Find the indicated term for each geometric sequence.

2,8,32…; the 9th term

According to SAS congruent the △abc congruent △def. Thus using the given information, it can be prove.

What is congruent?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

There are four rules to prove congruency. They are SAS, AA, ASA, and SSS.

Given that ∠c ≅ ∠f

ab ≅ de

bc ≅ ef.

According to SAS rule, if two sides and one angle of a triangle is equal to two sides and one angle of another triangle, they the triangle are congruent.

Here two sides and one angle of △abc  is congruent of two sides and one angle of △def.

Therefore △abc congruent △def.

To learn more about congruency, click on below link:

https://brainly.com/question/20333087

#SPJ4

The given measurement not forming the right triangle. So the option D is correct.

In the given question, we have to determine if a triangle with the following measurements is a right triangle.

The given measurement is:

a=14, b=16, c=18

We have to explain why or why not the given statement is correct or not.

The given options are:

(a) No. 14+16 does not equal 18

(b) Yes. 14^2+16^2=18^2

(c) Yes. The longest side is c, which is 18.

(d) No. 14^2+16^2 does not equal 18^2

As we know that the given measurement form right triangle we he follows the Pythagorean Theorem.

To prove the right triangle, the square of largest value is equal to the sum of square of other two values. So;

18^2 = 14^2+16^2

324 = 196 + 256

324 = 452(False)

So, the given measurement not forming the right triangle. So the option D is correct.

To learn more about Pythagorean Theorem link is here

brainly.com/question/14930619

#SPJ4

The actual average score on the vocabulary test is 91.8.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Here, Mr. Johnson predicted the average score on the vocabulary test he gave would be 85 points and his prediction was 8% lower than the actual average score.

The actual score will be:

= 85 + (8% × 85)

= 85 + 6.8

= 91.8

The actual score is 91.8.

Learn more about percentages on:

brainly.com/question/24304697

#SPJ1

The inequality of the solution is  x   >   15.

Make use of the following procedures to solve an inequality:

We need to eliminate the coefficient that multiplies the variable in this linear inequality in order to isolate it.

By dividing both sides by 4, this may be done.

The inequality of  the solution is

  4x≥60.

=[tex]\frac{4x}{4} \geq\frac{60}{4} \\\\= \frac{x}{1} \geq 15\\\\x\geq 15[/tex]

The inequality of the solution is  x   >   15.

To learn more about inequality refer to:

https://brainly.com/question/24372553

#SPJ1

The value of h in the statement one-seventh plus h equals nine sevenths

is 8/7.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The main concept of numerical expression is to interpret the data and convert it into numbers and their operations.

The given statement one seventh plus h equals nine sevenths can be numerically expressed as (1/7) + h = (9/7).

h = 9/7 - 1/7.

h = (9 - 1)/7.

h = 8/7.

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ1

The equation that is a quadratic is 2(x + 5)4 + 2x² + 5 = 0

Option C is the correct answer.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

A quadratic equation is an equation with a second degree in x.

Now,

[tex]x^4[/tex] – 6x² – 27 = 0

This is not second-degree in x.

3[tex]x^4[/tex] = 2x

3x³ = 2

This is not the second degree in z.

2(x + 5)4 + 2x² + 5 = 0

8x + 40 + 2x² + 5 = 0

2x² + 8x + 45 = 0

This is in the second degree in x.

6(2x + 4)2 = (2x + 4) + 2

24x + 48 = 2x + 4 + 2

22x + 42 = 0

This is not in the second degree of x.

6[tex]x^4[/tex] = -x² + 5

This is not in the second degree of x.

8[tex]x^4[/tex] + 2x² – 4x = 0

This is not in the second degree of x.

Thus,

The quadratic equation is 2(x + 5)4 + 2x² + 5 = 0

Option C is the correct answer.

Learn more about polynomials here:

https://brainly.com/question/2284746

#SPJ1

The corresponding sides of two triangles are proportionate if they are identical then the length of side ZX exists 10.5 units.

