Laurie needs at least 40 pounds of topsoil for a new flower bed. Each bag of topsoil is 200 ounces. Laurie determines that if she buys 3 bags of topsoil she will have enough for the flower bed. Is Laurie correct? Why or why not?

Answer:

The equation of the ellipse is [tex]\frac{(x-2)^{2}}{8^{2}}+\frac{(y-10)^{2}}{10^{2}} = 1[/tex].

Step-by-step explanation:

The statement is incomplete, the most probable outcome may be the equation of the ellipse based on information given.

The equation of an ellipse whose major axis is vertical and is centered at a point different from origin is defined by:

[tex]\frac{(x-h)^{2}}{b^{2}} + \frac{(y-h)^{2}}{a^{2}} = 1[/tex] (1)

Where:

[tex](h,k)[/tex] - Coordinates of the center of the ellipse.

[tex](x,y)[/tex] - Coordinates of a point in the line of the ellipse.

[tex]a[/tex] - Length of the major semiaxis.

[tex]b[/tex] - Length of the minor semiaxis.

The coordinates of the center of the ellipse is midpoint of the segment between vertices, which are collinear with foci:

[tex](h,k) = \frac{1}{2}\cdot V_{1} (x,y) + \frac{1}{2}\cdot V_{2}(x,y)[/tex] (1)

Where [tex]V_{1} (x,y)[/tex] and [tex]V_{2} (x,y)[/tex] are the coordinates of the vertices.

If we know that [tex]V_{1} (x,y) = (2,0)[/tex] and [tex]V_{2} (x,y) = (2, 20)[/tex], then the coordinates of the center ellipse are:

[tex](h,k) = (2, 10)[/tex]

The length of the semimajor axis can be determined by using the following vectorial expression, which is equivalent to the Pythagorean Theorem:

[tex]a = \sqrt{[(h,k)-V_{1}(x,y)]\,\bullet\,[(h,k)-V_{1}(x,y)]}[/tex] (2)

If we know that [tex](h,k) = (2, 10)[/tex] and [tex]V_{1} (x,y) = (2,0)[/tex], then the length of the semimajor axis is:

[tex]a = \sqrt{(2-2)^{2}+(10-0)^{2}}[/tex]

[tex]a = 10[/tex]

And the length of the minor semiaxis is found by means of this Pythagorean identity:

[tex]b = \sqrt{a^{2}-c^{2}}[/tex] (3)

Where [tex]c[/tex] is the length between the center and any of the foci. This distance can be found by using this vectorial formula:

[tex]c = \sqrt{[(h,k)-F_{1}(x,y)]\,\bullet\,[(h,k)-F_{1}(x,y)]}[/tex] (4)

If we know that [tex](h,k) = (2, 10)[/tex] and [tex]F_{1} (x,y) = (2,4)[/tex], then the length between the center and any of the foci is:

[tex]c = \sqrt{(2-2)^{2}+(10-4)^{2}}[/tex]

[tex]c = 6[/tex]

And the length of the minor semiaxis is:

[tex]b = \sqrt{10^{2}-6^{2}}[/tex]

[tex]b = 8[/tex]

FInally, the equation of the ellipse is [tex]\frac{(x-2)^{2}}{8^{2}}+\frac{(y-10)^{2}}{10^{2}} = 1[/tex].

Answer:

2.9 km

Step-by-step explanation:

Just add up the two distances:  2.3 km + 600 m = 2.3 km + 0.6 km = 2.9 km total

Answer:

[tex]a^7-7a^6b+21a^5b^2-35a^4b^3+35a^3b^4-21a^2b^5+7ab^6-b^7[/tex]

Step-by-step explanation:

There are multiple ways of expanding a polynomial expression to a high degree. One way of doing it is to write out the problem in the multiplication form, multiply (a - b) by itself (7) times.

