A rectangular corral is to be built using 70m of fencing. If the fencing has to enclose
all four sides of the corral, what would be the dimensions to produce the maximum
possible area and what would the area of the corral be? Include a complete solution

Step-by-step explanation:

Answer: (8,10)

Step-by-step explanation:

To go from A to C, we go right 2 units and up 6 units.

So, if we let the fourth vertex be D, then to go from B to D, we must also go right 2 units and up 6 units from B.

Therefore, the answer is (8, 10).

While solving the pictogram, we get that the number of hamsters owned  are 4.

Solution:

total number of pets = 33

total number of cats = 12

total number of dogs = 11

total number of rabbits = 6

then total number of hamsters = total pets - total cats, dogs, and rabbits

total number of hamsters = 33 - ( 12 + 11 + 6)

total number of hamsters = 4

also, on the pictogram one block represents 4 animal. then, total number of hamsters will be represented by one block.

view the second attachment for answer.

What is pictogram?

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I hope you are trying to ask the question below in the image

Hello,

John : n

Brad : n + 12

n + n + 12 = 84

2n + 12 = 84

2n = 84 - 12

2n = 72

n = 72/2

n = 36

John $36 and Brad $36 + $12 = $48

Answer:

jhon =36 brad=48

Step-by-step explanation:

B=J+12

J+B=84

12+J+J=84

2J=72

J=36

B=J+12=36+12=48

Answer:

0.40x = 320

Step-by-step explanation:

If 40% of the total houseplants watered = 320

0.40 times x (total houseplants) = 320

Answer:

[tex]\frac{x}{0.40} = 320 Plants[/tex]

Step-by-step explanation:

[tex]\frac{x}{0.40} = 320 Plants[/tex]

[tex]X = (0.40)(320)Plants[/tex]

[tex]X = 128Plants[/tex]

Answer:

There are 35 Men, 12 Children, and 18 Women

Step-by-step explanation:

Men(M), Women(W) and Children(C)

We learn that:

M = 35

W = 1.5C , and

M+W+C = 65

----

M+W+C = 65

M+1.5C+C = 65

35+1.5C+C = 65

2.5C = 30

C = 12

If C=12 and W=1.5C, then W=18

----

There are 35 Men, 12 Children, and 18 Women

(35+12+18) = 65 participants

Answer:

pretzel: 2

hotdog: 3

Step-by-step explanation:

Let h be the hotdog price and p the pretzel price.

We know that:

h + p = 5

and

2h + 3p = 12

We can solve this system of equations:

h = 5-p

2(5-p) + 3p = 12

So the second eq. becomes:

10 - 2p + 3p = 12

10 + p = 12

p = 2

Sub in the first:

h = 5 - p = 5-2 = 3

So p = 2, h = 3

Answer: $3 / hot dog

Step-by-step explanation:

Given information:

1 hot dog + 1 pretzel = $5

2 hot dogs + 3 pretzels = $12

Set variables:

Let x be the price per hot dog

Let y be the price per pretzel

Set system of equations:

x + y = 5

2x + 3y = 12

Multiply the first equation by 3:

3x + 3y = 15

2x + 3y = 12

Subtract the second equation from the first equation (Elimination):

(3x + 3y) - (2x + 3y) = 15 - 12

3x + 3y - 2x - 3y = 3

(3y - 3y) + 3x - 2x = 3

0 + x = 3

[tex]\boxed{x=3}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer: 433.33 cm^3

Step-by-step explanation: Since the base is a square, volume = base area × height / 3

10*10 = 100,  100 * 13 = 1300, divided by 3 = 433.33 cm^3

The probability that battery lasts more than 3 years is [tex]e^{-0.6 }[/tex].

Parameter of Exponential Distribution

It is given that the average lifespan of the car battery = 5 years

⇒ μ = 5

And, we have to find the probability that the car battery lasts more than 3 years.

Now, the relation between the parameter of exponential distribution, λ and average, μ is given as,

1/ λ = μ

⇒ λ = 1/5

Calculating the Probability

The probability for the car battery to lasts more than 3 years is given by P(N>3). Here, N is the lifespan of the car battery.

P(N>3) = 1 - P(N≤3)

P(N>3) = 1-F(4)

Here, F is the exponential distribution  for the lifespan of the car battery.

