Quadrilateral PQRS is parallelogram.What is the length of the diagonal SQ?
ST=x^2-8
TQ=3x+2
​

9514 1404 393

Answer:

  x = 50

Step-by-step explanation:

The sum of exterior angles of a convex polygon is 360°.

  130° + x° + 30° + 100° + x° = 360°

  2x° = 100° . . . . . . . . . subtract 260° and collect terms

  x = 50 . . . . . . . . divide by 2°

_____

Additional comment

If you reduce each side length to nothing, then you find the angles are measured around a central point. It becomes more clear that their sum is 360°.

You can try to show this by induction:

• According to the given closed form, we have [tex]S_1=3\times2^{1-1}+2(-1)^1=3-2=1[/tex], which agrees with the initial value S₁ = 1.

• Assume the closed form is correct for all n up to n = k. In particular, we assume

[tex]S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}[/tex]

and

[tex]S_k=3\times2^{k-1}+2(-1)^k[/tex]

We want to then use this assumption to show the closed form is correct for n = k + 1, or

[tex]S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}[/tex]

From the given recurrence, we know

[tex]S_{k+1}=S_k+2S_{k-1}[/tex]

so that

[tex]S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)[/tex]

[tex]S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}[/tex]

[tex]S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)[/tex]

[tex]S_{k+1}=3\times2^k-2(-1)^k[/tex]

[tex]S_{k+1}=3\times2^k+2(-1)(-1)^k[/tex]

[tex]\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}[/tex]

which is what we needed. QED

Answer:

The answer is in the image below

Answer:

7 and 8

Step-by-step explanation:

[tex]7^{2} =49\\\\8^{2} =64[/tex]

Answer:

9 Loaves of Bread

Through dividing 6(total bread) by 8(total cups) you get 3/4C per bread

So you multiply 12 by 3/4 or 0.75 to get 9

Answer:The mode is equal to the minimum

Step-by-step explanation:

Answer: The mode is equal to the minimum

Step-by-step explanation:

Answer:

420 + 69 = 489

Step-by-step explanation:

HOPE THIS HELPS

brainliest pls :)

Answer:

489

Step-by-step explanation:

420 + 69 = 489

Answer:

choice D) d ≥ 5

Step-by-step explanation:

Answer:

D

Step-by-step explanation: A filled bubble means that it is equal to and whichever way the arrow is point represents whether the answer is greater than or less than.

The graph representing the inequality x ≥ 23 is shown on the number line begining from 23 with a closed and shaded circle.

An inequality is an expression that shows the non equal comparison of two or more numbers and variables.

A number line can be used to represent numbers placed on regular intervals. A number line can be used to represent an inequality.

The graph representing the inequality x ≥ 23 is shown on the number line begining from 23 with a closed and shaded circle.

Find out more on inequality at: https://brainly.com/question/24372553

Answer:

72°

Step-by-step explanation:

To convert from degrees to radians, multiply the degrees by [tex]\frac{\pi }{180}[/tex].

To convert from radians to degrees, multiply the radians by [tex]\frac{180}{\pi }[/tex].

Right now you're in radians, so multiply it by [tex]\frac{180}{\pi }[/tex].

[tex]\frac{12\pi }{5}* \frac{180}{\pi }[/tex]=[tex]432[/tex]°.

Now we need to find the reference angle for 432°.

If you draw 432° starting from the right and going clockwise (because it is a positive angle, if it was negative you would go counterclockwise), it will make one full rotation, which is 360°, and you will end up in the 1st quadrant, 72° past 360°.

Depending on the quadrant you land in, there might be different operations to perform. Please check the attached image.

In this case, we're in the 1st quadrant so we can leave the angle as is.

The answer is 72°.

9514 1404 393

Answer:

  25 km/h

Step-by-step explanation:

The relation between speed, time, and distance is ...

  speed = distance/time

  distance = speed × time

__

The distance relation is used to find the distance on the first line of the table. The problem statement tells you all of the distances are the same.

The speed relation is used to find the speed on the remaining lines of the table. For the average speed, the total distance and total time are used in the computation.

The average speed is 25 km/h.

Answer:

what exactly are we solving

Step-by-step explanation:

Answer:

Each piece is 1.25m

Step-by-step explanation:

If you divide 12 1/2 by 10 you would get 1.25

Answer:

[tex] 1\frac{1} {4} \: m[/tex]

Step-by-step explanation:

Length of wire = 12½ m = 12.5 m

Number of pieces = 10

Length of each piece = 12.5/10= 1.25 m [tex] =1\frac{1} {4} \: m[/tex]

Hence, the study would require at least 385 more adult Americans to be sampled as the degree of inaccuracy is E. (e.g., 0.05).

