the first 3 terms of a geometric sequence are as follows. -2, 10, -50. find the next 2 terms

Answer:

40,000 ft

Step-by-step explanation:

The area of a rectangle is weight*length, and the perimeter is the sum og the four sides, which are 2 lengths sides ans 2 width sides, so:

area = w*l

perimeter = 2w + 2l

If the perimeter is 1000 ft:

2w + 2l = 1000

Also, the length is 300 ft more than width, so:

l = 300 +w

So, our system is:

2w + 2l = 1000 (equation 1)

l =300 + w (equation 2)

Son, we can solve it by replacing equation 2 in equation 1:

2w + 2(300 +w) = 2w + 600 + 2w = 4w + 600 = 1000

Now, subtract 600 in both sides:

4w + 600 - 600 = 1000 - 600

4w = 400

Divide both sides by 4:

4w/4 = 400/4

w = 100

Lets replace this w value in equation 2 to find l:

l = 300 + 100 = 400, so l=400

Finally we can find the area using the area formula:

area = 400*100 = 40,000 ft2

So, the area is 40,000 ft2

Final answer:

The area of the pasture is found by setting up and solving a linear system (1000 = 2w + 2(w + 300)); the dimensions of the rectangle are found to be 100 feet in width and 400 feet in length. The area is then calculated by multiplying the width by the length, yielding an area of 40,000 square feet.

Explanation:

To solve the problem, we need to establish a system of linear equations to find the dimensions of the pasture. Given that the perimeter of a rectangle is 2 times the width plus 2 times the length (P = 2w + 2l), and the length is 300 feet more than its width (l = w + 300), we can set up the following equations:

P = 2w + 2l

l = w + 300

Since we know the perimeter is 1000 feet, we substitute this value into the first equation:

1000 = 2w + 2(w + 300)

1000 = 2w + 2w + 600

1000 = 4w + 600

400 = 4w

w = 100 feet

Once we have the width, we can substitute this into the second equation to find the length (l):

l = 100 + 300

l = 400 feet

To find the area of the pasture, we multiply the width by the length:

Area = width × length = 100 feet × 400 feet = 40,000 square feet

The area of the pasture is 40,000 square feet.

Answer:

(4,0) and (-2,0)

Step-by-step explanation:

(x-4)(x+2)

one of the brackets must equal zero; hence, we equal each brakcet to zero and solve the equation.

x-4=0

x=4

__________________________________

x+2=0

x=-2

To lay this out in coordinate format we would get:

(4,0) and (-2,0)

so our answers are the first and second option.

Answer:

B) 113.1 cm³

Step-by-step explanation:

The cross-section of a sphere is a circle.  The area of a circle is:

A = πr²

The largest cross section passes through the center of the sphere, where the radius of the circle equals the radius of the sphere.

28.27 = πr²

r = 3.00

The volume of the sphere is therefore:

V = 4/3 π r³

V = 4/3 π (3.00)³

V = 113.1

Answer:

B

Step-by-step explanation:

Answer:

8a-28b+15c

Step-by-step explanation:

4(2a)+7(-4b)+(3*c*5)

8a-28b+15c

Step-by-step explanation:

You must exclude any intersecting faces (faces that are shared), because these faces are not on the surface.

For example, an ice cream cone can be approximated as a composite figure of a hemisphere on top of a cone.  The circular base of the hemisphere and the circular base of the cone are intersecting, so you must exclude it when finding the surface area.

Answer:When two figures are placed together, one of each of their surfaces meets. The surfaces come together on the inside of the figure, and are no longer a part of the surface. These surfaces are a part of the individual figures’ surface area, but not of

Step-by-step explanation:

Did the test (this is the sample response)

Answer:

42.5 square centimeters

Step-by-step explanation:

The area of the parallelogram is

[tex]A=a\cdot b\cdot \sin \alpha,[/tex]

where a and b are adjacent sides and [tex]\alpha[/tex] is inckuded angle.