P(N>3) = 1-(1-e^(-λn))

P(N>3) = [tex]e^{-3/5}[/tex]

Thus, the required probability is,

P(N>3) = [tex]e^{-0.6 }[/tex]

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Hi! ❄

  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

The eccentricity of the conic section below is 1, since the conic section given is a parabola.

The eccentricity of a parabola is 1.

Hope that made sense !!

  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\star\tiny\pmb{_{calligraphy}}\star[/tex]

Hi!

[tex]{}[/tex] - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

The eccentricity of the conic section below is 1, since the conic section given is a parabola.

What is parabola?

a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. The name "parabola" is due to Apollonius, who discovered many properties of conic sections. conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.

#CarryOnLearning

Answer:

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle

Answer:

In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

Hi

How are you?

Kya kar rahi hoo?

Answer:

12 units^2

Step-by-step explanation:

Area of a triangle = 1/2 * base * height

  base goes from -4 to +4  = 8 units

  Height goes from 1 to 4  = 3 units

    area = 1/2 * 8 * 3 = 12 units^2

The ship captain should be turned 129.49 so it's heading straight for Island B.

Given Island A is 160 miles from Island B and the captain of a ship travels 170 miles from Island A and then discovers that he is off course and 200 miles from island B.

So we gave it

a = 200 feet

b = 170 feet

c = 160 feet

We need to find angle C which goes directly to island B.

We apply the "cosine law":

[tex]\begin{aligned}\cos C&=\frac{a^2+b^2-c^2}{2ab}\\ &=\frac{(200)^2+(170)^2-(160)^2}{2\times 200\times 170}\\ &=\frac{40000+28900-25600}{68000}\\ &=\frac{43300}{68000}\\ &=0.636\end[/tex]

Now we multiply both sides by cos⁻¹, we get

cos⁻¹(cos C)= cos⁻¹(0.636)

C = 50.51

The interior angle is 50.51°

We need to find the outer angle to find the bearing the captain needs to turn

Applying the additional angle ruler:

The outside angle = 180 - 50.51 = 129.49°

Therefore, he must turn so as to head directly for Island B, where Island A is 160 miles from Island B and the captain is sailing 170 miles.

from Island A and then discovers that it is off-road and 200 miles away

Island B is 129.49.

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Answer:

It will be a more accurate thing to put it into the mean.

Step-by-step explanation:

Mainly, there is a lot of numbers in the data. So the reason Mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric.

Hoped this helped. Please mark me brainliest!

Answer: 120 hr

Step-by-step explanation: 15$ every hr so for 120 hrs it would be 1,800$ plus the signing bonus of 200$ would total 2,000$ but with out the bonus she would have to work 134 hrs for 2,010$

The expression that is not equivalent to (1 - sin²(x)) tan(-x) is D. (cos²x - 1)(cot -x).

It should be noted that (cos²x - 1)(cot -x). is not equivalent to the given expression.

This is illustrated as:

(cos²x - 1)(cot -x)

= (-sin²x) × (-cot x)

= sin²x × cosx/sin x = sinxcosx

In conclusion, the correct option is D.

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The expression _______ is not equivalent to (1 − sin2(x)) tan(-x).

a. (1 - cos^2(x)) cot(-x)

b. (cos^2(x) - 1) cot(x)

c. (sin^(x) - 1) tan(x)

d. (cos^2(x) - 1) cot(-x)

Answer:

Step-by-step explanation:

Givens

Line: y = 3x + 3

Point: (7,3)

Discussion

The easiest variation on line problems is one like this one. The reason is that all you need do is read the slope of the given line.

m = 3 of the given line. Also the slope of the new line.

What you have so far is

y = 3x + b

The point is used to find b -- the y intercept.

x = 7

y = 3

You are not given this, but what you want to think is that when x = 7, y = 3

Substitute into the new equation

3 = 3*7 + b

3 = 21 + b                         Subtract 21 from both sides.

3 - 21 = 21-21 + b

- 18 = b

Answer

y = 3x - 18

Answer:

-2/3x+23/3

Step-by-step explanation:

y= mx+c

where

m is the slope c is the y-intercept.

