Find the 10 th term of each geometric sequence. a₁₁ =-5, r=-1/2

Answer:

Graph attached

Step-by-step explanation:

Find algebraically y values for x = -2 and x = 2 and connect the two points by a line

Equation: y = 3x + 2

For x = -2, y = 3(-2) + 2 = -6 + 2 = -4

For x = 2, y = 3(2) + 2 = 6 + 2 = 8

So the two points are (-2, -4) and (2, 8)

We have proved that , the ΔABE is congruent to ΔCDE i.e., ΔABE ≅ ΔCDE

It is given that AB║ CD and AB ≅ DC.

We have to prove that ΔABE is congruent to ΔCDE i.e., ΔABE ≅ ΔCDE.

What is the SAS rule of congruency of triangles ?

SAS axiom states that if two sides and the included angle of one triangle are equal to two sides and included angle of other triangle, then triangles are congruent.

As per the question ;

AB║ CD and AB ≅ DC

The two triangles are ΔABE and ΔCDE

So ,

AB = CD (from given data)

also ;

Included angles of two triangles are equal ;

∴

∠ABE = ∠CDE (from given data)

and

BE = BE (common)

∴ Both triangles are congruent to each other ;

i.e.,

ΔABE ≅ ΔCDE.

by SAS axiom.

Thus , the ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX

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If TQ = 2x - 6 and RQ = x + 3 then the measure of TQ = 12.

The perpendicular bisector theorem states that if a point is on a segment's perpendicular bisector, it is equidistant from the segment's endpoints.

According to the perpendicular bisector theorem, any point on the perpendicular bisector is equidistant from both ends of the line segment on which it is drawn. If a pillar stands at an angle in the center of a bridge, all of its points will be equidistant from the bridge's end points.

Where, TQ = 2x - 6 and RQ = x + 3

By the Perpendicular Bisector Theorem, RQ = TQ.

2x - 6 = x + 3

x = 9

Substitute the value of x in TQ, we get

TQ = 2(9) - 6

= 18 - 6

= 12

Therefore, the value of TQ = 12.

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The given situation shows an arithmetic sequence and the number of sales in the week 50 can be determined by using the nth term formula of arithmetic sequence. The sales in all 50 weeks can be determined by using the formula for sum of finite arithmetic sequence.

An arithmetic sequence is an ordered set of numbers that have a constant difference called a common difference between consecutive terms. Each term is obtained by adding the common difference to the previous term.

In the given situation, the first term (a) is the number of sales to be made in the first week. Hence, a = 10

The common difference (d) is the number added to get the number of sales in the next week. Hence,

d = 1

Hence, in the 2nd week the number of sales should be 11 and in 3rd week it should be 12.

Using the formula for nth term and n = 50,

an=a+(n-1)d

a50=10+(50-1)1

a50=10+(49)1

a50=10+49=59

The formula of finding the sum of the finite arithmetic sequence:

Sn=(n/2)(a1+an)

S50=(50/2)(10+59)

S50=25(69)=1725

Hence, the number of sales in the 50th week is 59 and the total number of sales made in the 50 weeks is 1725.

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Answer:

hu7

h

Step-by-step explanation:

jjjuuuuyyytfgggggggg

The glide reflection  ( x + 5.5 , y ) is  that is reflected in the line that separates the left prints from the right prints.

A glide translation is what?

Now, let's assume that the initial position is (x , y) .

Since, the average stride length of a turkey is about 11 inches; also since the turkey has two legs, therefore, the average stride length between the two legs is as shown below:

average = 11/2  = 5.5

Thus, the glide reflection is ( x + 5.5 , y )

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Answer:

Step-by-step explanation:

Point slope form y-y₁ = m(x-x₁)

y-4 = 6(x + 1)

y-4 = 6x + 6

y = 6x + 10

Answer :f(x) = -5x + 250

Step-by-step explanation:

* Lets  explain how to solve the problem

- In week 10 the manufacturer fixed 200 cars

- In week 15, the manufacturer fixed 175 cars

- the reduction in the number of cars each week is linear

- The form of the linear equation is y = mx + c, where m is the slope of

the line which represent the equation and c is the y-intercept

- The slope of the line m =

 where (x1 , y1) and (x2 , y2) are two points on the line

* Lets solve the problem

- Assume that the weeks' number is x and the cars' number is y

∴ (10 , 200) and (15 , 175) are two points on the line which represent

 the linear equation between the cars' numbers and the weeks

 numbers

∵ Point (x1 , y1) is (10 , 200) and point (x2 , y2) is (15 , 175)

∴ x1 = 10 , x2 = 15 and y1 = 200 and y2 = 175

- Use the rule of the slope above to find m

∴

- Substitute the value of x in the form of the linear equation above

∴ y = -5x + c

- To find c substitute x and y by one the coordinates of one of the

 two points

∵ x = 10 when y = 200

∴ 200 = -5(10) + c

∴ 200 = -50 + c

- Add 50 to both sides

∴ 250 = c

- Substitute the value of c by 250

∴ y = -5x + 250, where the number of cars seen each week is y and

 x is the number of the week

∵ f(x) = y

∴ f(x) = -5x + 250

Step-by-step explanation:

Answer:

its B

Step-by-step explanation:

The ladder can reach 21.17 feet high up of Denise's house.

