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The 17 th term of the Arithmetic Progression (AP) is found to be a₁₇ = 26.

In Arithmetic Progression (AP), the difference between the two numerical orders is a constant value. Arithmetic Sequence is another name for it.

We'd come across a few important words in AP, denoted as:

The AP may also be characterized in concepts of common distinctions, as shown below.

Now, as per the given data in the question;

16th term; a₁₆ = 18

Common difference; d = 5

Then, the 17th term would be calculated as;

Use the common difference formula;

d = a₁₇ - a₁₆

a₁₇ = a₁₆ + d

a₁₇ = 21 + 5

a₁₇ = 26

Therefore, the value of the 17th term of a AP is found as 26.

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Answer:

infinite number of solutions

Step-by-step explanation:

3(n + 11) - 5n = - 2(n - 12) + 9 ← distribute parenthesis on both sides

3n + 33 - 5n = - 2n + 24 + 9 , that is

- 2n + 33 = - 2n + 33

since the expressions on both sides are the same then any value of n will make the equation true.

thus the equation has an infinite number of solutions

Answer:

Any real value. Infinite no. of solutions.

Step-by-step explanation:

Let's open the bracket first. Multiply the term outside the bracket with each term inside the bracket.

[tex]\Rightarrow[/tex] 3(n+11)-5n = -2(n-12)+9

[tex]\Rightarrow[/tex] 3n + 33 - 5n = -2n + 24 + 9

Now simplify the n terms on both sides

[tex]\Rightarrow[/tex] -2n + 33 = -2n + 33

Here both LHS and RHS are same. And the terms gets canceled. Any real value of n satisfy the above equation.

There are points P, M & Q collinear are not collinear because they didn't lie in the same line but they are coplanar.

Collinear points are defined as points that are along a straight line represented by a collinear. Because a straight line may be drawn continuously between any two points, they are always collinear. There can be a collinear relationship from three or more points, although it is not necessary.

We have given a line and a planar surface with points O, M, N, Q, P, S, and T.

Here three planes that intersect at point P which are PMN plane, PQM plane and QST plane.

Here three planes that intersect at point S which are STN plane, MNS plane and QST plane.

Here points P, M & Q collinear are not collinear because they didn't lie in the same line but they are coplanar.

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Answer:

x = 16

Step-by-step explanation:

16 and x have the same length.

Answer:

sum is 82

Step-by-step explanation:

[tex]\sf \textsf{The 9th square number is }9^2 = 81[/tex]

[tex]\sf \textsf{The 1st square number is }1^2 = 1.[/tex]

In order to find the sum of these two square numbers, simply add them together:

[tex]\sf Sum = 81 + 1 = 82[/tex]

The sum of the 9th square number and the 1st square number is 82.

Answer:

The expression that is equivalent to -2y-8+4y is 2y-8.

The exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).

Exterior Angle Inequality Theorem

According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles. The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.

A triangle's exterior angle is always greater than its two remote interior angles.

By the Exterior Angle Inequality Theorem, the exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).

m ∠ 7 < m ∠ 5 and m ∠ 8 < m ∠ 5 .

Therefore, the correct answer is ∠ 7 and ∠ 8.

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Answer:

1.-150 250-400 is -150

2. 6570 6288+282=6570

3.123 because 102+21 is 123

Step-by-step explanation:

can i have the brainlieast award?

Answer:

13 cups of milk I think

Step-by-step explanation:

Answer:

i just need a points thnkyuuuu

The principal of the car loan is $23,400, the interest rate of the car loan is 1.60% and the monthly payment is $375.

Given that, balance after 3 months = 22,275 and balance after 12 months = 18,900.

Average payment rate means, for any date of determination, the sum of the monthly payment rates for the prior three monthly periods divided by three.

Now, the difference of payment = 22,275 - 18,900

= $3,375

The difference of time = 12 - 3 = 9 months

So, the payment per month = 3,375 / 9

= $375 per month.

Now, 375 x 12 = $4,500

Principal amount = 4,500 + 18,900

= 23,400

Rate = 375 / 23400 × 100

= 0.016 × 100 = 1.60%

Therefore, the principal of the car loan is $23,400, the interest rate of the car loan is 1.60% and the monthly payment is $375.

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Distance between the points A and B are equal to distance between points B and C.

So, The given triangle is isosceles.

And, . By using distance formula we have to write an expression for BC as,

⇒ [tex]D_{BC} = \sqrt{4a^2+b^2}[/tex]

Here,

The vertices of a triangle are A (0, 0), B (2a, b) and C (4a, 0)

We have to check the triangle is isosceles.

And, Write an expression for BC.

What is Isosceles triangle?

When two sides of a triangle are equal then the triangle is said to be isosceles triangle.

Now,

The vertices of a triangle are A (0, 0), B (2a, b) and C (4a, 0)

We have to check the triangle is isosceles.

For this we use distance formula and prove that the two sides of triangle are equal.

Distance between the points A (0, 0) and B (2a, b) is;

[tex]D_{AB} = \sqrt{(2a-0)^2 + (b-0)^2} = \sqrt{4a^2+b^2}[/tex]

And, Distance between the points B (2a, b) and C (4a, 0) is;

[tex]D_{BC} = \sqrt{(4a-2a)^2 + (0-b)^2} = \sqrt{4a^2+b^2}[/tex]

Hence, Distance between the points A and B are equal to distance between points B and C.

So, The given triangle is isosceles.

c. By using distance formula we have to write an expression for BC as,

⇒ [tex]D_{BC} = \sqrt{(4a-2a)^2 + (0-b)^2} = \sqrt{4a^2+b^2}[/tex]

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Answer: number 1. 4 number2. 7

Step-by-step explanation:

I hope this helps!