In your case,

[tex]a=11\ cm\\ \\b=5\ cm\\ \\ \alpha=50^{\circ}6'[/tex]

Thus,

[tex]A=11\cdot 5\cdot \sin 50^{\circ}6'\approx 42.5\ cm^2[/tex]

Answer:

AB = 9.6 cm

Step-by-step explanation:

ΔAPQ and ΔABC are similar triangles, thus ratio of corresponding sides are equal, that is

[tex]\frac{AP}{AB}[/tex] = [tex]\frac{PQ}{BC}[/tex], substitute values

[tex]\frac{8}{AB}[/tex] = [tex]\frac{10}{12}[/tex] ( cross- multiply )

10AB = 96 ( divide both sides by 10 )

AB = 9.6 cm

Answer:

[tex]\displaystyle [\frac{9}{11}, 1\frac{111}{143}][/tex]

Step-by-step explanation:

{10x - 26y = −38

{6x + 13y = 28

½[10x - 26y = −38]

{5x - 13y = −19 >> New Equation

{6x + 13y = 28

___________

[tex]\displaystyle \frac{11x}{11} = \frac{9}{11}[/tex]

[tex]\displaystyle x = \frac{9}{11}[/tex][Plug this back into both equations above to get the y-coordinate of 1 111⁄143]; [tex]\displaystyle 1\frac{111}{143} = y[/tex]

I am joyous to assist you anytime.

Answer:

In litres the volume of the pot of soup is 18.93litre

Step-by-step explanation:

This problem seeks to examine our understanding of unit conversion

Step one

Convert quarts to liters

Definition of quart (symbol: qt)

Quart is a unit of volume in the United States customary and imperial systems of measurement. Multiple.

Step two

If 1 qt=0.946353 litre

20qt=x litre

By cross multiplication we have

x litre = 20*0.946353 litre

x=18.93litre

In litres the volume of the pot of soup is 18.93litre

To convert 20 quarts to liters, you would use the conversion factor of 1 liter equating to 1.06 quarts. Following this conversion, the volume of the soup pot would be approximately 18.87 liters.

You're asked about the volume of a soup pot that contains 20 quarts and wants it to be converted to liters. Based on our comparison, 1 liter is approximately equivalent to 1.06 quarts. So to convert from quarts to liters, you'd divide the amount in quarts by the conversion factor.

Here is a step-by-step process to convert 20 quarts to liters:

 Identify the conversion factor: 1 liter = 1.06 quarts

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Answer:

4, 16 and 10

Step-by-step explanation:

Here we would like to work with a system of 3 equations, we need ti find them. Lets call s the 10oz coffees, m the 14oz and l the 20oz.

As Kyle sold $37.2 selling 3 different types of coffee at their respective prices we can say:

revenue = s*0.95 + m*1.15 + l*1.5 = 37.2 [equation 1]

And as he sold 30 cups:

s + m + l = 30 [equation 2]

And as the total volume of coffee is 464 oz:

s*10 + m*14 + l*20 = 464 [equation 3]

So, we have a system of 3 equations with three unknowns s, m and l.

Take the eq 2 and subtract m and l in both sides:

s = 30 - m - l

Now, take it and replace in the other 2:

(30 - m - l)*10 + 14m + 20l = 464 [eq 3]

0.95(30 - m - l) + 1.15m + 1.5l = 37.2 [eq 1]

Working with equation 3:

300 -10m -10l + 14m + 20l = 464

300 + 4m + 10l = 464

4m + 10l = 164 [equation 3']

Now with eq 1:

0.95(30 - m - l) + 1.15m + 1.5l = 37.2

28.5 - 0.95m - 0.95l + 1.15m + 1.5 l = 37.2

28.5 + 0.2m + 0.55l = 37.2

0.2m + 0.55l = 8.7 [equaiton 1']

Now we passed to a 2-equation system with eq 1' and eq 3'.

