Fine the 8th term of the geometric sequence 10,50,250

Answer:

35.7 ft

Step-by-step explanation:

Given

Hypotenuse (length of the ladder) = 50 ft

Base (distance from the ladder to wall) = 35 ft

Height (of the wall) = [tex]\sqrt{50^{2}-35^{2} }[/tex] = [tex]\sqrt{1275}[/tex] = 35.7 ft

Answer:

Step-by-step explanation:

The given expression is: 14x^(2n+1) + 7x^(n+3) - 21^(n+2)

Unfortunately, it seems there is a missing exponent for the term "21" in the expression. Please provide the correct exponent for 21, and I'll be happy to help you further simplify the expression.

Step-by-step explanation:

The area of the shaded region is the difference between the area of the entire polygon and the area of the unshaded part inside the polygon

Answer:

AB = √3

Step-by-step explanation:

Since ABCD is a rectangle, all angles are 90°

∠CDA = 90°

⇒ ∠CDB + ∠BDA = 90

⇒ ∠BDA = 60

In ΔABD,

sin(∠BDA) = opposite/ hypotenuse = AB / BD

⇒ sin(60) = AB/2

⇒ AB = 2 sin(60)

⇒ AB = 2 (√3)/2

AB = √3

Approximately 4.6 pounds of pecans are needed for one pecan pie.You should buy approximately 41.4 pounds of pecans to make 9 pecan pies.

To determine the number of pounds of pecans needed to make 9 pecan pies, we need to consider the amount of pecans required per pie and the number of pies we are making.

The recipe calls for 1 cup of pecans per pie, but we don't have a measuring cup available. However, we do have nutritional information from a bag of pecans, which states that there are 684 calories in 1 cup (99g) of pecans.

To find out how many pecans are in a pound, we can use the information that 1 cup of pecans weighs 99 grams. Since there are 454 grams in a pound, we can set up the following proportion:

1 cup (99g) = x pounds (454g)

Cross-multiplying, we get:

99g * x pounds = 1 cup * 454g

Simplifying, we have:

99x = 454

Dividing both sides by 99, we find:

x ≈ 4.5959 pounds

So, approximately 4.6 pounds of pecans are needed for one pecan pie.

Since we are making 9 pecan pies, we multiply the amount needed for one pie by the number of pies:

4.6 pounds/pie * 9 pies = 41.4 pounds

For more such questions on pounds visit:

https://brainly.com/question/12983359

#SPJ8

Answer:

There are 12 blocks in the bottom layer

Step-by-step explanation:

We see from the diagram that in the bottom layer,

length = 3 cm

width = 4 cm

And that there are 3 blocks for the 3 cm length,

Hence each block has a length of 1 cm (the 3 then make up 3 cm)

And there are 4 blocks for the 4 cm width

Hence the width is also 1 cm (4 of these make up 4 cm width)

Now, to find the total number of blocks,

we just multiply the length and width,

so, (3)(4) = 12

so there are 12 blocks in the bottom layer

Answer:

We don't need to worry about the displaystyle- {3} −3 anyway, because we dcided in the first step that displaystyle {x}ge- {2} x ≥ −2. So the domain for this case is displaystyle {x}ge- {2}, {x}ne {3} x≥ −2,x≠ 3, which we can write as displaystyle {left [- {2}, {3}right)}cup {left ({3},inftyright)} [−2,3)∪(3,∞).

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

parallel lines have the same gradient

The sentence that contains no errors in subject-verb agreement is: "Those people whose long lives are about to end feel reassured by this belief."

This sentence correctly matches the plural subject "Those people whose long lives are about to end" with the plural verb "feel." The verb "feel" agrees in number with the subject "people."

The other sentences have subject-verb agreement errors:

"Those people whose long lives are about to end feels reassured by this belief."

The verb "feels" does not agree with the plural subject "Those people." It should be "feel."

"A person whose long life is about to end feel reassured by this belief."

The verb "feel" does not agree with the singular subject "A person." It should be "feels."

"A person whose long life are about to end feels reassured by this belief."

The verb "are" does not agree with the singular subject "A person." It should be "is."

Therefore, the sentence with no errors in subject-verb agreement is: "Those people whose long lives are about to end feel reassured by this belief."

