33.4 cm

The perimeter is

27.3 + 33.4 + 37.3 = 98 cm

Answer:

n =3

Step-by-step explanation:

20 minutes to 1 hour can also be written as 20 minutes to 60 minutes.

when simplified, you get 1:3

Answer:

1:30

Step-by-step explanation:

minutes : hour
20           : 1
convert the hour into minutes
1 hr = 60 minds

20            : 60
it was simplified so that 20 = 1
so they did 20 divided by 20 to get it to equal to 1
1                 : _____
u need to equalise it and do the same to the other side so 60 divided by 20 as well ( this equals 30)
now the ratio is:
1                 : 30

Answer:

X =30/7

Step-by-step explanation:

The first way would be something like:

-7x + 10 = -20. The first thing we would do is to subtract 10 from both sides.

Therefore,

-7x+10-10=-20-10

Simplified, we get

-7x=-30

Remove the negative symbols

7x =30

x=30/7

Second example:

10=7x - 20

Add 20 to both sides.

10+20=7x-20+20

Simplified,

30=7x

x = 30/7

Answer:

What is the solution?

✔ x = 30/7

Step-by-step explanation:

You can take this equation into two approaches.

#1 subtracting 4x from both sides:

-3x+10=4x-20 (subtract 4x from each side)

-7x+10=-20 (then subtract 10 from each side)

-7x=-30 (then divide by -7 to get x by itself)

x=30/7

#2 Add 3x to both sides:

-3x+10=4x-20 (Add 3x to both sides)

10=7x-20 (then add 20 to each side)

30=7x (divide both sides by 7)

30/7=x

Either way you do it you will get x=30/7 as your answer.

Answer:

[tex]50.27[/tex] [tex]cm[/tex]

Step-by-step explanation:

[tex]\pi r^2h \times 1/3[/tex]

[tex]\pi \times 2^2 \times 12 \times 1/3[/tex]

[tex]\pi \times 4 \times 12 \times 1/3[/tex]

[tex]16\pi[/tex]

[tex]\approx 50.265482[/tex]

Answer:

16π cm^3  or 50.27 cm^3 to the nearest hundredth.

Step-by-step explanation:

V = 1/3 π r^2 h

= 1/3 π 2^2 12

= 16π cm^3.

Answer:

Y-intercept: 59

Step-by-step explanation:

Y=mx+b, in which b stands for y intercept

Answer:

59

Step-by-step explanation:

Question - Find the y-intercept of the following equation. Simplify your answer.

We write graphical equation as:

y = mx + b

where:

y: point on y axis

m: gradient/ slope (RISE/RUN)

x: point on x axis

b: y intercept (point where the line touches the y axis)

Now in:

y  =  –6 7  x  +  5 9

y-intercept = 59

Answer:

I think the function is that she is working.

Answer:

A. XY

Step-by-step explanation:

XY because it's opposite to the greatest angle.

Answer:

A.XY

Step-by-step explanation:

Answer:

The other leg is about 21.3 cm

Step-by-step explanation:

Pythagorean Theorem: a²+b²=c²

11²+b²=24²

121+b²=576

Subtract 121 from both sides

b²=455

b=[tex]\sqrt{455}[/tex]

b≈21.3

Answer:

21.3 cm

Step-by-step explanation:

We need to apply the Pythagorean Theorem.

The Pythagorean Theorem is an equation that can only be applied to right triangles. It states that for a right triangle with legs (two shorter sides) a and b and hypotenuse (longest side) c:

a² + b² = c²

Here, we know the hypotenuse is 24 cm and that one of the legs is 11 cm. We can hence say that c = 24 and a = 11 (or b = 11, but it doesn't really matter). Plug these values into the equation to find the other leg length:

a² + b² = c²

11² + b² = 24²

121 + b² = 576

b² = 576 - 121 = 455

b = √(455) ≈ 21.3 cm

Thus, the answer is 21.3 cm.

~ an aesthetics lover

Answer:

(2,17)

Step-by-step explanation:

This is because x is the input and y is the output. All you have to do is create a value for x the substitute it in the equation. Next solve for y 0.5 times 2 is 1, plus 16 is 17. Then just put your values in an order pair.

Answer:

8,20

Step-by-step explanation:

Answer:

(x+9)(x+3)

x*x = x^2

x*3 = 3x

9*x = 9x

9*3 = 27

Answer = x^2 + 12x + 27

Hope this helps

Answer:

x^2+12x+27

Step-by-step explanation:

have a nice day:)

The right answer is √74 units.

Please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

56

Step-by-step explanation:

The size of angle x is 54°.

A triangle is a three-sided polygon that consists of three edges and three vertices.

All the diagonals of a pentagon are equal so, their opposite angles of equal diagonals are also equal.

The angle  'O' is a complete angle

∴ ∠O = 360°

Angle between diagonals =360/5= 72°

The sum of all interior angles of triangle is 180°

x+x+ 72°=180°

2x=180-72

2x=108°

x=54°

Hence, the size of angle x is 54°.