Take eq 3' and subtract 4m in both sides:

10l = 164 - 4m

Now divide by 10 in both sides

l = [164 - 4m]/10

Now, with this value for l replace in eq 1':

0.2m + 0.55 ( [164 - 4m]/10) = 8.7

0.2m + 0.055 (164 - 4m) = 8.7

0.2m + 9.02 - 0.22m = 8.7

- 0.02m = -0.32

m = -0.32/-0.02

m = 16 ----> 16 14oz coffees

Now replace m=16 in eq 1' or 3' to find l:

4m +10l = 164

64 + 10l = 164

10l = 100

l = 10 ----> 10 20oz coffees

So, finally we replace l=10 and m=16 in equaiton 2:

s + m + l = 30

s + 16 +10 = 30

s = 30 - 26

s = 4

So, Kyle filled 4 10oz coffes, 16 14oz coffees and 10 20oz coffees.

Option 2: [tex]\frac{4x-3y}{3x+4y}[/tex] is the right answer

Step-by-step explanation:

Given fraction is:

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

To solve the fraction, Taking LCM in denominator and numerator

[tex]=\frac{\frac{4x-3y}{12} }{\frac{3x+4y}{12}}[/tex]

When the numerator and denominator both have fractions, the simplified form is obtained be multiplying the numerator with reciprocal of the denominator. So,

[tex]= \frac{4x-3y}{12} * \frac{12}{3x+4y}\\=\frac{4x-3y}{3x+4y}[/tex]

Hence,

Option 2: [tex]\frac{4x-3y}{3x+4y}[/tex] is the right answer

Keywords: fractions, simplification

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Answer:

[tex]CD=(3-\sqrt{3})\ cm[/tex]

Step-by-step explanation:

step 1

Find the length side AB

In the right triangle ABD

[tex]sin(30\°)=\frac{AB}{AD}[/tex]

[tex]AB=sin(30\°)(AD)[/tex]

we have

[tex]AD=2\sqrt{3}\ cm[/tex]

[tex]sin(30\°)=\frac{1}{2}[/tex]

substitute

[tex]AB=\frac{1}{2}(2\sqrt{3})[/tex]

[tex]AB=\sqrt{3}\ cm[/tex]

step 2

Find the length side BD

In the right triangle ABD

[tex]cos(30\°)=\frac{BD}{AD}[/tex]

[tex]BD=cos(30\°)(AD)[/tex]

we have

[tex]AD=2\sqrt{3}\ cm[/tex]

[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]

substitute

[tex]BD=\frac{\sqrt{3}}{2}(2\sqrt{3})[/tex]

[tex]BD=3\ cm[/tex]

step 3

Find the length side BC

In the right triangle ABC

we know that

BC=AB -----> is an 45°-90°-45° triangle

therefore

[tex]BC=\sqrt{3}\ cm[/tex]

step 4

Find the length side CD

we know that

[tex]BD=BC+CD\\CD=BD-BC[/tex]

substitute the values

[tex]CD=(3-\sqrt{3})\ cm[/tex]

Answer:

139.5/1 or 1395/10

Step-by-step explanation:

Answer:

0.16

Step-by-step explanation:

Use long division

Answer:

0.16

Step-by-step explanation:

4÷25 = 0.16

Answer:

So the greatest common factor 42 and 98 is 14.

Answer:

28 students

Step-by-step explanation:

you get 28.3 if you divide 85 by 3

Answer:

Therefore, the percent error in 1.   20%

          and the percent error in 2.    6%  

Step-by-step explanation:

Given:

1. In estimation of 30 people only 25 people attended.

2. In estimated length of 150 feet the measurement was 142 feet.

Now, in first case for the percent error we would calculate the difference between the people attended:

[tex]30-25=5[/tex]

And then, we will get the percentage error :

[tex]\frac{5}{25} \times 100[/tex]

[tex]\frac{500}{25}[/tex][tex]=20[/tex].

Therefore, the percentage error is 20%.