If one of the triangle's angles is 90 degrees, the triangle is said to be right-angled. 90 degrees is the sum of the other two angles. Perpendicular and the triangle's base make up the sides that the right angle is formed from. The hypotenuse, or third side, is the longest of the three. It is also known as the hypotenuse.

If two triangles are similar, then their corresponding sides are proportional.

Since [tex]$\triangle A B C \sim \triangle X Y Z$[/tex], therefore

AB/X Y = BC/YZ = CA/ZX

substitute the values in the above equation, we get

2/7 = 4/14 = 3/N

2/7 = 2/7 = 3/N

2/7 = 3/N

On cross multiplication, we get

2 × N = 3 × 7

2N = 21

Divide both sides by 2

N = 21/2

N = 10.5

Therefore, the length of side ZX exists 10.5 units.

The complete question is:

In the figure below, ABC is similar to XYZ . What is the length of ZX ? Enter only the number as an integer or decimal. An image shows two similar right triangles, A B C and X Y Z. Triangle A B C is smaller than triangle X Y Z. In triangle A B C, side A B is 2, side B C is 4, and side C A is 3. In triangle X Y Z, side X Y is 7, side Y Z is 14, and side Z X is labeled N.

To learn more about similar right triangles refer to:

https://brainly.com/question/8119934

#SPJ1

Answer: $647,574

Step-by-step explanation:

Capital assets are significant pieces of property such as homes, cars, investment properties, stocks, bonds, and collectibles or art. For businesses, a capital asset is an asset with a useful life longer than a year that is not intended for sale in the regular course of the business's operation.

The capital asset is recorded as its value regardless of any loan that may have been used to purchase it.

Capital assets here are: Home value, work equipment, car, and investments.

All other items are liabilliabilities.

The total value of the doctor's capital assets will be $647,574. Then the correct option is D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

Significant pieces of property including houses, automobiles, rental properties, stocks, bonds, and collectibles or works of art are referred to as capital assets. An asset having a useful life longer than a year that is not intended for sale during normal company operations is referred to as a capital asset for enterprises.

The assets and liabilities of a doctor are listed below.

Home Value                         $475,732

Mortgage                              $105,678

Credit Card Balance             $7,264

Owned Work Equipment     $45,798

Car Value                              $50,761

Investments                          $75,283

Personal Loan                      $32,187

The total value of the doctor's capital assets will be given as,

⇒ $475,732 + $45,798 + $50,761 + $75,283

⇒ $647,574

The total value of the doctor's capital assets will be $647,574. Then the correct option is D.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

Answer:

Triangle PQR maps onto triangle KLM. This is possible because △PQR ≅ △KLM by ASA, and one congruent figure can be mapped onto another using rigid motions.

Step-by-step explanation:

For the first blank, we are given congruence statements for 1 side on each triangle and their two adjacent angles. This means we can use the Angle-Side-Angle theorem to declare △PQR and △KLM congruent.

For the second blank, we know that rigid transformations do not change the figure, they simply move its position on a plane, so this is the correct answer; had the △PQR and △KLM not been congruent, a non-rigid transformation would have to have occured, but this is not the case here.

Answer:

Step-by-step explanation:

Given triangles PQR and KLM with QR ≅ LM, ∠Q ≅ ∠L, and ∠R ≅ ∠M, you want to know the applicable congruence postulate and whether the triangles are mapped to each other by rigid or non-rigid motion.

The segment QR has angle Q at one end and angle R at the other end. That means the side lies between the two angles. Likewise, segment LM lies between angles L and M.

When claiming congruence of these triangles, the appropriate postulate is the one that refers to the geometry with the congruent side between the congruent angles: ASA.

"Rigid" motion is motion that preserves angle and length measures. By contrast, "non-rigid" motion may involve stretching or compression in one or more directions. It may or may not preserve angles or lengths.

Congruence is about showing that angles and lengths are the same from one figure to another. If you want to map congruent figures to each other, you must do so using rigid motion.