Given,

The length of ladder Denise used to clean the outside of her second story windows = 24 feet

The distance between the base of the ladder and house = 13 feet

We have to find the height of the house which the ladder can reach:

For that we can use Pythagorean Theorem.

That is,

Hypotenuse² = Altitude² + Base²

Here,

Hypotenuse is the length of the ladder = 24 feet

Altitude is the height of the house ladder can reach = x

Base is the distance between base of the ladder and house = 13 feet

Therefore,

24² = x² + 13²

576 = x² + 169

x² = 576 - 169

x² = 407

x = [tex]\sqrt{407}[/tex]

x = 21.17

That is, the ladder can reach 21.17 feet high up of Denise's house

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Answer:

15.71 cm

Step-by-step explanation:

circumference is [tex]\pi[/tex]d

diameter is 2r

radius = 2.5 cm so the diameter is 2.5*2 = 5 cm

circumference = [tex]\pi[/tex] (5) -> 15.707

rounded to the nearest hundredth is 15.71 cm

∠1 and ∠11 are corresponding angles.

The alternates interior angles are formed when the transversal line intersects the two  coplanar lines as the name the angles are interior to the figure and are alternative to each other as well.

Alternate exterior angles are at the opposite side of the transversal line and are at external to the figure or we can say that on outside boundaries of the figure.

These angles are the same side of any two of the parallel lines in the figure cut by the transversal line . They show a correspondence behavior with respect to each other.

When any of the two lines in figure are cut by a transversal line, then the pair of angles on any of the one side of the transversal  line and interior of  the two lines are called the consecutive interior angle.

According to given question ∠1 and ∠11 are corresponding angles.

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The complete question :

Identify pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

∠1 and ∠ 11

For the linear equation C = kl, where c, cost is the local variable and it takes 49.4 cents more for a 30 min local call. The dependent variable is the price of a local call.

There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.

The equation representing the situation

C = kl

where c depicts the cost and l is the length of call.

The dependent variable is the price of a local call.

The term "mord more" denotes that we are searching for the price difference between a 4 minute call and a 30 minute call, or the price of a 26 minute call.

The cost for 26 minutes will be 49.4 cents.

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Answer:

The area of each cookie is 254.3

Answer: It is 32

Step-by-step explanation:

Answer: Maybe f I'm not sure

Step-by-step explanation:

Answer:

226.2 miles

Step-by-step explanation:

8.7 x 26 = 226.2

The solution of the equation is  (-3, 6).

-3c - 3y = -9

5c - 2y = -27

Therefore, using elimination method, the equation can be solved as follows:

multiply equation(ii) by 1.5(3  /2)

-3c - 3y = -9

7.5c - 3y = - 40.5

subtract equation(i) from equation(ii)

10.5c = - 31.5

divide both sides by 10.5

c = -31.5 / 10.5

c = -3

Therefore,

5c - 2y = -27

5(-3) - 2y = -27

-15 - 2y = -27

-2y = -27 + 15

-2y = - 12

divide both sides by -2

y = -12 / -2

y = 6

Therefore, the solution of the equation is  (-3, 6).

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The value of x is 18° and the value of the angles A and B are 73° and 107° respectively.

We are given the angle measurements as:

A = (6x - 35)°

B = (3x + 53)°

We need to solve for x and find the values of A and B

We know that co- interior angles are supplementary.

So, we get that:

A + B = 180°

Substituting the values of A and B in the above equation, we get that:

6 x - 35 + 3 x + 53 = 180

9 x + 18 = 180

9 x = 180 - 18

9 x = 162

x = 162 / 9

x = 18

So, we now get that:

A = (6x - 35)°

A = (6(18) - 35)°

A =(108 - 35)°

A = 73°

B = (3 x + 53)°

B = (3 (18) + 53)°

B = ( 54 + 53 )°

B = 107°

Therefore, we get that the  value of x is 18° and the value of the angles A and B are 73° and 107° respectively.

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Yes, the results of dividing X by a negative value and dividing X by a positive value are different. If we divide X by a negative value, the result will be negative, and if we divide X by a positive value, the result will be positive.