Now, in second case for the percent error we would repeat the above process as done in first case:

[tex]150-142=8[/tex]

And then:

[tex]\frac{8}{142}\times 100[/tex]

[tex]\frac{800}{142}[/tex][tex]=5.63[/tex]

Therefore, the percentage error is 6% (approximately).

Therefore, the percent error in 1. is   20%

          and the percent error in 2. is  6%  

Answer:

643999001

Step-by-step explanation:

The linear function represents the amount of money, m, that Carla has saved after w weeks is m = 25 w + 80

Step-by-step explanation:

Carla is saving money for a trip this summer. She already has some money in her savings account and will add the same amount to her account each week

Write a linear function in the form y = m x + b to represent the amount of money, m, that Carla has saved after w weeks

The linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept

The formula of the slope is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are 2 points on the line

∵ The slope is the rate of change of y and x

∴ The same amount of money that Carla add every week = m

∵ At the end of 2 weeks, Carla has $130

∴ The first point is (2 , 130)

∵ At the end of 8 weeks, she has $280

∴ The second point is (8 , 280)

∵ [tex]m=\frac{280-130}{8-2}=\frac{150}{6}=25[/tex]

∴ The same amount of money that Carla add every week = $25

∵ The amount of money that Carla saved after w week is m

∴ m = 25 w + b, where b is the initial amount of money that she

   saved in her account

To find b substitute w and m by the coordinates of one of the two

given points, let us use the first point

∵ w = 2 and m = 130

∵ m = 25 w + b

∴ 130 = 25(2) + b

∴ 130 = 50 + b

- Subtract 50 from both sides

∴ 80 = b

∴ m = 25 w + 80

The linear function represents the amount of money, m, that Carla has saved after w weeks is m = 25 w + 80

Learn more:

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Answer:

12/4=3

Step-by-step explanation:

12/4

The expression that could be used to find the no of batches she makes is [tex]= 12\div 4[/tex]

Given that,

Based on the above information, the calculation is as follows:

[tex]= 12\div 4[/tex]

= 3

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Answer:

The correct answer is s = 27.

Step-by-step explanation:

This problem already gives us an equation so all we need to do is plug in the numbers:

c = 39.95 + 0.15(s + r) becomes 53.45 = 39.95 + 0.15(s + 63). Now to solve:

53.45 = 39.95 + 0.15(s + 63)

13.50 = 0.15(s + 63)                     Subtract 39.95 from both sides

13.50 = 0.15s + 9.45                    Distribute 0.15 to s and 63

4.05 = 0.15s                                 Subtract 9.45 from both sides

27 = s                                           Divide both sides by 0.15

Hope this helps,

❤A.W.E.S.W.A.N.❤

Answer:

The percent increase is 157%

Explanation:

Average after tax income 20 years before: $263,700

Average after tax income after 20 years: $677,900

Increased average after tax  income : $677,900-$263,700

                                                            =$414,200

Hence,  

Percent increase = [tex]\frac{Increased amount}{original amount} \times 100[/tex]

=[tex]\frac{414,200}{263,700} \times 100[/tex]

=157.07%

After Rounding off:

=157%

157%  is the percent increase

Answer:

See below

Step-by-step explanation:

To construct a confidence interval we use the following formula:

ci = (sample mean) +- z*(sd)/[n^(1/2)]

The sample mean is 57, the standard deviation is 2.36, n s 25 and z is the  upper (1-C)/2 critical value for the standard normal distribution. Here, as we want a confidence interval at a 90% we have (1-C)/2=0.05 we have to look at the 1-0.05=0.95 value at the normal distribution table, which is 1.65 approximately. Replacing all these values:

ci = 57 +- 1.65*(2.36)/[25^(1/2)]

ci = 57 +- 3.894*/(5) = 57 +- 0.78

ci => (56.22 , 57.78)

Answer:

Step-by-step explanation:

[tex]-2y+10<-14\qquad\text{subtract 10 from both sides}\\\\-2y+10-10<-14-10\\\\-2y<-24\qquad\text{change the signs}\\\\2y>24\qquad\text{divide both sides by 2}\\\\\dfrac{2y}{2}>\dfrac{24}{2}\\\\y>12[/tex]

Positive integers are 20,22 and negative integers are -22,-20.