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ2

Answer:

14x=0

Step-by-step explanation:

Answer

14x+3=3

add 10x to both sides

Answer:

Linear Function

Step-by-step explanation:

8x-3y = -2

-3y = 8x-2

3y = -8x+2

y = [tex]\frac{-8x+2}{3}[/tex]

y = [tex]-\frac{8}{3}x+\frac{2}{3}[/tex]

Linear Function

Answer: Inequality

Step-by-step explanation:

From the question, if we can describe 15×-10 as an expression, then we would describe 6×-2< 35 as an inequality. An

inequality is used to compare two values, and shows if one is less than, or greater than, or maybe not equal to the other value.

For example, a ≠ b means that a is not equal to b and a < b means a is less than b while a > b means a is greater than b. From the question, 6×-2< 35 means that 6x - 2 is less than 35.

Answer:

c=10

Step-by-step explanation:

c² =8²+6²

c² =64+36

c²= 100

[tex] \sqrt{100} [/tex]

= 10

Answer:

67.6

Step-by-step explanation:

Since 67.56 is 6 and above so, it is rounded to 6 so, it is 67.6.

Answer:

1.5808

Step-by-step explanation:

rounded

hundreds

1.58

tens

1.6

first

2

Answer:

When we have a translation T(a, b) and we apply it to a ordered pair (x, y), the translated pair will be (x + a, y + b)

Here whe have the translation T(-2, 5)

a) if our pair is (2, 5) then:

T(-2, 5) applied to (2, 5) = (2 + (-2), 5 + 5) = (0, 10)

b) if our pair is (-1, 7)

T(-2, 5) applied to (-1, 7) = (-1 + (-2), 7 + 5) = (-3, 12)

Answer:

0.50

Step-by-step explanation:

The individuals that do and do not wear glasses are evenly split, it is 2/4, therefore the probability that a teenager wears glasses AND watched TV is 0.50.

Answer:

Expected Payoff ⇒ $ 1.50 ; Type in 1.50

Step-by-step explanation:

Considering that 1 out of the 100 tickets will have a probability of winning a 150 dollar prize, take a proportionality into account;

[tex]100 - Number of Tickets,\\1 - Number of Tickets You Can Enter,\\\\1 / 100 - Probability of Winning,\\$ 150 - Money Won,\\\\Proportionality - 1 / 100 = x / 150, where x - " Expected Payoff "\\\\1 / 100 = x / 150,\\100 * x = 150,\\\\Conclusion ; x = 1.5 dollars[/tex]

Thus, Solution ; Expected Payoff ⇒ $ 1.50

Answer:

The set of all pages in the book:

S={1, 2, 3, ..., 428}

Step-by-step explanation:

The sample space is the set containing all possible outcomes for the experiment. In this problem, the experiment is stopping at a random page of the textbook, and the sample space is the set of all pages in the book:

S={1, 2, 3, ..., 428}.

Answer:

s

Step-by-step explanation:

Answer:

s=-4

Step-by-step explanation:

Bring the S to one side and the numbers to the other

-11/4s=11

Then just divide, but when dividing fractions you have to switch the fraction so..

s=11*(-4/11)

s=-4

Answer:

[tex] = 3 {a}^{4} [/tex]

Step-by-step explanation:

[tex] \frac{4a \times 6 {a}^{5} }{8 {a}^{2} } \\ = \frac{24 {a}^{1 + 5} }{8 {a}^{6} } \\ = \frac{24 {a}^{6} }{8 {a}^{2} } \\ = 3 {a}^{6 - 2} \\ = 3 {a}^{4} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

The right answer is 3a^4

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

$144

Step-by-step explanation:

[tex]\dfrac{\$3}{\text{lap}} \cdot \dfrac{4\text{ laps}}{\text{mile}}\cdot 12\text{ miles} =[/tex]

[tex]\boxed{\$144}[/tex]

Hope this helps!

Step-by-step explanation:

an angle that is complementary to one of the interior angles of the triangle because interior angle+exterior angle add up to 180°

Answer:mode is 0

`

Step-by-step explanation:mode is the most repeated value

Answer:

The sum is a binomial with a degree of 6

Step-by-step explanation:

we have

(3x^{2}y^{2}-2xy^{5})+(-3x^{2}y^{2}+3x^{4}y)

Group terms that contain the same variable

(3x^{2}y^{2}-3x^{2}y^{2})-2xy^{5}+3x^{4}y

0-2xy^{5}+3x^{4}y

-2xy^{5}+3x^{4}y

The sum is a binomial ( two terms) with a degree of 6  

-2xy^{5} has a degree of 6 (x has an exponent of 1, y has 5, and 1+5=6)

Answer:

D. The sum is a binomial with a degree of 6

Step-by-step explanation:

Answer:

It will take 4 seconds. She will have to run 32 meters

Step-by-step explanation:

The formula to calculate the distance in terms of speed and time is:

distance = speed x time

Let x represent the distance Bridget run. Since Tylor starts 4 meters ahead, the distance for the Tylor is x-4. The time is same for both of them, let us represent it with t.

The distance by Bridget: x = 8t → t = x/8

The distance by Tylor: x - 4 = 7t → t = (x-4)/7

→ x/8 = (x-4)/7

→ 7x = 8(x-4)

→ 7x = 8x - 32

→ x = 32

Since x = 32 and t = x/8

→ t = 32/8 = 4