Geometry: complete this proof of theorem 18, ASAP!!!

(Theorem 18: if the side of one angle are parallel to the sides of another angle, right side to left side and left side to right side, then the angle are supplementary)

The answer is 38cm.

The formula used is perimeter of rectangle so in this case it will be 2(PQ+QR).

So,

=2×(12+7)

=2×19

=38cm

The fact family model that shows the relationship between the numbers 8, 7, and 15 in a triangle means that 15 is 7 more than 8.

An equation is an expression that shows the relationship between two numbers and variables.

The fact family (number family) is a group of equations that derive from a set of numbers.

Fact Family Triangle are used for Addition, Subtraction, Multiplication and Division

The fact family model that shows the relationship between the numbers 8, 7, and 15 in a triangle means that 15 is 7 more than 8.

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Answer:

Step-by-step explanation:

Set it up like an equation first:

[tex]\frac{\frac{-7}{25} }{x}=-\frac{1}{15}[/tex] and then bring up the lower fraction, flip it, and multiply:

[tex]-\frac{7}{25}*\frac{1}{x}=-\frac{1}{15}[/tex]

Simplify to

[tex]-\frac{7}{25x}=-\frac{1}{15}[/tex] and cross multiply to get

-25x = -105 and divide both sides by -25 to get that

[tex]x=\frac{105}{25}=\frac{21}{5}[/tex]

Answer: 1/2

Step-by-step explanation:

The probabilities must add to 1, so:

[tex]P(x < 9) +P(X=9)+P(X > 9)=1\\\\\frac{1}{6}+P(X=9)+\frac{1}{3}=1\\\\P(X=9)=\boxed{\frac{1}{2}}[/tex]

Answer: False

Step-by-step explanation:

The base is more than 1, so the function is increasing.

The average view of the dress code is that this dress is not good

For Rashad's sample to be a random sample gotten from the population, the following must be considered.

To do this, we simply create a bar graph.

The response would go into the x-axis, while the number of people would go into the y-axis

See attachment for bar graph

The average view of the dress code is that this dress is not good

It is considered the average view of the dress code because it is the opinion with the most frequency

The number of students that do not like the dress as:

210 + 206 + 770 = 1186

Their percentage is

Percentage = 1186/(210 + 206 + 770 + 358)

Percentage = 77%

This means that

Yes, the dress will change

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idrk but I hope you have a good day and good luck with ur answer

Answer:

[tex]x^{2} +10x+24[/tex]

Step-by-step explanation:

Answer:

=(x+1)^2-25

Step-by-step explanation:

=x(x−4)+6(x−4)

=x^2−4x+6x−24

=x^2+2x−24

=x^2+2x+1−25

=(x+1)^2-25

A situation where peace is being enforced refers to a peacekeeping mission.

Peacekeeping missions refer to actions by regional and global international bodies to maintain the peace in an area.

For instance, if there has been conflict in an area, a peacekeeping force will work to prevent further violence between the parties in conflict.

An example of such missions include the United Nations Peacekeeping mission to the Democratic Republic of Congo and the African Union Peacekeeping mission to Somalia.

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Answer: 16.63 cm

Step-by-step explanation:

The length of the arc = [tex]\frac{360-130}{360}[/tex] * 2[tex]\pi[/tex]y = [tex]\frac{23}{18}[/tex][tex]\pi[/tex]y

The perimeter = [tex]\frac{23}{18}[/tex][tex]\pi[/tex]y + y + y = y([tex]\frac{23}{18}[/tex][tex]\pi[/tex] + 1 + 1) = 6.01y = 1 m

y = 16.63 cm

Answer: x = 3.5

Step-by-Step Solution:

Let us first label the figure.

Let the Triangle be ABC with a line DE || BC.

Now, in ∆ABC,

DE || BC (given)

=> AD/DB = AE/EC (by B.P.T)

Substituting the given values,

AD/DB = AE/EC

2/4 = x/7

1/2 = x/7

2x = 7

x = 7/2

=> x = 3.5

Therefore, x = 3.5

A correlation coefficient between average temperature and coat sales exists most likely to be between 0 and -1.

The correlation coefficient exists as the exact measure that quantifies the power of the linear relationship between two variables in a correlation analysis. A correlation coefficient between average temperature and coat sales exists most likely to be between 0 and -1.

A negative correlation suggests two variables that tend to move in opposite directions. A correlation coefficient of -0.8 or lower displays a strong negative relationship, while a coefficient of -0.3 or lower signifies a very weak one.

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Answer:

0 and -1

Step-by-step explanation:

Got it right on the test.