[tex](a-b)^7[/tex]

[tex]=(a-b)(a-b)(a-b)(a-b)(a-b)(a-b)(a-b)[/tex]

Now simplify, multiply two terms together,

[tex]=(a^2-2ab+b^2)(a^2-2ab+b^2)(a^2-2ab+b^2)(a-b)[/tex]

Repeat this process,

[tex]=(a^4-4a^3b+6a^2b^2-4ab^3+b^4)(a^3-3a^2b+3ab^2-b^3)[/tex]

Repeat this process one final time,

[tex]a^7-7a^6b+21a^5b^2-35a^4b^3+35a^3b^4-21a^2b^5+7ab^6-b^7[/tex]

Answer:

x=5

Step-by-step explanation:

5-3=2

Answer:

1st option is the correct answer

Answer:

m<ADE = 59°

Step-by-step explanation:

Each angle of a rectangle = 90°

Therefore:

m<ABE + m<CBE = 90°

(4x + 15)° + (13x + 7)° = 90°

Solve for x

4x + 15 + 13x + 7 = 90

17x + 22 = 90

17x = 90 - 22

17x = 68

x = 68/17

x = 4

✔️Opposite sides (AB and DC) of the rectangle are parallel, therefore:

m<ADE = m<CBE

m<ADE = (13x + 7)° (Substitution)

Plug in the value of x

m<ADE = 13(4) + 7

m<ADE = 52 + 7

m<ADE = 59°

Answer:

Yes.

Step-by-step explanation:

If you change nothing but the angle and positioning of the original shape, then it is congruent.

Answer:

The answer is D

Step-by-step explanation:

Since the input is -6, you input it into the equation. That would make it f(-6)=-(-6)-1 which would be equivalent to f(-6)=6-1 , as the negatives at the beginning of the equation cancel each other out and make it positive. Then you solve and get 5, which is your output. Hope I could help :)

Answer:

x = 12

Step-by-step explanation:

(8x - 1) + (3x + 4) + (3x + 9) = 180 degrees

14x + 12

180 - 12 = 168

14x = 168

/14  |   /14

x = 12

Top left angle: (8x - 1)

8*12 - 1

96 - 1

= 95

Sorry! gtg I hope this helps!

Step-by-step explanation:

hsusbdjdhssjzssisbzjshzbzbaizussbissbisbsisbsssj

I hope this helps you

8^2=4.(4+x)

64=4.(4+x)

16=4+x

x=12

Answer:

Hey! do not go to brainly for this, sometimes brainly can be no help and people will scam for points, or maybe try to hack you (pt virus) with those links saying the answers there.. I am not saying this for points but go to https://www.varsitytutors.com/basic_geometry-help/how-to-find-the-distance-between-clock-hands for that

Step-by-step explanation:

So don't waste your time on brainly finding answers, you can run out of points fast, some people wont answer at all.

Answer:

less than -1

less than -1

greater than 1

greater than 1

Step-by-step explanation:

[tex] - 7 + - 4 = - 7 - 4 = - (7 + 4) = - 11[/tex]

LESS THAN -1

________________________________

[tex] - ( \frac{3}{2} ) = - (1.5) = - 1.5[/tex]

LESS THAN -1

________________________________

[tex] \frac{( - 5)}{( - 3)} = \frac{5}{3} = 1.66..[/tex]

GREATER THAN 1

________________________________

[tex]( - 9) - 6 = - 9 - 6 = - (9 + 6) = - 15[/tex]

LESS THAN -1

________________________________

The function rule is f(x) = x - 12 and the complete table is

Input(x) Output(y)

32 20

14 2

6 −6

-2 -14

-10 -22

From the question, we have the following parameters that can be used in our computation:

Input(x) Output(y)

32 20

14 2

? −6

-2 -14

-10 ?