__

Additional comment

The rigid motions include ...

<95141404393>

Answer:

x = 17√3 ;  y = 34√2 ; z = 34

Step-by-step explanation:

angle 30° = hypotenuse double of leg

hypotenuse = 17 · 2 = 34

x = 17 · √3 = 17√3

Angle of 45 degrees = two equal legs

z = 34

For the Pythagorean theorem

y = [tex]\sqrt{34^2 + 34^2} = \sqrt{2 (34)^2} = 34\sqrt{2}[/tex]

Answer:

Your answer is: x = 17√3 ;  y = 34√2 ; z = 34. Hope it helps.

Step-by-step explanation:

Answer:

To approximate the square root of 46 to the tenths place, we need to find the two-digit number that is closest to the square root of 46. Since the square root of 46 is between 6 and 7, we can estimate that it is about 6.5. We can check this estimate by finding the square of 6.5, which is 42.25. This is close to 46, but it is still a little bit lower than 46, so we can estimate that the square root of 46 is slightly larger than 6.5. Therefore, an approximation of the square root of 46 to the tenths place is 6.6.

Step-by-step explanation:

Step-by-step explanation:

3x(-2x + 5) = 3×-2×x×x + 3×5×x =

= -6x² + 15x

so, the 4th answer option is correct.

The system A has no solution.

The system B has the solution y=( 3-x )/3

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

System A:

x+3y=9..........(1)

-x-3y=9 ..........(2)

(1) => x=9-3y........(3)

Substitute (3) into (2)

(2) = >  - ( 9-3y ) - 3y = 9

          -9 + 3y - 3y = 9

          -9 =9

This is false.

So, the system has no solution.

System B:

-x-3y=-3..........(1)

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

(2) => x=3-3y........(3)

Substitute (3) into (1)

-(3-3y)-3y=-3

-3+3y-3y= -3

-3=-3

This is true,

So, the solution is:

x=3-3y

=> 3y= 3-x

=> y=( 3-x )/3

To learn more about the solution of an equation from the given link

https://brainly.com/question/22688504

#SPJ1

The value of x is 11.8. So the option c is correct.

In the given question, we have to find the value of x.

The given options are:

(a) 12.2

(b) 24.5

(c) 11.8

(d) 8.4

To find the value of x we use the trigonometry ratio.

As we know that cosine is the ration of adjacent side and hypotenuse.

From the given diagram

Cos(46) = x/17

Now simplifying

0.695=x/17

Multiply by 17 on both side, we get;

x = 11.8

Hence, the value of x is 11.8. So the option c is correct.

To learn more about the trigonometry ratio link is here

brainly.com/question/25122835

#SPJ4

The equations are x+y=50 and 7x + 12y = 450

x = the number of mirrors = 30

y = the number of pouches = 20

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Let x be the number of mirrors

Let y be the number of pouches

x+y=50......(1)

Each mirror is $7

cost of x mirrors = 7x

Each pouch is $12.

cost of y pouches = 12y

7x + 12y = 450 .........(2)

(1) => x=50-y ...........(3)

Substitute (3) into (2)

(2) =>  7(50-y)  + 12y = 450

          350 - 7y + 12y = 450

               5y = 450 -   350 = 100

                 y= 100/5 = 20

(1) => x = 50 - 20 = 30

Thus,  x = the number of mirrors = 30

          y = the number of pouches = 20

To learn more about the solution of an equation from the given link

https://brainly.com/question/22688504

#SPJ1

Using the corresponding angle theorem, the value of y is 36 degree.

In the given question, b||c.

We have to find the value of y.

Given: b||c

Find: Value of y

Let x be the value of side angle of (2y+34) degree.

So, using the corresponding angle theorem

x = 74 degree

As we know that the sum of straight line is 180 degree.

So 2y+34+x = 180

Now putting the value of x

2y+34+74=180

After simplifying

2y+108=180

Subtract 108 on both side, we get

2y=72

Divide by 2 on both side, we get

y=36

Hence, the value of y is 36 degree.

