Two sandboxes with the same area are shown. The equation represents the area of Sandbox 2 in terms of its width. Which is the approximate length of the longest side of Sandbox 2? Round the answer to the nearest hundredth of a meter. 2.72 meters 3.06 meters 9.16 meters 10.18 meters

Answer:

90°

Step-by-step explanation:

cosx = y=1

Therefore cosx =1

For cosx= 1

x= 90°, 450°, 810° ... etc.

Now 0° ≤ x ≤ 360°

The only value that satisfies both relations is 90°

Therefore, x= 90°

Answer:

1 < x < 7.5

Step-by-step explanation:

This problem can be solved using given below property of triangle.

Sum of two sides is always greater than third side of triangle.

Difference of two sides is always lesser than third side of triangle.

_______________________________________________

Given

sides length

6.5 units

3.5 units

Third side is 2.5 +  x

using the property, Sum of two sides is always greater than third side of triangle.

6.5 + 3.5 > 2.5 +x

=>10 >2.5 + x

=>2.5 + x< 10

=> x< 10 -2.5

=> x < 7.5

using the property, Difference of two sides is always lesser than third side of triangle.

6.5 - 3.5 >  2.5 +x

=>3.5 >  2.5 +x

=> 2.5 +x  > 3.5

=> x  > 3.5 - 2.5

=> x  > 1

combining both we have

1 < x < 7.5

out of the given option none is 1 < x < 7.5

hence, correct answer will be 1 < x < 7.5 and wrong option can be claimed by student.

The inequality that represents the values of x that ensure triangle ABC exists is A. 0.5 < x < 7.5

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

Given that the side lengths of a triangle are as; 6.5 units, 3.5 units, and 2.5 + x units

By using the property, the Sum of two sides is always greater than third side of triangle, then;

6.5 + 3.5 > 2.5 +x

=>10 >2.5 + x

=>2.5 + x< 10

=> x< 10 -2.5

=> x < 7.5

Also, by using the property, Difference of two sides is always lesser than third side of triangle then we get;

6.5 - 3.5 >  2.5 +x

=>3.0 >  2.5 +x

=> 2.5 +x  > 3.0

=> x  > 0.5

Now combining both we have;

. 0.5 < x < 7.5

Learn more about inequality ;

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Answer:

700 eggs

Step-by-step explanation:

First take the cartons and determine the number of eggs

32 cartons * 18 eggs per carton

576 eggs

Add the  eggs not in cartons

576+123 =699

Answer:

x = -8/3

Step-by-step explanation:

1/2x+3 = 2/3+1

Combine like terms

1/2x+3 = 2/3 + 3/3

1/2x + 3 = 5/3

Subtract 3 from each side

1/2x + 3-3 = 5/3 - 3

1/2x = 5/3 - 9/3

1/2x = -4/3

Multiply each side by 2

1/2x *2 = -4/3*2

x = -8/3

Answer:

It's 180 degrees? I'm not so sure.

Step-by-step explanation:

Answer:

diameter = two times the radius

2r

the area = πr²

the circumference= 2πr

hope it helps

Answer:

6:12=1:2

Step-by-step explanation:

as we will cut 6:12 by 6 . please mark me as brainliest and follow me

Answer:

1:2

Step-by-step explanation:

6 and 12 are divisible by 6

6 ÷ 6 = 1

12 ÷ 6 = 2

Answer:

[tex](7x - 9) + (3x + 14) = 10x + 5[/tex]

Step-by-step explanation:

[tex]\left(7x-9\right)+\left(3x+14\right)[/tex]

Remove parentheses: [tex]\left(a\right)=a[/tex]

[tex]=7x-9+3x+14[/tex]

Group like terms:

[tex]=7x+3x-9+14[/tex]

Add similar elements: [tex]7x+3x=10x[/tex]

[tex]=10x-9+14[/tex]

Add/Subtract the numbers: [tex]-9+14=5[/tex]

[tex]=10x+5[/tex]

Hope I helped. If so, may I get brainliest and a thanks?

Thank you. Have a good day! =)

Answer:

pls refer to the pic

Step-by-step explanation:

Answer:

x5

Step-by-step explanation:

Answer:

(x - 1) (x + 4)

Step-by-step explanation:

｡☆✼★ ━━━━━━━━━━━━━━  ☾  

g(x) = h(x - 7) + 5

The plus 5 on the outside of the brackets represents the graph moving up by 5 units

The minus 7 on the inside of the brackets represents the graph moving right by 7 units.