For instance:

It is true that 8 > 2 is unequal.

Divide both sides by 2, then:

True inequality also exists when 4 > 1. Due to the fact that we divided by a positive number, the inequality symbol remained.

Let's begin once more with

8 > 2, and apply a -2 to both sides.

-4 > -1 is erroneous. The inequality is no longer valid if the inequality sign changes when both sides are divided by a negative integer. When dividing both sides by a negative integer, the inequality sign must be changed in order to maintain its validity.

8 > 2

Add a -1 to both sides.

True for -4 < -1.

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Answer: 1/6

Step-by-step explanation:

[tex]\displaystyle\\\frac{2}{12} =\\\\\frac{2}{2*6}=\\\\\frac{1}{6}[/tex]

Sn = a(1 - rⁿ)/(1 - r) is the formula for the sum of a finite number of terms in a geometric series, where is the number of terms, is the first term, and is the common ratio.

The sum of the finite geometric series Σ⁴ n=1 (1/2)ⁿ⁺¹ is 0.46875.

The equation be Sn = a(1 - rⁿ)/(1 - r), where s exists the total, a1 exists the series first term, and r exists the common ratio, is a general formula for estimating the sum of an finite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.

Let the sum of the finite geometric series be Σ⁴ n=1 (1/2)ⁿ⁺¹

Σ⁴ n=1 (1/2)ⁿ⁺¹ = (1/2)¹⁺¹ + (1/2)²⁺¹ +(1/2)³⁺¹ + (1/2)⁴⁺¹

simplifying the above equation, we get

= (1/2)² + (1/2)³ + (1/2)⁴ + (1/2)⁴⁺¹

= (1/4) + (1/8) + (1/16) + (1/32)

Where, the first term is a = 1/4

common ratio be r = 1/2

n th term be n = 4

Let the equation be Sn = a(1 - rⁿ)/(1 - r)

substitute the values in the above equation, we get

S4 = (1/4) (1-(1/2)⁴) / (1 - (1/2))

simplifying the above equation, we get

S4 = (1/4) (15/16) × 2 = 15/32 = 0.46875

Therefore, the sum of the finite geometric series Σ⁴ n=1 (1/2)ⁿ⁺¹ is 0.46875.

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Carter needs to ride 3.9 miles per day on an average to meet his target of riding 28.7 miles in a week.

We are given that:

The total number of miles that needs to be ridden by Carter = 28.7 miles

Now, he has already ridden 17 miles this week

So, the miles left to be ridden = 28.7 miles - 17 miles

Number of miles left = 11.7 miles.

Now, he has 3 more days to finish his target.

So, on an average, he should ride:

Average = 11.7 miles / 3 days = 3.8 miles per day

Therefore, Carter needs to ride 3.9 miles per day on an average to meet his target of riding 28.7 miles in a week.

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Answer:

Step-by-step explanation:

A 270 degrees anticlockwise rotation is the same result as the rotation of the 90 degrees.

Money received in tenth month: $104.

A formula that describes this arithmetic sequence: [tex]a_n=a_{n-1}+n[/tex], n > 1., where n = number of month.

A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:

Money received in first four months: $50, $52, $55, %59.

To find: Money received in tenth month.

Finding:

As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.

That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.

Thus, for the tenth month, we can use the formula of recursion, given by: [tex]a_n=a_{n-1}+n[/tex], n ≥ 1.

For a₁ = 50, a₂ = a₁ + 2

=> a₂ = 50 + 2

This way, a₅ = a₄ + 5

=> a₅ = 59 + 5 = 64

a₆ = a₅ + 6

=> a₆ = 64 + 6 = 70

a₇ = a₆ + 7

=> a₇ = 70 + 7 = 77

a₈ = a₇ + 8

=> a₈ = 77 + 8 = 85

a₉ = a₈ + 9

=> a₉ = 85 + 9 = 94

a₁₀ = a₉ + 10

=> a₁₀ = 94 + 10 = 104

Thus, the payment received in tenth month will be $104.

A formula that describes this arithmetic sequence: [tex]a_n=a_{n-1}+n[/tex], n > 1., where n = number of month.

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Using direct variation, the value of x for equation y = 5/-3 (x) is 3/5 when y = -1

When x is not equal to zero, an equation of the form y = kx describes the linear function known as direct variation. When x is not equal to zero and k is a nonzero real number constant, the equation of the form xy = k describes the nonlinear function known as inverse variation.

Using direct variation,

y = kx

⇒ 5 = k(-3)

⇒ k = 5 / -3

for y = -1

y = 5/-3 (x)

⇒ -1 = 5/-3 × x

⇒ x = 3/5

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