Answer:

  3

Step-by-step explanation:

The quadratic formula is used to solve a quadratic equation in standard form, based on the values of the coefficients.

The standard-form quadratic ax² +bx +c = 0 has solutions given by the quadratic formula:

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

For the quadratic 3x² +4x -2 = 0, we have a=3, b=4, c=-2 and the formula gives ...

  [tex]x=\dfrac{-4\pm\sqrt{4^2-4(3)(-2)}}{2(3)}=\dfrac{-4\pm\sqrt{16+24}}{6}\\\\x=\dfrac{-4\pm 2\sqrt{10}}{6}=\dfrac{-2\pm\sqrt{10}}{3}[/tex]

The denominator in the solution is 3.

Answer:

The answer is x=(-2±√10)/3

Step-by-step explanation:

The value of the x from the given equation is 1 and 6/7.

According to the statement

we have given that the quadratic equation and we have to find the solve for the value of the x.

So, For this purpose we know that the

A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers.

So, The given equation is

7x^2 -x -6 =0

Find the factors of the equation

7x^2 -7x + 6x -6 =0

7x(x-1) -6(x-1) = 0

(x-1)(7x-6) =0

here the values of x becomes 1 and 6/7.

So, The value of the x from the given equation is 1 and 6/7.

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109x is the expression that could be used to determine the total number of cupcakes made given that a parent made x cupcakes for each of the 109 students in the fourth grade. This can be obtained by forming the algebraic expression for the given conditions.

Given that,

A parent made x cupcakes for each of the 109 students in the fourth grade.

The total number of students in the class = 109

The number of cupcakes one student gets = 1 × x = x

⇒ The number of cupcakes 109 student gets = 109 × x = 109x

Hence 109x is the expression that could be used to determine the total number of cupcakes made given that a parent made x cupcakes for each of the 109 students in the fourth grade.

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The 90% confidence interval for the true difference between the population proportions is [ - 0.0908, - 0.0092]

Given,

[tex]N_{1}[/tex] = 731

[tex]N_{2}[/tex] = 644

[tex]P_{1}[/tex] = 0.33

[tex]P_{2}[/tex] = 0.28

z score for 90% confidence interval = 1.645

Here, the confidence interval formula :

( [tex]P_{1} -P_{2}[/tex]) ± z [tex]\sqrt{\frac{P_{1}(1-P_{1}) }{N_{1} }+ \frac{P_{2}(1-P_{2}) }{N_{2} } }[/tex]

Substituting the values, we get

    (0.33 - 0.28) ± 1.645 [tex]\sqrt{\frac{0.33(1-0.33)}{731}+\frac{0.28(1-0.28)}{644} }[/tex]

=   0.05 ± 1.645 [tex]\sqrt{0.0003024624+0.0003130435}[/tex]

=   0.05 ± 1.645 [tex]\sqrt{0.0006155059}[/tex]

=    0.05 ± 1.645 × 0.0248093914

=    0. 05 ± 0.0408114489

Confidence interval:

- 0.05 - 0.0408114489 = - 0.0908114489 ≈ - 0.0908

- 0.05 + 0.0408114489 = - 0.0091885511 ≈ - 0.0092

The confidence interval for the true difference between the population proportions is [ - 0.0908, - 0.0092]

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The time it takes them working together to paint the room is 3.08 hours

Rational expression are equation written as a ratio of two expressions or equations.

If Wes can paint a certain room in 8 hours, she can paint 1/8 of the room in 1 hr

Similarly, if Sally can paint the same room in 5 hours, , she can paint 1/5 of the room in 1 hr

Determine the time it takes them to paint the room altogether.

Time together = x

Using the expression below to determine the value of x

1/x = 1/8 + 1/5

1/x = 5+8/40

1/x = 13/40
x = 40/13

x = 3.08

Hence the time it takes them working together to paint the room is 3.08 hours

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Answer:

135 is correct answer of this question

Answer:

x= -3.936 and -0.064

Step-by-step explanation:

I simplified the equation to 40u^2 +16u + 1. Then I just graphed it and found that the zeroes were -3.936 and -0.064.