[tex]\cfrac{5}{6}\div 5\implies \cfrac{5}{6}\div \cfrac{5}{1}\implies \cfrac{5}{6}\cdot \cfrac{1}{5}\implies \cfrac{1}{6}\cdot \cfrac{5}{5}\implies \cfrac{1}{6}\cdot 1\implies \cfrac{1}{6}[/tex]

Answer:

2/3*2/1

this is the answer

Answer:

2/3 × 2/1

Hope this helps :)

Explanation below.

Step-by-step explanation:

To find the multiplication expression, use the Keep, Change, Flip (KCF) method.

Answer:

This will be a 30°-60°-90° triangle because the hypotenuse is 2 cm, which is twice the length of the shorter leg.

Option C: The value of m ∠3 is 30° (C).

As per the question, ∠4 and ∠5 form a linear pair. Therefore the sum of ∠4 and ∠5 is 180° so, so the sum of the remaining m∠1,m∠2, and m∠3 angles is 180°.

So, m∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360° (as the total angle is 360°).

Now, m∠4 + m∠5 = 180°(∠4 and ∠5 form a linear pair). (∴ m∠1 + m∠2 + m∠3 = 180°). Now we will put the given values and will try to find out the value of x.

2x + (3x-20) + (x-4) = 180

[m ∠1 = 2 x, m ∠2 = 3 x-20, and m ∠3 = x-4]

or,

6x-24=180

or,

6x = 180+24

or,

6x = 204

or, x = 204/6

or. x = 34

As per the question we have to find out the value of m ∠3.

m ∠3 = 34° - 4° = 30° (as x = 30°)

So, m ∠3 is 30°.

If ∠4 and ∠ 5 form a linear pair. And, m ∠1=2 x, m ∠2=3 x-20, and m ∠3=x-4, the value of ∠3 is 30°. Therefore, Option C is the correct answer.

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The distance between each pair of parallel lines with the given equations y = x-11 and y = x-7 is 4 units.

We can find the points passing through the lines

Hence,

The points passing through the line y = x - 11  are:-

Let x = 11

y = 11 - 11 = 0

(11,0)

and;

Let x = 12

y = 12 -11 = 1

(12,1)

The points passing through the line y = x - 7 are:-

Let x = 7

y = 7 - 7 = 0

(7,0)

and;

Let x = 8

y = 8 -7 = 1

(8,1)

Hence, using distance formula, the distance between the parallel lines will be:-

[tex]\sqrt{(1-1)^2+(12-8)^2} =\sqrt{0+16}=\sqrt{16} =4 units[/tex]

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An arithmetic sequence (AP) is a progression in which the difference (called the tolerance) between two consecutive terms in the passage/progression is constant.

Therefore, the expression for the nth term is,

an = a₁ + (n − 1) d

and in general

an = am + (n - m) d.

where d is the difference.

For an arithmetic series with initial term a₁ and difference between terms of d

an = a₁ + (n − 1) d

We are given some of the values,

d = 6 and

S8 = 440

So, we will put the values in the formula and calculate the desired value,

a1 = 440 = a1 + ( 8 - 1 ) * 6 = a1 + 42

a1 = 440 - 42 = 398.

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Answer:

144 mg

Step-by-step explanation:

Answer:

                           11

8z² + 9z + 12 + -------

                         z  - 1

Step-by-step explanation:

x - c = x - 1

change the sign of -1 to +1

8z³ + z² + 3z -1

1 |  8     1    3   -1

     ↓     8   9   12

-------------------------

     8     9   12   11

8z² + 9z + 12 remainder of 11

I hope this helps!

Answer:

$5.05

Step-by-step explanation:

.85($5.60) + $1.79 - $1.50

$4.76 + $1.79 - $1.50 = $5.05

35 mph= .58 of a mile per minute

21 miles in 30 minutes= .7 of a mile per minute

if you multiply by 60 to see the distance in the same amount of time:

rabbit: 35 mph

fox: 42

So the fox would run a greater distance in the time given. Hope this helps!

The length of the side m are obtained using the theorem of Pythagoras and proportional triangles to give;

a) m ≈ 28.4

b) m ≈ 12.09

c) m ≈ 9.38

a) The given triangle, is a right triangle.

The length of the legs of the triangle are; 33 and 56.

According to Pythagorean theorem, the length of the hypotenuse side, l, is therefore;

l = √(33² + 56²) = 65

From the formula for the area of a triangle, we have;

Area of a triangle, A, equals half the base length multiplied by the height.

A = 0.5 × Base length × Height

For the right triangle, we have;

A = 0.5 × Leg 1 × Leg 2

Which gives;

A = 0.5 × 33 × 56 = 924

However;

A = 0.5 × l × m

Where;

l = The hypotenuse = The base length = 65

m = The height of the triangle

Which gives;

A = 0.5 × 65 × m = 924

m = 924/(0.5 × 65) ≈ 28.4

b) The side m is parallel the 14 units long side.

The proportion the side m divides a side of the triangle = 3 and 19

Given that the triangle formed by m is proportional to the larger triangle, we have;

m/14 = 19/(19+3)

c) From the proportionality of similar triangles, we have;

m/16 = 17/(14+15)

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The glide reflection  ( x + 2.5 , 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 = 5/2  = 2.5

Thus, the glide reflection is ( x + 2.5 , y )

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Step-by-step explanation:

in the morning, 222k + 111d

in the evening, 222k + 111d

grams, g = 444k + 222d