1-getting the slope:

we are given that the line we are looking for is parallel to the line

y=-2/3x+3

this means that the slope of the two lines are equal . comparing the general formula with the given line , we would find that the slope of the given lines -2/3.this means that the slope of the lines we are looking for is also -2/3

The equation of the line now becomes:y=-2/3x+c

2-getting the value of c

to get the value of c, we will use a point that belongs to the line (7,3),substitute in the equation and solve for c as follows:

y=-2/3x+c

3=(-2/3)(7)+c

3=-14/3+c

c=3+14/3

c=23/3

Based on the above, the equation of the line we are looking for is:

y=-2/3x+23/3

The simplification of the polynomial expression will give 3x² - 20x + 8.

The polynomial expression is given as:

(5x² + 13x4) (17x² + 7x - 19) + (5x-7)(3x + 1)

= 5x² + 13x - 4 - 17x² - 7x + 19 + 15x² + 5x - 21x - 7

Then collect like terms

= 5x² + 15x² - 17x² + (13x - 7x + 5x - 21x) - 4 - 7 + 19

= 3x² - 20x + 8.

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Answer:

2 face cards

Step-by-step explanation:

By definition, there are 12 face cards (Kings, queens, and jacks) and 36 numbered cards (2's through 10's) in a standard deck of 52 cards.  Aces are not considered face cards (no face on the card).

The ratio of face cards in a full deck is (12/52) or slightly over 23%.

The likelihood of a face card in a hand of 8 cards is:

(8 cards)*(12 face cards/52 cards) = 1.85 cards.  We need to round to the nearest whole card, so the expected number of face cards in a hand of 8 is 2 cards.  

Answer:

sin(x - y) = 0.21

Step-by-step explanation:

we have the sin values which we need to get cos values

sin (A-B) = sin A cos B - sin B cos A

sin² A + cos² A = 1

sin x = 4/9

cos² x = 1 - sin² x = 1 - 16/81 = 65/81

cos² x = 65/81

cos x = √65/9

sin y = 1/4

cos² y = 1 - sin² y = 1 - 1/16 = 15/16

cos² y = 15/16

cos y = √15/4

sin(x − y) = sin x cos y - sin y cos x

sin(x - y) = 4/9 √15/4 - 1/4 √65/9

sin(x - y) = (4√15-√65)/36

sin(x - y) = 0.21

socratic Narad T

Answer: C

Step-by-step explanation:

on edg

Answer:

36

Step-by-step explanation:

Hello!

Area of a Parallelogram: [tex]A = b*h[/tex]

Given our shape:

Don't forget, the height is the altitude to the base, which means it forms a perpendicular intersection. The height is not the slant height of the parallelogram.

The area is 36 un².

Answer:

there should have been names of every line and joining parts

The least and greatest amounts that the two friends could spend on food are 100 and 140 respectively

Functions and values

Functions are expressions written in terms of letters known as variables. Given the equation that represents the food budget of two friends as shown;

1/2(x-120)=10

where x is the amount spent on food.

In order to determine the least and greatest amounts that the two friends could spend on food,

For the least amount

-(x-120) = 20

-x+120 = 20

x = 100

For the greatest amount

(x-120) = 20

x = 140

Hence the least and greatest amounts that the two friends could spend on food are 100 and 140 respectively

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The arc length of [tex]y=2\cos(3x)[/tex] on the interval [tex][a,b][/tex] is

[tex]\displaystyle \int_a^b \sqrt{1 + (y')^2} \, dx = \int_a^b \sqrt{1 + (-6\sin(3x))^2} \,dx = \boxed{\int_a^b \sqrt{1+36\sin^2(3x)} \, dx}[/tex]

The triangle is illustrated below.

The first thing you should find are the new vertices:

(x, y) ---> (2x, 2y) ---> (x', y')

(0, 0) ---> (2 (0), 2 (0)) ---> (0, 0)

(-4, 4) ---> (2 (-4), 2 (4)) ---> (-8, 8)

(-4, -2) ---> (2 (-4), 2 (-2)) ---> (-8, -4)

Then, you must join the ordered pairs and graph the new triangle.

See the attached graph.

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The sine and cosine rule is typically used to find the measure of angles in trigonometry.

It should be noted that the sine rule is used when we are given:

The cosine rule is used when we are given:

The advantage is that it can help us understand the connections between the sides and their angles.

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Answer:

a) Perfect square.

b) 9

Step-by-step explanation:

The given numbers are perfect squares.

64 = 8*8

49 = 7*7

36 = 6*6

25 = 5*5

16 = 4*4

So, the next number will be 3 *3 = 9