The slope is calculated as

m = (2 - 20)/(14 - 32)

m = 1

So, the equation is

y = mx + c

Using the points, we have

1(32) + c = 20

Evaluate

c = -12

So, we have

f(x) = x - 12

Using the above function, we have the following function values

f(-10) = -10 - 12 = -22

x - 12 = -6

x = 6

So, the complete table is

Input(x) Output(y)

32 20

14 2

6 −6

-2 -14

-10 -22

Read more about linear relation at

https://brainly.com/question/30318449

#SPJ1

Answer:

1. x=12

2. x=7

Step-by-step explanation:

Answer:

1 1/5 miles or 1/2 miles

Step-by-step explanation:

1/5 x 6 = 6/5 = 1 1/5 or 1/2 miles

Answer:1

Step-by-step explanation:

4x-4x+4=4h(x)

4=4h(x)

h(x)=1

h(-3)h(-3)=(1)(1)=1

Answer:

960 minutes

Step-by-step explanation:

If there are 24 hours a day with 60 minutes then there are 1440 hours a day.

There 16 hours multiplied by 60 minutes will give you your answer! [tex]16*60=960[/tex]

it is 690 minutes per 16 hours

Answer:

B. 25

Step-by-step explanation:

Answer:

1. y=2

2. y= - 2

Step-by-step explanation:

Thats my answer hope it helps

Answer:

the solution is : (2 , 3)

Step-by-step explanation:

hello :  here is an solution

3x + 2y=12.....(*)

y=2x -1​.....(**)

put the value for y  in (*) :

3x + 2(2x-1)=12

3x+4x-2 = 12

7x =14

so : x =2

but : y=2x -1

y =2(2)-1 = 3

the solution is : (2 , 3)

Answer:

Angle A: 90

Angle B: 48

Angle C: 42

Side length A (Hypotinuse): 23.9

SIde length B (Opposite): 17.8

Side length C (Adjacent): 16

Step-by-step explanation:

https://www.calculator.net/triangle-calculator.html?vc=42&vx=&vy=&va=90&vz=16&vb=&angleunits=d&x=0&y=0

Answer: 15

Step-by-step explanation:

The answer is because if you divide 14,130 by 3.14. You'll get 4500 and then divide that by 300 and your finally is 15

The radius of the inflated beach ball is equal to 58 inches.

Surface Area of a Sphere. A = 4 π r². The volume of a Sphere. V = (4 ⁄ 3) π r³. Where r is the radius of the circle.

Given: The volume of the sphere is 14,310 inches³

we know the volume of the sphere is  4/3 πr³

Thus equating we get

4/3 × 3.14×r³=14310

r³=3417.99

r³=3418

r=58.463 or 58 (approx)

Learn more about sphere here:

https://brainly.com/question/2855746

#SPJ6

Answer:

1. if y varies directly as x, and y = 6 when x = 2, the constant of variation is k = 6/2= 3. Thus, the equation describing this direct variation is y = 3x.

2. Partial Variation, where two variables are related by a formula, such as the formula for a straight line (with a non-zero y-intercept)

example :

in the milk factory Carol makes $10 per hour but gets an extra $20 from another job. since Carol gets a $20 allowance regardless of how much she works, if we want to represent Carol's situation in the form of an equation, it would be

Y=10x + 20

therefore if she worked zero hours

(Y=10(0) + 20),

she would still make $20 unconditionally and for every hour she works, she gets $10 more including the initial $20.

thus Carol's equation would be a partial variation, since her income doesn't entirely depend on how much she works.

3. a relation is non linear because it is has a direct relationship between an independent variable and a dependent variable.

In a relation, changes in the output do not change in direct proportion to changes in any of the inputs.

relations does not create a straight line but instead creates a curve.

Answer:

56

Step-by-step explanation:

x=5

so x for the gym is 5 and x+3=5+3=8

add 5 and 8 because that is a whole side.

we are trying to find perimeter which us the outside of the shape. you are just going to "walk the fence" . so now, we have two sides of 15 and two sides of 13 (5+8). 13+13=26. 15+15=30

add the 26 and 30