To learn more about Corresponding Angle Theorem link is here

brainly.com/question/16017873

#SPJ4

Answer:

[tex]\sqrt[3]{3375}=15[/tex]

Step-by-step explanation:

[tex]3375=15^2 \implies \sqrt[3]{3375}=15[/tex]

Answer:5/5

Step-by-step explanation:

5 divided by 5 is 1

If the fixed cost is $15, it is able to be removed from the two-hour charge to give the charge of ONLY the two hours, which is $150.

This means the hourly charge is $150÷2, which is $75

Answer:

98.3% or 98% if your doing sig. figs.

Step-by-step explanation:

you take 14.75 (the approximated) and divide it by the actual 15

Cost of shrub is $4 and Cost of hosta is $3. Cost is the value of money that was spent on producing or providing a service and is therefore no longer available for use.

The term "cost" can refer to the amount of money or other resources that are required to produce, acquire, or obtain something. In business and economics, cost is often used to refer to the total expense associated with a product or service, including materials, labor, and other expenses.

Micaela spent a total of $33 on 3 hostas and 6 shrubs. Since the cost of the hostas is H x 3 and the cost of the shrubs is S x 6, we can write the following equation:

H * 3 + S * 6 = 33

Similarly, Sumalee spent a total of $42 on 6 hostas and 6 shrubs, so we can write the following equation:

H * 6 + S * 6 = 42

cost 3 hostas and 6 shrubs = $33

cost 6 hostas and 6 shrubs = $42

Cost difference 33 - 42 = 9

So, cost of 3 hostas = $9

Cost of one hosta = $9/3 = $3

$9 + cost of 6 shrubs = $33

cost of 6 shrubs = $33- $9 = $24

Cost of one shrub = $24/6 = $4

Cost of shrub is $4 and Cost of hosta is $3.

To learn more about cost refer :

https://brainly.com/question/28424365

#SPJ1

Answer:

To solve the equation X/5 = -2 in one step, we can multiply both sides of the equation by 5 to isolate the variable X. This gives us the equation X = -2 * 5 = -10. Therefore, the value of X that satisfies the equation X/5 = -2 is X = -10.

Step-by-step explanation:

Percent to the nearest whole number = 7%

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Probability = (Number of possible outcomes)/(Total number of outcomes)

Total number of outcomes = 2 + 15 + 2 + 11 = 30

Number of possible outcomes = 2

Probability = 2/30 = 1/15 = 0.0666

Percent to the nearest whole number =  0.0666 *100 = 7%

To learn more about the probability from the given link

https://brainly.com/question/24756209

#SPJ1

Answer:7

Step-by-step explanation:

Answer:

x=8/7

Step-by-step explanation:

16+7/x=24

Subtract 16 on each side

7/x=8

multiply 1/7 on each side

x=8/7

The expression for the nth term is aₙ = 37+6n

An arithmetic sequence is a type of sequence in which the difference between the successive and preceding term is constant.

Given that, The 9th term of an arithmetic sequence is -5 and the 15th term is 31

The formula for nth term is given by;

aₙ = a+(n-1)xd

Where, a is the first term

n = number of terms

d = common difference

a₉ = a+(9-1)xd

a+8d = -5.......(i)

And

a₁₅ = a+(15-1)xd

a+14d = 31........(ii)

Solving the equation, we get,

d = 6

Putting, d = 6 in eq(i)

a+8x6 = -5

a = -5+48

a = 43

Now solving for nth term,

aₙ = 43+(n-1)x6

aₙ = 43+6n-6

aₙ  = 37+6n

Hence, the nth term is (37+6n)

For more references on arithmetic sequence, click;

https://brainly.com/question/15412619

#SPJ1

Answer: rotation 90 degrees counterclockwise about the origin I believe. lmk

Step-by-step explanation: counterclockwise is the key word. im jus using common sense cuz counterclock wise is from the left, and there is a rotation. lmk if it wrong tho