In mathematics, proportionality is the connection between two factors that maintains a fixed ratio called scale factor. Or, to put it another way, if one variable is increased or divided by a specific number, the second variable will also be doubled or divided by that identical number, maintaining their proportionality. Calculus, algebra, and geometry are three areas of mathematics where this idea is frequently applied.

given

(a) If 20% of adult Americans favour the suggested reforms, the sample size needed at the very least is:

n = [(zα/2)² * p * (1-p)] / E²

where z/2 is the standard normal distribution's critical value for the chosen degree of confidence (e.g., 1.96 for a 95% confidence level).

The population proportion is p. (0.2 in this case)

The degree of inaccuracy is E. (e.g., 0.05)

When we enter the values, we obtain:

n = [(1.96)² * 0.2 * (1-0.2)] / 0.05²

n = 1536.64

Thus, the study would require at least 1537 more adult Americans to be sampled.

(b) The minimal sample size needed if the proposed modifications are

supported by 25% of all adult Americans is:

n = [(zα/2)² * p * (1-p)] / E²

where:

The standard normal distribution's critical value, z/2, depends on the desired level of confidence (e.g., 1.96 for a 95% confidence level).

The population proportion is p. (0.25 in this case)

The degree of inaccuracy is E. (e.g., 0.05)

When we enter the values, we obtain:

n = [(1.96)² * 0.25 * (1-0.25)] / 0.05² \sn = 384.16

Hence, the study would require at least 385 more adult Americans to be sampled as the degree of inaccuracy is E. (e.g., 0.05).

To know more about proportionality visit:

https://brainly.com/question/29126727

#SPJ1

Answer:

The triangle is a right triangle

Step-by-step explanation:

a4.4 x b11.7=c12.5                          a4.4=19.36   b11.7=136.89   12.5=156.25                  if you add a squared and b squared you get 156.26 which means its an right triangle

Answer: 40 unit²

Step-by-step explanation:

A square pyramid is composed of 1 square and 4 congruent triangles

STEP ONE. Find the area of the square.

A=b²

b=base

A=b²=4²=14

STEP TWO. Find the area of the triangle

A=(1/2)bh

b=base

h=height

A=(1/2)bh

A=(1/2)(4)(3)

A=(1/2)(12)

A=6

There are 4 congruent triangles, so 6×4=24

The surface area of whole=24+16=40 unit²

Hope this helps!! :)

Please let me know if you have any questions

Answer:

It is a rate,

A rate is the ratio between two related quantities in different units.

Miles and hours are two different units and its 50 miles per 2 hours.

Answer:

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Arrange in order

1,1,2,3,4,4,5,7,8,9

Cross off each number from each side little by little

1,2,3,4,4,5,7,8

2,3,4,4,5,7

3,4,4,5

4,4

There are two numbers left so we would find whats between them. But, since it is the same number, you just write the same one as the median.

median= 4

Answer:

18057

Step-by-step explanation:

uh just 200 x 10 = 200 add that to the 6 to make 18057$ which is the price of the second van.

Answer:

rectangular prism

Step-by-step explanation:

maybeeee

sorry if it wrong :l

Answer:

Solution is at the image

Step-by-step explanation:

Answer:

x=7

z=79

Step-by-step explanation:

13x+10=101

13x=91

x=7

180-101=79

Answer:

where is the figure

Step-by-step explanation:????

Answer:

73/80

Step-by-step explanation:

multiples of 11 between 1 and 80 are 11,22,33,44,55,66,77

number of terms=7

P(multiple of 11)=7/80

P(not a multiple of 11)=1-7/80=73/80

Answer:

9

Step-by-step explanation:

Answer:

? = 3×8/12 = 24/12 = 2

Step-by-step explanation:

Here it is, it is correct.

Answer: (2) /3

Step-by-step explanation:

#1 Way: Solve by a proportion

Let x be the unknown number

Given

8/12=x/3

Cross-multiply

12x=24

x=2

Ans: (2)/3

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

#2 Way: Look at the product between numbers

Given

8/12=?/3

From this, we can see the difference (quotient) between the known value 3 and 12 is 4, meaning 12÷3=4.

Applying the same factor, 8÷4=2

Ans: (2)/3

Hope this helps!! :)

Please let me know if you have any questions

Answer:

no

Step-by-step explanation:

the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4