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

Let's calculate its discriminant :

[tex]\qquad \sf  \dashrightarrow \: 4 {u}^{2} + 16u + 41 = 40[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4 {u}^{2} + 16u + 41 - 40 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4 {u}^{2} + 16u + 1 = 0[/tex]

Here, if we equate it with general equation,

[tex]\qquad \sf  \dashrightarrow \: disciminant = {b}^{2} - 4ac[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = (16) {}^{2} - (4 \times 4 \times 1) [/tex]

[tex]\qquad \sf  \dashrightarrow \: d = (16) {}^{2} - (16) [/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 16(16 - 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 16(15)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 240[/tex]

Now, since discriminant is positive ; it has two real roots ~

The roots are :

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - b \pm \sqrt{ d } }{2a} [/tex]

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - 16\pm \sqrt{ 240 } }{2 \times 4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - 16\pm 4\sqrt{ 15 } }{8} [/tex]

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ 4(- 4\pm \sqrt{ 15 }) }{8} [/tex]

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - 4\pm \sqrt{ 15 } }{2} [/tex]

So, the required roots are :

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - 4 - \sqrt{ 15 } }{2} \: \: and \: \: \dfrac{ - 4 + \sqrt{15} }{2} [/tex]

Answer:

D 34.8

Step-by-step explanation:

[tex]\frac{31+36+28+52+27}{5}[/tex]

Answer:

D) 3

Step-by-step explanation:

22 * 2 = 44

To have a remainder 3, the number should be 44 + 3 = 47

47 ÷ 22 , leaves a remainder 3.

47 +22 = 69

69 ÷ 3  leaves a remainder 3.

69 +22 = 91

91 ÷ 3 leaves a remainder 3.

Answer: 47 , 69 , 91

Answer:B:1

Step-by-step explanation:

Write each number out and divide by 22 until you get one that’s answer is 3

The first five terms of the given arithmetic sequence are:

1/5, 2/5, 3/5, 4/5, 1 (Fourth option)

The arithmetic sequence is given as follows,

f(n) = f(n-1) + 1/5 ............ (1)

Now, for finding the first five term of this arithmetic sequence, we will substitute n as 1, 2, 3, 4, and 5 one by one. Using the above formula for the arithmetic sequence, we can deduce the first five terms.

It is already given that f(1) = 1/5 ......... (2)

f(1) is the first term of the sequence.

Now, putting n=2 in equation (1), we get,

f(2) = f(2-1) + 1/5

f(2) = f(1) + 1/5

Substitute f(1) = 1/5 from equation (2)

⇒ f(2) = 1/5 + 1/5

f(2) = 2/5

To find the third term of the arithmetic sequence, put n = 3 in equation (1)

f(3) = f(3-1) + 1/5

f(3) = f(2) + 1/5

⇒ f(3) = 2/5 + 1/5

f(3) = 3/5

Similarly, we can find the fourth and fifth terms of the arithmetic sequence by substituting n = 4 and n = 5 respectively.

∴ f(4) = f(3) + 1/5

⇒ f(4) = 3/5 + 1/5

f(4) = 4/5

Likewise, f(5) = f(4) + 1/5

⇒f(5) = 4/5 + 1/5

f(5) = 1

Thus, using the recursive formula, the first five terms of the arithmetic sequence come out to be:

1/5, 2/5, 3/5, 4/5, 1

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Using the Fundamental Counting Theorem, it is found that 60 different possible student council teams could be elected from these students.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Considering the number of options for president, vice president, treasurer and secretary the parameters are:

n1 = 5, n2 = 2, n3 = 2, n4 = 3.

Hence the number of different teams is:

N = 5 x 2 x 2 x 3 = 60.

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Answer:

Height = 19mm.

Step-by-step explanation:

Area of a regular polygon =  (A * P) / 2 where A = side / (2 * Tan (π / N)) where, N = Number of sides, A = Apothem,  P = Perimeter.

Here A = 5, P = 5*12 = 60 so

Area  of the base  = (5 * 60) / 2 = 150 mm^2.

Volume = area base * height so

Height = volume / area of base

            = 2850 / 150

            = 19 mm.

The height of the prism is h = 19 mm

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

The volume of a prism is the product of its base area and height

Volume of Prism = B x h

where B = base area of prism

h = height of prism

Given data ,

A regular pentagonal prism has a volume of 2,850 millimeters³

The pentagonal base has side edge labeled 12 millimeters.

And , Apothem from center to a base edge is labeled 5 millimeters

Area of a regular polygon =  (A x P) / 2

where A = side / (2 * Tan (π / N))

and , N = Number of sides, A = Apothem,  P = Perimeter

h = 2850 / 150

On simplifying , we get

h = 19 mm

Hence , the height is 19 mm

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Answer:

32 mm²

Step-by-step explanation:

perimeter of left rectangle = 2(9 mm + 3 mm) = 24 mm

length of right rectangle = L

perimeter of right rectangle = 2(L + 4 mm) = 2L + 8

perimeter of right rectangle = 24 mm

The perimeter of the right triangle is 2L + 8 and also 24, so 2L + 8 must equal 24. We can solve for L and find the length of the right rectangle.