For more such questions on errors

https://brainly.com/question/28771966

#SPJ8

Answer:

A

Step-by-step explanation:

3x16

+

4x18
+

5x17

Answer:

40, 50, 30 Yes

13, 5, 12 Yes

10, 10, 15 Yes

41, 9, 40 Yes

Step-by-step explanation:

16, 10, 6

10 + 6 = 16

No

40, 50, 30

30 + 40 > 50

Yes

13, 5, 12

5 + 12 > 13

Yes

70, 20, 25

20 + 25 < 70

No

10, 10, 15

10 + 10 >15

Yes

41, 9, 40

9 + 40 > 41

Yes

Answer:

acute triangle

Step-by-step explanation:

for the given sides to form a triangle

the sum of any 2 sides must be greater than the third side

given 56 , 90 , 100

56 + 90 = 146 > 100

56 + 100 = 156 > 90

90 + 100 = 190 > 56

the condition is met so the 3 lengths will form a triangle.

let a = 56 , b = 90 and c = 100 , where c represents the longest of the 3 sides , then

• if a² + b² = c² , then triangle is right

• if a² + b² > c² , then triangle is acute

• if a² + b² < c² , then triangle is obtuse

a² + b² = 56² + 90² = 3136 + 8100 = 11,236

c² = 100² = 10, 000

since a² + b² > c² , then triangle is acute

To find the value of the cosine of angle M in triangle AMNO, we can use the Law of Cosines. The Law of Cosines states that in a triangle with sides [tex]\displaystyle a[/tex], [tex]\displaystyle b[/tex], and [tex]\displaystyle c[/tex], and angle [tex]\displaystyle C[/tex] opposite side [tex]\displaystyle c[/tex], the following equation holds:

[tex]\displaystyle c^{2} =a^{2} +b^{2} -2ab\cos( C)[/tex]

In triangle AMNO, we have the following information:

[tex]\displaystyle AM=17[/tex] (side [tex]\displaystyle a[/tex])

[tex]\displaystyle MN=15[/tex] (side [tex]\displaystyle b[/tex])

[tex]\displaystyle AN=8[/tex] (side [tex]\displaystyle c[/tex])

Angle M = 90 degrees

We can apply the Law of Cosines to find the value of [tex]\displaystyle \cos( M)[/tex]:

[tex]\displaystyle AN^{2} =AM^{2} +MN^{2} -2\cdot AM\cdot MN\cdot \cos( M)[/tex]

Substituting the given values:

[tex]\displaystyle 8^{2} =17^{2} +15^{2} -2\cdot 17\cdot 15\cdot \cos( M)[/tex]

Simplifying:

[tex]\displaystyle 64=289+225-510\cdot \cos( M)[/tex]

[tex]\displaystyle 64=514-510\cdot \cos( M)[/tex]

Rearranging the equation:

[tex]\displaystyle 510\cdot \cos( M) =514-64[/tex]

[tex]\displaystyle 510\cdot \cos( M) =450[/tex]

Dividing both sides by 510:

[tex]\displaystyle \cos( M) =\frac{450}{510}[/tex]

Simplifying:

[tex]\displaystyle \cos( M) =\frac{15}{17}[/tex]

Therefore, the value of the cosine of angle M in triangle AMNO, to the nearest hundredth, is approximately [tex]\displaystyle 0.88[/tex].

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Based on the given transformations, the correct graph that represents function g(x) = tan(x-4) + 2 is option c.

To determine the graph that represents function g(x) = tan(x-4) + 2, we can analyze the transformations applied to the parent tangent function.

The parent tangent function has the form f(x) = tan(x). The given function g(x) = tan(x-4) + 2 introduces two transformations:

1. Horizontal shift: The function is shifted 4 units to the right compared to the parent function f(x) = tan(x). This means the graph of g(x) will be shifted to the right by 4 units.

2. Vertical shift: The function is shifted 2 units up compared to the parent function f(x) = tan(x). This means the graph of g(x) will be shifted upward by 2 units.

Based on the given transformations, the correct graph that represents function g(x) = tan(x-4) + 2 is option c. The graph in option c shows a rightward shift of 4 units (horizontal shift) and an upward shift of 2 units (vertical shift), matching the transformations described for g(x).

Learn more about function at  https://brainly.com/question/11624077

#SPJ1

Hello,

Answer:

[tex]30+((-2\times(25- (13-3)))[/tex]

[tex]=30+((-2\times(25- 10))[/tex]

[tex]=30+(-2\times 15)[/tex]

[tex]=30+(-30)[/tex]

[tex]=30-30[/tex]

[tex]=\boxed{0}[/tex]

Approximately 76.5% of the student body at Walton High School loves math.

To determine the percentage of the student body that loves math, we need to consider the proportions of males and females in the Walton High School student body and their respective percentages of loving math.

Given that 45% of the student body are males, we can deduce that 55% are females (since the total percentage must add up to 100%). Now let's calculate the percentage of the student body that loves math:

For the females:

55% of the student body are females.

90% of the females love math.

So, the percentage of females who love math is 55% * 90% = 49.5% of the student body.

For the males:

45% of the student body are males.

60% of the males love math.

So, the percentage of males who love math is 45% * 60% = 27% of the student body.