Step-by-step explanation:

Let,

2 positive integers are x, x+2

According to given statement;

[tex]x(x+2)=440\\x^{2}+2x=440\\x^{2}+2x-440=0\\x^{2}+22x-20x-440=0\\x(x+22)-20(x+22)=0\\(x+22)(x-20)=0\\Either,\\x+22=0\\x=-22\\Or,\\x-20=0\\x=20[/tex]

If x=-22

Then,

x+2 = -22+2 = -20

Or,

x=20

x+2 = 20+2 = 22

Positive integers are 20,22 and negative integers are -22,-20.

Keywords: Integers, Multiplication

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The two consecutive even integers whose product is 440 are 20 and 22. When considered as positive and negative, they are +20 and -20, +22 and -22, respectively.

To find the two consecutive even integers whose product is 440, we need to employ some algebraic reasoning. Let's denote the first of the two consecutive even integers as x.

Given that even integers follow a pattern of +2, we can denote the next consecutive even integer as x + 2.

Hence, we're solving for the equation x * (x + 2) = 440. Solving this equation will give us our consecutive even integers, which are 20 and 22. In terms of positive and negative integers, they would be represented as +20 and -20, +22 and -22, respectively.

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Answer:

Infinitely many solutions. The value of x can be any real number.

Step-by-step explanation:

6 times 1/3x = 2x

6 times 1/2 = 3

6 times (1/3x + 1/2) = 2x+3

The left side of the original equation becomes 2x+3. The right side is also 2x+3. Both sides are the same, so we get infinitely many solutions.

We have,

[tex]6(\frac{1}{3}x+\frac{1}{2})=2x+3[/tex]

First distribute 6 through parentheses

[tex]2x+3=2x+3[/tex]

We can see both sides are equal hence for all x the equation will result with tautology (undeniable equality).

The answer is [tex]x \in \mathbb{R}[/tex].

Hope this helps.

Answer:

3. The superhero is afraid of heights.

"The superhero is afraid of heights." is independent clause because the sentence contains a subject and verb and it's a complete sentence.  

Step-by-step explanation:

An independent clause is a group of words that contains a subject and verb and expresses a complete thought. An independent clause is a sentence.

          Jim studied in the Sweet Shop for his chemistry quiz.

A dependent clause is a group of words that contains a subject and verb but does not express a complete thought. A dependent clause cannot be a sentence. Often a dependent clause is marked by a dependent marker word.  A dependent marker word is a word added to the beginning of an independent clause that makes it into a dependent clause. Some common dependent markers are: after, although, as, as if, because, before, even if, even though, if, in order to, since, though, unless, until, whatever, when, whenever, whether, and while.

          When Jim studied in the Sweet Shop for his chemistry quiz . . .

         (What happened when he studied? The thought is incomplete.)

Answer: choice 3. The superhero is afraid of heights

The other choices are sentences that are incomplete because they need more structue to them. For example, sentence 1 implies that something else is going on during Marvin's guitar time. The other sentences have cliffhangers as well and they arent fully independent or on their own. Sentence 3 expesses a single complete thought without introducing some other related or tangential thought needed to complete that idea.

Final answer:

To express y in terms of x, rearrange the equations to isolate y. The equation expressing y in terms of x is (4x + 20)/3.

Explanation:

To express y in terms of x, we need to isolate y in the given equations.

From the first equation, x = 3t - 8, we can rearrange to solve for t: t = (x + 8)/3.

Substituting this expression for t into the second equation, y = 4 + t, gives us y = 4 + (x + 8)/3. Simplifying further, we have y = (4x + 20)/3.