Note: When it is on the inside of the brackets, you would do the opposite of what it suggests.

Normally, minus 7 would mean the graph shifts to the left, however, it means the opposite in this case.

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Answer:

Juan can make 6 groups having the same number of pencil

Step-by-step explanation:

42/7=6

36/6=6

42+36=78

78/6=13

Each group will get 13 pencils

Answer:

0 < y <= 6

Step-by-step explanation:

Given:

√(x² - 6x + 9)

if -3 <= x < 3

you can write (x² - 6x + 9)

as (x-3) * (x- 3) which is (x-3)²

so now you have √{(x-3)²}, which is the same as the absolute value of x-3. In mathematics it is written as:

| x - 3 |

So √(x² - 6x + 9) = | x - 3 |

See the graph in the attachment.

for -3 <= x < 3

you get the y values bigger then ( but not equal to) 0 and smaller then or equal to 6.

This is written as 0 < y <= 6

Answer:

x-3

Step-by-step explanation:

[tex]\sqrt{x^2 -x+9\\[/tex]

First rewrite 9 as 3^2 so... [tex]\sqrt{x^2 -6x+3^2}[/tex]

Next multiply the equation by 2ab so... 2ab =  2 · x · -3

Simplify so... 2ab = -6x

Then use the Perfect Square Trinomial rule: a^2 - 2ab + b^2 = (a-b)^2

so.. a = x and b = -3 to look like this: [tex]\sqrt(x- 3^2)[/tex]

And then finally pull out terms under the radical to get...

x-3

Answer:

C. 1 hundred 9 tens 15 ones

Step-by-step explanation:

Which shows how to regroup 205 to subtract 205-147?

A. 2 hundreds 9 tens 15 ones

B. 1 hundred 10 tens 15 ones

C. 1 hundred 9 tens 15 ones

D. 1 hundred 8 tens 15 ones

To regroup 205, you can write 1 hundred, 9 tens, and 15 ones or option C.

Since 100+90+15=205.

Answer:

B, x=40 is the right answer

Step-by-step explanation:

DAC is one half of the right angle and CAB is another half. So, you know that since a right angle is 90 degrees, DAC + CAB must equal 90.

They have given you equations for both angles, so now its just a matter of rearranging and solving for x.

DAC = x

CAB = 2x - 30

DAC + CAB = 90

Using the equations above, we can come up with this final equation:

x + 2x - 30 = 90

If we add the x together:

3x - 30 = 90

If we move the 30 to the other side by adding it to 90

3x = 90 + 30

3x = 120

If we divide 120 by 3:

x= 40

Therefore, the answer is B

Hope this helped : )

Answer:

y- intercept = 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

[tex]\frac{x}{3}[/tex] + [tex]\frac{y}{2}[/tex] = 1

Multiply through by 6 to clear the fractions

2x + 3y = 6 ( subtract 2x from both sides )

3y = - 2x + 6 ( divide all terms by 3 )

y = - [tex]\frac{2}{3}[/tex] x + 2 ← in slope- intercept form

with y- intercept c = 2

Answer:

The mileage of the car is 30 miles per gallon

Step-by-step explanation:

Here, we are interested in calculating the gas mileage of the car.

The gas mileage refers to the number of kilometers the car can travel on a particular amount of fuel.

The full capacity of the car tank is 15 gallon

Now after traveling 300 miles, it stops for gas and 10 gallons of fuel are added to make the car full again.

What this means is that the car used up a total of 10 gallons of fuel for the 300 miles

Thus, the gas mileage of the car is that it used 10 gallons to travel a total of 300 miles

Expressing this as a ratio, we have 300 miles/10 gallons = 30 miles/ gallon

This means that on a gallon of fuel, the car can travel 30 miles

Answer:

C = 25.1 cm

Step-by-step explanation:

C = 2(3.142r)

C = 2(3.142*4)

C = 2(12.568)

C = 25.136

Round to the nearest hundredth

C = 25.1

Answer:

One solution

Step-by-step explanation:

By inspection, you can see that adding either 3x or 4x to y yields the same result of 7, meaning that x must be 0. If x is 0, y must be 7, meaning that this equation has only one solution. Hope this helps!