To find the total percentage of the student body that loves math, we add the percentages of females who love math and males who love math:

49.5% + 27% = 76.5%

As a result, 76.5% of Walton High School's student body enjoys maths.

for such more question on percentage

https://brainly.com/question/24877689

#SPJ8

1/3 of a full rotation: (-0.5, √3/2)

1/2 of a full rotation: (-1, 0)

2/3 of a full rotation: (0.5, -√3/2)

These are the coordinates of point P after the corresponding rotations around the unit circle's center.

To find the coordinates of point P after the unit circle rotates a certain amount counter-clockwise around its center, we can use the properties of the unit circle and the trigonometric functions.

1/3 of a full rotation:

A full rotation in the unit circle corresponds to 360 degrees or 2π radians. Therefore, 1/3 of a full rotation is equal to (1/3) * 360 degrees or (1/3) * 2π radians.

When the unit circle rotates 1/3 of a full rotation, point P will end up at an angle of (1/3) * 2π radians or 120 degrees from the positive x-axis.

In the unit circle, the x-coordinate of a point on the circle represents the cosine of the angle, and the y-coordinate represents the sine of the angle.

At an angle of 120 degrees or (1/3) * 2π radians, the cosine is -0.5 and the sine is √3/2.

Therefore, the coordinates of point P after rotating 1/3 of a full rotation are (-0.5, √3/2).

1/2 of a full rotation:

Similarly, 1/2 of a full rotation is equal to (1/2) * 360 degrees or (1/2) * 2π radians.

When the unit circle rotates 1/2 of a full rotation, point P will end up at an angle of (1/2) * 2π radians or 180 degrees from the positive x-axis.

At an angle of 180 degrees or (1/2) * 2π radians, the cosine is -1 and the sine is 0.

Therefore, the coordinates of point P after rotating 1/2 of a full rotation are (-1, 0).

2/3 of a full rotation:

Again, 2/3 of a full rotation is equal to (2/3) * 360 degrees or (2/3) * 2π radians.

When the unit circle rotates 2/3 of a full rotation, point P will end up at an angle of (2/3) * 2π radians or 240 degrees from the positive x-axis.

At an angle of 240 degrees or (2/3) * 2π radians, the cosine is 0.5 and the sine is -√3/2.

Therefore, the coordinates of point P after rotating 2/3 of a full rotation are (0.5, -√3/2).

for such more question on coordinates

https://brainly.com/question/23907194

#SPJ8

Answer:

35

Step-by-step explanation:

18-4 = 14 minutes

number of words typed in 14 minutes is 765-275= 490 words

490 words/14 mins= appox 35

The graph of the function f(x) = 5(2)^x is an upward-sloping exponential curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing the x-axis.

The function f(x) = 5(2)^x represents exponential growth. Let's analyze its graph.

As x increases, the value of 2^x grows exponentially. Multiplying it by 5 further amplifies the growth. Here are a few key points to consider:

When x = 0, 2^0 = 1, so f(0) = 5(1) = 5. This is the y-intercept of the graph, meaning the function passes through the point (0, 5).

As x increases, 2^x grows rapidly. For positive values of x, the function will increase quickly. As x approaches positive infinity, 2^x grows without bound, resulting in the function also growing without bound.

For negative values of x, 2^x approaches zero. However, the function is multiplied by 5, so it will not reach zero. Instead, it will approach y = 0, but the graph will never touch or cross the x-axis.

The function is always positive since 2^x is positive for any value of x, and multiplying by 5 does not change the sign.

Based on these observations, we can conclude that the graph of f(x) = 5(2)^x will be an exponential growth curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing or touching the x-axis.

The graph will have a smooth curve that rises steeply as x increases. The rate of growth will be determined by the base, in this case, 2. The larger the base, the steeper the curve. The function will approach but never reach the x-axis as x approaches negative infinity.

for more question on graph visit:

https://brainly.com/question/19040584

#SPJ8

The function f(x) = -x³ - x is an odd function.

Given the function in the question:

f(x) = -x³ - x

To determine if a function is odd, we need to check if it satisfies the given property:

f(-x) = -f(x)

For all x in the domain of the function.

Given that:

f(x) = -x³ - x

Evaluate f(-x) for the given function f(x) = -x³ - x:

f(x) = -x³ - x

Replace x with -x

f(-x) = -(-x)³ - (-x)

f(-x) = -(-x³) + x

f(-x) = x³ + x

Now, check if -f(x) is equal to x³ + x:

-f(x) = -(-x³ - x)

-f(x) = x³ + x

Since -f(x) = x³ + x, f(x) = -x³ - x is an odd function.