2L + 8 = 24

2L = 16

L = 8

area of right triangle = length × width

area = 8 mm × 4 mm

area = 32 mm²

**Disclaimer** Hi there! I assumed the purple triangle to be the one on the right. The following answer will be according to this understanding. If I am wrong, please let me know and I will modify my answer.

Answer: [tex]\Large\boxed{Area=32~mm^2}[/tex]

Step-by-step explanation:

Given information

Rectangle A:

Rectangle B:

Both rectangles have the same perimeter

Given formula

1) P = 2 (b + h)

2) A = b × h

Substitute values into 1) formula to find the perimeter of rectangle A

P = 2 (b + h)

P = 2 (3 + 9)

Simplify by addition

P = 2 × 12

Simplify by multiplication

P = 24 mm

Substitute values into 1) formula to find the perimeter of rectangle B

P = 2 (b + h)

24 = 2 (4 + h)

Divide 2 on both sides

24 / 2 = 2 (4 + h) / 2

12 = 4 + h

Subtract 4 on both sides

12 - 4 = 4 + h - 4

h = 8 mm

Substitute values into 2) formula

A = b × h

A = 4 × 8

Simplify by multiplication

[tex]\Large\boxed{Area=32~mm^2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Step-by-step explanation:

17, 21, 22, 26, 28, 31, 33, 41, 46, 52

min: 17

Q1: 26

median: 28

Q3: 31

max: 52

Based on the radius of the being 4 units and the area of the equilateral triangle, the area of the shaded area is 32.85 units².

First, find the area of the triangle.

The center of a triangle divides the median into a 2:1 ratio which means that the radius can be found as:

Radius = 1/3 x Area of Equilateral triangle

4 = 1/3 x (√3/ 2)a

a can be worked out to be:

= 8√3

The area of the triangle is:

= (√3 / 4) x a²

=  (√3 / 4) x (8√3 )²

= 83.14 units ²

The area of the circle is:

= π x radius²

= 22/7 x 4 x 4

= 50.29 units²

The area of the shaded area is therefore:

= 83.14 - 50.29

= 32.85 units²

In conclusion, the area of the shaded area is 32.85 units².

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Answer:

The correct answer is the third option: y = 4x - 20

Step-by-step explanation:

To solve this problem, we should first find two points that are located along our line of best fit. We can see that the points (25,80) and (15, 40) are both located along the line. Next, we can calculate the slope using these two points.

slope = rise/run = Δy/Δx = (80-40)/(25-15) = 40/10 = 4

Therefore, the slope of the line of best fit is 4.

To find the y intercept, we can use our equation for slope and plug in one of our points.

y = mx + b

y = 4x + b

40 = 4(15) + b

40 = 60 + b

b = -20

Therefore, the y intercept is -20.

If we put both our slope and y intercept into one equation, we get:

y = mx + b

y = 4x - 20

The correct answer is the third option.

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The area of the adjoining trapezium is 276 [tex]cm^{2}[/tex].

Given the sides of trapezium be 16 cm, 15 cm, 30 cm, 13 cm.

We are required to find the area of adjoining trapezium.

Draw two perpendiculars on AD and the points will be E and F.

From triangles ABE and CFD.

let the length of AE=x, FD=30-16-x=14-x.

BE=[tex]\sqrt{169-x^{2} }[/tex], CF=[tex]\sqrt{225-(14-x)^{2} }[/tex]

BE=CF

[tex]\sqrt{169-x^{2} }[/tex]=[tex]\sqrt{225-(14-x)^{2} }[/tex]

Squaring both sides.

169-[tex]x^{2}[/tex]=225-196-[tex]x^{2}[/tex]+28x

140=28x

x=5 cm.

Put in BE=[tex]\sqrt{169-x^{2} }[/tex]

BE=[tex]\sqrt{169-25}[/tex]

=[tex]\sqrt{144}[/tex]

=12 cm.

Area of trapezium=1/2 (sum of parallel sides)*height

=1/2 (30+16)*12

=23*12

=276 [tex]cm^{2}[/tex]

Hence if the sides of trapezium are 16 cm, 15 cm, 30 cm, 13 cm then the area of the adjoining trapezium is 276 [tex]cm^{2}[/tex].

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The exponential function represented on the graph is defined by the following rule:

[tex]y = 3 \times 2^x[/tex]

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

From the graph, we get that when x = 0, y = 3, hence the initial value is of a = 3. Then the temporary definition is:

[tex]y = 3b^x[/tex]

Also from the graph, when x = 1, y = 6, hence we can apply to the definition to find b.

[tex]6 = 3b^1[/tex]

3b = 6

b = 2.

Hence the function is:

[tex]y = 3 \times 2^x[/tex]

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