Answer: 3 years

Step-by-step explanation:

The following can be gotten from the question:

Principal = $1600

Rate = 5%

Simple interest = $240

Time = Unknown

Interest = Principal × Rate × Time /100

240 = (1600 × 5 × Time)/100

240 = (8000 × Time)/100

240 × 100 = 8000 × Time

24000 = 8000 × Time

Time = 24000/8000

Time = 3 years

Answer:

a) 6

b) 37.5

c) 6th term

Step-by-step explanation:

a) plug in 2 for n

3(2)^2/2

6

b) plug in 5 for n

3(5)^2/2

37.5

c) since 5 is 37.5, I am going to check 6

3(6)^2/2

54

The 6th term will be the first to have a value higher than 50

Answer:

i think its 6

Step-by-step explanation:

The length of the diagonal of the rectangular prism will be √35 units. Then the correct option is B.

A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The dimension of the rectangular prism will be 3 units long, 5 units wide, and 1 unit high. Then the diagonal of the prism is given as,

D² = 3² + 5² + 1²

Simplify the equation, then we have

D² = 3² + 5² + 1²

D² = 9 + 25 + 1

D² = 35

D = √35 units

The length of the diagonal of the rectangular prism will be √35 units. Then the correct option is B.

More about the rectangular prism link is given below.

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Answer:

49

Step-by-step explanation:

y = 7^2

= 49

Answer:

They very according to the wealth of a country because the wealth of the country also reflects on how much supply there is, and if for example, there is a shampoo factory they will use less quality items because they don't have enough money or supplies to make good quality shampoo. The wealth of the country also affects how many sales are made from those lower quality items. Since the country is so poor, they don't have enough money to buy expensive products from overseas so they will buy the lower quality items, even if they know that they aren't the best quality. This might result to diseases in some serious cases, like in food industries of poor countries.

Step-by-step explanation:

it vary because if the country in which the company is being operated is a wealthy country it means that the company or industry will gain more customers than a country that is poor. Because if the country is wealthy people will come to that country because of it's rich economy but it also differs if the country in which the company is operating and does not offer quality service that industry will not be successful  

Answer:

Order from the greatest yield to the least as follows

1. Situation B=$2,119.8949

2. Situation A=$2,095.3078

3. Situation C=$2,022.7789

Step-by-step explanation:

Situation A

A=P(1+r/n)^nt

=500(1+0.12/12)^12*12

=500(1+0.01)^144

=500(1.01)^144

=500(4.1906155936008)

=$2,095.3078

Situation B

A=P(1+r/n)^nt

=500(1+0.1/4)^4*15

=500(1+0.025)^60

=500(1.025)^60

=500(4.3997897488150)

=$2119.8949

Situation C

A=P(1+r)^t

=500(1+0.15)^10

=500(1.15)^10

=500(4.0455577357079)

=$2022.7789

Order from the greatest yield to the least as follows

1. Situation B=$2,119.8949

2. Situation A=$2,095.3078

3. Situation C=$2,022.7789

Answer:

The area of the shaded region is [tex]49.5 cm^{2}[/tex] to 3. significant figures

Step-by-step explanation:

Step one: find the two diagonals of the kite.

The Horizontal diagonal can be obtained using the cosine rule:

[tex]AC^{2}=OA^{2}-OC^{2}- 2\times (OA)\times (OC)cos (\theta)[/tex]

[tex]AC^{2}=8^{2}+8^{2}- 2\times 8 \times 8 \times cos (120)= 212\\AC =\sqrt{212}=14.56cm[/tex]

The vertical diagonal of the kite can be obtained by Pythagoras' Theorem:

Please note the law in circle geometry which states that a radius and a tangent always meet at right angles.

This implies that triangle OBC is a right-angled triangle, with angle OCB being 90 degrees, and COB being 60 degrees. This is because the diagonal divides the 120-degree angle into half.

[tex]cos 60 = \frac{8}{OB}\\OB=\frac{8}{cos 60}= 16cm[/tex]

Step two: Use the dimensions of the two diagonals of the Kite to find the area:

The area of a Kite is obtained using this formula:

[tex]Area = \frac{pq}{2}[/tex], where p and q are the two diagonals.

hence,

[tex]Area = \frac{14.56 \times 16}{2}= 116.48cm^{2}[/tex]

Step three: Calculate the area of the sector of the circle.