Learn more about odd functions here: https://brainly.com/question/9854524

#SPJ1

Answer:

(x^3+2x-1) * (x^4-x^3+3)

Step-by-step explanation:

To simplify this expression, we can multiply each term in the first expression by each term in the second expression and combine like terms:

(x^3)(x^4) + (x^3)(-x^3) + (x^3)(3) + (2x)(x^4) + (2x)(-x^3) + (2x)(3) + (-1)(x^4) + (-1)(-x^3) + (-1)*(3)

Simplifying further:

x^7 - x^6 + 3x^3 + 2x^5 - 2x^4 + 6x - x^4 + x^3 - 3

Combining like terms:

x^7 - x^6 + 2x^5 - 3x^4 + 4x^3 + 6x - 3

Therefore, the expression representing the product of (x^3+2x-1) and (x^4-x^3+3) is x^7 - x^6 + 2x^5 - 3x^4 + 4x^3 + 6x - 3.

Answer: the answer is (3,-2)

Step-by-step explanation: when you rotate a point about the origin 180 degrees clockwise, (x,y) turns into (-x,-y)

therefore

(-3,2) becomes (3,-2)

I'm pretty sure

The solution to the system of equations is (a) (1, 0)

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

The graph

The point of intersection of the lines of the graph represent the solution to the system graphed

From the graph, we have the intersection point to be

(x, y) = (1, 0)

This means that

x = 1 and y = 0

Hence, the solution to the system of equations is (a) (1, 0)

Read more about equations at

brainly.com/question/148035

#SPJ1

You will need to purchase approximately 1/42 of a tube, which is less than a full tube. In practical terms, you would need to purchase at least one tube to meet your requirement of 42 ounces of capsaicin arthritis rub.

To determine the number of tubes of capsaicin arthritis rub you will need to purchase, we can divide the total required quantity by the quantity in each tube.

Given that the cost of capsaicin arthritis rub is $21 and you need to buy 42 ounces, we need to find out how many ounces are in each tube.

Let's assume that each tube contains x ounces of capsaicin arthritis rub.

Now we can set up a proportion to solve for x:

42 ounces / x tubes = 1 tube / x ounces

Cross-multiplying gives us:

42x = 1 * x

Simplifying the equation:

42x = x

Dividing both sides of the equation by x (since x cannot be zero):

42 = 1

Since this equation is not true, it means that there is an error in our assumption. We need to revise our assumption.

Let's assume that each tube contains 1 ounce of capsaicin arthritis rub.

Now we can set up a new proportion:

42 ounces / x tubes = 1 tube / 1 ounce

Cross-multiplying gives us:

42x = 1 * 1

Simplifying the equation:

42x = 1

Dividing both sides of the equation by 42:

x = 1/42

As a result, you will need to buy less than a full tube—roughly 1/42 of a tube. In order to get the 42 ounces of capsaicin arthritis rub you need, you would essentially need to buy at least one tube.

for such more question on purchase

https://brainly.com/question/28787564

#SPJ8

The given statement "An event with probability 3/4 is more likely to happen than an event with probability 4/5" is true.

The reason why we say an event with a higher probability is more likely to happen is because probability is the measure of how often an event will occur during a large number of trials.

Therefore, when we compare the probabilities of two events, we can expect that the one with the higher probability will occur more often and therefore is more likely to happen.For instance, in the context of a coin flip, the probability of getting heads is 1/2 while the probability of getting tails is also 1/2.

Therefore, both events are equally likely to happen. On the other hand, if we were to compare the probability of rolling a six-sided die and getting a 1, which has a probability of 1/6, with the probability of rolling the die and getting a number less than or equal to 4, which has a probability of 4/6 or 2/3, we can say that the latter is more likely to happen since it has a higher probability.

For more such questions on probability, click on:

https://brainly.com/question/13604758

#SPJ8

Step-by-step explanation:

in the formula

y = Ae^rt

y is 675,000

A is 250,000

r is 0.08

to get the value of t

y = Ae^rt

y/A = e^rt

ln(y/A) = rt

[ln(y/A)]/r = t

Answer:

  (a)  10, $2088.81

  (b)  see attached

  (c)  B. increases at a slower rate

Step-by-step explanation:

Given the cost function g(x) = -1736.7 +1661.4·ln(x) for the average dollar cost of health insurance in year x after 2000, you want the cost in 2010, a graph for the years 2006 to 2015, and a description of the shape of the curve.

The value of x is years after 2000, so for the year 2010, the value of x is ...

  x = 2010 -2000 = 10

Substituting 10 for x in the function will give the cost in 2010. That is ...

  g(10) = -1736.7 +1661.4·ln(10) ≈ 2088.81

The cost in 2010 is about $2088.81.

The second attachment shows a graphing calculator's rendition of the graph. We note it has positive slope everywhere, but does not intersect the lines y=1000 or y=3000. This eliminates choices A, C, and D, leaving choice B for the graph.

The logarithm function has positive and decreasing slope. The function here is a scaled and shifted version of the logarithm function, but it still has positive and decreasing slope. That is, ...

 the average cost increases at a slower rate as time goes on

<95141404393>