Area of the sector is obtained using this formula

[tex]Area = \frac{\theta}{360}\times \pi\times r^{2}\\Area = \frac{120}{360} \times \pi \times 8^{2}=67.03cm^{2}[/tex]

Step Four: Subtract the area of the sector from the area of the kite:

Area of the shaded region will be [tex]116.48cm^{2} -67.03cm^{2} = 49.45cm^{2}[/tex]

This will be[tex]49.5 cm^{2}[/tex] to 3. significant figures

Answer:

43.8 cm²

Step-by-step explanation:

1. Split the kite in two and find the length of OB

When split the kite in two, you will find that the 120° becomes 60°, as they are divided into two.

Then, use the sine rule we can find out the length of OB. It goes like this:

[tex]\frac{OB}{sin90} = \frac{8}{sin30}\\ \\{OB} = \frac{8sin90}{sin30}\\\\ {OB} = 16cm[/tex]

2. Calculate the area of the kite

Since we have split the kite into two triangles and we know two side of the triangles, then we can calculate the area of one triangle using the formula of [tex]area of triangle=\frac{1}{2}absinc[/tex].

[tex]\frac{1}{2}[/tex]×8×16×sin60 = [tex]32\sqrt{3}[/tex]

But as there are two triangles, we duplicate the answer.

2×[tex]32\sqrt{2}[/tex] = [tex]64\sqrt{3}[/tex]

2. Calculate the area of the sector

area of sector =[tex]\frac{angle of sector}{360} \\[/tex]×πr²

[tex]\frac{120}{360}[/tex]×8²π = [tex]\frac{64}{3}[/tex]π

3. Subtract the area of the sector from the area of the kite

[tex]64\sqrt{3}[/tex] - [tex]\frac{64}{3}[/tex]π = 43.83060841 ≈ 43.8 cm² (to 3 s.f.)

HOPE THIS WILL HELP YOU :)

Answer:

Option (4)

Step-by-step explanation:

The given system of equations is,

y = -2x + 4 ------ (1)

6x + 3y = a --------(2)

We have to find the value of a for which the system of equations will have infinitely many solutions.

Option (1). If a = -12

                6x + 3y = -12

                2x + y = -4

                        y = -2x - 4

Both the equations have same slope, therefore, they are parallel and will have no solutions.

Option (2). If a = -4

                 6x + 3y = -4

                         3y = -6x - 4

                           [tex]y=-2x-\frac{4}{3}[/tex]

Then equation (1) and (2) will intersect each other at least at one point Or there is exactly one solution of the system of the equations.

Option (3). If a = 4

                 6x + 3y = 4

                         3y = -6x + 4

                           y = -2x + [tex]\frac{4}{3}[/tex]

Then equation (1) and (2) will intersect each other at least at one point Or there is exactly one solution of the system of the equations.

Option (4). If a = 12

                  6x + 3y = 12

                           3y = -6x + 12

                             y = -2x + 4

Therefore, both the equations (1) and (2) are same for a = 12 and they will have infinitely many solutions.

This question is based on system of linear equation .Thus, for a=12 will have infinitely many solution.

Given:

y = -2x + 4 ------ (a)  

6x + 3y = a ------(b)

We need to determined the value of a for which the system gives infinitely many solution.

Now check all the options as given below:

Option(1)  a = -12 and put it in (b) we get,

6x + 3y = -12

 2x + y = -4

y = -2x - 4

Both the equations have same slope, therefore, they are parallel to each other and have no solutions.

Option(2)  a= -4 and put it in (b) we get,

6x + 3y = -4

3y = -6x - 4

[tex]y=-2x-\dfrac{4}{3}[/tex]

Therefore, the equation has unique solution. Thus, both lines intersect each other at one point and there is unique value of x and y.

Option(3) a= 4

6x + 3y = 4

3y = -6x + 4

[tex]y=-2x+\dfrac{4}{3}[/tex]

Therefore, the equation has unique solution. Thus, both lines intersect each other at one point and there is unique value of x and y.

Option(4) a= 12

6x + 3y = 12

3y = -6x + 12

y = -2x + 4

Both the  equation are same for a= 12.

Thus, for a=12 will have infinitely many solution.

For further details, please prefer this link:

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Answer:

Step-by-step explanation:

87